Wall functions for near wall treatment : k - epsilon model
I am building my own CFD code and I want to use a k-e 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
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 k-epsilon turbulence model on meshless techniques and especially on SPH?
Thanks in advance.
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 log-law.
U_tan = U - U_norm = U - U.n
The validity depends on your geometry. If you would encounter flow separation, consider low-Re k-e models or k-omega models.
Thanks everyone I' ve managed to figure it out.
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.
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