Low-order dynamical model for low-Prandtl number fluid flow in a laterally heated cavity

By applying proper orthogonal decomposition (method of snapshots) to low Prandtl number fluid flow in a laterally heated cavity of dimensions 4×2×1 in length × width × height , characteristic basic modes have been extracted. Using Galerkin projection of the governing equations on these basic modes, a low-dimensional dynamical model (set of ordinary differential equations) was constructed. Some results obtained from the low-order model are presented and compared with those calculated by direct numerical simulation (DNS). The factors influencing the reliability of the low-order model such as the length of the reference signal, the snapshot density, the number of modes chosen for Galerkin projection, the characteristic velocity, and the chosen expansions for velocity and temperature are discussed. It is found that the low-order model can exactly reproduce the results obtained by DNS at the design conditions (i.e., for the Grashof and Prandtl numbers at which the basic modes have been obtained). The model can also fairly well approach the DNS results in a domain around these conditions. Nevertheless, it seems that such models have to be used with care and that, in any case, they can qualitatively predict the DNS results only in a not very large range around the design conditions.