Simulation of a supersonic flow around a body with a frontal gas-permeable insert by using a skeleton model of a highly porous cellular material

Abstract

Abstract. Numerical simulation of supersonic flow past a cylinder with a frontal gas-permeable insert is performed using the skeleton model of a highly porous cellular material. Numerical simulation was carried out within the framework of two-dimensional RANS equations written in an axisymmetric form. The skeleton model is a system of coaxial rings of different diameters, arranged in staggered order. The calculations were carried out in a wide range of determining parameters: Mach numbers M ∞ =3, 4.85 and 7, unit Reynolds numbers Re 1 =13.8×10 5 ÷ 13.8×10 6 m -1 , the cylinder diameter 6÷40mm, the length of the porous insert 3÷45mm, the cell diameter of 1 and 3 mm. The results of the calculations are consistent with the available experimental data. The applicability of the skeleton model for the description of supersonic flow around axisymmetric bodies with front inserts from cellular-porous materials is shown. IntroductionGas-permeable porous materials in recent years have found application in promising methods of controlling supersonic aircraft [1][2][3]. Experimental studies in wind tunnels demonstrated the possibility of controlling supersonic flow and, in particular, controlling the aerodynamic drag of bodies by help of gas permeable highly porous cellular materials (HPCM) [1,4].HPCM ( Figure 1a) is formed when the foamed liquid metals solidify. The cellulars of the frozen foam form a spatial carcass from the partitions between the contacting cellulars. The porosity (the ratio of the total volume of the porous sample to the volume of the skeleton) of such a material lies in the range from 76% to 98%. The material ceases to be gas permeable with less porosity, and with greater porosity, a skeleton of the partitions is not formed. There are some recent applications of gas-permeable porous materials and in supersonic aerodynamics to suppress acoustic waves. In particular, it was possible to suppress acoustic disturbances in the shock layer on a plate in nitrogen stream at M = 21 with the help of inserts of foamed nickel in experiments [5]. These phenomena are based on dissipation of the energy of acoustic disturbances, which are a dominating mode of instability of a hypersonic boundary layer, owing to friction in pores of the coating. It was shown in experiments [6] that the intensity of perturbations is attenuated by a sound-absorbing coating from the HPCM by 20% at the plate in the flow of vibrationally excited mixtures of CO 2 with air.To increase the efficiency of the action of gas-permeable porous materials on a supersonic flow around various bodies and develop engineering methods for design of supersonic flying vehicles with porous control elements it is required to apply modern methods of numerical simulation of flow around bodies with porous inserts. At present, the main problem of numerical modeling is the optimal choice of the model of a gas permeable porous medium. Continuum models of a porous medium with a prescribed pressure gradient in the porous region as a function of the filtration rate in ac...