Hello,

I tried to simluate a turbulent boundary-layer separating flow in a curved-wall diffuser to compare the results by using different turbulence models.

The results are quite different. Any one has experience about which kinds of turbulence models can give better results.

Hi, I suppose that it is a question in general. However, I`d like to share my experience here.

Turbulent flows are characterized by fluctuating velocity fields. These fluctuations mixes transported quantities such as momentum, energy, and species concentration, and cause the transported quantities to fluctuate as well. Since these fluctuations can be of small scale and high frequency, they are computationally too expensive to simulate directly in practical engineering calculations.

Instead, the instantaneous governing equations can be time-averaged, ensemble-averaged, or otherwise manipulated to remove the small scales, resulting in a modified set of equations that are computationally less expensive to solve. However, the modified equations contain additional unknown variables, and turbulence models are needed to determine these variables in terms of known quantities.

Commercial softwares offers several choices of turbulence models. It is a fact that no single turbulence model is universally accepted as being superior for all classes of problems. The choice of turbulence model depends on considerations such as the physics encompassed in the flow, the established practice for a specific class of problems, the boundary conditions incorporated in the flow domain, the level of accuracy required, the available computational resources and the amount of time available for the simulation.

To make the most appropriate choice of model for the application, we need to understand the capabilities and limitations of various options available. With the knowledge of these capabilities and limitaions of various turbulence models available the best suitable model can be choosen. For that you may need to check few validations of simulation results with that of available Theoretical calculations.

Thanks and Regards

-mp

Hello Yin,

The two dominant physical influences of streamline curvature and adverse pressure gradient make the simulation of curved diffusers quite challenging for eddy-viscosity based turbulence models. Reasonable results can be gained from a variety of zero-equation, one-equation and two-equation closures. One popular two-equation model is the SST k-omega based turbulence model due to Menter (e.g., 1992, "Eddy Viscosity Transport Models and their Relation to the k-epsilon Model;" 1996, "A Comparison of Some Recent Eddy-Viscosity Turbulence Models"). Such researchers as Bardina et al. (1997, "Turbulence Modeling Validation, Testing, and Development") have shown this model, among others, to provide quite excellent results for adverse pressure gradient flows including separation. Other researchers such as Yaras & Grosvenor (2000, "Numerical Simulations of Diffusing S-Duct and Vortex-Generator-Jet Flows;" 2002, "An Evaluation of Several Low-Re Turbulence Models") have shown that, while the SST closure provides high prediction accuracy for flows including adverse pressure gradient, streamline curvature and separation, somewhat low numerical stability and high sensitivity to grid resolution of this turbulence model make it less than ideal for industrial CFD. All authors listed above have shown the one-equation model of Spalart and Allmaras (1992, "One Equation Turbulence Model for Aerodynamic Flows") to provide very close prediction accuracy to SST for this type of flow. A number of authors, such as Yaras & Grosvenor, identify additional benefits of the Spalart and Allmaras model as being both very stable numerically, and having a substantially lower sensitivity to grid resolution than two-equation models such as those listed herein.

NUMECA offers several choices of turbulence models, from zero- (e.g., Baldwin-Lomax) and one-equation (e.g., Spalart-Allmaras) to two-equation (e.g., k-epsilon). There are, of course, further developments in NUMECA's software from eddy-viscosity closures, such as the DES modeling that has been implemented in FINE/Hexa. However, restricting this conversation to models following the Boussinesq approximation, a general 'rule-of-thumb' based on experience (and trends demonstrated in a variety of open literature) is that zero and one-equation models will often tend to underpredict turbulent mixing in adverse pressure gradient flows, thereby overpredicting the tendency of a diffusing flow to separate and to overpredict the extent of a physical separation bubble. The contrary can often be seen with two-equation models. Such researchers as Hirsch and Khodak (1995, "Application of Different Turbulence Models for Duct Flow Simulation with Reduced and Full Navier-Stokes Equations") have shown certain versions of the k-epsilon two-equation turbulence closure to provide notable prediction accuracy for a diffusing S-duct. Furthermore, the possible advantages of improving prediction for flows with streamline curvature with so-called 'curvature correction' have been demonstrated by the same authors (1995, "Modeling of Complex Internal Flows with Reynolds Stress Algebraic Equation Model") - among many others. However, in general when using a code like FINE/Turbo, we would recommend using the Spalart-Allmaras model. Both the open literature, and our own testing at NUMECA have shown this turbulence closure to provide high prediction accuracy and robustness for diffusing flows with separation.

Fortunately, there exists a significant body of literature related to turbulence modeling for this type of flow. I'd invite you to use some of these papers to draw your own conclusions. Please let me know if you'd like some help finding these references.

Best regards,

Allan Grosvenor, Sales & Marketing Manager - NUMECA USA, Inc.

Hi Allan,

Menter's SST model has been successfully applied to many industrial CFD applications. As you are aware, the implementation of the model will have a great effect on the stability and performance. Is it possible that the low numerical stability revealed in your work with Yaras was due to the implementation and not the model itself?

On that note, does NUMECA have any plans to implement a SST model?

Regards, Guy

Hi Guy,

Thanks for your comments and questions. Please don't take my reply to Yin's question to mean that the SST model cannot be used for industrial CFD. Rather, I believe the answer is that Spalart-Allmaras (S-A) would perhaps be a better candidate – and I listed the reasons why. Rather than concentrating on literature that I have been involved with to address the stability issue, I'll rely on other references such as Hellsten's 1996 report on the Spalart-Allmaras Model ("Implementation of a One-Equation Turbulence Model into the FINFLO Flow Solver," Helsinki University of Technology Laboratory of Aerodynamics, Report No B-49 Series B, ISBN 951-22-3219-7). Conclusions regarding advantages of S-A listed in this report include the following: " – The free-stream boundary condition is trivial. Turbulent viscosity can be set to zero. This improves the ease of use at least for external flow problems. – The present model is somewhat more robust than Menter's SST model. – Transition can be specified in a natural way. – The CPU time requirement per iteration cycle is some 15-20% less than in the case of two equation models. " (Note that at NUMECA we've found the percentage listed in the last bullet to be significantly higher.)

From the second bullet it would seem that Yaras and I were not the first to make the observation regarding numerical stability of the SST model. That being said, you're right in suggesting that improvements can be achieved through implementation – but I've never heard of anyone achieving the same stability as S-A with SST. Likewise, it is well known that S-A is significantly less demanding in the number of grid nodes required, in terms of first node distance from the wall and number of nodes in the boundary layer. If there is documentation that demonstrates methods to remove these shortcomings that I've missed, please let me know.

When asked to suggest a turbulence model to use for curved diffuser flows, and not having prior knowledge that one particular turbulence model has been refined in terms of numerical stability in the given CFD code, I don't think it's unfair to suggest a model that is known to provide an excellent level of prediction accuracy, while being cheaper than alternatives and being notably robust. Such advantages as those listed above, combined with the results shown in the references I mentioned earlier should lead the reader to conclude that S-A can be expected to provide high prediction accuracy, higher robustness and lower computational expense – particularly for the test case described by Yin. The Spalart-Allmaras model has been shown to provide excellent accuracy for other types of flows as well, both internal and external. For instance, it is shown to be an excellent choice for the simulation of turbomachinery flows by Heidegger et al. (1999, NASA/CR-1999-206599 "Follow-on Low Noise Fan Aerodynamic Study, Task 15–Final Report"). This particular report demonstrates, among other things, the low sensitivity of S-A to y+ value.

To answer your question, implementation of SST has been considered by NUMECA, but there is no time frame set in place for this.

Regards, Allan

Hello, every body,

Many thanks for your replies. I have learned a lot from you. My experience was that k-e model uses wall shear velocity as a velocity scale, which is too small in separated region. Several researchers have suggested to use Umax = sqrt[(-uv)max], which may give better results. Any way, I will read the papers you suggested and make my own judgement. I will prepare a paper to show the comparison for a conference. I will let you know the results.

Many thanks!

yin

Hi Allan,

Clearly the advantages of S-A for specifying free-stream boundary conditions are not realized in a diffuser or turbomachinery simulation.

Given that separation is a result of boundary layer instability, it would appear to be necessary to integrate through the boundary layer. It is not terribly difficult to produce the mesh required for this if you are using a structured mesh generator or have a good inflation algorithm.

I agree that there are advantages to running a one equation model in terms of stability and performance, but what you gain there, you will lose in accuracy. Perhaps if separation is not an issue, S-A would be fine.

Langlois and Mokhtarian of Bombardier Aerospace demonstrated this nicely in their paper Validation of a Navier-Stokes Solver for Airfoil High-Lift Analysis, presented at ICAS 2002. They compare S-A to Menter's BSL model (the predecessor to SST) and found that the S-A model completely missed the separation, whereas BSL did a very good job. Considering that Menter's SST model further improves on this by accounting for shear stress transport, among other things, I expect it would do much better.

Anyhow, the question is moot if NUMECA does not include SST (assuming Yin is running NUMECA).

Actually, as far a NUMECA is concerned, how will it handle a separation zone in the first place? Being density based, will you not run into problems where the flow is at such a low velocity?

Regards, Guy

To Guy,

Density based codes are handling separation regions without any problems, as can be seen from the vast literature available. I suggest you go through some well-established journals, e.g. the AIAA journal or the Journal of Computational Physics and/or numerous books and conference proceedings to see countless examples of accurate handling of separation with density based codes.

On the theoretical side, the density based methods have an intrinsic higher level of accuracy than pressure correction methods (PCM) as they take into account the full and real physical coupling of the flow conservation equations, avoiding the unphysical decoupling between convection fluxes and pressure gradients as occurs in the pressure correction formulations. The very solid theoretical base of the density method, in terms of second order schemes with mononicity and TVD properties gives a natural and solid algorithmic base for high accuracy and CPU performance. This is also witnessed by the attempts done in the pressure correction codes to mimic and reproduce some of these properties, through sometimes quite artificial ways. In the same way as PCM based codes have extended their functionalities towards the compressible range, density based codes apply advanced preconditioning techniques to handle incompressible flows. This allows combining the main advantages of the density based methods with the ability to handle, in addition to incompressible fluids, flows having simultaneously regions of high speed and very low speeds.

The NUMECA codes, through this approach, handle very successfully numerous applications, ranging form flows of liquids, molten steel, non-Newtonian fluids. It includes also problems of cavitation, free surfaces in liquids, up to thermocapillary instabilities in liquid bridges, and other stationary or unsteady flow simulations of condensable fluids, such as LH2, freon gases, steam. There are basically no restrictions to the range of applications, as the preconditioning technique allows a "smooth" transition from very low speed to transonic or supersonic conditions, within a strong, rigorous and reliable approach.

With best regards,

Prof. Ch. Hirsch

Prof. Hirch,

Thanks for the thourough response.

Regards, Guy

Hi Guy,

Thanks again for your reply. This is an interesting debate we're having.

1) The main point of quoting Hellsten was to indicate the higher robustness of S-A, and faster solution. The free-stream insensitivity just happened to be at the top of Hellsten's list.

2) Menter himself demonstrates, in the 1996 paper that I listed earlier, the high prediction accuracy of S-A for separated flows in adverse pressure gradient. He uses the classical Driver and Johnston (1990) C.S0 separating adverse pressure gradient flow test case. Both SST and S-A are shown in this paper to predict the separation point and minimum value of Cf essentially identically – so one might question why you would spend more time and computer memory to solve the extra PDE (especially if you are running large simulations)? My answer would be, that you could certainly do this in a research setting - but it is not often practical in industry.

3) Thanks for the Langlois and Mokhtarian reference. I presented at this ICAS conference, so I had the proceedings handy. Dimitri Mavriplis' code, used in this study, is certainly very impressive. The plotted results do not show a massive difference from the SST and S-A predictions, although the SST is shown to capture a small separation bubble with better accuracy. I know of several companies in industry that still use algebraic turbulence models to speed up their design-cycle-analysis. I think any engineer with a real design schedule in front of them would generally accept such a small difference in prediction accuracy in exchange for the added speed and reduction in needed computer resources afforded by S-A. It would certainly be useful for a researcher to run both models if a detailed CFD study was desired though. I saw that solution-adaptive grid refinement was discussed in this paper. This process can become tremendously expensive, and minimizing computational cost has even greater importance in such cases.

4) I've listed several papers in my various messages that all show the Spalart-Allmaras model to provide excellent prediction accuracy for separated adverse pressure gradient flows subjected to streamline curvature (Yin's application). These are all excellent papers, but Menter's 1996 paper does a particularly good job of proving the strengths of S-A for separating adverse pressure gradient flow. With regard to streamline curvature, Rumsey et al. (1999, "Turbulence Model Predictions of Extra-Strain Rate Effects in Strongly-Curved Flows," AIAA Paper 99-0157) provide an excellent reference. The predictions of S-A & SST are shown to be almost identical, and the authors present the greater suitability of an algebraic stress model. Once might conclude from such results that you can either provide acceptable accuracy in many cases (while saving computational expense) using S-A, or if you don't mind higher computational cost you should perhaps bypass two-equation models and try a higher order closure.

5) As for density-based approaches, I think that Professor Hirsch has provided all the detail that could possibly be needed. I'd just like to point out that the code you've based your argument regarding S-A (in the ICAS paper - Dimitri Mavriplis' NSU2D) is a compressible flow solver (it even explicitly says this in that particular paper). If you believe that this code is capable of providing accurate enough prediction for separated flows to evaluate the effectiveness of turbulence models, how could you then question NUMECA's use of density-based approaches?

By the way, I have further information on NUMECA's implementation of the SST model. It has been scheduled for later this year. In the interim, if there are still any doubts regarding the abilities of S-A to predict separated flows, I'd be more than happy to provide appropriate results from NUMECA's public validation database.

In conclusion, industrial CFD studies are demanding on computer resources, and engineers need the answers as quickly as possible. Given the option of the Spalart-Allmaras turbulence model that has been widely demonstrated to provide high prediction accuracy, while being easier to attain convergence with, being less demanding on grid resolution, using less RAM and providing a solution quicker, I cannot see a reason not to use it.

Thanks again for your messages!

Best regards, Allan