Data-Driven Input-Output Analysis and Control Design of a 3D Supersonic Dual-Stream Jet

Input-output analysis provides insights into flow dynamics and often guides actuator design for complex turbulent flows. Operator-based methods, like the resolvent analysis, are commonly used on the linearized Navier-Stokes equations, but its construction and computation remains a daunting task, especially for 3D flows. This study presents a data-driven low-cost method to uncover the 3D perturbation dynamics of a supersonic dual-stream jet and economically identify effective control parameters. The nozzle houses Mach 1.6 core and Mach 1.0 bypass streams that mix downstream of the splitter plate trailing edge (SPTE), producing instabilities, high frequency tones, shock trains, and SBLIs. A dynamic mode decomposition reduced-order model (DMD-ROM) is employed, which projects baseline and forcing snapshots onto a reduced subspace and advances them in time. Gain is computed in the reduced space, allowing fast evaluation of the control input. The forcing is customizable to the flow problem and may be tailored to consider any set of actuator-specific parameters. For a 2D jet, DMD-ROM yields insights comparable to resolvent analysis with less cost. In this work, we demonstrate DMD-ROM on the 3D jet, with actuators arranged along the SPTE surface aimed at suppressing the resonant tone and mitigating the shock train and SBLIs. A range of forcing frequencies, actuation angles, and spanwise wavenumbers are considered, and optimal DMD-ROM parameters are used to guide 3D non-linear control in simulations.