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stephane baralon August 31, 1999 15:35

Wall function in adverse pressure gradients
I run a compressor computation with wall functions ( K-Epsilon ) to model the wall boundary layers. The pressure gradient is significantly adverse and my computation predict separation. My feeling is that wall functions should actually delay the advent of separation when compared to a low-Reynolds formulation of the k-e turbulence model with highly resolved B.L grid. Meaning that a more adverse gradient is necessary to separate a "wall function B.L.". Am I right? I base my reasoning on the fact that the wall friction velocity computed with wall functions would have a tendency to stay strictly positive whilst the separation point is characterized by a wall friction equal to zero. Is That correct ?

I am also wondering about the grid dependency of such computations.I know that for using wall func. , the cell center closest to the wall should be in the log-layer(y+ > 30). Unfortunately, for a same absolute distance, the y+ values of the cell center closest to the walls vary very much around the blade, whether you look at the leading edge , the first half of the chord on the suction side,etc. My question is: if the y+ values locally appears to be around 10, this means that i'm very close to the inner layer. What will be the effect of using a wall function based wall friction velocity for such a y+ value: too large or too low a value? Basically, am I "frictioning" too much ?

Thank you in advance.

John C. Chien August 31, 1999 16:18

Re: Wall function in adverse pressure gradients
(1). It is a tough world to live in. (2). I got e-mails asking me to keep answering questions. I also got impression that it is also a good idea for me not to answer any question here. (3). So, I decide to pick a random number, to answer your questions. (4). First of all, don't use your imagination in the turbulence modeling. So far, no one has shown that "his k-epsilon two-equation model and his low Reynolds number version of the k-epsilon two-equation model can produce identical results." (5). So, up to now, these are two independent models. They are not in any way correlated. (6). After having said that, I think there is no need to answer the first part of the question. These two models are not related and therefore can not provide any physical reasoning. (7). This is 1999, and the memory chips are very cheap. The wall function was invented back in 1960's when the computer memory was very small and the core momory was very expensive. There is no sense of using it now.(unless your are the expert.) (8). The flow separation is very common in turbomachinery. The secondary flow is also one of the most important issue. The minimum requirement is that the complete flow field must be covered in the calculation. You can use any of such models, for example, the Boldwin & Lomax model, Rodi's two-layer model, and ideally a low Reynolds number two-equation k-epsilon model (if you can find one which you like. most are fine tuned for particular applications.) (9). About the boundary layer over a 3-D turbomachinery blade, there are many regions with different characteristics. (10). In the mid-span section, the boundary is roughly 2-D (this is still over-simplified), and there are leading edge laminar flow region, transitional flow region and the turbulent flow region. So, it is not just the problem of next to the wall cell size problem. A good place to start is to read the book of boundary layer theory by Schlichting,(McGraw Hill publication). (11). Then next to the hub, there will be 3-D flow separation vortex in the leading edge region of the blade. You can't get that by wall function method. (12). As these vortices move down stream, it will move across the blade passage and eventually ended up on the suction side of the blade. Then it will merge with the wake flow to form the secondary flow. (13). So, think about solving such problems easily is somewhat an over-simplified exercise. It is an entire research field. (14). It is a good idea to read papers in ASME/ Journal of Turbomachinery, where you can get a good feeeling about the mesh density distributions used by other researchers. A 150,000 cells mesh for a blade row (one 3-D blade), is a bare minimum. (highly stretched near the wall, two layer model. For research, this is not adequate. (15). The simplest way to find out whether the mesh is good enough or not, is to plot the surface skin friction coefficient distribution vs mesh density. You should be able to find out the answer quickly. To be an expert, it is very important to go through this exercise to convince yourself first.

Jonas Larsson August 31, 1999 16:35

Re: Wall function in adverse pressure gradients
Stephane is running a 7-stage fan computation using 15 parallel HP J-2240 machines with 2 gigs of memory each ... resolving boundary layers with Low-Re models is out of the question.

Anyone else know if wall-functions in general have a tendency to separate too late or too early in this type of simulations? Is it even possible to say something general like that?

John C. Chien August 31, 1999 16:59

Re: Wall function in adverse pressure gradients
(1). What I have just said is the first-hand information. It is backed by the recent real 3-D calculations. (2). In industries, 3-D inviscid Euler equation is used for multi-stage design calculations. The 3-D viscous Navier-Stokes calculation is used for single row, or one-stage. (3). The need to use Navier-Stokes calculation is to provide viscous 3-D flow behavior for design and loss calculations. So, these have to be very accurate in order to capture the relatively small loss number under various design and off-design conditions. (4). For the multi-stage calculations, the added uncertainty is the mixing plane treatment. The size of the gap between rows can present strong interaction problem when the mixing plane averaging method is used. (5). I can not tell anyone how to run their analysis, I am just sharing my experience with you.

Stephane baralon August 31, 1999 17:00

Re: Wall function in adverse pressure gradients
thank you john for your LONG answer.

I am already experienced in 3D computations of transonic fans single rotors ( 1 blade passage ) using k-omega or k-epsilon (low reynolds type of grid refinement) with, as a minimum requirement, 400000 cells.

However, I should have mentioned that I am running a 7 blade rows fan case with already 1 millions cells. So, I thank the engineers in the 60's for their vision of the future: it is common now ( at least five articles in the latest ASME IGTI conferences) to run big cases for which low Reynolds type grid refinement is almost out of the question for design purposes.

Basically, I am just asking if someone took the time to thoroughly investigate the trends that the use of wall functions gives when facing adverse pressure gradients when compared to experiment or other turbulence models requiring a significantly more refined grid.

Surprisingly, little (to me at least) may be found in the turbulence modelling litterature about wall functions and their behaviour in various flow environment. It is a bit of a pity because running multistage turbomachinery cases with highly refined grids still belongs to a rather distant future.

John C. Chien August 31, 1999 17:29

Re: Wall function in adverse pressure gradients
(1). Sorry, I don't have information about your background, and I try not to store those information. (2). If you are running a true 3-D transient multi-stage calculation, then it is worthwhile to get the answer. (3). If you are using the steady mixing plane method with picth-wise average, then the multi-stage information can be transferred stage-by-stage. And in industries, the need to use multi-stage approach is to save time. (4). I have heard that P&W run multi-stage calculations on the routine basis. Maybe you can look into that area.(using large scale parallel processing on network workstations.) (5). In most cases, 4-processor per job is fairly common when running commercial CFD codes, currently. (6).The need to use the low Reynolds number model was identified and developed in early 70's. So, there is no need to justify it again. (7). You have a bigger problem to solve, because the compressor by nature does not like the flow separations. (8). As for the complexity of the problem and the turbulence modelling, I can only say that in some cases these models are not all published. And it is also very hard to do testing in turbomachinery to get detail data. But I think, the computer hardware limitation will be solved sooner than you think.

andy August 31, 1999 17:43

Re: Wall function in adverse pressure gradients
Why single out the wall functions? Pressure smoothing enhances reciculation (usually). Numerical diffusion will delay separation (and you have doubts there). The epsilon equation (not much real physics there) always used to be heavily slated for everything 10-15 years ago. The turbulent transport = diffusion assumption (on which the 2 equation models are based) breaks down in separations. How are you simulating the effects of the wakes passing down the stage? Etc...

Personally, I am still amazed that a reasonable amount of physics gets captured in complex 3D simulations given the high levels of assumptions in the models and the high levels of numerical error. 7 stages and only 1 million cells does seem to be pushing things a bit though.

Anyway, to partially answer you question. A long time ago, I investigated 5 alternative wall functions for Reynolds stress transport models, including one for adverse pressure gradients (based on the model of Townsend, 1961, JFM). They gave different answers for some flows and pretty much the same answer for others. I would guess that the best source of information for this sort of numerical detail are internal reports and Ph.D. theses from 20 to 30 years ago or, possibly, the manuals of some of the more open CFD companies.

Why are you using the k-e model rather than a more traditional "tuned-up" blading turbulence model?

Finally, as a sweeping statement (to which I do not wish to be held), one would usually expect a k-e turbulence model to delay separation. But...

Sung-Eun Kim August 31, 1999 20:56

Re: Wall function in adverse pressure gradients

It appears to me that the governing equation (turbulence model) is no less a real culprit than the boundary condition (wall functions). Sure, standard k-epsilon with "standard" wall functions (Launder & Spalding, 1974) tends to underpredict or delay separation. But some more recent two-equation models such as k-omega model, realizable k-epsilon, and Reynolds-stress transport models predict the onset and extent of separation remarkably well with the same wall function, as long as boundary layers are reasonably resolved. For the same flows, eschewing wall functions and resolving deep down to viscous sublayer (y+=0.1) using some well-know low-Re models doesn't seem to help much.

I'm the one of those who believe that, for high-Re industrial flows, wall function approach will dominate for quite some time as a practical near-wall treatment. Remember y+=1 roughly correspon to a physical distance of y/D = 10 /Re_D or y/L = 10/Re_L for many internal and external flows. For typical turbomachinery flows (Re_D ~ O(10 Million)), y+=1 translates to at ONE MILLIONTH of hydraulic diameter ! For flows around submarines (Re_L ~ O(Billion)), guess yourselves. To make the matters worse, you have to deal with multiple walls, down, up, sides, back, hubs, shroud, etc.

All this is not to say that all low-Re models are useless. All I'm saying is that not all low-Re models are good enough for the cost, and that, even if there are good low-Re models, using it can be very costly.

Dr. Hrvoje Jasak September 1, 1999 05:16

Re: Wall function in adverse pressure gradients

There is such a thing as "pressure gradient sensitised wall functions" (you really don't have any other option!). If I remember correctly, it is implemented in FLUENT. The only reference I can give you is the FLUENT manual, but I'm sure someone out there remembers the paper...

A word of warning: below y+ = 11.6, the wall function, switches off and you get the wrong wall drag. Thus, when taking account both the modelling error (law of the wall) and discretisation error (if the y+ is too big, you haven't got sufficient resolution), on balance you're better off taking some mesh out and increasing y+ to about 50. Yes, I know that it changes along the chord - just do the best you can and stop worrying about it!

BTW, 7-stage compressor sounds really impressive.

S.-H. Peng September 1, 1999 09:14

Re: Wall function in adverse pressure gradients

read the paper by Han (AIAA J. VOl. 27/9, pp1213-1219, 1987), which could give you some ideas about how the k-epsilon model + wall functions works on the flow past a 3D bluff body with a ground plane.

Just some additional hints to your question: 1). strictly (or academically) speaking, conventional wall-function approach should not be used for separated flow computations, because the wall function itself has been derived from local-equalibrium assumption. 2). k-epsilon model (with wall functions and LRN types) often overpredicts the near-wall turb. length scale (and thus the eddy viscosity) for wall-bounded flow in the presence of adverse pressure gradient, this is why the Yap Correcion is used in this case. 3). the k-omega model does not have the same problem as in the k-epsilon model. If you have to use wall-function approach, try k-omega model in conjunction with wall functions. 4). integrating the wall function down to y+ less than 10 is of course too large. The kinetic energy MIGHT be over-estimated.

Peng, S.-H.

Paulo Zandonade September 2, 1999 01:01

Re: Wall function in adverse pressure gradients
Dr. Jasak,

I believe the original paper on this subject is:

Wilcox, D.C., "Wall Matching, A Rational Alternative to Wall Functions," AIAA Paper 89-611

A short description is given on pg. 127 of Wilcox's book "Turbulence modelling for CFD" (pg. 174 in the second edition)

John C. Chien September 2, 1999 04:05

Re: Wall function in adverse pressure gradients
(1). Some in-house turbomachinery Navier-Stokes can handle a single row calculation overnight, with a Baldwin-Lomax model to cover the whole flow field including the sublayer, since early 90's. It can even handle the tip clearance gap flow correctly. (2). Some commercial turbomachinery codes can handle 2-layer model for a single row in a few hours. These can be used on the routine basis. (3). So, I think, if one look at the industrial problems from a commercial code point of view, then the resources requirement is always many times larger. For example, by running the same mesh size on a commercial, the RAM requirement can easily cost 5 times bigger. A 100 Meg job now requires 500 Meg RAM machine. (4). So, it is very easy for engineers to see why the commercial codes are having very difficult times. This overhead alone can push the commercial code to the sideline and idling. In the long run, I don't think any of the commercial code will be able to make itself to the turbomachinery design. (5). The ever increasing tight design cycle simply can not tolerate such high resources requirement.

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