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aamer December 11, 2010 06:16

Correct values of drag but high values of lift.
Hello all

i am validating experimental results of corrugated airfoil at low Reynolds number.... although i am getting reasonably accurate values for Cd for all angles of attack (5,7,15) but i am getting higher values of Cl for all angles of attack. I am using pressure based unsteady implicit solver, SA turbulence model and my y+ is equal to 0.5. velocity inlet and pressure outlet are the boundary conditions. the comparison of Cl with few angles of attack is as follow
angle of attack . 5 degree
experimental value .... (range of 0.387 to 0.469)
fluent calculated value 0.572

angle of attack . 7 degree
experimental value .... (range of 0.601 to 0.672)
fluent calculated value 0.745

angle of attack . 15 degree (stall region)
experimental value .... (range of 0.683 to 0.761)
fluent calculated value 0.821

expert opinion is requested..... what is wrong with my problem????

dandalf December 13, 2010 08:17

I am having similar problems trying to validate flow over a cylinder,
My calculated drag coeficients agree well with bench mark solutions, but the lift seems is always biased to one side of the object.

Are you by any chance using a staggered cartesian mesh for discretization, if so I suspect we migh have the same problem.

by experimentation I have discovered that the magnitude of the imbalence is in inverse proportion to the renolds nmber of the flow, so it must be a failure of symetry in the discretization of the viscous term. Running my calculations with only the viscous term produced a non symmetrical wake, which seems to confirm this,
However I have poured over my code for days and can not find a reason why the symetry would be failing,

I have tried two different approaches,
1: Calculation of second differeces,
((secdiff(W(vol).U,H(vol).U,E(vol).U,dx)+secdiff(S (vol).U,H(vol).U,N(vol).U,dy))*Mu/Rho)
2: Use of the viscous stress tensor,
((diff(W(vol).tao[0],H(vol).tao[0],dx) + diff(H(vol).tao[1] ,N(vol).tao[1],dy))/Rho)

(*vol).tao[0]= Mu*(2*diff(H(vol).U,E(vol).U,dx)-((2/3)*(diff(H(vol).U,E(vol).U,dx))+diff(H(vol).V,N(vo l).V,dy)));
(*vol).tao[1]= Mu*(diff(W(vol).V,H(vol).V,dx)+diff(S(vol).U,H(vol ).U,dy));
(*vol).tao[2]= Mu*(2*diff(H(vol).V,N(vol).V,dy)-((2/3)*(diff(H(vol).U,E(vol).U,dx))+diff(H(vol).V,N(vo l).V,dy)));

However both results seem to produce the same non symetry, when applied to a staggered grid,


siri December 13, 2010 09:50


(a) why are you not using a pressure farfield boundary condition (you wrote pressure outlet) ?

(b) I hope you have correctly modeled the fluid behavior - use of pressure based solver & low Re will mean that you would be simulating forincompressible flow. Check if that is true in expt.

(c) Finally few suggestions that may improve your solution:
i. replace the present choice of numerical schemes with more accurate higher order ones, if you haven't done it already
ii. check how you are computing pressure & try best available approach

Please post if it helps.

siri December 13, 2010 09:58


Originally Posted by dandalf (Post 287213)
Are you ... using a staggered cartesian mesh for discretization ... However both results seem to produce the same non symetry, when applied to a staggered grid,



How wide are your domain extents all around the cylinder ? did you try widening of the same, just in case ?

Does using a cartesian mesh for cylindrical geometry might be causing issues ?

dandalf December 13, 2010 10:30

1 Attachment(s)
Hi Siri

The goemetry I'm using was taken dirrectly from the benchmark test put forward in (Schaefer and Turrek, Benchmark computations of laminar flow around a cylinder: 1996).

I am constrained to using a cartesian mesh as I am developing the solver for a more complex morphing boundary problem, and I want to avoid the additional compuational burden of remeshing for each itteration in the time domain. My intention was to use the cylinder flow as a validation case before moving on to the more complex flows.

However to compensate for the poor adherance of cartesian mesh to cylindrical geometry, I have a near boundary grid size of 1/40 times the cylinder diameter decreasing with a finction of interest to 1/10 diameter further away,

I have tried altering the inflow conditions to force the lift to move to the other side, however the symmetry imbalence was so strong that I could not get the lift to change direction, regardless of inlet velocity profile.

I also tried streching my domain into a taurus to eliminate all external boundary conditions by creating a continuous surface, however this had no effect on the imbalance.

I still can't figure out why its not symetrical in the first place... I'm going slightly loopy on this one.


siri December 13, 2010 10:54


I have seen the attachment. I feel that your domain boundaries are too close to the body. I guess you are trying to duplicate these values from some experimental set-up, but then you cannot have the same values for CFD simulation.

There is no exact formula to guide in fixing the location of wall, inlet & outlet boundaries, but a thumbrule is usually followed for external flows which seems to be good enough: exppressed in terms of characteristic dimension, which in your case is cylinder diameter (d)

Then boundaries should be located as follows (distances away from body surface)
Inlet: 5d-10d;
Outlet: 10d-30d;
upper &lower walls: 10d-15d

I kind of believe the walls are interfering with your flow right row. So update if this suggestion works.

dandalf December 13, 2010 11:33


The exact same geometry was put forward in Griebel et al , Numerical Simulation in fluid dynamics; a practical Introduction, Siam , 1998.

The in the benchmark upper and lower boundaries are solid,

I did try with wider boundaries but the outcome was the same.
As I mentioned before I also tried without any external boundaries, by looping the axis to create a continuous domain.

I have tried running the calculations with each part of the conservation equations in isolation, and the only term that seems to result in a non symmetrical result is the viscous term.

As specified by the benchmark test I have a quadraic inlet velocity function, which therfore has a constant second differential.

I also tried with a constant inlet velocity profile, which should certainly have a constant second differential. However the result was always the same.


aamer December 13, 2010 14:45

Dear Siri...
i am not using pressure far field because that is applicable to compressible flows only. my case is low Reynolds number i.e 34000, the case is incompressible (confirmed from experiments). i am already using higher order discretization scheme and pressure based solver. Moreover, my pressure interpolation scheme at present, is second order upwind..... so the problem stays unresolved.
i have one question. can i use "outflow" as exit boundary condition instead of "pressure outlet" for such an "incompressible, low Re, external flow" over airfoil as mine. {actually, presently, for pressure outlet B.C i am assuming that the gauge pressure at exit is zero and operating pressure is 101325 pascals}. your expert opinion on use and reason of using outflow B.c is requested, if you recommend it for use, in such a case.

just for info: i am using 10 C domain in all directions.

siri December 14, 2010 00:34


I think most of the settings you are doing right now seem to be okay i.e if it was analysis for a standard airfoil profile. but in your case, the airfoil is corrugated and also perhaps geometrically order of magnitudes smaller than ordinary aircraft (wing) airfoil or wind turbine blade airfoil.

So I presume that the flow separation effects might be more predominant (i can't confirm unless i see your airfoil) than for the standard shapes. I would then recommend to use one of the 2-eqn turb models such as (k-omega) to capture the flow in more detail. However, since your Cd is matching well to expt, i am surprised if this would resolve the case.

On other hand, I didn't understand if you must go for implicit solution apart from solving transient case at one go. How about solving for a steady flow explicitly and restrart from there to run transient ?

Since the problem seems to be with Lift values, which come from pressure difference, during the explicit solution, using a simpler scheme like SIMPLE might resolve the pressure gradients better. This is just a suggestion that you may try if you go by this argument. What do you say ?

siri December 14, 2010 00:44


Supposing that your finding about the viscous term is indeed the cause, then what could be done to counteract this ?

Do you account for these - turb.viscosity, visc.dissipation in the turbulence model of your present code ?

How are you specifying turbulence at the inlet ? Are they same as in your reference papers ?

dandalf December 14, 2010 06:34


I am using a central difference mehod to directly solve the navier-stokes equation for the conservation of momentum, and mass. i am representing the system isentropicaly, thus disregarding energy losses from the system through heat generated through friction.

All turbulence should be fully modelled by this approach, this seems to be teh same approach used in the reference papers.

I suspect it might be an issue with grid missalingment, as that could cause a failure in symmetry of a central difference scheme, but then that doesn't explain why the terms deendent on first derrivetives seem to be acting properly, whereas the terms dependent on second derivetives are missbehaving.

As for the inlet turbulence, the benchmark caled for a lamina quadratic inflow velocity profile,


Where H is the total height of the inlet apeture, U max is the velocity at the center of the channel and y is the height of a given point.


siri December 14, 2010 10:23


I couldn't quite relate to how the lift alone and not drag computation gets affected due to "grid misalignment" or whether your mesh was non-symmetric w.r.t cylinder (isn't it structured/hexa mesh?)

Myself haven't worked much on the meshing part of codes, so won't be able to comment on it.

However, I have some doubts about the solving process. Are you running transient solution? If time stepping is there, do you use CDS for this ?

aamer December 14, 2010 11:59

Hello Siri.....
my airfoil is only 101 mm in length and flow separation effects are also dominant, so u r right that i should go for 2 equation model to capture flow physics. so i am trying to run the case with sst k-w transitional now. As far as turbulence parameters of B.C are concerned, i only know the turbulance intensity at inlet from the experiment as 1%. so i am using that value. Moreover, i have used turbulent viscosity ratio of 1 for my case.

Siri..... u didnt mention, whether its okie to use "outflow" boundary condition at outlet or not???? what are the disadvantages, if i go for outflow condition?

i have used simpler pressure interpolation as SIMPLE but it has not substantially effected my simulation.

siri December 15, 2010 00:25


Well, for incompressible flow it doesnot matter. However if you specified a pressure outlet BC, you must be very cautious about the pressure value you prescribed .. it has to be a known value or established from expt.

When one is not sure, Outflow BC helps. Apart from this, I don't see any cause for concern except that I haven't come across such usage yet.

Since nothing else seems to be working, i think as a last resort, you may want to try few things, as an attempt to understand the flow behavior better.

i) scale up your model following Similarity principles, remesh if required and run the simulations to see, if you find same thing happening or problem is resolved.

ii) simplify the corrugations to reduce it to standard airfoil, if possible test exptallly & compare with CFD.

The second step may not resolve your problem, but can confirm if the corrugated airfoil requires further inspection / root cause analysis

aamer December 15, 2010 02:10


i have given gauge pressure of 0 Pascal and operating pressure of 101325 PAscal for pressure outlet.... nothing is given to me in experiment, as far as outlet values are concerned. so actually, i am taking assumption that the outlet boundary condition is at atmospheric pressure. isnt that true for external aerodynamics, when the outlet is at 10 chord lengths from the arfoil?

siri December 15, 2010 09:31

Well, the rule of book is never to use a pressure outlet BC if you didnot know with certainity, what the actual pressure there is as this BC tends to fix the value you prescribed & might effect the flow conditions esp for internal flows

Outflow BC is safe for all cases. For incompressible flows, it is common practice to set your operating point to locate close to inlet/outlet & obtain the relative pressure gradient throughout the domain.

aamer December 16, 2010 05:44

Dear Siri......
thanks a lot for enlightening me on the subject. i will get back to your after implementing what all you have said...

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