Towards an efficient method for calculating design parameter derivatives in super- and hypersonic flow

Abstract: Access to derivatives (sensitivities) between flow properties and design parameters that alter the shape of objects in super- or hypersonic flow is highly desirable for many engineering and design applications. Current methods to calculate such derivatives are either computationally expensive to evaluate, even for moderate numbers of design parameters (more than 3), or require specialist flow solvers that must be deeply converged. An alternative is to use approximate methods based on asymptotic solutions, isentropic or shock processes that bracket the exact solution. In this work, we examine the derivation of both these methods and show how they bracket the exact sensitivities. Next, we look at two case studies: a three-ramp inlet and a low-drag body to assess the accuracy of the methods. Based on the findings, a hybrid approach for approximate sensitivity calculations is proposed, which can estimate drag sensitivities with an error of no more than 4.0% and typical errors of less than 0.5%. Keywords: Euler equations, design parameter gradients, MDAO, hypersonics