Hybrid modeling of time-dependent rarefied gas expansion

Abstract

The time evolution of the flow parameters in a system where gas is expanded from a high pressure chamber through a tube toward a low pressure chamber is investigated. During the process, the pressure in the two chambers is changing in the opposite direction, while the flow rate is reduced until the system reaches its equilibrium state. Rarefied conditions may be present. Based on the observation that the characteristic time in the chambers is several orders of magnitude larger than that in the tube, the evolution of the flow is modeled in a hybrid manner. At each time step, based on kinetic theory, a steady-state flow configuration is solved to estimate the amount of gas passing through the tube (micromodel) and then the pressure of the two vessels is updated by applying the mass conservation principle and the equation of state (macromodel). The pressure and the flow rate variation with respect to time are provided for several time-dependent configurations and the dependency of the results on the initial Knudsen number and pressure ratio as well as on the length of the tube is analyzed. The proposed methodology, which is applicable when the volume of the chambers is significantly larger than the volume of the tube, is valid in the whole range of the Knudsen number and computationally very efficient.