A Fuzzy-Pod Based Estimation of Unsteady Mixed Convection in a Partition Located Cavity with Inlet and Outlet Ports

Abstract

In the present study, a novel approach based on Proper Orthogonal Decomposition (POD) and fuzzy clustering method is utilized to predict the flow field and heat transfer for the unsteady mixed convection in a square enclosure with two ventilation ports. An adiabatic thin fin is placed on the bottom wall of the cavity and all walls of the enclosure are kept at constant temperature. An oscillating velocity is imposed at the inlet port for a range of Strouhal numbers between 0.1 and 1. Reduced order models of the system are obtained with fuzzy-POD approach for Richardson number of 1 and 100. The estimation data set is obtained for Strouhal numbers 0.1 and 0.5, and the validation data set is obtained for Strouhal number of 0.25. A comparison of the modal coefficients obtained from the proposed approach compares well with the modal coefficients obtained by projecting the CFD data at Strouhal number of 0.25 onto the POD modes. The proposed approach is computationally efficient and the problem of numerical instability in the computation with the conventional Galerkin-POD approach can be circumvented.