Fluctuations of thermodynamic variables in compressible isotropic turbulence laden with inertial particles

Abstract

The modifications of thermodynamic fluctuations by inertial particles are investigated in decaying compressible isotropic turbulence with an initial turbulent Mach number of 1.2 through direct numerical simulations. The particles interact with turbulence through two-way coupling under the Eulerian–Lagrangian point-source framework. Five simulations with different particle diameters (Stokes numbers) are conducted and compared with the particle-free simulation. The underlying modulation mechanisms are revealed through analyzing the transport equations of thermodynamic variables. The fluctuation features are similar for density, pressure, and temperature in compressible isotropic turbulence. The addition of particles enhances the mean pressure and temperature, and the enhancement becomes more significant with the increment of the Stokes numbers. Nevertheless, the thermodynamic fluctuations are attenuated, and the attenuation is greater for larger particles. Additionally, the thermodynamic fluctuations deviate from isentropic behavior in compressible turbulence, and the deviations are further augmented by the inertial particles. As the particle inertia increases, the departures from isentropic fluctuations gradually increase at small scales, but decrease at large scales. The decay of thermodynamic fluctuations is dominated by the correlation between thermodynamic variables and dilatation. Because of the high inertia, the particles retain their kinetic energy longer than the surrounding fluid and continuously perform positive work on the internal energy of fluid. The mean pressure and pressure-dilatation correlation are thus augmented, resulting in the attenuation of the fluctuations of pressure and other thermodynamic variables.