Sliding adaptive cartesian grids method for computing particles gas-dynamic interaction with the shock layer in the supersonic flow


Аuthors

Sposobin A. V.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: spise@inbox.ru

Abstract

The article deals with the up-to-date problem of the multiphase flow studying, namely numerical modeling of gas flows with an admixture of solid particles. Modern scientific literature pays much attention to this topic. The article presents in detail the method of sliding Cartesian meshes for numerical simulation of the large particles motion in the shock layer emerging near the surface of a blunted body flown-around by supersonic flow. Experimental studies revealed that structure modifications of the gas flow in the shock layer leads to a multiple increase of the heat flux from the gas to local zones of the surface. In previously published works, a numerical study on the large particle motionalong the axis of symmetry of the axisymmetric body in the supersonic flow based on the high-resolution Cartesian grid model has been performed. The two-dimensional model of sliding meshes presented in the articleemploys adaptive Cartesian grids moving in space along with particles. It allows employing computing resources more efficiently than the highresolution static Cartesian grid-based model. With correction for the two-dimensional character of the model, a possibility to study trajectories of the particles motion that are more complex, as well as collective effects, caused by the gas-dynamic interaction of several large particles in the flow, appears. The gas flow model is being describedby the two-dimensional unsteady Navier-Stokes equations in Cartesian coordinates. The numerical solution of the Navier-Stokes equations is being performed by the finite volume method with a second-order scheme. Computing of non-viscous fluxes is realized by the AUSM+ (Advection Upstream Splitting Method Plus) scheme. Implementation of boundary conditions on the hard surface is being realized by the ghost cell-based immersed boundary method. Integration of the system of differential equations is being performed by the explicit three-stage Runge-Kutta method. Computing of each solid body flow-around by the gas flow is being performed in its own coordinate system on the separate computational grid. The central blunted body flown-around by a supersonic flow is assumed motionless together with its coordinate system and computational grid. The particles in the flow move under the impact of the aerodynamic drag force. Cartesian grids adapted to the geometry of the area are being employed to discretize the gas dynamics equations system. The local coordinate system attached to the particle moves forward relative to the main one along with its computational grid. In the outer zone of the local grid Dirichlet boundary conditions are being set, calculated on the gas parameters from the main grid at the corresponding points in space with account for the particle locationand its velocity. The zone of space corresponding to the inner part of the local computational grid attached to the particle is being excluded from the computation on the main grid and filled with gas parameters by transferring them in the reverse direction, i.e. from the local grid to the main one. Parameters exchange between the computational gridsis being performed at each computing step, which value is being determined by the Courant rule. The gas parameters at a certain point in space are being computed employing the procedure of bilinear interpolation of values from the nearest nodes of the source grid, and account for the speed of the relative movement of the grids. The software implementation of the described algorithms was elaborated usingOpenCL technology for parallel computations on CPU and GPU. A series of calculations was conducted to verify the presented mathematical model. Computational results of the free flow-around of a motionless body and a body motion in the still air were compared. The obtained flow patterns and gas parameters on the streamlined surface turned out to be identical. A series of calculations has been performed to simulate the motion of the group of particles reflected from the surface of the circular cylinder streamlined by the supersonic air flow [13]. A significant change of the gas flow structure in the shock layer was observed, followed by multiple increase of the convective heat flux in the local zones on the cylinder surface. Simultaneous presence of several particles kept an increased heat flux for on a longer time intervals.

Keywords:

numerical simulation, adaptive sliding Cartesian grids, supersonic heterogeneous flow, flow-around of around moving bodies, highly-inertial particle

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