Explicit approximate solutions to two transcendental equations in two-phase stratified flow

doi:10.1007/s10483-025-3299-6

Abstract

Abstract:

Stratified flow is a common phenomenon in horizontal tubes of two-phase flow systems. However, the existing methods for calculating the wetted angle of the flat interface model and the central angle of the two-circle model rely on solving implicit transcendental equations, which require iterative numerical root-finding methods, thereby introducing computational complexity and inefficiency. This paper proposes the high-precision explicit approximate solutions for the two models, directly correlating the geometric parameters with the flow parameters, thus significantly enhancing the efficiency and accuracy of two-phase flow analysis.

Key words: two-phase stratified flow, horizontal circular tube, wetted angle, central angle, Padé (rational) approximation, Schr?der iteration

2010 MSC Number:

O359⁺.1

Baisheng WU, Yixin ZHOU, Zeyao CHEN, Siukai LAI. Explicit approximate solutions to two transcendental equations in two-phase stratified flow. Applied Mathematics and Mechanics (English Edition), 2025, 46(10): 2007-2016.

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Figures/Tables 7

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