A mathematical relation is formulated to calculate the properties of oblique shocks generated from swept ramps. Ramp sweep extends the oblique shock relations from two to three dimensions in a manner analogous to the way unswept ramp deflection extends the Rankine–Hugoniot shock relations from one to two dimensions. A new theta–beta–Mach-sweep (θ–β–Mach-sweep) relation is formulated, which reduces to the standard theta–beta–Mach (θ–β–Mach) relation for the special case of two-dimensional shocks from unswept ramps. The swept formulation may be expressed as a cubic equation with coefficients that are simple modifications of the cubic coefficients for the standard unswept formulation. The solution of this swept cubic equation allows the shock angle and downstream properties to be determined directly from the upstream Mach number, geometric ramp angle, and sweep. Several notable properties of sweep on the “strong” and “weak” solutions are depicted and discussed. The new formulation simplifies the process of placing, aligning, and focusing shocks for a sequence of swept ramps.
General Three-Dimensional Relation for Oblique Shocks on Swept Ramps
AIAA journal ; 54 , 1
2016
Aufsatz (Zeitschrift)
Englisch
A General 3D Relation for Oblique Shocks on Swept Ramps
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