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受径向振荡激励的黏弹性液滴稳定性分析

姚慕伟 富庆飞 杨立军

姚慕伟, 富庆飞, 杨立军. 受径向振荡激励的黏弹性液滴稳定性分析. 力学学报, 2021, 53(9): 2468-2476 doi: 10.6052/0459-1879-20-416
引用本文: 姚慕伟, 富庆飞, 杨立军. 受径向振荡激励的黏弹性液滴稳定性分析. 力学学报, 2021, 53(9): 2468-2476 doi: 10.6052/0459-1879-20-416
Yao Muwei, Fu Qingfei, Yang Lijun. Stability analysis of viscoelastic liquid droplets excited by radial oscillations. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2468-2476 doi: 10.6052/0459-1879-20-416
Citation: Yao Muwei, Fu Qingfei, Yang Lijun. Stability analysis of viscoelastic liquid droplets excited by radial oscillations. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2468-2476 doi: 10.6052/0459-1879-20-416

受径向振荡激励的黏弹性液滴稳定性分析

doi: 10.6052/0459-1879-20-416
基金项目: 国家自然科学基金项目资助(11922201)
详细信息
    作者简介:

    富庆飞, 研究员, 主要研究方向: 液体火箭发动机雾化机理. E-mail: fuqingfei@buaa.edu.cn

  • 中图分类号: O351

STABILITY ANALYSIS OF VISCOELASTIC LIQUID DROPLETS EXCITED BY RADIAL OSCILLATIONS

  • 摘要: 当液滴受到外部周期性的径向激励时, 在其表面会形成驻波模式的不稳定, 这就是在球面上的Faraday不稳定问题. 不稳定的表面波的振荡频率根据流体物性参数和所施加激励条件的不同呈现为谐波或是亚谐波模式的振荡. 本文基于线性小扰动理论, 研究了受径向振荡体积力的黏弹性液滴表面波的不稳定性. 振荡的体积力导致动量方程为含有时间周期系数的Mathieu方程, 系统因此变成参数不稳定问题, 采用Floquet理论进行求解. 本模型中将黏弹性的特征处理为与流变模型参数相关的等效黏度, 从而简化了问题的求解. 基于对中性稳定曲线及增长率的分析, 研究了黏弹性参数对液滴稳定性的影响. 结果表明零剪切黏度和应变驰豫时间的增加具有抑制液滴表面波增长的作用, 提高了使液滴表面发生谐波不稳定的激励幅值. 随着振荡幅值的增加, 增长率不稳定的区域减少, 且随着振荡频率的增加, 液滴表面波增长率减小. 通过对增长率的分析可以得出, 应力松弛时间的增加使得增长率增加, 从而促进了液滴表面波的增长.

     

  • 图  1  液滴受径向振荡示意图

    Figure  1.  Schematic diagram of a droplet subjected to radial oscillation

    图  2  基本工况条件下的中性稳定曲线(ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.758 8 Pa·s, λ1 = 0.163 s, λ2 = 0.016 3 s)

    Figure  2.  Neutral stability curve under base case condition (ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.758 8 Pa·s, λ1 = 0.163 s, λ2 = 0.016 3 s)

    图  3  不同零剪切黏度下的中性稳定曲线(ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, $\mu_0^* $ = 0.7588 Pa·s, λ1 = 0.163 s, λ2 = 0.0163 s)

    Figure  3.  Neutral stability curve under different zero-shear viscosity conditions (ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, $\mu_0^* $ = 0.7588 Pa·s, λ1 = 0.163 s, λ2 = 0.0163 s)

    图  4  不同应力松弛时间下的中性稳定曲线(ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.758 8 Pa·s, $\lambda_1^* $ = 0.163 s, λ2 = 0.0163 s)

    Figure  4.  Neutral stability curve under different stress relaxation time conditions (ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, $\lambda_1^* $ = 0.163 s, λ2 = 0.0163 s)

    图  5  不同应变驰豫时间下的中性稳定曲线(ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.758 8 Pa·s, λ1 = 0.163 s, $\lambda_2^* $ = 0.016 3 s)

    Figure  5.  Neutral stability curve under different deformation retardation time conditions (ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3,σ = 0.07555 N/m, μ0 = 0.758 8 Pa·s, λ1 = 0.163 s, $\lambda_2^* $ = 0.016 3 s)

    图  6  不同加速度振荡幅值条件下增长率随振荡频率的变化(ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ1 = 0.163 s, λ2 = 0.0163 s, l =20)

    Figure  6.  The variation of growth rate versers oscillation frequency under different acceleration conditions (ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ1 = 0.163 s, λ2 = 0.0163 s, l =20)

    图  7  不同振荡幅值的三次方曲线与第一谐波不稳定区域轮廓线相交(ρl = 1000.9 kg/m3, ρg = 0 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ1 = 0.163 s, λ2 = 0.0163 s, l = 20)

    Figure  7.  The intersection of different oscillation amplitude cubic curves with the contours of the first harmonic instability region (ρl = 1000.9 kg/m3, ρg = 0 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ1 = 0.163 s, λ2 = 0.0163 s, l = 20)

    图  8  不同球波数l条件下增长率随振荡频率的变化(ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ1 = 0.163 s, λ2 = 0.0163 s, A0 = 30 m/s2)

    Figure  8.  The variation of growth rate versers oscillation frequency under different spherical wavenumber conditions (ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ1 = 0.163 s, λ2 = 0.0163 s, A0 = 30 m/s2)

    图  9  不同零剪切黏度条件下增长率随振荡频率的变化(ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, λ1 = 0.163 s, λ2 = 0.0163 s, A0 = 30 m/s2, l = 20)

    Figure  9.  The variation of growth rate versers oscillation frequency under different zero-shear viscosity conditions (ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, λ1 = 0.163 s, λ2 = 0.0163 s, A0 = 30 m/s2, l = 20)

    图  10  不同应力松弛条件下增长率随振荡频率的变化(ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ2 = 0.0163 s, A0 = 30 m/s2, l = 20)

    Figure  10.  The variation of growth rate versers oscillation frequency under different stress relaxation time conditions (ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ2 = 0.0163 s, A0 = 30 m/s2, l = 20)

    图  11  不同应变驰豫时间条件下增长率随振荡频率的变化(ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ1 = 0.163 s, A0 = 30 m/s2, l = 20)

    Figure  11.  The variation of growth rate versers oscillation frequency under different deformation retardation time conditions (ρl = 1000.9 kg/m3, ρg = 1.225 kg/m3, σ = 0.07555 N/m, μ0 = 0.7588 Pa·s, λ1 = 0.163 s, A0 = 30 m/s2, l = 20)

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出版历程
  • 收稿日期:  2020-12-04
  • 录用日期:  2021-08-29
  • 网络出版日期:  2021-08-30
  • 刊出日期:  2021-09-18

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