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► This Week in CFD
  27 May, 2022

The weekend is nigh and if you’re in the U.S. the long Memorial Day weekend beckons and if you work for a top 100 best place to work company the extra long weekend has already started. What better way to … Continue reading

The post This Week in CFD first appeared on Another Fine Mesh.

► This Week in CFD
  20 May, 2022

These past three weeks of CFD news threaten to turn this regular post into This Month in CFD if the burst of business travel doesn’t abate. But the more content the merrier. For those of you up for some fluids … Continue reading

The post This Week in CFD first appeared on Another Fine Mesh.

► This Week in CFD
  29 Apr, 2022

It’s been three weeks since the last collection of CFD news and notes was published so you can only imagine the backlog. This summer looks to be the return of a lot of in-person conferences and I am looking forward … Continue reading

The post This Week in CFD first appeared on Another Fine Mesh.

► This Week in CFD
    8 Apr, 2022

This is the first CFD news roundup of 2022 Q2 and it comes with the implication – or at least hope – that everyone’s Q1 was productive. We’re meshing a lot of rotating machinery this week, we have several job … Continue reading

The post This Week in CFD first appeared on Another Fine Mesh.

► This Week in CFD
  25 Mar, 2022

This week’s compilation of CFD news is highly image-oriented which might make it easier to read and maybe more enjoyable. But don’t skip over the event news, several CFD jobs, mesh generation resources, and your assigned reading for hypersonics. Shown … Continue reading

The post This Week in CFD first appeared on Another Fine Mesh.

► This Week in CFD
  18 Mar, 2022

Welcome to the “ides of March” roundup of CFD happenings. If you’re not currently enjoying spring break, check your knives at the door and dive into advice for engineering students from Jousef Murad that I couldn’t resist commenting on. Speaking … Continue reading

The post This Week in CFD first appeared on Another Fine Mesh.

F*** Yeah Fluid Dynamics top

► “Volcano Pilot”
  27 May, 2022

Today’s video is something a little different. Rather than looking at fluids and their physics directly, we’ll take a step back and think about how people relate to the subject. This short film, “Volcano Pilot,” follows Haraldur Unason Diego as he reflects on his life’s work. It’s a beautiful and moving glimpse of the life and philosophy of a small aircraft pilot. Many people never have the opportunity to see the world from cockpit of a Cessna or similar small aircraft, and I think there are few experiences that can better connect someone to the fluids-in-action that is aviation. (Image and video credit: M. Aberra et al.)

► Dripping Impact
  26 May, 2022

How does water drip, drip, dripping onto stones erode a crater? Water is so much more deformable that it seems impossible for it to wear harder materials away, even over thousands of impacts. To investigate this, a team of researchers developed a new measurement technique: high-speed stress microscopy. In the process, they found that water owes its incredible erosive power to three factors: 1) The drop’s impact creates surface shock waves along the material, which helps increase erosive power; 2) After the shock wave passes, a decompression wave in the material helps loosen surface matter; and 3) The spreading drop sends a non-uniform wave of stress across the material that simultaneously presses and scrubs at the surface. Together, these factors enable simple, repetitive droplet impacts to wear away at hard surfaces. (Image credit: cottonbro; research credit: T. Sun et al.; via Cosmos; submitted by Kam-Yung Soh)

► Inside Viscous Fingers
  25 May, 2022

Sandwich a viscous fluid between two transparent plates and then inject a second, less viscous fluid. This is the classic set-up for the Saffman-Taylor instability, a well-studied flow in which the interface between the two fluids forms a wavy edge that develops into fingers. Despite its long history, though, there is still more to learn, as shown in this video. Here, researchers alternately injected a dyed and undyed version of the less viscous fluid. The result (Image 3) is a set of concentric dye rings that show how the fluid moves far from the fingers along the edge. Notice that the waviness of the fingers appears in the flowing fluid well before it approaches the interface. (Image and video credit: S. Gowan et al.)

► Coalescence Symmetry
  24 May, 2022

When droplets coalesce, they perform a wiggly dance, gyrating as the capillary waves on their surface interfere. When the droplets have matching surface tensions, like the two water droplets in the animation on the lower left, the coalescence dance is symmetric. But for differing droplets, like the water and ethanol droplets merging on the lower right, coalescence is decidedly asymmetric.

The asymmetry arises from the droplets’ different surface tensions. The size and speed of the capillary waves that form on a droplet depend on surface tension, so droplets of different liquids have inherently different capillary waves. During merger, the interference of these capillary waves causes the asymmetry we see. (Image credit: top – enfantnocta, coalescence – M. Hack et al.; research credit: M. Hack et al.)

► Blowing Up Euler
  23 May, 2022

The mathematics of fluid dynamics still have many unknowns, which makes them an attractive playground for mathematicians of all stripes. One perennial area of interest is the Euler equations, which describe an ideal (i.e., zero viscosity), incompressible fluid. Mathematicians suspect that these equations may produce impossible answers — vortices with infinite velocities, for example — under just the right circumstances, but so far no one has been able to prove the existence of such singularities.

A recent Quanta article delves into this issue and the race between researchers using traditional methods and those using new deep learning techniques. Will the singularities be found and who will get there first? It’s well worth a read, whether theoretical mathematics is your thing or not. (Image credit: S. Wilkinson; see also Quanta; submitted by Jo V.)

► Martian Flyover
  20 May, 2022

Fly over a Martian crater in this incredibly detailed 8K video built from Mars Reconnaissance Orbiter imagery. Like Earth’s deserts, Mars is largely shaped by wind, and we get some fantastic views of sand ripples in this flyover. For reference, the vertical scale covered in the video image is roughly 1 kilometer. It’s pretty astounding to see this kind of detail from a spacecraft 250 kilometers away! (Video and image credit: S. Doran/NASA; via Colossal)

CFD Online top

► 2 Easy MPI pieces
    8 May, 2022
Anyone who has a minimum working experience with MPI (the Message Passing Interface for distributed parallel computing) has certainly had the chance to meet certain coding patterns multiple times, especially if working with a CFD (or any other computational physics like) code.

Regrettably, MPI and parallel distributed computing is one of those areas where textbooks and online examples (even SO) are largely useless, as most (if not all) of them just simply go into the details of how to use this or that feature. But most examples are so toy level that you even find cases where the presented code just works for a fixed number of processes (aaargh!).

Every MPI use case is very specific but, I want to present here two examples that are so simple and stupid that it is a shame they are not present in every single book or tutorial. Yet, they have both very practical use cases.

The first MPI piece I want to present is, superficially, related to the necessity to perform a deadlock avoiding loop among all processes. This problem, however, really is a twofold one. On one side, the main issue is: how do I automatically schedule the communications between N processes so that, for any couple of processes i and j, if the k^{th} communication partner of process i is process j then the k^{th} communication partner of process j is process i? With a proper communication schedule in place, avoiding deadlock, which is the second part of the problem, is then definitely a triviality (also present in most MPI examples). It turns out that such communication schedule is a triviality as well, to the point of being a single liner solution, so it really is a shame that it is not presented anywhere (to the best of my knowledge). So, here it is a pseudocode example of a loop where each process communicates with each other process (including itself) without deadlock (full Fortran example here):

nproc = mpi_comm_size  !How many processes
myid  = mpi_comm_rank !My rank among processes

!Loop over all processes
for i = 1 : nprocs
   !My communication partner at the i-th stage
   myp = modulo(i-myid-1,nproc)
   if (myid>myp) then
      !The process with higher rank sends and then receives
   elseif (myid<myp) then
      !The process with lower rank receives and then sends
      !This is me, no send or recv actually needed
where the modulo operation is intended as the Fortran one. All the magic here happens in the determination of myp, the communication partner for the given process at the i-th stage, which is different for each process at each stage, but exactly match between them at any given stage.

Now, the pseudo-code above (and the one in the linked gist as well) is just an example, and you should not, DEFINITELY, do this sort of loops in your code. Also, you should not use blocking sends and recvs as well (I used them in the example to prove its very point). However, even for non blocking send/recv, and even when each process just has to communicate with a limited set of different processes, it turns out that this schedule is extremely efficient, as very little to none is spent in the handling of non matched send/recv calls. Now, for how stupid and simple this might look, most codes, even large scale ones, simply don't schedule their communications, which is the reason I thought to share this simple piece of code. In practice I have several variants of it (I provided 2 of them in the linked gist) as today I use it to schedule different pieces of communications in my code.

The second easy MPI piece is related to a very simple case: how would you write your own reduce operation without using mpi_reduce but just mpi_send/recv? While this might just look like a textbook exercise, it is indeed relevant for those cases where the needed reduce operation is not among the intrinsic ones of MPI (SUM, MAX, etc.). I first had a need for it when working on parallel statistics (e.g., how to compute the spatial statistics of a field variable in a finite volume code without using allreduce, which costs just like an mpi_barrier?).

For the most complex cases, MPI provides both an mpi_type_create_struct routine to create a generic user-defined data type and mpi_op_create routine to define a custom reduction operation for said data type (see, for example, here, here and here). Unfortunately, they can't actually cover all use cases, or at least not so straightforwardly.

However, if there are no specific needs in terms of the associativity of the reduce operator, it turns out that you can write your own reduce algorithm with no more than 25 lines of code (full Fortran example here). The algorithm has 3 very simple steps:
  1. Determine pp2, the largest power of 2 integer smaller than or equal to the current number of processes
  2. If the current number of processes is above pp2, ranks beyond pp2 just send their data to ranks that are lower by exactly pp2 (e.g., for 7 processes, zero indexed, ranks from 4 to 6 will send, respectively, to ranks from 0 to 2), which will perform the reduce operation
  3. Log2(pp2) iterations are performed where, at each iteration, the higher half of ranks up to a given power of 2, ppd (=pp2 at the beginning of the first iteration), send their data to the lower half (shifting by ppd/2), which will then reduce it. At the end of each iteration ppd is divided by 2.

The final reduce operation will then be available to the process with rank 0 (which could simply send it to the required root, if different). Note that the algorithm still needs nproc-1 messages to be sent/received but, differently from the naive case where a root process directly receives all the messages one after the other, here the messages of each stage are always between different couples of processes. Of course, by using such simple approach you abandon the possibility to use any possible optimizations on the MPI side (which, however, might not be available at all for the user defined data type and operator), but there is a very large gain in flexibility and simplicity.

If there are associativity needs, you can instead follow this Fortran example, where the MPICH binomial tree algorithm is used. The algorithm (which is shorter and largely more elegant, yet a bit dense in its logic) performs the reduction by following the rank order of the processes, so it is very easy to map them in order to follow a more specific order.
► Closing on wall functions - part 8: coupled/thin wall boundary conditions
  27 Apr, 2022
It might happen that wall functions for temperature or scalars are needed when the assigned boundary condition is not simply the assigned flux or temperature/scalar, but rather a more complex one. One example is when the wall is a coupled one, with either a fluid or a solid on the other side, or it has some thickness, possibly with source terms in it and, say, radiation or convective boundary conditions assigned on the other side, or maybe some other combination of the above.

In all such cases, the formulas presented before are still valid but need a slight rearrangement in order to fit the new conditions. Nothing of this is really new, the concpet is as old as the book of Patankar (probably older) and this is just one of the latest additions. Also, major commercial CFD codes have been offering this for decades. Still, I am not aware of full formulas available in the more general case. Everything I write here for the temperature just straightforwardly applies to other scalars with similar equations. Of course, as per the original wall function ODE, the assumption is that of steady state. That is, the solved problem might or not be steady, but the boundary conditions are, in fact, derived by solving a steady state problem (this was, as a matter of fact, true also for the wall function ODE, even if the unsteady term was considered among the non equilibrium ones).

We start by noting that the wall heat flux formula provided here can actually be rewritten as follows (also taking into account that the original derivation used a wrong sign for ease of exposition):

q_w = -\frac{\left\{\frac{\left[T\left(y\right) - T_w\right]}{y} \left(\frac{\mu C_p}{Pr}\right) - y\sum_{i=0}^{N}\frac{F_T^i}{i+1}\left(\frac{y}{y_p}\right)^i\left(\frac{{s_T^i}^+}{{y^+}^{i+2}}\right) \right\}}{\left(\frac{{s_T^{-1}}^+}{y^+}\right)} = -\frac{\left(T_p - T_w\right)}{y_p} k_p C_{WF} + \dot{Q}_p

Where C_{WF}=1/\left(\frac{{s_T^{-1}}^+}{y^+}\right) and it is recognized that, being independent, at the first order, from the flow conditions and being an integral that grows with wall distance, the non equilibrium terms are, indeed, just an explicit source term \dot{Q}_p for the near wall cell. In practice, the source term is also assimilable to a non orthogonal correction thus, in the following, we will simply consider the point p, with temperature T_p and distance from the wall y_p to be along the normal to the wall. A similar reasoning can also be done for the viscous dissipation that, as presented here, is independent from the temperature distribution and can be absorbed by the same source term as well.

We want to extend the formula above to the case where neither T_w nor q_w are actually given. Also, we assume that T_w=T_n and q_w=q_n, that is, they are only known as the values at the extreme of an n layers thin wall. So we have T_n, T_{n-1}, ..., T_1 and T_0, and the same for q. They are are the temperatures and fluxes at the intefraces between the n layers of the thin wall. Each one of these n layers will have its own thickness \Delta x_i, thermal conductivity k_i and possibly a source term \dot{Q}_i. Finally, we want to consider two possible boundary conditions, either T_0 directly given or q_0 given as:

q_0 = h_{\infty}\left(T_{\infty}-T_0\right) + \epsilon_R \sigma \left(T_R^4-T_0^4\right) = h_{\infty}\left(T_{\infty}-T_0\right) + \widetilde{h}_R\left(T_R-T_0\right)

with \widetilde{h}_R = \epsilon_R \sigma \left(T_R+T_0\right)\left(T_R^2+T_0^2\right) being non-linearly dependent from T_0 and where we assumed that the q_i are positive if entering the domain.

In order to formalize a solution, we need to complement the fundamental conservation statement that holds for a layer in the thin wall q_i=q_{i-1}+\dot{Q}_i \Delta x_i with a similar relation for the temperature jump across the layer, T_i-T_{i-1}. Considering that, in our model, the heat conduction equation that holds in each layer has the form:

\frac{d^2T}{dx^2} + \frac{\dot{Q}}{k} = 0

solving it with proper boundary conditions one easily obtains that:

T_i-T_{i-1} = -\frac{\Delta x_i}{k_i}\left(q_{i-1}+\frac{\dot{Q}_i \Delta x_i}{2}\right)

The two jump relations for single layers above can then be used to obtain jump relations across the whole thin wall of n layers. For the flux it is just, again, a simple conservation statement:

q_n = q_0 + \sum_{i=1}^n \dot{Q}_i \Delta x_i

For the temperatures one obtains:

T_n - T_0 = \sum_{i=1}^n \left(T_i -T_{i-1}\right) = -q_0 \sum_{i=1}^{n}\frac{\Delta x_i}{k_i} - \sum_{i=1}^{n} \frac{\Delta x_i}{k_i} \left(\frac{\dot{Q}_i \Delta x_i}{2} + \sum_{j=1}^{i-1}\dot{Q}_j \Delta x_j\right)


h_p = \frac{k_p C_{WF}}{y_p}

R_T = \sum_{i=1}^{n}\frac{\Delta x_i}{k_i}

\alpha = \sum_{i=1}^{n} \frac{\Delta x_i}{k_i} \left(\frac{\dot{Q}_i \Delta x_i}{2} + \sum_{j=1}^{i-1}\dot{Q}_j \Delta x_j\right)

\beta = \sum_{i=1}^n \dot{Q}_i \Delta x_i

where the latter 3 can all be pre-computed and stored, then it is a matter of simple manipulation (yet a quite long one, which is omitted here), to show that our initial formula can now be generally expressed as follows:

q_w = \left(T_w - T_p\right)h_p + \dot{Q}_p = \frac{\left(T^*-T_p\right)+\left(R^*\beta-\alpha\right)}{R^*+\frac{1}{h_p}} + \dot{Q}_p

where T^* and R^* depend from the specific boundary condition in use. More specifically, for T_0 directly assigned, one has T^*=T_0 and R^*=R_T. For the general convection/radiation boundary condition (or just one of the two, by zeroing the coefficient of the other) one has:

R^* = R_T + \frac{1}{h_{\infty}+\widetilde{h}_R}

T^* = \frac{h_{\infty}T_{\infty}+\widetilde{h}_R T_R}{h_{\infty}+\widetilde{h}_R}

Finally, the coupled case is simply obtained by using \widetilde{h}_R = 0, h_{\infty} = h_{pc} and T_{\infty}=T_{pc} where the subscript pc refers to the quantities taken from the coupled side.

The corresponding value of T_w is instead given by:

T_w = \frac{T^*+R^*\left(\beta+h_pT_p\right)-\alpha}{1+h_pR^*}

The last step missing is the determination of \widetilde{h}_R, which depends from T_0. A relation for the latter can be obtained, but itself, of course, will depend from \widetilde{h}_R. This relation (whose derivation is again simple but long, so it is omitted here) can then be used in tandem with the one for \widetilde{h}_R iteratively:

\widetilde{h}_R = \epsilon_R \sigma \left(T_R+T_0\right)\left(T_R^2+T_0^2\right)

T_0 = \frac{\left(h_{\infty}T_{\infty}+\widetilde{h}_R T_R\right)\left(R_T+\frac{1}{h_p}\right)+T_p+\alpha+\frac{\beta}{h_p}}{\left(h_{\infty}+\widetilde{h}_R\right)\left(R_T+\frac{1}{h_p}\right)+1}

I have found that, starting from T_0=T_p no more than 10 iterations are necessary to converge on \widetilde{h}_R and T_0.

One thing which is worth highlighting here in the more general context of wall functions is that, as a matter of fact, non equilibrium/viscous dissipation terms (from both sides of the thin wall, if a coupled bc is used) do not directly enter the modifications presented above. That is, they still appear as in the original wall function formulation. This might very easily go unnoticed if a thermal wall function is just presented as a single relation for T^+ without distinguishing the roles of the terms.

Another thing worth noting is that, if one decided to solve the original ODE as it was (say, with a tridiagonal algorithm as in one of the scripts provided here), instead of directly integrating it as done here, it would have been impossible to let the exact form above emerge, leading to 3 major consequences: 1) inability to separate the non-equilibrium/viscous dissipation part from the rest (that is, in the ODE solution one only has the wall values, not their dependence), 2) either the need to solve the 1D problem also in the thin wall and/or coupled side or the need to iterate the solution on both sides exchanging wall values at each iteration and 3) which is a consequences of 1 and 2, the impossibility to set up the problem for an implicit implementation in the coupled case, which might have major consequences on convergence in certain cases.

Finally, I want to mention that all the above developments are also relevant for the Musker-modified Spalart-Allmaras model for which, given the proper conditions (equilibrium for the velocity, steady state in general), they represent a full analytical solution, which now is thus extended to the present more general boundary conditions.
► Closing on wall functions - part 7: starting from a profile
  26 Apr, 2022
It might happens that one doesn't have a turbulent viscosity profile but actually has just an equilibrium profile for velocity or temperature. More specifically:

T^+ = Pr \left(\frac{{s_T^{-1}}^+}{y^+}\right)  y^+

with its obvious extension to the velocity case. In order to go back to the framework presented here one should notice that:

\frac{d}{dy^+}\left({s_T^{-1}}^+\right) = \frac{1}{1+\frac{Pr}{Pr_t}\frac{\mu_t}{\mu}}

from which, it follows that:

\frac{Pr}{Pr_t}\frac{\mu_t}{\mu} = \frac{1}{\frac{d}{dy^+}\left({s_T^{-1}}^+\right)}-1

which is all that is needed to compute (numerically if not doable analytically) the remaining integrals for non equilibrium and/or TKE production terms.

For the non equilibrium terms this leads to the following:

{s_T^i}^+ = \int_0^{y+}{\frac{z^{i+1}}{\left[1+\left(\frac{Pr}{Pr_t}\right)\left(\frac{\mu_t}{\mu}\right)\right]}dz} = \int_0^{y+}z^{i+1}\frac{d}{dz}\left({s_T^{-1}}^+\right)dz

Hence, integration by parts finally leads to:

\left(\frac{{s_T^i}^+}{{y^+}^{i+2}}\right) = \left(\frac{{s_T^{-1}}^+}{y^+}\right)-\frac{\left(i+1\right)}{{y^+}^{i+2}} \int_0^{y+}z^is_T^{-1}dz

Formally, this is the generalized trick that I used here to extend the Reichardt wall law to constant only non equilibrium cases (i.e., i=0).
► Closing on wall functions - part 6: viscous dissipation
  24 Apr, 2022
One thing which is missing in the previous derivations is the viscous dissipation term in the temperature equation. Let's reconsider the initial temperature equation when it is present:

\frac{d}{dy}\left[C_p\left(\frac{\mu}{Pr}+\frac{\mu_t}{Pr_t}\right)\frac{dT}{dy}\right]=F_T - \frac{d}{dy}\left[\left(\mu+\mu_t\right)U\frac{dU}{dy}\right]

A first integration leads to:

\left(\frac{C_p \mu}{Pr}\right)\left(1+\frac{Pr}{Pr_t}\frac{\mu_t}{\mu}\right)\frac{dT}{dy}=q_w+ yG_T - \mu\left(1+\frac{\mu_t}{\mu}\right)U\frac{dU}{dy}

where yG_T is the integral of F_T and G_T has the same form we assumed for F_T, just with its coefficients divided by i+1. Then a further integration leads to:

T\left(y\right) = T_w + \left(\frac{Pr}{\mu C_p}\right) \int_{0}^{y}\frac{q_w+ zG_T}{\left(1+\frac{Pr}{Pr_t}\frac{\mu_t}{\mu}\right)}dz - \left(\frac{Pr}{C_p}\right) \int_{0}^{y}\frac{\left(1+\frac{\mu_t}{\mu}\right)}{\left(1+\frac{Pr}{Pr_t}\frac{\mu_t}{\mu}\right)}U\frac{dU}{dz}dz

The first integral in the equation above has been the subject of the previous posts, while the neglected viscous dissipation term is the last term in the equation. Now, there are two ways which could be used to proceed. A first one involves invoking the velocity equation and transforming the viscous dissipation term as follows:

D\left(y\right)=-\left(\frac{Pr}{C_p}\right) \int_{0}^{y}\frac{\left(1+\frac{\mu_t}{\mu}\right)}{\left(1+\frac{Pr}{Pr_t}\frac{\mu_t}{\mu}\right)}U\frac{dU}{dz}dz = -\left(\frac{Pr}{\mu C_p}\right)\int_{0}^{y}\frac{\left(\tau_w+zG_U\right)U}{\left(1+\frac{Pr}{Pr_t}\frac{\mu_t}{\mu}\right)}dz

where G_U has the same form as G_T, but with the velocity coefficients. At this point, then, one can note that the integral has the exact same form of the first one, but with the additional velocity U in it. I have not attempted to solve it with none of the models presented but, even if doable, I expect high levels of cumbersomeness.

One could approximate the integral by assuming a constant, representative, value for U, say, \widetilde{U} and take it out of the integral. In this case, while one should still be careful in mixing the velocity numerator with the temperature denominator in the integrand, the resulting integral would be formally identical to the first one, which we have solved in previous posts.

A second, preferred way to proceed would instead first recognize that the integral above can be transformed as:

D\left(y\right)=-\left(\frac{Pr}{C_p}\right) \int_{0}^{y}\frac{\left(1+\frac{\mu_t}{\mu}\right)}{\left(1+\frac{Pr}{Pr_t}\frac{\mu_t}{\mu}\right)}U\frac{dU}{dz}dz = -\left(\frac{Pr}{C_p}\right) \int_{0}^{y}\frac{\left(1+\frac{\mu_t}{\mu}\right)}{\left(1+\frac{Pr}{Pr_t}\frac{\mu_t}{\mu}\right)}\frac{d}{dz}\left(\frac{U^2}{2}\right)dz

Hence integration by parts leads to the following result:


At this point we are still left with an even more cumbersome integral to evaluate, if possible at all. However, this integral is exactly 0 in two special cases: fully laminar ones (\mu_t/\mu=0) and when Pr/Pr_t=1. Another advanatge of this form is that if we now assume a constant, representative, value for U, say, \widetilde{U} and take it out of the integral, we are left with no more work to do and just obtain:


which also always works in the cases where the integral is exactly 0. Of course, we are now left with determining \widetilde{U}^2, but this seems a more reasonable task, also because it must be representative just for the region where derivative in the integrand is not 0 and not the full y length. A value for \widetilde{U} commonly used with standard wall functions is the velocity at {y_T}^+. By extension, for the Musker-Monkewitz wall function one could use the velocity at y^+=\widetilde{a}, the profile constant modified by the Pr/Pr_t ratio (see here). However, this is an approximate solution to the original problem, that's why I left it out of the general discussion of the previous posts.
► Closing on wall functions - part 5: testing scripts
  24 Apr, 2022
I provide here a set of MATLAB scripts to test all the claims made in the first 4 parts.

The first group of scripts is actually made of functions, that you are not supposed to directly call or modify:
  • muskersp.m: returns \left(\frac{{s_{U,T}^i}^+}{{y^+}^{i+2}}\right), \left(\frac{{p^i}^+}{{y^+}^{i+2}}\right) and {q^i}^+ as shown here. It only works for N up to 0 (constant non equilibrium terms)
  • standardsp.m: returns the same quantities but for the standard wall function presented here. It works for arbitrary N but the scripts below only test it up to 0 (constant non equilibrium terms)
  • iteryv.m: returns the value of y_T^+ needed by standardsp.m for Pr>Pr_t
  • numericalsp.m: a generic wall function that takes as input a function handle for the turbulent viscosity ratio and provides the required integrals by numerical integration. It works for arbitrary N (but, again, it is only tested for N up to 0). It only works for turbulent viscosities going to 0 at least as fast as {y^+}^2.
  • standard.m: the actual standard wall function adapted to the present framework for comparisons. Only works for equilibrium cases (N=-1)
  • spiter.m: the function that performs the iterations on the wall functions to find \tau_w following what is presented here
  • sa1d.m: solves the original ODE of the problem (actually a slightly more general one) using a second order cell centered finite volume discretization, the Spalart-Allmaras turbulence model (actually a generalized version that also works with the Musker profile) and the tridiagonal solver

The second group of scripts is the one actually making the tests and the comparisons:
  • check.m: for given flow conditions, it tests that a) the analytical musker profile in muskersp is consistent with the one obtained trough numerical integration with numericalsp, b) that the numerical musker profile (and, by point a above, also the analytical one) is consistent with the Spalart-Allmaras direct solution of the ODE with a properly modified fv1 function c) that the numericalsp routine (already tested in a and b above) is consistent with the non modified Spalart-Allmaras solution of the ODE when the relative turbulent viscosity profile is used. Note that the velocity wall function can only match the Spalart-Allmaras solution in the equilibrium case (dpdx=0), but in the same case the temperature equation can have non equilibrium terms and the solutions will match.
  • wfiter.m: for a given wall function (user selectable) and flow conditions plots the iterations to find \tau_w as produced by itersp.m
  • wfcompare.m: a straightforward comparison of multiple wall functions for given flow conditions
  • wfmap.m: for the musker profile (but easily adaptable to other profiles) it maps the solution \theta_p of the iterative procedure to find \tau_w in a certain range of Re_p and {F_p}^0 parameters.
  • apr.m: a comparison of the variations of the constant a in the Musker profile and y_T^+ in the standard profile as a function of Pr/Pr_t giving a sensation of how the variation of the Musker constant with Pr/Pr_t is, indeed, a sort of Jayatilleke term.

Few comments on the use of the scripts above and some claims made in previous posts.

In the second post of this series I mentioned that, when using the Spalart-Allmaras model, one could avoid iterations to find \tau_w by using y_p^+ = \frac{\rho \widetilde{\nu}_p}{\mu \kappa}. This is confirmed in check.m where the Spalart-Allmaras boundary conditions for the solution of the 1D ODE are obtained from the relation above using as input the y_p^+ value obtained by the underlying wall function.

In the same post it is also mentioned that one could precompute the wall function for a given range of parameters and later interpolate from it. Such precomputation is what the script wfmap.m does, and you can also see from the commented parts how it could be adapted to directly use the 1D ODE solution instead of the musker profile actually used by the script.

Still in the same post, I mentioned how, for non equilibrium cases, the iterative computation of \tau_w might become cumbersome as multiple solution branches might exist for non favourable pressure gradients. This can be easily visualized by using wfiter.m.

It has been mentioned here that y_T^+ in the standard profile can be obtained by few iterations of the Halley's method. The specific implementation is in iteryv.m.

In the last post I have mentioned that the van Driest damped mixing length is, indeed, mostly equivalent to the Musker profile for the incompressible formulation used here. This is clearly shown in wfcompare.m. While I don't directly provide the 1D ODE solution with the mixing length (just its wall function form trough numericalsp), I do for two different turbulent viscosity formulations trough the Spalart-Allmaras model in check.m and show that they correspond to the analogous formulation used as wall function.

All the scripts are in a zipped folder for convenience (as a maximum of 5 files can be uploaded here) and have been tested with MATLAB R2022a.
Attached Files
File Type: zip (14.2 KB, 49 views)
► Closing on wall functions - part 4: a Musker-Monkewitz wall function
  23 Apr, 2022
In the Musker-Monkewitz wall function the following assumption is made on the turbulent viscosity profile:

\frac{\mu_t}{\mu} = \frac{\left(\kappa y^+\right)^3}{\left( \kappa y^+\right)^2+\left(\kappa a \right)^3-\left(\kappa a \right)^2}

where \kappa is the von Karman constant and a is a constant that specifies the y^+ for which \frac{\mu_t}{\mu} =1 but, in practical terms has the same role of y_v^+ in the standard wall function of the previous post.

There are really several reasons for which this profile is relevant. First of all, it is a continuous, all y^+ profile which has the correct limiting near wall C{y^+}^3 behavior as well as the correct \kappa y^+ logarithmic behavior. Second, as already mentioned here, it has a nice closed form solution. The third reason, as already stated here, but worth restating here, it allows computing the temperature integrals:

{s_T^i}^+ = \int_0^{y+}{\frac{z^{i+1}}{\left[1+\left(\frac{Pr}{Pr_t}\right)\left(\frac{\mu_t}{\mu}\right)\right]}dz}

from the same formula for the velocity integrals:

{s_U^i}^+ = \int_0^{y+}{\frac{z^{i+1}}{\left[1+\left(\frac{\mu_t}{\mu}\right)\right]}dz}

by properly redefining the two profile constants \kappa and a, so it works for arbitrary Pr/Pr_t ratios (or, seen differently, the constant redefinition of the model is, in its own, a model like the Jayatilleke term for the standard wall function). Finally, the model has a strong similarity with the behavior that the Spalart-Allmaras turbulent viscosity assumes in equilibrium conditions (a=4.6228/k in the SA model):

\frac{\mu_t}{\mu} = \frac{\left(\kappa y^+\right)^4}{\left( \kappa y^+\right)^3+\left(\kappa a \right)^4-\left(\kappa a \right)^3}

Which means that, for a properly coded Spalart-Allmaras model, changing a constant and an exponent is all that is required to let it have a closed form analytical solution for arbitrary Pr/Pr_t ratios which is also, obviously, its own wall function.

Note that the original Spalart-Allmaras turbulent viscosity can be analytically integrated as well. But differently from the Musker one, the solution is only known in terms of numerical constants. Which means that, for each given Pr/Pr_t ratio, the numerical constants must be recomputed, which is not very useful.

Back to the present Musker-Monkewitz solution, after substitution of the turbulent viscosity profile in the integrals above, and reminding that we only need the one for the velocity (from which temperature and scalars can be obtained), one obtains:

{s_U^i}^+ = \frac{1}{\kappa^{i+2}}\int_0^{ky+}{\frac{x^{i+1}\left(x^2+c^3-c^2\right)}{x^3+x^2+c^3-c^2}dx}

for the velocity and:

{p^i}^+ = \frac{1}{\kappa^{i+2}}\int_0^{ky+}{\frac{x^{i+4}\left(x^2+c^3-c^2\right)}{\left(x^3+x^2+c^3-c^2\right)^2}dx}

for the average turbulent kinetic energy production, with c=\kappa a. Now, it is easy to obtain closed form solutions to the integrals above for each value of i, but a closed form solution that works for arbitrary i seems out of reach. In the final scripts I will provide a solution just for the constant non equilibrium term (thus for i=-1 and i=0), but here I just want to highlight that, heuristically, solutions to the integrals above seem to have the following forms (x=\kappa y^+):

{s_U^i}^+ = \frac{1}{\kappa^{i+2}}\left[a_1 f_1\left(x,c\right)+a_2 f_2\left(x,c\right) + a_3 f_3\left(x,c\right) +\sum_{j=1}^{i+1} a_{3+j}x^j\right]

{p^i}^+ = \frac{1}{\kappa^{i+2}}\left[b_1 f_1\left(x,c\right)+b_2 f_2\left(x,c\right) + b_3 f_3\left(x,c\right) + f_4\left(x,c\right)+\sum_{j=1}^{i+1} b_{6+j}x^j\right]


f_1\left(x,c\right) = \ln{\left(\frac{x+c}{c}\right)}

f_2\left(x,c\right) = \ln{\left[\frac{x^2+\left(c-1\right)\left(c-x\right)}{c\left(c-1\right)}\right]}

f_3\left(x,c\right) = \frac{\arctan{\left[\frac{2x-\left(c-1\right)}{\sqrt{\left(c-1\right)\left(3c+1\right)}}\right]} + \arctan{\left[\frac{\left(c-1\right)}{\sqrt{\left(c-1\right)\left(3c+1\right)}}\right]}}{\sqrt{\left(c-1\right)\left(3c+1\right)}}

f_4\left(x,c\right) = \frac{b_4x^2+b_5x+b_6}{x^3+x^2+c^2\left(c-1\right)}-\frac{b_6}{c^2\left(c-1\right)}

where the a_j and b_j are constants which are only function of c. Thus, notably, one only has to compute a given integral with a symbolic toolbox and pick up the constants expressions, as the functions f_i are fixed (and 3 of 4 common between the two integrals).

The last thing which is worth mentioning about the Musker-Monkewitz wall function is that, as will be shown running the scripts provided in the last post of this series, it very closely follows a turbulent viscosity prescription which is very popular in the LES community that directly solves the original ODE with a tridiagonal solver (like this), the van Driest damped mixing length:

\frac{\mu_t}{\mu} = \kappa y^+ \left(1-e^{-\frac{y^+}{A^+}}\right)^2

Thus, the take home message here is that, unless you are adding compressibility effects, you are wasting resources, because the Musker-Monkewitz profile is, to all the practical means, identical. Large differences only arise at very large Pr/Pr_t ratios, say, 100 or more.

Finally, following the general discussion here, it is worth mentioning that the same feature that makes the Musker-Monkewitz profile adaptable to any Pr/Pr_t ratio, also makes it easily adaptable to any relevant turbulence model (yet, of course, not exactly). What is needed is just a different law to modify the profile constant, one that can be derived by adapting the Musker profile to the given model profile instead of the one embedded in the model. Such adaptation, which should be done in equilibrium conditions, can be very easily performed as a non linear least-squares optimization.

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► Challenges in Meshing Scroll Compressors
  25 Mar, 2022

Figure 1: Structured multi-block mesh for scroll compressors with tip seal.

804 words / 4 minutes read

Scroll compressors with deforming fluid space, narrow flank, and axial clearance pose immense meshing challenges to any mesh generation technique.


Scroll compressors and expanders have been in extensive usage in refrigeration, air-conditioning, and automobile industries since the 1980s. A slight improvement in scroll efficiency results in significant energy savings and reduction in pollution on the environment. It is therefore important to minimize frictional power loss at each pair of the compressor elements and also the fluid leakage power loss at each clearance between the compressor elements. So developing ways to minimize leakage losses is essential to improve scroll performance.

Scroll Compressor CFD Challenges

Unlike other turbomachines like compressors and turbines, Positive Displacement (PD) machines like scroll suffer from innovative designs and performance enhancements. This is mainly due to difficulties in applying CFD to these machines because of the challenges in meshing , fluid real equations and long computational time.

Scroll compressor Working
Figure 3: Deforming fluid pockets at different stages in the compression process. Image source Ref [11].

Geometric Challenges for meshing

Deforming Flow Field:

The fluid flow is transient and the flow volume changes with time (Figure 3). The fluid is compressed and expanded as it passes through different stages of the compression process. The mesh for the fluid space should be able to ‘follow’ the deformation imposed by the machine without losing its quality.

When the deformation is small, the initial mesh maintains cell quality, however, for large deformations, mesh quality deteriorates and collapses near the contact points between the stator and moving parts.

Scroll compressors - leakage through flank clearance.
Figure 4: Leakage through flank clearance. Image source – Ref [10].

Flank Clearance:

The narrow passage between the stationary and moving scroll in the radial direction is called the Flank clearance. A clearance of [~ 0.05 mm] is generally used to avoid contact, rub and tear.

Adequately resolving this clearance with a fine mesh is one of the key factors in obtaining an accurate CFD simulation. However, the narrowness of this gap poses meshing challenges for many grid generators.

scroll compressor - leakage through axial clearance.
Figure 5: Leakage through axial clearance. Image source – Ref [10].

Axial Clearance:

The narrow passage between the stationary and moving scroll in the axial direction is called the Axial clearance. The axial clearance is about one thousand of the axial scroll plate height, which is much smaller than the flank clearance.

The gap actually forces to have separate zones of mesh in some cases. Adequate resolution of axial clearance gaps is also equally important since it leads to inaccurate flow field prediction.

Scroll compressor tip seal.
Figure 6: Tip seal used to reduce axial clearance leakage. Image source Ref [5, 8].

Tip Seal Modeling:

Tip seals are used to reduce axial leakages which are caused due to wear and tear. The tip seals influence the mass flow rate of the fluid. Modeling internal leakages with tip seals would require many numerical techniques ranging from fluid-structure interaction to special treatments for thermal deformation and tip seals efficiency.

GridPro's structured mesh for capturing axial gap and tip seal in scroll compressor.
Figure 7: GridPro’s structured mesh for capturing axial gap and tip seal: a. With axial gap. b. Axial gap with tip seal.

Discharge Check Valve Modeling:

Valves called reed valves are installed at the discharge to prevent reverse flow. Understanding the dynamics of the check valves is important because they significantly influence scroll efficiency and noise levels. The losses at the discharge can significantly reduce the overall efficiency.

However, modeling the valve with appropriate simplification is a challenge for any meshing technique.

Reed valve and flip valve's in scroll compressors.
Figure 8: a. Reed valve geometry. b. Flip valve geometry. Image source Ref [2].

Influence of Mesh Element Type

A lot of different meshing methods have been employed from tetrahedral to hexahedral to polyhedral cells to discretize the fluid passage. However, researchers who tend to weigh more on the accuracy of the solution tend to weigh more to mesh with structured hexahedral cells.

Hexahedral meshing outweighs other element types w.r.t grid quality, domain space discretization efficiency, solution accuracy, solver robustness, and convergence levels.

One of the reasons why structured hexahedral mesh offers better accuracy is that it can be squeezed without deteriorating the cell quality. This allows to place, a large number of mesh layers in the narrow clearance gap. Better resolution of the critical gap results in better CFD prediction.

Parting Remarks

Understanding the key meshing challenges before setting forth to mesh scrolls is very essential. Becoming aware of the regions that pose difficulties to mesh and regions that strongly influence the accuracy of the CFD prediction is critically important. More importantly, which meshing approach to pick – structured, unstructured, or cartesian also influence the quality and accuracy of your CFD prediction.

In the next article on Automating meshing for scroll compressors, we discuss, how we can mesh scroll compressors in GridPro.


1.“Study on the Scroll Compressors Used in the Air and Hydrogen Cycles of FCVs by CFD Modeling”, Qingqing ZHANG et al, 24th International Compressor Engineering Conference at Purdue, July 9-12, 2018.
2. “Numerical Simulation of Unsteady Flow in a Scroll Compressor”, Haiyang Gao et al, 22nd International Compressor Engineering Conference at Purdue, July 14-17, 2014.
3. “Novel structured dynamic mesh generation for CFD analysis of scroll compressors”, Jun Wang et al, Proc IMechE Part A: J Power and Energy 2015, Vol. 229(8), IMechE 2015.
4. “Modeling A Scroll Compressor Using A Cartesian Cut-Cell Based CFD Methodology With Automatic Adaptive Meshing”, Ha-Duong Pham et al, 24th International Compressor Engineering Conference at Purdue, July 9-12, 2018.
5. “3D Transient CFD Simulation of Scroll Compressors with the Tip Seal”, Haiyang Gao et al, IOP Conf. Series: Materials Science and Engineering 90 (2015) 012034.
6.“CFD simulation of a dry scroll vacuum pump with clearances, solid heating and thermal deformation”, A Spille-Kohoff et al, IOP Conf. Series: Materials Science and Engineering 232 (2017).
7.  “Structured Mesh Generation and Numerical Analysis of a Scroll Expander in an Open-Source Environment”, Ettore Fadiga et al, Energies 2020, 13, 666.
8. “Analysis of the Inner Fluid-Dynamics of Scroll Compressors and Comparison between CFD Numerical and Modelling Approaches”, Giovanna Cavazzini et al, Energies 2021, 14, 1158.
9. “FLOW MODELING OF SCROLL COMPRESSORS AND EXPANDERS”, by George Karagiorgis, PhD- Thesis, The City University, August 1998.
10. “Heat Transfer and Leakage Analysis for R410A Refrigeration Scroll Compressor“, Bin Peng et al, ICMD 2017: Advances in Mechanical Design pp 1453-1469.
11. “Implementation of scroll compressors into the Cordier diagram“, C Thomas et al, IOP Conf. Series: Materials Science and Engineering 604 (2019) 012079.

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► Automation of Hexahedral Meshing for Scroll Compressors
  25 Mar, 2022

Figure 1: Structured multi-block mesh for scroll compressors.

1167 words / 5 minutes read

Developing a three-dimensional mesh of a scroll compressor for reliable Computational Fluid Dynamics (CFD) Analysis is challenging. The challenges not only demand an automated meshing strategy but also a high-quality structured hexahedral mesh for accurate CFD results in a shorter turnaround time.


The geometric complexities of Meshing Scroll Compressors discussed in our previous article give us a window into the need for creating a high-quality structured mesh of scroll compressors.

A good mesher should handle the following challenges in a positive displacement machine:

  • The continuously deforming pocket volume.
  • Since its a complex and time-dependent fluid dynamic phenomena. The mesher should be able to accurately “follow” the deformation imposed by the machine moving part without losing the mesh quality.
  • The mesh should not suffer quality decay, or have uncontrolled mesh refinements and mesh collapses near contact points between the stator and moving parts, etc.
  • Should offer higher accuracy of numerical simulations and the short simulation turn-around time.

Meshing Strategy

The scroll compressor fluid mesh region on a given plane is a helical passage, with varying thickness, expanding, and contracting based on the crank angle and the fluid domain is topologically a rectangular passage. So we use the same approach as that of meshing a rectangle for the Scroll Compressor.

scroll compressor structured mesh blocking: Blocking for a linear and curved rectangular passage.
Figure 2: Blocking for a linear and curved rectangular passage.
Animation video 1: Block creation by sweeping in GridPro.

Mesh Topology

One of the main obstacles for simulation in scroll compressors is the generation process of dynamic mesh in fluid domains, especially in the region of flank clearance. The topology based approach offers a perfect solution for such scenarios. Primarily because the deforming fluid domain in the Scroll compressor does not change the topology of the fluid region.

Animation video 2: Mesh at every time step for a scroll compressor.

Advantages of Topology based Meshing:

  • At each time step, when the orbiting rotor moves to a new position, the new mesh is generated without any user intervention.
Animation video 3: Mesh in the Discharge Chamber of the Scroll Compressor.
  • The block built becomes a template for a new variation of the scroll rotors, this makes it ideal for optimization and even meshing variable thickness scroll compressors.
  • Since meshes share the same topology, i.e. the number of blocks and their connectivity and cells remain the same, which avoids the need for interpolation of results. The computational effort is significantly reduced and the mesh quality is high, leading to reliable CFD analysis.

Flank Clearance and it’s Meshing Needs

The flank clearance could reduce to as low as 0.05 mm and an adequate resolution of the flank clearance with low skewness is the key reason for better prediction of performance by structured meshes when compared to unstructured meshes.

Animation video 4: Mesh in the flank clearance at different scroll rotor positions. 12 layers of cells finely discretize the narrow flank clearance.

The dynamic boundary conforming algorithm of GridPro moves the blocks into the compressed space automatically and generates the mesh. The smoother ensures that the mesh has a homogenous mesh distribution and is orthogonal. Orthogonality is another important mesh quality metric that sets structured meshes against moving mesh approaches. Orthogonality improves the numerical accuracy, stability of the solution and prevents numerical diffusion.

Solid Scroll Meshing for FSI

Understanding the heat transfer towards and inside the solid components is important since the heat transfer influences the leakage gap size. Heat transfer analysis is especially required in vacuum pumps where the fluid has low densities and low mass flow rates.

Structure multi-block mesh for the solid and fluid zone in a scroll compressor.
Figure 4: Structure Hexahedral mesh for the solid and fluid zone in a scroll compressor.


One of the major drawbacks of scroll compressors is the high working temperature (maximum temperature of up to 250 degrees Celsius is reported [Ref 3]). The higher temperatures increase excessively the thermal expansion of scroll spirals, leading to significant increments of internal leakages and thereby affecting the efficiency.

A mesh created for conjugate heat transfer has to model the in-between compression chamber, the scrolls and the convective boundary condition at the outer surface of the scrolls. This type of mesh enables to get consistent temperatures in the solids, to calculate the thermal deformation of the scrolls.

Automation and Optimization of Scroll Compressor

Even though scroll compressors enjoy a high volumetric efficiency in the range of 80-95%, there is still room for improvements. Optimization of the geometric parameters is necessary to reduce the performance degradation due to leakage flows in radial and axial clearances.

CFD as a design tool plays a significant role in optimizing scroll geometry. The major advantage of a 3D CFD simulation combined with fluid-structure interaction (FSI) is that the 3D geometry effect is directly considered. This makes CFD analysis highly suitable for the optimization of the design.

GridPro provides an excellent platform for automating hexahedral meshing through because of its working principle and the python based API.

The key features are:

  • Quick set up of a CFD model from CAD geometry.
  • Parametric design of geometry can be incorporated into the same blocking and can be used even for variable thickness scrolls.
  • The mesh at each time interval is of high quality with orthogonal cells and even distribution.
  • The other advantage of this strategy is that it is respectful of the space conservation law while conserving mass, momentum, energy, and species.

Since GridPro offers both process automation through scripting and API level automation. The automation can either be triggered outside of a CAD environment or inside the CAD environment.

This flexibility provides companies and researchers to develop full-scale meshing automation with GridPro while the user only interacts with CAD / CFD or any software connector platform.

GridPro coupled with CAESES software connector to generate meshes automatically for every change in geometry.
Figure 5: GridPro coupled with CAESES software connector to generate meshes automatically for every change in geometry.

Parting Remarks

The generation of a structured mesh for the entire scroll domains, including the port region, is a very challenging task. It could be very difficult to model narrow gaps and complex features of the geometry. However, with GridPro’s template-based approach and dynamic boundary conforming technology the setup is reduced to a few specifications and the user can develop his own automation module for structured hexahedral meshing.

If scroll compressor meshing is your need and you are looking out for solutions. Feel free to reach out to us at:

Contact GridPro


1.”Analysis of the Inner Fluid-Dynamics of Scroll Compressors and Comparison between CFD Numerical and Modelling Approaches“, Giovanna Cavazzini et al, Advances in Energy Research: 2nd Edition, 2021.

2. “Structured Mesh Generation and Numerical Analysis of a Scroll Expander in an Open-Source Environment”, Ettore Fadiga et al, Energies 2020, 13, 666.

3. “Waste heat recovery for commercial vehicles with a Rankine process“, Seher, D.; Lengenfelder, T.; Gerhardt, J.; Eisenmenger, N.; Hackner, M.; Krinn, I., In Proceedings of the 21st Aachen Colloquium on Automobile and Engine Technology, Aachen, Germany, 8–10 October 2012; pp. 7–9.

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► GridPro Version 8.1 Released
  16 Feb, 2022

About GridPro Version 8.1 

The GridPro version 8.1 release marks the completion of yet another endeavor to provide a feature-rich, powerful and reliable package to the Structured meshing software to the CAE community.

In every cycle of development, we fulfill the feature requests from our users, improve workflow challenges and democratize the feature to enable newer users to transition without much learning. Along the way, we are improvising on the performance of the tool with the increasing demand to handle challenging geometries in meshing.

Here is a quick Preview of the Major Features:

  • New License Monitoring System for Network license users.
  • Automatic grouping of Boundary faces for quicker workflow.
  • New Face display for better understanding of Topology.
  • Faster and Robust block extrusion for Tubular geometries ( ducts, arteries, volutes, etc).

Major Highlights of Version 8.1

License Monitoring System

Network / Float Licenses

The License Management System now has GUI access to most of the features that a user or a system admin would look for. The License Manager GUI now displays all the license-related information. When the user loads the license file and starts the license manager, all the initialization process is done before the license manager is started. The license manager also displays the number of licenses used and the MAC id/ hostname of the user using the license.

Node-locked / Served Licenses

The client license management system is now packaged along with the GUI. When the GUI is opened for the first time the license popup appears where the user is asked to upload the license and Initialise. The initialization process runs in the background and opens up the GUI. This process irons out the need to go through a list of specific commands listed in section 9.11 of the utility manual.

Smart Face Groups to Enhance user workflow in GridPro

The quest to improve user experience and provide easy access to the entities continues. The current version has made a major stride in this direction. From version 8.1 onwards the user has a list of smart selections of face groups available as a part of the Selection Panel. From the blocking, the algorithm calculates the boundary faces and smart groups, based on certain checks. These face groups are displayed and the user can select a single group or a combination of groups to progress in further modifying the structure or assigning to surfaces.

The selection pane also has a temporary selection group to provide flexibility in the workflow. In the past, the user had to select a group to select the entities in the GL. However, the present version enables the users with an alternative workflow where they can right-click and drag in the GL to select faces /blocks. These selected blocks/faces/edges/corners are stored in the Selection Group. It is overwritten when the next selection is made. However, the user has an option to move the selection into one of the permanent groups.

Topology now has Face Display for Better Visualization

The topology now has a Face display along with the corners and edges. The face display now helps the user to have a better perception of the faces and blocks both displayed in the GL and grouped in individual groups. To reassure the user of the topology entities selected, the display mode is automatically changed to face display mode in the following scenarios.

  • User selects corners and edges into a group.
  • Wrap displays the new faces created after an operation.
  • Copy shows the blocks that are created when a face/s are created.
  • Extrude displays the output blocks created.

There are many such scenarios where the user is provided feedback on the operations visually.

Fast Blocking for Tubular Geometries (Arteries, Ducts, etc)

The improved centreline evaluation tool is now robust and fast. This speeds up the topology building for geometries like pipes and human arteries and ducts. The algorithm extrudes the given input along the centreline of the geometry resection the change in cross-sectional area change. The algorithm is now available under extrude option in the GUI.

For more details about the new features, enhancements, and bug fixes please, refer to:

Supported Platforms

GridPro WS works on Windows 7 and above, Ubuntu 12.04 and above, Rhel 5.6 and above, MacOS 10 and above.

The support for the 32-bit platform has been discontinued for all operating systems.

GridPro AZ will be discontinued from version 9 onwards.


GridPro Version 8.1 can be downloaded by registering here.

All tutorials can be found in the Doc folder in the GridPro Installation directory. Alternatively, it can be downloaded from the link here.

All earlier software versions can be found in the Download sections.

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► Turbopumps – A Unique Rotating Machine
  10 Dec, 2021

Figure 1: Structured multi-block grid for turbopumps.

1050 words / 5 minutes read

Turbopumps help rockets achieve high power to weight ratio by feeding pressurized propellant to the rocket’s combustion chamber. The success of rocket launch missions is heavily influenced by the design of inducers in the turbopumps. 

The Rocket Challenge

Turbopump in a liquid propellant rocket engine configuration
Figure 2: Turbopump in a liquid propellant rocket engine configuration.

Human conquest of space has advanced at full speed over the last few years. According to Forbes, there are 10,000 space companies globally. This massive growth has triggered competition in the global space transportation business which is fueling innovations. Reports indicate that nearly 59 % of rocket launch failures are due to propulsion system failures. In this article, we will discuss how the industry is focused on increasing reliability and reducing the cost of development of launch vehicles by improving the design of liquid-propellent rocket engines.

The main reason for propulsion system failure is due to instabilities in the combustor or turbopump. It is estimated that up to 50% of a rocket development program’s cost goes into the design and development of turbopumps.

Failed Missions

Despite many years of extensive research, unsteady cavitation instabilities in turbopumps are a significant problem and are not entirely understood. Further, there are no well-established procedures for predicting its onset during the early design phase.

Cavitation instabilities that can trigger severe load and vibrations within turbopumps cause engine thrust fluctuations and sometimes even total mechanical failure. Historically, cavitation instabilities have caused failed missions in almost all rocket development programs, including Apollo (NASA), Space Shuttle main engines (NASA), Fastrac (NASA), Vulcain (ESA), and LE-7 (JAXA).

Hence, it is critical to identify the mechanisms governing cavitation instabilities to pave the way for building principle-based design guidelines for inducers to suppress cavitation instabilities in turbopump. The beneficial outcome of this exercise will be – more affordable, reliable, and higher-performance turbopumps.

Cavitation is turbopump inducers
Figure 3: Cavitation is turbopump inducers.

Why Turbopump in Rockets?

Liquid oxidizers and fuels like hydrogen or methane must be fed into the combustion chamber at a higher pressure than the existing chamber at a sufficient flow rate. It is done either by having pressurized tanks or by using a pump. Pressurized tanks tend to be heavy and bulky and are less preferred since they add to the overall rocket system weight.

On the other hand, turbopumps serve as a better alternative due to their compact nature and low weight. Rockets can achieve a high power-to-weight ratio since turbopumps only need a lightweight, low-pressure feed tank.

Challenges in Turbopump Design

One of the main goals of a rocket designer is to stretch the maximum possible delivery payload. Maintaining high thrust chamber pressure and reducing the inert weight of the rocket to a minimum can help achieve this goal. Reduction in system weight is possible by lowering the turbopump size and mass. But, to maintain the same pressure and flow rate, the turbopump needs to run at a high rotational speed. Unfortunately, running at high speed leads to cavitation problems. Coming up with ways to mitigate this issue is a critical design challenge.

 Inducer and impeller in rocket engine turbopumps
Figure 4: Inducer and impeller of a rocket engine turbopump.

The second design challenge arises when the turbopumps are expected to work in off-design conditions. Such a need arises because rocket engines often face varying thrust requirements during their flight. For example, the designer needs to make appropriate design decisions to alleviate the problems of vibrations due to cavitation when the liquid pressure is lowered below the vapour pressure limits. Hence, coming up with ways to reduce performance degradation under cavitation conditions is essential.

Other design challenges which come in more significant magnitudes, unlike in compressors include, high radial and axial thrusts, leakages, increased disk friction, etc. It is up to the designer to develop tricks to manage the tradeoffs and make specific design choices to overcome these problems.

Inducer and impeller in turbopumps
Figure 5: Inducer and impeller of a turbopump.

Importance of Inducer in Turbopumps

Designing small and compact turbopumps rotating at high speed can reduce the total weight of rockets. However, at higher speeds, cavitation onsets, causing machine noise and vibration, erosion, loss of head and efficiency, etc.

An anti-cavitation component called the inducer is axially placed upstream of the impeller to overcome these challenges. The inducer, acting as a pre-pump, increases the pressure of the fluid by a sufficient amount to minimize cavitation and improve the performance of the impeller. They are sometimes expected to sacrifice themselves to safe-guard the impeller blade from cavitation.

Unlike the impeller, the inducer blades are fewer in number and are lengthier and wider. Further, they have larger stagger angles, increasing pitch between blades, high blade solidity, and usually small angles of incidences.

With these unique features, inducer blades have minimal blockage due to cavitation, thereby allowing them to operate under very low suction pressure conditions without deteriorating the pump performance. In general, inducers have a minimal effect on the efficiency and head of the pump but offer a dramatic impact on the cavitation performance. Further, they reduce noise and vibration. But more importantly, inducers decrease the pump’s critical NPSH by more than three times.

Structured multi-block mesh for an inducer
Figure 6: Structured multi-block mesh for an inducer.

Parting Remarks

Cavitation surge and inlet backflows are inevitable in turbopumps. All we can think of is finding ways to suppress them to some extent. Suppression can be done by using an obstruction plate or by connecting a smaller diameter suction pipe upstream of the inducers. Backflow suppression helps to narrow the onset range of cavitation surge. Even if they occur, their amplitudes are weakened and subdued by the suppression devices. This helps in achieving improved surge performance.

However, these two suppression techniques are effective when the flow rates are healthy but show their limitations at extremely low flow rates. Researchers recommend combining these suppressing methods with inducer blade shapes suitable for reducing inlet backflows for such extreme conditions.

Further Readings

  1. Meshing of Rocket Engine Nozzles for CFD
  2. Spiked Blunt Bodies for Hypersonic Flights
  3. Know Your Mesh for Reentry Vehicles


1. “Studies of cavitation characteristics of inducers with different blade numbers“, Lulu Zhai et al., AIP Advances 11, 085216; 12 August 2021.

2. “Numerical and experimental study of cavitating flow through an axial inducer considering tip clearance“, Rafael Campos-Amezcua et al., Proc IMechE Part A: J Power and Energy 227(8) 858–868, IMechE 2013.

3. “Suction Performance and Cavitation Instabilities of Turbopumps with Three Different Inducer Design“, Tatsuya Morii et al., International Journal of Fluid Machinery and Systems, Vol. 12, No. 2, April-June 2019.

4. “A Study on the Design of LOx Turbopump Inducers“, Lucrezia Veggi et al., International Symposium on Transport Phenomena and Dynamics of Rotating Machinery Maui, Hawaii, December 16-21, 2017.

5. “Study on Hydraulic Performances of a 3-Bladed Inducer Based on Different Numerical and Experimental Methods“, Yanxia Fu et al., Hindawi Publishing Corporation International Journal of Rotating Machinery, Volume 2016, Article ID 4267429.

6. “Study on inducer and impeller of a centrifugal pump for a rocket engine turbopump“, Soon-Sam Hong et al., Proc IMechE Part C: J Mechanical Engineering Science 227(2) 311–319, IMechE 2012.

7. “Turbopump Design: Comparison of Numerical Simulations to an Already Validated Reduced-Order Model“, A Apollonio et al., Journal of Physics: Conference Series 1909 (2021) 012029, ISROMAC18.

8. “Effect of leading-edge sweep on the performance of cavitating inducer of LOX booster turbopump used in semi cryogenic engine“, Arpit Mishra et al., IOP Conf. Series: Materials Science and Engineering 171 (2017).

9. “Design and Analysis of a High Speed, High-Pressure Peroxide/RP-1 Turbopump“, William L. Murray et al., AIAA paper.

10. “A Body Force Model for Cavitating Inducers in Rocket Engine Turbopumps“, William Alarik Sorensen et al., MS Thesis, Massachusetts Institute of Technology, September 2014.

11. “Rocket engine inducer design optimization to improve its suction performance“, M. J. Lubieniecki, M S Thesis, Delft University of Technology, 7 December 2018.

12.” Modeling Rotating Cavitation Instabilities in Rocket Engine Turbopumps“, Adam Gabor Vermes, M S Thesis, Delft University of Technology.

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The post Turbopumps – A Unique Rotating Machine appeared first on GridPro Blog.

► Aircraft Vortex Generators – The Nacelle Strakes
  14 Oct, 2021

Figure 1: Structured multi-block meshing for aircraft vortex generators – the nacelle strakes.

1100 words / 5 minutes read


In modern transport aircraft, underwing engine nacelle installation is the most common design choice. Here, the engine nacelles which are tightly coupled with the wing have a huge impact on the maximum lift and stall angle of the wing. With the usage of larger by-pass ratio engines over the years, the adverse effects of the nacelle on the wing’s performance have increased dramatically, especially so when the high lift devices are deployed.

The nacelles hamper the wing’s desired performance by triggering premature massive flow separation on the main element and decrease the CL_max and stall angle. We cover more of this is in our earlier article Engine Nacelle Aerodynamics.

In order to attenuate the negative influence of nacelle, most aircraft manufacturers employ vortex generators called strakes or more popularly known as chines at appropriate locations on the nacelle.

Nacelle strakes are small delta-shaped or triangular panel sheets positioned strategically on the nacelle to induce longitudinal vortices. In short –  vortex generators mounted on nacelles are called strakes.

Usually, a pair of strakes are mounted on the nacelles to generate additional vortices to control the flow separation on the wing. Depending on the mounting location and the nacelle-pylon-wing flow field, the generated strake vortices can avoid the generation of slower nacelle vortex or sometimes even interact with nacelle vortex and increase their axial core speed. Thus they affect the position and strength of the installation vortices leading to an increase in maximum achievable lift. Since strakes directly influence the wing’s lift generation capabilities, their design demands careful attention.

Aircraft vortex generators: Single strake and Double strake
Figure 2: a. Aircraft vortex generators: Single strake. b. Double strake. Image source Ref [1].

Effectiveness of strake installation

For underwing nacelle configurations without strakes, at alphas near to stall, a large zone of low energy flow gets set above the main wing. The creation of this low energy zone is due to the nacelle blocking the flow from passing over the upper surface of the wing at high alphas. Any further increase in the angle of attack results in premature flow separation.

Reduction in upwash flow due to nacelle strakes: Strake off. Strakes on.
Figure 3: Surface oil flow visualization. Reduction in upwash flow. a. Strake off. b. Strakes on. Images source Ref [3].
When strakes are installed, the flow field is made more conducive for achieving higher lift by two mechanisms. Firstly, the nacelle strakes reduce the nacelle upwash and thereby relieve the adverse flow effects at the wing-pylon intersection. Figure 3 and 4 shows the reduction in upwash and the reduction in cross-flow separation on the nacelle near the pylon junction.

Aircraft vortex generators: Nacelle strakes particle traces
Figure 4: Aircraft vortex generators: Nacelle strakes particle traces. Image source Ref [3].
By a second mechanism, the strakes vortices provide a downwash on the upper surface of the wing which energizes the boundary layer and eliminates the low energy zone. This happens as the strake vortex with high kinetic energy passes through the low energy zone and the neighboring high total pressure air rushes into the low energy zone. In this way, the flow gets reenergized and the flow separation gets delayed. This positive effect of strake installation can clearly be seen in Figure 5. For an alpha beyond stall, the configuration without strake gets stalled, while in the configuration with strake, the flow separation is suppressed and the stall is delayed.

Total pressure coefficient contours: Without strake, With strake
Figure 5: Total pressure coefficient contours. a. Without strake. b. With strake. Image source Ref [4].
This positive effect of strake installation can also be seen in the Cp distribution, as shown in Figure 6. Here we can notice the elimination of flow separation on the upper surface of the main wing and the flap with the strakes mounted. As an outcome, the lift on the main wing and flap is recovered. Further, the maximum lift is enhanced and the stall is delayed. Studies show that nearly 60 to 70% loss in maximum lift can be recovered and an improvement in lift coefficient by 0.3 and stall angle by 3 degrees is possible by using strakes.

Nacelle strakes: Cp distribution at 35% spanwise station
Figure 6: Cp distribution at 35% spanwise station. Image source Ref [4].
In one study, usage of a single strake showed improvement in the stall angle by 1 degree but without any larger change in maximum lift. However, adding another strake was observed to increases the maximum lift from 2.26 to 2.3. When a third strake on the nacelle lip was introduced, the maximum lift became 2.34 and the stall angle further increased by 1 degree.

Parametric design of nacelle strake

The effectiveness of the strakes is directly related to the strake’s geometry and installation location. The strength and trajectory of the strake vortex depend on the strake area, deflection angle, axial position, and azimuth location.

Parametric variants of nacelle strakes: Variants generated based on changing axial position and area
Figure 7: Parametric variants of nacelle strakes. Variants generated based on changing axial position and area. Image source Ref [4].
Figure 7 shows a parametric study where the axial location and the area were varied. Strake 2 is observed to achieve higher lift compared to other configurations. Strake 2, 1, and 4 have the same area, but their axial positions are sequentially increased from the nacelle’s trailing edge. As can be observed in Figure 8a, the maximum lift coefficient also decreases in the same order. What this implies is that strakes axial location is a key factor in determining the stall-delay capabilities of strakes. The closer the strake placement to the nacelle trailing edge, the higher is the achievable lift coefficient.

Also, strake 2 and strake 3 have the same exact position, but strake 3 has an area that is two-thirds that of strake 2. Since the location is the same, there is hardly any difference in lift coefficients between strake 2 and 3, before stall. However, after the stall, the strake with a smaller area (strake 3) produces an abrupt drop in lift coefficient.

vortex generators: CL vs alpha plot, Total pressure coefficient contours for different strakes geometries
Figure 8: a. CL vs alpha plot. b. Total pressure coefficient contours for different strakes geometries. Image source Ref [4].
From Figure 8b, we can observe that strake 4 is least effective in controlling the flow. Careful observation reveals that the vortex generated by strake 2 is strongest among all while that from strake 4 is the weakest. From Figures 8a and 8b we can conclude that the strength of the strake vortex is another key factor that affects the strake’s performance. And there is a direct correlation between the strake vortex axial strength and its installation location.

vortex generators: Surface streamlines around different strake variants
Figure 9: Surface streamlines around different strake variants. Image source Ref [4].
Studies of the local flow fields using surface streamlines reveal that the circumferential velocity component decreases when the distance between the strake and the nacelle trailing edge increases. This means the strength of the strake vortex is determined by the strake’s local angle of attack. It is for this reason that, strake 2 vortex is strongest while the strake 4 vortex is weakest.

With these observations, we can conclude that the axial positioning of the strake determines the circumferential component of the flow, which in turn determines the strake’s local angle of attack. For a fixed azimuth positioning, the local alpha is a key factor influencing the strength of the vortex. In turn, strake’s vortex strength is a key factor in strake’s effectiveness in delaying the stall.

aircraft vortex generators - the nacelle strakes, Gridpro structured multiblock grids
Figure 10: Multi-block surface mesh using GridPro on the nacelle in the near vicinity of the strakes.

aircraft vortex generators - the nacelle strakes, multi-block mesh
Figure 11: Multi-block structured surface mesh on the strakes using GridPro.

Parting thoughts

Even though aircraft vortex generators, the nacelle strakes are proven devices to enhance lift for underwing mounted nacelle configurations, they are observed to be less effective for larger UHBR nacelles. For larger bypass ratio engines, they are unable to energize the flow sufficiently and make the flow remained attached to the wing surface. For such nacelles, researchers are working on developing active flow control devices such as pulsed jet blowing to control flow separation.

Nevertheless, strakes which are successfully deployed by all aircraft manufacturers around the world for many decades, will continue to be in use for small and medium-sized aircraft because of their simplicity, cost-effectiveness, and more importantly for their effectiveness in controlling the flow.

Further Reading

  1. Engine Nacelle Aerodynamics
  2. Role of Vortex Generators in Diffuser S-Ducts of Aircraft


1. “Modelling the aerodynamics of propulsive system integration at cruise and high-lift conditions”, Thierry Sibilli, PhD Academic Year: 2011-2012, Cranfield University.

2. “CFD Prediciton of Maximum Lift Effects on Realistic High-Lift-Commercial-Aircraft-Configurations within the European project EUROLIFT II”, H. Frhr. v. Geyr et al, Second Symposium “Simulation of Wing and Nacelle Stall”, June 22nd – 23rd, 2010, Braunschweig, Germany.

3. “Navier-Stokes Analysis of a High Wing Transport High-Lift Configuration With Externally Blown Flaps”, Jeffrey P. Slotnick et al, NASA.

4. “Numerical Research of the Nacelle Strake on a Civil jet“, Wensheng Zhang et al, 28TH International Congress of the Aeronautical Sciences, ICAS 2012.

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► Role of Vortex Generators in Diffuser S-Ducts of Aircraft
  21 Sep, 2021

Figure 1: Structured multi-block grid for an aircraft intake S-Duct with vortex generators.

2300 words / 11 minutes read

Highly offset modern-day S-ducts need flow control mechanisms like vortex generators or synthetic jets to control the flow. The general consensus among researchers is that RANS solvers are in-capable of meeting the challenges of S-duct internal flow fields, while DES is considered the most promising candidate. Lastly, structured grids are observed to provide superior flow field prediction for S-ducts on a fraction of a grid size than that needed for unstructured grids.


The design of an optimized intake-duct is a trade-off between multiple requirements. This includes high-pressure recovery, low installation drag, low radar, and noise signatures, as well as minimum weight and cost. These requirements are driving the development of modern fighter aircraft and UAVs towards compact designs. This in turn has resulted in having a high degree of offset between the intake and engine face, leading to the design of highly bent S-ducts or serpentine ducts.

However, higher bend ducts lead to larger flow separation and vortex formation. With the compact nature of the duct, the available duct length is not good enough for the diffusion and dissipation of these secondary flows. This results in total pressure loss and higher flow non-uniformity at the engine fan face. This is something unpleasant, as flow distortion at the inlet can lead to reduced stability margin for the compressor or fan. Further, inlet distortion can cause high cycle fatigue resulting in increased maintenance costs, loss of aircraft operability, and even catastrophic loss of the aircraft.

Natural vortices in serpentine ducts. b. Vortices in a highly-bend modern-day S-duct.
Figure 2: a. Natural vortices in serpentine ducts. b. Vortices in a highly-bend modern-day S-duct. Image source Ref [7].
So, current industry research in S-duct is mainly focused on developing flow control systems to reduce and control flow distortion and flow losses while maintaining steady mass flow for optimal engine performance. Passive flow control using vortex generators and active flow control systems like synthetic jets are currently being studied.

CFD as a design tool is used extensively for accurate aerodynamic prediction of highly offset diffuser shapes. Attention is paid to understanding the variation in distortion levels and pressure recovery at the AIP with changes in duct shape. CFD is quite handy in studying the parametric variations of vortex generators and synthetic jets. Figure 3 shows the reduction in flow separation with the introduction of vortex generators.

Passive flow control by vortex generators

The effectiveness of the VGs depends on a number of parameters, but the main ones are the height of the VG, the orientation angle of the VG relative to the free stream and the number of VGs used. Hence testings’ are done by tweaking these parameters to study their influence on the flow.

Effect of Number of VGs: The placement of the VGs starts from the symmetry plane. The first one is placed near the symmetry plane and subsequent ones are placed in the circumferential direction at constant x. As can be observed in Figure 3, the flow quality improves with the usage of additional VGs in the form of diminishing of low Mach number region and the recovery of the pressure loss.

VG number effects - a. Mach contour on the symmetry plane. b. AIP. c. Separated area
Figure 3: VG number effects – a. Mach contour on the symmetry plane. b. AIP. c. Separated area. Image source Ref [2].
Effect of VG Height: The VG height has a decisive role in making VGs an effective flow control tool. The height of VGs is determined by the thickness of the local boundary layer and usually, a height of about 6 mm is considered as an optimal height. As can be observed in Figure 4c, the separated area decreases as the VG height increases from 3 mm to 6 mm, but when the height is made 9 mm, severe flow separation occurs.

VG height effects - a. Mach contour on the symmetry plane. b. AIP. c. Separated area.
Figure 4: VG height effects – a. Mach contour on the symmetry plane. b. AIP. c. Separated area. Image source Ref [2].
Effect of VG orientation: A typical orientation of VGs is around 18 degrees relative to the free stream direction. If the orientation is varied from 8 degrees to 28 degrees, it is observed that the contour plots for 8, 13, and 18 degrees are very similar, but a slightly more separated area is seen for the 8-degree configuration. For the 28 degrees case, the flow separation increases by a large magnitude.

VG orientation effects - a. Mach contour on the symmetry plane. b. AIP. c. Separated area
Figure 5: VG orientation effects – a. Mach contour on the symmetry plane. b. AIP. c. Separated area. Image source Ref [2].
Overall, for use of VGs help in improving the pressure recovery and reduction of distortion at the AIP. While the pressure recovery is only marginal at about 0.8%, the reduction in distortion is significant, reaching up to 45% for certain geometric variants of VGs.

Active flow control by synthetic Jets

Passive flow control techniques have been in existence for decades, but active flow control (AFC) methods like constant or pulsed air jets are a new budding research area. Here, the improvement in flow efficiency is accomplished through a delay in flow separation.

Figure 6 shows AFC configurations for constant blowing jets with three slit areas with different widths. Studies show that improvement in recovery and reduction of distortion happens with an increase in the mass flow rate of the jets. However, beyond a certain value, a further increase in mass flow rate makes the AFC less effective. Best performance is shown by the smaller area and higher jet velocity configuration. A maximum pressure recovery of 1.15% and distortion reduction by 60-80 percent have been reported.

Jet area effects - a. Mach contour on the symmetry plane. b. AIP. c. Separated area.
Figure 6: Jet area effects – a. Mach contour on the symmetry plane. b. AIP. c. Separated area. Image source Ref [2].
Overall, the AFC techniques are observed to achieve better pressure recovery and lower distortion compared to passive flow control techniques like VGs. In both methods, secondary flows at the first bend are reduced, while they fail to reduce the secondary flows effectively at the second bend.

The S-duct’s challenge to the CFD community

Accurate prediction of large separated flow regions such as seen in S-ducts by CFD is very difficult. Currently, efforts are put to evaluate and understand the capabilities and limitations of RANS, URANS, and DES methods in modeling the flow physics and performance characteristics of highly offset intake diffusers.

The general consensus among researchers is that RANS solvers are in-capable of meeting the challenges of S-duct internal flow fields. URANS shows better predictions capabilities by capturing the time-evolution of the flow. Further research and development are needed to make it more accurate. DNS or LES methods at least in principle are capable to make accurate predictions of the flow physics to the required level. However, being computationally expensive, they are still not feasible. Only DES – Detached Eddy Simulation, is considered among many researchers as the potential candidate for predicting unsteady flow fields, involving high levels of turbulence and occurrences of instantaneous flow phenomena.

DES, which is nothing but a hybrid of RANS-LES turbulence methods has computational costs which are quite acceptable. DES offers a nice balance by providing the physical accuracy of the LES with the cost-effectiveness of the RANS. Since building a DES code involves, only coupling the pre-existing RANS and LES code, they reduce the time and cost needed for development.

Wall streamlines from the wall shear stress distributions for a. RANS b. X-LES-medium simulations
Figure 7: Wall streamlines from the wall shear stress distributions for a. RANS b. X-LES-medium simulations. Image source Ref [4].
The RANS and the LES inside a DES code: In standard DES, RANS is used to treat the boundary layer where the turbulent length scales are smaller, while LES is applied in regions with more uniform properties, larger turbulent length scales, and in locations where more physical relevance is required. Provision for implicit switching between RANS and LES is made depending on the RANS length scale and LES filter width.

This bifurcation of the regions is essential because there are major differences between RANS and LES arising due to the different turbulence modeling approaches. LES resolves the larger scales of the flow and models only the smaller scales. While, RANS on the other hand does not explicitly resolve any scales, but calculates the mean flow quantities and models the turbulent scales.

Since in LES, the flow turbulent scales are explicitly resolved, the generated eddy viscosity is smaller compared to that in RANS. As a result, LES reduces the viscous dissipation and diffusion in the flow, thereby allowing weaker flow structures to sustain in the solution.

Another difference between RANS and LES is the grid dependency. In RANS, the turbulence model is based on flow quantities and is similar for every grid, while in LES, the filter width is directly dependent on the grid-spacing. What this means is that any grid refinement in LES not only influences the numerical accuracy, but also the subgrid-scale turbulence model. As a consequence, unlike in RANS, grid-refinement beyond a point of convergence in LES will not produce the same solution.

When we consider standard DES in general, it can be noticed that there is a large dependency on the RANS part of the simulation, which requires a tangential grid spacing on the wall to be greater than the local boundary layer thickness. Sticking to this gridding requirement may be very difficult inside the duct. In such circumstances, if the switching to LES occurs inside the RANS boundary layer, then there will be an underestimation of the skin friction coefficient.

So, in order to overcome this grid-induced separation, newer approaches like DDES – Delayed Detached Eddy Simulation and ZDES – Zonal Detached Eddy Simulation have been developed. In DDES, the switch to LES mode is delayed while in ZDES, the RANS and DES zones are selected individually, to have clarity of the role of each region. These steps are undertaken to avoid ‘model stress depletion’ and grid-induced flow separation.

Comparison of diffuser flow solutions  a. time-averaged.  b. instantaneous flow field. Schlieren-like visualization with different physical time steps applied
Figure 8: Comparison of diffuser flow solutions  a. time-averaged.  b. instantaneous flow field. Schlieren-like visualization with different physical time steps applied. Image source Ref [4].
To a good extent, the global flow features are correctly captured by RANS and time-averaged DES. The computed total pressure loss and Mach number at the engine face agree well with the experimental results. When compared to experimental results, Mach number from RANS differs by about 9% while URANS differs by 5%.

In RANS alone, the predicted flow distortion and pressure recovery depend highly on turbulence modeling. Depending on the turbulence model chosen, the total pressure recovery is reported to vary from 0.1% to -1.8%, while flow distortion is observed to differ widely from +37% to +126%.
However, many major differences exist between the numerical results and experiments. The region with total pressure losses doesn’t conform with the experiments. The distortion parameter is systematically overestimated, with the DES solution differing from experiments by a larger value than RANS, as DES overestimates the separated flow region. Also, DES shows a delay in the development of the instabilities in the shear layer.

Grids for S-duct. a. Structured. b. Unstructured.
Figure 9: Grids for S-duct. a. Structured. b. Unstructured. Image source Ref [1].

Which grid type is better for S-duct?

Just like the need to pick the right solver type, there is a need to pick the right grid type to do accurate CFD prediction for S-ducts. Studies have shown that grid generation both in structured and unstructured ways for S-ducts is quick, efficient, and reliable. However, structured meshes tend to achieve superior performances than high-quality unstructured meshes says a research study by ANSA, BETA CAE system.

Surface mesh for an S-duct without vortex generators using GridPro
Figure 10: Surface mesh for an S-duct without vortex generators using GridPro.

Solution differences between the structured medium grid and fine grid were observed to be very small. Even though the grid size nearly doubles in between the medium and fine grids, the AIP back pressure was seen to make only a marginal variation of 0.05% between the two grids. On the other hand, notable differences were noticed between the unstructured medium grid and fine grid simulation results. The difference in predicted backpressure between the two grids is about 1%.

Structured multi-block grid for an S-duct with vortex generators using GridPro
Figure 11: Structured multi-block grid for an S-duct with vortex generators using GridPro.

When the flow field as generated by equivalently resolved unstructured and structured grids was compared, the differences were significant. To make the grids more relatable to each other, the fundamental cell size was kept the same for the two different mesh setups. Tetrahedral cells being isotropic in nature needs more mesh cells to achieve a roughly equivalent sized structured grid cell.

Nested multi-block grid for an S-duct with vortex generators using GridPro
Figure 12: Nested multi-block grid for an S-duct with vortex generators using GridPro.

Thus, the structured mesh outperforms the unstructured hybrid grid despite having a far lower cell count. The structured grid with a cell count of 4.2 million predicts a more greatly resolved flow solution than its equivalent unstructured counterpart. Interestingly, to achieve a similarly resolved flow solution, the unstructured approach demanded a grid of size 31.2 million.

Nested grids around the vortex generators using GridPro
Figure 13: Nested grids around the vortex generators using GridPro.

What we can conclude from these gridding experiments is that, at least for flows in S-duct with significant shear, an order of magnitude more unstructured cells are needed to match an equivalent structured grid in terms of solution accuracy and flow field resolution. Even with VGs, structured meshes require far fewer cells. Thus, structured meshes require lesser computational resources to predict higher-quality flow fields than higher-density unstructured grids.

Structured grids and unstructured grids around vortex generators
Figure 14: Structured grids and unstructured grids around vortex generators. Image source Ref [1].

Parting Remarks

This brings us to the end of this article. Complete elimination of flow distortions in S-duct at all flight conditions is impossible. The use of flow control mechanisms like vortex generators or synthetic jets is the way to go forward in dealing with flow separations.

Evaluation of the distortion parameter results from steady and dynamic simulations at the engine face reveal that only dynamic simulations can provide the correct assessment of the performance parameters considering the distortion limits as required by the engine manufacturers. Compared to RANS, DES results, in general, are in accordance with the experiments, but in the future, its capabilities need to be further enhanced to improve its accuracy to the level required by industrial standards.

Physical time step size and grid resolution have an important role in the outcome of the computational results. For DES simulations, a strong association exists between the grid and the ability of the algorithm to correctly manage the varying turbulent scales.

Structured meshes are reported to provide superior solutions compared to unstructured meshes. Needing only a fraction of the cell count as needed by unstructured meshes, structured grids are observed to provide a better-resolved flow field and tend to take far lesser computational resources.

Further Reading

  1. Aircraft Vortex Generators – The Nacelle Strakes
  2. Engine Nacelle Aerodynamics
  3. A Whale of an Idea in Wing Design


1. “Numerical Simulations of Flow Through an S-Duct”, Pravin Peddiraju, Arthur Papadopoulos, Vangelis Skaperdas, Linda Hedges, BETA CAE Systems, 6th BETA CAE International Conference.

2. “CFD Simulation of Serpentine S-Duct with Flow Control”, Lie-Mine Gea, 51st AIAA/SAE/ASEE Joint Propulsion Conference, July 27-29, 2015, Orlando, FL.

3. “CFD Validation and Flow Control of RAE-M2129 S-Duct Diffuser Using CREATE-AV Kestrel Simulation Tools”, Pooneh Aref et al, Aerospace 2018, 5, 31.

4. “Numerical simulations for high offset intake diffuser flows”, T.M. Berens et al, NLR-TP-2014-096.

5. “A Multi-objective shape optimization of an S-Duct intake through NSGA-II genetic algorithm”, Aurora Rigobello, 5 Dicembre 2016, Universita’ Degli Studi Di Padova.

6. “S-Duct Inlet Design for a Highly Maneuverable Unmanned Aircraft”, Jacob Brandon, Thesis, The Ohio State University, 2020.

7. “Effectiveness of a Serpentine Inlet Duct Flow Control Scheme at Design and Off-Design Simulated Flight Conditions”, Angela C. Rabe, Doctor Of Philosophy In Mechanical Engineering, Virginia Polytechnic Institute and State University, August 1, 2003.

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The post Role of Vortex Generators in Diffuser S-Ducts of Aircraft appeared first on GridPro Blog.

Hanley Innovations top

► Aerodynamics of a golf ball
  29 Mar, 2022

 Stallion 3D is an aerodynamics analysis software package that can be used to analyze golf balls in flight. The software runs on MS Windows 10 & 11 and can compute the lift, drag and moment coefficients to determine the trajectory.  The STL file, even with dimples, can be read directly into Stallion 3D for analysis.

What we learn from the aerodynamics:

  • The spinning golf ball produces lift and drag similar to an airplane wing
  • Trailing vortices can be seen at the "wing tips"
  • The extra lift helps the ball to travel further

Stallion 3D strengths are:

  • The built-in Reynolds Averaged Navier-Stokes equations provide high fidelity CFD solutions
  • The grid is generated automatically 
  • Built-in  menus are used to specify speed, angle, altitude and even spin
  • Built-in visualization
  • The numbers are generated to compute the trajectory of the ball
  • The software runs on your laptop or desktop under Windows 7, 10 and 11
More information about Stallion 3D can be found at
Thanks for reading 🙋

► Accurate Aircraft Performance Predictions using Stallion 3D
  26 Feb, 2020

Stallion 3D uses your CAD design to simulate the performance of your aircraft.  This enables you to verify your design and compute quantities such as cruise speed, power required and range at a given cruise altitude. Stallion 3D is used to optimize the design before moving forward with building and testing prototypes.

The table below shows the results of Stallion 3D around the cruise angles of attack of the Cessna 402c aircraft.  The CAD design can be obtained from the OpenVSP hangar.

The results were obtained by simulating 5 angles of attack in Stallion 3D on an ordinary laptop computer running MS Windows 10 .  Given the aircraft geometry and flight conditions, Stallion 3D computed the CL, CD, L/D and other aerodynamic quantities.  With this accurate aerodynamics results, the preliminary performance data such as cruise speed, power, range and endurance can be obtained.

Lift Coefficient versus Angle of Attack computed with Stallion 3D

Lift to Drag Ratio versus True Airspeed at 10,000 feet

Power Required versus True Airspeed at 10,000 feet

The Stallion 3D results shows good agreement with the published data for the Cessna 402.  For example, the cruse speed of the aircraft at 10,000 feet is around 140 knots. This coincides with the speed at the maximum L/D (best range) shown in the graph and table above.

 More information about Stallion 3D can be found at the following link.

About Hanley Innovations
Hanley Innovations is a pioneer in developing user friendly and accurate software that is accessible to engineers, designers and students.  For more information, please visit >

► 5 Tips For Excellent Aerodynamic Analysis and Design
    8 Feb, 2020
Stallion 3D analysis of Uber Elevate eCRM-100 model

Being the best aerodynamics engineer requires meticulous planning and execution.  Here are 5 steps you can following to start your journey to being one of the best aerodynamicist.

1.  Airfoils analysis (VisualFoil) - the wing will not be better than the airfoil. Start with the best airfoil for the design.

2.  Wing analysis (3Dfoil) - know the benefits/limits of taper, geometric & aerodynamic twist, dihedral angles, sweep, induced drag and aspect ratio.

3. Stability analysis (3Dfoil) - longitudinal & lateral static & dynamic stability analysis.  If the airplane is not stable, it might not fly (well).

4. High Lift (MultiElement Airfoils) - airfoil arrangements can do wonders for takeoff, climb, cruise and landing.

5. Analyze the whole arrangement (Stallion 3D) - this is the best information you will get until you flight test the design.

About Hanley Innovations
Hanley Innovations is a pioneer in developing user friendly and accurate software the is accessible to engineers, designs and students.  For more information, please visit >

► Accurate Aerodynamics with Stallion 3D
  17 Aug, 2019

Stallion 3D is an extremely versatile tool for 3D aerodynamics simulations.  The software solves the 3D compressible Navier-Stokes equations using novel algorithms for grid generation, flow solutions and turbulence modeling. 

The proprietary grid generation and immersed boundary methods find objects arbitrarily placed in the flow field and then automatically place an accurate grid around them without user intervention. 

Stallion 3D algorithms are fine tuned to analyze invisid flow with minimal losses. The above figure shows the surface pressure of the BD-5 aircraft (obtained OpenVSP hangar) using the compressible Euler algorithm.

Stallion 3D solves the Reynolds Averaged Navier-Stokes (RANS) equations using a proprietary implementation of the k-epsilon turbulence model in conjunction with an accurate wall function approach.

Stallion 3D can be used to solve problems in aerodynamics about complex geometries in subsonic, transonic and supersonic flows.  The software computes and displays the lift, drag and moments for complex geometries in the STL file format.  Actuator disc (up to 100) can be added to simulate prop wash for propeller and VTOL/eVTOL aircraft analysis.

Stallion 3D is a versatile and easy-to-use software package for aerodynamic analysis.  It can be used for computing performance and stability (both static and dynamic) of aerial vehicles including drones, eVTOLs aircraft, light airplane and dragons (above graphics via Thingiverse).

More information about Stallion 3D can be found at:

► Hanley Innovations Upgrades Stallion 3D to Version 5.0
  18 Jul, 2017
The CAD for the King Air was obtained from Thingiverse

Stallion 3D is a 3D aerodynamics analysis software package developed by Dr. Patrick Hanley of Hanley Innovations in Ocala, FL. Starting with only the STL file, Stallion 3D is an all-in-one digital tool that rapidly validate conceptual and preliminary aerodynamic designs of aircraft, UAVs, hydrofoil and road vehicles.

  Version 5.0 has the following features:
  • Built-in automatic grid generation
  • Built-in 3D compressible Euler Solver for fast aerodynamics analysis.
  • Built-in 3D laminar Navier-Stokes solver
  • Built-in 3D Reynolds Averaged Navier-Stokes (RANS) solver
  • Multi-core flow solver processing on your Windows laptop or desktop using OpenMP
  • Inputs STL files for processing
  • Built-in wing/hydrofoil geometry creation tool
  • Enables stability derivative computation using quasi-steady rigid body rotation
  • Up to 100 actuator disc (RANS solver only) for simulating jets and prop wash
  • Reports the lift, drag and moment coefficients
  • Reports the lift, drag and moment magnitudes
  • Plots surface pressure, velocity, Mach number and temperatures
  • Produces 2-d plots of Cp and other quantities along constant coordinates line along the structure
The introductory price of Stallion 3D 5.0 is $3,495 for the yearly subscription or $8,000.  The software is also available in Lab and Class Packages.

 For more information, please visit or call us at (352) 261-3376.
► Airfoil Digitizer
  18 Jun, 2017

Airfoil Digitizer is a software package for extracting airfoil data files from images. The software accepts images in the jpg, gif, bmp, png and tiff formats. Airfoil data can be exported as AutoCAD DXF files (line entities), UIUC airfoil database format and Hanley Innovations VisualFoil Format.

The following tutorial show how to use Airfoil Digitizer to obtain hard to find airfoil ordinates from pictures.

More information about the software can be found at the following url:

Thanks for reading.

CFD and others... top

► A Benchmark for Scale Resolving Simulation with Curved Walls
  28 Jun, 2021

Multiple international workshops on high-order CFD methods (e.g., 1, 2, 3, 4, 5) have demonstrated the advantage of high-order methods for scale-resolving simulation such as large eddy simulation (LES) and direct numerical simulation (DNS). The most popular benchmark from the workshops has been the Taylor-Green (TG) vortex case. I believe the following reasons contributed to its popularity:

  • Simple geometry and boundary conditions;
  • Simple and smooth initial condition;
  • Effective indicator for resolution of disparate space/time scales in a turbulent flow.

Using this case, we are able to assess the relative efficiency of high-order schemes over a 2nd order one with the 3-stage SSP Runge-Kutta algorithm for time integration. The 3rd order FR/CPR scheme turns out to be 55 times faster than the 2nd order scheme to achieve a similar resolution. The results will be presented in the upcoming 2021 AIAA Aviation Forum.

Unfortunately the TG vortex case cannot assess turbulence-wall interactions. To overcome this deficiency, we recommend the well-known Taylor-Couette (TC) flow, as shown in Figure 1.


Figure 1. Schematic of the Taylor-Couette flow (r_i/r_o = 1/2)

The problem has a simple geometry and boundary conditions. The Reynolds number (Re) is based on the gap width and the inner wall velocity. When Re is low (~10), the problem has a steady laminar solution, which can be used to verify the order of accuracy for high-order mesh implementations. We choose Re = 4000, at which the flow is turbulent. In addition, we mimic the TG vortex by designing a smooth initial condition, and also employing enstrophy as the resolution indicator. Enstrophy is the integrated vorticity magnitude squared, which has been an excellent resolution indicator for the TG vortex. Through a p-refinement study, we are able to establish the DNS resolution. The DNS data can be used to evaluate the performance of LES methods and tools. 


Figure 2. Enstrophy histories in a p-refinement study

A movie showing the transition from a regular laminar flow to a turbulent one is posted here. One can clearly see vortex generation, stretching, tilting, breakdown in the transition process. Details of the benchmark problem has been published in Advances in Aerodynamics.
► The Darkest Hour Before Dawn
    2 Jan, 2021

Happy 2021!

The year of 2020 will be remembered in history more than the year of 1918, when the last great pandemic hit the globe. As we speak, daily new cases in the US are on the order of 200,000, while the daily death toll oscillates around 3,000. According to many infectious disease experts, the darkest days may still be to come. In the next three months, we all need to do our very best by wearing a mask, practicing social distancing and washing our hands. We are also seeing a glimmer of hope with several recently approved COVID vaccines.

2020 will be remembered more for what Trump tried and is still trying to do, to overturn the results of a fair election. His accusations of wide-spread election fraud were proven wrong in Georgia and Wisconsin through multiple hand recounts. If there was any truth to the accusations, the paper recounts would have uncovered the fraud because computer hackers or software cannot change paper votes.

Trump's dictatorial habits were there for the world to see in the last four years. Given another 4-year term, he might just turn a democracy into a Trump dictatorship. That's precisely why so many voted in the middle of a pandemic. Biden won the popular vote by over 7 million, and won the electoral college in a landslide. Many churchgoers support Trump because they dislike Democrats' stances on abortion, LGBT rights, et al. However, if a Trump dictatorship becomes reality, religious freedom may not exist any more in the US. 

Is the darkest day going to be January 6th, 2021, when Trump will make a last-ditch effort to overturn the election results in the Electoral College certification process? Everybody knows it is futile, but it will give Trump another opportunity to extort money from his supporters.   

But, the dawn will always come. Biden will be the president on January 20, 2021, and the pandemic will be over, perhaps as soon as 2021.

The future of CFD is, however, as bright as ever. On the front of large eddy simulation (LES), high-order methods and GPU computing are making LES more efficient and affordable. See a recent story from GE.

the darkest hour is just before dawn...

► Facts, Myths and Alternative Facts at an Important Juncture
  21 Jun, 2020
We live in an extraordinary time in modern human history. A global pandemic did the unthinkable to billions of people: a nearly total lock-down for months.  Like many universities in the world, KU closed its doors to students since early March of 2020, and all courses were offered online.

Millions watched in horror when George Floyd was murdered, and when a 75 year old man was shoved to the ground and started bleeding from the back of his skull...

Meanwhile, Trump and his allies routinely ignore facts, fabricate alternative facts, and advocate often-debunked conspiracy theories to push his agenda. The political system designed by the founding fathers is assaulted from all directions. The rule of law and the free press are attacked on a daily basis. One often wonders how we managed to get to this point, and if the political system can survive the constant sabotage...It appears the struggle between facts, myths and alternative facts hangs in the balance.

In any scientific discipline, conclusions are drawn, and decisions are made based on verifiable facts. Of course, we are humans, and honest mistakes can be made. There are others, who push alternative facts or misinformation with ulterior motives. Unfortunately, mistaken conclusions and wrong beliefs are sometimes followed widely and become accepted myths. Fortunately, we can always use verifiable scientific facts to debunk them.

There have been many myths in CFD, and quite a few have been rebutted. Some have continued to persist. I'd like to refute several in this blog. I understand some of the topics can be very controversial, but I welcome fact-based debate.

Myth No. 1 - My LES/DNS solution has no numerical dissipation because a central-difference scheme is used.

A central finite difference scheme is indeed free of numerical dissipation in space. However, the time integration scheme inevitably introduces both numerical dissipation and dispersion. Since DNS/LES is unsteady in nature, the solution is not free of numerical dissipation.  

Myth No. 2 - You should use non-dissipative schemes in LES/DNS because upwind schemes have too much numerical dissipation.

It sounds reasonable, but far from being true. We all agree that fully upwind schemes (the stencil shown in Figure 1) are bad. Upwind-biased schemes, on the other hand, are not necessarily bad at all. In fact, in a numerical test with the Burgers equation [1], the upwind biased scheme performed better than the central difference scheme because of its smaller dispersion error. In addition, the numerical dissipation in the upwind-biased scheme makes the simulation more robust since under-resolved high-frequency waves are naturally damped.   

Figure 1. Various discretization stencils for the red point
The Riemann solver used in the DG/FR/CPR scheme also introduces a small amount of dissipation. However, because of its small dispersion error, it out-performs the central difference and upwind-biased schemes. This study shows that both dissipation and dispersion characteristics are equally important. Higher order schemes clearly perform better than a low order non-dissipative central difference scheme.  

Myth No. 3 - Smagorisky model is a physics based sub-grid-scale (SGS) model.

There have been numerous studies based on experimental or DNS data, which show that the SGS stress produced with the Smagorisky model does not correlate with the true SGS stress. The role of the model is then to add numerical dissipation to stablize the simulations. The model coefficient is usually determined by matching a certain turbulent energy spectrum. The fact suggests that the model is purely numerical in nature, but calibrated for certain numerical schemes using a particular turbulent energy spectrum. This calibration is not universal because many simulations produced worse results with the model.

► What Happens When You Run a LES on a RANS Mesh?
  27 Dec, 2019

Surely, you will get garbage because there is no way your LES will have any chance of resolving the turbulent boundary layer. As a result, your skin friction will be way off. Therefore, your drag and lift will be a total disaster.

To actually demonstrate this point of view, we recently embarked upon a numerical experiment to run an implicit large eddy simulation (ILES) of the NASA CRM high-lift configuration from the 3rd AIAA High-Lift Prediction Workshop. The flow conditions are: Mach = 0.2, Reynolds number = 3.26 million based on the mean aerodynamic chord, and the angle of attack = 16 degrees.

A quadratic (Q2) mesh was generated by Dr. Steve Karman of Pointwise, and is shown in Figure 1.

 Figure 1. Quadratic mesh for the NASA CRM high-lift configuration (generated by Pointwise)

The mesh has roughly 2.2 million mixed elements, and is highly clustered near the wall with an average equivalent y+ value smaller than one. A p-refinement study was conducted to assess the mesh sensitivity using our high-order LES tool based on the FR/CPR method, hpMusic. Simulations were performed with solution polynomial degrees of p = 1, 2 and 3, corresponding to 2nd, 3rd and 4th orders in accuracy respectively. No wall-model was used. Needless to say, the higher order simulations captured finer turbulence scales, as shown in Figure 2, which displays the iso-surfaces of the Q-criteria colored by the Mach number.    

p = 1

p = 2

p = 3
Figure 2. Iso-surfaces of the Q-criteria colored by the Mach number

Clearly the flow is mostly laminar on the pressure side, and transitional/turbulent on the suction side of the main wing and the flap. Although the p = 1 simulation captured the least scales, it still correctly identified the laminar and turbulent regions. 

The drag and lift coefficients from the present p-refinement study are compared with experimental data from NASA in Table I. Although the 2nd order results (p = 1) are quite different than those of higher orders, the 3rd and 4th order results are very close, demonstrating very good p-convergence in both the lift and drag coefficients. The lift agrees better with experimental data than the drag, bearing in mind that the experiment has wind tunnel wall effects, and other small instruments which are not present in the computational model. 

Table I. Comparison of lift and drag coefficients with experimental data

p = 1
p = 2
p = 3

This exercise seems to contradict the common sense logic stated in the beginning of this blog. So what happened? The answer is that in this high-lift configuration, the dominant force is due to pressure, rather than friction. In fact, 98.65% of the drag and 99.98% of the lift are due to the pressure force. For such flow problems, running a LES on a RANS mesh (with sufficient accuracy) may produce reasonable predictions in drag and lift. More studies are needed to draw any definite conclusion. We would like to hear from you if you have done something similar.

This study will be presented in the forthcoming AIAA SciTech conference, to be held on January 6th to 10th, 2020 in Orlando, Florida. 

► Not All Numerical Methods are Born Equal for LES
  15 Dec, 2018
Large eddy simulations (LES) are notoriously expensive for high Reynolds number problems because of the disparate length and time scales in the turbulent flow. Recent high-order CFD workshops have demonstrated the accuracy/efficiency advantage of high-order methods for LES.

The ideal numerical method for implicit LES (with no sub-grid scale models) should have very low dissipation AND dispersion errors over the resolvable range of wave numbers, but dissipative for non-resolvable high wave numbers. In this way, the simulation will resolve a wide turbulent spectrum, while damping out the non-resolvable small eddies to prevent energy pile-up, which can drive the simulation divergent.

We want to emphasize the equal importance of both numerical dissipation and dispersion, which can be generated from both the space and time discretizations. It is well-known that standard central finite difference (FD) schemes and energy-preserving schemes have no numerical dissipation in space. However, numerical dissipation can still be introduced by time integration, e.g., explicit Runge-Kutta schemes.     

We recently analysed and compared several 6th-order spatial schemes for LES: the standard central FD, the upwind-biased FD, the filtered compact difference (FCD), and the discontinuous Galerkin (DG) schemes, with the same time integration approach (an Runge-Kutta scheme) and the same time step.  The FCD schemes have an 8th order filter with two different filtering coefficients, 0.49 (weak) and 0.40 (strong). We first show the results for the linear wave equation with 36 degrees-of-freedom (DOFs) in Figure 1.  The initial condition is a Gaussian-profile and a periodic boundary condition was used. The profile traversed the domain 200 times to highlight the difference.

Figure 1. Comparison of the Gaussian profiles for the DG, FD, and CD schemes

Note that the DG scheme gave the best performance, followed closely by the two FCD schemes, then the upwind-biased FD scheme, and finally the central FD scheme. The large dispersion error from the central FD scheme caused it to miss the peak, and also generate large errors elsewhere.

Finally simulation results with the viscous Burgers' equation are shown in Figure 2, which compares the energy spectrum computed with various schemes against that of the direct numerical simulation (DNS). 

Figure 2. Comparison of the energy spectrum

Note again that the worst performance is delivered by the central FD scheme with a significant high-wave number energy pile-up. Although the FCD scheme with the weak filter resolved the widest spectrum, the pile-up at high-wave numbers may cause robustness issues. Therefore, the best performers are the DG scheme and the FCD scheme with the strong filter. It is obvious that the upwind-biased FD scheme out-performed the central FD scheme since it resolved the same range of wave numbers without the energy pile-up. 

► Are High-Order CFD Solvers Ready for Industrial LES?
    1 Jan, 2018
The potential of high-order methods (order > 2nd) is higher accuracy at lower cost than low order methods (1st or 2nd order). This potential has been conclusively demonstrated for benchmark scale-resolving simulations (such as large eddy simulation, or LES) by multiple international workshops on high-order CFD methods.

For industrial LES, in addition to accuracy and efficiency, there are several other important factors to consider:

  • Ability to handle complex geometries, and ease of mesh generation
  • Robustness for a wide variety of flow problems
  • Scalability on supercomputers
For general-purpose industry applications, methods capable of handling unstructured meshes are preferred because of the ease in mesh generation, and load balancing on parallel architectures. DG and related methods such as SD and FR/CPR have received much attention because of their geometric flexibility and scalability. They have matured to become quite robust for a wide range of applications. 

Our own research effort has led to the development of a high-order solver based on the FR/CPR method called hpMusic. We recently performed a benchmark LES comparison between hpMusic and a leading commercial solver, on the same family of hybrid meshes at a transonic condition with a Reynolds number more than 1M. The 3rd order hpMusic simulation has 9.6M degrees of freedom (DOFs), and costs about 1/3 the CPU time of the 2nd order simulation, which has 28.7M DOFs, using the commercial solver. Furthermore, the 3rd order simulation is much more accurate as shown in Figure 1. It is estimated that hpMusic would be an order magnitude faster to achieve a similar accuracy. This study will be presented at AIAA's SciTech 2018 conference next week.

(a) hpMusic 3rd Order, 9.6M DOFs
(b) Commercial Solver, 2nd Order, 28.7M DOFs
Figure 1. Comparison of Q-criterion and Schlieren  

I certainly believe high-order solvers are ready for industrial LES. In fact, the commercial version of our high-order solver, hoMusic (pronounced hi-o-music), is announced by hoCFD LLC (disclaimer: I am the company founder). Give it a try for your problems, and you may be surprised. Academic and trial uses are completely free. Just visit to download the solver. A GUI has been developed to simplify problem setup. Your thoughts and comments are highly welcome.

Happy 2018!     

AirShaper top

► Electrict Aviation - The Byfly Seaplane
  26 Apr, 2022
We are designing a versatile all-electric amphibious aircraft to transport people and goods. The amphibious aircraft concept we are developing is a flying boat type and it uses a hull-based fuselage to meet the hydrodynamic requirements for the aircraft to take-off and land on the water bodies. Operation from land airports is achieved through the retractable landing gear system onboard the aircraft.
► Helping teams understand the aero of a Trans-Am TA2 Mustang
  19 Apr, 2022
TFB Performance used RapidScan and AirShaper to understand and optimise the aerodynamics of the Trans-Am TA2 racecar for its customers
► The technology behind the Sōr wheel
  12 Apr, 2022
The Sōr wheel is a revolutionary new type of wheel that has been designed to automatically adapt its shape according to the riding conditions. This avoids the instability and buffeting issues which are common with other aero wheel designs.
► Our guide to the best Aerodynamic resources
    3 Mar, 2022
There are so many resources now available to develop your aerodynamic skills and knowledge, we decided to pick the best aerodynamic resources and list them in this helpful guide.
► EV Range - The Race For Aerodynamic Efficiency
    2 Feb, 2022
The case for streamlined cars isn't new - for decades, mankind has searched for higher top speeds, especially in racing.
► Accelerating the aerodynamic design process
  25 Jan, 2022
Whether it is a virtual or physical wind tunnel, newly emerging technologies are speeding up the design process at a fraction of the regular cost.

Convergent Science Blog top

  13 Apr, 2022

Jameil Kolliyil

Engineer, Documentation

Wind energy has emerged as one of the major types of renewable energy sources in recent times. In the United States alone, the past decade has seen a 15% growth per year in wind power capacity, making wind energy the largest source of renewable power in the U.S.1 And as the market for wind energy grows, wind turbines and farms are subsequently becoming larger (some of these wind turbines are over 100 meters tall!). With such large turbine structures, in addition to wake effects from other wind turbines, the effect of the atmospheric boundary layer (or ABL, which is the lowest part of the atmosphere directly influenced by the earth’s surface) also becomes significant. The turbulence in the ABL can affect the efficiency and lifetime of wind farms, and the wake flows from the farms can alter the structure of the ABL. So when designing and optimizing large wind farms, you have to consider the complex interaction between the farm and the ABL. 

So the all-important question is whether computational fluid dynamics can help you design better wind farms. Can it? Well, the short answer is yes, but the biggest hurdle to performing full-scale CFD simulations becomes immediately apparent: the massive disparity in length and time scales. In a comprehensive simulation of such systems, you will have length scales ranging from millimeters, corresponding to the thickness of the boundary layer on the turbine rotor, to tens of kilometers, corresponding to the size of a wind farm. Simulations of this magnitude would be expensive and resource-intensive, to put it mildly. The industry has therefore turned to actuator models. These models replace the rotor blade with lines (actuator line model) or discs (actuator disc model) that impose body forces corresponding to blade loading on the flow field. Meanwhile, a three-dimensional Navier-Stokes solver is used to simulate the flow field. This circumvents the need for a fine mesh around the rotor blade while maintaining adequate refinement to capture turbulence and wake characteristics. Developed in 2002 by Sorensen and Shen2, the actuator line model (ALM) has gained popularity in recent years and has been extensively used in wind turbine simulations. The main challenges in developing ALM involve determining the relative velocity at each discrete point on the actuator line and deciding how to project the aerodynamic forces back onto the flow field. State-of-the-art ALM codes use an interpolation method (where velocity is interpolated from nearby fluid points to AL points) or an integral method (where a force projection weighted velocity integral is used to retrieve the free upwind velocity) for calculating the relative velocity. A Gaussian function is used for projecting the aerodynamic forces onto the fluid flow.

At Convergent Science, we’re constantly pushing the envelope and looking to improve existing models. Dr. Shengbai Xie (Principle Research Engineer at Convergent Science) published a research paper in which he employed alternate velocity-sampling and force projection functions. Instead of interpolating velocity from nearby fluid points, Dr. Xie’s approach used a Lagrangian-averaged velocity sampling technique. Instead of a Gaussian force projection function, he used a piecewise function3. He implemented these modifications in CONVERGE CFD software and simulated a 5MW NREL (National Renewable Energy Laboratory) reference wind turbine4. Figure 1 shows steady-state rotor power and torque predictions from other ALM implementations, Dr. Xie’s approach, and reference curve from Jonkman et al., 20094

Figure 1: Steady-state responses of (A) rotor power and (B) rotor torque as a function of wind speed for CONVERGE’s novel Lagrangian technique versus conventional approaches.

As you can see in Figure 1, Dr. Xie’s novel approach produces a better match to the reference curve when compared to the interpolation and integral methods. Dr. Alessandro Bianchini’s Wind Section group at the University of Florence has already employed this new approach to simulate a DTU 10 MW reference wind turbine; Figure 2 shows an animation from their work. You can find more information about the new approach and detailed comparisons with other ALM implementations in Dr. Xie’s research paper here

Figure 2: Simulation of a DTU 10 MW reference wind turbine with Q-criterion isosurface to visualize vortices. Animation credit: Wind Section, REASE group, University of Florence.

CONVERGE’s trademark autonomous meshing, Adaptive Mesh Refinement (AMR), and smooth handling of moving geometries make it uniquely suitable for simulating wind turbines. Check out our wind turbine webpage to see how CONVERGE can bolster your wind turbine simulations! 


[1] Wind Energy Technologies Office, “Advantages and Challenges of Wind Energy”,, accessed on Aug 10, 2021.

[2] Sorensen, J. N., Shen, W. Z., “Numerical modelling of wind turbine wakes,” J. Fluids Eng., 124, 393-399, 2002. DOI: 10.1115/1.1471361

[3] Xie, S., “An actuator-line model with Langrangian-averaged velocity sampling and piecewise projection for wind turbine simulations,” Wind Energy, 1-12, 2021. DOI: 10.1002/we.2619

[4] Jonkman, J., Butterfield, S., Musial, W., Scott, G., “Definition of a 5-MW reference wind turbine for offshore system development,” NREL, 2009,

► Urea Deposits: Risk Assessment or Direct Prediction?
  29 Mar, 2022

Scott Drennan

Director of Aftertreatment Applications

Pengze Yang

Senior Research Engineer

Prevention of solid deposit formation in urea/Selective Catalytic Reduction (SCR) aftertreatment systems is a primary concern for design engineers. There are significant resource and reputation costs associated with urea deposits if they arise in the field. It is imperative that aftertreatment system designers evaluate and mitigate the potential for urea deposit formation.

Though we colloquially refer to “urea deposits”, the actual deposit species are byproducts of urea decomposition. Within a narrow temperature range, ammelide and cyanuric acid (CYA) form hard crystalline deposits of considerable size on the walls of the exhaust system. These crystalline structures are exceedingly difficult to remove once they form, and the deposits decompose only at very high temperatures. Computational fluid dynamics (CFD) tools can provide valuable design information to mitigate urea deposit formation if the tool is both accurate and fast enough to meet tight design schedules.

Urea deposits form over a long period of operation. Some deposits are not even visible for up to five minutes of operation time, and many experiments consider runs of more than one hour. Running CFD for one hour of simulated time is not currently feasible. However, we can get closer to a fully developed film prediction and steady formation rate of deposits with a few minutes of simulation time. Unfortunately, even simulating several minutes with traditional CFD approaches is unacceptably expensive in a production environment, perhaps taking many weeks. Of course, an overnight run would be best, but a valuable result would be worth a few days of wall-clock time. How do we speed things up? How do we ensure that our result will be a valuable one? CONVERGE offers two key answers to those questions.

First Principles: Urea Decomposition Chemistry

A urea-water solution (UWS), also called Diesel Exhaust Fluid (DEF), is injected upstream of the SCR catalyst as a feedstock for the ammonia needed to reduce NOx. At exhaust gas temperatures, after the solvent water evaporates, the urea thermally decomposes into ammonia (NH3) and isocyanic acid (HNCO), as seen on the left side of Figure 1. The HNCO then hydrolyzes into ammonia and water, either before the SCR or inside of it. The most common method of modeling urea decomposition is to treat the urea, after the evaporation of water, as a molten solid that decomposes into gaseous ammonia and HNCO1. This decomposition happens in both droplets and films.

Figure 1: Detailed urea kinetics reaction diagram2.

Unfortunately, urea films at temperatures from 130°C to 165°C can form crystalline deposits that require very high temperatures to remove. Deposit removal is accomplished through decomposition, as shown in the right side of Figure 1. Biuret is formed first, which then converts into CYA and ammelide. These latter species require temperatures as high as 360°C to decompose.

Challenges of Urea Deposit Risk Assessment

Traditionally, deposit formation has not been simulated directly due to long simulation times and the lack of accurate deposit kinetics that we mentioned earlier. Many aftertreatment system modelers use a CFD approach that focuses on assessing the risk of urea deposit formation based on film temperatures and other local film conditions. Urea deposit risk models are highly empirical, requiring extensive tuning of key urea film parameters such as temperature, shear, etc. The payoff: after investing significant time in tuning the parameters, users can predict which walls are at risk for deposit formation. There is no information provided on the growth rate, shape, or composition of the deposit, or on other key parameters designers need to know. At Convergent Science, we invested in integrating an accurate detailed decomposition mechanism for urea into CONVERGE, then worked to accelerate simulation speeds to make direct prediction of urea deposits possible at reasonable runtimes.

CONVERGE’s detailed decomposition mechanism for urea was originally developed by our partners at IFP Energies nouvelles. Prior validation work by IFPEN has shown the urea mechanism to be accurate in several fundamental validation cases (e.g., heated decomposition, or single drop and spray ammonia conversion2).

CONVERGE’s detailed urea decomposition model has been used successfully to determine where deposits will form on a commercial validation case for a medium-duty diesel engine with Isuzu-Americas, shown in Figure 23. Isuzu had a wide range of experimental data on deposits, and CONVERGE was used to determine which of the cases formed deposits of the crystalline species biuret, ammelide, and CYA. Isuzu was able to determine the composition of the deposits, with the ratio of CYA to ammelide being an important parameter. These experimental results for ratio of CYA to ammelide in the deposit are well predicted by the CONVERGE detailed decomposition simulation for the location of the sample.

Now that we have a fully-coupled modeling capability with accurate deposit chemistry, spray-wall interactions, and conjugate heat transfer for accurate metal and film temperatures, it’s time to speed things up to address the long runtimes needed in deposit simulations.

Figure 2: Isuzu-Americas medium-duty diesel engine urea deposit location and chemical analysis match CONVERGE urea detailed decomposition prediction for ratio of cyanuric acid to ammelide3.

Speedup: Fixed Flow Advantages

We can harness our understanding of typical urea/SCR systems to optimize our solution strategy and provide a dramatic simulation speedup. The DEF injection duration is relatively short compared to the pulse frequency, and the spray momentum flux is very small compared to the gas momentum flux. Therefore, the gas flow is relatively consistent in between the spray pulses. CONVERGE has implemented what we call a fixed flow solver approach to take advantage of this quasi-steady-state behavior. This technique exploits the disparity in time scales, solving the full spray and Navier-Stokes equations only during the spray pulse. The flow state is then fixed for the interval between sprays. Simulations for urea/SCR applications are sped up many times with fixed flow, achieving up to 30 seconds per day on a typical commercial aftertreatment system (e.g., approximately 2 million cells on 96 processors).

Such an achievement in speedup must be properly validated to determine the effects on accuracy. The most common validation case to demonstrate accuracy in urea spray, splash, film heat transfer and evaporation, and metal temperature prediction is the Birkhold filming spray-wall validation case4. This case has a pulsed urea/water spray impinging on a thin flat metal plate, with hot air flowing above and below the plate. A thermocouple is located at the leading edge of the film pool. Successful validation of this case requires prediction of the initial slope of the temperature drop during dry cooling, capturing the temperature when films begin to form with a rapid temperature drop, and the final temperature as the film becomes fully developed. The CONVERGE fixed flow results for the Birkhold filming case are shown on the left side of Figure 3, and we see good agreement on all three key behaviors5. Note that achieving this accuracy requires some initial tuning of the Kuhnke splash model constant. However, once tuned, the same model constants produced accurate results for the Birkhold non-filming cases.

Figure 3: Fixed flow results for Birkhold spray-wall interactions. Results for the filming case on left and non-filming cases on right5.

Putting it Together: Speed and Accurate Deposit Chemistry

Detailed decomposition of urea in CFD offers the promise of moving from empirical predictions of risk to actual predictions of deposit formation through detailed chemistry. CONVERGE’s detailed decomposition model for urea has been validated against fundamental urea validation cases2,6 and in commercial cases3.

A recent validation of CONVERGE’s urea deposit prediction ability was conducted with some experimental data from Prof. Deutschmann at Karlsruhe University7. In this experiment, three different exhaust gas temperatures and DEF spray conditions were operated for many minutes (see Figure 4). The available experimental data in this study include the outer wall temperature of the exhaust pipe, the shape of the deposit, and the chemical composition of the deposit. Unfortunately, no information was available on the mass of the deposit formed.

Figure 4: Urea deposit experimental layout, operating conditions, and deposit composition7 compared to CONVERGE simulation8.

The CONVERGE deposit simulations included fixed flow for speed and the accurate spray-wall interaction, conjugate heat transfer with super-cycling, and the decomposition of urea mechanism for accuracy of wall film temperature and deposit chemistry. The simulations predicted the outer wall temperature quite well, including the location and shape of the wall film (see Figure 5). The predictions of the crystalline deposit species also matched quite nicely with the experiment. CONVERGE achieved 30 seconds of simulation time per day for this nearly 2 million-cell model when coupled with the fixed flow approach.

Figure 5: Comparison of outer wall temperature at the location of the deposit (experiment on left and CONVERGE results on right).

The next step in urea deposit predictions is to achieve deposit growth estimates based on accurate deposit species growth rates in a fully-developed urea film. The growth rates of species such as biuret, ammelide, and CYA must be calculated at their exact location, allowing prediction of the shape, size, and weight of the deposit. This deposit growth projection capability must predict the mass, location, and speciation of deposits over many minutes or hours in duration. Many commercial customers are now using CONVERGE to conduct urea deposit predictions and for comparison to their experimental data.

Figure 6: Urea deposit growth projections based on the species growth rates predicted by CONVERGE.

It is important that the urea decomposition model be fully coupled with the spray, film, gas, and metal models to obtain the accurate film conditions that are required to correctly predict the chemical kinetics. The main drawback of this full coupling had been the computational cost associated with the film kinetic calculation.


CONVERGE’s detailed decomposition model is now delivering the same simulation speed as the lower-fidelity molten-solid model and urea deposit risk approach. The detailed decomposition model is a direct and fully coupled calculation of the deposit species of interest (i.e., CYA, ammelide, and biuret). Therefore, it is a more fundamental approach, requiring little or no tuning for accurate predictions of urea deposits. The urea deposit risk model was once the state of the art, and it delivered value to design engineers, but we now have something better that is just as fast. Why just assess risk when you can know when, where, and what kind of deposits are formed?


[1] Quan, S., Wang, M., Drennan, S., Strodtbeck, J., and Dahale, A., “A Molten Solid Approach for Simulating Urea-Water Solution Droplet Depletion,” ILASS Americas 27th Annual Conference on Liquid Atomization and Spray Systems, Raleigh, NC, United States, May 17–20, 2015.

[2] Habchi, C., Quan, S., Drennan, S.A., and Bohbot, J., “Towards Quantitative Prediction of Urea Thermo-Hydrolysis and Deposits Formation in Exhaust Selective Catalytic Reduction (SCR) Systems,” SAE Paper 2019-01-0992, 2019. DOI: 10.4271/2019-01-0992

[3] Sun, Y., Sharma, S., Vernham, B., Shibata, K., and Drennan, S., “Urea Deposit Predictions on a Practical Mid/Heavy Duty Vehicle After Treatment System,” SAE Paper 2018-01-0960, 2018. DOI: 10.4271/2018-01-0960

[4] Birkhold, F., Meingast, U., Wassermann, P., and Deutschmann, O., “Modeling and Simulation of the Injection of Urea-Water-Solution for Automotive SCR DeNOx-Systems,” Applied Catalysis B: Environmental, 70, 119-127, 2007. DOI: 10.1016/j.apcatb.2005.12.035

[5] Maciejewski, D., Sukheswalla, P., Wang, C., Drennan, S.A., and Chai, X., “Accelerating Accurate Urea/SCR Film Temperature Simulations to Time-Scales Needed for Urea Deposit Predictions,” SAE Paper 2019-01-0982, 2019. DOI: 10.4271/2019-01-0982

[6] Ebrahimian, V., Nicolle, A., and Habchi, C., “Detailed Modeling of the Evaporation and Thermal Decomposition of Urea-Water Solution in SCR Systems,” AIChE Journal, 58(7), 1998-2009, 2011. DOI: 10.1002/aic.12736

[7] Brack, W., Heine, B., Birkhold, F., Kruse, M., and Deutschmann, O., “Formation of Urea-Based Deposits in an Exhaust System: Numerical Predictions and Experimental Observations on a Hot Gas Test Bench,” Emission Control Science and Technology, 2, 115-123, 2016. DOI: 10.1007/s40825-016-0042-2

[8] Yang, P. and Drennan, S., “Predictions of Urea Deposit Formation With CFD Using Autonomous Meshing and Detailed Urea Decomposition,” SAE Paper 2021-01-0590, 2021. DOI: 10.4271/2021-01-0590

► 2021: Making Waves with CONVERGE
  30 Dec, 2021

2021 was a complicated year. The second full year of the pandemic offered reasons for hope and optimism, along with times of hardship and uncertainty. I sincerely hope that this next year is a turning point in the pandemic and that we see significant improvement around the world.

Despite the continuing pandemic, there have been exciting developments and opportunities for Convergent Science this past year. We are releasing CONVERGE 3.1, a major version of our software that includes many new features and enhancements. We strengthened relationships with our partners and collaborators, and forged new ones with universities around the world through our CONVERGE Academic Program. We were honored to receive several awards, and we have pushed further into new market segments and application areas. All the while, we have continued to strive to improve CONVERGE in a way that best meets your simulation needs and to provide our customers with the best possible support.

CONVERGE 3.1 Release

Offshore wind turbine simulated using CONVERGE’s implicit FSI approach and mooring model.

We’re pleased to be releasing a new major version of our software: CONVERGE 3.1. During development of this version, we focused on expanding CONVERGE’s physical modeling capabilities, improving user experience, and simplifying the workflow for advanced simulations. We added several new volume of fluid (VOF) modeling approaches for multi-phase flows that reduce numerical diffusion at fluid interfaces and enable you to simulate the separation of phases or immiscible liquids under the influence of gravity. CONVERGE 3.1 also offers implicit fluid-structure interaction (FSI) modeling, which increases the stability of the solver when simulating floating objects or simulating fluids and solids with similar densities. To complement this capability, CONVERGE 3.1 contains tools to generate realistic wind and wave fields. This set of features opens the door to many offshore and marine applications, such as floating offshore wind turbines and boat or ship hulls.

CONVERGE 3.1’s multi-stream simulation capability allows you to apply different solver settings and physical models to different regions of the domain. Using the multi-stream approach, you can model complex, multi-physics problems in a single simulation, which offers a simpler workflow than running multiple independent simulations. Another workflow enhancer in 3.1 is the ability to couple CONVERGE with ParaView Catalyst to perform in situ post-processing of your simulation results. You’ll find many other enhancements in CONVERGE 3.1, including moving inlaid meshes, the capability to simulate solid particles, and more flexibility for wall motion. We’re very excited about this new release, and we think it will greatly benefit users across many application areas.

Award-Winning Collaborations

At Convergent Science, we’re dedicated to creating innovative tools and methods that industry can leverage to accelerate the development of cutting-edge technology. We couldn’t achieve this goal without the invaluable collaborations we have with world-class institutions and companies. This year, several of our collaborative projects were recognized for their merit and contributions to the research community and society at large.

TCF Award

This summer, Convergent Science and Argonne National Laboratory were awarded funding through the U.S. Department of Energy’s 2021 Technology Commercialization Fund (TCF) to continue developing a deep learning framework called ChemNODE, which accelerates detailed chemistry CFD simulations for reacting flows. The goal of ChemNODE is to enable engineers to use detailed mechanisms that, compared to skeletal mechanisms, provide more predictive results for combustion simulations, without incurring such a large computational expense. 

HPCwire Awards

In the fall, Convergent Science received two 2021 HPCwire Awards. 

With Aramco Research Center – Detroit and Argonne National Laboratory, we received the 2021 Editors’ Choice Award for Best Use of HPC in Industry. We were recognized for our work using high-performance computing and CONVERGE simulations to evaluate engine cold-start operations, during which the majority of emissions are formed in modern vehicles. We achieved a 26% improvement in combustion efficiency at cold conditions for a heavy-duty engine.

The second HPCwire Award we received was for a collaborative project with Argonne National Laboratory and Parallel Works. Together, we have been developing an automated machine learning-genetic algorithm (ML-GA) approach to accelerate design optimization and virtual prototyping. We coupled ML-GA with CONVERGE to perform a design optimization of a gasoline compression ignition engine and found that this approach sped up the process by ten times compared to the industry standard.

Convergent Science Partner Updates

Another key way we are able to deliver top-notch products to our customers is through our partnerships. In 2021, we strengthened our partnership with Tecplot as we work to provide a seamless simulation workflow from pre- to post-processing. Tecplot for CONVERGE is included with a CONVERGE license, and now users have the convenient option to buy a full Tecplot 360 license directly from our Convergent Science sales team. 

This year we also introduced GT-CONVERGE, a specialized version of CONVERGE that is fully integrated into GT-SUITE. GT-CONVERGE replaced our previous GT-SUITE product, CONVERGE Lite, and offers many more features and greater functionality, including conjugate heat transfer, a steady-state solver, automatic export of 3D visualization slices, enhanced wall models, and much more. 

Computational Chemistry Consortium

Another collaborative effort, the Computational Chemistry Consortium (C3) concluded Phase 1 of operations in 2021, culminating in the public release of C3MechV3.3. C3Mech is a new detailed kinetic model for surrogate fuels consisting of 3,761 species and 16,522 reactions. It contains chemistry for small species such as hydrogen, syngas, natural gas, and methanol; important surrogate fuel components for gasoline, diesel, and jet fuel; and NOx and PAHs. The mechanism represents the first time that the combustion community has developed and validated a mechanism combining small, intermediate, and large species in a self-consistent, comprehensive, and hierarchical way. C3Mech will help facilitate the study of low-carbon, carbon-neutral, and carbon-free fuels, which are going to play a critical role in the decarbonization of industry. If you’re interested in checking out the mechanism, it will soon be available to download on the C3 website.

CONVERGE Academic Program

At Convergent Science, we have always been strong believers in the importance of training the next generation of engineers, and we greatly value our relationships with universities and other academic institutions. Now, we have dedicated personnel to help cultivate these relationships. Our goal with the CONVERGE Academic Program is to make it easier for students around the world to access our software and to better support them throughout their academic journey. 

This year, we also launched the CONVERGE Academic Competition, a simulation competition for students around the world. We’re challenging participants to design and execute a novel CONVERGE simulation that doesn’t just look nice, but also accurately captures the relevant physics of their system. We’re looking forward to seeing the creative simulations the competitors come up with, and we’re excited to showcase their work when the winners are announced next summer!

2021 Global CONVERGE User Conference

This year we held the first-ever global edition of our CONVERGE User Conference, with the goal of exposing attendees to research they might not otherwise come across. To accommodate attendees in different time zones, we hosted each of the four presentation sessions twice. In addition, we offered attendees the option to watch the presentations on-demand, and we also unveiled on-demand CONVERGE training. Each day of the conference, our support engineers hosted office hours so attendees could meet one-on-one with a CONVERGE expert to get answers to any questions they had. The event was a great success, with more than 400 attendees from six continents and nearly 30 countries. While we hope future user conferences can once again take place in person, we were thrilled to be able to host this virtual global event.

On-Demand CONVERGE Training

As I mentioned above, we introduced a new resource for CONVERGE users at our fall conference: on-demand training. Both introductory and advanced training courses are available on the Convergent Science Hub, and we’ll keep adding and updating courses as we go. We hope this convenient option helps you get up and running with CONVERGE on your own schedule—and our Support team is always available if you have questions. We’ll continue to offer live training throughout the year as well, virtually at the beginning of 2022 and hopefully (!) in person later in the year. 

Convergent Science Around the Globe

The primary mission of Convergent Science is twofold: (1) help current clients run the best CFD simulations possible, and (2) discover other industries that can benefit from CONVERGE’s unique combination of features. Our offices around the world are dedicated to fulfilling both parts of this mission.

In Europe, we’ve had a great year for bringing on new clients in a variety of industries, who plan to use CONVERGE for a broad array of applications: oil and gas, hydrogen injectors and engines, vacuum pumps, compressors and engines for refrigeration applications, fuel cells, marine technology, construction and agricultural engines, redesigning racing engines as motorsports move to renewable fuels, and more. We attended a wide variety of conferences, both virtually and in person, that covered topics ranging from tunnel safety to space propulsion to compressors. Our European team grew, and we expanded our office space to accommodate more growth in the future.

This year, our India branch celebrated its four-year anniversary. Our team in India continued to grow, gaining seven new employees in 2021. The team is busy exploring how to most effectively apply CONVERGE to applications such as motor cooling, battery thermal runaway, flexible fuel engines, pumps, and more. In addition, the India office is working to bridge the gap between industry and academia by helping students gain exposure to simulation software.

In the United States, our world headquarters in Madison, Wisconsin continued to thrive, with more than a dozen new hires this year. We’re continuing to branch out into exciting application areas including hydrogen, aerospace, batteries, biomedical applications, and renewable energy. With our dedicated university relations team, we strengthened our relationships with existing academic users and forged many new relationships as well. In 2021, we gained more than 180 new academic users in North and South America across 36 different labs and 14 universities. 

Our partners at IDAJ continue to provide excellent support to CONVERGE users in China, Korea, and Japan. Major areas of focus for IDAJ include hydrogen engines and non-engine applications such as rotating machinery, battery burning, and spray painting. They hosted their popular IDAJ Conference Online 2021, which garnered over 2,800 attendees. In addition, we worked with IDAJ to port CONVERGE on Fugaku, the world’s fastest supercomputer. IDAJ demonstrated CONVERGE on Fugaku by running high-fidelity combustion simulations using large eddy simulations (LES) and detailed chemistry. 

A Look Forward

Despite the ongoing challenges of the pandemic, 2021 has been a successful year, and we’re looking forward to new opportunities in 2022. While virtual events have been a great way to connect during the pandemic, they just aren’t the same as seeing your colleagues face-to-face. We hope to be able to hold our next user conference in person and to attend more in-person tradeshows in the new year. We’re also looking forward to our next CONVERGE release—we have many great features under development, and we can’t wait to share them with you. We’re excited to continue to delve into new application areas and to strengthen our collaborations and partnerships. Above all, we look forward to helping you run novel simulations and providing you with the tools you need to create next-generation technology.

► Efficient and accurate modeling of heat transfer in an engine head and block
    4 Nov, 2021

The extreme conditions in internal combustion (IC) engines make it important to understand the thermal and structural stresses experienced by critical components of the device. In the cylinder, studying the temperature distribution and the thermal stresses caused by combustion is essential to determine the durability of the engine. For such conjugate heat transfer (CHT) problems, where the heat transfer occurs simultaneously within and between the fluid and solid regions, CONVERGE offers a novel time control approach to accelerate the simulations without decreasing accuracy: super-cycling.

In super-cycling, CONVERGE alternates between two solution methods. First, CONVERGE runs a fully-coupled fluid-solid transient solver to convergence. Then, CONVERGE uses the solution of that solver to update the boundary conditions for a steady-state solid-only simulation. The solid-only results feed back new boundary condition information to the transient solver. This alternating process repeats until the global simulation is complete. Super-cycling also makes it possible to map heat transfer results from one cylinder to all the other cylinders in the geometry, obviating the need to model combustion in all cylinders and further accelerating the simulation.

Here, we’ll briefly look at a study demonstrating how CONVERGE can accurately predict the temperature distribution in the engine head and block. For more details, please see our white paper on the topic.

In this study, the geometry is half of a V6 engine, including the engine head and block. We solve the case by two different approaches which are described below.

Option 1: Engine block and combustion gas—water jacket

Because of the different time-scales of combustion and heat transfer in the engine’s solid components compared to heat transfer in the coolant, CONVERGE’s methodology involves running two separate simulations and mapping results between the two in an iterative process to obtain converged temperature predictions. This procedure allows for optimal settings for both the coolant and the chamber simulations to enhance the overall simulation accuracy and speed.

In this option, the first simulation is of the coolant flow and the heat transfer between the coolant and the solid materials of the engine head. The second simulation is a CHT simulation that models the combustion process and heat transfer between the combustion chamber and the engine block and head. Figure 1(a) shows the engine coolant system, and Figure 1(b) shows the geometry for the combustion simulation.

Figure 1(a): Geometry for the coolant flow simulation.
Figure 1(b): Geometry for the combustion simulation.

Option 2: Engine block and water jacket—combustion

The second approach also iterates between two simulations. To efficiently determine the requisite solid temperature field, we first perform simulations to model combustion in the engine cylinder. These simulations may take longer to run. We then perform a CHT simulation to model heat transfer between the coolant and the solid material.

Figure 2(a): Normalized surface temperature distribution for the coolant passages.
Figure 2(b): Normalized surface temperature distribution for the combustion side.


The results from both of the iterative approaches were in good agreement with experimental data. The normalized surface temperature distribution results are shown in Figure 2. These approaches combine the accurate and detailed simulation of combustion kinetics with CHT to develop a realistic temperature distribution in the solid components of an engine. With CONVERGE, engineers can efficiently include the details of gas flow, combustion, and coolant flow to predict the temperature field for optimal design of solid engine components without the additional complexity of building a mesh. To learn more, please check out our CHT white paper!

► Concurrent Perturbation Method: A Timesaving Alternative to Capture Cycle-to-Cycle Variability
    8 Oct, 2021

Significant cycle-to-cycle variations (CCV) in internal combustion (IC) engines can lead to undesirable effects like noise and vibration, engine damage, and poor drivability. It is important for engineers to estimate quantities such as peak cylinder pressure, combustion duration, and coefficient of variance of indicated mean effective pressure (IMEP) to design better engines. Moderating CCV can open doors to many advanced combustion concepts, such as low-temperature combustion strategies, to reduce emissions and increase efficiency. 

To accurately estimate CCV, you need to perform many engine cycle simulations—on the order of 100 consecutive cycles. Typically, simulating one engine cycle that follows our recommended best practices in CONVERGE takes a few hours with sufficient computational resources. Continuing that simulation for 100 consecutive cycles is a painstaking process (on the order of a few months) and hence a computationally expensive one.

Is there an alternate method to capture CCV?

The answer is yes! We know that long runtimes are unacceptable for many industry research timelines, and so we have applied an alternate method, called the concurrent perturbation method (CPM), to capture CCV in CONVERGE. This method was first proposed and published by Ameen et al. (2016)1 at Argonne National Laboratory.

What is the concurrent perturbation method?

Instead of solving 100 cycles consecutively, with CPM, CONVERGE solves 100 cycles concurrently. Given sufficient computational resources, CPM reduces the overall turnaround time to the time taken to simulate one engine cycle. At this point, you might be asking yourself how it is possible to run the cycles concurrently when the result of one cycle can be determined only after knowing the results of the cycle preceding it. 

Figure 1: Workflow for CPM.

This is where the perturbation in CPM comes into play. We start by simulating one or more engine cycles to wash out the homogenized initial conditions that are defined while setting up the case. The combustion event and exhaust process of the first cycle(s) produces a representative velocity, pressure, temperature, and species field. The outcome of the initial cycle(s) is used to initialize each of the concurrent cycles, which are set up as independent cases. Each individual cycle’s flow field is then perturbed in order to yield a distinct cycle as the simulation proceeds (Figure 1). We apply only a miniscule perturbation to each flow field so as to not significantly change it. The perturbation is simply a noise field applied on top of the velocity field. The solution naturally develops into a different realization due to the chaotic nature of the combustion system. 

What do the results show?

Figure 2 shows a comparison of the cylinder pressure obtained from consecutively and concurrently run simulations performed by Probst et al. (2020).2 The results are similar, and the predicted pressure lies within the maximum and the minimum pressure cycle of the measured data.

Additionally, Probst et al. found that starting the concurrent cycle simulations at intake valve opening (IVO) is sufficient to yield distinct and valid cycles. In contrast, when running cycles consecutively, it is necessary to simulate the full cycle. The required core hours for concurrently run cycles, as a result, are fewer than for consecutively run cycles. So, by concurrently running cases, multiple engine cycles can be completed in far less wall-clock time and with fewer core-hours compared to consecutive simulations.

Figure 2: CCV obtained from a consecutively run simulation (left) versus CCV obtained from a concurrently run simulation (right) for the same case.

Are you ready to try CPM to speed up your projects? Check out the video below to learn how CPM works, how to set up CPM in CONVERGE, and the conditions in which it will work best. 


[1] Ameen, M., Yang, X., Kuo, T., and Som, S., “Parallel methodology to capture cyclic variability in motored engines”, International Journal of Engine Research, 18(4), 366-377, 2016. DOI: 10.1177/1468087416662544

[2] Probst, D., Wijeyakulasuriya, S., Pomraning, E., Kodavasal, J., Scarcelli, R., and Som, S., “Predicting Cycle-to-Cycle Variation With Concurrent Cycles In A Gasoline Direct Injected Engine With Large Eddy Simulations”, Journal of Energy Resources Technology, 142(4), 2020. DOI: 10.1115/1.4044766

► In Memoriam: Remembering Tarique Shaikh, Our Colleague and Friend
  13 Sep, 2021

Tarique Shaikh joined Convergent Science in March 2018, after earning his master’s degree from the Technical University of Munich Asia. In his three and a half years with us, Tarique made a significant and lasting impact on both the company and his coworkers. Ashish Joshi, general manager of Convergent Science India, grew to know Tarique well on a professional and a personal level:

“Tarique joined Convergent Science as an applications engineer in our India office to support customers in a variety of industries. He worked on several interesting simulations, including one of flow over an entire city. This was a new application for Convergent Science, and his work in this area was greatly appreciated. Tarique, however, didn’t want to be a ‘Jack of all trades’, but instead a ‘master of one’. It was then that I recommended him for the Gas Turbine Applications team.”

The Gas Turbine Applications team at Convergent Science studies key issues related to the safety, operability, and environmental impact of aviation engines. The team simulates phenomena including lean blow-off, a scenario in which an airplane engine goes out; high altitude relight, which investigates how to relight an engine that goes out mid-flight; and methods for reducing harmful emissions from gas turbine engines. As the leader of the Gas Turbine Applications team, Scott Drennan worked closely with Tarique:

“Tarique worked in the Gas Turbine Applications group for a little over three years. In that time, Tarique developed a deep understanding of gas turbine combustion and became a valued member of the team. Specifically, he handled the creation of marketing materials to demonstrate CONVERGE’s capabilities for hydrogen combustion in gas turbines. He developed a simulation of fuel switchover from methane to hydrogen in a gas turbine combustor. In addition, he generated comparison videos of lean blow-off (LBO) for methane and hydrogen, demonstrating CONVERGE’s ability to use the SAGE detailed chemistry solver to simulate a dynamic (changing) operating condition. Tarique also developed a microturbine ignition marketing animation and helped on ignition modeling with a commercial customer. Tarique was a key contributor in a recent commercial evaluation with an aviation engine manufacturer using a combination of high-fidelity models for turbulence, heat transfer, combustion, and emissions in CONVERGE, and comparing the results to experimental wall temperature and emissions data for NOx, CO, and soot. Recently, Tarique was working on validation of our Thickened Flame Model (TFM) in a commercial combustor and testing CONVERGE’s hybrid turbulence model on wall cooling validation cases. 

Tarique was a thoughtful, smart, hardworking engineer and a key contributor to the Gas Turbine Applications team. He will be greatly missed.”

Tarique’s legacy at Convergent Science extends far beyond his technical contributions. He was a kind and caring person, with whom his colleagues greatly enjoyed working. Many of his coworkers from the Convergent Science India office and the Gas Turbine team wished to provide their thoughts and reflections on knowing and working with Tarique:

“I remember one time when the Convergent Science owners asked me who my favorite colleague from the India team was. It was very difficult to give just one name, but Tarique was definitely one of my favorites. We would discuss many topics apart from work: food, religion, politics, and fitness, just to name a few. One thing we bonded over was our love for biryani.”

Ashish Joshi, General Manager, India office

“While pursuing my master’s degree, Tarique and I spent a lot of time together since we both belonged to the Aerodynamics and Fluid Mechanics lab at the Technical University of Munich (TUM). We were both from the Indian subcontinent, so we were hardly prepared for the European winters. During those harsh winter days in Munich, Tarique used to invite a few of us to his place for delicious dinners, which he prepared with such fervor. Cooking for friends and family was one of the things that Tarique dearly loved. As international students, a lot of us struggled with cooking, but Tarique tried to motivate us to cook. Whenever we felt homesick, he was always there to cook some of the most delicious meals I had during my student days. Those memories with Tarique are something I will cherish all my life. We will miss you, Tarique.”

Harshan Arumugam, Business Development Manager, India office

“Tarique had a great love for food. Whenever we traveled together, he wanted to have a scrumptious meal; I really enjoyed seeing his joy for food. During our visit to the IIT Madras Gas Turbine Conference, he twice had me run to the nearby store to get cans of coke so he could have them with his five-course meal.”

Abhishek Sinha, Sr. Business Development Manager, India office

“Tarique was a very friendly person who was always willing to offer help. He was good at technical discussions and meticulous at his work. In one of our first interactions, we bonded over the fact that he was originally from Sawantwadi, a place close to where I’m from.”

Viraj Shirodkar, Research Engineer, Software Development, India office

“Tarique was a cleanliness freak. I remember when I visited his house for the first time, no one would believe that it was a bachelor’s home. He proudly showed us the different kinds of vacuum cleaners he used to clean his house. On my first day in the office, he was annoyed when I mistakenly took his chair and removed its plastic cover. Everyone joked that Tarique would be very angry. Little did I know that he was a sweetheart and took everything as a good sport. I’m glad we crossed each others’ paths in life.”

Apurva Bhagat, Research Engineer, Software Development, India office

“Tarique made a courageous decision when he voluntarily switched to the Gas Turbine team, because I believe this to be one of the most challenging applications of CFD. Needless to say, in only a short time, he turned out to be one of the most valuable members of the team. One of his qualities that I admired the most was that whenever we discussed a problem, he was never hesitant to take out a pen and a piece of paper and immerse himself in analytical equations.

If there is one word that can describe Tarique, it is no doubt ‘caring’. If anyone around him was in need of any kind of help, be it professional or personal, you could always count on him to be the first one to offer help. On more occasions than I can remember, he offered me rides, especially when I had a leg procedure and had difficulty walking. His nurturing nature was further evident from his ardent love for plants, of which he had a great collection at home. I have always taken inspiration from him and hope to be able to integrate these qualities of his into my life.”

Geet Nautiyal, Research Engineer, QA, India office

“It is very difficult to write about Tarique in the past tense, but time doesn’t care for feelings and emotions. Tarique—the name itself is a treasure trove of memories. When I joined Convergent Science India back in 2018, it was Tarique who trained me on CONVERGE Studio and the solver. Tarique helped me a lot in setting up a fixed inlaid mesh for a rectangular bluff body for turbulence validation in 2019. Our last work-related interaction was when he helped correct the heat transfer validation slides. 

Tarique and I shared a passion for general knowledge and current affairs, which led to many funny conversations. Our company trek to the Singahad fort was an epic one, in which Tarique set off quickly ahead of us, but ended up last to 900m. I used to call him ‘Gibraltar’, which is the Spanish version of the Arabic name Jabel al Tarique (Rock of Tarique). Tarique, my friend, why so early?”

Akshay Iyer, Research Engineer, Validation, India office

“Tarique was a valuable member of our India team. Although we did not have the pleasure of interacting with him as much as some in the company, his contributions did not go unnoticed. He was a hardworking engineer who tackled some of the most challenging problems with our software. During our first Indian CONVERGE User Conference in Bengaluru, Tarique was tasked with providing a demo of our software to a large audience of CFD enthusiasts. This was a critical part of introducing many Indian engineers to CONVERGE, and Tarique did a wonderful job. He will be missed.”

Dan Lee, Eric Pomraning, Keith Richards, Kelly Senecal, and Rainer Rothbauer, Convergent Science Owners, U.S. and Europe offices

“Tarique was an invaluable member of the Convergent Science family and the Gas Turbine team. Over the last year and a half, we had grown to be more than just colleagues—we had become good friends. He was kind, amicable, and easy to talk to. I never got to meet Tarique in person, but we worked closely every day. He has left a lasting impression through his dedication, hard work, and team spirit. He approached his work with determination and diligence, and he was a quick learner who had a huge appetite for knowledge. He was always eager to pick up tasks that needed research and reading. He was a true team player who always put the goals of the team first, and he was always very accommodating and helpful. Scheduling meetings between India and the U.S. offices is always a challenge due to the time difference. I was humbled that Tarique always insisted I choose a time convenient for me because I had a small child at home. The work he did as part of the Gas Turbine team helped immensely in the support and evaluation efforts of gas turbine customers and in the continuous improvement of the CONVERGE solver and graphical user interface. Some of his work, like the microturbine and annular combustor example cases, will be used by the team for years to come. Tarique will be greatly missed.”

Gaurav Kumar, Principal Engineer, U.S. office

“Working from the U.S., I was never able to meet Tarique in person, instead working closely with him via Zoom meetings, phone calls, etc. Even through these somewhat impersonal media, it was clear that Tarique was a thoroughly kind, trustworthy, and caring person and a sharp engineer to boot. If I ever needed to dive deep into a challenging problem or diagnose a tricky issue, Tarique was the first person I turned to. He approached his work with diligence, determination, positivity, and attention to detail, and I learned a lot from watching him attack problems without ever giving up. On days when our shared projects weren’t going the best, we would often meet well past midnight U.S. time. These interactions were always lighter, and we would joke our way through to finding a solution to whatever was stumping us. I will miss him.”

Gabe Jacobsohn, Research Engineer, U.S. office

Tarique touched many of our lives during his time at Convergent Science, and he will continue to have a presence at our company. Tarique’s father donated his collection of CFD books to Convergent Science, which we are using to make a small memorial library at our India office. In addition, Tarique had a penchant for gardening and a love for plants, and one of his plants will now brighten our India office’s reception area. We are grateful for the opportunity to keep Tarique’s memory alive with these donations. We will miss him greatly.

Numerical Simulations using FLOW-3D top

► Dr. Tony Hirt, Founder of Flow Science, Inc. Receives the John Campbell Award
  11 May, 2022

Santa Fe, NM, May 11, 2022 — Flow Science, Inc. founder Dr. C.W. “Tony” Hirt was awarded the prestigious John Campbell Medal at the Institute of Cast Metals Engineers award ceremony on March 25, 2022, in London. Dr. Hirt received the award for his unique, long-lasting contributions to the science and practice of metal casting through his development of the CFD software FLOW-3D and its casting-specific version, FLOW-3D CAST.

Dr. John Campbell presented the award to Dr. Hirt, “In gratitude for making significant, really significant benefit to the foundry industry which we continue to enjoy to this day.” The award was accepted on behalf of Dr. Hirt by Flow Science’s Chief Technology Officer, Dr. Michael Barkhudarov.

The John Campbell Medal is awarded to an individual who has made a sustained contribution to the science and understanding of metal casting through research and development. Each year, the Institute writes to leading international castings research organizations and individuals, including Dr. John Campbell, the relevant Department Heads of the University of Birmingham and Mississippi State University, CAST-CSIRO, VDG and Cti, requesting nominations for an award shortlist.

Tony’s contribution to simulation is not only in developing useful modeling tools based on fundamental principles of physics but mentoring several generations of engineers that continue in his steps. The award is also welcome as a recognition that simulation tools have become an integral part of casting design and production as the industry matures and evolves, commented Dr. Michael Barkhudarov.

Dr. Hirt pioneered the Volume-of-Fluid (VOF) method while working at the Los Alamos National Lab. He went on to found Flow Science in 1980. FLOW-3D is a direct descendant of his development of the VOF method. This approach was expanded and perfected in FLOW-3D to the TruVOF technology, with cutting-edge and groundbreaking improvements in speed and accuracy in the simulation of flow with different liquid and gas interfaces. Today, Flow Science products offer complete multi-physic solutions with diverse modeling capabilities, including fluid-structure interaction, moving objects, and multiphase flows.

About Flow Science

Flow Science, Inc. is a privately held software company specializing in computational fluid dynamics software for industrial and scientific applications worldwide. Flow Science has distributors and technical support services for its FLOW-3D products in nations throughout the Americas, Europe, Asia, the Middle East, and Australasia. Flow Science is headquartered in Santa Fe, New Mexico.

Media Contact

Flow Science, Inc.

683 Harkle Rd.

Santa Fe, NM 87505

+1 505-982-0088

► Optimization of a Sand Casting with FLOW-3D CAST
  20 Apr, 2022

Optimization of a Sand Casting with FLOW-3D CAST

This blog was contributed by Malte Leonhard, Flow Science Deutschland.

The goal of a casting simulation is to predict casting defects and find the corrective measures to avoid such defects. To achieve this, the casting simulation must accurately predict the physical results. In this article, we illustrate a validation of FLOW-3D CAST by comparing simulation results with experimental findings. For this validation, we selected an aluminum casting with significant porosity defects. The extent of the porosities meant that the casting would not fulfill the functional specification and would be rejected.

Optimization of casting design and runner/riser system supported by simulation

In order to verify that FLOW-3D CAST can reliably predict such casting defects, the existing casting was simulated and the results compared with the real casting defects. This video shows that the FLOW-3D CAST defect analysis correctly reproduced the defects and their position.

The simulation results suggested that reversing the casting direction might be beneficial, so the casting part was rotated by 180° in the mold. Next, the runner and riser system were modified so that most of the risers were integrated into the runner (“hot risers”).

Additionally, design changes of the casting, which we will discuss later in the article, were introduced in order to achieve a directed solidification to the risers and to avoid porosities in the casting.

Finally, chills were applied in areas of large mass accumulations to reduce shrinkage defects.

A filling and solidification simulation showed that these measures significantly reduced the casting defects. These simulation results were again validated by X-rays. Near the “cold risers”, those not integrated into the runner system, not all defects could be avoided due to the risers’ insufficient size.

In the last version, the two cold risers were enlarged. Minor design changes of the casting were introduced to improve the directional solidification to the risers.

Compared to the original design, the casting quality was substantially improved and the amount of return scrap reduced. The use of chills improved the quality in critical areas within the casting. Overall, the casting process is now more efficient and cost-effective for the foundry.

Total sprue material 3,73 kg (-3,3 kg)
Pouring weight 8,93 kg (-3,19 kg)
Yield 58 % (+24%)
Chills 1,53 kg (+1,26 kg)

Design modifications of the casting

In many cases it is not sufficient to optimize the runner and riser system to achieve a sufficient casting quality. Instead, the design of the casting itself needs to be changed for the sake of “castability”.

The functional design of a casting often includes mass accumulations that prove problematic in the casting process. To achieve a high-quality microstructure, the wall thickness should always increase towards the risers according to the thermal modulus method.

To illustrate the effect of the casting design modifications, two geometry versions with identical runner and riser systems are compared. The adjustments are shown in the figure below. Several wall thicknesses and ribs between material accumulations have been enlarged.

For demonstration purposes, the two marked ribs will be examined. In both cases, porosities occur at the junctions, which is not acceptable.

By increasing the wall thicknesses of the ribs, the junctions are connected to the feeders adjacent to the casting edge and a directed solidification toward the risers is achieved.

The video shows large porosities in the initial version on the left side due to large hot spots within the casting where solidification-induced shrinkage creates a deficit.

In the optimized version on the right, the melt solidifies in the direction of the risers. This means that the deficit can be compensated by the riser and no porosity is created in the casting.

This validation shows a good correlation between reality and simulation in FLOW-3D CAST. The software is an effective tool for the development of castings, casting systems, feeder dimensions/shapes, and casting processes to ensure optimal quality and efficiency.

► Speakers Announced
  12 Apr, 2022

We are very pleased to announce the speakers for the FLOW-3D World Users Conference 2022! Users in industry and academia will present their work in metal casting, additive manufacturing, civil and environmental engineering, coastal structures, and maritime engineering. FLOW-3D engineers and associates will present on the latest features, upcoming developments, and future plans of FLOW-3D, and our esteemed keynote speaker Hubert Lang will share the 15-year history of FLOW-3D at BMW.

Company overview and future direction
Dr. Amir Isfahani, CEO, Flow Science

FLOW-3D 2022R2: New Features, advances in accuracy and performance 
Dr. Michael Barkhudarov, Chief Technology Officer, Flow Science

Keynote Address: 15 years of FLOW-3D at BMW – from a stand-alone application to an integral part of the development process
Hubert Lang, BMW  

FLOW-3D (x): Expand your simulation experience
Stefano Mascetti, Managing Director, XC Engineering

FLOW-3D AM: New features and planned developments
John Wendelbo, Director of Sales, Flow Science

Postprocessing capabilities with FLOW-3D POST 2022R1
John Wendelbo, Director of Sales, Flow Science

Numerical modeling of chromatography columns
Dr. Julien Bœuf, Roche Diagnostics GmbH

Controlling drop size and drop volume through pulse control
Kaushik Balasubramanian, Kaushiks International

Upcoming developments
Dr. Michael Barkhudarov, Chief Technology Officer, Flow Science

Numerical simulation of the casting manufacturing process of a press sleeve used within the press section of a paper machine
Dr. Marcus Britz, J.M. Voith SE & Co. KG

FLOW-3D used to model the solidification behavior of advanced non-ferrous metals
Nadira Surghani, Colorado School of Mines

Use of computational fluid dynamics in the design and comparison of metal casting running systems
C.A. Jones, Cranfield University

Computational fluid dynamics modelling of the dimensional stability of deposited layers in material extrusion additive manufacturing
Md Tusher Mollah, Technical University of Denmark

Cast metal structures improving heat flow in the energy storage systems
Natalia Raźny, Wroclaw University of Science and Technology

Rheological model for semi solid casting
Benjamin Bode, Project Engineering

Runner air entrapment removal: A case study
Dr. Arunvinay Prabakaran, Dietech India Pvt Ltd

A multi-physics CFD study on the part-to-part gap during remote laser welding of copper-to-steel battery tab connectors with beam wobbling
Giovanni Chianese, University of Naples Federico II and University of Warwick

Metal casting roundtable
Moderated by Dr. Michael Barkhudarov and Dr. Amir Isfahani, Flow Science and Dr. Matthias Todte, Flow Science Deutschland

Integrating FLOW-3D HYDRO into a modern 3D-planning workflow
Julien Barbier, FICHTNER Water & Transportation GmbH

FLOW-3D tailings model with hyperconcentrated, non-Newtonian fluid, Brazil case study
Dr. Matthias A. Haselbauer, Winderl Ingenieure and Rodrigo de Almeida L. Barbosa, POTAMOS

Evaluation of hydrodynamic forces on Tainter gates
Prashant Huddar P.E., HPD consultants

Using FLOW-3D for the operational optimization of the run-of-the-river HIDRALPOR’s hydroelectric power plants
Santiago Iopera, MINCIVIL

Intake capacity improvement at Douglas run-of-the-river hydropower plant
Pouyan Ahmadpanah, Innergex Renewable Energy

Numerical and experimental investigation of  streamlined fish-friendly fine screens
Dr. Serhat Kucukali, Hacettepe University

Effect of bed dimensions and flow conditions on the hydrodynamics of a step-pool fishway
Sruthi Thazhathe Kalathil and Venu Chandra, Indian Institute of Technology Madras

Numerical simulations of breaking wave loading on vertical seawalls using FLOW-3D HYDRO and validation
Ramtin Sabeti, Brunel University London

Analysis of the hydrodynamic behavior platform to support wind generators in deep water
Ignacio Berenguer Pérez, HIDTMA,S.L. and Ignacio Cobian Babé, BERIDI,S.L.

Reconstruction and extension of the Méricourt locks: study of the hydraulic operation of the structure
Gwenaël Chevallet, BRL Ingénierie

Numerical and experimental investigation of scour development caused by ship propeller
Cansu Özyaman, Ege University

Use of building and plant information modeling  for an optimized operation management in drinking water treatment
Randy Schäfer, IWW

Simulations for the sewer system of Doha
Dr. Boris Huber, Vienna University of Technology

Thermal plume studies – lessons learned
Jeroen Adema, Arcadis Netherlands

Aerated grit chamber analysis
Dr. Tomas Studnicka, AQUATIS a.s.

► FLOW-3D World Users Conference 2022
  29 Mar, 2022

We invite our customers from around the world to join us at the FLOW-3D World Users Conference 2022.The conference will be held on May 16-18, 2022 at the Maritim Hotel in Munich, Germany. Join engineers, researchers and scientists from some of the world’s most renowned companies and institutions to hone your simulation skills, explore new modeling approaches and learn about the latest software developments. The conference will feature application-specific tracks, advanced training sessions, in-depth technical presentations by our customers, and the latest product developments presented by Flow Science’s senior technical staff. The conference will be co-hosted by Flow Science Deutschland

Speakers Announced!

We are very pleased to announce the speakers for the FLOW-3D World Users Conference 2022! Users in industry and academia will present their work in metal casting, additive manufacturing, civil and environmental engineering, coastal structures, and maritime engineering. FLOW-3D engineers and associates will present on the latest features, upcoming developments, and future plans of FLOW-3D, and our esteemed keynote speaker Hubert Lang will share the 15-year history of FLOW-3D at BMW.

Keynote Speaker Announced! 15 years of FLOW-3D at BMW

Hubert Lang, BMW, Keynote Speaker
Hubert Lang, BMW, Keynote Speaker at the FLOW-3D World Users Conference 2022

We are extremely pleased to confirm that Hubert Lang of BMW will be the conference keynote speaker. Hubert studied Mechanical Engineering with a focus on automotive engineering at Landshut University of Applied Sciences. In 1998, he started in BMW’s Light Metal Foundry in Landshut, working in their tool design department, where he oversaw the development of casting tools for six-cylinder engines. In 2005, Hubert moved to the foundry’s simulation department, where he was introduced to FLOW-3D’s metal casting capabilities. Since then, he has led considerable expansion in the use of FLOW-3D, both in the volume of simulations as well as the number of application areas.

Today BMW uses FLOW-3D for sand casting, permanent mold gravity casting, low pressure die casting, high pressure die casting, and lost foam casting. FLOW-3D has also been applied to several special projects at BMW: supporting the development of an inorganic binder system for sand cores through the development of a core drying model, calculation of the heat input during coating of cylinder liners, the development of the casting geometry for the injector casting procedure, and the layout and dimensioning of cooling systems for casting tools. 

Social Events - Updated Tour & Reception Information!

Tour at BMW Classic

We are pleased to offer a guided tour of BMW Classic on Monday, May 16 as part of the conference offerings. There will be three, one-hour guided tours available to choose from, followed by a reception at the M1 Bistro at the BMW Museum. Conference attendees can meet in the lobby of the conference hotel to go together to BMW Classic or meet the group there. We will separate into tour groups at BMW Classic. Masks are required at the BMW Classic.

  • 17:30-18:30 (in English)
  • 17:45-18:45 (in English)
  • 18:00-19:00 (in German)

Reception at M1 Restaurant

The reception will take place at the M1 Bistro at the BMW Museum which is a 15 minute walk from BMW Classic. The reception will be held from 18:45-21:15 and will feature a Flying Dinner at 19:15.

Conference Dinner

The conference dinner will be held in the ever-popular Augustiner-Keller. All conference attendees and their guests are invited to join us on Tuesday, May 17 at 19:00 for a traditional German feast in a beautiful and famous beer garden. The conference dinner is a 15 minute walk from the conference hotel.

Directions from the Conference Hotel –> Augustinerkeller (English)

Directions from the Conference Hotel –> Augustinerkeller (German)

Conference Information

Important Dates

  • March 18, 2022: Abstracts Due
  • April 1, 2022: Abstracts Accepted
  • May 6, 2022: Presentations Due
  • May 16, 2022: Advanced Training Sessions
  • May 16, 2022: Tour of the BMW Museum
  • May 17, 2022: Conference Dinner

Registration Fees

  • Day 1 and 2 of the conference: 300 €
  • Day 1 of the conference: 200 €
  • Day 2 of the conference: 200 €
  • Guest Fee (social events only): 50 €
  • Training Sessions: 100 € each
  • BMW Tour: included with registration
  • Conference Dinner: included with registration

Advanced Training Sessions

Taught by senior technical staff and experts in their fields, advanced training sessions include Version Up seminars for FLOW-3D CAST, FLOW-3D AM, FLOW-3D HYDRO and FLOW-3D. The courses are scheduled so that everyone, regardless of their application, can participate in the FLOW-3D POST training session. You can sign up for these training sessions when you register online. All training sessions cost 100 €, and training fees are waived for presenters.

Time Saal Nürnberg Saal Ulm
13:00-14:00 FLOW-3D AM FLOW-3D
14:15-15:15 FLOW-3D CAST FLOW-3D HYDRO
15:15-15:45 Coffee Break Coffee Break
15:45-16:45 FLOW-3D POST

Presenter Information

Each presenter will have a 30 minute speaking slot, including Q & A. All presentations will be distributed to the conference attendees and on our website after the conference. A full paper is not required for this conference. Please contact us if you have any questions about presenting at the conference. Flow Science Deutschland will sponsor the Best Presentation Award.


Conference Hotel

There is no special conference code or rate at the Maritim. Please book with the hotel directly.

Maritim Hotel Munich
+49 (0) 89 55235-0
Goethestraße 7
80336 München

► Training Sessions at the FLOW-3D World Users Conference 2022
    7 Mar, 2022

Advanced Training Sessions

In conjunction with the FLOW-3D World Users Conference 2022, advanced training sessions will be held the afternoon of May 16, 2022 at the conference hotel. Taught by senior technical staff and experts in their fields, advanced training sessions include Version Up seminars for FLOW-3D CASTFLOW-3D AMFLOW-3D HYDRO and FLOW-3D as well as a FLOW-3D POST session focused on best practice workflows and commonly-asked support questions. The courses are scheduled so that everyone, regardless of their application, can participate in the FLOW-3D POST training session. All training sessions cost 100 €, and training fees are waived for presenters. You can sign up for multiple training sessions when you register online.

Saal Ulm

Version Up: FLOW-3D

Instructor: Marcin Serdeczny, CFD Engineer, Flow Science

The FLOW-3D training session will focus on the following advanced topics in fluid flow modeling: a new log-conformation tensor approach for the solution of visco-elastic fluid flows, advances in two-phase flow modeling, improvements to the VOF method using a new VOF-to-particle model, expanded Active Simulation Control using sampling volumes, non-Newtonian fluids with training on Herschel Bulkley fluids, and using 2D tables to characterize complex fluid properties, for example where the viscosity is a function of both temperature and strain rate.

Training Details

Date: Monday, May 16, 2022
Time: 13:00-14:00
Cost: 100 €

Saal Ulm

Saal Nürnberg

Version Up: FLOW-3D AM

Saal Nürnberg

Instructor: John Wendelbo, Director of Sales, Flow Science

This training session is geared towards FLOW-3D AM users as well as those interested in exploring the powerful capabilities of FLOW-3D AM for simulating additive manufacturing and laser welding processes. An overview of how to integrate FLOW-3D AM with FLOW-3D (x) and cloud-based HPC resources will showcase how batch simulations with different process parameters can be run in an automated manner with the goal of process optimization. Next, Python’s interoperability with FLOW-3D POST and FLOW-3D (x) is leveraged to extract simulation data to help build process maps for melt pool dimensions, temperature gradients and cooling rates. 

Training Details

Date: Monday, May 16, 2022
Time: 13:00-14:00
Cost: 100 €

Version Up: FLOW-3D HYDRO

Instructor: John Wendelbo, Director of Sales, Flow Science

The FLOW-3D HYDRO session covers four development topics: the new cutcell method, a simplified axial pump model, the new dissolved oxygen model, and 2D tables that are used to characterize complex fluid property dependencies. In addition, we will explore how FLOW-3D HYDRO and FLOW-3D POST can be integrated into the FLOW-3D (x) workflow for automated parameter studies, optimization and postprocessing.

Training Details

Date: Monday, May 16, 2022
Time: 14:15-15:15
Cost: 100 €

Saal Nürnberg

Version Up: FLOW-3D CAST

Instructor: Dr.-Ing. Dipl.-Phys. Matthias Todte, Flow Science Germany

This one-hour FLOW-3D CAST training course will begin with an introductory overview and a review of the new features and GUI design changes in FLOW-3D CAST v5.1. Through examples, new workspaces will be covered in detail, including Investment Casting, Continuous, Sand Core Making, Centrifugal as well as the new Exothermic Sleeve capabilities and database. We will also discuss the new chemistry-based solidification model available in FLOW-3D CAST v5.1.

Training Details

Date: Monday, May 16, 2022
Time: 14:15-15:15
Cost: 100 €

15:15-15:45: Coffee Break
Saal Ulm

Creating Optimal Workflows with FLOW-3D POST

This training session is intended for all users of FLOW-3D products, regardless of application.

Instructor: Marcin Serdeczny, CFD Engineer, Flow Science

Powered by the ParaView engine, FLOW-3D POST provides modelers with superior analysis capabilities within an intuitive postprocessing interface. Training will begin with a review of the workflow that users are encouraged to adopt for effective postprocessing. In the second part of the training, we will review and answer the most common support questions we have received since FLOW-3D POST was released in early 2021. The third part of the training will focus on implementing batch postprocessing in order to automate analysis and visualization workflow.

Training Details

Date: Monday, May 16, 2022
Time: 15:45-16:45
Cost: 100 €

► Senior Software Engineer
    4 Mar, 2022

We sponsor H1B visas. We are open to employees working remotely from CO, TX, AZ, OR, IL, MD, NC, SC, FL, or possibly others..

Flow Science is a software company based in Santa Fe, New Mexico USA, which develops and distributes the CFD (computational fluid dynamics) simulation software suite, FLOW-3D.  Founded in 1980 by one of the principals who pioneered the “Volume-of-Fluid” (or VOF) method while working at Los Alamos National Labs, Dr. C.W. (Tony) Hirt, FLOW-3D provides users the ability to model and visualize complex fluid flow problems, servicing users from commercial, academic and government domains all over the globe.  FLOW-3D is used in a variety of application areas; everything from water/environmental, to metal casting, aerospace, and additive manufacturing industries.  In the last few years, Flow Science has expanded its product line, creating application specific variants of FLOW-3D, aimed at providing each application area a more streamlined, tailored workflow for simulating problems specific to their industry.

The Role

We are looking for an experienced, knowledgeable, and versatile Senior Software Engineer to help drive the software development lifecycle of our FLOW-3D user interfaces using the latest object oriented techniques and best practices.

Successful Candidates Will:

  • Be quick to learn and excited about learning, as well as teaching, new software methods, technologies, and ideas
  • Be passionate about keeping up to date with software best practices and code quality
  • Be a strong advocate for software craftsmanship and take pride in your work
  • Thrive in environments with minimal guidance
  • Take initiative to help improve software development processes
  • Enjoy collaborating across teams with excellent communication


  • Participates and contributes to the design, implementation and maintenance of new elements in our FLOW-3D user interfaces and supporting applications
  • With minimal oversight beyond high level direction, utilize expertise to problem solve given limited information
  • Help ensure all designs are implemented as safely and as robustly as possible and adhere to proper software engineering guidelines and practices
  • Actively participate in identifying inefficiencies in the software development process and work with team members to continuously improve these processes
  • Identify risks in code, features and designs; communicate risks appropriately and take necessary action
  • Focus on high priority tasks and assignments while simultaneously supporting the team to ensure overall success
  • Collaborate with support/sales team when necessary to help resolve customer issues/questions
  • Encourage, train, and mentor team members to help them grow and excel
  • Conduct code reviews

Desired Qualifications

  • Bachelor’s degree or higher in software engineering, computer engineering, or computer science
  • Deep understanding of modern C++ (including standards); object-oriented principles and design, especially design patterns (3+ years)
  • Strong ability to read and learn from existing code
  • Strong understanding of 3D Graphic libraries such as VTK, Vulkan, or OpenGL (2+ years)
  • Experience developing cross-platform applications, specifically on Windows and Linux (3+ years)
  • Experience employing systems, tools, standards, and procedures to drive performance
  • Extensive experience developing, deploying, and integrating software solutions, preferably in an Agile environment
  • Experience designing user interfaces (2+ years)
  • Strong understanding of CI/CD concepts and test-driven development
  • Outstanding interpersonal and communication skills


  • Experience with some of our tools and secondary languages: Qt framework, FORTRAN, Python, Bash scripting, CMake, Git, and JIRA
  • Experience with other CAE or visualization software


Flow Science offers an exceptional benefits package to full-time employees including medical, dental, vision insurances, life and disability insurances, 401(k) and profit-sharing plans with generous employer matching, and an incentive compensation plan that offers a year-end bonus opportunity up to 30% of base salary.

Apply for Senior Software Engineer

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Mentor Blog top

► News Article: Graphcore leverages multiple Mentor technologies for its massive, second-generation AI platform
  10 Nov, 2020

Graphcore has used a range of technologies from Mentor, a Siemens business, to successfully design and verify its latest M2000 platform based on the Graphcore Colossus™ GC200 Intelligence Processing Unit (IPU) processor.

► Technology Overview: Simcenter FLOEFD 2020.1 Package Creator Overview
  20 Jul, 2020

Simcenter™ FLOEFD™ software, a CAD-embedded computational fluid dynamics (CFD) tool is part of the Simcenter portfolio of simulation and test solutions that enables companies optimize designs and deliver innovations faster and with greater confidence. Simcenter FLOEFD helps engineers simulate fluid flow and thermal problems quickly and accurately within their preferred CAD environment including NX, Solid Edge, Creo or CATIA V5. With this release, Simcenter FLOEFD helps users create thermal models of electronics packages easily and quickly. Watch this short video to learn how.

► Technology Overview: Simcenter FLOEFD 2020.1 Electrical Element Overview
  20 Jul, 2020

Simcenter™ FLOEFD™ software, a CAD-embedded computational fluid dynamics (CFD) tool is part of the Simcenter portfolio of simulation and test solutions that enables companies optimize designs and deliver innovations faster and with greater confidence. Simcenter FLOEFD helps engineers simulate fluid flow and thermal problems quickly and accurately within their preferred CAD environment including NX, Solid Edge, Creo or CATIA V5. With this release, Simcenter FLOEFD allows users to add a component into a direct current (DC) electro-thermal calculation by the given component’s electrical resistance. The corresponding Joule heat is calculated and applied to the body as a heat source. Watch this short video to learn how.

► Technology Overview: Simcenter FLOEFD 2020.1 Battery Model Extraction Overview
  17 Jun, 2020

Simcenter™ FLOEFD™ software, a CAD-embedded computational fluid dynamics (CFD) tool is part of the Simcenter portfolio of simulation and test solutions that enables companies optimize designs and deliver innovations faster and with greater confidence. Simcenter FLOEFD helps engineers simulate fluid flow and thermal problems quickly and accurately within their preferred CAD environment including NX, Solid Edge, Creo or CATIA V5. With this release, the software features a new battery model extraction capability that can be used to extract the Equivalent Circuit Model (ECM) input parameters from experimental data. This enables you to get to the required input parameters faster and easier. Watch this short video to learn how.

► Technology Overview: Simcenter FLOEFD 2020.1 BCI-ROM and Thermal Netlist Overview
  17 Jun, 2020

Simcenter™ FLOEFD™ software, a CAD-embedded computational fluid dynamics (CFD) tool is part of the Simcenter portfolio of simulation and test solutions that enables companies optimize designs and deliver innovations faster and with greater confidence. Simcenter FLOEFD helps engineers simulate fluid flow and thermal problems quickly and accurately within their preferred CAD environment including NX, Solid Edge, Creo or CATIA V5. With this release, Simcenter FLOEFD allows users to create a compact Reduced Order Model (ROM) that solves at a faster rate, while still maintaining a high level of accuracy. Watch this short video to learn how.

► On-demand Web Seminar: Avoiding Aerospace Electronics Failures, thermal testing and simulation of high-power semiconductor components
  27 May, 2020

High semiconductor temperatures may lead to component degradation and ultimately failure. Proper semiconductor thermal management is key for design safety, reliability and mission critical applications.

Tecplot Blog top

► Plotting Transient Data with XY Line Plots and Exporting Animations
  26 May, 2022

This video will demonstrate time animation using the Probe to Create Time Series Plot tool as an example. We will create an XY line plot on top of a contour plot, link the frames by solution time, and provide time animation export recommendations.

Probe Over Time Plot

Starting with a simple 2D transient plot, our goal is to create a probe over time plot which will graph the data in a separate XY line frame.

First, select Tools > Probe to Create Time Series Plot, and click on the plot in a region of interest.

This creates an XY line plot on screen.

Second, select Frame>Frame Linking… and you can see that both frames are linked by solution time. If we un-toggle this option for either of the plots, they will not play concurrently. Leave these frames linked by solution time.

Notice also that the XY plot has a Solution Time x-axis marker. Turn this on and off in the plot with a macro command. See this example for how to use that macro. If you are interested in creating an XY line plot that will draw the line as time progresses, see this other macro file on our GitHub (.mcr) as an example.

Third, move the XY Line plot on top of the 2D contour plot. Give it a transparent background by double-clicking the edge of the Frame to bring up the Edit Active Frame dialog. Toggle off Show background.

In an earlier video, we demonstrated placing text annotations on the plot. Here, we input the current solution time dynamic text on the plot in scientific notation, and increase or decrease the precision.

Text annotations for time animation

Export Your Animation

Now we are ready to export an animation of our plot. In some cases, you may want to create an .mp4 animation file directly using the Tecplot 360 GUI. However, for large data sets, we recommend exporting a sequence of images (demonstrate on screen and make sure to click antialiasing). This option can be found in the time animation details dialog after clicking export to file, and selecting Export format:

Export Format for time animations

Exporting a sequence of high-quality images provides flexibility. It allows you to manually step through each image.

Additionally, using a tool such as ImageMagick or FFmpeg (executable shipped with Tecplot 360), you can create a variety of animations with different framerates, in formats like .mp4 or .gif. You can also take advantage of our GitHub script, to automate this process with Python.

If you want to export images more quickly, you can automate the process in parallel, see this parallel image creator script for more details.

This concludes this tutorial on working with transient data. Thank you for watching.

The post Plotting Transient Data with XY Line Plots and Exporting Animations appeared first on Tecplot.

► A Tight Cooperation Towards Ocean Sustainability
  18 May, 2022

At blueOASIS, Tecplot 360 is an essential tool for Making the World Green and the Oceans Blue. Either in the CFD simulation of offshore energy harvesting devices (wind, wave and current) and their impact on the maritime life; or other projects such as:

  • Analyzing naval vessels and alternative ship propulsion systems
  • Investigating ocean cleaning devices
  • Studying and optimizing offshore floating platforms for multiple purposes

All our Renewables and Ocean Sustainability projects generate large amounts of raw data which require an efficient, yet powerful tool to generate comprehensive, easy interpretable and fine-looking results. Our tool of choice is Tecplot 360.

blueOASIS - Figure 1

Figure 1. Maritime & Naval applications: validation of limiting streamlines vs experimental data for a model-scale KVLCC2 ship. Effect of turbulence modelling (reference).

The engineers at blueOASIS have gained 20 years of experience using both open-source and commercial visualization packages, and still use both types of tools. But one of the key advantages of Tecplot 360 is the simplicity and intuitive character of its graphical user interface (GUI), which enables new users to quickly start using it. Another feature that sets Tecplot 360 apart from other solutions is its scripting capabilities using the Python API. PyTecplot provides a platform for simple scripts that can be executed within the GUI or in batch, which harness the full functionality of the software in streamlining complex workflows, saving valuable time in projects.


Figure 2. Renewable Energy: simulation of a floating offshore wind platform. Surface grid, free-surface iso-surface and vorticity distribution at symmetry plane.

Obviously, Tecplot 360 also excels at data visualization; It provides control and flexibility over the resulting image, vector, or animation in a user-friendly manner. Multiple views of the same data are easily set-up using separate frames, which can be either independent or dependent from one another and are fully customizable. Another advantage of Tecplot 360 is having several visualization modes, including XY plots, which can be easily overlapped and even time-synchronized with regular 2D/3D views. These functionalities enable the creation of data-rich graphics, suitable for reports and presentations.

Renewable Energy Video: Simulation of a free-floating offshore wind platform. Geometry, free-surface iso-surface colored with x-velocity component. It includes platform attitude time history xy plots.

Tecplot 360 Simplifies Tedious Tasks

The crucial CFD-oriented operations embedded into Tecplot 360 are vital for our Renewables and Ocean Sustainability projects. Tasks that are tedious and unreliable in open-source tools are simplified and reliable in Tecplot 360. One example is the easy calculation and setup of surface limiting streamlines (or shear-stress lines). Because this is an important fluid mechanics feature to analyze flow patterns, recirculation and separation areas, and drive geometry optimization, it is just one of the many crucial features for any CFD practitioner. But there are more examples, such as one-button contour plots with colors and lines, tangent vectors in slices, arbitrary slice shape creation, volume streamlines control and accuracy, memory management, and more.


Figure 3. Maritime & Naval applications: simulation of a propelled appended ship including free-surface effects. Geometry, free-surface iso-surface, slice at symmetry place of the x-component of the velocity field and surface limiting streamlines.

Moreover, the easily accessible online tutorials and training sessions enable us to continuously learn more on how to fully take advantage of Tecplot 360’s functionalities. blueOASIS uses both open-source tools and Tecplot 360, which means we can combine the best features of both worlds. Currently, we are working on the coupling between Tecplot 360/PyTecplot and Blender, a popular high-level rendering open-source tool, to create (even) more realistic pictures and animations.


Figure 4. Current/tidal turbine: limiting streamlines and q-factor iso-surface showing the cells used.

All in all, Tecplot 360/PyTecplot is the preferred choice of blueOASIS’s for data treatment and visualization in Renewables and Ocean Sustainability projects, since it provides a complete and efficient sustainable solution on our quest to seek new solutions for old problems.

Blog submitted by:

  • Guilherme Beleza Vaz, R&D Manager/ CFD Developer
  • Tiago Gomes, Research/CFD Developer

Learn more about blueOASIS

Request a Free Trial of Tecplot 360

The post A Tight Cooperation Towards Ocean Sustainability appeared first on Tecplot.

► Key Frame Animation
  28 Apr, 2022

Key Frame Animations allow you to easily animate a smooth progression through two or more specified views (key frames) and export them as an animation. You can zoom, rotate, and translate in these animations. In addition, you can create “fly around” movies or first-person animations. The animation you see here explores a “fly-around” of air flowing through a duct.

Create a Key Frame Animation

  1. Select Animate > Key Frame Animation. Note that the Key Frame Animations can be used only in the 3D Cartesian plot type. Rotate and/or zoom the plot to the initial view for the animation and then select the [Append] button in the dialog. Change the name of the view (key frame) by selecting it (“View 1”) in the Key Frame box and editing the name in the View Name field.
  2. Rotate and/or zoom the plot to the next view you wish your animation to include and select the [Append] button to add that view to the end of the animation. Or you can select the [Insert] button to insert a view above the selected one in the list. These key frames are snapshots of the view in Tecplot 360, so limit the rotations to 180 degrees or less between key frames, or else the animation may not rotate as expected.
  3. Continue to rotate and/or zoom and select [Append] or [Insert] to add additional key frames to your animation. If you want to replace a saved key frame view with the current plot view, click the [Update] button.
  4. Because this is also a transient data set, you can animate the solution time concurrently with the key frames by selecting Options>Animate Time Concurrently. Time Animation Options lets you select from multiple time animation operations.
  5. When finished adding key frames, select [Animate All] to perform a complete animation of your views, or [Animate Selected] to animate only the views selected in the Key Frame box. Tecplot 360 will interpolate between the saved views to create an animation.

Export an Animation

To export an animation, change the Destination from “On Screen” to “To File”. Then select the [Animate All] or [Animate Selected] to open the Export Options dialog. We recommend exporting to MPEG-4 format as it offers a high quality to file-size ratio, and it can play-back on many media players.

Saving and Reloading a Key Frame Animation

Key Frames are not saved with the layout, so to save your key frame views, go to File > Save Animation File, to choose a location to save your *.keyframe.

To reopen your plot after restarting Tecplot 360, open your saved layout and then in the Key Frame Animation dialog, click File > Open Animation File and select the saved key frames.

The Key Frame Animation tool can also be helpful for users that want to save and return to multiple different views. Instead of creating an animation, you can simply append any important views you want of your layout and save them in a *.keyframe file. In the Key Frame dialog, to get back to a saved view, select the view and click [Apply]. This will snap the selected frame to your saved view.

Learn More

For more details, especially for concurrent time animation, check-out the documentation in the User’s Manual.

Thank you for watching!

Get a Free Trial of Tecplot 360

The post Key Frame Animation appeared first on Tecplot.

► Tecplot 360 and PyTecplot are like LEGOs
  12 Apr, 2022
Blog submitted by Scott Fowler,
Tecplot Product Manager

If you’re anything like me, you probably played with LEGOs as a kid (and probably continue to play with LEGOs as an adult).
I love LEGOs for the fact that you can take just a few building blocks and make nearly anything you want out of them. But LEGOs can be frustrating when you can’t find the one piece you need for your project.

In my years at Tecplot I’ve started to think of Tecplot 360 and PyTecplot like LEGOs. There are a lot of building blocks that can help you do many types of visualization and analysis. Some building blocks are easy to find (like slices, iso-surfaces, and streamtraces), but other building blocks are a bit harder to find (like spanwise integrations and time averages).

Thankfully Tecplot has a team that can help you find these build blocks if you’re having a hard time finding them yourself (kind of like my mom, who could always find the LEGO piece when I needed it).

That’s great Scott, but what’s the point?

We recently had a user contact us wanting to “extract a line that represents the minimum pressure location as a function of Z.” Whew – now that’s a building block that’s hard to find. Sometimes you need to build your own – so that’s what Tecplot support engineers did for this user.

Let’s set up the problem

This user has Tecplot for Barracuda to visualize their results from Barracuda Virtual Reactor. They want to understand where the minimum pressure is throughout the height of their cyclone. With Tecplot 360 you can easily create a series of slices (as pictured at left) to visually understand the minimum pressure location. But it can be challenging to see this visually since the pressure values vary so much in the vertical direction you get little variation across each slice.

So you can see the need for a more quantifiable approach.

PyTecplot to the rescue

PyTecplot, the Python API of Tecplot 360, gives you direct access to the raw data in your simulation results. Using PyTecplot we were able to extract the minimum pressure location at defined Z-locations within the volume. With the set of XYZ minimum pressure locations we were then able to generate a new zone which is the “line that represents the minimum pressure location as a function of Z.”

Sure, this took a few lines of Python (about 30 lines), but through the power of Tecplot 360, PyTecplot, and an amazing technical support staff, we were able to use the building blocks provided by Tecplot products to build an analysis routine that we hadn’t seen before.

Support and GitHub

An example of the script is on the Tecplot GitHub site. And the next time you’re working on an analysis problem and can’t find the LEGO piece you need, make sure to call mom, er, I mean

The post Tecplot 360 and PyTecplot are like LEGOs appeared first on Tecplot.

► Extracting Surface Slices in XY Line Data
  25 Feb, 2022

In this video, we will give a simple demonstration of plotting surface slices, extracting them, and creating an XY line plot from the results.

First, we’ll open our data set. In this demonstration, we are using the Onera wing example found in the Tecplot 360 installation directory. This data set has Pressure Coefficient variable values on the wing surface, and I want to plot a Y-slice of this data in an XY plot.

We can toggle on the contour layer and display the Pressure Coefficient.

Adjusting the Slice

Toggle on Slices in the plot sidebar to place a slice on the plot; Use the slice placement tool to place a slice on the wing surface.

This isn’t in the orientation or slice type that we want, so we will open the Slice Details dialog to adjust it:

  • Instead of placing slices in the x-direction, we’ll set them in the y-planes direction. In this case, parallel to the direction of the flow.
  • Set slice through to surface zones.
  • Then, set the primary slice to Y=0.595.
  • Before we extract a slice, we have a few options we will demonstrate:
    • If you want to extract multiple slices, you can use start and end slices with intermediate slices (at y=0 and y=1.19, with 1 intermediate slice); But for this example, we will only extract the primary surface slice.
    • In Tecplot 360, we extract slices to create new, separate entities in our data set called zones. Once these slices are zones, we can do further analysis, such as plotting, integrations, or exporting the extracted slice.
  • Now, click “Extract slices…” and, keep the default options in the dialog:
    • We want the default slice group (slice group 1), but we could easily extract another group, or all of them, if we wanted.
    • If we had transient data, we could choose if we want a single slice, or the slice extracted through time.
    • You can make extractions per slice or per connected region. Connected regions include zone boundaries where the slice goes across multiple zones and when a single zone has distinct regions such as a wing with multiple sections. In our case, both options will give the same result since there is only a single zone and a single region.
    • By default, Tecplot 360 will attempt to extract the line as I-ordered data, but extraction as a finite-element line segment format is also possible.
  • Next, click extract. In the Zone Style dialog, you should see another zone appear at the bottom of the list. See the Slice zone below for instance.


Mapping Style

Now create a new Frame, and change to the XY Line plot type, and note the option of creating new mappings for all linear zones. This option is useful if multiple slices are extracted. For the X axis we’ll choose the normalized X variable which I calculated beforehand. For more information on how I calculated this normalize variable, see our Getting Started Guide. For the Y axis we can select the Pressure Coefficient variable. We could name the XY mapping something more useful, but we will take advantage of an intrinsic variable later in the Mapping Style dialog.

Create Mappings

After the XY line mappings have been created, I want to edit one of my axes. I want to reverse the Y-variable direction because a y-axis ranging from positive to negative values is typical for a Cp line plot. To reverse the Y axis direction, double click the axis in the plot, or select Plot>Axis, and toggle on Reverse axis direction in the Range tab of the Y1 axis.

Now, tile the frames so that they do not overlap (Frames>Tile Frames…)


And now we have our XY line plot showing the extracted slice from the wing surface. I can change the line color to (blue) and turn-on the line legend. To change the map name to the zone name, in the Mapping Style dialog we can right-click on the mapping and choose zone name by double-clicking on it:


This concludes the tutorial on surface slice extraction. Thank you for watching.

For more advanced information on how to perform other data extractions, check out our other videos linked below.

The post Extracting Surface Slices in XY Line Data appeared first on Tecplot.

► Tour the Academic Suite
  24 Feb, 2022

Webinar Agenda

  • Disciplines using Tecplot software.
  • What is the Tecplot Academic Suite?
  • Who can use the Tecplot Academic Suite?
  • Research applications
  • Commercial applications
  • How to get started

Q&A from the Webinar

Is there a trial version of the software?

Yes! Here are links to request a free trial of 360, FieldView, and RS

Where can I apply for a Suite license?

You can get the Application for Academic pricing and request a quote on our Academic Suite webpage. Or simply contact us – email or call 1.800.763.7005 .

Where can I learn more about the Tecplot Academic Suite?

The post Tour the Academic Suite appeared first on Tecplot.

Schnitger Corporation, CAE Market top

► Ansys adds Zemax optical imaging system simulation to its portfolio
  31 Aug, 2021

Ansys adds Zemax optical imaging system simulation to its portfolio

Ansys has announced that it will acquire Zemax, maker of high-performance optical imaging system simulation solutions. The terms of the deal were not announced, but it is expected to close in the fourth quarter of 2021.

Zemax’s OpticStudio is often mentioned when users talk about designing optical, lighting, or laser systems. Ansys says that the addition of Zemax will enable Ansys to offer a “comprehensive solution for simulating the behavior of light in complex, innovative products … from the microscale with the Ansys Lumerical photonics products, to the imaging of the physical world with Zemax, to human vision perception with Ansys Speos [acquired with Optis]”.

This feels a lot like what we’re seeing in other forms of CAE, for example, when we simulate materials from nano-scale all the way to fully-produced-sheet-of-plastic-scale. There is something to be learned at each point, and simulating them all leads, ultimately, to a more fit-for-purpose end result.

Ansys is acquiring Zemax from its current owner, EQT Private Equity. EQT’s announcement of the sale says that “[w]ith the support of EQT, Zemax expanded its management team and focused on broadening the Company’s product portfolio through substantial R&D investment focused on the fastest growing segments in the optics space. Zemax also revamped its go-to-market sales approach and successfully transitioned the business model toward recurring subscription revenue”. EQT had acquired Zemax in 2018 from Arlington Capital Partners, a private equity firm, which had acquired Zemax in 2015. Why does this matter? Because the path each company takes is different — and it’s sometimes not a straight line.

Ansys says the transaction is not expected to have a material impact on its 2021 financial results.

► Sandvik building CAM powerhouse by acquisition
  30 Aug, 2021

Sandvik building CAM powerhouse by acquisition

Last year Sandvik acquired CGTech, makers of Vericut. I, like many people, thought “well, that’s interesting” and moved on. Then in July, Sandvik announced it was snapping up the holding company for Cimatron, GibbsCAM (both acquired by Battery Ventures from 3D Systems), and SigmaTEK (acquired by Battery Ventures in 2018). Then, last week, Sandvik said it was adding Mastercam to that list … It’s clearly time to dig a little deeper into Sandvik and why it’s doing this.

First, a little background on Sandvik. Sandvik operates in three main spheres: rocks, machining, and materials. For the rocks part of the business, the company makes mining/rock extraction and rock processing (crushing, screening, and the like) solutions. Very cool stuff but not relevant to the CAM discussion.

The materials part of the business develops and sells industrial materials; Sandvik is in the process of spinning out this business. Also interesting but …

The machining part of the business is where things get more relevant to us. Sandvik Machining & Manufacturing Solutions (SMM) has been supplying cutting tools and inserts for many years, via brands like Sandvik, SECO, Miranda, Walter, and Dormer Pramet, and sees a lot of opportunity in streamlining the processes around the use of specific tools and machines. Light weighting and sustainability efforts in end-industries are driving interest in new materials and more complex components, as well as tighter integration between design and manufacturing operations. That digitalization across an enterprise’s areas of business, Sandvik thinks, plays into its strengths.

According to info from the company’s 2020 Capital Markets Day, rocks and materials are steady but slow revenue growers. The company had set a modest 5% revenue growth target but had consistently been delivering closer to 3% — what to do? Like many others, the focus shifted to (1) software and (2) growth by acquisition. Buying CAM companies ticked both of those boxes, bringing repeatable, profitable growth. In an area the company already had some experience in.

Back to digitalization. If we think of a manufacturer as having (in-house or with partners) a design function, which sends the concept on to production preparation, then to machining, and, finally, to verification/quality control, Sandvik wants to expand outwards from machining to that entire world. Sandvik wants to help customers optimize the selection of tools, the machining strategy, and the verification and quality workflow.

The Manufacturing Solutions subdivision within SMM was created last year to go after this opportunity. It’s got 3 areas of focus: automating the manufacturing process, industrializing additive manufacturing, and expanding the use of metrology to real-time decision making.

The CGTech acquisition last year was the first step in realizing this vision. Vericut is prized for its ability to work with any CAM, machine tool, and cutting tool for NC code simulation, verification, optimization, and programming. CGTech is a long-time supplier of Vericut software to Sandvik’s Coromant production units, so the companies knew one another well. Vericut helps Sandvik close that digitalization/optimization loop — and, of course, gives it access to the many CAM users out there who do not use Coromant.

But verification is only one part of the overall loop, and in some senses, the last. CAM, on the other hand, is the first (after design). Sanvik saw CAM as “the most important market to enter due to attractive growth rates – and its proximity to Sandvik Manufacturing and Machining Solutions’ core business.” Adding Cimatron, GibbsCAM, SigmaTEK, and Mastercam gets Sandvik that much closer to offering clients a set of solutions to digitize their complete workflows.

And it makes business sense to add CAM to the bigger offering:

  1. Sandvik has over 100,000 machining customers, many of which are relatively small, and most of which have a low level of digitalization. Sandvik believes it can bring significant value to these customers, while also providing point solutions to much larger clients
  2. Software is attractive — recurring revenue, growth rates, and margins
  3. CAM lets Sandvik grow in strategic importance with its customers, integrating cutting and tool data with process planning, as a way of improving productivity and part quality
  4. The acquisitions are strong in Americans and Asia — expanding Sandvik’s footprint to a more even global basis

To head off one question: As of last week’s public statements, anyway, Sandvik has no interest in getting into CAD, preferring to leave that battlefield to others, and continue on its path of openness and neutrality.

And because some of you asked: there is some overlap in these acquisitions, but remarkably little, considering how established these companies all are. GibbsCAM is mostly used for production milling and turning; Cimatron is used in mold and die — and with a big presence in automotive, where Sandvik already has a significant interest; and SigmaNEST is for sheet metal fabrication and material requisitioning.

One interesting (to me, anyway) observation: 3D Systems sold Gibbs and Cimatron to Battery in November 2020. Why didn’t Sandvik snap it up then? Why wait until July 2021? A few possible reasons: Sandvik CEO Stefan Widing has been upfront about his company’s relative lack of efficiency in finding/closing/incorporating acquisitions; perhaps it was simply not ready to do a deal of this type and size eight months earlier. Another possible reason: One presumes 3D Systems “cleaned up” Cimatron and GibbsCAM before the sale (meaning, separating business systems and financials from the parent, figuring out HR, etc.) but perhaps there was more to be done, and Sandvik didn’t want to take that on. And, finally, maybe the real prize here for Sandvik was SigmaNEST, which Battery Ventures had acquired in 2018, and Cimatron and GibbsCAM simply became part of the deal. We may never know.

This whole thing is fascinating. A company out of left field, acquiring these premium PLMish assets. Spending major cash (although we don’t know how much because of non-disclosures between buyer and sellers) for a major market presence.

No one has ever asked me about a CAM roll-up, yet I’m constantly asked about how an acquirer could create another Ansys. Perhaps that was the wrong question, and it should have been about CAM all along. It’s possible that the window for another company to duplicate what Sandvik is doing may be closing since there are few assets left to acquire.

Sandvik’s CAM acquisitions haven’t closed yet, but assuming they do, there’s a strong fit between CAM and Sandvik’s other manufacturing-focused business areas. It’s more software, with its happy margins. And, finally, it lets Sandvik address the entire workflow from just after component design to machining and on to verification. Mr. Widing says that Sandvik first innovated in hardware, then in service – and now, in software to optimize the component part manufacturing process. These are where gains will come, he says, in maximizing productivity and tool longevity. Further out, he sees, measuring every part to see how the process can be further optimized. It’s a sound investment in the evolution of both Sandvik and manufacturing.

We all love a good reinvention story, and how Sandvik executes on this vision will, of course, determine if the reinvention was successful. And, of course, there’s always the potential for more news of this sort …

► Missed it: Sandvik also acquiring GibbsCAM, Cimatron & SigmaNEST
  25 Aug, 2021

Missed it: Sandvik also acquiring GibbsCAM, Cimatron & SigmaNEST

I missed this last month — Sandvik also acquired Cambrio, which is the combined brand for what we might know better as GibbsCAM (milling, turning), Cimatron (mold and die), and SigmaNEST (nesting, obvs). These three were spun out of 3D Systems last year, acquired by Battery Ventures — and now sold on to Sandvik.

This was announced in July, and the acquisition is expected to close in the second half of 2021 — we’ll find out on Friday if it already has.

At that time. Sandvik said its strategic aim is to “provide customers with software solutions enabling automation of the full component manufacturing value chain – from design and planning to preparation, production and verification … By acquiring Cambrio, Sandvik will establish an important position in the CAM market that includes both toolmaking and general-purpose machining. This will complement the existing customer offering in Sandvik Manufacturing Solutions”.

Cambrio has around 375 employees and in 2020, had revenue of about $68 million.

If we do a bit of math, Cambrio’s $68 million + CNC Software’s $60 million + CGTech’s (that’s Vericut’s maker) of $54 million add up to $182 million in acquired CAM revenue. Not bad.

More on Friday.

► Mastercam will be independent no more
  25 Aug, 2021

Mastercam will be independent no more

CNC Software and its Mastercam have been a mainstay among CAM providers for decades, marketing its solutions as independent, focused on the workgroup and individual. That is about to change: Sandvik, which bought CGTech late last year, has announced that it will acquire CNC Software to build out its CAM offerings.

According to Sandvik’s announcement, CNC Software brings a “world-class CAM brand in the Mastercam software suite with an installed base of around 270,000 licenses/users, the largest in the industry, as well as a strong market reseller network and well-established partnerships with leading machine makers and tooling companies”.

We were taken by surprise by the CGTech deal — but shouldn’t be by the Mastercam acquisition. Stefan Widing, Sandvik’s CEO explains it this way: “[Acquiring Mastercam] is in line with our strategic focus to grow in the digital manufacturing space, with special attention on industrial software close to component manufacturing. The acquisition of CNC Software and the Mastercam portfolio, in combination with our existing offerings and extensive manufacturing capabilities, will make Sandvik a leader in the overall CAM market, measured in installed base. CAM plays a vital role in the digital manufacturing process, enabling new and innovative solutions in automated design for manufacturing.” The announcement goes on to say, “CNC Software has a strong market position in CAM, and particularly for small and medium-sized manufacturing enterprises (SME’s), something that will support Sandvik’s strategic ambitions to develop solutions to automate the manufacturing value chain for SME’s – and deliver competitive point solutions for large original equipment manufacturers (OEM’s).”

Sandvik says that CNC Software has 220 employees, with revenue of $60 million in 2020, and a “historical annual growth rate of approximately 10 percent and is expected to outperform the estimated market growth of 7 percent”.

No purchase price was disclosed, but the deal is expected to close during the fourth quarter.

Sandvik is holding a call about this on Friday — more updates then, if warranted.

► Bentley saw a rebound in infrastructure in Q2 but is cautious about China
  18 Aug, 2021

Bentley saw a rebound in infrastructure in Q2 but is cautious about China

Bentley continues to grow its deep expertise in various AEC disciplines — most recently, expanding its focus in underground resource mapping and analysis. This diversity serves it well; read on.

In Q2,

  • Total revenue was $223 million, up 21% as reported. Seequent contributed about $4 million per the quarterly report filed with the US SEC, so almost all of this growth was organic
  • Subscription revenue was $186 million, up 18%
  • Perpetual license revenue was $11 million, down 8% as Bentley continues to focus on selling subscriptions
  • Services revenue was $26 million, up 86% as Bentley continues to build out its Maximo-related consulting and implementation business, the Cohesive Companies

Unlike AspenTech, Bentley’s revenue growth is speeding up (total revenue up 21% in Q2, including a wee bit from Seequent, and up 17% for the first six months of 2021). Why the difference? IMHO, because Bentley has a much broader base, selling into many more end industries as well as to road/bridge/water/wastewater infrastructure projects that keep going, Covid or not. CEO Greg Bentley told investors that some parts of the business are back to —or even better than— pre-pandemic levels, but not yet all. He said that the company continues to struggle in industrial and resources capital expenditure projects, and therefore in the geographies (theMiddle East and Southeast Asia) that are the most dependent on this sector. This is balanced against continued success in new accounts and the company’s reinvigorated selling to small and medium enterprises via its Virtuosity subsidiary — and in a resurgence in the overall commercial/facilities sector. In general, it appears that sales to contractors such as architects and engineers lag behind those to owners and operators of commercial facilities —makes sense as many new projects are still on pause until pandemic-related effects settle down.

One unusual comment from Bentley’s earnings call that we’re going to listen for on others: The government of China is asking companies to explain why they are not using locally-grown software solutions; it appears to be offering preferential tax treatment for buyers of local software. As Greg Bentley told investors, “[d]uring the year to date, we have experienced a rash of unanticipated subscription cancellations within the mid-sized accounts in China that have for years subscribed to our China-specific enterprise program … Because we don’t think there are product issues, we will try to reinstate these accounts through E365 programs, where we can maintain continuous visibility as to their usage and engagement”. So, to recap: the government is using taxation to prefer one set of vendors over another, and all Bentley can do (really) is try to bring these accounts back and then monitor them constantly to keep on top of emerging issues. FWIW, in the pre-pandemic filings for Bentley’s IPO, “greater China, which we define as the Peoples’ Republic of China, Hong Kong and Taiwan … has become one of our largest (among our top five) and fastest-growing regions as measured by revenue, contributing just over 5% of our 2019 revenues”. Something to watch.

The company updated its financial outlook for 2021 to include the recent Seequent acquisition and this moderate level of economic uncertainty. Bentley might actually join the billion-dollar club on a pro forma basis — as if the acquisition of Seequent had occurred at the beginning of 2021. On a reported basis, the company sees total revenue between $945 million and $960 million, or an increase of around 18%, including Seequent. Excluding Seequent, Bentley sees organic revenue growth of 10% to 11%.

Much more here, on Bentley’s investor website.

► AspenTech is cautious about F2022, citing end-market uncertainty
  18 Aug, 2021

AspenTech is cautious about F2022, citing end-market uncertainty

We still have to hear from Autodesk, but there’s been a lot of AECish earnings news over the last few weeks. This post starts a modest series as we try to catch up on those results.

AspenTech reported results for its fiscal fourth quarter, 2021 last week. Total revenue of $198 million in DQ4, down 2% from a year ago. License revenue was $145 million, down 3%; maintenance revenue was $46 million, basically flat when compared to a year earlier, and services and other revenue was $7 million, up 9%.

For the year, total revenue was up 19% to $709 million, license revenue was up 28%, maintenance was up 4% and services and other revenue was down 18%.

Looking ahead, CEO Antonio Pietri said that he is “optimistic about the long-term opportunity for AspenTech. The need for our customers to operate their assets safely, sustainably, reliably and profitably has never been greater … We are confident in our ability to return to double-digit annual spend growth over time as economic conditions and industry budgets normalize.” The company sees fiscal 2022 total revenue of $702 million to $737 million, which is up just $10 million from final 2021 at the midpoint.

Why the slowdown in FQ4 from earlier in the year? And why the modest guidance for fiscal 2022? One word: Covid. And the uncertainty it creates among AspenTech’s customers when it comes to spending precious cash. AspenTech expects its visibility to improve when new budgets are set in the calendar fourth quarter. By then, AspenTech hopes, its customers will have a clearer view of reopening, consumer spending, and the timing of an eventual recovery.

Lots more detail here on AspenTech’s investor website.

Next up, Bentley. Yup. Alphabetical order.

Symscape top

► CFD Simulates Distant Past
  25 Jun, 2019

There is an interesting new trend in using Computational Fluid Dynamics (CFD). Until recently CFD simulation was focused on existing and future things, think flying cars. Now we see CFD being applied to simulate fluid flow in the distant past, think fossils.

CFD shows Ediacaran dinner party featured plenty to eat and adequate sanitation

read more

► Background on the Caedium v6.0 Release
  31 May, 2019

Let's first address the elephant in the room - it's been a while since the last Caedium release. The multi-substance infrastructure for the Conjugate Heat Transfer (CHT) capability was a much larger effort than I anticipated and consumed a lot of resources. This lead to the relative quiet you may have noticed on our website. However, with the new foundation laid and solid we can look forward to a bright future.

Conjugate Heat Transfer Through a Water-Air RadiatorConjugate Heat Transfer Through a Water-Air Radiator
Simulation shows separate air and water streamline paths colored by temperature

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► Long-Necked Dinosaurs Succumb To CFD
  14 Jul, 2017

It turns out that Computational Fluid Dynamics (CFD) has a key role to play in determining the behavior of long extinct creatures. In a previous, post we described a CFD study of parvancorina, and now Pernille Troelsen at Liverpool John Moore University is using CFD for insights into how long-necked plesiosaurs might have swum and hunted.

CFD Water Flow Simulation over an Idealized PlesiosaurCFD Water Flow Simulation over an Idealized Plesiosaur: Streamline VectorsIllustration only, not part of the study

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► CFD Provides Insight Into Mystery Fossils
  23 Jun, 2017

Fossilized imprints of Parvancorina from over 500 million years ago have puzzled paleontologists for decades. What makes it difficult to infer their behavior is that Parvancorina have none of the familiar features we might expect of animals, e.g., limbs, mouth. In an attempt to shed some light on how Parvancorina might have interacted with their environment researchers have enlisted the help of Computational Fluid Dynamics (CFD).

CFD Water Flow Simulation over a ParvancorinaCFD Water Flow Simulation over a Parvancorina: Forward directionIllustration only, not part of the study

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► Wind Turbine Design According to Insects
  14 Jun, 2017

One of nature's smallest aerodynamic specialists - insects - have provided a clue to more efficient and robust wind turbine design.

DragonflyDragonfly: Yellow-winged DarterLicense: CC BY-SA 2.5, André Karwath

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► Runners Discover Drafting
    1 Jun, 2017

The recent attempt to break the 2 hour marathon came very close at 2:00:24, with various aids that would be deemed illegal under current IAAF rules. The bold and obvious aerodynamic aid appeared to be a Tesla fitted with an oversized digital clock leading the runners by a few meters.

2 Hour Marathon Attempt

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curiosityFluids top

► Creating curves in blockMesh (An Example)
  29 Apr, 2019

In this post, I’ll give a simple example of how to create curves in blockMesh. For this example, we’ll look at the following basic setup:

As you can see, we’ll be simulating the flow over a bump defined by the curve:

y=H*\sin\left(\pi x \right)

First, let’s look at the basic blockMeshDict for this blocking layout WITHOUT any curves defined:

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:
    \\  /    A nd           | Version:  6
     \\/     M anipulation  |
    version     2.0;
    format      ascii;
    class       dictionary;
    object      blockMeshDict;

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

    (-1 0 0)    // 0
    (0 0 0)     // 1
    (1 0 0)     // 2
    (2 0 0)     // 3
    (-1 2 0)    // 4
    (0 2 0)     // 5
    (1 2 0)     // 6
    (2 2 0)     // 7

    (-1 0 1)    // 8    
    (0 0 1)     // 9
    (1 0 1)     // 10
    (2 0 1)     // 11
    (-1 2 1)    // 12
    (0 2 1)     // 13
    (1 2 1)     // 14
    (2 2 1)     // 15

    hex (0 1 5 4 8 9 13 12) (20 100 1) simpleGrading (0.1 10 1)
    hex (1 2 6 5 9 10 14 13) (80 100 1) simpleGrading (1 10 1)
    hex (2 3 7 6 10 11 15 14) (20 100 1) simpleGrading (10 10 1)


        type patch;
            (0 8 12 4)
        type patch;
            (3 7 15 11)
        type wall;
            (0 1 9 8)
            (1 2 10 9)
            (2 3 11 10)
        type patch;
            (4 12 13 5)
            (5 13 14 6)
            (6 14 15 7)
        type empty;
            (8 9 13 12)
            (9 10 14 13)
            (10 11 15 14)
            (1 0 4 5)
            (2 1 5 6)
            (3 2 6 7)

// ************************************************************************* //

This blockMeshDict produces the following grid:

It is best practice in my opinion to first make your blockMesh without any edges. This lets you see if there are any major errors resulting from the block topology itself. From the results above, we can see we’re ready to move on!

So now we need to define the curve. In blockMesh, curves are added using the edges sub-dictionary. This is a simple sub dictionary that is just a list of interpolation points:

        polyLine 1 2
                (0	0       0)
                (0.1	0.0309016994    0)
                (0.2	0.0587785252    0)
                (0.3	0.0809016994    0)
                (0.4	0.0951056516    0)
                (0.5	0.1     0)
                (0.6	0.0951056516    0)
                (0.7	0.0809016994    0)
                (0.8	0.0587785252    0)
                (0.9	0.0309016994    0)
                (1	0       0)

        polyLine 9 10
                (0	0       1)
                (0.1	0.0309016994    1)
                (0.2	0.0587785252    1)
                (0.3	0.0809016994    1)
                (0.4	0.0951056516    1)
                (0.5	0.1     1)
                (0.6	0.0951056516    1)
                (0.7	0.0809016994    1)
                (0.8	0.0587785252    1)
                (0.9	0.0309016994    1)
                (1	0       1)

The sub-dictionary above is just a list of points on the curve y=H\sin(\pi x). The interpolation method is polyLine (straight lines between interpolation points). An alternative interpolation method could be spline.

The following mesh is produced:

Hopefully this simple example will help some people looking to incorporate curved edges into their blockMeshing!


This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software via, and owner of theOPENFOAM®  andOpenCFD®  trademarks.

► Creating synthetic Schlieren and Shadowgraph images in Paraview
  28 Apr, 2019

Experimentally visualizing high-speed flow was a serious challenge for decades. Before the advent of modern laser diagnostics and velocimetry, the only real techniques for visualizing high speed flow fields were the optical techniques of Schlieren and Shadowgraph.

Today, Schlieren and Shadowgraph remain an extremely popular means to visualize high-speed flows. In particular, Schlieren and Shadowgraph allow us to visualize complex flow phenomena such as shockwaves, expansion waves, slip lines, and shear layers very effectively.

In CFD there are many reasons to recreate these types of images. First, they look awesome. Second, if you are doing a study comparing to experiments, occasionally the only full-field data you have could be experimental images in the form of Schlieren and Shadowgraph.

Without going into detail about Schlieren and Shadowgraph themselves, primarily you just need to understand that Schlieren and Shadowgraph represent visualizations of the first and second derivatives of the flow field refractive index (which is directly related to density).

In Schlieren, a knife-edge is used to selectively cut off light that has been refracted. As a result you get a visualization of the first derivative of the refractive index in the direction normal to the knife edge. So for example, if an experiment used a horizontal knife edge, you would see the vertical derivative of the refractive index, and hence the density.

For Shadowgraph, no knife edge is used, and the images are a visualization of the second derivative of the refractive index. Unlike the Schlieren images, shadowgraph has no direction and shows you the laplacian of the refractive index field (or density field).

In this post, I’ll use a simple case I did previously ( as an example and produce some synthetic Schlieren and Shadowgraph images using the data.

So how do we create these images in paraview?

Well as you might expect, from the introduction, we simply do this by visualizing the gradients of the density field.

In ParaView the necessary tool for this is:

Gradient of Unstructured DataSet:

Finding “Gradient of Unstructured DataSet” using the Filters-> Search

Once you’ve selected this, we then need to set the properties so that we are going to operate on the density field:

Change the “Scalar Array” Drop down to the density field (rho), and change the name to Synthetic Schlieren

To do this, simply set the “Scalar Array” to the density field (rho), and change the name of the result Array name to SyntheticSchlieren. Now you should see something like this:

This is NOT a synthetic Schlieren Image – but it sure looks nice

There are a few problems with the above image (1) Schlieren images are directional and this is a magnitude (2) Schlieren and Shadowgraph images are black and white. So if you really want your Schlieren images to look like the real thing, you should change to black and white. ALTHOUGH, Cold and Hot, Black-Body radiation, and Rainbow Desatured all look pretty amazing.

To fix these, you should only visualize one component of the Synthetic Schlieren array at a time, and you should visualize using the X-ray color preset:

The results look pretty realistic:

Horizontal Knife Edge

Vertical Knife Edge

Now how about ShadowGraph?

The process of computing the shadowgraph field is very similar. However, recall that shadowgraph visualizes the Laplacian of the density field. BUT THERE IS NO LAPLACIAN CALCULATOR IN PARAVIEW!?! Haha no big deal. Just remember the basic vector calculus identity:

\nabla^2\left[\right]  = \nabla \cdot \nabla \left[\right]

Therefore, in order for us to get the Shadowgraph image, we just need to take the Divergence of the Synthetic Schlieren vector field!

To do this, we just have to use the Gradient of Unstructured DataSet tool again:

This time, Deselect “Compute Gradient” and the select “Compute Divergence” and change the Divergence array name to Shadowgraph.

Visualized in black and white, we get a very realistic looking synthetic Shadowgraph image:

Shadowgraph Image

So what do the values mean?

Now this is an important question, but a simple one to answer. And the answer is…. not much. Physically, we know exactly what these mean, these are: Schlieren is the gradient of the density field in one direction and Shadowgraph is the laplacian of the density field. But what you need to remember is that both Schlieren and Shadowgraph are qualitative images. The position of the knife edge, brightness of the light etc. all affect how a real experimental Schlieren or Shadowgraph image will look.

This means, very often, in order to get the synthetic Schlieren to closely match an experiment, you will likely have to change the scale of your synthetic images. In the end though, you can end up with extremely realistic and accurate synthetic Schlieren images.

Hopefully this post will be helpful to some of you out there. Cheers!

► Solving for your own Sutherland Coefficients using Python
  24 Apr, 2019

Sutherland’s equation is a useful model for the temperature dependence of the viscosity of gases. I give a few details about it in this post:

The law given by:

\mu=\mu_o\frac{T_o + C}{T+C}\left(\frac{T}{T_o}\right)^{3/2}

It is also often simplified (as it is in OpenFOAM) to:

\mu=\frac{C_1 T^{3/2}}{T+C}=\frac{A_s T^{3/2}}{T+T_s}

In order to use these equations, obviously, you need to know the coefficients. Here, I’m going to show you how you can simply create your own Sutherland coefficients using least-squares fitting Python 3.

So why would you do this? Basically, there are two main reasons for this. First, if you are not using air, the Sutherland coefficients can be hard to find. If you happen to find them, they can be hard to reference, and you may not know how accurate they are. So creating your own Sutherland coefficients makes a ton of sense from an academic point of view. In your thesis or paper, you can say that you created them yourself, and not only that you can give an exact number for the error in the temperature range you are investigating.

So let’s say we are looking for a viscosity model of Nitrogen N2 – and we can’t find the coefficients anywhere – or for the second reason above, you’ve decided its best to create your own.

By far the simplest way to achieve this is using Python and the Scipy.optimize package.

Step 1: Get Data

The first step is to find some well known, and easily cited, source for viscosity data. I usually use the NIST webbook (, but occasionally the temperatures there aren’t high enough. So you could also pull the data out of a publication somewhere. Here I’ll use the following data from NIST:

Temparature (K) Viscosity (Pa.s)
400 0.000022217
600 0.000029602
800 0.000035932
1000 0.000041597
1200 0.000046812
1400 0.000051704
1600 0.000056357
1800 0.000060829
2000 0.000065162

This data is the dynamics viscosity of nitrogen N2 pulled from the NIST database for 0.101 MPa. (Note that in these ranges viscosity should be only temperature dependent).

Step 2: Use python to fit the data

If you are unfamiliar with Python, this may seem a little foreign to you, but python is extremely simple.

First, we need to load the necessary packages (here, we’ll load numpy, scipy.optimize, and matplotlib):

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

Now we define the sutherland function:

def sutherland(T, As, Ts):
    return As*T**(3/2)/(Ts+T)

Next we input the data:



Then we fit the data using the curve_fit function from scipy.optimize. This function uses a least squares minimization to solve for the unknown coefficients. The output variable popt is an array that contains our desired variables As and Ts.

popt = curve_fit(sutherland, T, mu)

Now we can just output our data to the screen and plot the results if we so wish:

print('As = '+str(popt[0])+'\n')
print('Ts = '+str(popt[1])+'\n')


plt.xlabel('Temperature (K)')
plt.ylabel('Dynamic Viscosity (Pa.s)')
plt.legend(['NIST Data', 'Sutherland'])

Overall the entire code looks like this:

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

def sutherland(T, As, Ts):
    return As*T**(3/2)/(Ts+T)

T=[200, 400, 600,


popt, pcov = curve_fit(sutherland, T, mu)
print('As = '+str(popt[0])+'\n')
print('Ts = '+str(popt[1])+'\n')


plt.xlabel('Temperature (K)')
plt.ylabel('Dynamic Viscosity (Pa.s)')
plt.legend(['NIST Data', 'Sutherland'])

And the results for nitrogen gas in this range are As=1.55902E-6, and Ts=168.766 K. Now we have our own coefficients that we can quantify the error on and use in our academic research! Wahoo!


In this post, we looked at how we can simply use a database of viscosity-temperature data and use the python package scipy to solve for our unknown Sutherland viscosity coefficients. This NIST database was used to grab some data, and the data was then loaded into Python and curve-fit using scipy.optimize curve_fit function.

This task could also easily be accomplished using the Matlab curve-fitting toolbox, or perhaps in excel. However, I have not had good success using the excel solver to solve for unknown coefficients.

► Tips for tackling the OpenFOAM learning curve
  23 Apr, 2019

The most common complaint I hear, and the most common problem I observe with OpenFOAM is its supposed “steep learning curve”. I would argue however, that for those who want to practice CFD effectively, the learning curve is equally as steep as any other software.

There is a distinction that should be made between “user friendliness” and the learning curve required to do good CFD.

While I concede that other commercial programs have better basic user friendliness (a nice graphical interface, drop down menus, point and click options etc), it is equally as likely (if not more likely) that you will get bad results in those programs as with OpenFOAM. In fact, to some extent, the high user friendliness of commercial software can encourage a level of ignorance that can be dangerous. Additionally, once you are comfortable operating in the OpenFOAM world, the possibilities become endless and things like code modification, and bash and python scripting can make OpenFOAM worklows EXTREMELY efficient and powerful.

Anyway, here are a few tips to more easily tackle the OpenFOAM learning curve:

(1) Understand CFD

This may seem obvious… but its not to some. Troubleshooting bad simulation results or unstable simulations that crash is impossible if you don’t have at least a basic understanding of what is happening under the hood. My favorite books on CFD are:

(a) The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab by
F. Moukalled, L. Mangani, and M. Darwish

(b) An introduction to computational fluid dynamics – the finite volume method – by H K Versteeg and W Malalasekera

(c) Computational fluid dynamics – the basics with applications – By John D. Anderson

(2) Understand fluid dynamics

Again, this may seem obvious and not very insightful. But if you are going to assess the quality of your results, and understand and appreciate the limitations of the various assumptions you are making – you need to understand fluid dynamics. In particular, you should familiarize yourself with the fundamentals of turbulence, and turbulence modeling.

(3) Avoid building cases from scratch

Whenever I start a new case, I find the tutorial case that most closely matches what I am trying to accomplish. This greatly speeds things up. It will take you a super long time to set up any case from scratch – and you’ll probably make a bunch of mistakes, forget key variable entries etc. The OpenFOAM developers have done a lot of work setting up the tutorial cases for you, so use them!

As you continue to work in OpenFOAM on different projects, you should be compiling a library of your own templates based on previous work.

(4) Using Ubuntu makes things much easier

This is strictly my opinion. But I have found this to be true. Yes its true that Ubuntu has its own learning curve, but I have found that OpenFOAM works seamlessly in the Ubuntu or any Ubuntu-like linux environment. OpenFOAM now has Windows flavors using docker and the like- but I can’t really speak to how well they work – mostly because I’ve never bothered. Once you unlock the power of Linux – the only reason to use Windows is for Microsoft Office (I guess unless you’re a gamer – and even then more and more games are now on Linux). Not only that- but the VAST majority of forums and troubleshooting associated with OpenFOAM you’ll find on the internet are from Ubuntu users.

I much prefer to use Ubuntu with a virtual Windows environment inside it. My current office setup is my primary desktop running Ubuntu – plus a windows VirtualBox, plus a laptop running windows that I use for traditional windows type stuff. Dual booting is another option, but seamlessly moving between the environments is easier.

(5) If you’re struggling, simplify

Unless you know exactly what you are doing, you probably shouldn’t dive into the most complicated version of whatever you are trying to solve/study. It is best to start simple, and layer the complexity on top. This way, when something goes wrong, it is much easier to figure out where the problem is coming from.

(6) Familiarize yourself with the cfd-online forum

If you are having trouble, the cfd-online forum is super helpful. Most likely, someone else is has had the same problem you have. If not, the people there are extremely helpful and overall the forum is an extremely positive environment for working out the kinks with your simulations.

(7) The results from checkMesh matter

If you run checkMesh and your mesh fails – fix your mesh. This is important. Especially if you are not planning on familiarizing yourself with the available numerical schemes in OpenFOAM, you should at least have a beautiful mesh. In particular, if your mesh is highly non-orthogonal, you will have serious problems. If you insist on using a bad mesh, you will probably need to manipulate the numerical schemes. A great source for how schemes should be manipulated based on mesh non-orthogonality is:

(8) CFL Number Matters

If you are running a transient case, the Courant-Freidrechs-Lewis (CFL) number matters… a lot. Not just for accuracy (if you are trying to capture a transient event) but for stability. If your time-step is too large you are going to have problems. There is a solid mathematical basis for this stability criteria for advection-diffusion problems. Additionally the Navier-Stokes equations are very non-linear and the complexity of the problem and the quality of your grid etc can make the simulation even less stable. When I have a transient simulation crash, if I know my mesh is OK, I decrease the timestep by a factor of 2. More often than not, this solves the problem.

For large time stepping, you can add outer loops to solvers based on the pimple algorithm, but you may end up losing important transient information. Excellent explanation of how to do this is given in the book by T. Holzmann:

For the record, this points falls into point (1) of Understanding CFD.

(9) Work through the OpenFOAM Wiki “3 Week” Series

If you are starting OpenFOAM for the first time, it is worth it to work through an organized program of learning. One such example (and there are others) is the “3 Weeks Series” on the OpenFOAM wiki:

If you are a graduate student, and have no job to do other than learn OpenFOAM, it will not take 3 weeks. This touches on all the necessary points you need to get started.

(10) OpenFOAM is not a second-tier software – it is top tier

I know some people who have started out with the attitude from the get-go that they should be using a different software. They think somehow Open-Source means that it is not good. This is a pretty silly attitude. Many top researchers around the world are now using OpenFOAM or some other open source package. The number of OpenFOAM citations has grown every year consistently (

In my opinion, the only place where mainstream commercial CFD packages will persist is in industry labs where cost is no concern, and changing software is more trouble than its worth. OpenFOAM has been widely benchmarked, and widely validated from fundamental flows to hypersonics (see any of my 17 publications using it for this). If your results aren’t good, you are probably doing something wrong. If you have the attitude that you would rather be using something else, and are bitter that your supervisor wants you to use OpenFOAM, when something goes wrong you will immediately think there is something wrong with the program… which is silly – and you may quit.

(11) Meshing… Ugh Meshing

For the record, meshing is an art in any software. But meshing is the only area where I will concede any limitation in OpenFOAM. HOWEVER, as I have outlined in my previous post ( most things can be accomplished in OpenFOAM, and there are enough third party meshing programs out there that you should have no problem.


Basically, if you are starting out in CFD or OpenFOAM, you need to put in time. If you are expecting to be able to just sit down and produce magnificent results, you will be disappointed. You might quit. And frankly, thats a pretty stupid attitude. However, if you accept that CFD and fluid dynamics in general are massive fields under constant development, and are willing to get up to speed, there are few limits to what you can accomplish.

Please take the time! If you want to do CFD, learning OpenFOAM is worth it. Seriously worth it.

This offering is notapproved or endorsed by OpenCFD Limited, producer and distributorof the OpenFOAM software via, and owner of theOPENFOAM®  andOpenCFD®  trade marks.

► Automatic Airfoil C-Grid Generation for OpenFOAM – Rev 1
  22 Apr, 2019
Airfoil Mesh Generated with

Here I will present something I’ve been experimenting with regarding a simplified workflow for meshing airfoils in OpenFOAM. If you’re like me, (who knows if you are) I simulate a lot of airfoils. Partly because of my involvement in various UAV projects, partly through consulting projects, and also for testing and benchmarking OpenFOAM.

Because there is so much data out there on airfoils, they are a good way to test your setups and benchmark solver accuracy. But going from an airfoil .dat coordinate file to a mesh can be a bit of pain. Especially if you are starting from scratch.

The two main ways that I have meshed airfoils to date has been:

(a) Mesh it in a C or O grid in blockMesh (I have a few templates kicking around for this
(b) Generate a “ribbon” geometry and mesh it with cfMesh
(c) Or back in the day when I was a PhD student I could use Pointwise – oh how I miss it.

But getting the mesh to look good was always sort of tedious. So I attempted to come up with a python script that takes the airfoil data file, minimal inputs and outputs a blockMeshDict file that you just have to run.

The goals were as follows:
(a) Create a C-Grid domain
(b) be able to specify boundary layer growth rate
(c) be able to set the first layer wall thickness
(e) be mostly automatic (few user inputs)
(f) have good mesh quality – pass all checkMesh tests
(g) Quality is consistent – meaning when I make the mesh finer, the quality stays the same or gets better
(h) be able to do both closed and open trailing edges
(i) be able to handle most airfoils (up to high cambers)
(j) automatically handle hinge and flap deflections

In Rev 1 of this script, I believe I have accomplished (a) thru (g). Presently, it can only hand airfoils with closed trailing edge. Hinge and flap deflections are not possible, and highly cambered airfoils do not give very satisfactory results.

There are existing tools and scripts for automatically meshing airfoils, but I found personally that I wasn’t happy with the results. I also thought this would be a good opportunity to illustrate one of the ways python can be used to interface with OpenFOAM. So please view this as both a potentially useful script, but also something you can dissect to learn how to use python with OpenFOAM. This first version of the script leaves a lot open for improvement, so some may take it and be able to tailor it to their needs!

Hopefully, this is useful to some of you out there!


You can download the script here:

Here you will also find a template based on the airfoil2D OpenFOAM tutorial.


(1) Copy to the root directory of your simulation case.
(2) Copy your airfoil coordinates in Selig .dat format into the same folder location.
(3) Modify to your desired values. Specifically, make sure that the string variable airfoilFile is referring to the right .dat file
(4) In the terminal run: python3
(5) If no errors – run blockMesh

You need to run this with python 3, and you need to have numpy installed


The inputs for the script are very simple:

ChordLength: This is simply the airfoil chord length if not equal to 1. The airfoil dat file should have a chordlength of 1. This variable allows you to scale the domain to a different size.

airfoilfile: This is a string with the name of the airfoil dat file. It should be in the same folder as the python script, and both should be in the root folder of your simulation directory. The script writes a blockMeshDict to the system folder.

DomainHeight: This is the height of the domain in multiples of chords.

WakeLength: Length of the wake domain in multiples of chords

firstLayerHeight: This is the height of the first layer. To estimate the requirement for this size, you can use the curiosityFluids y+ calculator

growthRate: Boundary layer growth rate

MaxCellSize: This is the max cell size along the centerline from the leading edge of the airfoil. Some cells will be larger than this depending on the gradings used.

The following inputs are used to improve the quality of the mesh. I have had pretty good results messing around with these to get checkMesh compliant grids.

BLHeight: This is the height of the boundary layer block off of the surfaces of the airfoil

LeadingEdgeGrading: Grading from the 1/4 chord position to the leading edge

TrailingEdgeGrading: Grading from the 1/4 chord position to the trailing edge

inletGradingFactor: This is a grading factor that modifies the the grading along the inlet as a multiple of the leading edge grading and can help improve mesh uniformity

trailingBlockAngle: This is an angle in degrees that expresses the angles of the trailing edge blocks. This can reduce the aspect ratio of the boundary cells at the top and bottom of the domain, but can make other mesh parameters worse.


12% Joukowski Airfoil


With the above inputs, the grid looks like this:

Mesh Quality:

These are some pretty good mesh statistics. We can also view them in paraView:

Clark-y Airfoil

The clark-y has some camber, so I thought it would be a logical next test to the previous symmetric one. The inputs I used are basically the same as the previous airfoil:

With these inputs, the result looks like this:

Mesh Quality:

Visualizing the mesh quality:

MH60 – Flying Wing Airfoil

Here is an example of a flying with airfoil (tested since the trailing edge is tilted upwards).


Again, these are basically the same as the others. I have found that with these settings, I get pretty consistently good results. When you change the MaxCellSize, firstLayerHeight, and Grading some modification may be required. However, if you just half the maxCell, and half the firstLayerHeight, you “should” get a similar grid quality just much finer.

Grid Quality:

Visualizing the grid quality


Hopefully some of you find this tool useful! I plan to release a Rev 2 soon that will have the ability to handle highly cambered airfoils, and open trailing edges, as well as control surface hinges etc.

The long term goal will be an automatic mesher with an H-grid in the spanwise direction so that the readers of my blog can easily create semi-span wing models extremely quickly!

Comments and bug reporting encouraged!

DISCLAIMER: This script is intended as an educational and productivity tool and starting point. You may use and modify how you wish. But I make no guarantee of its accuracy, reliability, or suitability for any use. This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software via, and owner of the OPENFOAM®  and OpenCFD®  trademarks.

► Normal Shock Calculator
  20 Feb, 2019

Here is a useful little tool for calculating the properties across a normal shock.

If you found this useful, and have the need for more, visit One of STF Solutions specialties is providing our clients with custom software developed for their needs. Ranging from custom CFD codes to simpler targeted codes, scripts, macros and GUIs for a wide range of specific engineering purposes such as pipe sizing, pressure loss calculations, heat transfer calculations, 1D flow transients, optimization and more. Visit STF Solutions at for more information!

Disclaimer: This calculator is for educational purposes and is free to use. STF Solutions and curiosityFluids makes no guarantee of the accuracy of the results, or suitability, or outcome for any given purpose.


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