Heat and Mass Transfer

, 44:275 | Cite as

Turbulent flow simulation of liquid jet emanating from pressure-swirl atomizer

  • Chun-Lang YehEmail author
Technical Note


The performances of three linear eddy viscosity models (LEVM) and one algebraic Reynolds stress model (ARSM) for the simulation of turbulent flow inside and outside pressure-swirl atomizer are evaluated by comparing the interface position with available experimental data and by comparing the turbulence intensity profiles at the atomizer exit. It is found that the turbulence models investigated exhibit zonal behaviors, i.e. none of the models investigated performs well throughout the entire flow field. The turbulence intensity has a significant influence on the global characteristics of the flow field. The turbulence models with better predictions of the turbulence intensity, such as Gatski-Speziale’s ARSM model, can yield better predictions of the global characteristics of the flow field, e.g. the reattachment lengths for the backward-facing step flow and the sudden expansion pipe flow, or the discharge coefficient, film thickness and the liquid sheet outer surface position for the atomizer flows. The standard kε model predicts stronger turbulence intensity as compared to the other models and therefore yields smaller film thickness and larger liquid sheet outer surface position. In average, the ARSM model gives both quantitatively and qualitatively better results as compared to the standard kε model and the low Reynolds number models.


Turbulence Intensity Reattachment Length Turbulence Intensity Profile Atomizer Flow Algebraic Reynolds Stress Model 
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List of symbols


orifice diameter


swirl chamber diameter


upstream tube diameter of the sudden expansion swirling flow


downstream tube diameter of the sudden expansion swirling flow


volume fraction of liquid in a grid cell


non-dimensionalized turbulence kinetic energy;


k*/ū in *2 for sudden expansion swirling flow;


\( \equiv \,k^{*} /\ifmmode\expandafter\bar\else\expandafter\=\fi{u}^{{*2}}_{{e}} \) for atomizer flow


Reynolds number;


ρ*u in * D 1/μ * for sudden expansion swirling flow;


\( \equiv \rho ^{*}_{l} \ifmmode\expandafter\bar\else\expandafter\=\fi{u}^{*}_{e} d/\mu ^{*}_{l} \) for atomizer flow


non-dimensionalized physical velocity;


≡ (u*, v*, w*)/u in * for sudden expansion swirling flow


\( \equiv \,(u^{*} ,v^{*} ,w^{*} )/\ifmmode\expandafter\bar\else\expandafter\=\fi{u}^{*}_{e} \) for atomizer flow


non-dimensionalized turbulence dissipation rate;


ε*/(u in *3 /D 1) for sudden expansion swirling flow;


\( \equiv \varepsilon ^{*} /(\ifmmode\expandafter\bar\else\expandafter\=\fi{u}^{{*3}}_{e} /d) \) for atomizer flow


non-dimensionalized viscosity;


≡ 1 for sudden expansion swirling flow;


μ*/μ l * for atomizer flow


non-dimensionalized density;


≡ 1 for sudden expansion swirling flow;


ρ*/ρ l * for atomizer flow





atomizer exit


downstream tube inlet or swirl chamber inlet







dimensional quantity


average quantity


  1. 1.
    Yeh CL (2005) Turbulent flow investigation inside and outside plain-orifice atomizers with rounded orifice inlets. Heat Mass Transf 41(9):810–823CrossRefGoogle Scholar
  2. 2.
    Yeh CL (2004) Numerical investigation of liquid jet emanating from plain-orifice atomizers with chamfered or rounded orifice inlets. JSME Int J Ser B 47(1):37–47CrossRefGoogle Scholar
  3. 3.
    Yeh CL (2003) Effect of inlet turbulence intensity on discharge coefficients for liquid jet emanating from a plain-orifice atomizer:a numerical study. J Aeronaut Astronaut Aviat 35(3):299–306Google Scholar
  4. 4.
    Yeh CL (2002) Numerical study of inlet and geometry effects on discharge coefficients for liquid jet emanating from a plain-orifice atomizer. J Mech Ser A 18(3):153–161Google Scholar
  5. 5.
    Launder BE, Spalding DB (1974) The numerical computations of turbulent flows. Comput Methods Appl Mech Eng 3:269–289CrossRefzbMATHGoogle Scholar
  6. 6.
    Launder BE, Sharma BI (1974) Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett Heat Mass Transf 1:131–138CrossRefGoogle Scholar
  7. 7.
    Nagano Y, Hishida M (1987) Improved form of the kε model for wall turbulent shear flows. J Fluids Eng 109:156–160CrossRefGoogle Scholar
  8. 8.
    Gatski TB, Speziale CG (1993) On explicit algebraic stress models for complex turbulent flows. J Fluid Mech 254:59–78zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phy 39:201–225zbMATHCrossRefGoogle Scholar
  10. 10.
    Brackbill JU, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100:335–354zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Jeng SM, Jog MA, Benjamin MA (1998) Computational and experimental study of liquid sheet emanating from simplex fuel nozzle. AIAA J 36:201–207Google Scholar
  12. 12.
    Thompson JF, Warsi ZUA, Mastin CW (1985) VI. Elliptic generation systems, numerical grid generation. North-Holland, Amsterdam, pp 188–271Google Scholar
  13. 13.
    Van Doormaal JP, Raithby GD (1984) Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numer Heat Transf 7:147–163zbMATHCrossRefGoogle Scholar
  14. 14.
    Hayase T, Humphrey JAC, Grief R (1992) A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures. J Comput Phys 98:108–118zbMATHCrossRefGoogle Scholar
  15. 15.
    Driver DM, Seegmiller HL (1985) Features of a reattaching turbulent shear layer in divergent channel flow. AIAA J 23:163–171CrossRefGoogle Scholar
  16. 16.
    Durret RP, Stevenson WH, Thompson HD (1988) Radial and axial turbulent flow measurements with an LDV in an axisymmetrical sudden expansion air flow. J Fluids Eng 110:367–372Google Scholar
  17. 17.
    Martin JC, Moyce WJ (1952) An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos Trans R Soc Lond 224(A):312–324Google Scholar
  18. 18.
    Dellenbach PA (1986) Heat transfer and velocity measurements in turbulent swirling flows through an abrupt axisymmetric expansion. PhD Thesis, Arizona State UniversityGoogle Scholar
  19. 19.
    Lilley DG, Rhode DL (1982) A computer code for swirling turbulent axisymmetric recirculating flows in practical isothermal combustor geometries. NASA CR-3442Google Scholar
  20. 20.
    Koo JY, Martin JK (1995) Near-nozzle characteristics of a transient fuel spray. Atomization Sprays 5:107–121Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Aeronautical EngineeringNational Formosa UniversityYunlinTaiwan, ROC

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