Modelling of the impact of air shock wave on obstacle covered by porous screen

Abstract

The procedure based on the modified two-step Lax-Wendroff scheme has been suggested for calculation of one-dimensional non-stationary motion of porous media described by the mathematical two-velocity model with two stress tensors. Results of computer modeling of the processes of passing the boundary between gas and porous medium by air shock wave and the reflection from rigid wall covered by the porous layer are presented.

Numerical study of the transfer of shock-wave loading to a screened flat wall through a layer of a powdered medium and a subsequent air gap

“…(1)-(5) with the initial and boundary conditions (6) and (7) was performed by the Lax-Wendroff shock-capturing method by the algorithm developed in [30,32]. The accuracy of computations was monitored by verifying conservation of the integrals of mass, momentum, and energy of the phases and also by repeated computations with reduced steps in time and space.…”

“…The following assumptions are used to describe the motion of this system: the particles of the powdered medium are incompressible singlefraction spherical solid inclusions; the particle sizes in the mixture are much greater than the molecularkinetic scales and much smaller than distances that reveal noticeable changes in macroscopic parameters of the phases (outside the shock waves); viscous and heatconduction effects are significant only in interphase interaction processes; processes of interphase mass transfer, fragmentation, and sintering of particles are ignored; effects of fluctuating motion of the phases are negligibly small; the change in internal energy of the powdered medium owing to the work of the interphase friction force occurs completely in the gas phase; the elastic component of internal energy of particles is a constant, and the thermal component depends on the work of forces of interparticle interaction (dry friction) and interphase heat transfer; the powdered medium has a viscoelastic skeleton with minor deformations; the gas phase is an ideal gas; there are no external mass forces; there is no heat transfer with the ambient medium; the contribution of the unsteady Basset force to the total force of interphase interaction is ignored, but the contribution of the unsteady force of added masses is taken into account; the motion of the gas and particles of the powdered medium is assumed to be one-dimensional, planar, and unsteady. Under the assumptions made, the governing equations of motion of the phases of the porous granular medium have the following form [29][30][31][32]:…”

“…Kutushev et al [21][22][23][24] used the assumption of a nonlinear-elastic behavior of the "skeleton" of the porous medium with the equation of state [33] and numerically integrated the equations of motion of the gaseous and disperse phases by the method of coarse particles by the algorithm developed in [34]. Gubaidullin et al [25][26][27][28][29][30][31][32] used the assumption of the linear-viscoelastic deformation of the powder skeleton by the scheme proposed in [35], and the numerical solution of the equations of motion of the phases of the medium saturated by a gas was performed by the LaxWendroff method [30,32]. The numerical data were compared in [21,29] with the experimental results of [12,17], and it turned out that the models of motion of the phases offer satisfactory descriptions of the wave processes in screening layers of porous powdered media.…”

“…The goal of the present work, which is a logical continuation of [21][22][23][24][25][26][27][28][29][30][31][32], was a numerical study of the action of an air shock wave on a solid flat wall through a screening layer of a porous powdered medium and a subsequent gap filled by a gas.…”

“…The theoretical activities [21][22][23][24][25][26][27][28][29][30][31][32] were aimed at a detailed study of the action of a shock wave on a solid flat wall screened by a layer of a porous powdered medium with the use of various models of two-velocity, two-temperature, two-stress contact mixtures of a gas and solid particles. Kutushev et al [21][22][23][24] used the assumption of a nonlinear-elastic behavior of the "skeleton" of the porous medium with the equation of state [33] and numerically integrated the equations of motion of the gaseous and disperse phases by the method of coarse particles by the algorithm developed in [34].…”