Temporal instability analysis of a power-law sheet in a gas velocity oscillation field was performed with linear stability analysis. The oscillation of gas velocity induced the momentum equation to be a Hill equation with a time period coefficient, which was solved using Floquet theory. For different oscillation amplitudes and frequencies, the effects of the generalized Reynolds number, power-law index and dimensionless velocity factor on various unstable regions were studied. Results show that the increase of the oscillation amplitude or the decrease of the oscillation frequency will increase the number of unstable regions of the sheet, and the maximum growth rate, dominant wave number and cut-off wave number of the Kelvin-Helmholtz (K-H) unstable region increase with the increase of the oscillation amplitude and frequency. The increase in generalized Reynolds number, power-law index and dimensionless velocity factor enhances the instability of the K-H unstable region, causing the growth rate in the parametric instability region to decrease first and then increase. The variations of the oscillation amplitude do not change the rheological parameters corresponding to the transition of the maximum growth rate. When the oscillation frequency is small, the increase of power-law index or dimensionless velocity factor leads to monotonous increase of the maximum growth rate in the parametric instability region.
YAO Muwei
,
JIA Boqi
,
YANG Lijun
,
FU Qingfei
. Instability of power-law liquid sheets in presence of gas velocity oscillations[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020
, 41(11)
: 123873
-123873
.
DOI: 10.7527/S1000-6893.2020.23873
[1] SQUIRE H B. Investigation of the instability of a moving liquid film[J]. British Journal of Applied Physics, 1953, 4:167-169.
[2] DOMBROWSKI N, JOHNS W R. The aerodynamic instability and disintegration of viscous liquid sheets[J]. Chemical Engineering Science, 1963, 18:203-214.
[3] LIN S P, LIAN Z W, CREIGHTON B J. Absolute and convective instability of a viscous liquid sheet[J]. Journal of Fluid Mechanics, 1990, 220:673-689.
[4] LI X, TANKIN R S. On the temporal instability of a two-dimensional viscous liquid sheet[J]. Journal of Fluid Mechanics, 1991, 226:425-443.
[5] LI X. Spatial instability of plane liquid sheet[J]. Chemical Engineering Science, 1993, 48:2973-2981.
[6] BARRERAS F, LOZANO A, DOPAZO C. Viscous linear instability analysis of the viscous longitudinal perturbation on an air-blasted liquid sheet[J]. Atomization and Sprays, 2001, 11:139-154.
[7] DOMBROWSKI N, HOOPER P C. The effect of ambient density on drop formation in sprays[J]. Chemical Engineering Science, 1962, 17(4):291-305.
[8] IBRAHIM E A, JACKSON S L. Spatial instability of a liquid sheet in a compressible gas[J]. Journal of Colloid and Interface Science, 1996, 180(2):629-631.
[9] SUJITH R I. An experimental investigation of interaction of sprays with acoustic fields[J]. Experiments in Fluids, 2005, 38(5):576-587.
[10] SIVADAS V, FERNANDES E C, HEITOR M V. Acoustically excited air-assisted liquid sheets[J]. Experiments in Fluids, 2003, 34(6):736-743.
[11] YANG L, JIA B, FU Q, et al. Stability of an air-assisted viscous liquid sheet in the presence of acoustic oscillations[J]. European Journal of Mechanics:B Fluids, 2018, 67:366-376.
[12] JIA B, XIE L, CUI X, et al. Linear stability of confined coaxial jets in the presence of gas velocity oscillations with heat and mass transfer[J]. Physics of Fluids, 2019, 31:092101.
[13] SIVADAS V, HEITOR M V. Visualization studies of an acoustically excited liquid sheet[J]. Annals of the New York Academy of Science, 2002, 972:292-298.
[14] MULMULE A S, TIRUMKUDULU M S. Liquid sheet instability in the presence of acoustic forcing[C]//43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. Reston:AIAA, 2007.
[15] TIRUMKUDULU M S, MULMULE A S, RAMAMURTHI K. Stability of a thin radially moving liquid sheet in the presence of acoustic excitation[C]//International Congress of Theoretical and Applied Mechanics. Adelaide:[s.n.], 2008.
[16] MULMULE A S, TIRUMKUDULU M S, RAMAMU-RTHI K. Instability of a moving liquid sheet in the presence of acoustic forcing[J]. Physics of Fluids, 2010, 22(2):022101.
[17] JIA B Q, XIE L, YANG L J, et al. Linear instability of viscoelastic planar liquid sheets in the presence of gas velocity oscillations[J]. Journal of Non-Newtonian Fluid Mechanics, 2019, 273:104169.
[18] KUMAR K, TUCKERMAN L S. Parametric instability of the interface between two fluids[J]. Journal of Fluid Mechanics, 1994, 279(1):49-68.
[19] 常青. 幂律流体射流破碎机理的理论与实验研究[D].天津:天津大学, 2014:44-46. CHANG Q. Theoretical and experimental study on the breakup mechanisms of power law liquid jets[D]. Tianjin:Tianjin University, 2014:44-46(in Chinese).
[20] WANG Y B, GUO J P, BAI F Q, et al. Influence of bounded and compressible gas medium on the instability of an annular power-law liquid jet[J]. Atomization and Sprays, 2018, 28(5):389-402.
[21] DIGHE S, GADGIL H. Atomization of acoustically forced liquid sheets[J]. Journal of Fluid Mechanics, 2019, 880:653-683.
CJA