The Zuppinger water wheel, developed in the 1850s, is one of the most efficient water wheels and is commonly used for low-head hydropower generation. The high efficiencies of the wheel over a wide operating range, its simplicity in design and slow rotational speed offer a low-cost and environmentally friendly low-head hydropower solution. A physical and numerical model study of a wheel is presented in this paper. Three-dimensional numerical simulations were performed using the computational fluid dynamics (CFD) code Flow-3D. The influence of grid size on the results of the numerical model was assessed using a systematic grid refinement study. Grid convergence indices (GCIs) were calculated for two grid sets each, with three different grid sizes, using a constant grid refinement ratio. The GCIs were reduced to levels below 5% for the selected quantities of interest. The CFD model results were compared with physical model results at different operating points of the wheel. The maximum differences in power output and efficiency between the physical and numerical model results were 2.5% and 8%, respectively.

中文翻译：

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祖平格水车模型的实验与数值研究

1850年代开发的祖平格水车是效率最高的水车之一，常用于低水头水力发电。轮子在广泛的工作范围内的高效率、其设计简单和低转速提供了一种低成本和环保的低水头水电解决方​​案。本文介绍了车轮的物理和数值模型研究。使用计算流体动力学 (CFD) 代码 Flow-3D 进行三维数值模拟。使用系统的网格细化研究评估了网格大小对数值模型结果的影响。使用恒定的网格细化率计算了两个网格集的网格收敛指数 (GCI)，每个网格集具有三种不同的网格大小。对于选定的感兴趣数量，GCI 降低到低于 5% 的水平。将 CFD 模型结果与车轮不同工作点的物理模型结果进行了比较。物理和数值模型结果之间功​​率输出和效率的最大差异分别为 2.5% 和 8%。