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J Keays. November 15, 2000 08:41

realizable k-epsilon turbulence model.
Hi, I am wondering if the realizable k-epsilon model is isotrpic or non-isotropic? I am modelling a flow with large body forces where the turbulence will be generated in a very non-isotropic manner. I want to know which turbulence models are good (I use this term loosely) for which applications. Any information on places on the web where I can find such information would be appreciated also,

Thanks. J.

Sebastien Perron November 15, 2000 14:10

Re: realizable k-epsilon turbulence model.
You might find some good info in wilcox's book: Wilcox, C.D. Turbuelnce Modeling for CFD.

La Canada, Calif. : DCW Industries , 1993

Thomas P. Abraham November 15, 2000 17:57

Re: realizable k-epsilon turbulence model.
Hello Keays,

You could call Realizable k-epsilon model as an anisotropic model. Like RNG version of the k-e model, it does a better job when anisotropic effects dominate the physics better than the standard k-e model. In that sense, standard k-e model would be an isotropic model.



Abhijit Tilak November 16, 2000 00:41

Re: realizable k-epsilon turbulence model.
hi keays,

The standard k-e (high re-form) is isortopic. if u are solving turbulence problem involving body-forces, (depending on what type of body forces) it is likely that those forces will reflect as source/sink terms in k and e equation. in such cases isotropic models are of no use. u may have to solve for reynolds stresses or use computationally cheap models like EARSM. which will model (rotation and buoyancy) such forces in natural way. let me know what type of body forces u hav. if its rotation and bouyancy i have lot of references that i can pass on to u. i am currently working on this.

Abhijit Aero Engg Dept IIT Bombay

J Keays. November 16, 2000 07:26

Re: realizable k-epsilon turbulence model.
Hi Abhijit,

I am working on a centrifugal pump. Specifically, it is a single bladed pump ( one spiral shaped vane). So the body forces I am speaking about are rotational. I have run a model for various heads and hence I get a certain flow rate and average (I,m running the problem unsteady) torque on the blade over a cycle. I expect the power required by the blade to increase with an increase in flow rate(i.e. reduction in head), however, I am getting a reduction. I don't know why, so I am trying to find out if the turbulence model would have such an effect. thanks for your help, Jack.

sylvain November 17, 2000 05:35

Re: realizable k-epsilon turbulence model.
For the case of rotating flow, most (not to say all) of the usual turbulence models fail to predict the correct behavior for the main flow. In fact, they don't "see" the rotation.

You could find some article about that if you look to publications from Jacquin or Cambon or Godeferd or Mansour or Speziale or Shih or Reynolds in the Journal of Fluid Dynamic and/or Physics of Fluids.

J Keays. November 17, 2000 06:33

Re: realizable k-epsilon turbulence model.
THanks Sylvain,

Does anything think that a turbulence model could give such incorrect results as to reverse the trend of power at the blade versus flow rate? My CFD curve is failing with an increase in Flow rate...whereas the experimental curve increases....would a turbulence model cause such a large discrepency?? Thanks for a ll the advise. Jack.

Frank November 17, 2000 19:04

Re: realizable k-epsilon turbulence model.
k-e is well known to fail when there is a significant amount of streamline curvature. This curvature has two effects, one is to increase the length scale of the turbulence and the other is anisotropy.

To account for anisotropy in an eddy viscosity model would mean using different eddy viscosities for different directions. However, previous work has shown that accounting for this anisotropy is not as important as accounting for the increase in length scale.

To account for the increased length scale it is possible to add a term to the dissipation equation. This term is based on a swirl Richardson number. Check out this paper by Launder:

'The Calculation of Turbulent Boundary Layers on Spinning and Curved Surfaces.' Journal of Fluids Engineering. March 1977 pg 231-239

Abhijit Tilak November 18, 2000 03:33

Re: realizable k-epsilon turbulence model.
hi keays

one thing i would like to know is what is your error margin is it too large? The other thing is are you using moving grids, i mean what is ur frame of reference, since the expression for fluid velocity changes with frame of reference. when i solved a problem of rotating duct my coordinate system was fixed to the duct. Inconsistency in frame of refernece can introduce significant errors. My gut feeling tells me the problem is not with the turbulence model(s) you are using. For basic derivation on non-inertial frames refer "Introduction to Fluid Mechanics" by Fox and McDonald.). I followed their notation and got good matching of my results with others. I hope this helps

andy November 18, 2000 13:38

Re: realizable k-epsilon turbulence model.
Hmm. Surely the most striking effect of strong streamline curvature on turbulence is to strongly enhance or reduce the level of the turbulent fluctuations? Isn't this driven predominantly by the curving of the mean rate of strain field relative to the predominantly convected Reynolds stress field? (other effects such as pressure-strain are almost certainly significant so it is not black and white).

Since a 2 equation eddy viscosity based model is going to rotate the Reynolds stress field along with the mean rate of strain field how can fiddling with the length scale even begin to simulate the physics of whats taking place? Surely the absolute minimum has got to be a model that takes some account of the convection of the stress field relative to the strain field - a 3 equation model?

andy November 18, 2000 13:53

Re: realizable k-epsilon turbulence model.
The possibility exists since the turbulence model can significantly affect the onset of stall which, in turn, is going to significantly affect the work of your blade. However, coarse grids, inappropriate exit boundary treatment, poor moving mesh/static mesh treatment, etc... can all produce even bigger effects. If the flow is well behaved and not stalling I would place the turbulence model low down on the list of possibilities. An easy check to see if the turbulence model might be having a significant influence is simply to repeat the calculation with it turned off.

Frank November 19, 2000 20:59

Re: realizable k-epsilon turbulence model.

I believe that streamline curvature affects turbulent dissipation by influencing the transer of energy from large eddies to smaller ones (thus changing the length scale). By adding a source or sink term to the dissipation equation (depending on the sign of the Richardson number) this effect is accounted for.

Granted a second order closure or some other model (3 equation) may be a better choice than k-e, but the above approach has been shown to give excellent results in the literature. A good place to start a literature review is Launder's 1977 paper.

I think that when it comes to turbulence modeling, the absolute minimum that we must settle for is a model that matches the physics enough to give the correct result in a reasonable amount of time. Unfortunately, RSM models often take too long to run to be of practical use in complex geometries.


andy November 20, 2000 07:23

Re: realizable k-epsilon turbulence model.
Since the larger eddies are going to have longer lives than the smaller ones the energy transfer between them will certainly be affected. But, this still strikes me as more of a consequence than a cause. It is also not a particularly useful one since all that one can draw from it is the need for sources and sinks.

I was not advocating any particular approach other than to point out that a 2 equation eddy viscosity model fails to represent the effects of streamline curvature in a way that is expressible in terms of the Reynolds stresses (i.e. what the turbulence model is used to represent in the momentum equations). This is useful for drawing conclusions about how to fix the problem.

I cannot agree with your claim that k-e plus Richardson Number tuning gives excellent results in swirling flows - far too much important physics is not represented in the model. However, that such a model can probably be "tuned-up" to work well for a limited set of swirling flows I would not dispute. My limited experience with such models for curved flows was not good.

Again, my experience with RST models seems counter to yours. I had few problems using them in complex geometries but had more in simple 2D flows. The problems were mainly to do with the numerics - the absence of all that helpful modelled diffusion in the k-e model. What to do with any caught non-realizable regions was a concern. Their behaviour in swirling flows was physically reasonable (unlike the k-e model) but there was no universally usable set of model coefficients (i.e. strongly swirling flows wanted one set to give good answers and boundary layers another) which is pretty serious deficiency. Further development could probably have evolved a robust and universalish RST model but the will to do so seems to have evaporated during the late 80s and 90s.

clifford bradford November 23, 2000 21:58

Re: realizable k-epsilon turbulence model.
From what I know k-eps or any other two equation eddy viscosity will not do a good job of predicting anisotropic turbulence. after all weren't they developed assuming isotropic turbulence? Personally I don't have much confidence in the RSM models either because many of the model constants are developed from isotropic assumptions. And from the derivtion I couldn't see how they were supposed to give better result by definition. personally the only model I'd have confidence saying I could or couldn't use in a given situation is the Baldwin Lomax model and that's the first thing you need in model.

J keays November 24, 2000 11:20

Re: realizable k-epsilon turbulence model.
Anyone like to enlighten me as to what the ASM model does to allow for the body forces , i.e..aniostropic conditions??...thank you...

Apurva Shukla December 6, 2000 02:57

Re: realizable k-epsilon turbulence model.
Hi Abhijeet,

Can you provide me refrences about EARSM model and other models which can be used with rotation and bouyancy. Also do you have reference on ASM model.

Thanks & Regards Apurva

Abhijit Tilak December 6, 2000 04:27

Re: realizable k-epsilon turbulence model.
hi apurva,

The best place u can look for is prof Lars Davidson's (Chalmers university thermo-fluids department.) web site look for a guy called Jonas Bredberg's phd thesis on internal cooling of turbine blades. u will find most of references there. there is also a paper by Prof Launder (1997)mentioned in his thesis on Cubic Eddy viscosity model for Low Re k-e model(close to EARSM).u can download his phd thesis. It's the best site of a prof that i have visited so far. Hey man!! are u by any chance from IIT Bombay? bcos i read some report by u on gradient calculation some time back.?

I hope This helps

Abhijit Tilak Aero Dept IIT Bombay.

Apurva Shukla December 6, 2000 04:47

Re: realizable k-epsilon turbulence model.

I was from IIT Bombay, M Tech propulsion (1998-2000), under Prof Marathe, presently at Fluent.

Regards Apurva

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