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July 8, 2009, 05:49 
Wall functions for near wall treatment : k  epsilon model

#1 
Senior Member
Phoevos
Join Date: Mar 2009
Posts: 103
Rep Power: 9 
Hi everyone,
I am building my own CFD code and I want to use a ke turbulence model. So I would like to ask for some more information from people with more experience, on the subject of the wall functions. Form what I have already read, the continuity, momentum, k and epsilon equations are solved only for the nodes/cells away from the walls. On the other hand, nodes which are located near the wall (y_plus less than 300) have prescribed values for velocity, K and e and to be more specific : U_plus= 1/0.41 * ln (y_plus) + 5.1 where U_plus=U_average / U_shear and y_plus=U_shear*perpendicular_distance_from_wall/kinematic_viscosity Also K= U_shear ^ 2 / sqrt (0.09) and epsilon = U_shear ^3 / (0.41* delta ) where delta is an arbitarily set small distance, less than the cell size. So my question is how do you exactly implement these wall functions and especially the log  law ? I mean : I can understand how to find the shear velocity (which on complex geometries has to be calculated as the directional derivative of the velocity towards the normal of the wall) and consequently calculate the y_plus, K and epsilon values. But what about the velocity? I mean that shear velocity is a scalar value, how can I find the three components of the velocity (u,v,w) for the area in which the log  law is valid ? Also something else : Has anyone implemented a kepsilon turbulence model on meshless techniques and especially on SPH? Thanks in advance. 

July 8, 2009, 08:47 

#2 
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M. Nabi
Join Date: Jun 2009
Posts: 44
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you need to find the parallel velocity to the boundary/solid. you need to find the normal vector to the solid, and then the tangent vector can be found. By mapping the celocity to the tangential vector, you can find the tangential component of velocity. It is the velocity that must be used for the loglaw.
U_tan = U  U_norm = U  U.n U_t=norm2(U_tan) 

July 9, 2009, 03:26 

#3 
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N/A
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The validity depends on your geometry. If you would encounter flow separation, consider lowRe ke models or komega models.


July 13, 2009, 01:23 

#4 
Senior Member
Phoevos
Join Date: Mar 2009
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Thanks everyone I' ve managed to figure it out.


April 27, 2011, 07:44 

#5 
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jk
Join Date: Jun 2009
Posts: 64
Rep Power: 9 
Dear Mr Fivos,
I have written a code for laminar flow with colocated grid arrangement. Now i am trying to implement k epsilon turbulence model (high Re) in that. I really dont know where i am going wrong in my code. It is implemented in the following way: Initialising all the variables (utou, tou_w, etc..) for the near wall grid node following source term is added to the u momentum equation ro(k).value * (cmeu ^ 0.25) * (kp(k).value ^ 0.5) * delx / uplus(k).value for the y momentum equation the velocity value (v velocity) is set to zero at the near wall grid node. for the k equation source2 = ro(k).value * (cmeu ^ 0.75) * (kp_old(k).value ^ 0.5) * uplus(k).value * 2 * delx above source term will go into "ap" expression su_ke = (2 * meut(k).value * sij * delx * dely)  (ro(k).value * ep(k).value * delx * dely) + (tou_w(k).value * u1(k).value * (2 * delx)) above source will go as "Su" in the ap_kp equation above two source terms will be added to the near wall node equation for the dissipation equation ep(k).value = (cmeu ^ 0.75 * (kp(k).value ^ 1.5)) / (0.41 * 0.5 * dely) found out directly for the epsilon value at the near grid node. I have a doubt in the source term of my k and epsilon equation especially the production and dissipation terms. I am just using central difference term for finding the Sij terms (vorticity). Please tell me your suggestion so that i can improve my code to run with the kepsilon model. many thanks jyothish 

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