An Assessment of the Drag Models in the Case of a Shock Interacting With a Fixed Bed of Point Particles

Abstract

In this work, three-dimensional Euler-Lagrange point-particle simulations of a shock wave interacting with a fixed bed of particles are carried out. The results from the particle-resolved simulations are used to assess the performance of the point-particle drag models during short time scales. We demonstrate that in a one-way coupled regime, the point-particle simulations recover the dominant gas dynamic features of the flow and are in a good agreement with the exact Riemann solution of a shock traveling through a sudden area contraction. Although the particle-resolved simulations are inviscid, we show that a dissipative drag is necessary to predict the mean behavior of the gas. As a model for the inviscid shock-induced drag two different models are presented in lieu of the quasi-steady drag. Finally, two-way coupled simulations are performed at four different particle volume fractions f0.10, 0.15, 0.20, 0.25g and three different incident shock Mach numbers f1.22, 1.66, 3.0g and compared against the data from particle-resolved inviscid simulations. At a lower Mach number (1.22), averaged flow quantities from the two-way coupled simulations agree well with the particle-resolved simulations. As the Mach number increases, we observe that the discrepancies between the point-particle and the particle-resolved simulations grow. A sensitivity analysis of the drag models involved reveals a strong influence of the inviscid-unsteady force on the gas quantities especially in the case of a strong shock interacting with a dense bed of particles. The use of Mach correlation beyond the subcritical regime coupled with the model for volume fraction correction is identified as a probable cause for the additional drag.

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“…which is valid for random arrays of spheres in incompressible low Reynolds number flow when φ p < 0.3. Such a simple expression for the inviscid unsteady force has received mixed success when applied to shock-particle interactions (Parmar et al, 2009;Koneru and Balachandar, 2021;Osnes and Vartdal, 2021). An interesting alternative to modeling the inviscid unsteady force was recently proposed by Fox et al (2020), and demonstrated to be a key ingredient in restoring hyperbolicity of the compressible two-fluid equations (refer back to Sec.…”

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“…In fact, there are indications that a reduction, rather than an amplification, of the inviscid unsteady force is appropriate for shock-particle interaction in random particle arrays [43].…”