2019, 40(4): 398-407.
doi: 10.21656/1000-0887.390102
Abstract:
Through numerical simulation of the basic equations for 2D fluid mechanics, the convection patterns and the critical conditions for pattern transition in an inclined rectangular cavity with Prandtl number Pr=6.99 were studied. According to the variations of inclination angle θ and relative Rayleigh number Rar, the convection patterns in the inclined layer can be divided into the convection single-roll pattern, the multi-roll pattern filling the cavity and the multi-roll pattern in the transitional stage. With constant inclination angle θ,the system transforms from the multi-roll pattern filling the cavity to the single-roll pattern with the decrease of relative Rayleigh number Rar, where the convection amplitude and Nusselt number Nu increase with Rar. For Rar=9,the system transforms from the multi-roll pattern filling the cavity to the single-roll pattern with the increase of inclination angle θ,where the convection amplitude decreases with θ,and the Nusselt number increases with θ.The simulation results of the transition from multi-roll to single-roll patterns in plane θc-Rar show that, for Rar=2,the multi-roll pattern is not found in the cavity. For Rar=2.5 or so, the transition from the multi-roll pattern to the single-roll pattern appears in the cavity. The critical θc value for the transition from the multi-roll to the single-roll patterns increases with the decrease of Rar for θc<10. The θc value increases with Rar for θc>10, where θc increases rapidly with Rar for Rar≤5,and increases slowly with Rar for Rar>5. The relation between θc and Rarθ is similar to θ.
