Abstract Targeting a pseudoplastic fluid, we propose a method to simultaneously estimate viscosity and pressure fields from the velocity field data of particle image velocimetry (PIV). As a two-dimensional case study, we chose a steady two-dimensional wake structure behind a circular cylinder where local viscosity and pressure are mechanically coupled. The method involves PIV, momentum conservation equation of non-Newtonian fluids and rheological constitutive equations. The CMC (Carboxy Methyl Cellulose) aqueous solution of weight concentration of 0.1% is used as a test case of pseudoplastic fluid. Viscosity distribution is obtained through power law model and Carreau-Yasuda model as the constitutive equation. Pressure distribution is then calculated by substituting the viscosity into the momentum conservation equation. Applied results show pressure-lowering at the vortex cores and viscosity-lowering at their perimeters, stabilizing vortex attachment to the cylinder in the pseudoplastic fluid. We also analyze error propagation characteristics to conclude the feasibility of the present method and highlight the difference in error propagation characteristics during pressure estimation between Newtonian and pseudoplastic fluid flows.

中文翻译：

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基于 PIV 的稳态假塑性流动粘度和压力场估计

摘要 针对假塑性流体，我们提出了一种从粒子图像测速 (PIV) 的速度场数据中同时估计粘度场和压力场的方法。作为二维案例研究，我们在圆柱体后面选择了稳定的二维尾流结构，其中局部粘度和压力机械耦合。该方法涉及PIV、非牛顿流体动量守恒方程和流变本构方程。以重量浓度为0.1%的CMC(Carboxy Methyl Cellulose)水溶液作为假塑性流体的测试用例。粘度分布是通过幂律模型和Carreau-Yasuda模型作为本构方程得到的。然后通过将粘度代入动量守恒方程来计算压力分布。应用结果表明，涡核的压力降低，其周边的粘度降低，稳定了假塑性流体中涡旋附着在圆柱体上。我们还分析了误差传播特性，以得出本方法的可行性，并强调牛顿流体和假塑性流体流动之间压力估计过程中误差传播特性的差异。