User-defined Scalar setup

[bernardombraga]

To set up a user-defined scalar for a turbulent flow in Baram 25.1, the user should specify a laminar coefficient (alphaD) and a turbulent coefficient (alphaDt):
alphaD = 1/Sc
Sc = ν/D
alphaDt = 1/Sct
Sct = νt/Dt
Where Sc is the Schmidt number for the scalar, ν is the kinematic viscosity of the fluid (m²/s), D is the molecular diffusivity of the scalar (m²/s), Sct is the turbulent Schmidt number for the scalar, νt is the turbulent viscosity of the flow (m²/s) and Dt is the turbulent viscosity of the flow (m²/s).

While the coefficients alphaD and alphaDt are required by OpenFOAM, their specification is inconvenient for the user. As a new feature, Baram could allow the user to entry alternatively with the molecular diffusivity (D) and the turbulent Schmidt number (Sct). In this case, Baram would calculate internally alphaD and alphaDt to fill the OpenFOAM dictionary.

[kdg5424]

Hello @bernardombraga. This is Donggyu.

We consider Schmidt number in species model.
Why don't you use it?
Is there any reason you should use User-defined Scalar?

Best Regards

Donggyu Kim

[bernardombraga]

Hello Donggyu!

The species model considers a two-way coupling between fluid flow and species transport. On the other hand, the user-defined scalar is a passive scalar, then one-way coupling is considered in the simulation.

Since the species model is more general, I could use it. However, it may also be more unstable and computationally expensive. The user-defined scalar is well-suitable to simulate tracers (e.g. KCl in water).

[jiban]

Hello, Bernardo.
Thank you for the valuable suggestion.

There will be two input parameters, D(molecular diffusivity) and Sct(Turbulent Schmidt number).
And two parameters required by OpenFOAM, alphaD and alphaDt.

When it comes to alphaDt, I understand that it's just an inverse of Sct.
Yet I'm not sure how I could calculate alphaD from D since ν(kinematic viscosity) is not always guaranteed to be a constant.
Maybe I need to modify solver code.
What do you think about it?

Best regards,
Jake

[bernardombraga]

Hello @jiban,

Exactly, alphaDt is just the inverse of Sct. Sct's advantage is that reference values are reported in the literature.

When I wrote my post, I was considering fluids with constant properties, where ν, D, and alphaD are constants. For an ideal gas, ν and D are not constants, but as a first approximation, alphaD is constant (see below).

According to Bird's book on Transport Phenomena, the dynamic viscosity (μ) of an ideal gas is approximately:

And the diffusivity (D) is approximately:

So, alphaD = ν/D = μ/(ρD) is a constant.

If the solver now only supports alphaD to be constant, it can handle the two cases I mentioned above. For more general cases, the solver would need to be modified.

Best regards,
Bernardo.