The study of hypersonic flow about different types of bodies has assumed increasing importance with the progress that has been made in the design of spacecraft. Existing hypersonic wind runnels do not permit complete modeling of flight conditions at high Math numbers (M~, > 20). In addition, only certain gasdynamic parameters can be measured in experiments. This has enhanced the importance of methods for numerically modeling hypersonic flows. Such modeling makes it possible to simultaneously determine all of the parameters of a flow within the framework of the chosen model throughout the investigated region. However, no modeling is absolute, and the results must be substantiated by comparison with experimental data. On the other hand, combining these two approaches also gives the researcher greater confidence that the experimental methodology is correct.A common object of investigation is the flow on a plate with a sharp edge at a zero angle of attack. The electron-beam [1-4] and electron-probe [5] methods were used earlier to measure the distribution of mean density near the sharp edge of a plate for low Reynolds numbers (Re x < 3-104). There is no measurement data for higher Reynolds numbers. Results of a numerical study of hypersonic flow past a plate in a locally self-similar approximation were presented in [6]. This problem was solved more accurately in [7], where allowance was made for the structure of the shock wave (SW). The region of applicability of the Rankine-Hugoniot conditions on the wave were determined. Both investigations studied the region near the leading edge of the plate, where the local Reynolds numbers were on the order of 104 .In this study, we describe the experiment and present results of use of the method of electron-beam fluorescence to measure profiles of density in the flow of nitrogen about a plate at a zero angle of attack. The experiments were conducted with a Mach number for the incoming flow M~, = 21 and a unit Reynolds number per meter Re 1 = 6-105. The model of a viscous shock layer was used to develop an algorithm to calculate hypersonic flow about the plate. We present calculated prof'fles of velocity, temperature, and density. The latter are compared with the experiment in a number of the sections.1. Experimental Method. The measurements were made in hypersonic nitrogen wind tunnel T-327 at the ITPM (Institute of Theoretical and Applied Mechanics of the Siberian branch of the Russian Academy of Sciences) [8] with stagnation parameters Po = 8 MPa, T O = 1100 K. The radius of the uniform core of the flow was 5-10 -2 m, while the density of the particles in the flow was 7.1021 m -3. The density of the flow decreased rapidly outside the core, reaching = 6.1020 m -3 at a distance of 0.1 m from the axis.The plate model was in the form of a trapezoid. The widths of the leading and trailing edges were 8-10 -2 and 6-10 -2 m and the length of the plate L = 3.6.10 -1 m. The leading edge of the plate had the form of a wedge with an angle of 7 ~ The radius of curvature of "the leading e...

A two-phase flow with high Reynolds numbers in the subsonic, transonic, and supersonic parts of the nozzle is considered within the framework of the Prandtl model, i.e., the flow is divided into an inviscid core and a thin boundary layer. Mutual influence of the gas and solid particles is taken into account. The Euler equations are solved for the gas in the flow core, and the boundary-layer equations are used in the near-wall region. The particle motion in the inviscid region is described by the Lagrangian approach, and trajectories and temperatures of particle packets are tracked. The behavior of particles in the boundary layer is described by the Euler equations for volume-averaged parameters of particles. The computed particle-velocity distributions are compared with experiments in a plane nozzle. It is noted that particles inserted in the subsonic part of the nozzle are focused at the nozzle centerline, which leads to substantial flow deceleration in the supersonic part of the nozzle. The effect of various boundary conditions for the flow of particles in the inviscid region is considered. For an axisymmetric nozzle, the influence of the contour of the subsonic part of the nozzle, the loading ratio, and the particle diameter on the particle-flow parameters in the inviscid region and in the boundary layer is studied.Key words: two-phase flow, viscous flow in the nozzle, numerical methods.Introduction. Various gas-particle flows were studied in a number of papers where the gas flow was described by the full Navier-Stokes equations, Euler equations, and boundary-layer equations. The Eulerian approach is commonly used to study the behavior of particles, with all particle parameters being averaged over an elementary volume. A more recent trend is to use the Lagrangian approach where the parameters of each particle or a particle packet are computed.The flow in the boundary layer on a flat plate with a shock wave passing along the plate was considered in [1-3]. The gas motion was described by the equations of a compressible laminar boundary layer, and the motion of particles was computed by the Euler equations. Velocity and temperature profiles for the gas and particles were presented. Outa et al.[3] compared the numerical results with their own experiments conducted with glass spheres and found that particles 50 µm in diameter are concentrated near the boundary-layer edge. Saurel et al. [4] used the Euler equations for the gas and particles. It was shown that the equations for particles are degenerate hyperbolic equations, and a special numerical method was proposed to solve them. Results of computations of the flow in a curved channel with injection of particles through the side wall were presented. In [5,6], the gas flow was computed with the use of the full Navier-Stokes equations. The two-phase flow in a shock tube was studied with allowance for the lifting force for particles.An unsteady problem for a two-phase flow behind a shock wave passing through a dusty gas in a compression corner was considered in [7]. ...

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