Intensification of Turbulence by Chemical Heat Release

Volumetric chemical energy release is studied as a mechanism for enhancing the isotropic turbulent motion of a compressible fluid medium. Both the vortical and dilatational components are examined to determine the influence of irreversible heat addition from exothermic reactions. To a first-order approximation, the density fluctuations caused by eddy production and destruction are shown to be insensitive to the behavior of internal degrees of freedom in the gas (including chemistry). Based on this finding, the pressure fluctuations are determined from a linearized analysis of the combined chemical and gasdynamic response to density fluctuations. The results for amplitudes and phase relationship between pressure and density fluctuations are used to obtain an estimate of the power delivered. The leading contribution to the work integral is of second order in fluctuation amplitudes. A generalized rate model for a highly dissociated gas relaxing toward equilibrium is retained through-out the analysis. Limiting cases are examined by the use of the resulting general expression. The power delivered is proportional (in all cases) to the product of the mean reaction rate and the fourth power of turbulence Mach number (fluctuation velocity divided by local frozen acoustic velocity). For eddy lifetimes shorter than chemical relaxation times, it is shown that the power delivered is essentially independent of frequency.