Calculation of the large particle interaction with a supersonic shock layer using the meshless algorithm


DOI: 10.34759/trd-2022-125-07

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 presented work deals with the numerical modeling of the two-phase flows, namely, the computation of a blunt body supersonic flow-around by a viscous gas flow with an admixture of a small amount of large particles, which, after reflection from the surface, go outward the shock layer, being moved by the inertia towards the incoming flow. Test-bench and numerical experiments reveal that the motion of high inertia particles changes the structure of the gas flow in the shock layer, and impact jets herewith directed to the body being formed cause the gas pressure increase near the surface areas and a multiple growth of the convective heat flow.

A computational model of the blunt body supersonic viscous flow-around with an admixture of large solid particles was developed in three-dimensional space. The system of non-stationary Navier-Stokes equations in conservative variables is being numerically solved by the meshless method, which employs the cloud of points in space of computational nodes for the gas flow parameters representation. The spatial partial derivatives of gas-dynamic values and functions, containing them, are being approximated by the least square method on the set of nodes distributed in the area of computation. Non-viscous flows computing is being performed by the AUSMPW+ method in conjunction with the third order MUSCL-reconstruction, while viscous flows are being computed by the second-order scheme.

Each particle, as well as a barrier streamlined by a flow, is being surrounded by a cloud of computational nodes belonging to its domain and moving together with the particle in space. The computational nodes position is being adapted to the body shape and allows resolving the flow in the boundary layer with enough accuracy to determine the convective heat flow from the gas surface. The gas state computing at the nodes associated with the particles is being performed by solving the Navier-Stokes system of equations in a moving coordinate system attached to the moving particle. A model of evolution of a single cloud of computational nodes is built. The nodes that fall into the domains overlapping zone are being temporarily excluded from the calculation, and external nodes of one domain become neighbors of the nodes of another domain to compute both viscous and convective fluxes between nodes with account for transformation of the gas state vectors between moving coordinate systems. Integration of the gas-dynamic system of equations in both basic and local systems of coordinates is being performed by the explicit Runge-Kutta method. The proposed model was verified by comparing the gas flow-around of the stationary and moving particles while maintaining relative velocity of the incoming flow.

The software implementation of the presented algorithms based on the OpenCL parallel heterogeneous computing technology with the possibility of simultaneous usage of several GPUs for the calculation of the same task was performed.

The authors performed computations of the particles movement in the shock layer near the sphere surface flown around by the supersonic airflow with the Mach number of M = 6. The particle was being launched along the sphere axis of symmetry, as well as at an angle to it. Appearance of local zones of higher pressure and multiply strengthened heat flow on the sphere surface is being observed. Gas-dynamic interaction of a pair of particles in the shock layer, which started one after the other with a time interval between them, was simulated.

Having fallen into the supersonic wake region of the first particle, the second particle, moving under the action of aerodynamic drag force, moves away to a significantly smaller distance from the sphere surface than the first one.

The built computational model and the software, developed on its basis, provide wide opportunities for the numerical study of the gas-dynamic interaction of large particles with the shock layer.

Keywords:

numerical simulation, meshless method, unsteady Navier-Stokes equations, supersonic flows around bodies, convective heat flux

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