Spectra and scaling in chemically reacting compressible isotropic turbulence

Numerical simulations are carried out to study the spectra and statistics in chemically reacting compressible homogeneous isotropic turbulence at turbulent Mach number M-t from 0.1 to 1.0 and at Taylor Reynolds number Re-lambda from 54 to 103 with solenoidal forcing. A single-step irreversible Arrhenius-type chemical reaction is implemented to evaluate the influence of chemical reaction on spectra and flow statistics. It is shown that in the situation of isothermal reactions, both the ratio of compressible kinetic energy to solenoidal kinetic energy K-c/K-s and the ratio of compressible dissipation to solenoidal dissipation epsilon(c)/epsilon(s) exhibit a M(t)( )(4)scaling at low turbulent Mach numbers M-t < 0.4. At M-t >= 0.4, K-c/K-s and epsilon(c)/epsilon(s) exhibit M-t(2) and M-t(5) scaling behaviors, respectively, and the flow is in strong acoustic equilibrium. The spectra of velocity, pressure, density, and temperature are nearly unaffected by the isothermal chemical reaction. In contrast, heat release in exothermal reactions significantly enhances the spectra of velocity and thermodynamic variables in a wide range of length scales. It is found that the spectra of pressure and compressible velocity satisfy the strong acoustic equilibrium relation at M-t from 0.1 to 0.6, indicating that the acoustic mode dominates over the dynamics of compressible velocity and pressure. In the situation of exothermal reactions, K-c/K-s and epsilon(c)/epsilon(s) appear to be independent of turbulent Mach number. The normalized root-mean-square values of pressure, density, and temperature exhibit a M-t(2) scaling in the isothermal reactions and exhibit a M-t scaling in the exothermal reactions.