[论文解读] Spatial instability analysis and mode transition of a viscoelastic jet in a co-flowing gas stream

Jiawei Li, Ming Wang+3 more|arXiv (Cornell University)|Feb 28, 2026

Fluid Dynamics and Heat Transfer被引用 0

一句话总结

这篇论文对共流体系统中的黏弹性液体射流进行了空间线性不稳定性分析，识别出弹性驱动的模态转变，并通过流聚焦实验验证预测。

ABSTRACT

Spatial linear instability analysis is employed to investigate the instability of a viscoelastic liquid jet in a co-flowing gas stream. The theoretical model incorporates a non-uniform axial base profile represented by a hyperbolic tangent, capturing the shear layer. The Oldroyd-B model discretized with Chebyshev polynomials is employed, and energy budget analysis is used to interpret underlying mechanisms.At low Weber numbers, the jet evolves axisymmetrically and the instability is governed by interfacial gas-pressure fluctuations; as the Weber number increases, the growing inertia drives a transition of the predominant mode from axisymmetric to helical. At weak elasticity, the instability is also primarily governed by gas-pressure fluctuations. As elasticity increases, the predominant mode transitions from axisymmetric to helical. This transition is accompanied by a migration of disturbance structures from the interface toward the jet interior and an enhanced coupling between velocity perturbation and the basic flow. These trends reveal a new predominant instability mechanism -- the elasticity-enhanced shear-driven instability -- which is distinct from capillary or Kelvin-Helmholtz instabilities in Newtonian jets. A We-El phase diagram delineates the boundary between predominant modes, and experimental results obtained in a flow-focusing configuration validate the theoretical predictions.

研究动机与目标

• 研究黏弹性如何影响在流聚焦下同轴液体-气体射流的不稳定性模态。
• 建立捕捉非平行黏弹性射流下下游扰动放大的空间不稳定性框架。
• 明确决定轴对称模态与螺旋模态之间过渡的机制和参数边界。

提出的方法

• 使用Oldroyd-B本构方程对液体、牛顿流体的气体，建立黏弹性液体-气体同轴射流模型。
• 采用双曲正切基型轮廓表示界面处的剪切层。
• 进行带有方位模n=0和n=1的空间线性不稳定性分析，并在实频率ω下求解复数波数k的二次本征问题。
• 在Chebyshev谱点逼近方法中，采用Chebyshev多项式离散化。
• 应用能量预算分析以解释不稳定性机制并识别能量转移项。
• 构造一个El = Wi/Re关系来探索弹性效应并与实验数据对比。

Figure 1: Sketches of the azimuthal modes $n=0$ and $n=1$ . The black solid lines and red dotted lines represent the interface profiles before and after perturbation, respectively. (a) The axisymmetric ( $n=0$ ) mode in the $r$ – $z$ and $r$ – $\theta$ planes. (b) The non-axisymmetric ( $n=1$ ) mode

实验结果

研究问题

• RQ1 液体黏弹性（用El表示）如何影响在共流条件下黏弹性射流的主导不稳定模态（轴对称与螺旋）？
• RQ2 Weber数和黏弹性在驱动黏弹性射流不稳定机制转变中的作用是什么？
• RQ3 在流聚焦配置的黏弹性射流中，空间不稳定性框架是否能准确预测实验观测？
• RQ4 驱动弹性增强的剪切驱动不稳定性（ESI）的能量转移机制是什么？

主要发现

• 在低Weber数时，轴对称扰动占主导地位，不稳定性由界面气压扰动控制。
• 随着Weber数增大，惯性驱动从轴对称模态转变为螺旋模态。
• 黏弹性增加时，主导模态从轴对称转变为螺旋，扰动结构从界面向射流内部迁移，表明与基流耦合更强。
• 识别出弹性增强的剪切驱动不稳定性（ESI）作为与牛顿流体射流中的毛细不稳定性或Kelvin–Helmholtz不稳定性不同的独立机制。
• 一个El–Weber相图划定主导模态的边界，并与流聚焦实验结果一致，验证了对对流、非平行射流的空间不稳定性方法相较于时间分析的有效性。

Figure 2: Schematic of the theoretical model for viscoelastic liquid–gas coaxial jets, with the base flow represented by a hyperbolic-tangent velocity profile.