Mechanical Disturbances Arising from Thermal Power Deposition in a Gas

Abstract

Systematic asymptotic methods are used to formulate a mathematical model for the response of an inert gas to time-resolved, spatially distributed, thermal energy addition. A primary objective is to identify how thermal energy is converted to kinetic energy to predict the distribution of induced fluid motion and the presence of mechanical disturbances. The gas response to heating is found to depend on two independent parameters, one related to the amount of energy deposited into the volume relative to the initial internal energy present there and the other related to the deposition time scale relative to the characteristic acoustic time in the volume. Results are given for relatively fast (slow), high (low) intensity energy deposition into a wide range of volumes to quantify conditions leading to either near constant volume heating or those leading to near constant pressure processes. In each case, the local expansion Mach number is the fundamental source of mechanical disturbances, via the “piston effect.”