POD-ROM model for analyzing the onset of natural convection and stability in a differentially heated top open cavity

The deformation of the conduction layers in a differentially heated cavity leads to the onset of convection currents. The top open cavity investigated here showed lower critical Rayleigh number as compared to the classical Rayleigh-Benard convection, which can be due to the free interaction of cavity air with the external atmosphere due to the non-negligible vertical velocity component at the open surface. These conditions lead to the corner flow patterns in the cavity even at Rayleigh numbers below the critical limit. The corner flow leads to non-equilibrium condition before the onset of natural convection which complicates the stability analysis for this problem. One of the complication is due to non-equilibrium pre-convection flow conditions and Proper Orthogonal Decomposition (POD) of the numerical solutions is used to model the initial corner flow conditions. POD based Reduced Order Model (ROM) is then devised by projecting the Navier-Stokes-Boussinesq equations on empirical eigenvectors. The resulting ROM is used to predict the critical Rayleigh number and further bifurcation analysis. Some of the experimentally and numerically observed physics such as symmetry breakdown, mirror image solution have been analyzed using reduced order model.