, Volume 50, Issue 12, pp 2927–2947 | Cite as

Impinging cross-shaped submerged jet on a flat plate: a comparison of plane and hemispherical orifice nozzles

  • Kodjovi Sodjavi
  • Brice Montagné
  • Pierre Bragança
  • Amina MeslemEmail author
  • Florin Bode
  • Magdalena Kristiawan


It is well known that the transfer of heat, mass and momentum to a wall by an impinging jet is partially linked to the way in which jet generation is realized. The organization of the vortices at the jet exit depends on the upstream conditions and on the geometry of the nozzle. Particle image velocimetry (PIV) and electrodiffusion techniques were used to investigate the characteristics of different impinging jets and the resulting wall shear rates and mass transfer. Two cross-shaped orifice jets, one produced by a plane orifice nozzle (i.e. a cross-shaped orifice made on a flat plate, CO/P) and the second by a hemispherical orifice nozzle (i.e. a cross-shaped orifice made on a hemisphere, CO/H), were compared to a reference round jet produced by a convergent nozzle. The distance between the jet exit and the target wall was equal to two nozzle equivalent diameters (D e ), based on the free orifice area. The Reynolds number, based on D e and on the exit bulk-velocity, was 5620 for each flow. PIV measurements give an overall view of the flow characteristics in their free and wall regions. The switching-over phenomena observed in the CO/P nozzle case, and already described in the literature with similar nozzles, did not occur in the jet from the CO/H nozzle. Electrodiffusion measurements showed differences in the shape and level of radial distribution of the wall shear rates and mass transfer. One of the most important observations is the large difference in wall shear stress between the three jets. For the same exit bulk-velocity, the maximum wall shear rate in the CO/P and CO/H nozzle jets was almost two and three times higher, respectively, than that of the reference convergent jet. This higher wall shear rate is accompanied by higher mass transfer rate. It is demonstrated that the cross-shaped orifices enhance the mass transfer not only locally but also globally.


Impinging jet Lobed jet Wall-shear rate Mass transfer Flow dynamics 

List of symbols


Concentration of depolarizer in bulk (mol m−3)


Diffusion coefficient of depolarizer (m2 s−1)


Nozzle diameter for a round jet (m)


Equivalent diameter based on nozzle free area (m)


Width of the lobes (m)


Faraday constant (96,485 C mol−1)


Frequency (Hz)


Nozzle-to-plate axial distance


Coefficient of heat transfer (W m−2 °C−1)


Limiting diffusion current (A)


Density of limiting diffusion current (A m−2)

\( i_{S} \)

Current density at the stagnation point (A m−2)


Coefficient of mass transfer (m s−1)


Nusselt number (Nu = hD/λ)


The number of electrons taking part in the electrochemical reaction


Prandtl number (Pr = ν/α)


Volumetric flow (ml/mn)


Electrode radius (m)


Radial distance measured from stagnation point (m)


Reynolds number (W b D e /ν)


Strouhal number \( (f\uptheta_{0} /W) \)


Time (s)


Radial velocity (m/s)


Streamwise velocity (m/s)


Jet bulk velocity, 4Q/πD e 2 (m/s)

(X, Y, Z)

System of coordinates attached to the nozzle (m)


Axis normal to target wall with origin on the target wall, Z* = H − Z (m)


Radial distance at the periphery of the potential core where W(X 0.1) = 0.1 W 0 in the major plane (m)


Radial distance at the periphery of the potential core where W(S 0.1) = 0.1 W 0 in the minor plane (m)


Thermal diffusivity (m2 s−1)


Wall shear rate (s−1)


Wall shear stress, τ = μ·γ (N m−2)


Thermal conductivity (W m−1 °C−1)


Dynamic viscosity (Pa s)

\( \uptheta_{0} \)

Momentum thickness at the jet exit Z = 0.25D e (mm)


Displacement thickness at the jet exit Z = 0.25D e (mm)


Kinematic viscosity (m2 s−1)


Vorticity component (s−1)



Lévêque solution


Jet value at the center of the nozzle and at Z = 0.25D e


Jet centerline value


Axis taking its origin on the target wall



This work was supported by the Grants from the French National Agency of Research, the “FLUBAT” project and ANR-12-VBDU-0010.


  1. 1.
    Xu G, Antonia RA (2002) Effect of different initial conditions on a turbulent round free jet. Exp Fluids 33:677–683CrossRefGoogle Scholar
  2. 2.
    Romano GP (2002) The effect of boundary conditions by the side of the nozzle of a low Reynolds number jet. Exp Fluids 33:323–333CrossRefGoogle Scholar
  3. 3.
    Quinn WR (2006) Upstream nozzle shaping effects on near field flow in round turbulent free jets. Eur J Mech B Fluids 25:279–301zbMATHCrossRefGoogle Scholar
  4. 4.
    Mi J, Nathan GJ, Nobes DS (2001) Mixing characteristics of axisymmetric free jets from a contoured nozzle an orifice plate and a pipe. J Fluid Eng 123:878–883CrossRefGoogle Scholar
  5. 5.
    Husain ZD, Hussain AKMF (1979) Axisymetric mixing layer: influence of the initial and boundary conditions. AIAA J 17(1):48–55CrossRefADSGoogle Scholar
  6. 6.
    Nathan GJ et al (2006) Impacts of a jet’s exit flow pattern on mixing and combustion performance. Progress in energy and combustion science. Prog Energy Combust Sci 32(5–6):496–538CrossRefGoogle Scholar
  7. 7.
    Hussain AKMF (1981) Coherent structures and studies of perturbed and unperturbed jets. In: Jimenez J (ed) The role of coherent structures in modelling turbulence and mixing. Springer, Heidelberg, pp 252–291CrossRefGoogle Scholar
  8. 8.
    Hussain AKMF, Zaman KBMQ (1981) The ‘preferred mode’ of the axisymetric jet. J Fluid Mech 110:39–71CrossRefADSGoogle Scholar
  9. 9.
    Hussain F, Husain HS (1989) Elliptic jets. Part 1. Characteristics of unexcited and excited jets. J Fluid Mech 208:257–320CrossRefADSGoogle Scholar
  10. 10.
    Zaman KBMQ, Reeder MF, Samimy M (1994) Control of axisymmetric jet using vortex generators. Phys Fluids 6(2):778–793CrossRefADSGoogle Scholar
  11. 11.
    Gutmark EJ, Grinstein FF (1999) Flow control with noncircular jets. Annu Rev Fluid Mech 31:239–272CrossRefADSGoogle Scholar
  12. 12.
    Mi J, Nathan GJ (1999) Effect of small vortex-generators on scalar mixing in the developing region of a turbulent jet. Int J Heat Mass Transf 42:3919–3926zbMATHCrossRefGoogle Scholar
  13. 13.
    Zaman KBMQ, Wang FY, Georgiadis NJ (2003) Noise, turbulence and thrust of subsonic free jets from lobed nozzles. AIAA J 41(3):398–407CrossRefADSGoogle Scholar
  14. 14.
    Gardon R, Cobonpue J (1962) Heat transfer between a flat plate and jets of air impinging on it. In: Proceedings of the International Developments in Heat Transfer (ASME), New York, pp 454–460Google Scholar
  15. 15.
    Gardon R, Akfirat JC (1965) The role of turbulence in determining the heat-transfer characteristics of impinging jets. Int J Heat Mass Transf 8:1261–1272CrossRefGoogle Scholar
  16. 16.
    Gardon R, Akfirat JC (1966) Heat transfer characteristics of impinging two-dimensional air jets. J Heat Transf 88(1):101–107CrossRefGoogle Scholar
  17. 17.
    Popiel CO, Boguslawski L (1988) Effect of flow structure on the heat or mass transfer on a flat plate in impinging round jet. In: 2nd UK national conference on heat transferGoogle Scholar
  18. 18.
    Vejrazka J et al (2005) Effect of an external excitation on the flow structure in a circular impinging jet. Phys Fluids (1994–present) 17(10):105102CrossRefADSGoogle Scholar
  19. 19.
    Alekseenko SV et al (2007) Experimental study of an impinging jet with different swirl rates. Int J Heat Fluid Flow 28(6):1340–1359CrossRefGoogle Scholar
  20. 20.
    Roux S et al (2011) Experimental investigation of the flow and heat transfer of an impinging jet under acoustic excitation. Int J Heat Mass Transf 54:3277–3290CrossRefGoogle Scholar
  21. 21.
    Trávníček Z et al (2012) Axisymmetric impinging jet excited by a synthetic jet system. Int J Heat Mass Transf 55(4):1279–1290CrossRefGoogle Scholar
  22. 22.
    Sang-Joon L, Jung-Ho L, Dae-Hee L (1994) Local heat transfer measurements from an elliptic jet impinging on a flat plate using liquid crystal. Int J Heat Mass Transf 37(6):967–976CrossRefGoogle Scholar
  23. 23.
    Lee J, Lee SJ (2000) The effect of nozzle configuration on stagnation region heat transfer enhancement of axisymmetric jet impingement. Int J Heat Mass Transf 43:3497–3509CrossRefGoogle Scholar
  24. 24.
    Gao N, Sun H, Ewing D (2003) Heat transfer to impinging round jets with triangular tabs. Int J Heat Mass Transf 46(14):2557–2569CrossRefGoogle Scholar
  25. 25.
    Nakod PM, Prabhu SV, Vedula RP (2008) Heat transfer augmentation between impinging circular air jet and flat plate using finned surfaces and vortex generators. Exp Thermal Fluid Sci 32(5):1168–1187CrossRefGoogle Scholar
  26. 26.
    Violato D et al (2012) Three-dimensional vortex dynamics and convective heat transfer in circular and chevron impinging jets. Int J Heat Fluid Flow 37:22–36CrossRefGoogle Scholar
  27. 27.
    Herrero Martin R, Buchlin JM (2011) Jet impingement heat transfer from lobed nozzles. Int J Therm Sci 50(7):1199–1206CrossRefGoogle Scholar
  28. 28.
    Gulati P, Katt V, Prabhu SV (2009) Influence of the shape of the nozzle on local heat transfer distribution between smooth flat surface and impinging air jet. Int J Therm Sci 48:602–617CrossRefGoogle Scholar
  29. 29.
    Gutmark EJ, Ho CM (1983) Preferred modes and the spreading rates of jets. Phys Fluids 26(10):2932–2938CrossRefADSGoogle Scholar
  30. 30.
    Nastase I, Meslem A (2010) Vortex dynamics and mass entrainment in turbulent lobed jets with and without lobe deflection angles. Exp Fluids 48(4):693–714CrossRefGoogle Scholar
  31. 31.
    Hu H et al (2000) Particle image velocimetry and planar laser induced fluorescence measurements on lobed jet mixing flows. Exp Fluids (Suppl.) 29:S141–S157CrossRefGoogle Scholar
  32. 32.
    Vallis EA, Patrick MA, Wragg AA (1977) Techniques of wall measurements in fluid mechanics. In: Euromech.90. Nancy, FranceGoogle Scholar
  33. 33.
    Kataoka K et al (1982) Mass transfer between a plane surface and an impinging turbulent jet: the influence of surface-pressure fluctuations. J Fluid Mech 119:91–105CrossRefADSGoogle Scholar
  34. 34.
    Chin DT, Tsang CH (1978) Mass transfer to an impinging jet electrode. J Electrochem Soc 125(9):1461–1470CrossRefGoogle Scholar
  35. 35.
    Kataoka K, Mizushina T (1974) Local enhancement of the rate of heat-transfer in an impinging round jet by free-stream turbulence. In: Heat transfer 1974; proceedings of the fifth international conference, Volume 2, TokyoGoogle Scholar
  36. 36.
    Lytle D, Webb BW (1994) Air jet impingement heat transfer at low nozzle-plate spacings. Int J Heat Mass Transf 37(12):1687–1697CrossRefGoogle Scholar
  37. 37.
    Hadziabdic M, Hanjalic K (2008) Vortical structures and heat transfer in a round impinging jet. J Fluid Mech 596:221–260zbMATHCrossRefADSGoogle Scholar
  38. 38.
    Alekseenko SV, Markovich DM (1994) Electrodiffusion diagnostics of wall shear stresses in impinging jet. J Appl Electrochem 24:626–631CrossRefGoogle Scholar
  39. 39.
    Phares DJ, Smedley GT, Flagan RC (2000) The wall shear stress produced by the normal impingement of a jet on a flat surface. J Fluid Mech 418:351–375zbMATHCrossRefADSGoogle Scholar
  40. 40.
    Tummers MJ, Jacobse J, Voorbrood SGJ (2011) Turbulent flow in the near field of a round impinging jet. Int J Heat Mass Transf 54:4939–4948CrossRefGoogle Scholar
  41. 41.
    El-Hassan M et al (2012) Experimental investigation of the wall shear stress and the vortex dynamics in a circular impinging jet. Exp Fluids 52(6):1475–1489CrossRefGoogle Scholar
  42. 42.
    Hall JW, Ewing D (2006) On the dynamics of the large-scale structures in round impinging jets. J Fluid Mech 555:439–458zbMATHCrossRefADSGoogle Scholar
  43. 43.
    El-Hassan M, Meslem A (2010) Time-resolved stereoscopic PIV investigation of the entrainment in the near-field of circular and daisy-shaped orifice jets. Phys Fluids 22(035107):26Google Scholar
  44. 44.
    Kristiawan M et al (2012) Wall shear rates and mass transfer in impinging jets: comparison of circular convergent and cross-shaped orifice nozzles. Int J Heat Mass Transf 55:282–293CrossRefGoogle Scholar
  45. 45.
    Rajaratnam N (1976) Turbulent jets. Elsevier, AmsterdamGoogle Scholar
  46. 46.
    Belovich VM, Samimy M (1997) Mixing processes in a coaxial geometry with a central lobed mixer-nozzle. AIAA J 35(5):838–841CrossRefADSGoogle Scholar
  47. 47.
    Bolashikov Z et al (2013) Improved inhaled air quality at reduced ventilation rate by control of airflow interaction at the breathing zone with lobed jets. HVAC&R Res 20(2):238–250CrossRefGoogle Scholar
  48. 48.
    Meslem A et al (2013) Flow dynamics and mass transfer in impinging circular jet at low Reynolds number. Comparison of convergent and orifice nozzles. Int J Heat Mass Transf 67:25–45CrossRefGoogle Scholar
  49. 49.
    Scarano F, Riethmuller ML, Adrian RJ (2000) Advances in iterative multigrid PIV image processing. Exp Fluids 29(3):S51–S60CrossRefGoogle Scholar
  50. 50.
    Westerweel J (2000) Theoretical analysis of the measurement precision in particle image velocimetry. Exp Fluids 29(1):S003–S012Google Scholar
  51. 51.
    Reiss LP, Hanratty TJ (1962) Measurement of instantaneous rates of mass transfer to a small sink on a wall. AIChE J 8(2):245–247CrossRefGoogle Scholar
  52. 52.
    Nastase I, Meslem A, Gervais P (2008) Primary and secondary vortical structures contribution in the entrainment of low Reynolds number jet flows. Exp Fluids 44(6):1027–1033CrossRefGoogle Scholar
  53. 53.
    Hu H et al (2000) Research on the vortical and turbulent structures in the lobed jet flow using laser induced fluorescence and particle image velocimetry techniques. Meas Sci Technol 11:698–711CrossRefADSGoogle Scholar
  54. 54.
    Nastase I, Meslem A, El-Hassan M (2011) Image processing analysis of vortex dynamics of lobed jets from three-dimensional diffusers. Fluid Dyn Res 43(6):065502CrossRefADSGoogle Scholar
  55. 55.
    El-Hassan M, Meslem A, Abed-Meraïm K (2011) Experimental investigation of the flow in the near-field of a cross-shaped orifice jet. Phys Fluids 23(045101):16Google Scholar
  56. 56.
    Nastase I et al (2011) Lobed grilles for high mixing ventilation—an experimental analysis in a full scale model room. Build Environ 46(3):547–555MathSciNetCrossRefGoogle Scholar
  57. 57.
    Gorman JM, Sparrow EM, Abraham JP (2014) Slot jet impingement heat transfer in the presence of jet-axis switching. Int J Heat Mass Transf 78:50–57CrossRefGoogle Scholar
  58. 58.
    Baydar E, Ozmen Y (2006) An experimental investigation on flow structures of confined and unconfined impinging air jets. Heat Mass Transf 42(4):338–346CrossRefADSGoogle Scholar
  59. 59.
    Todde V, Spazzini PG, Sandberg M (2009) Experimental analysis of low-Reynolds number free jets. Evolution along the jet centerline and Reynolds number effects. Exp Fluids 47:279–294CrossRefGoogle Scholar
  60. 60.
    Cooper D et al (1993) Impinging jet studies for turbulence model assessment—I. Flow-field experiments. Int J Heat Mass Transf 36(10):2675–2684CrossRefGoogle Scholar
  61. 61.
    Kazuya I et al (2009) Heat transfer characteristics of a planar water jet impinging normally or obliquely on a flat surface at relatively low Reynolds numbers. Exp Thermal Fluid Sci 33(8):1226–1234CrossRefGoogle Scholar
  62. 62.
    Glauert MB (1956) The wall jet. J Fluid Mech 1(06):625–643MathSciNetCrossRefADSGoogle Scholar
  63. 63.
    Tummers MJ, Jacobse J, Voorbrood SGJ (2011) Turbulent flow in the near field of a round impinging jet. Int J Heat Mass Transf 54(23–24):4939–4948CrossRefGoogle Scholar
  64. 64.
    Xu Z, Hangan H (2008) Scale, boundary and inlet condition effects on impinging jets. J Wind Eng Ind Aerodyn 96(12):2383–2402CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Kodjovi Sodjavi
    • 1
  • Brice Montagné
    • 1
  • Pierre Bragança
    • 1
  • Amina Meslem
    • 2
    Email author
  • Florin Bode
    • 3
  • Magdalena Kristiawan
    • 4
  1. 1.LaSIE, Pôle Sciences et TechnologieUniversity of La RochelleLa RochelleFrance
  2. 2.LGCGM EA3913, Equipe Matériaux et Thermo-RhéologieUniversité Rennes 1Rennes Cedex 7France
  3. 3.Faculty of Mechanical EngineeringTechnical University of Cluj-NapocaCluj-NapocaRomania
  4. 4.Institut National de la Recherche AgronomiqueBIANantesFrance

Personalised recommendations