The influence of viscosity and turbulence on the supersonic flow compression and expansion corner

Abstract

Super- and hypersonic flow around aircraft elements is accompanied by the formation of a complex flow structure, which is characterized by the presence of strong shock waves, rarefaction waves, contact discontinuities, separation and reattachment of the flow. For such problems, the interaction of shock waves with viscous boundary layers is characteristic. Such interaction is quite complex and largely determines the effectiveness of aircraft. When flowing around complex structures of aircraft and their power plants in the vicinity of convex corner points of the geometry, compression and expansion flows are locally realized. The calculation of oblique shock waves, formed when flowing around the compression angle, and simple expansion waves, formed around the flowing angle of expansion, is included as an element of solving many problems of constructing streamlines and finding the pressure distribution on the streamlined surface. Based on the technology of adaptive meshes, a numerical model is proposed for studying two-dimensional effects arising from supersonic flow around the angles of compression and expansion. Numerical simulation was performed using various models such as inviscid, laminar or turbulent. In the calculations, the Mach number of the incident shock wave varies from 2 to 15, and the flow angle varies from 5 to 15 degrees. The Reynolds number, calculated from the characteristics of the unperturbed flow, is equal to 105. The working gas is air (γ = 1.4). A qualitative picture of the flow during diffraction of a shock wave on steps of different geometry is considered. When the shock wave interacts with the compression angle, flow separation and the formation of a recirculation region are observed, and when the shock wave interacts with the expansion angle, the Prandtl–Mayer wave is misaligned. The results of calculations are compared with theoretical data on the parameters of the flow behind the shock front or fan of the rarefaction wave. Studies have shown the influence of the effects of viscosity and turbulence on the flow structure and distribution of flow characteristics when flowing around the angles of compression and expansion. The simulation results can find application in solving problems related to the design of air intakes of high-speed flying aircrafts, in particular, in parametric and optimization calculations of gas-dynamic flows that arise in the elements of propulsion systems of supersonic and hypersonic aircraft.

Keywords

• shock wave
• diffraction
• compression corner
• expansion corner
• numerical simulation
• gas dynamics