Abstract

We examine the convective and absolute instability of a 2D axisymmetric viscoelastic liquid jet falling vertically in a medium of an inviscid gas under the influence of gravity. We use the upper-convected Maxwell model to describe the viscoelastic liquid jet and together with an asymptotic approach, based on the slenderness of the jet, we obtain steady-state solutions. By considering travelling wave modes, and using linear instability analysis, the dispersion relation, relating the frequency to wavenumber of disturbances, is derived. We solve this dispersion relation numerically using the Newton–Raphson method and explore regions of instability in parameter space. In particular, we investigate the influence of gravity, the effect of changing the gas-to-liquid density ratio, the Weber number and the Deborah number on convective and absolute instability. In this paper, we utilize a mapping technique developed by Afzaal (2014, Breakup and instability analysis of compound liquid jets. Doctoral Dissertation, University of Birmingham) to find the cusp point in the complex frequency plane and its corresponding first-order saddle point (the pinch point) in the complex wavenumber plane for absolute instability. The convective/absolute instability boundary is identified for various parameter regimes along the axial length of the jet.

中文翻译：

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下落的粘弹性液体射流被气体包围的对流和绝对不稳定性

摘要

我们研究了在重力作用下在粘性气体介质中垂直下落的二维轴对称粘弹性液体射流的对流和绝对不稳定性。我们使用上对流麦克斯韦（Maxwell）模型来描述粘弹性液体射流，并根据射流的细长度，采用渐近方法，获得稳态解。通过考虑行波模式，并使用线性不稳定性分析，得出了将频率与干扰波数相关的色散关系。我们使用牛顿-拉夫森（Newton-Raphson）方法数值求解该色散关系，并探索参数空间中的不稳定区域。特别是，我们研究了重力的影响，改变气液密度比的影响，对流和绝对不稳定的韦伯数和德博拉数。在本文中，我们利用Afzaal（2014年，复合液体射流的破裂和不稳定性分析。伯明翰大学博士学位）开发的映射技术在复数频率平面中找到尖点及其对应的一阶鞍点（收缩点）在复数波数平面中的绝对不稳定性。对流/绝对不稳定性边界沿射流的轴向长度确定了各种参数范围。伯明翰大学（University of Birmingham University）找到复数频率平面中的尖点，并在复数波数平面中找到其对应的一阶鞍点（夹点），以实现绝对不稳定性。对流/绝对不稳定性边界沿射流的轴向长度确定了各种参数范围。伯明翰大学（University of Birmingham University）找到复数频率平面中的尖点，并在复数波数平面中找到其对应的一阶鞍点（夹点），以实现绝对不稳定性。对流/绝对不稳定性边界沿射流的轴向长度确定了各种参数范围。