Impellers in stirred vessels are often characterized by dimensionless numbers such as the power and flow numbers. These are often crucial in determining mixing performance. Previous studies for high-shear mixers have yielded correlations between the power, flow, and mixer geometries, since in these mixers the flow can be independently varied. For stirred vessels, dimensional analysis is typically used to develop such correlations, leading to less accurate predictive models. Here, we combine an analysis based on a balance of angular momentum balance with computational fluid dynamics simulations to comprehensively study the effect of impeller geometry on the relationship between power and flow. The results allow for the prediction of the flow generated by the impeller based on the easily measurable impeller power consumption and the geometrical dimensions of the impeller. The models are accurate over a wide range of geometries. Furthermore, we are able to predict both the primary and total flows.

中文翻译：

---

径向叶轮几何形状对功率和流量数之间联系的影响

搅拌容器中的叶轮通常以无量纲数为特征，例如功率数和流量数。这些通常对于确定混合性能至关重要。先前对高剪切混合器的研究已经得出了功率、流量和混合器几何形状之间的相关性，因为在这些混合器中，流量可以独立变化。对于搅拌容器，通常使用尺寸分析来建立这种相关性，从而导致预测模型的准确性较低。在这里，我们将基于角动量平衡平衡的分析与计算流体动力学模拟相结合，以综合研究叶轮几何形状对功率与流量之间关系的影响。结果允许根据易于测量的叶轮功耗和叶轮的几何尺寸预测叶轮产生的流量。这些模型在各种几何形状上都是准确的。此外，我们能够预测主要流量和总流量。