倾斜层中的对流斑图及其临界条件

通过二维流体力学基本方程的数值模拟,探讨了Prandtl(普朗特)数Pr=6.99时,倾斜矩形腔体中的对流斑图和斑图转换的临界条件.根据倾角θ和相对Rayleigh(瑞利)数Ra_r的变化,倾斜矩形腔体中的对流斑图可以分为:单滚动圈对流斑图、充满腔体的多滚动圈对流斑图和过渡阶段的多滚动圈对流斑图.当θ一定时,随着Ra_r的减小,系统由充满腔体的多滚动圈对流斑图过渡到单滚动圈对流斑图.这时,对流振幅A和Nusselt(努塞尔)数Nu随着Ra_r的增加而增加.当Ra_r=9时,随着θ的增加,系统由充满腔体的多滚动圈对流斑图过渡到单滚动圈对流斑图,这时对流振幅A随着θ的增加而减小,Nusselt数Nu随着θ的增加而增加.在θ_c-Ra_r平面上对多滚动圈到单滚动圈对流斑图过渡的模拟结果表明,在Ra_r=2时,腔体中没有发现多滚动圈对流斑图.在Ra_r为2.5左右时,腔体中出现多滚动圈到单滚动圈对流斑图的过渡.当多滚动圈到单滚动圈对流斑图过渡的临界倾角θ_c<10°时,θ_c随着Ra_r的减小而增加.当θ_c>10°时,θ_c随着Ra_r的增加而增加,在Ra_r≤5时,θ_c随着Ra_r的增加而迅速增加;当Ra_r>5时,θ_c随着Ra_r的增加而缓慢增加.θ_c与Ra_rθ的关系与Ra_r类似.

Convection Patterns and Corresponding Critical Conditions in an Inclined Layer

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 Ra_r, 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 Ra_r, where the convection amplitude and Nusselt number Nu increase with Ra_r. For Ra_r=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 θ_c-Ra_r show that, for Ra_r=2,the multi-roll pattern is not found in the cavity. For Ra_r=2.5 or so, the transition from the multi-roll pattern to the single-roll pattern appears in the cavity. The critical θ_c value for the transition from the multi-roll to the single-roll patterns increases with the decrease of Ra_r for θ_c<10. The θ_c value increases with Ra_r for θ_c>10, where θ_c increases rapidly with Ra_r for Ra_r≤5,and increases slowly with Ra_r for Ra_r>5. The relation between θ_c and Ra_rθ is similar to θ.