The following work describes the process of finding the flow and the temperature fields for a given ventilation system configuration. In order to simplify the problem, the flow was characterized as 2D, incompressible, viscous and in constant state. First, the governing equations in terms of the stream function, vorticity and Reynolds number have been developed. The obtained mathematical model for the flow field is actually a pair of coupled elliptical partial differential equations. Solving the resulting equations was performed using SOR (successive over-relaxation) methods following upwind second-order finite differences. In the second stage, the temperature field was numerically calculated using the flow field data obtained in the first stage. In fact, as expected, the flow has been advanced from the left inlet opening to the right outlet opening. Also, the main flow was creating a vortex while above the main flow large vortex has been generated and surrounded by several small vortices around it. Last but not least, Reynolds (Re) number influence on the solution nature has been expressed by flow expansion in the whole ventilation cell. Finally, comparison between different Re numbers have proved the flow type dependency on the Re number and its effect on the temperature field.

中文翻译：

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混合垂直通风系统的数值模拟

以下工作描述了寻找给定通风系统配置的流量和温度场的过程。为了简化问题，流动被表征为二维、不可压缩、粘性和恒定状态。首先，建立了流函数、涡度和雷诺数方面的控制方程。得到的流场数学模型实际上是一对耦合的椭圆偏微分方程。根据逆风二阶有限差分，使用 SOR（连续过度松弛）方法求解所得方程。在第二阶段，利用第一阶段获得的流场数据对温度场进行数值计算。事实上，正如预期的那样，流体已从左入口孔推进到右出口孔。此外，主流正在形成一个漩涡，而在主流之上已经产生了一个大漩涡，并被几个小漩涡围绕着。最后但并非最不重要的是，雷诺 (Re) 数对溶液性质的影响已通过整个通风单元中的流动膨胀来表达。最后，不同 Re 数之间的比较证明了流类型对 Re 数的依赖性及其对温度场的影响。