Numerical simulations of shear‐thinning and shear‐thickening fluid flows past a circular cylinder are performed using a lattice Boltzmann method. In this study, the property of shear‐thinning and shear‐thickening fluids is expressed by the Carreau model. We focus on the definition of an effective (representative) Reynolds number for describing the flow of shear‐thinning and shear‐thickening fluids past a circular cylinder. The fluid flows and viscosity profiles are clearly shown for fluids flowing across a circular cylinder depending on the Reynolds and Carreau numbers and the power index. A large value of Carreau number lead to the formation of low‐viscosity regions for shear‐thinning and high‐viscosity regions for shear‐thickening around a circular cylinder. Meanwhile, the change in the viscosity around the cylinder is not remarkable for a small Carreau number. The formulation of the effective Reynolds number defined using effective shear rate and viscosity is proposed in order to organize and understand the flow of Carreau‐model fluids across a circular cylinder. The effective Reynolds number counseled in this study allows one to completely describe the flow state of Carreau‐model fluids past a circular cylinder on an equal footing with Newtonian fluid flows. The usefulness of the effective Reynolds numbers is discussed, and the feature of Carreau‐model fluid flows past a circular cylinder is considered in terms of the effective Reynolds number.

中文翻译：

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卡洛模型流体流过圆柱体的数值模拟

使用晶格玻尔兹曼方法对流过圆柱的剪切稀化和剪切稠化流体进行了数值模拟。在这项研究中，剪切稀化和剪切稠化流体的性质由Carreau模型表示。我们集中在有效（代表）雷诺数的定义上，以描述流过圆柱的剪切稀化和剪切增稠流体的流动。根据雷诺数和Carreau数以及功率指数，可以清楚地显示流过圆柱体的流体的流量和粘度曲线。较大的Carreau值会导致在圆柱体周围形成用于剪切稀化的低粘度区域和用于剪切稠化的高粘度区域。与此同时，对于较小的Carreau值，圆柱体周围的粘度变化并不明显。提出使用有效剪切速率和粘度定义有效雷诺数的公式，以组织和理解Carreau模型流体在圆柱体上的流动。这项研究中建议的有效雷诺数可以使人们完整地描述Carreau模型流体在与牛顿流体流相等的基础上通过圆柱体的流动状态。讨论了有效雷诺数的有用性，并根据有效雷诺数考虑了流过圆柱的Carreau模型流体的特征。提出使用有效剪切速率和粘度定义有效雷诺数的公式，以组织和理解Carreau模型流体在圆柱体上的流动。这项研究中建议的有效雷诺数可以使人们完整地描述Carreau模型流体在与牛顿流体流相等的基础上通过圆柱体的流动状态。讨论了有效雷诺数的有用性，并根据有效雷诺数考虑了流过圆柱的Carreau模型流体的特征。提出使用有效剪切速率和粘度定义有效雷诺数的公式，以组织和理解Carreau模型流体在圆柱体上的流动。这项研究中建议的有效雷诺数可以使人们完整地描述Carreau模型流体在与牛顿流体流相等的基础上通过圆柱体的流动状态。讨论了有效雷诺数的有用性，并根据有效雷诺数考虑了流过圆柱的Carreau模型流体的特征。