My group at NASA Glenn Research Center (formerly Lewis) is beginning work towards developing a Large Eddy Simulation capability - particularly for nozzle and jet aerodynamics simulations. As a newcomer to this field, I have read numerous papers, heard presentations on the LES field, and am trying to make sense of all of it. Recently, I have seen increased interest in what is called Very Large Eddy Simulation and Unsteady RANS. If what I understand about LES is correct (where you "directly" calculate large scales and model the smallest ones) - I am confused as to how VLES and unsteady RANS can work.....specifically, from my past RANS work, I know all eddy viscosity models act as diffusive factors in the NS equations - and as a result, replace or "model" an unsteady-turbulent flow as a steady flow with an effective variable viscosity (from the turbulence model) replacing the turbulent stresses. After this long introduction, my question for those in the field out there is: How can VLES or Unsteady RANS work to still give you a meaningful representation of the large scales? I would think that since you are replacing decent size scales of turbulence with a dissipative model (turbulence model for RANS, SGS model for VLES), your large scales do not have a hope to be useful.

I would appreciate any insight on this topic.

Nick Georgiadis NASA Glenn Research Center tonjg@grc.nasa.gov

This is an interesting topic - I think we had some discussions about this in the past. May I suggest you take a look at the paper by Speziale, C.G.: Turbulence modelling for time-dependent RANS and VLES: A review, AIAA Journal 36:173-184 (2), 1998. The answer I could offer is the following: RANS does not necessarily act as a dissipative factor (see second-order closure, for example) and is in fact based on the decomposition into the mean and the fluctuation. If you choose the mean to be the ensemble average, rather than, say, the time-average, you can still have unsteadiness in the mean, which should represent the "true" unsteadiness of the large scales (that's before the modelling!). There remains the question about which scales will now be resolved and which will be represented as "turbulence". In LES, the answer is clear: supergrid scales are resolved and the subgrid part is modelled. In unsteady RANS, we need to look at the nature of the flow. Unsteady RANS is in fact doing the decomposition based on the "spectral gap": it is assumed that the coherent structures (unsteadiness) is, in spectral space, separated from turbulent oscillations. Anything below the spectral gap (read: coherent structures) is resolved.

The problems start when there is no gap; from there on, I can't offer any help.

It depends on the physical processes being simulated. A large class of unsteady phenomena are only weakly influenced by turbulence and so can be successfully predicted by invalid approaches (in terms of turbulence modelling). That is, the important unsteady motion is on a scale too large to be "turbulence".

Unsteady RANS can be justified (to a small degree) if the resolved unsteady motion has no significant component in the turbulence scales. A high viscosity (often enhanced by the numerical scheme) arising from eddy viscosity based models such as k-e like will act to bring this about to some degree.

VLES is a term which has been appropriated and applied to more than one approach to turbulence modelling.

An LES turbulence model which is not dissipative is physically incorrect. It is also unusable for predictions with periodic streamwise boundary conditions (the usual boundary condition for the ever popular fully developed channel flow) since energy will accumulate if the numerical scheme conserves it (usual).

In order to determine if your large scales have a hope of being useful I would strongly advise performing an LES prediction and plotting first the predicted Reynolds stresses and then the sub-grid stresses. A reasonable reaction to this exercise would be to lose interest in turbulence modelling and become much more interested in the numerical properties of the convection terms. (This does not apply to flow regions such as that near walls, flame fronts, shocks and the like but here the problem is not to accurately simulate large scales but to accurately represent the small scales whose awkward behaviour is not reasonably represented by simple eddy viscosity based SGS models).

1. Contrary to the popular belief that RANS models cannot solve unsteady problems, a properly formulated two-equation or Reynolds stress model can capture the vortex shedding that occurs in a turbulent flow around a cylinder. There are different time scales in a turbulent flow. The averaged equations will not capture high frequency fluctuations. But it will capture fluctuations that has a larger time scale ( or lower frequency) than the time step used in the calculations. In RANS models, it is assumed that the equations are averaged over a time period which is smaller than the time step used in the calculations.

2. LES uses time dependent boundary conditions. Hence, the flow will be much more unsteady. But again , like RANS models, LES cannot capture time scales which are smaller than the the time step used in the calculations.

3. If you use time dependent boundary conditions in your RANS code, it will behave like an LES code.

4. In a way you could call unsteady, RANS formulation as VLES.

Good Luck with your LES efforts.

yours sincerely,

Para

Siva Parameswaran, Ph.D. Associate Professor Dept. of Mechanical Engineering Texas Tech University Mail Stop 1021 Lubbock, TX 79409, USA

better ... an unsteady turbulent flow as a mean steady flow.

In RANS you usually apply temporal averaging on the equations and assume that the flow is statistically steady. In your average operation you have to "choose" a period of averaging. Usually your choice leads to the cancellation of the temporal derivative in the equations. However you can see this average procedure as a spatio- temporal filter (characteristic time and length scales of eddies are related).

Furthermore, as you 're only interested in the very large scalesof the flow, small scales effect can be relatively well described with an eddy viscosity (due to the large scale separation).

I agree with much of what you say but feel obliged to answer one or two points.

Consider, say, imposing the solution from a DNS run as inlet conditions to the prediction of a simple boundary layer. An "unsteady RANS" code would predict nonsense with excessive Reynolds stresses (effectivley the ones from the RANS model of the "mean" flow plus stresses arising from the time resolved motion with a large coefficient of viscosity). It is very likely that these excessive stresses will progressively damp the resolved motion and far down stream all time varying motion would be absent. The boundary layer may now look sensible but performing a time resolved prediction is pointless.

Vortex shedding behind a cylinder/block is not turbulence and is an almost pointless test of a turbulence model (although it has been widely used as such in the LES community).

An "unsteady RANS" model can only capture any unsteady motion which can exist in the presence of the very large stresses which arise to oppose it from the RANS model. In general, this motion has to be on a scale substantially above that of the largest turbulent energy containing scale.

Traditional RANS turbulence models are not derived assuming an average time period based on the computational time step. They simply provide models for the Reynolds stresses.

You cannot arbitrarily choose a time step for an unsteady flow (whether "unsteady RANS", LES or DNS). If the time step is above that required to resolve the time varying motion then it is not a solution of the underlying equations.

Turbulent forced convection occurs in many important technological applications of importance to

mechanical, aerospace, electrical, computer, chemical, and nuclear engineers and flows of interest to

meteorologists and earth scientists. The three-dimensional unsteady Navier-Stokes (NS) equations are known to govern such flows. Direct numerical simulation (DNS), which involves numerically solving the full

unsteady NS equations is currently limited to only the simplest flow geometries and low Reynolds numbers.

This is because the computational resources required to resolve all length and time scales of turbulence is

prohibitively expensive. Alternatively, the Reynolds averaged Navier-Stokes (RANS) equations, obtained

from time averaging the unsteady NS equations, require much less computational resources and are used

successfully to compute many flows of practical importance. However, the turbulence models used in

conjunction with the RANS equations are not applicable to a wide range of flow geometries and are

unsuccessful for many turbulent flow situations. The major deficiency with the RANS equations is that one is

averaging over all the turbulence, so the models must account for all scales of turbulence. This makes it

difficult, if not impossible, to develop a universal turbulence model applicable to all flow situations.

Large eddy simulation (LES) is a compromise between DNS and RANS. LES relies on the fact that small

scales of turbulent motion are nearly isotropic and independent of the geometry, whereas the large scales of

turbulent motion are mostly anisotropic and vary from flow to flow. The small scale motion, which is mostly

a function of the amount of energy that must be dissipated and therefore more universal, is filtered out of the governing equations and modeled with a subgrid scale (SGS) model. The large scale motion is computed

directly by numerically solving the three-dimensional, time dependent filtered NS equations.

Although not as computationally expensive as DNS, LES still requires large amounts of computer resources. This is what Dr.P.Moin, Professor of Mechanical Engineering of Stanford University is saying that he learned from ..... authors.

Again, I have also looked at the AIAA Journal as mentioned by Dr. Hrvoje Jasak. There are also new models published in August, 1999 in 'Technical Note' of AIAA Journal where the author is claiming that his turbulence model for channel flows is better than previous models developed. I am a novice in this field and kind of confused and frustrated like you. Whose models should I trust?

Hi

I noticed that Andy referred to vortex shedding behind a cylinder/block as "not turbulent". I am no expert in the field of turbulence but have always wondered how one would be able to look at a flow field (without any prior knowledge about the Reynolds number) and determine whether it is turbulent or not. As I understand it "turbulence" is basically a mixture of different sizes of vortexes. To illustrate my question: How would one by looking at the vortex street behind a cylinder (again with no knowledge of the Reynolds number) determine whether it is turbulent or not since both the "laminar" and "turbulent" flow case are characterised by a host of different vortex sizes.

One may be wiser to rely on knowledge rather than trust as a basis for making decisions. It is initially more expensive but can often win out in the long run (assuming one stays in the field).

There is only one (reasonably) trustworthy universal model and that is DNS which is impractical for most engineering applications.

It is hard to give further advice unless you indicate the physical phenomena you wish to simulate. For example, RANS models generally predict steadily evolving boundary layers pretty well (in the absence of strong curvature, shocks and other nasties) but cannot reliably predict separation, recirculation and the like where large scale turbulent transport is an important physical process (one point RANS models adopt a model based on small scale turbulent transport in order to close the set of equations to be solved). LES on the other hand predicts such regions very well (as its name implies) but has problems handling flow regions where small scale turbulent motion is being generated/important/not behaving nicely (e.g. flame fronts, shocks, walls). A significantly large class of flows are not strongly influenced by turbulence at all for which it may be wisest to use the simplest viable turbulence model.

Channel flow is an excellent test case to start developing a turbulence model. However, all reasonably developed turbulence models, including the simplest RANS models, predict it well. It cannot really be used to sort the wheat from the chaff. One needs to use a series of different flow cases to demonstrate which flow regimes are handled well and which are not. You can be certain that some flow regimes will not be accurately simulated. Alternatively, one can often work this out by studying the basis of the modelling assumptions adopted in putting the model together.

Horses for courses is rarely the advice one wants to receive but can you trust my advice anyway?

P.S. The answer is no. Go and ...

If I may first consider the familiar evolving boundary layer where various flow regimes are distinct. Initially it is laminar, then "wavy" flow instabilities arise which grow then a "transition" region occurs where the coherence intermittently breaks down and finally turbulence sets in.

In "An Introduction to Turbulence and its Measurement" (a good introductory book) Peter Bradshaw defines turbulence as: "a three-dimensional time-dependent motion in which vortex stretching causes velocity fluctuations to spread to all wavelengths between a minimum determined by the viscous forces and a maximum determined by the boundary conditions of the flow. It is the usual state of fluid motion except at low Reynolds numbers." This a reasonable general definition although specialists will have to resist the temptation to qualify it in various ways (e.g. earlier discussion on 2D turbulence etc.).

The vortex shedding around a cylinder is a flow instability. In itself it is not turbulence but it is a source of turbulent motion and further downstream it will break down into "proper" turbulence if the Reynolds number is high enough to allow it. It is not turbulent motion because it does not fit the above defintion being largely coherent and orientated in one direction. At high Reynolds numbers, it can be successfully predicted using RANS codes as pointed out by Para.

So, in answer to your question, the presence of flow instabilities (vortex streets) next to the cylinder does not indicate whether the flow is laminar or turbulent. However, how the motion evolves further downstream will. If the streets keep growing it is low Reynolds numbers but if they stop growing in size and break down into turbulence it is high Reynolds number.

A model that gives good results (results that make phsically good sense) when applied for a particular type of problem should be acceptable and can be trusted. Peter Bradshaw is a teacher of turbulence fluid dynamics. His main concern is to teach his advanced graduate students about turbulence but not to turbulent specialists. Once a student is well trained then only he can figure out which model he should use for a particular problem or create his own model to do his research work.

As a newcomer in CFD, I am guessing that the analytical investigation of reduced forms of Navier-Stokes equations is still an active area of research as is the problem of turbulent closure for the Reynolds averaged form of the equations. Different models are created to solve the problem of turbulent closure by applying some kind of advanced mathematical approximation theory that can better approximate the flow of interest to obtain good results. I am curious to know about the model you have decided to apply to solve particularly for nozzle and jet aerodynamics simulations. I have long standing curiosity to know how to solve wild and untamed chemically reacting flows especially for non-equilibrium flow through rocket nozzles. Thank you.

(1). I am interested in this government lab's "Large Eddy simulation capability for nozzle and jet aerodynamics simulation". (2). Could you tell me more about the contents of this capability? What computer systems are you going to use for this Large Eddy simulation work? I mean the size of the problem and the size of the computer.

Forgive me for taking so long to reply.

Altough my direct co-workers and I are just starting LES-related work, and are complete novices, there has been a substantial amount of LES work at NASA Glenn Research Center in the past few years by Ray Hixon, Reda Mankbadi, and their coworkers towards developing LES techniques for jet aeroacoustics problems. They have several recent papers (mainly AIAA papers - see the AIAA J.) describing their work.

In my group, the nozzle branch, we have been responsible for conducting analyses in support of aero. programs such as the (now cancelled) High Speed Research program. Over the past 5 years, we also became directly involved in code development of the NPARC Navier-Stokes code (which is used widely across the U.S.), and purely out of need (not out of experience) we became involved in turbulence model development work for this code. In doing this, we have seen the deficiencies of standard RANS methods for predicting the details of nozzle and jet flows.....this led us to start looking toward LES for such work - our goal is to examine fluid mechanics as a 1st step, however, and not look at the jet acoustics problem - as the previously mentioned Glenn people are. We are currently building a LES based solver and are starting to examine it for baseline nozzle and mixing layer cases. So far, we have run on the NASA "NAS" Cray system, and also on our own 18-processor Power Challenge machine here at Glenn.

I am curious to know about the turbulence scientist who created LES first and where I can obtain more information about the advanced mathematical formulation of LES. Thank you very much for your information.

You can find information of the first steps of the filtering approach of the Navier-Stokes equation in Kampe de Feriet (1957) or in Monin & Yaglom (1971).

However modern (computer-based) LES has been initiated by Smagorinsky and Deardoff.

Concerning the mathematical formulation, look for instance at:

Germano in JFM 238 pp325-336 1990 "Turbulence: the filtering approach"

Ghosal in JCP 118 pp24-37 1995 "The basic equations for the LES of turbulent flows in complex geometry"

Ghosal in JCP 125 pp 187-206 1996 "An analysis of numerical errors in large-eddy simulations of turbulence"

Let us consider the case of aerodymamic breakup of Newtonian and Non-Newtonian fuels in high speed flows under strong shock conditions. As the Mach number of the flow stream increases, the fuel droplets in the flow stream tends to vaporize faster due to the increase in kinetic energy of the droplets. Again, higher the viscosity of the fuel used, less is the chance of the fuel jets to be vaporized. Viscoelastic fuel jets tends to being pulled into thread or rope like structure as Mach number of the flow stream is increased. It seems like that the motivation of the jet simulation is to improve the mixing enhancement of fuel and air to improve fuel economy and meet future stringent emissions goals. On the otherhand, non-equilibrium flows of fluid mixture or partially burned combustible gas mixture through convergent-divergent nozzle reduces thrust and specific impulse. It seems like another goal of this simulation is to optimize the design of the nozzle so that the fluid mixture while flowing through the nozzle will be in equilibrium (control turbulence).