Toward optimally seeded airflow on hypersonic vehicles using control theory

Following the renewed interest in hypersonic flight and the significant advances made recently, it is now the time to start looking at ways to optimize hypersonic vehicle designs in an efficient manner. Since the medium, in a hypersonic flow, can be locally ionized, it is possible to use electromagnetic actuators that induce an acting force to optimally control the flow. The local injection of substances that have a considerably lower ionization temperature than air into the airflow – flow seeding – leads to stronger local ionization levels at relatively low hypersonic speeds, amplifying the magnetic effects for the same imposed magnetic field intensity. Because much has been devoted to the analysis of such problems but no formal design approach as been persued to date, the main motivation for this work is to provide an efficient design framework built around high-speed magnetohydrodynamics (MHD) prediction capabilities that can be used in hypersonic control applications using magnetic effects. In particular, the design framework should provide information that leads to an optimal airflow seeding strategy in conjunction with an imposed magnetic field. The proposed framework is based on control theory, which implies developing an adjoint solver aimed to efficiently provide sensitivity analysis capability in arbitrary complex hypersonics MHD flows. Automatic differentiation tools are selectively used to develop the discrete adjoint, which make for a much shorter implementation time and greatly reduce the probability of programming errors. A generic hypersonic vehicle is used to demonstrate the sensitivity analysis capability of the implemented MHD adjoint solver. The precision of the computed adjoint-based sensitivities is established and the performance of the adjoint solver is analyzed. A sample design problem is included using a gradient-based optimizer.