Modeling supercritical heat transfer in compressible fluids

•Arbitrary precision analytical solution of the thermodynamic model.•Preconditioned density-based method for hydrodynamic model without acoustic filtering.•Thermodynamic and hydrodynamic model agreement depend on equation of state accuracy.•Classical expression for piston effect relaxation time underestimates simulated time.

Novel solutions have been derived for both thermodynamic and hydrodynamic models of the heat transfer inside a cavity containing supercritical fluid in zero gravity. A fully analytical solution of the thermodynamic model was obtained through a combination of the Generalized Integral Transform Solution and the Matrix Exponential Method. Its accuracy is entirely controlled by a single user prescribed parameter. Furthermore, a low Mach Preconditioned Density-Based Method was employed to generate a numerical solution of the hydrodynamic model, avoiding acoustic filtering and the need to resolve acoustic time scales without it. A proper model for the piston effect evolution in pseudo-time must be included to generate a physically correct description of its physical-time evolution. Furthermore, both models generate graphically identical results, but only upon a thermodynamically consistent selection of fluid properties and equation of state. Finally, the theoretical expression for the piston effect relaxation time underestimates the actual value of this characteristic time estimated from a simulation of the same model used to derive this expression. This feature is not an artifact of boundary condition choice.