Nonlinear Differential Equation of the Surface Section of Gas-Liquid

机译：气液表面截面的非线性微分方程

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Study of flow of thin layers of viscous liquids (liquid films) is of great theoretical and practical importance. For liquid films is the basis of technological processes in many industries: petrochemical, thermal power, food and other. The development of nonlinear mathematical models that adequately reflect the real flow of a liquid film, the contact and interaction between fluids (gas-liquid), the calculation characteristics of the film flow is an important task. Presents the nonlinear mathematical model of the state of free surface liquid film, accounting for the interaction with the gas flow is a nonlinear differential equation of fourth order for deflection of the free liquid surface from the unperturbed state ψ(x,t), where x - the spatial variable, t - time. The transition to the finite-difference equation is completed. Computational algorithms for the calculation of wave characteristics and deviation of free surface liquid film in contact with the gas stream are developed. The results of computational experiments for the vertical film of water at moderate Reynolds numbers are presented.

机译：研究粘性液体（液膜）薄层的流动具有重要的理论和实践意义。液膜是许多行业技术流程的基础：石化，火电，食品等。非线性数学模型的发展能够充分反映液膜的实际流量，流体（气-液）之间的接触和相互作用，膜流量的计算特性是一项重要的任务。提出了自由表面液膜状态的非线性数学模型，考虑了与气流的相互作用，这是一个四阶非线性微分方程，表示自由液面从不受扰动状态ψ（x，t）偏转，其中x -空间变量，t-时间。向有限差分方程的转换完成。开发了计算算法，用于计算与气流接触的自由表面液膜的波动特性和偏差。给出了中等雷诺数的垂直水膜计算实验的结果。

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来源
《Finite difference methods: theory and applications》|2018年|419-426|共8页
会议地点 Lozenetz(BG)
作者
L. A. Prokudina;
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作者单位

South Ural State University, pr. Lenina 76, Chelyabinsk, Russia;

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会议组织
原文格式 PDF
正文语种 eng
中图分类
关键词
Liquid film; Instability; Finite-difference equation; Reynolds number; Shear stress;

机译：液膜；不稳定；有限差分方程；雷诺数；剪应力;

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5. Geometrical aspects of linear differential equations over compact Riemann surfaces with reductive differential Galois group [D] . Sanabria Malagon, Camilo 2010

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6. Colloquium PaperNonlinear partial differential equations and applications: Some nonlinear elliptic equations from geometry [O] . YanYan Li 2007

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8. Some Results of Existence and Uniqueness for Nonlinear Partial Differential Equations and Remarks on the Approximation of Some Nonlinear Elliptic Equations [R] . Temam, R. 1968

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Nonlinear Differential Equation of the Surface Section of Gas-Liquid

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