Supersonic flow around a cylinder with a permeable high-porosity insert: experiment and numerical simulation

Abstract

Results of experimental and numerical investigations of a supersonic flow around a cylinder with a frontal gas-permeable insert made of a high-porosity cellular material are presented. The measurements are performed in a T-327 supersonic blowdown wind tunnel at the free-stream Mach numbers $M_{\infty }=4.85$, 7 and 21 in the range of the unit Reynolds numbers $Re_{1\infty }=(0.6{-}13.5)\times 10^{6}~\text{m}^{-1}$. The drag coefficients for a cylinder with an aerospike and a cylinder with a frontal gas-permeable porous insert are obtained. For the cylinder with the frontal gas-permeable porous insert, variations of the insert length, cylinder diameter and pore size are considered, and the mechanism of drag reduction is found, which includes two supplementary processes: attenuation of the bow shock wave in a system of weaker shock waves, and formation of an effective pointed body. The experiments are accompanied by numerical simulations of the flow around the cylinder with the frontal high-porosity insert: the fields of parameters of the external flow and the flow inside the porous insert are obtained, the drag coefficients are calculated, and the shape of the effective body for the examined model is found. The structure of the high-porosity material is modelled by a system of staggered rings of different diameters aligned in the radial and longitudinal directions (skeleton model of a porous medium). Numerical simulations of the problem are performed by means of solving two-dimensional Reynolds-averaged Navier–Stokes equations written in an axisymmetric form. The experimental and numerical data reveal significant drag reduction in a wide range of supersonic flow conditions. The results obtained on the drag coefficient for the cylinder are generalized with the use of a parameter which includes the ratio of the cylinder diameter to the pore diameter in the insert and the Mach number. This parameter is proposed as a similarity criterion for the problem of a supersonic flow around a cylinder with a frontal high-porosity insert.