Hi,

I'd like to know how the recomended y-plus value in the first cell close to a wall in the wall functions in a standard Wilcox k-w model varies with the Reynolds number. In the book of Wilcox, y+~80 is given for Reynolds numbers of the order of 1e6. What about Re~1.e9? For the k-e model, different values have been reported, all much larger with increasing Reynolds number (y+ : 500-5000).

Mathias

(1). The matching must be done in the law of the wall log-profile region. (2). The extend of this log-profile region varies from problem to problem. For example, if the boundary layer is under adverse pressure gradient, then then the wake portion of the profile will grow and the log-profile region will shrink. (3). So, in the actual calculation, you will have to do a parametric study to identify the log-profile section of the actual boundary layer solution, so that you know the extend of the log-profile of your problem and can position the matching location (or in your case the first cell, if you are using a FVM)properly in that region.

Thanks for your comments.

Actually, what one would like to know is the edge of the buffer layer, beyond which the wall functions can be applied (where production balances dissipation e.g. y+~30-40 k-e model and y+~80 k-w model for reasonable Reynolds numbers). One could go safe and take a large value, within the log-profile region defined as you sugested, but results varies a lot with the resolution close to the wall and the better resolution the better results. For example using wall functions the friction coefficient is better predicted with decreasing y+ (into the buffer and sub layers) in the first cell even though the wall functions are not valied very close to the wall and you should have used a low-Re model. So, finding the log-profile section helps but the dependence of the Reynolds number (<5.e9) of the edge of the buffer layer remains unknown.

(1).The impression that the wall function tends to produce better results than the low Re model is well known, because of the defect of the modelled epsilon equation. (2). I am saying this, is because back in late 80's, I have run many calculations with my epsilon equation, and the result of my low Re model was consistent with that of my wall function model. Both produced the same wall quantities. (3). It has been a long time since I studied the modeling, so I can't remember everything I did in the modeling. In other words, I don't want to discuss it here. But, I can say that wall function is not more accurate than the low Re model result, if epsilon equation is modelled correctly. (4). I don't have information about the near wall profile change as a function of Reynolds number, therefore, it is hard for me to give you any suggestion on the edge of the buffer layer. I think, the near wall layer including the buffer layer also changes as a function of the pressure gradient. This is because, after flow separation, the near wall region flow will have to move in the reverse direction.

Sorry for not expressing me distinct. I didn't mean that wall functions produce better results than than a low-Re model but higher resolution yields better results - computed only with with wall functions. I'm also not a fan of wall functions (for Re < 5.e7 I don't use wall functions) but for very high Reynolds numbers this is still the 'only' option at least for ship flow calculations including the free surface. I fully agree with you regarding your comments in (4) although experience of flat plate experiments and calculations are often used for more complicated flow situations as a very rough approximation in lack of alternatives.

(1). Yes, that is the engineering part of the analysis. (2). Only the research can improve the understanding of the flow modeling, thus provide some help to the engineering analysis. (3). Fine mesh is all right. Mesh independent solution is even better. But the matching location still must be located in the log-law region. (4). By the way, matching location and the fine mesh are two different things. But, still, if you think that moving the matching location into the buffle zone will improve the accuracy, then your log-law maybe somewhat shifted in your application problem. In other words, you can shift the log-law in the wall function.(assuming that you can do so in the code.)

(2): Yes, only the research can improve...but I don't want to reinvent the vehicle and thus asked if anyone have an analysis or other helpful information of this subject that he/she is prepared to share with me on this message board. (3)-(4): I don't think that moving the matching location into the buffer zone will improve my results. I promtly state that it is not allowed to apply any model e.g. wall functions outside its limits (for instance in the buffer zone). If you do that you are violating the physics and are solving the wrong set of equations or at least an even worse approximation than the original ones. The few computations I know about, where this was done as a numerical test, where nothing but the grid spacing close to the wall was changed, yielded better values for some quantities. There are probably several reasons for this. Maybe one of the most important one is that for very high Reynolds number flows we are still not in the monotonic region of convergence and thus we can not say very much about the results at all. I do not by any means say that the wall functions can be applied in the buffer zone. There are many errors involved, modeling errors, discretisitation errors etc. Apparently, for this case, other errors were lager than the one introduced by using the wall fuctions in the buffer region. I still don't think that you can apply the wall functions outside its limits. Now, when I use wall functions I want to generate a grid so that the wall functions are applied close to the matching location and for that I need to know where it is but I don't. It is probably a function of several variables (pressure gradient as you mentioned before) but at the moment I'll be happy to know it as a function of the Reynolds number (at most I'd like to not use them at all).

(1). Well, I think we are on the common ground. (2). Then, your question is really:"Is the universal law of the wall log-profile a function of Reynolds number? And if it is a function of Reynolds number, what is this relationship?" (3). I don't think that the universal law of the wall log-profile is a function of Reynolds number.

(1). My question is rather: Is the under limit (in wall distance) of the fully turbulent near wall layer a function of the Reynolds number. (2). The assumption that the flow is in local equilibrium has to be met when applying wall functions. (3). I think that the under limit (in wall distance) for which this holds, changes with the Reynolds number.

I personally hate wall function. Why don't you try Goldberg's "wall-distance-free" Low-Re model.

# Goldberg, U., O. Peroomian and S. Chakravarthy (1998), A wall distance-free k-epsilon model with enhanced near-wall treatment, ASME J. Fluid. Eng. vol. 120, pp 457.

I am currently experimenting with it. It very easy to implement. Just try and tell me what happens. Yes, you have to use fine mesh!!!!!!

I think wall function might be a function of Re_t. I may be wrong. If so pl. correct me.

GS

(1). As pointed out in a prior post, I usually don't use wall functions but at the moment our computer resources limit us to use them at very high Reynolds numbers (Re~1.e9-1.e10) in combination with realistic highly complex geometries. (2). I guess I just have to grab a y+ then.

hi Mathias,

Correct me if I am wrong. Isn't the law of the wall derived for the very high Reynolds number limit? I think it will not be valid near (after) the transitional region (say for a flat-plate BL).

The y+ restriction on the first grid node near the wall should be Re independent as mentioned by John Chien. Ofcourse since one does not know u_tau apriori it is not possible to make a grid that will ensure this condition everywhere for cases of interest. Some grid studies have to be performed to find this out for sure.

regards, chidu...

I do not think you are wrong. The log-law is derived to be valied in the fully turbulent near wall region . In this region local equilibrium is assumed and the kinetic energy and its dissipation are set in the first node. Many values for where this region begins (and to where it extends) figures in the literature for the flat plate case, y+ >30, 40, 70...I thougt this spreading might be due to different Reynolds numbers. From the replies here, obviously not. So, I guess my question is a sort of answered. There is no dependence. Thank you all contributers.