Adjoint-based aerodynamic design optimisation in hypersonic flow

Abstract

The drive for improved flexibility and reusability in satellite launch systems has brought a resurgence in the popularity of scramjet-powered access-to-space launch vehicle concepts. A challenge in scramjet-powered accelerator vehicles is achieving positive thrust margins at the high-speed end of their flight envelopes. As a consequence, scramjet-powered vehicles typically rely on highly integrated airframe-engine configurations. However, due to the tight integration, the geometries and the flow physics are complex. An automated optimisation method seems an excellent candidate approach to explore the complex design space of hypersonic vehicles. This thesis focuses on the development and application of a particular optimisation method, adjoint-based optimisation, to aid in efficient aerodynamic design in hypersonic flows. Shape optimisation of scramjet-powered vehicles requires many design parameters to capture the geometric detail, and, since the flow physics is complex, the fidelity of Reynolds-Averaged Navier-Stokes (RANS) analyses is desirable. The combination of many design parameters and an expensive objective function evaluation drives the need for gradient evaluation methods that scale well with the number of design variables. An advantage of the adjoint method is that all shape sensitivities for an objective function are evaluated at the cost of only one flow solution and one adjoint solution. As a result of its efficiency, the adjoint method has become widely used for aircraft design, evolving to the design optimisation of full configurations. Despite the wide use of adjoint methods in aircraft optimisation, there has been very little application to hypersonic vehicle design. Several high-speed adjoint solvers have been reported in the literature, however, a majority of these works have only verified the adjoint sensitivities, few have followed on to demonstrate the method for use in design optimisation. The contribution of this work is the description and application of a discrete adjoint solver in high-speed compressible flow optimisation. What is unique in this work is a demonstration that complex-step differentiation works well to linearise a second-order spatially accurate unstructured RANS solver. In particular, the approach presented in this work utilises the k − ω turbulence model in high-speed ducted flow configurations. As part of this work, to provide flow analysis with a rapid turnaround , an unstructured steadystate RANS solver driven by a Jacobian-Free Newton-Krylov method was developed. Turbulence is modelled using the two-equation k − ω turbulence model. The Newton method is globalised by using the pseudo-transient approach. A restarted GMRES method is used to solve the system of linear equations arising when solving for the Newton steps. Evaluation of the matrix-vector products required in the GMRES algorithm is accomplished by Fréchet derivatives using imaginary perturbations in the complex plane. This is necessary to achieve robust convergence of the types of turbulent hypersonic flows...

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