Adjoint analysis and control opportunities in a 2D jet

Model predictive control (via adjoint-based optimization) has already been applied successfully to large nonlinear systems for which the delay between the control actuation and the resulting effect on the metric of interest is large. This method extends naturally to high-dimensional discretizations of infinite-dimensional multiscale PDE systems such as compressible turbulent jet flows, for which the dimension of the system when discretized in space can be on the order of N∼O(10⁷). Such optimizations involve an expensive iterative procedure; our lab is currently gearing up to perform such supercomputer-based optimizations of 3D compressible turbulent jet systems. As an intermediate result, much may be learned from 2D adjoint calculations in this system to identify the sensitivity of the system to control actuation at various locations. The suitability of different types of control at different locations may be inferred from this sensitivity. It is seen that modification of the high-frequency noise radiated to the far field is possible with low-frequency actuation near the jet nozzle, and that mass sources are more effective than heat sources for modifying the acoustic field via forcing of the hydrodynamic field.