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Application of Proper Orthogonal Decomposition in Fluid Mechanics and Heat Transfer Problems

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If you have a question about this talk, please contact Professor Sanjeev Sanghi.

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 data for the POD analysis is obtained by numerical integrations of the governing equations of mass, momentum and energy. 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 translational symmetry in both space and time of the pair of modes having degenerate (equal) eigenvalues confirms the presence of traveling waves in the flow for several cases. The shifts in space and time of the structure of the degenerate modes, is utilized in the estimation of wave speeds in a given direction. 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 to supersonic flow past a triangular protuberance 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.

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