Cavities
Understand how the flow solver computes reference temperatures differently for enclosed cavities and cavities with openings.
Enclosed cavities
In an enclosed cavity, with no communication of pressure level to the outside, Tr is arbitrary: the temperature and velocity fields are independent of reference temperature. The pressure reacts with differing linear variations superimposed on an unchanging field. In effect, different Tr values only create different hydrostatic pressure variations in P*. Tr is selected such that the total buoyancy force summed over the whole domain is zero.
The buoyancy source term is
This code reference temperature is computed internally to minimize the summed effect of the buoyancy term:
where V is the volume of fluid, and the sums are over the whole domain. Substituting this expression for Tr into the equation for the buoyancy source term and then summing the result over the whole domain gives a zero buoyancy force.
Cavities with openings
Consider a simple cavity, open to a large domain at the top and the bottom, and heated from its internal walls. Physically, natural convection results with fluid entering through the bottom and heated fluid leaving through the top.
If Tr is computed from the reference temperature equation for enclosed cavities in a model with cavities open to external fluid domains then, by design, there will be a zero total buoyancy force and with the zero force from the P* pressure boundary conditions there will be no net movement of the fluid through the cavity. Because of this potential problem, the reference temperature for open cavities Tr is taken as the maximum of all the openings temperatures in the enclosure, given by: