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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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File Type: txt wallfn.txt (2.2 KB, 536 views)
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A generalized thermal/dynamic wall function: Part 2

Posted October 17, 2016 at 08:24 by sbaffini (NuTBox)
Updated April 28, 2022 at 07:50 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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