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Erich F. June 9, 1999 14:45

Turbulence in Turbomachinery
Anyone have any recommendations on turbulence models for turbomachinery?

What are the basic differences between K-e, K-e Kato-Launder, and K-e RNG for turbomachinery use?

Have heard the k-e turbulence model overpredicts performance, but any advice would be appreciated.

John C. Chien June 9, 1999 16:47

Re: Turbulence in Turbomachinery
(1). Pick one which will give you good convergent solutions. You don't want to spend a lot of time waiting for the solutions to converge. (2). Once you have the converged solution, you can check whether you like it or not. (3). I would predict that most of the time you are not going to be satisfied. If so, you can join the facinating world of turbulence modeling. (4). The difference between turbulence models is similar to that in the world of pizza. It is the source of unlimited creativity. Otherwise, a pizza is a pizza. And a model is just a model. They are all good to try.

AndiMiller June 9, 1999 17:05

Re: Turbulence in Turbomachinery
a really good answer. we made several tests with tet-grids, mesh-density and the turbulence-modells k-e and k-e-rng and a third k-e-modification. the results are: the results changed much more with the mesh-density than with the turbulence-modell (if the "better" modells converged, that is allways the question) one thing I heard but never checked: if you have strongly swirling flows, you "must" take the reynolds-stress-modell (and hope that it converges)

Erich F. June 9, 1999 17:16

Re: Turbulence in Turbomachinery
Thanks John, I like your analogy. I have found in converged solutions a variance in pressure rise from model to model - so where do you sign up for the world of turbulence modeling?:) I would guess, like pizza, no one model has the perfect taste for every problem. I guess the k-e would be pepperoni... just hoping for any advice/papers/books specific to turbomachinery that might help.

John C. Chien June 9, 1999 23:29

Re: Turbulence in Turbomachinery
(1). There is a relatively new book (1996) on turbomachinery . The name of the book is "Fluid Dynamics and Heat Transfer of Turbomachinery", by Budugur Lakshminarayana, a Penn State University Professor, published by John Wiley & Sons, Inc. in 1996. ISBN 0-471-85546-4. (2).It is a good reference book with everything in it, including a good portion of CFD. The reference section is almost 50 pages long. It should be vey handy for anyone involved in turbomachinery. It has a very complete view of turbomachinery CFD. (3).Although the author is not an expert in turbulence modeling, he and students have published many turbomachinery CFD related papers. The book is not cheap, it's about 80 dollars three years ago. (4). The other source is the ASME meeting papers and the ASME/Journal of Turbomachinery. (5). Back to the basic. The difficulties involved in turbomachinery turbulence modeling is that the flow is highly three-dimensional, and transient. For a stator/rotor stage calculation, you are talking about 200x60x60 mesh in order to get good solution. That is 720,000 cells. On a workstation, it will take a week at least to converge, using compressible flow formulation ( it is faster using incompressible pressure-based approach). (6). So, it is very expensive to do any turbulence modeling. Unless you are working in a research lab with super-computer and the money to do the research, the engineering results obtained simply are not good enough to do the parametric study. It is useless to do turbulence modeling when the result is a function of the 3-D mesh and the degree of convergence. ( It is possible in 2-D to do good turbulence modeling, but the result is in general not good for 3-D flows. (7). It is a good idea to keep the turbulence model as simple as possible, so that one can first obtain reliable soultions. Then a slight adjustment to the model can be carried out to fine tune the result. The Baldwin and Lomax model is always a good starting point. (8). the nice thing about the two-equation k-epsilon model is that you don't have to worry about the length scale distribution. But it has its own consistency problem. Beyond this point, it is a research area. It is a good idea to get hold of the book I just mentioned. Have a nice trip to the world of turbulence modeling.

AndiMiller June 10, 1999 01:55

Re: Turbulence in Turbomachinery
What do you calculate with the 720000 cells ? steady ? unsteady ? axial ? radial ? a complete machine ? Greetings from AndiMiller

Jonas Larsson June 10, 1999 03:33

Re: Turbulence in Turbomachinery
A few quick answers:

The k-epsilon Kato-Launder model is the basic k-epsilon model where you in the turbulent energy production term have replaced the square of the strain rate with a product of vorticity and strain rate. This has the effect that turbulent production is reduced or turned off in irrotational flows. In boundary layer flows, the strain rate and vorticity are the same, so there this modification doesn't have any effect (the standard k-epsilon model works quite well in these regions anyway).

Essentially what this Kato-Launder mod. does is that it turns off the turbulence model outside wakes and boundary layers. Often this avoids problems in regions where you have large normal strain (stagnation regions, strongly accelerated regions, shocks, ...). The classical k-epsilon model behaves quite badly in these regions. However, the Kato-Launder modification is an ugly ad-hoc modification. The production term is an exact term that follows directly from the Boussinesq assumption. Instead of modifying the production term the incorrect underlying Bousinesq assumption should be modified, in my opinion. I have used the Kato-Launder model for several turbine blade heat transfer computations. It often gives almost laminar heat-transfer results in the leading edge region and it does not give the correct sensitivity to a realisticly high free-stream turbulence levels. I can image that this model could work quite well as a fix for wings and fans etc. though, where you don't have a lot of turbulence coming in.

The RNG k-epsilon model is a slightly different variant on the standard k-epsilon model. The RNG model is derived in a mathematical framework (Re-Normalization Group theory) and it has a different set of modeling constants. It's form is also different. The most important difference is the that the RNG model has an extra source term in the epsilon equation. This source term increases epsilon in regions with rapid strain and thus also keep down k in these regions. This results in a lower eddy-viscosity compared to the standard k-epsilon model (often something good). The RNG model is also said to be better in handling streamline curvature. Several years ago I tried the classical RNG k-epsilon model in turbine computations. It didn't improve things much and I haven't used it since. This model, originally developed by Yakhot and Orzag, was pushed quite heavily by Fluent a few years ago, but lately they seem to be less optimistic about it. I think that there are better fixes around. I don't understand the RNG derivation though, so I might be partial ;-)

I'd recommend you to take a look at "realizability fixes" and "non-linear" variants of the k-epsilon or k-omega model. These seem to be more general and I've found them to work better. Look for papers by for example Shih, Lumley, Speziale and Durbin. Good luck!

Erich F. June 10, 1999 10:02

Re: Turbulence in Turbomachinery
Thanks all for your input. I wish my graduate school time had been spent with turbulence modeling, but one might consider this more of a lifetime endeavor... I am fortunate to have an SGI Octane R12000 with a gig of ram so those large (500k+) problems are not inconceivable. Have been doing a variety of 2d sliding mesh and 3d MFR problems for almost 4 years mainly using k-e, so I have much to learn. thanks again, erich

John C. Chien June 10, 1999 10:24

Re: Turbulence in Turbomachinery
(1).On a routine calculation basis, a mesh size of 170x40x40 is used for axial turbine stage (including one stator and one rotor ) for steady , 3-D flows using a compressible CFD code ( a design code). The computing time is about 100 hours to 120 hours for 24000 and 30000 iterations to reach convergence ( these numbers are used to ensure convergence). (2). A mesh size larger than this is not practical on the routine calculation basis on the workstation (say three years old) I am using. (3). The secondary flow features can be captured quite nicely with 170x40x40, even though 40x40 is a bare minimum. 80x80 would be a good choice for the cross-stream resolution. The results from a 200x60x60 mesh would be considered good for the combined stage. (4). Baldwin-Lomax model is used in the code. (5). "routine" means " on the daily basis".

MOTI MITTAL June 10, 1999 13:04

Re: Turbulence in Turbomachinery
I suggest using LES for turbulence. It is computationally expensive but will give much better results than K -e.

John C. Chien June 10, 1999 17:17

Re: Turbulence in Turbomachinery
Can you give us a rough number about the number of hours required to do CFD analysis with a LES model?

Joern Beilke June 11, 1999 02:30

Re: Turbulence in Turbomachinery
If you run a complete machine with a k-e type turbulence-model we can assume to have about 500.000 Cells. To run this in a moving mesh analysis it might take more than a week to reach a periodic solution even on a vector supercomputer (e.g. NEC SX4). For LES we need a finer mesh so we start to double the cells in each direction and get 8 times the original mesh size (4 million)

Now a transient calculation will be very funny and might take a year. (Don't forget to decrease the time step size by using a finer mesh)

John C. Chien June 11, 1999 03:01

Re: Turbulence in Turbomachinery
(1). It is probably a good project for the government laboratories with super-computers. This should keep the computer busy all the time. (2). Under such conditions, I think, it is possible to come up with some new data for turbulence modeling. A three-year project could produce some useful results.

Richard Carroni June 11, 1999 04:01

Re: Turbulence in Turbomachinery
I like the pizza analogy... On a more serious note, I have used a variety of turbulence models (k-e, RNG, nonlinear model, RSM) in simulations of strongly swirling pipe flows. Only the RSM model was able to predict the central recirculation bubble. When discussing this issue with a colleague who was investigating highly swirling flows in an annulus (for turbomachinery purposes), he found that the Kato-Launder modified k-e model yielded satisfactory results. This is because the actual flow contained no central recirculation region. In short, I don't think the RSM model is necessary for certain turbomachinery flows.

Hope this is of use.


R.Kurz June 21, 1999 16:59

Re: Turbulence in Turbomachinery
First of all you need to decide what your main goal is: -Accurate prediction of bulk parameters (such as mass flow, efficiency etc): Use the simplest possible turbulence model, or use (works particularly nice in 2-D)a inviscid code coupled with a separate bounadry layer code. -Good qualitative resolution of details: Use a two or three parameter turbulence model.

Perennial problem with all turbulence models:

-Correct Transition from laminar to fully turbulent flow. -Introduction of spurious reynolds stress in the free stream flow, thus creating artificial losses.

M. Rahman June 22, 1999 23:37

Re: Turbulence in Turbomachinery
Yes, Renold's Stress Model is a good model to try.

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