Similarity parameter for the drag coefficient of a cylinder with a high-porosity frontal insert aligned at an angle of attack in a supersonic flow

Results of an experimental and numerical study of a supersonic flow around a cylinder with a gas-permeable cellular-porous frontal insert aligned at various angles of attack are reported. The experiments are performed in the T-327 wind tunnel based at the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences at the Mach number of 7 and Reynolds number of $1{,}5 \cdot 10^{6}$m$^{-1}$. The forces and moments are measured on models with diameters of 10.0, 14.5, 24.0, and 34.0 mm. The models are equipped with porous inserts whose length is equal to two diameters of the cylinder, the porosity value is 95%, and the pore diameters are 1, 2, 3, and 4 mm. The angle of attack is varied in the interval 0–25$^\circ$C. The numerical simulations are performed by means of solving three-dimensional Reynolds-averaged Navier–Stokes equations with the use of the ($k$–$\omega$)-SST turbulent model and a toroidal skeleton model of the porous material. Based on generalization of experimental and numerical data for the normalized drag coefficient at various angles of attack, empirical dependences of this quantity on the similarity parameter including the ratio of the pore diameter to the cylinder diameter and the Mach number are derived.