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A generalized thermal/dynamic wall function: Part 4

Posted February 7, 2019 at 10:29 by sbaffini (NuTBox)

In previous posts of this series I presented an elaboration of the Musker-Monkewitz analytical wall function that allowed extensions to non equilibrium cases and to thermal (scalar) cases with, in theory, arbitrary Pr/Pr_t (Sc/Sc_t) ratios.

In the meanwhile, I worked on a rationalization and generalization of the framework, derivation of averaged production term for the TKE equation, etc.

While the new material is presented in a substantially different manner and will...
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File Type: txt musker.txt (930 Bytes, 49 views)
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A generalized thermal/dynamic wall function: Part 3

Posted October 17, 2016 at 11:25 by sbaffini (NuTBox)
Updated November 18, 2018 at 05:57 by sbaffini

In this post i summarize the initial problem and the procedure to determine the wall function value (i.e., the solution) for given y^+,F_T^+,Pr and Pr_t.

We looked for a solution T^+\left(y^+,F_T^+,Pr,Pr_t\right) to the problem:

\frac{dT^+}{dy^+}=\frac{Pr\left(1+F_T^+y^+\right)}{\left[1+\left(\frac{Pr}{Pr_t}\right)\left(\frac{\mu_t}{\mu}\right)\right]}

with:

\frac{\mu_t}{\mu}=\frac{\left(ky^+\right)^3}{\left(ky^+\right)^2+\left(ka_0\right)^3-\left(ka_0\right)^2}...
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A generalized thermal/dynamic wall function: Part 2

Posted October 17, 2016 at 08:24 by sbaffini (NuTBox)
Updated December 21, 2016 at 09:07 by sbaffini

In the first part of this post we left with the problem of computing the following integral:

f^+\left(y^+,\frac{Pr}{Pr_t}\right)=\int_0^{y+}{\frac{1}{\left[1+\left(\frac{Pr}{Pr_t}\right)\left(\frac{\mu_t}{\mu}\right)\right]}dz^+}

with:

\frac{\mu_t}{\mu}\left(y^+,a,k\right)=\frac{\left(ky^+\right)^3}{\left(ky^+\right)^2+\left(ka\right)^3-\left(ka\right)^2}

I added all the explicit functional dependencies here because we know f^+\left(y^+,1\right)...
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A generalized thermal/dynamic wall function: Part 1

Posted October 14, 2016 at 12:27 by sbaffini (NuTBox)
Updated December 21, 2016 at 09:07 by sbaffini

In a previous post i wrote about an extension of the Reichardt law of the wall to pressure gradient effects. That was derived by assuming the Reichardt profile as a solution for the case without pressure gradient and using integration by parts. In particular, given the the Reichardt function (k is the Von Karman constant):

f^+\left(y^+\right) = \frac{1}{k}\log\left(1+ky^+\right) +A\left(1-e^{-\frac{y^+}{B}}-\frac{y^+}{B}e^{-\frac{y^+}{C}}\right)

with:
...
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A semi-analytical extension of the Reichardt wall law to pressure gradient effects

Posted April 17, 2015 at 07:40 by sbaffini (NuTBox)
Updated December 21, 2016 at 09:07 by sbaffini

I recently worked on wall functions, especially those based on simplified 1D numerical integration (e.g., http://link.springer.com/chapter/10....-642-14243-7_7) and i found a relatively simple, analytical, formulation that takes into account pressure gradient effects.

In practice, this is an extension of the Reichardt wall law to pressure gradient effects.

It is semi-analytical because it takes as assumption that the base Reichardt law is an exact solution of the...
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