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.