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Dean flow of a Bingham fluid in a curved rectangular duct
Journal of Non-Newtonian Fluid Mechanics ( IF 3.1 ) Pub Date : 2020-11-02 , DOI: 10.1016/j.jnnfm.2020.104440
Miguel Moyers-Gonzalez , Ian A. Frigaard

In this paper we study the flow of a Bingham fluid on a curved (rectangular) pipe. Flows in this kind of geometries present secondary flows due to presence of centripetal forces in the radial direction. This so called Dean Flow has been extensively studied for Newtonian fluids. In considering a yield stress fluid in similar geometries the picture is less clear. Unfortunately, there is not an analytical solution, so the flow has been barely studied. Thus the purpose of this work. We consider only steady flow and develop a solution as a perturbation series in terms of the Dean number, Dn. The leading order solution is an axisymmetric azimuthal flow, driven by the pressure gradient. We compute this flow numerically using an augmented Lagrangian method on a regular rectangular mesh. We have also studied the limiting case of zero flow and we give a general expression for the critical Bingham number, Bc, for this to happen. The first order velocity perturbation produces 2 recirculating vortices, at top and bottom walls, analogous to those of the Newtonian flow. The size of the vortices appears to decrease slightly as BBc, and the magnitude of the secondary flow decays to zero significantly faster than that of the leading order flow. Finally we discuss the short comings of the perturbation series approach and propose how to overcome them.



中文翻译:

宾汉流体在弯曲的矩形导管中的迪安流动

在本文中,我们研究了宾厄姆流体在弯曲(矩形)管道上的流动。由于在径向方向上存在向心力,这种几何形状的流动呈现二次流动。对于牛顿流体,已经广泛研究了这种所谓的Dean Flow。在考虑类似几何形状的屈服应力流体时,情况不太清楚。不幸的是,由于没有分析解决方案,因此对流动的研究还很少。从而达到这项工作的目的。我们仅考虑稳定流,并根据Dean数将其作为扰动序列来开发解决方案,dñ。领先的解决方案是由压力梯度驱动的轴对称方位角流。我们在规则矩形网格上使用增强拉格朗日方法以数值方式计算此流量。我们还研究了零流量的极限情况,并给出了临界宾厄姆数的一般表达式,C,以实现此目标。一阶速度摄动在顶壁和底壁产生了两个循环涡旋,类似于牛顿流。旋涡的大小似乎随着C-,次流的幅度衰减到零的速度比先导流的衰减快得多。最后,我们讨论了摄动级数法的不足之处,并提出了如何克服它们的建议。

更新日期:2020-11-06
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