thermal wall function calculation?
I'm trying to understand how exactly Fluent calculates . From the procedure explained in the attached pdf (above Eqn. 4-285), here is what I understand:
1. Pr is determined from fluid conditions.
2. from the procedure, "given the molecular Prandtl number, the thermal sublayer thickness, , is computed from the intersection of the linear and logarithmic profiles, and stored." => does it mean that egality between linear and logarithmic profiles of (4-283) is posed, and this egality is solved for ? i.e.:
solved for (those are the simplified profiles for incompressible flow).
3. the determined from the above egality is the thermal sublayer thickness: . Then, this is compared against the actual value (from turbulence model) and either the linear or logarithmic thermal profile of (4-283) is choosen for the calculation of .
Am I right, is it how is determined? I'm not sure if my step 2. above is right, please correct me if I'm wrong.
You are pretty much correct. Except that you may still be slightly confused on step 2.
Once the thermal properties are known, the egality of is computed and then stored. This means equation the linear and log laws, and solving for the value of at which they intersect. Note that this special intersection is then called . This value is only computed once. The thermal wall functions only needs the value, but it needs a way of determining which law to use.
During the computation, the local is compared to the pre-calculated value to determine which law to use.
The thermal wall functions are identical to the velocity wall functions. However, for the velocity functions we know beforehand the intersection of the linear and log regions since these are independent of fluid properties. The thermal law of the wall instead can only be computed after all thermal boundary conditions have been applied.
About step 2, I'm still under the impression that in order to find where the 2 profiles intersect, a clever way is to equate their equations. What am I missing? Fluent equates the profiles and performs some iteration process (like narrowing the right value starting with a low and high value...)?
Correct, computed only once. In other words, it is not recomputed on subsequent iterations. This computation is probably done during the initialization step.
You must equate the equations,that is the only way to do it, I would not describe that as a clever equating. I imagine Fluent calculates it by some iterative process like you described, but ignoring the details of how it is calculated, it is a simple find the intersection of two curves problem.
Pretty much any algorithm will work. Bisection works. Fixed-point iteration and Newton-Raphson are also guaranteed to work since one of the equation is a line, and that would converge very quickly (Richardson extrapolation can be used to speed up convergence also). I am sure that Fluent has these algorithms pre-packaged in the background somewhere since they are also needed when solving the large systems of equations during the iteration process.
All right, thanks for the clarifications. Case closed.
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