The complex fluid dynamics mechanism of multi-shaft stirring systems has constrained their application in industrial production. In this work, we have extracted torque signals to correlate power consumption with rotational speeds across single, dual, and triple shaft stirred reactors. Remarkably, the reasons behind the unique linear power consumption-rotational speed relationship exhibited in triple-shaft reactor, through the application of Fractional Fourier Transform. Our comparative analysis, through mixing energy, reveals multi-shaft systems' superiority in energy-efficient mixing. More importantly, the interaction between impellers and fluid within a reactor is reflected in the evolving of torque chaotic attractors. We have established a novel characterization strategy by fractal dimension of attractors which reflect the reactors' mixing efficiency. By mathematically modeling these attractors, we have demonstrated their potential as a tool for establishing the internal dynamics equations of stirred reactors. This approach offers a new method for evaluating mixing effectiveness and automated control of stirring machinery.

中文翻译：

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多轴搅拌反应器混合效率：基于混沌吸引子的快速表征策略


多轴搅拌系统复杂的流体动力学机理制约了其在工业生产中的应用。在这项工作中，我们提取了扭矩信号，将单轴、双轴和三轴搅拌反应器的功耗与转速相关联。值得注意的是，通过分数阶傅里叶变换的应用，三轴反应堆表现出独特的线性功耗-转速关系背后的原因。我们通过搅拌能量的对比分析，揭示了多轴系统在节能搅拌方面的优越性。更重要的是，反应器内叶轮和流体之间的相互作用反映在扭矩混沌吸引子的演变中。我们通过吸引子的分形维数建立了一种新颖的表征策略，反映了反应器的混合效率。通过对这些吸引子进行数学建模，我们证明了它们作为建立搅拌反应器内部动力学方程的工具的潜力。这种方法为评估混合效果和搅拌机械的自动控制提供了一种新方法。