IHTC14-22439 FLOW CHARACTERISTICS AND STRUCTURES OF THREE-DIMENSIONAL UNSTEADY THERMAL CONVECTION IN A CONTAINER

ABSTRACT In this study, we numerically investigates the flow and thermal characteristics of the three-dimensional thermal convection in a cubic cavity heated below in the gravitational field, concerning about spatially-averaged kinetic energy K , Nusselt number Nu and flow structure. We assume Prandtl number Pr = 7.1 (water) and Rayleigh number Ra = 1.0×10 4 -3.5×10 5 . As a result, we have specified two of three important values of the Rayleigh number which demarcate different flow bifurcations and are referred to as the second and third critical Rayleigh numbers Ra c2 and Ra c3 . We have found that Ra c2 and Ra c3 are roughly 2.6×10 5 and 3.1×10 5 , respectively. We have observed a histerisis effect upon the value of Ra c2 with chaotic behaviour at c2 Ra Ra ≈ , and revealed flow structures. In addition, we investigate the relationship between Ra and the oscillatory-convection frequency. The increasing rate of the mean K with increasing Ra shows a different manner from that of Nu inflow-ave, mean . That is, the former is progressive and the latter is asymptotic, as Ra increases. Both the values of mean K and Nu inflow-ave, mean in oscillatory flow tend to be smaller than those in steady flow, respectively. Then, there exist small jumps/drops of mean K and Nu inflow-ave, mean at Ra = Ra c2

Stable branch and hysteresis effect of steady cubic convection

Both spatially-averaged kinetic energy K and influx-averaged Nusselt number Nuinflux are numerically investigated concerning the three-dimensional thermal convection in a cubic cavity heated from a bottom wall and chilled from its opposite top wall. Nuinflux represents the total influx of heat normalised by an area. Assuming incompressible fluid with a Prandtl number of 7.1 (water) in a Rayleigh-number range of 1.0×104– 1.0×105, the authors solve the three-dimensional Navier-Stokes equations with the Boussinesq approximation, using the finite difference method. As a result, in the Rayleigh-number range, hysteresis effects appear accompanying various steady flow structures. Hence, there can exist multiple values of K and multiple values of Nuinflux for the same Ra due to the different steady flow structures. As Rayleigh number gradually increases or decreases, there exist four stable branches. On the branches, the authors reveal the relation between K and flow structure and the relation between Nuinflux and flow structure. Besides, a steady flow structure becomes oscillatory on one branch, as Rayleigh number gradually increases