Hi: I met a problem when I decided to use the wall functions. A project I'm working with needs to calculate the external airfoil aerodynamics(2D.),and I want to use the stantard k-e model accompanying with the wall functions in the near wall region. I got the two-layer and three layer model for wall functions in the Amano's paper("Development of a Turbulence Near Wall Model and its Application to Separated and Reattached Flows" in 1984). However,I don't know how to calculate the turbulence shear stess(¦Ó) in the Log-Law layer and the outer region. In the visous sublayer,it assumes that ¦Ó is zero .However, in the Log-Law layer ,¦Ó is accquired by interpolation of ¦Ón and ¦Ów,where ¦Ón is the turbulence shear stress of the north boundary of the first node,and ¦Ów ,of the wall. And here comes the problem.Can I calculate the turbulence shear stress in the log-law layer through the following relation: ¦Ó=Mut*(§ïUi/§ïxj+§ïUj/xi)? I wonder if those who have the experience of using wall functions would give me a hand. Thanks.

Maybe my question is very easy to most of you,but it has puzzled me for a long time beacuse i am new for CFD. Please help me and give me some suggestions. Thanks a lot!!

I think that u have to iterate there u have the vorticity omega lets say multply it with the laminar coeff of viscosity and get the shear from there calculare the k and epsilon then from the k and the epsilon calculate the turb viscosity and add it to the first equation.Now this time, u multiply the vorticity by the summation of the turbulent and laminar viscosity and get the shear. make a loop for this! I didn't do that when I faced such a problem rather I used the baldwin-lomax there instead and mached with the k-epsolin in the log layer and it was much better and efficient....however, its your choice. I hope I could help....Good luck...Others might have better ideas...look around

I thought of it and I thing that if u're not well in the log layer( which should be the case) u shouldnt even consider the shear with the turbulent viscousity coefficient coz the turb vis is negligible in the sublayer and I think u were confused and made me confused at the begining (in my previous reply)

Hi,Michel: Thanks a lot for your reply and consideration .Maybe I have not expressed my question clealy,so it makes u confused.I will emphasized my question on the two layer model. (1)In Amano's paper I mentioned in the topic message ,the near wall region is divided into two parts:a viscous sublayer region(0<y_plus<11) and an overlap layer(11<y_plus<400).Here the overlap layer is the so-called log-law layer( in the paper it was called the fully turbulent region).In the visous sublayer,the turbluence shear stress is negligible and the paper assumes that ¦Ó=0.However ,in the log-law layer region where the first point is set,the turbulence shear stress can not be neglected and it is assumed to vary linearly.So the ¦Ó in the log law region are expressed as follows:¦Ó=¦Ów+(¦Ón-¦Ów)y/yn.It is a linear formulation,but how to get the ¦Ón? Without ¦Ón the formulation is useless and I am puzzled by ¦Ón.I am not sure if ¦Ón can be acquired from the definition of turbulence shear stress.(2)I must get the expression of ¦Ó in all the two regions,because it is necessary in the calculation of the mean generation and destruction rate in the k and e equations for the first point.For 2D conditions,the generation rate of k can be written as P=¦Ó(§ïU/§ïy+§ïV/x),and for e, it can be expressed as (C1*e*P/k),then the mean generation rate of k and e can be acquired by integration from the wall to yn,where yn is the north boundary fo the first point. When the mean generation and destruction rate in the k and e equations are acquired,the k,e eqution for the first point can be sovled.(3)To include the mean generation and destruction rate into the k and e equations for the first point,it is said that it can reflect the influence of the molecule viscosity in the near wall region. (4)By the way I am also intrested in the hybrid method with B-L model and k-e model you have mentioned before. If I can't solve the problem of wall functions well,maybe I will have a try of that hybrid method. (5)I am not sure if I have expressed it clealy this time,Michel. (6)Expecting your response and thanks a lot lot lot. Maximus

Hi,Michel: Sorry,perhaps I wrote a too long message,so only part of it can be showed here.I do not know if there is a limitation of the message length. I have sent a email to u. Thanks a lot. Maximus

Hi,Michel: Thanks a lot for your reply and consideration .Maybe I have not expressed my question clealy,so it makes u confused.I will emphasized my question on the two layer model. (1)In Amano's paper I mentioned in the topic,the near wall region is divided into two parts:a viscous sublayer region and an overlap layer.Here the overlap layer is the so-called log-law layer( in the paper it was called the fully turbulent region).In the visous sublayer,the turbluence shear stress is negligible and the paper assumes that ¦Ó=0.However ,in the log-law layer region where the first point is set,the turbulence shear stress can not be neglected and it is assumed to vary linearly.So the ¦Ó in the log law region are expressed as follows:¦Ó=¦Ów+(¦Ón-¦Ów)y/yn.It is a linear formulation,but how to get the ¦Ón? Without ¦Ón the formulation is useless and I am puzzled by ¦Ón.I am not sure if ¦Ón can be acquired from the definition of turbulence shear stress.(2)I must get the expression of ¦Ó in all the two regions,because it is necessary in the calculation of the mean generation and destruction rate in the k and e equations for the first point.For 2D conditions,the generation rate of k can be written as P=¦Ó(§ïU/§ïy+§ïV/x),and for e, it can be expressed as (C1*e*P/k),then the mean generation rate of k and e can be acquired by integration from the wall to yn,where yn is the north boundary fo the first point. When the mean generation and destruction rate in the k and e equations are acquired,the k,e eqution for the first point can be sovled.(3)To include the mean generation and destruction rate into the k and e equations for the first point,it is said that it can reflect the influence of the molecule viscosity in the near wall region. (4)I am not sure if I have expressed it clealy this time,Michel. (5)By the way I am also intrested in the hybrid method with B-L model and k-e model you have mentioned before. If I can't solve the problem of wall functions,maybe I will have a try of that hybrid method. (6)Expecting your response and thanks a lot lot lot. Maximus

Hi there. Eventhough I've not worked with the Amano model, I used the earlier two-layer model the Chieng-Launder model (Num. Heat Transfer 1980, #3 pp 189-207). First of all you should not expect stellar result from these models, the may give some improvements as compared with standard wall functions however at a price of being less stable. I would rather suggest you to use a low-Reynolds model. Anyhow in the Chieng-Launder the first node is divided into two parts the laminar and the turbulent part. In the laminar part the turbulent viscosity is zero, while in the turbulent part it varies linearly: tau_turb=tau_wall+(tau_north-tau_wall)*y/y_north with tau_wall computed from the log-law: U\sqrt(k_v)\rho/tau_wall=ln(E*y*\sqrt(k_v)/\nu)/kappa E (=5.0) and kappa (=0.23) is changed compared to standard values. k_v is the turbulent kin energy at the edge of the viscous sub-layer. k_v is computed from k/k_v=(y/y_v)**2 and y_v is set from y_v=20\nu/sqrt(k_v), where 20 is the viscous sub-layer Reynolds number which is roughly equal to y+=11, (the buffer-layer where the linear and log-law intersect). Chieng-Launder then perform the integrated production and dissipation term in k-equation and set epsilon in the first node, see the paper or contact me. The values for the north face is given from interpolate values from node 1 and node 2. The turbulent shear stress could only be evaluate using mu_t*dU/dy in regions of small variation of dU/dy and mu_t. In the near wall region such a formulation is only approriate for a low-Reynolds number model, where the variation is well discretized using several cells. Using wall functions the log-law is applied instead. The formulation is ok in the log-law (y+>30).

Best of luck.. Jonas