| |

Steady and Self-Oscillatory Regimes of Water Natural Convection in Square Cavity | |

The steady and unsteady solutions in the problem of the natural convection of water near its density maximum (about 4^oC) in a square cavity with the large Grashof numbers (which varied from 29000 up to 950000) are considered. Vertical walls of cavity are adiabatic and horizontal walls are isothermal. The temperature on top Tu is less than the temperature on bottom T_d, and they are symmetrical relatively to the temperature of density maximum T_{inv}. The control volume method with SIMPLE and SIMPLER algorithms is used in numerical calculations. The present problem has at least four different kinds of steady convective solutions and three kinds of unsteady oscillatory solutions with various Grashof numbers and initial conditions. The three kinds of steady solutions have been obtained earlier (with Grashof numbers less than 29000) and other solutions are studied in detail in the present paper. The existence of steady solutions at the various Grashof numbers is regarded, the critical Grashof numbers are also investigated. The Fourier analysis for oscillations of the average Nusselt numbers on top and bottom of the cavity is made. The influence of Grashof number changing on the average Nusselt numbers, amplitudes and frequencies of oscillations are presented. The isotherms and streamlines are shown for all kinds of solutions. |