CFD Online Discussion Forums - Wall function formulation in CFX and Fluent

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:

$u_{\tau *}$ yields

and yields $u_\tau$

$u_{\tau *}$ and $u_\tau$ yields $\tau_w$

In Fluent on the other hand, a dimensionless velocity

is defined by:

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

is calculated by the expression for $y^*_{Fluent}$ above, which then yields from (eq. 4.12-1)

is used in (eq. 4.12-2) to yield $\tau_w$

I assume that

is equivalent to

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

) 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.