Actuator selection and placement for linear feedback control of compressible flows

Actuator and sensor placement for active control of high-Reynolds number flows is largely based on experience and trial-and-error because of the system’s large dimensionality and complexity. A novel strategy for estimating how to select and place a linear feedback control system using co-located actuator(s)/sensor(s) suitable for affecting the dynamics of compressible, viscous flows is developed. The methodology uses the flow’s gain and receptivity information from the forward and adjoint global modes of the baseflow obtained from direct/large eddy simulations. The baseflow can be an equilibrium (steady-state) or a time-averaged solution of the compressible Navier Stokes equations. The method uses structural sensitivity arguments to determine regions of the flow-field with high dynamical sensitivity, and a search procedure determines effective actuator/sensor locations. The control algorithm is flexible, and different types of control and feedback can be considered. The efficacy of the method is demonstrated with three different flow control problems: flow stabilization in a Mach 0.65 diffuser, noise reduction of an axisymmetric Mach 1.5 jet, and noise reduction of a turbulent Mach 0.9 jet. For the diffuser, global stabilization is achieved for low Reynolds numbers resulting in complete suppression of vortex shedding. For longer domains and higher Reynolds number flows in the diffuser, although significant reduction in growth rates of the unstable modes was achieved, complete stabilization could not be attained. For the axisymmetric Mach 1.5 jet, equilibrium and time-averaged configurations are compared to examine the differences in global stability. The jet’s optimal transient response that leads to the largest pressure fluctuations away from the jet is used to relate the global modes needed for the control methodology to the radiated sound. The spectrum also contains modes that are hydrodynamically bound to the jet, without significant sound field contributions. Direct numerical simulations using the control show significant noise reduction, with additional reduction with increase in control gain. Eigenanalysis of the controlled mean flows reveal fundamental changes in the spectrum at frequencies lower than that used by the control, with the quieter flows having unstable eigenvalues that correspond to eigenfunctions without significant support in the acoustic field. Analysis of the mean flow quantities shows that the control induced mean flow changes only become obvious beyond 15 radii from the nozzle. Reduced order analysis using Proper Orthogonal Decomposition (POD) shows flow regularization in the quieter flows. The active control strategy is then applied to a Mach 0.9 turbulent jet. The global analysis of the time-and-azimuthal averaged baseline flow showed that the flow supports acoustically efficient super-directive and multi-directive global modes. Significant noise reduction was obtained and, similar to the axisymmetric case, the global analysis of the time-and-azimuthal averaged flow for the quiet jet show the existence of an unstable mode at a low Strouhal number, that lacks any significant sound-field support. The variation of mean quantities at the centerline and the lipline for the loud and quiet jets also showed trends similar to the axisymmetric case