The mechanism analysis of the oscillatory flow of Oldroyd-B fluid in a tube with a right triangular cross-section

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED
Lin Liu , Sen Zhang , Lang Liu , Chiyu Xie , Lixiu Wang , Yijia Liu , Jing Zhu , Libo Feng
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引用次数: 0

Abstract

This paper considers the oscillatory flow of the Oldroyd-B fluid in a tube with a right triangular cross-section. The partial differential equation for describing the unidirectional flow of Oldroyd-B fluid is derived. For treating the triangular region, the unstructured mesh finite element method is applied. For verifying the accuracy of the finite element method, the source term is introduced and the exact solution is constructed. We obtain an analytical solution for the isosceles triangular cross-section tube and analyze the effects of different parameters on the velocity amplitude and phase difference of the Oldroyd-B fluid flow. In addition, the dynamic characteristics for the unsteady-state Oldroyd-B fluid flow are discussed and the influence of the involved parameters, such as the pressure gradient, the relaxation and retardation time parameters on the velocity distribution are also investigated and the flow mechanism is analyzed graphically. At the same condition, we find that only the tube with an isosceles right triangle cross-section can produce the oscillatory flow. Finally, the fluid mechanism between the Newtonian fluid and the Oldroyd-B fluid for special cases is analyzed and discussed in detail.
oldyd - b流体在直角三角形截面管内振荡流动的机理分析
本文研究了Oldroyd-B流体在直角三角形截面管内的振荡流动。推导了描述oldyd - b流体单向流动的偏微分方程。对于三角形区域的处理,采用非结构网格有限元法。为了验证有限元法的精度,引入源项,构造了精确解。得到了等腰三角形截面管的解析解,并分析了不同参数对Oldroyd-B流体流动速度、振幅和相位差的影响。讨论了非定常oldyd - b流体流动的动态特性,研究了压力梯度、弛豫时间和缓速时间等相关参数对速度分布的影响,并对流动机理进行了图形化分析。在相同的条件下,我们发现只有横截面为等腰直角三角形的管才能产生振荡流。最后,对特殊情况下牛顿流体与Oldroyd-B流体之间的流体机理进行了详细的分析和讨论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Computers & Mathematics with Applications
Computers & Mathematics with Applications 工程技术-计算机:跨学科应用
CiteScore
5.10
自引率
10.30%
发文量
396
审稿时长
9.9 weeks
期刊介绍: Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).
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