I'm simulating the flow in the diffuser of the impeller of a radial compressor with the NUMECA/Fine Turbo solver. I'm using the Baldwin-Lomax tubulence model. Has anybody some experiece with this turbulence model combined with this flow solver? If yes, can You tell me, for which range of the law-of-the-wall coordinate y+ at the first node from the wall You obtain acceptable results concerning total pressure losses? The manual gives ranges for k-epsilon models but none for Baldwin-Lomax.

Thank You for Your help!

(1). You must study turbulence modeling before attempt to solve turbulent flows. (2). Please do yourself a favor and read the book such as "Turbulence Modeling For CFD" by David C. Wilcox, or the like. It is on pages 76 through 79. (3).Running a code without basic training is like suicide. As a matter of fact, Baldwin-Lomax model is not suitable for flow with strong adverse pressure or flow separations, which exist in pump or compressor flows. It also does not use wall function treatment. (4). Good Grief! I hope the world is not collapsing.

Dear M. Beretta,

The Baldwin-Lomax model is indeed an algebraic 0-equation model and since it does not include any wall function, it can be seen as belonging to the family of the low-Reynolds number models.

This means that to get accurate loss predictions at the walls using FINE/Turbo, you have to use a mesh density at the walls which is sufficiently fine to well capture all the layers of a typical turbulent boundary layer. You can ensure that this objective is reached by checking the dimensionless parameter y+. It is related to the stresses exerted at the walls and can therefore be accessed through FINE/Turbo after calculation. Its value at the first cell near the wall should be close to 1 and certainly less than 5. Also, you should have enough points in the whole layer to have a nice description of the flow behavior.

We are using this model as our default turbulence model for all turbomachinery applications. Although some literature indicates that it might not be adapted to some classes of flows, we succeeded to get accurate predictions of turbomachinery performances (with comparison with experimental data on complex configurations) in a very large number of applications including radial compressors, providing some classical rules in particular related to the mesh are respected. I therefore agree that k-e models can give midly better predictions in a certain number of configurations but this is certainly not a generality.

I woud be pleased to discuss this point further with you. Please do not hesitate to contact us directly for any support or request you may require for your specific calculations

Best regards

Dr Frederic Wilquem Consulting & Support Manager, NUMECA Int.

Dear Mr Wilquem

I've spoken to Mr Hildebrandt at NUMECA's office in Germany. He gave me the same recommandation on the range of the y+-values (1..5). He also gave me a hint to a formula that gives an idea of the optimal distance of the first gridline from the wall based on Reynolds number, a characteristic length and the disired y+ value. I'll use these recommandations and will let You know if I obtain more accurate results with my calculations.

Thank You for Your help! A. Beretta

(1). It has long been established that the Baldwin-Lomax algebraic turbulence model is not suitable for flow with strong adverse pressure gradient or flow with separation. (2). Please read the Chapter-3 of David C. Wilcox's book, "Turbulence Modeling for CFD". In the Section 3.8, Range of Applicability, he said "However, neither model (Baldwin-Lomax model and Cebeci-Smith model) is reliable for separated flows. Despite this 'well-known limitation', many incautious researchers have applied the Baldwin-Lomax model to 'extraordinarily complex flows' where its only virtue is that it doesn't cause the computation to blow up." (3). This is exactly what I have just said in another message that the two main issues in CFD are: (a). convergence, and (b). turbulence modelling. When the two are combined, you have a very difficult problem of convergence in turbulence flow calculation. (4). So, the poor turbulence model is used to obtain converged solution, which in turn will cast uncertainty on the design. And the rest of the effect will be history. (5). I think, anyone who is dealing with turbulent flow in CFD should have a copy of David C. Wilcox's book, "Turbulence Modeling for CFD". This includes the project managers in CFD. I hope that someone is reading this message and understand the importance of it.. (6). I agree with David's statement, and I also have used codes in turbomachinery using Baldwin-Lomax model. And I am sure that at this time, codes in turbomachinery are being developed using the Baldwin-Lomax model. This is exactly the reason why the product designed this way using such poor model will eventually fail.(for lack of experimental validation, I guess) At some point, the company will not be able to run the test to validate the CFD solution, in order to reduce the costs. It is then not difficult to understand why the creative new design fails.

Yes John is correct. The Baldwin Lomax model (or most other 0 eqtn models, I'd say any except my English teacher told me to avoid absolute statements) does not do a good job of simulating separated flows as you'd expect in your situation. it's was developed for streamlined flows. Supposedly your better choice would be a differential model (k-eps, k-omega etc), but you need a lot of skill to use these for three dimensional flows. I have heard of people sucessfully using B-L for turbomachinery but that was for axial flow machines where the above assumption is more appropriate. B-L is not what you want to use for your situation despite the "success" Numeca has had with it.

I completely agree with John and Clifford here. One has to be very careful to the claims of success when the physical modelling is not right. The CFD has too major errors - error from numerical discretisation and error from physical modelling. Even one reaches ZERO numerical error, it still does not mean the result is right - the CFD result can at best be as good as equations used behind it.

"The Baldwin-Lomax model is indeed an algebraic 0-equation model and since it does not include any wall function, it can be seen as belonging to

the family of the low-Reynolds number models."

I'm here quoting Mr. Wilquem who works for Numeca. It seems strange to me that a company like Numeca that seems to havea great deal of knowledge of turbomachinery would make such statements.

It was my impression from reading Baldwin and Lomax's original paper that this model was for high Re flows. I was not under the impression that models without wall functions are by default low Re models. In addition the Baldwin Lomax does have some Wall function-like characteristics so the statement is incorrect anyway.

I've not had the opportunity to read Mr. Wilcox's book but I have attended a presentation by him where the topic was the suitability of different turbulence models for various types of calculation. Of course he gave the same conclusion as he did in his book: zero equation models are not for separated flow. (I'm not convinced that the k-e model is much better).

The Baldwin Lomax model is a great model: it's dominance in the zero equation model world is evidence of that. However users should be aware of its (or any other model's) strengths and weakness. Indeed one of the main strengths of the model is that it is easy to figure out when it can or cannot be used.

(1). An algebraic turbulence model does not solve a model equation, and thus it is called zero-equation model. (2). In the two-equation model, there are two model governing equations to be solved. Depending upon the assumption used, there are two versions of these equations. The low Reynolds number version of the governing equations(the k- and epsilon- equations) has extra terms and additional coefficient functions. (3). So, the high Reynolds number version and the low Reynolds number version are related to the different versions of the governing equations. (4). If a high Reynolds number version of the two equation model is used for wall flow, then it is necessary to use wall function treatment, otherwise, the model alone is good enough. On the other hand, the low Reynolds number version of the modelled equation (k- and epsilon-equations) can be used for flows with or without walls.

Eh, the Baldwin-Lomax model uses the Prandtl-van Driest formula in the inner parts of the boundary layers, hence it is valid in the low-Re region. Most implementations of the Baldwin-Lomax models are also low-Re implementations, meaning that the model is meant to be used through the boundary-layers down to the walls, without any wall-functions. In other words - Numeca's statement seems correct!

The Baldwin-Lomax model is suitable for high-speed flows with thin boundary-layers, typically present in aerospace applications. These flows are often also called high-Re flows. Perhaps this is what you mean with that the Balwin-Lomax model is for high-Re flows? However, this notation of course has nothing to do with the resolution of the boundary-layer grid and the fact that most implementations of the Baldwin-Lomax model should have a low-Re grid close to the wall.

In the original paper (AIAA 78-257) Baldwin and Lomax states that all presented simulations were made with a y+ below 2 for the cell closest to the wall - clearly in the low-Re region. They also mention the possibility of using their model in conjuction with wall-functions, but present a few results that show that this doesn't work as well as using it as a low-Re model.

I would also like to say that I agree with Numeca - the Baldwin-Lomax model is a very useful model that can give good results for most turbomachinery-applications. People who say that 2-eq models in general are more suitable for turbomachinery-applications clearly haven't done a lot of validations using std k-eps etc. in turbomachinery applications. To get a 2-eq model to behave well in a complex turbomachinery-simulations isn't easy. Baldwin-Lomax isn't exactly state-of-the-art, but it seldom behaves completely wrong.

It has to be understood that all turbulence models become doubtful in largely separated regions, while most of them, including algebraic models, give adequate results in attached flows. With regard to turbomachinery applications, it appears that the sensitivity of performance predictions to the turbulence models depends on the dominating physics. In subsonic centrifugal impellers, the choice of the turbulence models, at least around the design conditions, does not appear to have a major effect. On the other hand in transonic axial compressors, where interactions between shocks and boundary layers, as well as between shocks and tip clearance vortex have a strong effect, the predictions are more sensitive to turbulence models and two equation models may be more accurate, although algebraic models are also widely used in industry. At off-design conditions however, the question remains widely open, as more work is still required on the physics of turbulence models, in particular with regard to the inclusion of curvature and rotation effects.

(1). Yes, I think, the state of the art of the turbulence modeling is still not capable of predicting the separated flow accurately. (2). In David Wilcox's book, Section 3.6 Separated Flows, he stated "Menter(1992b) applied the Baldwin-Lomax model to an axisymmetric flow with a strong adverse pressure gradient. The experiment was conducted by Driver(1991). Inspection of the skin friction shows that the Baldwin-Lomax model yields a separation bubble nearly twice as long as the experimentally observed bubble. The corresponding rise in pressure over the separation region is 15% to 20% higher than measured. As pointed out by Menter, the Cebeci-Smith model yields similar results." (3). The question I have is: if an application engineer run the code with Baldwin-Lomax model and obtain the reault with flow separation, then based on the Menter's study, it is not possible for the application engineer to know whether the real flow is separated or not. Menter was very lucky because he is using the experimental data performed by Driver, so he was able to spot the poor performance of the Baldwin-Lomax model. But for the application engineer using the model, I don't think he will ever conduct the experiment to see whether his case is actually separated or not. The experiment to verify the flow separation in turbomachinery is very difficult to perform. (4). At the research level, this is just another opportunity to do research. But for the application engineer, what is going to happen to the results with flow separation? and also the subsequent designs in the real product? (I guess, it's his problem, if he is not reading this forum.)

You are quite right with your comments, as the original Baldwin-Lomax model indeed tends to overpredict separation bubbles. However, there are ad-hoc modifications which reduce this effect. For instance, the predictions of separation are quite sensitive to the Cwk coefficient and higher values than the original ones are known to restrict the early separation. Also, the Granville corrections take partly into account adverse pressure gradient effects, which attenuate the original weaknesses. This to mention that the model can be made to work in an efficient and adequate way for practical applications, without forgetting that, like all algebraic models, it contains less physics than two equation models, which in turn contain less physics than full Reynolds stress models. But particularly for separation predictions, much research is still needed to obtain reliable predictions with any turbulence model.