The interaction of a planar shock wave with a dense particle curtain is investigated through modeling and experiments. The physics in the interaction between a shock wave with a dense gas-particle mixture is markedly differently from that with a dilute mixture. Following the passage of the shock wave, the dense particle curtain expands rapidly as it propagates downstream and pressures equilibrate throughout the flow field. In the simulations, the particles are viewed as point-particles and are traced in a Lagrangian framework. A physics-based model is then developed to account for interphase coupling. Compared to the standard drag law, four major improvements are made in the present interphase coupling model to take into account: (1) unsteady force contributions to particle force; (2) effect of compressibility on hydrodynamic forces; (3) effect of particle volume fraction on hydrodynamic forces; (4) effect of inter-particle collision. The complex behavior of the dense particle curtain is due to the interplay between two-way coupling, finite particle inertia, and unsteady forces. Incorporation of these effects through significant modeling improvements is essential for the simulation results to agree well with the experimental data. As a result of the large pressure gradient inside the particle curtain, the unsteady forces remain significant for a long time compared to the quasi-steady force and greatly influence the particle curtain motion.

Interaction of a planar shock wave with a dense particle curtain: Modeling and experiments

Currently there is a substantial lack of data for interactions of shock waves with particle fields having volume fractions residing between the dilute and granular regimes. To close this gap, a novel multiphase shock tube has been constructed to drive a planar shock wave into a dense gas–solid field of particles. A nearly spatially isotropic field of particles is generated in the test section by a gravity-fed method that results in a spanwise curtain of spherical 100-micron particles having a volume fraction of about 20%. Interactions with incident shock Mach numbers of 1.66, 1.92, and 2.02 are reported. High-speed schlieren imaging simultaneous with high-frequency wall pressure measurements are used to reveal the complex wave structure associated with the interaction. Following incident shock impingement, transmitted and reflected shocks are observed, which lead to differences in particle drag across the streamwise dimension of the curtain. Shortly thereafter, the particle field begins to propagate downstream and spread. For all three Mach numbers tested, the energy and momentum fluxes in the induced flow far downstream are reduced about 30–40% by the presence of the particle field.

A multiphase shock tube for shock wave interactions with dense particle fields

http://www.math.hkbu.edu.hk/ICM/pdf/08-05.pdf

A high-order WENO-Z finite difference based particle-source-in-cell method for computation of particle-laden flows with shocks

Formation of cellular detonation in a stoichiometric mixture of aluminum particles in oxygen is studied by means of numerical simulation of shock-wave initiation of detonation in a flat and rather wide channel. By varying the channel width, the characteristic size of the cells of regular uniform structures for particle fractions of 1–10 µm is determined. The calculated cell size is in agreement with the estimates obtained by methods of an acoustic analysis. A relation is established between the cell size and the length of the characteristic zones of the detonation-wave structure (ignition delay, combustion, velocity and thermal relaxation).

Numerical Simulation of Formation of Cellular Heterogeneous Detonation of Aluminum Particles in Oxygen

Evaluation of convergence behavior of metamodeling techniques for bridging scales in multi-scale multimaterial simulation

The present paper is devoted to experimental and theoretical investigation of the shock wave (SW) propagation in a mixture of gas and solid particles in the presence of explicit boundaries of the two-phase region (cloud of particles). The effect of the qualitative change in the supersonic flow behind the SW in a cloud of particles within the range of the volume concentration of the disperse phase 0.1-3% is experimentally shown and theoretically grounded.

Shock wave interaction with a cloud of particles

The present paper is devoted to experimental and theoretical investigation of shock-wave propagation in a mixture of a gas and solid particles with clearly defined boundaries of the two-phase region (cloud of particles). The effect of qualitative transformation of supersonic flow behind a shock wave in a cloud of particles is shown experimentally and substantiated theoretically for volume concentrations of the dispersed phase of 0.1–3%.

Interaction of a shock wave with a cloud of particles

A study is made of dust ignition during transient interaction of an incident shock wave with an extended dust cloud. It has been shown experimentally that in the presence of dispersed phase with volume concentration of ∼10−3 the temperature behind a shock wave with Mach number Ms=4.5 can exceed the ambient one by 400 K or more. A physical mechanism is proposed for carrier phase heating, based on the effect of supersonic flow braking behind the shock wave under constraints created by dust particles during velocity relaxation. The gasdynamic functions are obtained as analytic functions of the flow Mach number M. In particular, it is shown that the equation T/T0=M0/M is valid for the temperature. The form of M as a function of dispersed-phase parameters and the quantitative nonsteadiness criterion are found. The function M was found to agree well with experiment.

Mechanism of dust ignition in incident shock waves

We present the results from an experimental study into the dynamics involved in the formation and the unique features of ignition in shock gas suspensions of coal dust with a dispersion of<40 μm and a volatile content of 9, 26, and 55%. We have determined the ignition delays τig for coal dusts in air and in pure oxygen for a range of Mach numbers from 2.6 to 4.0 in an incident shock wave. We have established that the quantity τig as well as the nature of the function τig(1/T) are significantly affected by the kinetics of the volatile yield, in addition to the kinetics of volatile ignition. We have derived an approximation expression for τig as a function of the content of volatiles, the temperature of the medium, and the partial pressure of the oxygen.

Effect of volatiles on ignition delay in coal dust gas suspensions within shock waves

The liquid film destruction in passing shock wavefront is examined in the range Mach number 2.0-3.0 and at an initial gas pressure of 0.1 MPa, obtained by the method of multiframe laser visualization, permitting observation of the dynamics of development of this process with a time resolution of approximately 30 nsec. A sample of shadow photographs illustrating the dynamic behavior of a film of VM-4 oil is shown. It is shown that the character of the interaction with the shoulder depends significantly on the properties of the liquid and is largely similar to the character of shock wavefront interaction with a drop.

A. N. Papyrin

Papers

Shock wave interaction with a cloud of particles

Interaction of a shock wave with a cloud of particles

Mechanism of dust ignition in incident shock waves

Effect of volatiles on ignition delay in coal dust gas suspensions within shock waves

Dynamics of the destruction of a liquid film behind a shock wavefront