Defining a Thermal Expansion Coefficient Varying with Temperature

I am running a closed system multiphase buoyancy problem in Ansys Fluent where the density of the liquid phase is described by the Boussinesq model. Is it possible to define a thermal expansion coefficient that varies with temperature? This property seems to only allow constant values. This is the case even when a UDF definition is available.

The Boussinesq model is the only variable density model that treats density as a constant in the equations. (The second term in the equation below is implemented as a momentum source term.)

rho(T) = rho(To) + [d(rho)/d(T)]@To * (T - To)

The assumption is that rho(T) can be expressed as above at a given reference temperature, To (entered in operating conditions). The corresponding density is rho(To) (entered in materials) and the corresponding thermal expansion coefficient is beta(To).

The derivative in the second term, [d(rho)/d(T)]@To is related to the thermal expansion coefficient by -1*beta(To)*rho(To). The Boussinesq approximation for density is part of a Taylor series expansion, and would theoretically stop making sense if the derivative were taken at arbitrary T instead of prescribed To. To is generally set at the midpoint of the temperature range for the problem. Unless the temperature range is very large, using a single-valued beta at the evaluated at the midpoint is normally quite accurate.

Since the second term, -1*beta(To)*rho(To)* (T - To) is treated as a momentum source term in the Boussinesq model, it would be possible to isolate this and implement your own using a DEFINE_SOURCE UDF.

To do this:
1. Set the material density to constant rho(To).
2. Deactivate gravity so that the effect of the source term on the fluid phase is not duplicated.
3. Define a source term equal to -g*beta(T)*rho(To)* (T - To) using DEFINE_SOURCE.

NOTE:

If the other phase has a slip velocity defined, this will have to be modified with DEFINE_VECTOR_EXCHANGE_PROPERTY UDF to account for the missing effect of gravity.