Direct numerical simulations of two-dimensional chaotic natural convection in a differentially heated cavity of aspect ratio 4
Direct numerical simulations of two-dimensional chaotic natural convection in a differentially heated cavity of aspect ratio 4
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DOI：
10.1017/s0022112095004356
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发表时间：
1995-12
影响因子：
3.7
通讯作者：
S. Xin;P. Quéré
中科院分区：
文献类型：
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作者：
S. Xin;P. Quéré
采用直接数值积分的方法研究了绝热水平壁、高宽比为4的差热空气空腔内的混沌自然对流。时间积分是使用切比雪夫空间近似和二阶有限差分时间步进计划的频谱算法。渐近解已获得三个值的瑞利数的基础上腔高度高达1010。时均流场表明，流动结构越来越偏离众所周知的层流。随着瑞利数的增加，位于边界层外缘的大回流区形成并向上游移动。与时间相关的解由在边界层中向下游流动的行波组成。这些波的振幅增长，因为他们的旅行下游和钩状的温度图案形成在热边界层的外缘。在最大的瑞利数调查，他们成长到这样一个点，他们导致在形成大的不稳定的涡流，完全破坏边界层。这些涡流将热流体和冷流体抛入核心区域的上部和下部，导致热更均匀的顶部和底部区域，其挤压靠近腔体中部高度的增加分层的区域。这些大的非定常涡使层化核心区的内波保持激发状态。这些模拟还提供了二阶统计，如湍流动能，热和粘性耗散，雷诺应力和湍流热通量。
Chaotic natural convection in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is investigated by direct numerical integration of the unsteady two-dimensional equations. Time integration is performed with a spectral algorithm using Chebyshev spatial approximations and a second-order finite-difference time-stepping scheme. Asymptotic solutions have been obtained for three values of the Rayleigh number based on cavity height up to 1010. The time-averaged flow fields show that the flow structure increasingly departs from the well-known laminar one. Large recirculating zones located on the outer edge of the boundary layers form and move upstream with increasing Rayleigh number. The time-dependent solution is made up of travelling waves which run downstream in the boundary layers. The amplitude of these waves grows as they travel downstream and hook-like temperature patterns form at the outer edge of the thermal boundary layer. At the largest Rayleigh number investigated they grow to such a point that they result in the formation of large unsteady eddies that totally disrupt the boundary layers. These eddies throw hot and cold fluid into the upper and lower parts of the core region, resulting in thermally more homogeneous top and bottom regions that squeeze a region of increased stratification near the mid-cavity height. It is also shown that these large unsteady eddies keep the internal waves in the stratified core region excited. These simulations also give access to the second-order statistics such as turbulent kinetic energy, thermal and viscous dissipation, Reynolds stresses and turbulent heat fluxes.