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首页> 外文会议>FED-vol.260; ASME International Mechanical Engineering Congress and Exposition; 20041113-19; Anaheim,CA(US) >RIMMING FLOW OF NON-NEWTONIAN FLUIDS
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RIMMING FLOW OF NON-NEWTONIAN FLUIDS

机译：非牛顿流体的起伏流动

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摘要

The present study is related to the rimming flow of non-Newtonian fluid on the inner surface of a horizontal rotating cylinder. Using a scale analysis, the main characteristic scales and non-dimensional parameters, which describe the principal features of the process, are found. Exploiting the fact that one of the parameters is very small, an approximate asymptotic mathematical model of the process is developed and justified. For a wide range of fluids, a general constitutive law can be presented by a single function relating shear stress and shear rate that corresponds to a generalized Newtonian model. For this case, the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a steady-state solution is proved. Within the bounds stipulated by this condition, film thickness admits a continuous solution, which corresponds to subcritical and critical flow regimes. It is proved that for the critical regime solution has a corner on the rising wall of the cylinder. In the supercritical flow regime, a discontinuous solution is possible and a hydraulic jump may occur. It is shown that straightforward leading order steady-state theory can work well to study the shock location and height. For the particular case of a power-law model, the analytical solution of steady-state equation for the fluid film thickness is found in explicit form. More complex rheological models, which show linear Newtonian behavior at low shear rates with transition to power-law at moderate shear rates, are also considered. In particular, numerical computations were carried out for Ellis model. For this model, some analytical asymptotic solutions have been also obtained in explicit form and compared with the results of numerical computations. Based on these solutions, the optimal values of parameters, which should be used in the Ellis equation for correct simulation of coating flows, are determined; the criteria that guarantee the steady-state continuous solutions are defined; the size and location of the stationary hydraulic jumps, which form when the flow is in the supercritical state, are obtained for the different flow parameters.
机译：本研究与水平旋转圆柱体内表面上的非牛顿流体的边缘流动有关。使用规模分析，找到描述过程主要特征的主要特征规模和无量纲参数。利用其中一个参数很小的事实，开发并证明了该过程的近似渐近数学模型。对于广泛的流体，可以通过与剪切应力和剪切速率相关的单个函数来表示一般的本构定律，该函数对应于广义牛顿模型。在这种情况下，得出了边沿流动的径流条件。如果满足径流条件，则证明存在稳态解。在此条件规定的范围内，膜厚允许连续的溶液，这对应于亚临界和临界流动状态。事实证明，对于临界状态，解决方案在圆柱体的上升壁上有一个角。在超临界流态下，可能会出现不连续的解，并且可能会发生水力跃变。结果表明，直接的前导稳态理论可以很好地研究激波的位置和高度。对于幂律模型的特定情况，以显式形式找到了流体膜厚度稳态方程的解析解。还考虑了更复杂的流变模型，该模型显示了低剪切速率下的线性牛顿行为，并在中等剪切速率下转换为幂律。特别是，对Ellis模型进行了数值计算。对于该模型，还以显式形式获得了一些解析渐近解，并将它们与数值计算结果进行了比较。基于这些解决方案，确定了应该在Ellis方程中用于正确模拟涂层流动的参数的最佳值。确定保证稳态连续解的标准；对于不同的流量参数，获得了当流体处于超临界状态时形成的固定水力跃迁的大小和位置。

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