Controlling Multi-Component Flow Instabilities Using Adjoints

Flow instabilities are ubiquitous in nature and industrial applications. Controlling such flows is critical for increasing the efficiency of engineering systems. In this talk, adjoint-based optimization is used to control late-time nonlinear evolution of a Rayleigh–Taylor (RT) instability by systematically adjusting the initial interfacial perturbations. The adjoint governing equations for multi-component fluids provide sensitivity of RT mixing or growth at different stages of the instability. Three surrogate objective functions are considered: (i) a mixing quantity based on mole fraction variance; (ii) an energy norm based on the velocity normal to the interface; and (iii) a norm based on the deviation of mole fraction from an initially unperturbed state. Sensitivity of these objective functions to initial interfacial perturbations are used in a gradient-based optimization framework that seeks to both enhance and suppress the RT instability while keeping the initial perturbation energy constant. The optimized perturbations are reported for each case and compared against results from linear stability theory. In addition, the effect of different objective functions and integration durations on the optimized solutions are discussed.