Abstract In this study, an effect of a three-dimensional obstacle of natural convection in a horizontal enclosure was discussed. Geometry which was taken into account was horizontal enclosure with unit aspect ratio and length of π along spanwise direction. The enclosure was heated from the bottom wall, and then was cooled down from above. An obstacle was located in the middle of the enclosure to examine its effect. A three-dimensional solution was obtained using Chebyshev spectral multi-domain methodology for different Rayleigh number at which the thermal behavior was evolved from a steady state to a chaotic pattern. As the geometry was elongated in conjunction with periodic boundary conditions to allow lateral freedom for the convection cells, longitudinal geometry along spanwise direction was discretized through a Fourier series expansion with a uniform mesh configuration. An adiabatic obstacle played a different role in determining the thermal behavior: No-slip condition of the surface of the obstacle disturbed the overall plume behavior in terms of the momentum transfer, whereas the adiabatic boundary condition did not influence significantly in terms of energy transfer. At a low Rayleigh number, thermal behavior in three-dimensional enclosure showed steady invariant solution along spanwise direction which is identical to two-dimensional result. With increasing buoyant force, spanwise invariance of longitudinal roll cell was collapsed and three-dimensional mode was obtained following flow regime transition. After undergoing periodically oscillatory phase, a chaotic flow transition occurred. At a high Rayleigh number, three-dimensional thermal plume oscillates freely in elongated geometry and consequently yields higher heat transfer rate. In addition, the thermal flow field was captured by visualizing the three-dimensional vortical structure. The chaotic three-dimensional flow behavior was quantitatively examined by obtaining the turbulent statistics.

中文翻译：

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水平围护结构中自然对流的数值模拟：第 I 部分。关于中间绝热障碍物的影响

摘要 本研究讨论了水平围护结构中自然对流的三维障碍物的影响。考虑的几何形状是水平围护结构，单位纵横比和长度为 π 沿展向。外壳从底壁加热，然后从上方冷却。一个障碍物位于围栏的中间，以检查其效果。对于不同的瑞利数，使用切比雪夫谱多域方法获得了三维解决方案，在该方法中热行为从稳态演变为混沌模式。由于几何形状与周期性边界条件一起被拉长，以允许对流单元的横向自由，沿展向方向的纵向几何形状通过具有均匀网格配置的傅立叶级数展开离散化。绝热障碍物在确定热行为方面发挥了不同的作用：障碍物表面的无滑移条件在动量传递方面干扰了整体羽流行为，而绝热边界条件在能量传递方面没有显着影响。在较低的瑞利数下，三维围护结构中的热行为在展向方向上呈现稳定不变的解，这与二维结果相同。随着浮力的增加，纵向滚动单元的展向不变性被破坏，并在流态转变后获得三维模式。在经历周期性振荡阶段后，发生了混乱的流转换。在高瑞利数下，三维热羽流在细长的几何形状中自由振荡，从而产生更高的传热率。此外，通过可视化三维涡流结构来捕获热流场。通过获得湍流统计量来定量检查混沌三维流动行为。