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Scattering indicatrices of nonspherical particles rebounding from a smooth and a rough surface are obtained by direct Monte Carlo simulations. Particles shaped as ellipsoids of revolution, rectangular prisms, and prisms with truncated vertices are considered. Surface roughness is defined as a twodimensional profile whose scattering characteristics are close to those of real roughness induced by abrasive erosion of the surface in a high-speed gas-particle flow. Impact interaction of an individual particle with the surface is considered in a three-dimensional formulation. The scattering indicatrices of reflected particles are found to depend substantially on the particle shape in the case of rebound from a smooth surface and to be almost independent of the particle shape if the particles rebound from a rough surface.Key words: impact interaction of particles with the wall, nonspherical particles, smooth and rough surfaces, scattering indicatrices.Introduction. In a two-phase gas-particle flow over a body or an obstacle, the particles usually collide with the surface and rebound (reflect) from the latter. Particle reflection plays an important role in formation of the flow structure and the fields of parameters of the disperse phase. In most papers dealing with numerical simulations of confined gas-particle flows, the particles are assumed to be spherical and the surfaces are assumed to be smooth; in addition, various models of reflection of an individual particle from the wall are used. In real dusty gas flows, however, the particle shape normally differs from spherical (ashes, silica sand, and various commercial powders), which is responsible for the random character of their reflection. Such particles are scattered after rebounding from the surface, even if the surface is smooth. Real surfaces are normally rough owing to their prior mechanical treatment. Moreover, even an initially smooth surface rapidly becomes rough in a high-speed flow because of abrasive erosion. Surface roughness is the second important factor responsible for the random character of particle reflection.It was noted [1-3] that it is important to take surface roughness into account, and various approaches to roughness modeling were proposed. Tsirkunov and Panfilov [4] reviewed and analyzed various models of surface roughness. Sommerfeld [5] demonstrated that the calculated and experimental parameters of motion of reflected particles can be substantially different because of the assumption of a spherical shape, even in the case of isometric particles. Crowe et al. [6] described the general approach to formulating and solving the problem of rebound of an arbitrarily shaped particle from a smooth surface, as applied to modeling of two-phase gas-particle flows. The increasing interest in effects of surface roughness and nonspherical particle shapes is caused by the development of more realistic numerical models of two-phase flows in the vicinity of confining surfaces.The main objective of the present work was to study the characteristics of random...

Time-dependent two-dimensional (2D) §ow of dusty gas through a set of two cascades of airfoils (blades) has been studied numerically. The ¦rst cascade was assumed to move (rotor) and the second one to be immovable (stator). Such a §ow can be considered, in some sense, as a §ow in the inlet stage of a turbomachine, for example, in the inlet compressor of an aircraft turbojet engine. Dust particle concentration was assumed to be very low, so that the interparticle collisions and the e¨ect of the dispersed phase on the carrier gas were negligible. Flow of the carrier gas was described by full Navier Stokes equations. In calculations of particle motion, the particles were considered as solid spheres. The particle drag force, transverse Magnus force, and damping torque were taken into account in the model of gas particle interaction. The impact interaction of particles with blades was considered as frictional and partly elastic. The e¨ects of particle size distribution and particle scattering in the course of particle blade collisions were investigated. Flow ¦elds of the carrier gas and §ow patterns of the particle phase were obtained and discussed.

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Within the scope of the research work, we have developed the methods and software package for solving the conjugate heat and hydraulic problems based on the classical approach to performing hydraulic calculations and modeling thermal processes by means of the finite volume method in the ANSYS Fluent software package. The developed means allowed us to efficiently calculate the thermal state of complex technical objects. The study gives mathematical formulation of the methods and suggests the results of their approbation and verification