What would be the best nonlinear Algebraic Stress model?
 

It is well known that the linear stress-strain rate model for representing the Turbulent stresses via the eddy viscosity concept is not valid under several conditions. For example, linear models do not produce secondary motion due to corners.

The literature is full of several nonlinear Algebraic stress models which vary in their complexities and their efficiencies; however, no one model is known to be accepted by the CFD community (at least to me).

Stress transport models on the other hand have limitations (especially being complex and computationally expensive). So I am not sure if they should be included in this discussion.

What would be the best nonlinear Algebraic Stress model?. I hope your answer is substantiated based on using whatever you suggest or through evidences by other investigations.

One can either adopt an appropriate turbulence model for the type of flow being simulated or a general turbulence model. If the flow is strongly turbulent and curving then Reynolds stress transport model can be appropriate because the production and transport terms are significant in size and handled exactly. A few extra equations isn't much of an overhead these days but it can be more appropriate to move to LES to better capture turbulent diffusion and low frequency instabilities if these are present and significant.

Where turbulence has relatively modest influence on what is of interest then the simplest model that has enough parameters to curve fit to a representative set of flows of interest can be a reasonable thing to do. Problems arise when one has tuned up a set of coefficients for one kind of turbulent flow and then uses the same set for a different kind of turbulent flow and get poor results. If you are not capturing more relevant physics in the way Reynolds stress transport models may then the model will not be a better general model just a better tuned up one for specific flows.

I played around a fair bit with higher order turbulence models in the 80s and broadly concluded Reynolds stress transport models with the simplest turbulent diffusion model that could reasonably match near wall modelling for impinging and boundary layer flows looked worthwhile for a general turbulence model. Never fully sorted out the near wall treatment w.r.t. impinging flows but it may have been doable with more effort. Big complex models for turbulent diffusion in RST models never looked appropriate to me for general engineering use because they were always going to be poor to very poor for some terms in circumstances where they became large enough to be important. In these cases LES seemed the appropriate approach.

For most engineering flows where turbulence has a modest influence on what is being studied 1 or 2 equation turbulence can be made to work reasonably well. Never saw much point to algebraic stress models for general flows because they tend to predict certain flows poorly. They can however be tuned up to predict specific flows better than a general 1 or 2 equation model so can be appropriate in some circumstances. It depends on the type of flow being studied and how reliable turbulence related quantities need to be. There is almost certainly no best general algebraic stress model just ones that are better for specific types of flow.

When it comes to turbulence, I am of the opinion that there is no such thing as best model.

Imagine that you have the best turbulence model (if there is such thing) on paper and when you try to use it, the grid is not perfect and due to descretization errors your result is off now. Then there might be another turbulence model that is on paper not so great but these descretization errors work in such a way that the results are now better.


You would thing it does not happen but this scenario is quite common in practice. One example is turbulence model under predicts but diffusive scheme in momentum makes up for that turbulent viscosity that the model under predicts.

As far as RANS formulation is considered, by definition you can never define a general turbulence model simply because the statistical approach affects the role of the boundary conditions. The formulation assumes a fully developed turbulence, in statistical energy equilibrium. But that is differently in act when you have different geometries, inflow conditions, etc.

Consider simulated a developing channel flow. Take the conditions half way along as input conditions for a half length channel. Would you get the development over the latter half of the original channel flow or something else?

Not sure if you are talking about the temporal or spatially developing flow...
On the other hand, if you are talking about RANS, you are looking for just a steady solution

Taking the profile of the variables at half channel as inflow for the next part could be done provided you consider the correct BCs.

What is the goal of your question?

Illustrating a case where the source and sink of turbulence differ and the boundary conditions follow.

That is somehow similar to the standard case of the channel flow with periodic conditions where the outflow becomes the inflow.

No. Not sure we aren't at cross purposes somewhere. It was meant to illustrate that RANS doesn't assume fully developed turbulence on the boundary.

I don’t agree at all! You prescribe, by definition of RANS, the statistically averaged velocity, density, temperature and so on for all the variable along the boundaries!
You cannot prescribe a laminar profile hoping to see a transition towards fully developed turbulence.

Yes but why does that mean the production of turbulence is in balance with the dissipation of turbulence?

I still suspect we are at cross purposes about something because this would seem to be a basic simulation that has been performed countless times.

Are you referring to the way turbulence is typically kicked off via wall treatments of various kinds? The role of nonlinearity in the length scale related quantity? This could be introduced by diffusion from the wall without assuming equilibrium although typically equilibrium is assumed and the length scale related quantity set accordingly.

Equilibrium between production and dissipation is implied by the assumption that RANS solves only for a steady state. This hypothesis is at a fundamental level of the used equations, not only in the next level of the turbulence model.

To clarify. Are you stating that a steady state RANS models cannot predict a developing boundary layer with, say, a flat profile at the inlet and a fully developed one at the outlet with the appropriate distance in between? Obviously there are zillions of such simulations so are they incorrect in some way at a fundamental level? Or is this not an example of what you are talking about?

Perhaps there is confusion over the quantities that are being produced and dissipated? Or perhaps local vs global balance?

I don't understand what you mean by next level of the turbulence model which might help.

By the way I am not saying you are wrong but that I am baffled.

There is no physical meaning in such a simulation using RANS. The reason is that such a statistical formulation uses models that are not able to vanish automatically when the flow is laminar.
If I am wrong, write an algebric eddy viscosity model and show me that it provides a vanishing contribution for the laminar Poiseulle flow. Since the du/dy is not zero the only way to get a vanishing eddy viscosity would be to get zero for the mixing lenght. Otherwise, RANS cannot clearly work on transition from laminar to turbulent flows.

The title of the PhD in which the k-e turbulence model is first introduced back in 1971 is "Laminarisation in strongly accelerated boundary layers". It discusses how this is handled in the length scale related transport equation. There are better later references on handling low Reynolds number effects (an aspect of the discussion in the PhD is incorrect) but since this is the original reference for the k-e turbulence model it seemed appropriate.

There are a lot of works in the '70th (for example the works of Spalding) that presumed at that time to solve any kind of flow problem using RANS. The path of the researches during the next decades allowed us to provide a rigorous theoretical ground for the statistical apporaches.
The paper you linked used the approximation for the turbulent BL and can be debated nowdays.


From Wilcox textbook:


3.5.1 Channel and Pipe Flow
Like the free shear flow applications of Section 3.3, constant-section channel and pipe flow are excellent building-block cases for testing a turbulence model. Although we have the added complication of a solid boundary, the motion can be described with ordinary differential equations and is therefore easy to analyze mathematically. Also, experimental data are abundant for these flows.
The classical problems of flow in a channel, or duct, and a pipe are the
idealized case of an infinitely long channel or pipe (Figure 3.10). This ap-
proximation is appropriate provided we are not too close to the inlet of the channel/pipe so that the flow has become fully-developed. For turbulent flow in a pipe, flow becomes fully developed approximately 50 pipe diameters downstream of the inlet.

This appears to be the conditions to get fully developed flow in a simple test case. I fail to see what relevance it has to RANS turbulence modelling, equilibrium, laminarisation, transition, or anything beyond the conditions for fully developed flow in a simple test case.

To get back on track post #4 claimed we cannot have a general RANS turbulence. We can but it will normally require at least 2 transport equations for the time and length scale of the turbulent motion since a general model cannot rely on quantities like distance to wall. RANS formulations do not assume fully developed turbulence which is just as well given there are almost no practical flows of interest that involve fully developed flows. This is no different on the boundary as I seem to have failed to illustrate with my example.

Turbulence modelling is a challenging subject with a wide range of interesting edge cases due to the sheer amount of information to be assumed away in the modelling. When someone says something odd it can sometimes lead to something interesting which is why I was asking for the basis for post #4 rather than refuting it.

Ok, we don’t agree about the theoretical foundation of RANS. Again, that has nothing to do with the model but with the statistical meaning of the variable.
I still agree with the statements of Wilcox.

PS: there is no time scale in RANS…

I have hopefully put a red ring round post #4 for future readers and said why. We have wandered off the topic of the thread and I rather doubt the discussion is going to become any more productive if we continue. I am going to stop at this point tempted though I am to question your previous post.

What is not clear is also if you are discussing about RANS or URANS.
But I agree to stop the discussion in this thread.