CFD Online Discussion Forums - Entries for April 23, 2022

Closing on wall functions - part 5: testing scripts

Posted April 23, 2022 at 21:26 by sbaffini (NuTBox)
Updated June 3, 2022 at 08:02 by sbaffini

I provide here a set of MATLAB scripts to test all the claims made in the first 4 parts.

The first group of scripts is actually made of functions, that you are not supposed to directly call or modify:

muskersp.m: returns $\left(\frac{{s_{U,T}^i}^+}{{y^+}^{i+2}}\right)$ , $\left(\frac{{p^i}^+}{{y^+}^{i+2}}\right)$ and ${q^i}^+$ as shown here. It only works for N up to 0 (constant non equilibrium terms) EDIT: There is an apparently innocuous mistake in the limiting behavior of s,

...

Attached Files

wallfunction.zip (14.2 KB, 525 views)

sbaffini

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Closing on wall functions - part 4: a Musker-Monkewitz wall function

Posted April 23, 2022 at 17:53 by sbaffini (NuTBox)
Updated April 26, 2022 at 16:49 by sbaffini

In the Musker-Monkewitz wall function the following assumption is made on the turbulent viscosity profile:

$\frac{\mu_t}{\mu} = \frac{\left(\kappa y^+\right)^3}{\left( \kappa y^+\right)^2+\left(\kappa a \right)^3-\left(\kappa a \right)^2}$

where $\kappa$ is the von Karman constant and

is a constant that specifies the

for which $\frac{\mu_t}{\mu} =1$ but, in practical terms has the same role of

in the standard wall function of the previous post....

sbaffini

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Closing on wall functions - part 3: a standard wall function

Posted April 23, 2022 at 05:41 by sbaffini (NuTBox)
Updated May 15, 2022 at 03:20 by sbaffini

We make the following assumption for the turbulent viscosity ratio:

$\frac{\mu_t}{\mu} = \left\{ \begin{array}{ll} 0 & \text{for } y^+ < y_v^+ \\ \kappa y^+ & \text{for } y^+ \geq y_v^+ \end{array} \right.$

where $\kappa$ is the von Karman constant and

is, for the moment, an unspecified positive parameter. One can then show that the following results:

...

sbaffini

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Closing on wall functions - part 2: the iterative procedure

Posted April 23, 2022 at 05:39 by sbaffini (NuTBox)
Updated May 14, 2022 at 16:30 by sbaffini

The first step in the wall function approach delineated in the first post of this series requires determining $\tau_w$ from

$\tau_w = \frac{\left[\left(U_p - U_w\right) \left(\frac{\mu}{y_p}\right) - y_p\sum_{i=0}^{N}\frac{F_U^i}{i+1}\left(\frac{{s_U^i}^+}{{y^+}^{i+2}}\right)\bigg\rvert_{y_p^+} \right]}{\left(\frac{{s_U^{-1}}^+}{y^+}\right)\bigg\rvert_{y_p^+}}$

with analogous steps also required for the temperature and scalars. If one has a mean to univocally/externally...

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Closing on wall functions - part 1: Problem statement and general solution

Posted April 23, 2022 at 05:36 by sbaffini (NuTBox)
Updated May 14, 2022 at 16:55 by sbaffini

This is the last series of posts on wall functions, where I summarize previous findings and give them a broader context. I won't provide derivations (hopefully I'll have time to put this in a larger note), but just few statements with the proper scripts to test them.

This all started with the aim to solve the following problem:

$\frac{d}{dy}\left[C_p\left(\frac{\mu}{Pr}+\frac{\mu_t}{Pr_t}\right)\frac{dT}{dy}\right]=F_T$

with boundary conditions...

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