Optimal control of shock wave attenuation in single - and two-phase flow with application to ignition overpressure in launch vehicles
Moshman, Nathan D.
Sritharan, Sivaguru S.
Hobson, Garth V.
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NASA and private launch providers have a need to understand and control ignition overpressure blast waves that are generated by a solid grain rocket during ignition. Research in accurate computational fluid dynamics prediction of the launch environment is underway. A clearer picture is emerging from empirical data which more precisely categorizes all the dissipative mechanisms present in droplet-shock interactions. In this dissertation, water droplets and their effects due to vaporization are represented as a control action and two new optimal control problems are formulated concerning unsteady shock wave attenuation. A single-phase control problem is formulated by representing the effect of droplet vaporization as an energy sink on the right hand side of the unsteady Euler Equations in one dimension. Results for the optimal distribution of equivalent mass of water vaporized for a given level of attenuation are presented. A two-phase control problem consists of solving for the initial optimal water droplet distribution. Results are presented for constrained and unconstrained water volume fraction distributions over increasing levels of attenuation. New adjoint-based algorithms were constructed which leave the final time free and satisfy all first order necessary conditions as well as avoid taking a variation at the shock front.
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