## Abstract

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 numbers. 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 expression for the shock standoff

distance given in Equation (32). 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 solutions 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 numbers

distance; however, limitations to these methods fail to produce excellent results across the entire

range of Mach numbers. 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 expression for the shock standoff

distance given in Equation (32). 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 solutions 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 numbers

Original language | English |
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Article number | 026102 |

Journal | Physics of Fluids |

DOIs | |

Publication status | Published - 22 Feb 2017 |