A Technique for Computing Dense Granular Compressible Flows with Shock Waves

Abstract

A numerical procedure was developed for solving equations for compressible granular multiphase flows in which the particle volume fraction can range dynamically from very dilute to very dense. The procedure uses a low-dissipation and high-order numerical method that can describe shocks and incorporates a particulate model based on kinetic theory. The algorithm separates edges of a computational cell into gas and solid sections where gas-and granular-phase Riemann problems are solved independently. Solutions from these individual Riemann problems are combined to assemble the fully coupled convective fluxes and nonconservative terms for both phases. The technique converges under grid refinement even with very high volume fraction granular interfaces. The method can advect sharp granular material interfaces that coincide with multi-species gaseous contact surfaces without violating the pressure nondisturbing condition. The procedure also reproduces known features from multiphase shock tube problems, granular shocks, transmission angles of compaction waves, and shock wave and dust-layer interactions. This approach is relatively straightforward to use in an existing code based on Godunov's method and can be constructed from standard compressible solvers for the gas-phase and a modified AUSM + -up scheme for the particle phase.

Comparative Study of Numerical Schemes for Granular Combustion of Boron Potassium Nitrate

“…The drag effects are accounted for by the correlation given by Saurel et al [9]. In the solid volume fraction evolution equation, the pressure of each phase relaxes each other to a common equilibrium at a rate controlled by the pressure relaxation parameter [9] in Equation (16).…”

“…The flux computation using the HLLC-AUSM scheme is as follows. Houim and Oran have used the HLLC-AUSM scheme in most of their works [16,17].…”

“…In the present study, the complete physics of granular combustion is modeled. In the literature, compressible multiphase applications are numerically solved mainly by using either of the three upwind schemes, viz., HLLC [13,14], AUSM family [15], and a combination of the two, known as HLLC-AUSM [16,17]. Various studies using these schemes have been carried out in the literature, and comparative studies have been carried out within the same family of schemes.…”