Spectral analysis of turbulence in anisothermal channel flows

In very anisothermal turbulent flows, the temperature gradient and turbulence are strongly coupled. The impact of the temperature gradient on turbulent kinetic energy (TKE) balance terms is of particular importance. It is investigated using direct numerical simulations and large eddy simulations of a fully developed anisothermal channel flow. A low Mach flow at two turbulent Reynolds number (180 and 395) is considered. The temperatures of the two channel walls are 293 K and 586 K. Comparison with isothermal channel flows are carried out. The turbulent kinetic energy spectral evolution equation is established and is decomposed into the three distinctive mechanisms: production, nonlinear transfer and viscous effects. The decomposition isolates the terms that vanish in the isothermal case, namely purely anisothermal effects. The behavior of each term is first discussed in the isothermal case. The alteration of the TKE balance terms with the temperature gradient is then analysed relatively to the Reynolds number variation. The thermal gradient effect is characterized by the combined effect of local Reynolds number variation and the complex interaction between temperature and turbulence. The purely anisothermal contribution moves the energy from the hot side to the cold side and accounts for near 10% of the total process.