Investigation and quantification of flow unsteadiness in shock-particle cloud interaction

Abstract

This work aims to study the interaction of a shock wave with a cloud of particles to quantify flow unsteadiness and velocity fluctuations using particle-resolved direct numerical simulation (PR-DNS). Three cases are studied, with each case revealing one aspect of the intricate flow phenomena involved in this interaction. The unsteady interaction of a shock wave with a transverse array of particles reveals the origin of unsteadiness under the effect of mutual wave-wave and wave-wake interactions between the particles. In the second case, the interaction of a shock with a particle cloud is studied, with a focus on the interaction of the complex wave system with the vortical structure. A budget analysis of the vorticity equation reveals the sources of strong unsteadiness in the particle cloud. A detailed analysis of the velocity fluctuation and kinetic energy in the fluctuating motion is performed to ascertain the importance of the velocity fluctuations that arise from the strong unsteadiness. An analogous analysis is presented, in the third case, for a gradually-induced flow on the same particle cloud along with a comparison to the shock induced case to assess the impulsive effect of shock on intensity of the fluctuating field statistics.

Computational analysis of shock-induced flow through stationary particle clouds

“…Previous studies of shock interaction with particle arrays have estimated grid qualities by examining the drag-coefficient on a single particle (Mehta et al, 2016(Mehta et al, , 2018bHosseinzadeh-Nik et al, 2018). It is important that the particle forces are well reproduced in the simulation, since they are central to the problem under investigation.…”

“…This causes the difference between the velocity in the separated flow regions behind the particles in this region and the mean flow to increase, and since the spanwise fluctuations are not increased similarly, the anisotropy increases. The importance of particle scale fluctuations in shock-wave particle-cloud interaction was previously examined in two-dimensional configurations using inviscid simulations by Regele et al (2014), and viscous simulations by Hosseinzadeh-Nik et al (2018), where the particle volume fraction was 0.15. Both studies featured a M a = 1.67 shock wave, which is significantly weaker than the shock waves studied here.…”

A volume-filtered description of compressible particle-laden flows

“…While this term is typically neglected in incompressible flow models, recent work has shown that these unresolved velocity fluctuations can contribute to a significant portion of the total kinetic energy during particle-shock interactions [24,35,48].…”

“…In the context of shock-particle interactions for moderately dilute and dense suspensions, small-scale velocity fluctuations are produced in particle interstitial sites and advected downstream with the mean flow [24,35,48] (see Fig. 1 (b)).…”

“…Because such fluctuations exist even in laminar flow (e.g., steady wakes), it is often referred to as pseudo-turbulent kinetic energy (PTKE). While this term is typically neglected in incompressible flows without significant consequence, recent DNS have shown that PTKE can contribute between 30% and 100% of the resolved kinetic energy in compressible flows [24,35,39,48]. Its strength has been shown to increase as the particle volume fraction and the incident shock Mach number increase [35].…”