Dynamic Modeling and Flow Control Strategies for Rectangular Jets: Application of POD and Wavelet Analysis

摘要

This research effort has as its objectives: the experimental characterization and low order modeling of the coherent structure dynamics of high Reynolds number rectangular jets of low and moderate aspect ratios via a joint application of the proper orthogonal decomposition (POD) and wavelet analysis techniques. This includes the extraction and characterization of the u, v, and w-component POD eigenfunctions and associated eigenvalues. The rectangular jet dynamics (embodied in the POD temporal coefficients) is obtained by projection of the POD eigenfunctions onto instantaneous realizations of the flow field. This projection is performed via wavelet analysis. Similarly Galerkin projection of a truncated subset of the empirical eigenmodes onto the Navier-Stokes equations is used to develop a low-order dynamical systems model of the rectangular jet flow field. The validity of assumptions associated with the treatment of the truncated modes and their effect on the coherent structure is established by comparing the dynamic behavior resulting from the model ODE's with those from projection of POD modes onto the actual flow. The dynamical system model of the rectangular jet will be utilized for the establishment of rectangular jet flow control strategies. The flow control algorithm will be demonstrated via both the model and laboratory jet flows.