Hypersonic Reusable Technologies for Access to Space

This research investigation concerned the analysis and design optimization of hypersonic reusable technologies for access to space. The specific design problem undertaken was the optimization of a scramjet inlet, investigating methods of sensitivity calculation to address a wider range of objectives than was previously possible with the adjoint method. Scramjets have the potential to facilitate more efficient transatmospheric flight and airplane-like operations of launch vehicles. A scramjet is an airbreathing engine that uses the compression of air over the forebody and inlet to achieve the conditions necessary for supersonic combustion, using no mechanical compressor, as illustrated in Figure 1. These engines operate in hypersonic conditions, ranging from Mach 5 to Mach 10 at current levels of technology. Ramjets have flown up through Mach 5.5, and at Mach numbers of around that magnitude it becomes more efficient to use supersonic combustion. Flight tests of the HIFiRE, X-51 and X-43A have had success in achieving positive thrust, while also highlighting the difficulties of designing hypersonic airbreathing engines, as detailed by Hank [1], Marshall [2], and Jackson [3][4]. Figure 1 Scramjet flowpath with methods used to simulate each component and inputs/outputs indicated along the lower boundary. Station numbers and component labels are included on the upper boundary. The continuous adjoint method was first applied to aerodynamic optimization by Jameson [5]. This methodology provides the surface sensitivity for a chosen functional at the cost of a single function evaluation, and unlike the finite difference method the cost is independent of the number of design variables. These sensitivities or gradients can be used in shape optimization as well as to accelerate uncertainty quantification. Work by Giles & Pierce [6], Castro [7] et. al., Hayashi [8], and Economon [9] provide further details for the derivation and solution of adjoint equations. In relation to inlet flows, Papadimitriou & Giannakoglou [10] derived the adjoint for a total pressure objective function at an outlet, and Othmer [11] provides a continuous formulation for incompressible ducted flows. Adjoint methods have been applied in many problems, but the work thus far has been generally limited to the use of a single, relatively simple, functional. As a result, the full potential of adjoint-based design has not been realized. Multiple relevant performance and stability measures have been ignored, and the simulations tend to involve isolated sub-components of the propulsion flowpath, particularly when using high-fidelity simulations. The result of this research is a methodology which produces low-cost gradients for a generalized functional defined in terms of averaged outflow quantities of a Computational Fluid Dynamics (CFD) volume. The use of a generalized form allows a much broader range of objectives, including objectives defined in external models that depend on information outside the CFD volume – for example, a combustion model used to predict the thrust. Using the continuous adjoint method, gradients can be found at a computational cost approximately equal to a single CFD evaluation for an arbitrary number of design variables. The use of the adjoint method with information produced outside the adjoint computational volume was not previously possible. This methodology was used to analyze the sensitivity of a scramjet inlet with respect to multiple functions, and to optimize that geometry for a selection of objective functions. Multi-objective optimization was also undertaken, examining the trade-offs between heat flux into the surface of the inlet and the thrust of the engine. The conclusions of this research included that accounting for flowpath performance and additional design considerations downstream of the scramjet inlet will produce a different result than optimizing for the isolated component performance, and that external gradients can be effectively fed into a continuous adjoint formulation facilitating a much broader and more flexible range of objectives.