perhaps the most idiotic question I ever asked.
people throw around the parameter $y^+$, as if it is the be all and end all of CFD (Computational Fluid Dynamics) parameters and use it as if everyone and their dog know how to calculate it. (Specially in CFD literature)
Now the question,
$u_\tau = (\tau/\rho)^{1/2}$
where $ u_\tau $ = frictional velocity and $\tau$ is wall stress.
also $\tau = \mu*\left(\dfrac{du}{dy}\right)$
$\mu$ = co-efficient of viscosity
$\dfrac{du}{dy}$ = velocity gradient normal to wall (this formula holds near wall)
and
$y^+ = u_\tau \dfrac{y}{\nu}$
where
$\nu = \mu/\rho$
I am totally down with all this (please correct any of the equations if I am wrong).
is there a way to calculate values of $y^+$ before running the simulation? I mean can we get good guess for $u_\tau$? If not what is the point of all this?
OK, maybe we can't reliably, it has to be done after/while simulation runs, again after how many time-steps, should I consider that I am getting overall correct values of $y^+$ (both (min,max) and avg)
openFoam provides such function called yPlusRAS / yPlusLES.
Now if we need to calculate all the values to get $y^+$, what is the point of log law? (What are we modelling exactly? because we calculated $u$ and $du/dy$ anyway)
$$u^+ = (1/\kappa) \ln(y^+) + C^+$$
