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

Posted April 23, 2022 at 18:53 by sbaffini (NuTBox)
Updated April 26, 2022 at 17:49 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 a is a constant that specifies the y^+ for which \frac{\mu_t}{\mu} =1 but, in practical terms has the same role of y_v^+ in the standard wall function of the previous post....
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Closing on wall functions - part 3: a standard wall function

Posted April 23, 2022 at 06:41 by sbaffini (NuTBox)
Updated May 15, 2022 at 04:20 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 y_v^+ is, for the moment, an unspecified positive parameter. One can then show that the following results:

...
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Closing on wall functions - part 2: the iterative procedure

Posted April 23, 2022 at 06:39 by sbaffini (NuTBox)
Updated May 14, 2022 at 17:30 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 06:36 by sbaffini (NuTBox)
Updated May 14, 2022 at 17:55 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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A note for CFD developers and the Spalart-Allmaras model

Posted June 12, 2021 at 14:06 by sbaffini (NuTBox)
Updated June 3, 2022 at 07:44 by sbaffini

This is a pretty specific issue which relates to my experience working on wall functions and the Spalart-Allmaras model, but might be useful to others or, more importantly, the users of their code.

If you followed my previous posts here, you know I developed a wall function formulation based on the Musker wall function which, thanks to a math trick, is integrable also for arbitrary Pr/Pr_t (Sc/Sc_t) numbers and also for some forms of non equilibrium terms.

One of the...
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