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 Roued February 1, 2000 16:41

Reynolds Stress Models

Hi, every one

I have a general question about using the Reynolds Stress models (RSM and ASM).

When simulating air flow in ventilated enclosures like a building or a room, the quality of the prediction made by the Reynolds Stress models are poor compared to the two-equations model like k-eps, low-Reynolds k-eps or the low-Reynolds k-omega models. (Comparing velocity profiles, between different turbulence model and experiments).

The flow is in general low-Reynolds (RE approx. 4000-5000). Room has slot inlet and outlet in full width of the room. Low level of turbulence intensity (approx. 4%)

Why does the RSM make such a poor prediction ???

Any hint ???

Only standard parameter are used both in the Reynolds Stress Model and the other two-equations models.

Best Regards

Roued

 John C. Chien February 1, 2000 16:58

Re: Reynolds Stress Models

(1). I just hope that those who are working in this field would make some comments on it. (2). Since I have been working on the k-epsilon side, it is hard for me to say anything useful at all. Professor Brian Launder would be the ideal person to provide some directions here. So, anyone who has any information about this mistry story are encouraged to give us a few words. (3). My theory is: Newton was a very lucky person, because he didn't have to invent the apple or the apple tree. Now it's your turn.

 Thomas P. Abraham February 1, 2000 17:37

Re: Reynolds Stress Models

This is what read in some papers before. This is why people ask the question whether it is really worth solving extra transport equations and getting slightly better solutions than the 2-equation models in a few cases and actually perfom worse in some other cases. So, I can believe what you are experiencing because I have read this before.

This would partly explain why RSTM models are not very popular. One major problem with these models is that a lot of terms are not well understood. Otherwise, you would find many people using it even though it takes much more memory compared to a 2-equation model.

Thanks,

Thomas

 Adrin Gharakhani February 1, 2000 18:10

Re: Reynolds Stress Models

I'm just wondering at such a (relatively) low Reynolds number why you aren't simulating the problem directly - without turbulence models!

Since the inlet and the outlet are along the entire width of the room, assuming the room itself (including furniture, etc.) is symmetric, then you can simplify the problem further by simulating in 2D. 3D effects at such a low Re will not be as significant - definitely, the errors in your turbulence model will overwhelm the errors incurred by ignoring 3D effects.

 Dr. Hrvoje Jasak February 2, 2000 05:21

Re: Reynolds Stress Models

Hi,

Let's first dispose of the idea of DNS: my estimate for a lower bound on the vortex size in a room is something like 1cm. Since I don't feel like discretising the geometry with a mesh fine enough to resolve 1cm vortices, this is out (unless you've got a couple of biiiig parallel boxes to spare...).

Now, we've got this business of k-e vs. RSTM. My rule is usually this: if the flow is swirling (i.e. you can guess that there's a lot of secondary motion or, in maths language, the Reynolds stress tensor is not aligned with the velocity gradient tensor), you need full RSTM. Using any of this quadratic, cubic etc non-linear k-e just won't do. To be precise, quadratic and cubic RSTM can predict the existence of secondary flows, but the magnitude is completely wrong!

If the flow is not swirling, and k-e will do, so why not go for the simplest!

Looking at your particular problem, it seems to me that: a) the Re number is low-ish, b) there's no particular reason for secondary flows c) mesh resolution might play an important role and d) you might have buoyancy effect (is there heating switched on? radiation? what's the temperature of the air coming in; are you solving the energy equation at all?). If you've got buoyancy, I would suggest looking at the modelling of this in k-e and RSTM and seeing if you can recognise some inconsistencies.

Overall, I believe you'd be best off with some sort of low-Re model that does not have distance to the wall (Launder-Sharma), as this should (in principle) also pick up the low-Re effects in the bulk of the flow. Answering to your original question, I see no reason why RSTM should be awful when k-e is behaving well - after all, k-e is a reduction of RSTM modelling and should give the same result!

A while back Jonas (I think) said that it is a perfectly common sense for a turbulence modeller to get dissapointed, cynical etc. and decide to go surfing for the rest of his (her) life instead. I couldn't agree more...

 John Law February 2, 2000 08:32

Re: Reynolds Stress Models

Turbulence modelling is one of the most, if not the most, difficulty area of fluid mechanics - that's why so many people are employed around the world for this research - when one mentions CFD results, people tend to forget that CFD results can only be as good as physical modelling behind it. The RSM model is only better in theory than other models because physically it contains terms accounting for effects of non-isotropy, curvature and extra rate of strain etc. But these terms in the RSM model have to be MODELLED - once this is done, it loses its generality - that's why there are so many forms of RSM model - especially the pressure-strain term. I remember Prof Peter Bradshaw (originally at Imperial College, now at Stanford Uni.) once said that RSM is the most disappointing thing for the modelling community because we put so much hope into it, but tends out to be not as successful.

 John C. Chien February 2, 2000 11:10

Re: Reynolds Stress Models

(1). I like this idea with vision. (2). It's going to take some resources, I guess.

 John C. Chien February 2, 2000 11:14

Re: Reynolds Stress Models

(1). I think you are right. It is not totally hopeless. (2). If somehow one has the access to the code, he can run some parametric study (or numerical modeling and optimization).

 John C. Chien February 2, 2000 11:23

Re: Reynolds Stress Models

(1). So, I think, Peter Bradshaw has been looking for Newton's apple tree. (2). Do you think that it is easier to find a good apple tree in Washington, or maybe in New York? (3). I normally find the apple in the supermarket, not the apple tree. (4). I got the feeling that most people are playing the stokes market games, very few are looking for the real apple tree. So, it is still waiting to be found.

 Luo February 2, 2000 14:16

Re: Reynolds Stress Models

Hi Roued,

Perhaps you can loor for the article by Prof. Chen Qinyan of MIT:

Chen Q., Prediction of Room Air Motion by Reynolds-Stress Models, Building and Environment 31(3), 233-244, 1996

in that article he reported that for the thermal plume flow, RSM works better than k-e model, but in isothermal condition, it doesn't give better results. I don't find the orginal article, just read an abstract, perhaps there are some more explications in the full articles. Or you can email him at qchen@mit.edu.

Hope this can help a little.

 Adrin Gharakhani February 2, 2000 16:41

Re: Reynolds Stress Models

> (2). It's going to take some resources, I guess.

Sure, it's going to take more resources compared to the average code out there. However, (a) for a simple geometry like this (again I'm assuming the room is not cluttered with junk :) ) the resources will not be prohibitive, (b) The resource expenditure is well worth the eradiction of confusion as to what turbulence model to use - especially when turbulence is really not an issue here; i.e., Re=small and we are not trying to study turbulence (as verified by the very fact that models with ad hoc constants are being used).

 Adrin Gharakhani February 2, 2000 16:51

Re: Reynolds Stress Models

> Let's first dispose of the idea of DNS: my estimate for a lower bound on the vortex size in a room is something like 1cm. Since I don't feel like discretising the geometry with a mesh fine enough to resolve 1cm vortices, this is out (unless you've got a couple of biiiig parallel boxes to spare...).

The nature of flow in an enclosure (in a mean sense) is one of large vortical structures - not multiples of small vortices. The only place that really needs good resolution is across the jet "boundary/shear layers) at/near the inlet. In this region, then, adaptive gridding down to the order of 1 cm will not be an issue here - nor a problem in terms of requiring supercomputers.

I can do a 2D DNS of this flow at higher Reynolds numbers than 4000 using a single processor workstation. The full 3D may be possible in a couple years from now (using today's resources)

 John C. Chien February 2, 2000 16:57

Re: Reynolds Stress Models

(1). Well, it's getting closer. The furniture can be included later on. (2). In this case, the geometry is just a rectangular box. And one can start with a small room first.(3). I think, it should be simple enough for the average commercial CFD codes.

 Dr. Hrvoje Jasak February 4, 2000 05:06

Re: Reynolds Stress Models

How many times does this need to be repeated:

The main mechanism for energy transfer between large and small scales is VORTEX STRECHING! This means that a vortex tube gets bent in space and desintegrates into smaller vortices, right? In 2-D this mechanism does NOT exist and the energy transfer in 2-D turbulence goes the other way: small vortices merge and create a big one which is then stable for a long period of time. If you don't trust me, you can look at the weather forecast (atmospherical vortices are approximately 2-D: 10ish km thick and about 150km diameter!): these big things that spin around and carry clouds are what happens in 2-D turbulence.

If you want to simulate a room (or any other flow that people other than meteorologists call turbulent) you NEED 3D. So, I don'y care what you waste your computer resources on, but you cannot pretend for half a minute that you're doing DNS in 2D!!!!! Books are good things, maybe you should try one from time to time - I would recommend Tennekes and Lumley: A First Course in Turbulence.

Thanks,

Hrv

 Adrin Gharakhani February 4, 2000 15:33

Re: Reynolds Stress Models

It is an interesting coincidence that you'd have to stress vortex stretching (when dealing with turbulence), and the difference between 2D & 3D vorticity dynamics. I _just_ made a presentation to a few scientists at Boeing _yesterday_ about vortex methods, and why if you want to capture the essence of turbulence (and the so-called 3D effects that everyone blames their 2D results for when they are no good) you have to look into and resolve 3D vorticity dynamics.

For someone who has spent over 10 years concentrating on the development of 3D vortex methods, I certainly understand and appreciate the importance of vorticity stretch. All you have to do (on the surface) is to look at the vorticity transport equations to recognize that unlike the velocity-pressure formulation the 2D vorticity equation is different from its 3D counterpart by a vorticity stretch.

Having said all that, I'd like to make the comment that vorticity stretch is not as severe for low Reynolds numbers, and especially when the geometry/flow is 2D. (I know about streamwise vortices even for flow over a 2D cylinder ... ).

Yet for all practical purposes for the problem at hand you will be able to capture the large vortical structures using a 2D simulation. You will end up having more clustured structures than in 3D (no stretch mechanism for energy transfer), but I'm still willing to bet that this "DNS" simulation will be just as (if not more) accurate, and will require NO empirical constants to "cheat" your way through a solution using the best of turbulence models out there.

If the argument is that you are interested in a solution that is good for engineering purposes, then you'd have a hard time convincing me that at such a low Reynolds number (and for this geometry) ANY turbulence model will be better than a 2D DNS; i.e., you'll get more info out of a model compared to a 2D DNS.

BTW, strictly speaking DNS means Direct Numerical Simulation. It does _not_ say simulation of turbulence! You can do a DNS of laminar flow. DNS means solving the equations at hand directly WITHOUT any empirical constants and models. When I say DNS in 2D, it means I can solve the 2D NS equations without turbulence models - a _perfectly_ valid claim. If the 2D NS equations do not correspond to physical reality, that's irrelevant as far as the meaning of DNS is concernced. If people intend to corrupt the meaning of DNS to exclusively associate it with simulating flow in a 1 mm^3 box that's their business!

 Dr. Hrvoje Jasak February 7, 2000 05:15

Re: Reynolds Stress Models

Thanks for your posting - I think I learned something here.

> Yet for all practical purposes for the problem at hand you > will be able to capture the large vortical structures
> using a 2D simulation.

That's useful - I definitely never heard this before.

> BTW, strictly speaking DNS means Direct Numerical
> Simulation. It does _not_ say simulation of turbulence!
> You can do a DNS of laminar

> flow. DNS means solving the equations at hand directly
> WITHOUT any empirical constants and models. When I say DNS
> in 2D, it means I can solve the 2D NS equations without
> turbulence models - a _perfectly_ valid claim.

Sure; I am perfectly happy to call all laminar solutions to N-S a Direct Numerical Simulation. As for the fact that 2-D DNS gives a better answer than the turbulence model, I need a bit more convincing - have you got any publications (with validation data) I can look up.

Thanks,

Hrv

 John C. Chien February 7, 2000 10:56

Re: Reynolds Stress Models

(1). It seems to me that we are focusing on the 2-D issue by accident. The original proposal for using DNS is in the right direction. (2). It is also hard to call solution to the Navier-Stokes equations laminar solutions ,even without turbulence modeling. It is just solution to N_S equations, that's all. (3). In the laminar flow regime, it is called laminar flow solution. In the turbulent flow regime, it will be turbulent.(even without turbulence models) (4). I have not done any direct simulation. So, I don't have any feeling about the importance of Re number and the effect of 2-D. (5). I think, in some cases, the global motion of the fluid will be 2-D, especially when there is no wall involved. (6). In, most cases, the turbulent fluctuation will be 3-D, but very close to the wall, it will become more toward 2-D side and the normal fluctuation component will become much smaller. (7). I think, it is all right to look into the possibility of getting useful solutions using 2-D equations. It is likely that the usefulness of the solution will be a function of Re and the particular problem involved. (8). Direct simulation of 3-D turbulence using N-S equation without modeling, I think, requires fine meshes. This could be the current limitation of computer hardware. But the future is wide open. Even with 3-D, I don't know whether DNS will always give satisfactory results. (9). So, in addition to the traditional turbulence modeling, we will have DNS approach in the future. Then there is always the experimental approach. Since it is not easy to repeat the DNS results, the only way to convince oneself is to actually carry out the simulation. The same is true with any commercial code. (10). So, I would leave the DNS field completely open. It is all right to use 1-D, 2-D , 2.5-D, or 3-D N_S equations in the simulation. But then the solution has to be validated for a particular problem at hand. (11). The situation is quite similar to the Reynolds stresses model vs k-epsilon model. One would say that Reynolds stresses model is more general, and is the right way to go. But in reality, we are not quite there yet. (12). In this case, it would be a good idea to demonstrate that under this low Re condition, whether the 2-D results are useful at all. This can be done by running both 2-D and 3-D simulation. Then the real problem will be how to actually transfer the DNS results into the conventional turbulence models. Until then, there will be a lot of work waiting to be carried out.

 Adrin Gharakhani February 7, 2000 15:09

Re: Reynolds Stress Models

Since we have digressed from the subject matter (and even my original proposal and its premise) I would like to reiterate myself, so that the more serious reader doesn't start thinking that I have no idea what I'm talking about :))

Point 1: The problem at hand is geometrically symmetric, most importantly the inlet and the outlet are along the entire width of the wall. Again assuming there are no serious (3D) obstacles inside the room, this is the first sign that a 2D simulation may be OK. I would have NEVER recommended a 2D simulation had the inlet and the outlet were, say little square holes. Obviously, the expansion of the incoming jet will give rise to 3D effects in this case, whether we have laminar or turbulent flow.

Point 2: The Reynolds number of the flow is low. I don't know whether we are in the dangerous transition region or not, but most turbulence models due to the underlying assumptions used in the model will have a very hard time to capture the essence of the flow in the room. The best approach is LES or DNS.

Point 3: 3D DNS is quite possibly out of the question now. So LES is the next best option. However, do we really need an LES for this problem? This is a ventilation problem, a field where most people are happy with just one number such as power input, power output, discharge coefficient, etc. So what is the point of getting an "accurate" solution using LES. Then, based on the previous two points and considering that this is an engineering project and not a scientific exercise in the study of turbulence, the 2D DNS will be a perfectly valid option. It will capture all the essential features of the flow quite nicely and with no empirical constants to play with. Of course 2D DNS cannot be 100 percent accurate but it will not be worse than any turbulence models with their inherently inaccurate assumptions of the flow characteristics.

 Adrin Gharakhani February 7, 2000 15:35

Re: Reynolds Stress Models

>Sure; I am perfectly happy to call all laminar solutions to N-S a Direct Numerical Simulation. As for the fact that 2-D DNS gives a better answer than the turbulence model, I need a bit more convincing - have you got any publications (with validation data) I can look up

I tried clarifying my position in a post to J.C. Chien. I would never claim that 2D DNS will _generally_ be more accurate than a 3D statistically based model. I recommended this approach for this particular problem. Please see my post to John.

As for a publication on this claim, unfortunately I don't have my observations to a similar (yet more complicated) problem published. I have emulated experiments of flow in axisymmetric IC engines in the past. This is obviously more complex than the flow in the room, due to the strong jetting effect off of the valve and the harmonic motion of the piston. The Reynolds number for the experiment was about 15000. I ran a case (axisymmetric) with Reynolds number 500, 1000, (and 10,000 for a short time - this was about 10 years ago when parallel computing was not a household commodity)

Sure this is axisymmetric and there is vorticity stretch. However, 3D effects are the result of the tilting of the vorticity vector, etc. So we may still think of this as not quite a 3D simulation. It turned out that even at the lower Reynolds number of 500 the large/primary vortical eddy, as well as the secondary torus about the jet (and below the cylinder top) were captured very well. Simulation results fell within experimental data for EVERY bit of information that was extracted from the experiment. There were no kinetic energy or dissipation information, yet my claim is not that we could capture them, my claim was that we could capture the main features of the flow quite well. In fact, for the same run, another simulation using k-epsilon model (of an unnamed commerical code) did not do as good a job as my LOW Reynolds number simulation.

My claim above is actually even more drastic than my previous claim. For the particular engine problem at hand the Reynolds number appeared to be unimportant (to the first order of accuracy, so to speak). I think I know why, but that's another topic. The issue is that the room problem looks somewhat similar to this engine problem in terms of the anticipated vortical structures.

If this is not convincing, perhaps you can find us a source of funding and we can solve this room problem jointly (and publish our findings) :)