低Pr数流体自然对流边界层流动的直接数值模拟

在太阳能采暖通风系统中，空气在太阳辐射作用下于吸热壁上所形成的非稳态自然对流边界 层流动是决定系统热性能的关键所在. 对于线性分层的低普郎特数($Pr<1$)流体而言，标度分 析表明在起始阶段边界层的发展是与高度无关而只依赖于时间的，而处于稳态时，各项标度 关系与处于起始阶段终结时刻的大不相同，且都与高度和时间无关，而只与$Pr$数和线性分 层度相关. 直接数值模拟计算结果表明由标度分析所得的各项标度关系揭示了流动的特性参 数与控制参数之间的决定性内在联系. 但同时也表明标度关系并没有充分体现出 对$Pr$数的所有依赖关系，这一不足可利用直接数值模拟计算结果得到弥补.

DIRECT NUMERICAL SIMULATION OF NATURAL CONVECTION BOUNDARY-LAYER FLOW OF LOW PRANDTL NUMBER FLUID

In solar heating and ventilation systems, the unsteady natural convection boundary-layer flow of air formed adjacent to the vertical plane where solar radiation is absorbed is the key to determine the thermal performance of the systems. For a $Pr<1$ linearly-stratified fluid, scaling analysis demonstrates that the development of the boundary layer at the start-up stage is independent of the height but depends on time, while the scaling laws at the steady state stage are quite different from those at the end of the start-up stage; they depend only on $Pr$ and the linear stratification parameter. Direct numerical simulation results show that the scaling laws obtained from the scaling analysis reveal the main dependences, however, they also show that there are further dependence of the scaling laws on $Pr$ which can be obtained by direct numerical simulation results.