Application of Proper Orthogonal Decomposition in Fluid Mechanics and Heat Transfer Problems
Sanjeev Sanghi
Engineering and Design, University of Sussex
Abstract:
The Proper Orthgonal Decomposition (POD) has beome a very useful tool in the analysis and low dimensional modeling of flows. It provides an objective way of identifying the 'coherent' structures in a turbulent flow. The application of POD to the case of a thermally driven two-dimensional flow of air in a horizontal rotating cylinder, subject to Boussinesq approximation, is presented. The decomposition based on the POD modes or eigenfunctions is shown to converge to within 5% deviation of the computational data for a maximum of 15 modes for the different cases. The low-dimensional models are constructed employing a Galerkin procedure. For each of the five cases, the low-dimensional models yield accurate qualitative as well as quantitative behaviour of the system. Not more than 20 modes are required in the low-dimensional models to accurately model the system dynamics. The ability of low-dimensional models to accurately predict the system behaviour for the set of parameters different from the one they were constructed from is also examined.
Further applications of POD as an interapolating and extrapolating tool in supersonic flow past a protrusion mounted on an axisymmetric body are also presented briefly.
Finally, novel (not related to fluid mechanics) applications of POD are presented where the method has been used to compress an audio file and for web search personalization.