The paper presents the details and validation for an analytical model for predicting shock stand-off distance from a blunt body at supersonic speeds. Comparisons are made to experimental data for Mach Numbers 1.2 to 6.0 with flat face objects. Additionally a method to predict the oblique shock shape is presented and qualitative comparisons are made to both experimental and computational data. The usefulness of such a predictive tool set provides help in interpreting experimental data such as Schlieren images and in capturing a shock location using computational methods with the initial grid comforming to the shock shape when known apriori. An example of such usage is given to help interpret a poor quality Schlieren from a Mach 3.0 test.
Nomenclatured = Cylinder diameter, angular distance between two circular sides of frustum e = Distance from control volume frustum to center of oblique shock wave h = Distance of height of control volume frustum starting from flat face object M1 = Mach Number upstream of oblique shock wave M2 = Mach Number immediately downstream of oblique shock wave at center Me = "exit" Mach Number aft of oblique shock wave expanding around blunt face Mi = Average Mach Number in ring segment of frustum P1 = Pressure upstream of oblique shock wave P2 = Pressure immediately downstream of oblique shock wave at center Pe = Pressure at exit Mach Number equal to unity Pi = Average pressure in ring segment of frustum R1 = Radius of control volume frustum R2 = Radius of blunt cylindrical geometry and second radius of control volume frustum T1 = Temperature upstream of oblique shock wave T2 = Temperature immediately downstream of oblique shock wave at center Te = Temperature at exit Mach Number equal to unity Ti = Average temperature in ring segment of frustum h = Height φ = Angle of curvature from shock tangent line to the intersection of the sonic line θ = Angle sonic line makes with surface geometry ρ1 = Density upstream of oblique shock wave 1 Retired, AIAA Retired Member. AIAA SciTech ρ2 = Density immediately downstream of oblique shock wave at center ρi = Average density in ring segment of frustum ψ = Shock wave cone angle δ = shock standoff distance
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