Thermocapillary instability of a liquid sheet with centrifugal force

Technical Paper
  • 21 Downloads

Abstract

The thermocapillary instability of liquid sheets subjected to a temperature gradient that is perpendicular to the gas–liquid interface and moving in a gas medium is investigated in this paper. A linear instability analysis accounting for the weak form of the centrifugal force along the flow direction is proposed. The instability of liquid sheets with a temperature gradient is compared to that of isothermal liquid sheets, and the effect of the temperature difference is analyzed. The effect of the centrifugal force is also investigated. Furthermore, the effect of the density ratio, viscosity of liquid sheet and Weber number are also discussed by solving the dispersion equation. The results show that, when the thermocapillary effects are taken into account, the temporal growth rate of the varicose mode can become greater than that of the sinuous mode, in contrast to the condition of an isothermal liquid sheet. When the Marangoni number is relatively small, the swirl decreases the maximum growth rate for the sinuous mode. In other conditions, the swirl has only minor effects on the stability of the liquid sheets. The increase of the density ratio and Weber number enhances the instability of the sheets, while the increased Prandtl number has the opposite effect. The effect of the Ohnesorge number is relatively complicated.

Keywords

Thermocapillary instability Liquid sheet Centrifugal force Temperature gradient 

References

  1. 1.
    Sirignano WA, Mehring C (2000) Review of theory of distortion and disintegration of liquid streams. Prog Energy Combust Sci 26:609–655CrossRefGoogle Scholar
  2. 2.
    Dumouchel C (2008) On the experimental investigation on primary atomization of liquid streams. Exp Fluids 45:371–422CrossRefGoogle Scholar
  3. 3.
    Senecal PK, Schmidt DP, Nouar I, Rutland CJ, Reitz RD, Corradini ML (1999) Modeling high-speed viscous liquid sheet atomization. Int J Multiph Flow 25:1073–1097CrossRefMATHGoogle Scholar
  4. 4.
    Fu QF, Yang LJ, Qu YY, Gu B (2010) Linear stability analysis of a conical liquid sheet. J Propul Power 26(5):955–968CrossRefGoogle Scholar
  5. 5.
    Moon Y, Kim D, Yoon Y (2010) Improved spray model for viscous annular sheets in a swirl injector. J Propul Power 26(2):267–279CrossRefGoogle Scholar
  6. 6.
    Jeandel X, Dumouchel C (1999) Influence of the viscosity on the linear stability of an annular liquid sheet. Int J Heat Fluid Flow 20:499–506CrossRefGoogle Scholar
  7. 7.
    Ashgriz N, Yarin AL (2011) Handbook of atomization and sprays theory and applications. Springer, New YorkGoogle Scholar
  8. 8.
    Dávalos-Orozco LA (1999) Thermocapillar instability of liquid sheets in motion. Colloids Surf A 157:223–233CrossRefGoogle Scholar
  9. 9.
    Tong MX, Yang LJ, Fu QF (2014) Thermocapillar instability of a two-dimensional viscoelastic planar liquid sheet in surrounding gas. Phys Fluids 26:033105CrossRefGoogle Scholar
  10. 10.
    Davis SH (1987) Thermocapillary instabilities. Annu Rev Fluid Mech 19:403–435CrossRefMATHGoogle Scholar
  11. 11.
    Ponstein J (1959) Instability of rotating cylindrical jets. Appl Sci Res 8(6):425–456MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Kang DJ, Lin SP (1989) Breakup of swirling liquid jets. Int J Eng Fluid Mech 2:47–62Google Scholar
  13. 13.
    Panchagnula MV, Sojka PE, Santangelo PJ (1996) On the three-dimensional instability of a swirling, annular, inviscid liquid sheet subject to unequal gas velocities. Phys Fluids 8(12):3000–3312CrossRefMATHGoogle Scholar
  14. 14.
    Loiseleux T, Chomaz JM, Huerre P (1998) The effect of swirl on jets and wakes: linear instability of the Rankine vortex with axial flow. Phys Fluids 10(5):1120–1134MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Liao Y, Jeng SM, Jog MA, Benjamin MA (2001) Advanced sub-model for airblast atomizers. J Propul Power 17:411–417CrossRefGoogle Scholar
  16. 16.
    Liao Y, Jeng SM, Jog MA, Benjamin MA (2000) Effect of air swirl profile on the instability of a viscous liquid jet. J Fluid Mech 424:1–20CrossRefMATHGoogle Scholar
  17. 17.
    Lian ZW, Lin SP (1990) Breakup of a liquid jet in a swirling gas. Phys Fluids A 2:2134–2139CrossRefMATHGoogle Scholar
  18. 18.
    Edgar P, Herrero EM, Del Valle M, Galan MA (2007) Instability study of a swirling annular liquid sheet of polymer produced by air-blast atomization. Chem Eng J 133:69–77CrossRefGoogle Scholar
  19. 19.
    Levich VG (1962) Physicochemical hydrodynamics. Prentice Hall, USAGoogle Scholar
  20. 20.
    Arun Vijay G, Shenbaga Vinayaga Moorthi N (2016) Improved linearized breakup model for the liquid sheets produced by swirl atomizers. J Propul Power 32(2):448–455CrossRefGoogle Scholar
  21. 21.
    Li X, Tankin RS (1991) On the temporal instability of a two-dimensional viscous liquid sheet. J Fluid Mech 226:425–443CrossRefMATHGoogle Scholar
  22. 22.
    Yang LJ, Qu YY, Fu QF, Gu B, Wang F (2010) Linear stability analysis of a non-Newtonian liquid sheet. J Propul Power 26(6):1212–1224CrossRefGoogle Scholar
  23. 23.
    Yang LJ, Xu BR, Fu QF (2012) Linear instability analysis of planar non-Newtonian liquid sheets in two gas streams of unequal velocities. J Nonnewton Fluid Mech 167–168:50–58CrossRefMATHGoogle Scholar
  24. 24.
    Yang LJ, Liu YX, Fu QF, Wang C, Ning Y (2012) Linear stability analysis of electrified viscoelastic liquid sheets. Atomization Sprays 22(11):951–982CrossRefGoogle Scholar
  25. 25.
    Tong MX, Fu QF, Yang LJ (2015) Two-dimensional instability response of an electrified viscoelastic planar liquid sheet subjected to unrelaxed axial elastic tension. Atomization Sprays 25(2):99–121CrossRefGoogle Scholar
  26. 26.
    Yang LJ, Wang C, Fu QF, Du M, Tong MX (2013) Weakly nonlinear instability of planar viscous sheets. J Fluid Mech 735:249–287MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Liu Z, Brenn G, Durst F (1998) Linear analysis of the instability of two-dimensional non-Newtonian liquid sheets. J Nonnewton Fluid Mech 78(2):133–166CrossRefMATHGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.School of Aerospace EngineeringTsinghua UniversityBeijingChina

Personalised recommendations