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A mathematical analysis of an isothermal tube drawing process
Alexandria Engineering Journal ( IF 6.8 ) Pub Date : 2020-07-02 , DOI: 10.1016/j.aej.2020.05.021
A.I.K. Butt , M. Abbas , W. Ahmad

The aim of this paper is to investigate stability of an isothermal glass tube drawing process through control parameters by the method of linear stability analysis. We want to see how the process parameters effect stability of the physical system being considered. For this purpose, we not only prove the existence and uniqueness of the solutions of steady state isothermal tube drawing model but also determine its numerical solution. To perform linear stability analysis, steady state numerical solution is incorporated in the eigenvalue problem, formulated by linearizing the isothermal model. The eigenvalue problem is then solved numerically to determine the critical draw ratio which indicates the onset of instabilities. To the end, stability of the process is analyzed using three different values of space step size. We also observe and discuss the effect of density, viscosity and pressure on stability of the isothermal tube drawing model.



中文翻译:

等温管拉伸过程的数学分析

本文的目的是通过线性稳定性分析方法,通过控制参数研究等温玻璃管拉制工艺的稳定性。我们想看看过程参数如何影响所考虑的物理系统的稳定性。为此,我们不仅证明稳态等温管拉伸模型解的存在性和唯一性,而且确定其数值解。为了进行线性稳定性分析,将稳态数值解合并到特征值问题中,该问题通过对等温模型进行线性化来表示。然后用数值方法解决特征值问题,以确定表明不稳定性开始的临界拉伸比。最后,使用空间步长的三个不同值来分析过程的稳定性。

更新日期:2020-07-02
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