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Flow of a Bingham fluid in a pipe of variable radius
Journal of Non-Newtonian Fluid Mechanics ( IF 3.1 ) Pub Date : 2020-09-19 , DOI: 10.1016/j.jnnfm.2020.104393
Lorenzo Fusi , Kostas D. Housiadas , Georgios C. Georgiou

We extend a method developed by Fusi and Farina (Appl. Math. Comp. 320, 1–15, 2018) to obtain semi-analytical lubrication-approximation solutions for the flow of a Bingham-plastic in a tube of variable radius. The proposed method is applicable provided that the unyielded core extends continuously from the inlet to the outlet. It turns out that the variable radius of the latter core obeys a stiff integral-algebraic equation which is solved both numerically and asymptotically. The pressure distribution is then obtained integrating a 1st-order ODE and the velocity components are computed using analytical expressions. Converging or diverging either linearly or exponentially, undulating and stenosed tubes are considered. The effects of the shape of the wall on the yield surface which separates the yielded region from the unyielded core and on the pressure difference required to drive the flow are investigated and discussed. The results show that the effect of the wall variation amplitude is greatly amplified as the volumetric flow rate (or, equivalently, the imposed pressure difference driving the flow) increases. It is also demonstrated that the pressure difference needed to achieve a given volumetric flow rate in a converging pipe is always higher than that for a diverging one.



中文翻译:

宾厄姆流体在可变半径的管道中的流动

我们扩展了由Fusi和Farina开发的方法(Appl。Math。Comp。320,1-15,2018年),以获取可变半径管中Bingham塑料流动的半解析润滑近似解。只要未屈服的铁芯从入口连续延伸到出口,建议的方法就适用。事实证明,后一个磁芯的可变半径服从一个刚性的积分-代数方程,该方程可以在数值上和渐近上求解。然后结合一阶ODE获得压力分布,并使用解析表达式计算速度分量。线性或指数收敛或发散,考虑起伏和狭窄的管。研究和讨论了壁的形状对屈服表面的影响,屈服表面将屈服区域与未屈服的岩心分开,并且对驱动流动所需的压力差也有影响。结果表明,随着体积流量(或等效地,施加的压差驱动流量)的增加,壁面变化幅度的影响会大大放大。还证明了在收敛管中达到给定体积流量所需的压差始终高于分流管。

更新日期:2020-09-23
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