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Wall function formulation in CFX and Fluent

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Old   May 4, 2010, 11:03
Default Wall function formulation in CFX and Fluent
Reine Granström
Join Date: Apr 2009
Location: Sweden
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Dear all,

I am trying to compare the wall function implementation in CFX and Fluent, and there are a few things I don't understand from reading the documentation. The problem is as follows:

As I understand it, at least in CFX the reason for using the form of nondimensionalized distance and velocity having superscript "*" rather than "+" is due to the law of the wall becoming singular at separation points. The definition of the dimensionless wall distance y* is the same in both codes: y^*_{Fluent}=\frac{\rho C_\mu^{1/4}k_P^{1/2}y_P}{\mu}, y^*_{CFX}=\frac{\rho u_{\tau *} \Delta y}{\mu}. Also, the dissipation \varepsilon is calculated by the same expression in both codes.

First, in CFX the friction velocity u_\tau=\left( \frac{\tau_w}{\rho} \right)^{1/2} is replaced by u_{\tau *}=C_\mu^{1/4}k^{1/2} (eq. 2.222) to get rid of the singularity issue. My interpretation is that the following is then done:
  1. u_{\tau *} yields y^*
  1. U_t and y^* yields u_\tau
  1. u_{\tau *} and u_\tau yields \tau_w

In Fluent on the other hand, a dimensionless velocity U^* is defined by:

U^*=\frac{1}{\kappa} ln \left( Ey* \right), (eq. 4.12-1)
U^*=\frac{U_PC_\mu^{1/4}k_P^{1/2}}{\tau_w/\rho} (eq. 4.12-2)

My guess is that the latter expression is used for the same reason as (eq. 2.222) is used in CFX, i.e. to cope with the singularity issue. My interpretation is that the following is done in Fluent:
  1. y^* is calculated by the expression for y^*_{Fluent} above, which then yields U^* from (eq. 4.12-1)
  1. U^* is used in (eq. 4.12-2) to yield \tau_w

I assume that U^* is equivalent to u^+ in the law of the wall, in the same way as (eq. 2.222) is equivalent to the friction velocity u_\tau.

If the dimensionless velocity in CFX (equivalent to Fluent's U^*) is u^*=\frac{U_t}{u_\tau}=\frac{1}{\kappa}ln (y^*)+C. Then, it seems to me that the wall function implementation differs between the codes. Are they different, or have I misunderstood something?

I appreciate any comments.

Last edited by gravis; May 5, 2010 at 03:07. Reason: Rephrasing and corrections
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