Interference and diffraction of pressure shocks in flow around bodies of revolution located near a surface

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This paper presents the results of experimental and computational investigations of a supersonic (M∞ = 4.03, Re1 = 55⋅10 6 m −1 ) flow around two bodies of revolution with conical noses with an opening θ = 40 o and cylindrical cases with an extension λ = 5 located near a flat surface at zero angles of attack at a relative distance from each other Z = 1.4. We have made a comparison between the structure of the shock waves formed in the zone of hydrodynamic interference of the bodies of revolution in free flight and in flight over the surface at a distance Y = 0.96. We have demonstrated the possibility of satisfactory prediction of the hy- drodynamic structure of the realized flows and aerodynamic characteristics of the bodies under investigation on the basis of the numerical solution of Euler equations. Introduction. The investigation of the supersonic flows realized in the flight of a group of vehicles near a surface is an urgent problem of modern aerogas dynamics. A detailed analysis of their gas-dynamic structure is neces- sary for explaining the effects of aerodynamic interference and predicting the appearance therewith of forces and mo- ments. Since experimental studies of such complex flows are very difficult and require considerable expenses, an important role in solving problems of the considered class is played by the methods of computational aerodynamics. As is known, more complete modeling of the real properties of flows connected with viscous effects is only possible with the use of the methods of solving Navier-Stokes equations with different turbulence models (RANS) or direct nu- merical simulation (LES). These methods require huge computational resources and a considerable time expenditure. Therefore, in many cases, for practical purposes simpler and cheaper methods of obtaining necessary information on the basis of solving Euler equations are used. This was demonstrated, for example, in (1-9) in which a comparison between the results of numerical calculations of a nonviscous flow and the experimental data was made. The above- mentioned works showed a satisfactory agreement between the calculated and experimental aerodynamic characteristics of the investigated bodies, although in a number of cases considerable discrepancies in local pressure distributions were observed. Such differences are most often explained by the boundary-layer separations that take place in the real flow and are formed under the action of pressure shocks (8, 9). The present work is a sequel of the investigations presented in (1-4, 6-8, 10-12). The aim of the work is to consider in detail the wave structures formed in the process of interference-diffraction phenomena in the space between the bodies and the plate, as well as to check further the possibilities of using numerical calculations within the frame- work of Euler equations for investigating such complex flows. Experimental. Experiments were carried out in a T-313 supersonic wind tunnel of the S. A. Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences at a Mach number M ∞ = 4.03 and a Reynolds number Re 1 55⋅10 6 m −1 . The model consisting of a flat plate FP and two iden- tical bodies of revolution (B 1 and B 2 ) with an opening of their noses θ = 40 o located over it parallel to the flow is