Proper Orthogonal Decomposition for Flow Calculations and Optimal Control in a Horizontal Cvd Reactor
چکیده
Proper orthogonal decomposition (which is also known as the Karhunen Lo eve decomposition) is a reduction method that is used to obtain low dimensional dynamic models of distributed parameter systems. Roughly speaking, proper orthogonal decomposition (POD) is an optimal technique of nding a basis which spans an ensemble of data, collected from an experiment or a numerical simulation of a dynamical system, in the sense that when these basis functions are used in a Galerkin procedure will yield a nite dimensional system with the smallest possible degrees of freedom. Thus the technique is well suited to treat optimal control and parameter estimation of distributed parameter systems. In this paper , the method is applied to analyze the complex ow phenomenon in a horizontal chemical vapor deposition (CVD) reactor. In particular, we show that POD can be used to eeciently approximate solutions to the compressible viscous ows coupled with the energy and the species equations. In addition, we also examined the feasibility and eeciency of POD method in the optimal control of the source vapors to obtain the most uniform deposition proole at the maximum growth rate. Finally, issues concerning the implementation of the method and numerical calculations are discussed.