CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums

Basic Fluid Mechanics and CFD

Register Blogs Members List Search Today's Posts Mark Forums Read

Basic Fluid Mechanics and CFD Anything related to the general theory of fluid flows and their computation
Old

A generalized thermal/dynamic wall function: Part 3

Posted October 17, 2016 at 12:25 by sbaffini (NuTBox)
Updated November 18, 2018 at 06:57 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}...
Attached Files
File Type: txt wallfn.txt (2.2 KB, 532 views)
sbaffini's Avatar
Senior Member
Views 1492 Comments 0 sbaffini is offline Edit Tags
Old

A generalized thermal/dynamic wall function: Part 2

Posted October 17, 2016 at 09:24 by sbaffini (NuTBox)
Updated April 28, 2022 at 08:50 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)...
sbaffini's Avatar
Senior Member
Views 1544 Comments 0 sbaffini is offline Edit Tags
Old

A generalized thermal/dynamic wall function: Part 1

Posted October 14, 2016 at 13:27 by sbaffini (NuTBox)
Updated December 21, 2016 at 10:07 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:
...
sbaffini's Avatar
Senior Member
Views 2134 Comments 0 sbaffini is offline Edit Tags
Old

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

Posted April 17, 2015 at 08:40 by sbaffini (NuTBox)
Updated December 21, 2016 at 10:07 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...
Attached Files
File Type: pdf wallf.pdf (36.5 KB, 515 views)
File Type: txt wallfn.txt (1.2 KB, 383 views)
sbaffini's Avatar
Senior Member
Views 4692 Comments 0 sbaffini is offline Edit Tags
Old

y+ calculator for equilibrium flows

Posted April 10, 2014 at 04:58 by sbaffini (NuTBox)
Updated December 21, 2016 at 10:08 by sbaffini

y+ calculation is, possibly, the most pervasive topic among CFD practitioners and, certainly, anybody doing CFD for more than a month already has his own tool to compute it.

Still, all the y+ calculators i am aware of rely on a very specific flow condition, namely, a flat plate boundary layer. This is probably the most common practical case but not the only option. For example, the fully developed flow in a pipe is cretainly different and possibly requires a different input for the...
Attached Files
File Type: xlsx yplus.xlsx (12.6 KB, 533 views)
sbaffini's Avatar
Senior Member
Views 2545 Comments 2 sbaffini is offline Edit Tags

All times are GMT -4. The time now is 02:16.