Preliminary:

In calculating turbulent flows with the help of k-epsilon model, we calculate wall shear stress from Tau_wall=den * Up * cmu**(1/4)*sqrt (k)*kappa/log (E*ypplus) Where Ypplus=den*cmu**(1/4)*sqrt(k)/yp We use this as a bc for the u momentum equation. Then for calculating depth averaged G term of the k-equation we use G = den*Up/yp And Depth averaged epsilon = cmu**(3/4)*(k)**(3/2) *log (E*ypplus)/(kappa*yp) Finally for giving b. c. for epsilon equation We use Epsilon= cmu**(3/4)*(k)**(3/2) /(kappa*yp)

My question : In my code I got good results with this formulation for flows where there is no recirculatin but for re-circulating flows, where there is a lot of disparity between scales, and you cannot make it sure that all the points lie in the layer where ypplus > 11.63 , this creates problems. Even if I derive all the above relations based on linear profile when ypplus < 11.63 , still I get results which are not perfect . Thus for re-circulating flows, is there any modification required to be done for the above formulation ?

one issue is using the k-ep model for recirculating flow, the other issue is how to address the wall. in the wall region, one has to keep y+ > 11.6 for smooth wall (see schlichting)where there is no presure grad. with k-ep it is advised to keep 200 > y+ > 50 (see for example papers by rodi, nalasamy,others)- remeshing may be required or one may opt for multilayer. perhaps a better proposition is addressing thru cebecci formulation and taking care of the pressure grad if it is present.

I simply want to know that the following formulae that we can derive are applicable to re-circulating flows or not : Tau_wall=den * Up * cmu**(1/4)*sqrt (k)*kappa/log (E*ypplus) Ypplus=den*cmu**(1/4)*sqrt(k)/yp Depth averaged G = den*Up/yp Depth averaged epsilon = cmu**(3/4)*(k)**(3/2) *log (E*ypplus)/(kappa*yp) Epsilon= cmu**(3/4)*(k)**(3/2) /(kappa*yp)

This is because my code works fine with the above formulae when there is no re-circulation but calculates -ve k or epsilon and blows up if it is applied for recirculating case.

Also one more doubt: Irrespective of the kind of flow (attached or recirculating), can we not put (G-den*epsl) = 0 i.e. source term of TKE equation = 0 ? Because anyhow this is the way we derive the boundary value of epsilon !!!!!! Thanks for your interest !

am i correct to understand that when you have parallel flow at/near wall, you don't have problem. you start having problem when there is recirculating flow at/near wall ?

yes u r right. Suppose I have a straight pipe . My code predicts this flow properly. But when I take up the case of flow over an expanding channel , which is similar to the flow over a backward facing step , then the code calculates -ve k or ep .

Now my problem is whether any modification is required in the formulae for wall shear stress, depth averaged G and ep or its just a matter of numerical implementation that I am getting -ve k/epsilon ?

In other words, is the formulation right and implementation need be altered or the formulation itself requires modification ?

If I am making the things complex, then I will want only this thing .

Do you know of any paper in which formulation (including wall boundary) & results of turbulent flow over a backward facing step (with k-epsilon)is available ? Thanking you .

(a) formulation incl wall bdy : suggest you look at "handbook of numerical heat transfer" ed. minkowicsz, et.el. - chapters therein.

(b) results backward facing step : gross results in terms of reattachment available in review papers by rodi/nallasamy/others.

(c) -ve k/ep : if you ref (a), in one chap it is suggested how to avoid it thru proper linearisation.

(d) my suggestion at this stage : take care of (c) and (a). you may have to choose different time steps for momentum and k-ep by applying proper judgement w.r.t scales. also you may have to underrelax your bc for turbulence (see patankar) dpending on the severity of the problem - however this should be the last option because any improper underrelaxation may shadow the lack of robust formulation .

wish you the best.

# I assume that you have not discarded the rotational source terms in your momentum equation.

# since K & E quations are coupled , strong interlinksge should be maintained while solving - they are interdependent.

# because there is recirculation, the continuity eq. needs more emphasis while solving.

Ya I think that I should follow (a) & (c) suggested . Thank you.

sometimes I wonder how really k-ep model can calculate the recirculating turbulent flows. The way wall functions are derived in the k-ep model, they will calculate the flows for which all the points are in the log layer or atleast ypplus > 5 becuase if ypplus < 5 then k-ep has no meaning as that point lie in the laminar region. Now in the case of straight channel flow e.g., we can manage to keep all the points in ypplus > 11.63 , but in case of say flow over a backward facing step, irrespective of the distance of a point from the wall we are bound to get one point where u = 0 and wall shear stress = 0 . From the definition of friction velocity , we get u_tau = 0 and hence ypplus = u_tau*yp/nu = 0 i.e. the point is absolutely in the laminar region from the turbulence model point of view. In this case we should not be solving k-ep equations at all. Thus does this not conclude that k-ep model with standard wall functions cannot solve flows with recirculation !!!!!! But then how people have publised backward facing step results with k-ep . CAN SOMEONE KINDLY EXPLAIN ??????????????? Thanking in advance !!!!!!!!1

may i refer to my posting of 12 nov : one issue is k-ep for recirculating flows. validity of using k-ep for any recirculation even in the bulk (there may be parallel flow at walls) is a question mark. what happens when a submerged jet impinges on a wall ? k-ep ? pressure grad towards wall ? these are the issues. referring to another thread (cfd research), we will want gurus to enlighten us re : present status and thinkings and prospective areas for learning and exploring. quick, dirty, engineering ,etc solutions as of date are : checking, remeshing, etc. little bit cleaner solutions are : cebecci type propositions, mixing length, etc. the clean and scientific solution : ??

The problem is not that the flow is laminar when the friction velocity vanishes it's that the log-law and hence the wall-functions are incorrect. In general the flow near separation, and within the recirculating eddy, will be Reynolds number dependent and highly intermittent. Most turbulence models (including some, if not all, LES) do not handle separation very well because they assume a log-law profile exists between the lowest grid point and the wall and this assumption is incorrect.