A theoretical approximation of the shock stand-off distance for the flows around a circular cylinder

Many previous studies have addressed the problem of theoretically approximating the shock standoff distance however limitations to these methods fail to produce excellent results across the entire range of Mach number. This paper proposes an alternative approach for approximating the shock standoff distance for supersonic flows around a circular cylinder. It follows the philosophy that the "modified Newtonian impact theory" can be used to calculate the size of the sonic zone bounded between the bow shock and the fore part of the body, and that the variation of the said zone is related to the standoff distance as a function of the upstream Mach number. Consequently, a reduction rate parameter for the after-shock subsonic region and a reduction rate parameter for the shock standoff distance are introduced to formulate such a relation, yielding a new form for the shock standoff distance given in equation (47). It is directly determined by the upstream Mach number and the location of the sonic point at the body surface. The shock standoff distance found by this relation is compared with the numerical solution obtained by solving the two-dimensional inviscid Euler equations, and with previous experimental results for Mach numbers from 1.35 to 6, and excellent and consistent agreement is achieved across this range of Mach number.