CFD Online Discussion Forums - Typo in alphatWallFunctionFvPatchScalarField.H ?

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Typo in alphatWallFunctionFvPatchScalarField.H ?

Hi does someone know if it is on purpose, that in alphatWallFunctionFvPatchScalarField.H calculation example in the description for alpha over Pr is done with mu instead of nu or is it a typo? It should be alpha=nu/Pr in my understanding.

Code:

The turbulent thermal diffusivity calculated using:



        \f[

            \alpha_t = \frac{\mu_t}{Pr_t}

        \f]

On the other side in the usage part stands the option to specify the field name with nut asn an example.

Code:

Usage

    \table

        Property     | Description             | Required    | Default value

        nut          | turbulence viscosity field name | no  | nut

        Prt          | turbulent Prandtl number | no          | 0.85

    \endtable

In the actual calculation in alphatWallFunctionFvPatchScalarField.C they also use

Code:

operator==(rhow*tnutw/Prt_);

So it seems that they really calculate it that way.

I do not really get it.

Ok there is no typo here they also discussed the topic:

https://www.cfd-online.com/Forums/op...-alphaeff.html

In short:

alpha or alphaeff is something like a energy diffusivity not the "textbook" thermal diffusivity and also not the thermal conductivity. It is the thermal diffusivity multiplied by density, or thermal conductivity divided by the isobaric heat capacity. (In most cases, there are some differences depending the energy you are solving for and or if you have a decoupled heat equation -> incompressible ... I think, feel free to correct me)

$\alpha = \frac{\lambda}{c_p}=\frac{\rho \nu}{Pr}=\rho a$

And the effective value ist the "laminar" value plus the turbulent value.
$\alpha_eff = \alpha_{lam} + \alpha_{turb}$