This paper presents the first solution of an optimal control problem concerning unsteadyblast wave attenuation where the control takes the form of the initial distribution of liquidwater droplets. An appropriate two-phase flow model is adopted for compressiblehomogeneous two-phase flows. The dynamical system includes an empirical model forwater droplet vaporization, the dominant mechanism for attenuating the jump in pressureacross the shock front. At the end of the simulation interval, an appropriate target state isdefined such that the jump in pressure of the target state is less than that of the simulatedblast wave. Given the nature of the non-linear system, the final time must also be a freevariable. A novel control algorithm is presented which can satisfy all necessary conditionsof the optimal system and avoid taking a variation at the shock front. The adjoint-basedmethod is applied to NASA’s problem of Ignition Overpressure blast waves generatedduring ignition of solid grain rocket segments on launch vehicles. Results are shown for arange of blast waves that are plausible to see in the launch environment of the shuttle.Significant parameters of effective droplet distributions are identified.
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