Direct numerical simulation of turbulence modulation by particles in compressible isotropic turbulence

In this paper, a systematic investigation of turbulence modulation by particles and its underlying physical mechanisms in decaying compressible isotropic turbulence is performed by using direct numerical simulations with the Eulerian–Lagrangian point-source approach. Particles interact with turbulence through two-way coupling and the initial turbulent Mach number is 1.2. Five simulations with different particle diameters (or initial Stokes numbers, $St_{0}$ ) are conducted while fixing both their volume fraction and particle densities. The underlying physical mechanisms responsible for turbulence modulation are analysed through investigating the particle motion in the different cases and the transport equations of turbulent kinetic energy, vorticity and dilatation, especially the two-way coupling terms. Our results show that microparticles ( $St_{0}\leqslant 0.5$ ) augment turbulent kinetic energy and the rotational motion of fluid, critical particles ( $St_{0}\approx 1.0$ ) enhance the rotational motion of fluid, and large particles ( $St_{0}\geqslant 5.0$ ) attenuate turbulent kinetic energy and the rotational motion of fluid. The compressibility of the turbulence field is suppressed for all the cases, and the suppression is more significant if the Stokes number of particles is close to 1. The modifications of turbulent kinetic energy, the rotational motion and the compressibility are all related with the particle inertia and distributions, and the suppression of the compressibility is attributed to the preferential concentration and the inertia of particles.