Development of low dimensional models for control of compressible flows

The ability to develop a reduced order model for compressible flows that can be used for control is examined. Data from the LES of a variable density subsonic mixing layer is chosen to apply the proper orthogonal decomposition (POD) and evaluate the dynamical evolution of the POD eigenmodes as a reduced-order system to study and eventually develop control strategies for such flows in the compressible regime. All variables of interest, density, velocity and temperature are decomposed via the POD and minimal approximation is made in their projection onto the Navier Stokes equations to yield the dynamical evolution equations for the various modes. Results obtained from this reduced order model compare well with the original data set and have encouraged us to pursue other complex flows of similar interest.