A meshless method for solving the Euler system of equations for the inviscid gas flow in a three-dimensional space is described in detail. Polynomial Least Squares approximation of partial spatial derivatives of gas-dynamic parameters and the transformation of an orthonormal coordinate system are used for calculating the fluxes between the computational nodes.
Oscillatory flow and heat transfer regimes arising from the gas-dynamic interaction between a high-inertial particle and a shock layer in a supersonic flow around bodies are under numerical research. Detailed space-time flow patterns were obtained using high-resolution adaptive grids and parallelization of computations using the graphic processing units.
A supersonic flow around a cylinder with a flat end is studied for the case in which a single particle is launched from the end surface towards the incident flow. Numerical modeling is carried out with allowance for the gas-dynamic interaction of the particle with the shock layer. High-resolution, adaptive, rectangular grids are used to obtain detailed spatial and temporal flow patterns. The calculation results are compared with experimental data. It is shown that a single, large particle moving along the axis of symmetry against the incident flow and crossing the bow shock wave causes a significant restructuring of the flow and the formation of complex shock-wave and vortex structures. An important role in the formation of the flow structure is played by the formation of a toroidal vortex, which leads to an “inviscid” separation of the incident flow from the axis of symmetry. A distinctive feature of the flow around a cylinder with a flat end is the oscillatory flow regime caused by alternating stages of growth and decay of a toroidal vortex. The patterns of the oscillating flow and the oscillation frequency obtained via numerical simulation are in good agreement with the experimental data.
The paper is devoted to the numerical study of the shock layer–particle interaction in a supersonic flow past bodies. The shock wave associated with a moving particle and the flow in the particle wake is taken into consideration. Distinctive features of the numerical technique are the adaptive Cartesian sliding grids of high resolution, a ghost cells immersed boundary method for the realization of conditions on curvilinear boundaries, parallelization of computations on graphics processors. The results of computational experiment obtained allows to study the characteristic shock and vortex structures formed during the passage of a particle rebounding from the surface through the bow shock wave. The oscillations observed for a flow over the fla-tended cylinder are discussed.
The results of numerical modeling of the gasdynamic interaction between a highly inertial particle and the shock layer are presented. The evolution of the shock-wave and vortex flow pattern that appears when a particle reflected from a streamlined surface passes through a shock wave is analyzed. It is shown that an essential part is played in the formation of a wave flow pattern by a toroidal vortex, which results in the “nonviscous” detachment of the near-axis incident flow from the symmetry axis and its further interaction with the outer flow and the body surface. It is indicated that an intensive pressure wave passes along the streamlined surface, thus creating the conditions for the intensification of convective heat transfer.
The work is devoted to numerical simulation of the flow around blunt bodies in supersonic streams containing solid polydisperse particles. We consider a widespread variant of two-parameter gamma function for the particle size distribution. To account for interparticle collisions and interactions of particles with a streamlined surface, the direct numerical simulation of collisional dynamics for the dispersed phase was used. The local particle size distribution near the streamlined surface is studied. The screening effect due to the interaction of the incident and reflected from the surface particles is analyzed. It is noted that the energy flux from a polydisperse admixture to the streamlined surface can be represented with sufficient accuracy by equivalent impact of monodisperse admixture.
This paper describes the problems of numerical simulation of supersonic gas-particle flow over blunt bodies. A complex mathematical model is proposed, coupling gas flow in the shock layer, particle advection in the carrying phase, and heatmass transfer in the body that is being destroyed. The Eulerian description fits best for the gas phase, and the Lagrangian description is most suitable for the dispersed phase. Particle dynamics is fully handled via the discrete-element method. The result is a numerical simulation of the thermoerosive destruction of a circular cylinder in two-phase flow. The authors present an analysis of multiple factors, such as interparticle collisions in a flow, particle reflection from a streamlined surface, dispersed admixture feedback on the carrier phase, and the influence of changing body geometry due to mass entrainment on two-phase shock layer parameters.
The problems of the numerical simulation of a dusty supersonic flow past a blunt body is examined. The model of a two-phase shock layer is presented. The Euler description of the gas phase and the Lagrange description of the dispersed phase that is used in combination is the basis of the present model. The complete variant of a discrete-elemental method, i.e., the direct numerical simulation of a dynamic admixture, is used. The effect of collisional and collisionless foreign particles on to the carrying gas flow and heat transfer is studied, as well as the direct impact of a two-phase gas flow onto a streamlined surface, by considering particle collisions and the dispersed phase’s reverse impact on the gas phase.
This paper is concerned with numerical simulation of two-phase flows in complex computational regions. Both nozzle flow and jet-obstacle interaction are considered. The presence of dispersed phase (solid or liquid particles) may lead to specific thermal and erosional interaction of inertial particles with the nozzle walls and the obstacle material. The latter makes the conjugated problem much more complicated. Therefore, we consider the complete flow field in the nozzle-jet-obstacle system. The present work is a continuation of the recent study by the authors [1, 2]. A unified approach to the general problem of a two-phase nozzle-jet-obstacle flow is suggested. In this approach, both the continuous and dispersed phase behavior is calculated using the fixed rectangular grids. The solution of transient conduction equation in the solid is also carried out on rectangular grids. Both dynamics and heating/cooling of particles are calculated using the discrete-element method in Lagrangian variables. The computational model includes many mechanical effects such as collisions of particles with each other, reflection of particles from the wall surface and the feedback effect of the dispersed phase on the gas flow. The distinctive feature is the direct numerical simulation of dispersed phase dynamics, where each single real particle in the flow has its computational counterpart. All governing equations for continuous fields are solved on rectangular grids using a ghost-cell immersed boundary method. This method provides discretization of the appropriate boundary conditions via a procedure of polynomial approximation. Such approach works well for both the incompressible and compressible flows. Rectangular grids allow a straightforward implementation of high order TVD and ENO schemes for the numerical simulation of gas flows. The immersed boundary method is perfectly suited for the problems within a computational domain of varying geometry, since it doesn’t require rebuilding the grid after each boundary movement. This feature was successfully used in the numerical simulation of erosive destruction of the circular cylinder in the two-phase flow [2], where the mass carried away from the body resulted in moving boundaries. The current work incorporates the previous methods and algorithms into the software package allowing the numerical investigation of heterogeneous flows in more complex configurations.
This work is dedicated to the problems of numerical simulation of supersonic flow with admixture of particles over blunt bodies. A complex mathematical model, governing two-phase flow in the shock layer and heat and mass transfer in the destructing body is presented. The model of two-phase shock layer is based on Euler description of the gas phase and Lagrangian description of the dispersed phase. The full-scaled variant of discrete-element method is used for direct numerical simulation of the particle dynamics. Results of numerical simulation of thermo-erosive destruction of circular cylinder in two-phase flow are presented. Analysis of multiple factors such as interparticle collisions in a flow, particles reflection from streamlined surface, dispersed admixture feedback on carrier phase and influence of changing body geometry due to mass, carrying away, on two-phase shock layer parameters is carried out.
This work is dedicated to the problems of numerical modeling of supersonic flow with an admixture of particles over blunt bodies. A complex mathematical model, including a model of two-phase flow in a shock layer and a model of heat and mass transfer in the destructing thermal protection coating is presented. The model of the two-phase shock layer is based on combination of an Euler description of the gas phase and a Lagrangian description of the dispersed phase. In so doing we use the full-scaled variant of the discrete-element method, i.e. it performs direct numerical modeling of the admixture dynamics. The effect of collisional and collisionless particle admixture on the flow of the carrying gas and convective heat transfer is studied as well as the direct impact of the two-phase flow on the streamlined body.
