Thermo-mechanics: The response of gases to spatially resolved, transient heat addition

The non-dimensional Navier-Stokes equations, including a generic heat source in the energy equation , are used to identify four non-dimensional parameters that can be used to characterize the thermo-mechanical response of the gas to energy deposition; μ, the ratio of the characteristic energy deposition time-scale of the defined source to the characteristic acoustic time-scale of the affected volume of gas; H_R, the ratio of the characteristic heat release relative to the initial internal energy in the affected volume; ε ,representative of a high activation energy Arrhenius reaction; and finally Kn, the local Knudsen number. The parameters are used to identify at least three remarkably diverse physical responses: Nearly constant volume heat addition, Nearly isobaric heat addition, Linear and non-linear wave propagation driven by heat addition. The first is characterized by the pressure rising with temperature and small changes in density and can include “explosive” energy release. The second is characterized by density reduction with rising temperature. Finally, the third describes the physical conditions necessary for traditional linear and non-linear wave propagation in the affected volume of gas, compatible with traditional thermo-acoustic studies.