Temperature turbulence spectrum for high-temperature radiating gases

Abstract

The influence of radiation on thermal turbulence spectra is studied theoretically in the case of homogeneous and isotropic turbulence in high-temperature radiating gases. A statistical narrow-band model is used to compute radiative properties of real gases such as CO2 and H2O, and an Onsager-type model is used as closure for the temperature variance spectrum equation. It is found that radiation acts as a dissipative process with a coefficient N(k) smaller than the conductive one ak for small eddies and greater than ak for large eddies. The critical wave number, for which conductive and radiative processes are of the same order of magnitude, is found to be close to k = 100 m for pure H2O or pure CO2 in the temperature range [400 K, 2000 K]. At high temperature and small values of the viscous dissipation rate of turbulent kinetic energy, e, radiation significantly modifies the temperature variance spectrum in the region typically between 10 ~ kd and kd, where kd is the Kolmogorov wave number. The effects of radiation increase with temperature but decrease with e.