Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-29T17:01:11.596Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental study on the oscillatory Kelvin–Helmholtz instability of a planar liquid sheet in the presence of axial oscillating gas flow

Published online by Cambridge University Press:  17 March 2023

Bo-qi Jia ,
Luo Xie ,
Xiang-dong Deng ,
Bo-shu He ,
Li-jun Yang Open the ORCID record for Li-jun Yang [Opens in a new window]  and
Qing-fei Fu Open the ORCID record for Qing-fei Fu [Opens in a new window]
Bo-qi Jia
Affiliation:
Institute of Combustion and Thermal Systems, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, PR China
Luo Xie*
Affiliation:
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, PR China
Xiang-dong Deng
Affiliation:
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China
Bo-shu He
Affiliation:
Institute of Combustion and Thermal Systems, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, PR China
Li-jun Yang
Affiliation:
School of Astronautics, Beihang University, Beijing 100083, PR China Aircraft and Propulsion Laboratory, Ningbo Institute of Technology, Beihang University, Ningbo 315800, PR China
Qing-fei Fu*
Affiliation:
School of Astronautics, Beihang University, Beijing 100083, PR China Aircraft and Propulsion Laboratory, Ningbo Institute of Technology, Beihang University, Ningbo 315800, PR China
*
† Email addresses for correspondence: xieluo@nwpu.edu.cn, fuqingfei@buaa.edu.cn
† Email addresses for correspondence: xieluo@nwpu.edu.cn, fuqingfei@buaa.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The oscillatory Kelvin–Helmholtz (K–H) instability of a planar liquid sheet was experimentally investigated in the presence of an axial oscillating gas flow. An experimental system was initiated to study the oscillatory K–H instability. The surface wave growth rates were measured and compared with theoretical results obtained using the authors’ early linear method. Furthermore, in a larger parameter range experimentally studied, it is interesting that there are four different unstable modes: first disordered mode (FDM), second disordered mode (SDM), K–H harmonic unstable mode (KHH) and K–H subharmonic unstable mode (KHS). These unstable modes are determined by the oscillating amplitude, oscillating frequency and liquid inertia force. The frequencies of KHH are equal to the oscillating frequency; the frequency of KHS equals half the oscillating frequency, while the frequencies of FDM and SDM are irregular. By considering the mechanism of instability, the instability regime maps on the relative Weber number versus liquid Weber number (Werel–Wel) and the Weber number ratio versus the oscillating frequency (Werel/Wel–$\varOmega$s2) were plotted. Among these four modes, KHS is the most unexpected: the frequency of this mode is not equal to the oscillating frequency, but the surface wave can also couple with the oscillating gas flow. Linear instability theory was applied to divide the parameter range between the different unstable modes. According to linear instability theory, K–H and parametric unstable regions both exist. However, note that all four modes (KHH, KHS, FDM and SDM) corresponded primarily to the K–H unstable region obtained from the theoretical analysis. Nevertheless, the parametric unstable mode was also observed when the oscillating frequency and amplitude were relatively low, and the liquid inertia force was relatively high. The surface wave amplitude was small but regular, and the evolution of this wave was similar to that of Faraday waves. The wave oscillating frequency was half that of the surface wave.

JFM classification

Instability: Parametric instability Interfacial Flows (free surface): Thin films Waves/Free-surface Flows: Wave breaking
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 959 , 25 March 2023 , A18
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arienti, M. & Soteriou, M.C. 2009 Time-resolved proper orthogonal decomposition of liquid jet dynamics. Phys. Fluids 21, 112104.CrossRefGoogle Scholar
Asare, H.R., Takahashi, R.K. & Hoffman, M.A. 1981 Liquid sheet jet experiments: comparison with linear theory. J. Fluids Engng 103, 595–603.CrossRefGoogle Scholar
Baillot, F., Blaisot, J.B., Boisdron, G. & Dumouchel, C. 2009 Behaviour of an air-assisted jet submitted to a transverse high-frequency acoustic field. J. Fluid Mech. 640, 305–342.CrossRefGoogle Scholar
Carpentier, J., Baillot, F., Blaisot, J. & Dumouchel, C. 2009 Behavior of cylindrical liquid jets evolving in a transverse acoustic field. Phys. Fluids 21, 023601.CrossRefGoogle Scholar
Chaussonnet, G., Muller, A., Holz, S., Koch, R. & Bauer, H.J. 2017 Time-response of recent prefilming airblast atomization models in an oscillating air flow field. Trans. ASME J. Engng Gas Turbines Power 139, 121501.CrossRefGoogle Scholar
Christou, T., Stelzner, B. & Zarzalis, N. 2021 Influence of an oscillating airflow on the prefilming airblast atomization process. Atomiz. Spray 31, 1–14.CrossRefGoogle Scholar
Crapper, G.D., Dombrowski, N. & Pyott, G.A.D. 1975 Large amplitude Kelvin–Helmholtz waves on thin liquid sheets. Proc. R. Soc. Lond. A 342, 209–224.Google Scholar
Dighe, S. & Gadgil, H. 2018 Dynamics of liquid sheet breakup in the presence of acoustic excitation. Intl J. Multiphase Flow 99, 347–362.CrossRefGoogle Scholar
Dighe, S. & Gadgil, H. 2019 a Atomization of acoustically forced liquid sheets. J. Fluid Mech. 880, 653–683.CrossRefGoogle Scholar
Dighe, S. & Gadgil, H. 2019 b Effect of transverse acoustic forcing on the characteristics of impinging jet atomization. Atomiz. Spray 29, 79–103.CrossRefGoogle Scholar
Dighe, S. & Gadgil, H. 2021 On the nature of instabilities in externally perturbed liquid sheets. J. Fluid Mech. 916, A57.CrossRefGoogle Scholar
Dombrowski, N. & Johns, W.R. 1963 The aerodynamic instability and disintegration of viscous liquid sheets. Chem. Engng Sci. 18, 203–214.CrossRefGoogle Scholar
Ficuciello, A., Baillot, F., Blaisot, J., Richard, C. & Theron, M. 2016 High amplitude acoustic field effects on air-assisted liquid jets. In 52nd AIAA/SAE/ASEE Joint Propulsion Conference, Salt Lake City, UT, USA.CrossRefGoogle Scholar
Ficuciello, A., Blaisot, J.B., Richard, C. & Baillot, F. 2017 Investigation of air-assisted sprays submitted to high frequency transverse acoustic fields: droplet clustering. Phys. Fluids 29, 067103.CrossRefGoogle Scholar
Gaster, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222–224.CrossRefGoogle Scholar
Jia, B., Xie, L., Yang, L., Fu, Q. & Cui, X. 2019 Linear instability of viscoelastic planar liquid sheets in the presence of gas velocity oscillations. J. Non-Newtonian Fluid Mech. 273, 104169.CrossRefGoogle Scholar
Jia, B., Xie, L., Yang, L., Fu, Q. & Cui, X. 2020 Energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations. Phys. Fluids 32, 083104.CrossRefGoogle Scholar
Kang, Z., Li, X. & Mao, X. 2018 Experimental investigation on the surface wave characteristics of conical liquid film. Acta Astronaut. 149, 15–24.CrossRefGoogle Scholar
Kelly, R.E. 1965 The stability of an unsteady Kelvin–Helmholtz flow. J. Fluid Mech. 22, 547–560.CrossRefGoogle Scholar
Kelvin, L. 1871 Influence of wind and capillarity on waves in water supposed frictionless. In Mathematical and Physical Papers, iv, vol. 42, pp. 76–85. Cambridge University Press.Google Scholar
Li, X. 1993 Spatial instability of plane liquid sheets. Chem. Engng Sci. 48, 2973–2981.CrossRefGoogle Scholar
Li, X. & Tankin, R.S. 1991 On the temporal instability of a two-dimensional viscous liquid sheet. J. Fluid Mech. 226, 425–443.CrossRefGoogle Scholar
Lin, S.P. 2003 Breakup of Liquid Sheets and Jets. Cambridge University Press.CrossRefGoogle Scholar
Miesse, C.C. 1955 The effect of ambient pressure oscillations on the disintegration and dispersion of a liquid jet. Jet Propul. 25, 525–534.CrossRefGoogle Scholar
Mulmule, A.S., Tirumkudulu, M.S. & Ramamurthi, K. 2010 Instability of a moving liquid sheet in the presence of acoustic forcing. Phys. Fluids 22, 022101.CrossRefGoogle Scholar
Paramati, M., Tirumkudulu, M.S. & Schmid, P.J. 2015 Stability of a moving radial liquid sheet: experiments. J. Fluid Mech. 770, 398–423.CrossRefGoogle Scholar
Poinsot, T., Le Chatelier, C., Candel, S.M. & Esposito, E. 1986 Experimental determination of the reflection coefficient of a premixed flame in a duct. J. Sound Vib. 107, 265–278.CrossRefGoogle Scholar
Qin, L., Yi, R. & Yang, L. 2018 Theoretical breakup model in the planar liquid sheets exposed to high-speed gas and droplet size prediction. Intl J. Multiphase Flow 98, 158–167.CrossRefGoogle Scholar
Sivadas, V., Balaji, K., Sampathkumar, M., Hassan, M.M., Karthik, K.M. & Saidileep, K. 2016 Empirical correlation of the primary stability variable of liquid jet and liquid sheet under acoustic field. J. Fluids Engng 138, 084501.CrossRefGoogle Scholar
Sivadas, V., Fernandes, E.C. & Heitor, M.V. 2003 Acoustically excited air-assisted liquid sheets. Exp. Fluids 34, 736–743.CrossRefGoogle Scholar
Squire, H.B. 1953 Investigation of the instability of a moving liquid film. Br. J. Appl. Phys. 4, 167–169.CrossRefGoogle Scholar
Tammisola, O., Sasaki, A., Lundell, F., Matsubara, M. & Söderberg, L.D. 2011 Stabilizing effect of surrounding gas flow on a plane liquid sheet. J. Fluid Mech. 672, 5–32.CrossRefGoogle Scholar
Tirumkudulu, M.S. & Paramati, M. 2013 Stability of a moving radial liquid sheet: time-dependent equations. Phys. Fluids 25, 102107.CrossRefGoogle Scholar
Yang, V. & Anderson, W.E. 1995 Liquid Rocket Engine Combustion Instability. AIAA.Google Scholar
Yang, L., Jia, B., Fu, Q. & Yang, Q. 2018 Stability of an air-assisted viscous liquid sheet in the presence of acoustic oscillations. Eur. J. Mech. (B/Fluids) 67, 366–376.CrossRefGoogle Scholar
Ye, H., Yang, L. & Fu, Q. 2016 Spatial instability of viscous double-layer liquid sheets. Phys. Fluids 28, 102101.CrossRefGoogle Scholar

Jia et al. Supplementary Movie 1

See "Jia et al. Supplementary Movie Captions"

Download Jia et al. Supplementary Movie 1(Video)
Video 1.5 MB

Jia et al. Supplementary Movie 2

See "Jia et al. Supplementary Movie Captions"

Download Jia et al. Supplementary Movie 2(Video)
Video 1.5 MB

Jia et al. Supplementary Movie 3

See "Jia et al. Supplementary Movie Captions"

Download Jia et al. Supplementary Movie 3(Video)
Video 1.5 MB

Jia et al. Supplementary Movie 4

See "Jia et al. Supplementary Movie Captions"

Download Jia et al. Supplementary Movie 4(Video)
Video 2 MB

Jia et al. Supplementary Movie 5

See "Jia et al. Supplementary Movie Captions"

Download Jia et al. Supplementary Movie 5(Video)
Video 2 MB

Jia et al. Supplementary Movie 6

See "Jia et al. Supplementary Movie Captions"

Download Jia et al. Supplementary Movie 6(Video)
Video 2.1 MB

Jia et al. Supplementary Movie 7

See "Jia et al. Supplementary Movie Captions"

Download Jia et al. Supplementary Movie 7(Video)
Video 2 MB

Jia et al. Supplementary Movie 8

See "Jia et al. Supplementary Movie Captions"

Download Jia et al. Supplementary Movie 8(Video)
Video 2 MB

Jia et al. Supplementary Movie 9

See "Jia et al. Supplementary Movie Captions"

Download Jia et al. Supplementary Movie 9(Video)
Video 1.9 MB
Supplementary material: File

Jia et al. Supplementary Movie Captions

Jia et al. Supplementary Movie Captions

Download Jia et al. Supplementary Movie Captions(File)
File 51.3 KB