Development of maximum conical shock angle limit for osculating cone waveriders

Abstract

Hypersonic waveriders are special shapes with leading edges coincident with the body's shock wave, yielding high lift-to-drag ratios. The waverider geometry results from streamline tracing using the solutions of a basic flow field such as the wedge or the cone for specified shock and base curves. The base and shock curves can be independently prescribed in the osculating cone method enabling a larger design space. Generally, low values of the conical shock angle (9∘−15∘) are used. The lack of any method to limit the maximum cone angle for osculating cone waverider motivates this study. Mathematical expressions are derived for geometrical conditions that result in successful osculating cone waverider generation. A power law curve and a Bézier curve are analyzed. Closed-form expressions for the maximum cone shock angle are obtained for the power law curve. A numerical procedure to solve the same for the Bézier curve is developed. The results, for a typical Mach number of 6.0, evidently show that the maximum cone shock angle for successful waverider generation is significantly lower than the maximum angle for attached shock solutions. The limiting conditions developed will be essential in constraining the waverider sample space for automated multi-objective optimization routines. CFD simulations were conducted on waveriders designed with traditional shock angle of 12∘ and near limiting shock angle of 18∘. The analysis revealed a substantial 50% increase in volumetric efficiency, albeit with a minor decrease in aerodynamic performance. This highlights the critical need for determining the maximum conical shock angle when aiming for specific high volumetric efficiency.