A numerical framework for linear stability analysis of two-phase stratified pipe flows

IF 2.2 3区工程技术 Q2 MECHANICS

Theoretical and Computational Fluid Dynamics Pub Date : 2023-07-13 DOI:10.1007/s00162-023-00667-w

Ilya Barmak, Alexander Gelfgat, Neima Brauner

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Abstract

A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the interface between two fluids, are considered. The proposed numerical framework is based on a finite volume method and allows solving the problem numerically in bipolar cylindrical coordinates. In these coordinates, both the pipe wall and the unperturbed interface (of a constant curvature, e.g., plane interface, as considered in this work) coincide with the coordinate surfaces. Thereby, the no-slip as well as the interfacial boundary conditions can be imposed easily. It also enables investigation of the local behavior of the flow field and shear stresses in the vicinity of the triple points, where the interface contacts the pipe wall. The results obtained in the bipolar coordinates are verified by an independent numerical solution based on the problem formulation in Cartesian coordinates, where the pipe wall is treated by the immersed boundary method. Two representative examples of gas–liquid and liquid–liquid flows are included to demonstrate the applicability of the proposed numerical technique for analyzing the flow stability.

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两相分层管流线性稳定性分析的数值框架

提出了两种不混相流体在水平圆管内两相分层流动的严格线性稳定性分析的数值框架。本文首次考虑了三维扰动，包括两种流体交界面处的扰动。所提出的数值框架基于有限体积法，可以在双极柱坐标下进行数值求解。在这些坐标中，管壁和未受扰动的界面(曲率恒定的界面，如本文所考虑的平面界面)与坐标表面重合。因此，可以很容易地施加无滑移以及界面边界条件。它还可以研究三点附近的流场和剪切应力的局部行为，即界面与管壁接触的地方。在直角坐标系下，用浸入边界法处理管壁，通过独立的数值解验证了在双极坐标系下得到的结果。以气液流动和液液流动为例，说明了所提出的数值方法在分析流动稳定性方面的适用性。

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来源期刊

Theoretical and Computational Fluid Dynamics 物理-力学

CiteScore

5.80

自引率

2.90%

发文量

审稿时长

>12 weeks

期刊介绍： Theoretical and Computational Fluid Dynamics provides a forum for the cross fertilization of ideas, tools and techniques across all disciplines in which fluid flow plays a role. The focus is on aspects of fluid dynamics where theory and computation are used to provide insights and data upon which solid physical understanding is revealed. We seek research papers, invited review articles, brief communications, letters and comments addressing flow phenomena of relevance to aeronautical, geophysical, environmental, material, mechanical and life sciences. Papers of a purely algorithmic, experimental or engineering application nature, and papers without significant new physical insights, are outside the scope of this journal. For computational work, authors are responsible for ensuring that any artifacts of discretization and/or implementation are sufficiently controlled such that the numerical results unambiguously support the conclusions drawn. Where appropriate, and to the extent possible, such papers should either include or reference supporting documentation in the form of verification and validation studies.