A similarity criterion for supersonic flow past a cylinder with a frontal high-porosity cellular insert

We have experimentally and numerically studied the influence of the ratio of the diameter of a cylinder with a frontal gas-permeable porous insert made of nickel sponge to the average pore diameter in the insert on the aerodynamic drag of this model body in supersonic airflow ( M$_\infty$ = 4.85, 7, and 21). The analytical dependence of the normalized drag coefficient on a parameter involving the Mach number and the ratio of cylinder radius to average pore radius in the insert is obtained. It is suggested to use this parameter as a similarity criterion in the problem of supersonic airflow past a cylinder with a frontal high-porosity cellular insert.