Numerical modeling of multi micro jet impingement cooling of a three dimensional turbine vane


This paper reports a numerical investigation on the prediction of the thermal and hydrodynamic flow fields of multi micro jet impingement cooling of three dimensional turbine vanes. A three dimensional vane is modeled with an in-line array of impinging jets of diameters 0.5 and 0.25 mm. The numerical model consists of the steady, Reynolds-Averaged Navier–Stokes equations and the Kω SST Turbulence model. The governing equations are solved using a finite volume method. The crossflow mass velocity (G c ) to jet mass velocity (G j ) ratio, and the average and local heat transfer distributions are analyzed with varying mass velocity and jet-to-target spacing. It is found out that a significant decrease in crossflow ratio occurs with the smaller diameters. Due to the lower crossflow and higher exit velocities of the smaller jets, the penetration into the crossflow is much higher. Moreover, at a constant mass flow, the use of micro-jets enhanced the overall average heat transfer coefficient by 63%, while at a fixed pressure drop across the vane instead of the mass flow, the smaller diameters will still yield an enhancement of 34.3% in the overall average heat transfer coefficient.

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  1. 1.

    The reader is referred to [26, 27] for specific details on GCI calculation.


A j :

Jet(s) exit area

A :

Total heated area

A f :

Open ratio, A j /A

D :

Jet diameter

C :

Curve length

C d :

Discharge coefficient

C p :

Specific heat

G :

Inlet mass flow per unit of heated area

G c :

Crossflow mass velocity

G j :

Jet mass velocity


Grid Convergence Index

H :

Nozzle to target plate distance

h :

Heat transfer coefficient (W/m2K)

k :

Thermal conductivity

Nu :

Nusselt number—hD/k

\( \dot{m}_{c} \) :

Average crossflow mass flow (kg/s)

\( \dot{m}_{j} \) :

Average jet mass flow (kg/s)

R 1/2 :

Jet thickness—radial distance to U 1/2

Re :

Reynolds number—ρUD

S :

Pitch—distance between jet centers

U 1/2 :

½ of maximum velocity U m

U m :

Maximum velocity—center line of jet

U :

Velocity—averaged on jet exit

X n :

Streamwise spacing

Y n :

Spanwise spacing


Non-dimensional wall distance

Z :

Vertical length coordinate—from nozzle to target plate


Flow distribution parameter, Eq. 4






Ratio of specific heats


  1. 1.

    Han J-C, Dutta S, Ekkad S (2001) Gas turbine heat transfer and cooling technology, 1st edn. Taylor & Francis, London

    Google Scholar 

  2. 2.

    De Paz ML (2009) A numerical study of micro-jet impingement cooling inside a high pressure turbine vane. M.A.Sci Thesis, Department of Aerospace Engineering, Ryerson University

  3. 3.

    Florschuetz LW, Metzer DE, Truman CR (1981, January) Jet array impingement with crossflow—correlation of streamwise resolved flow and heat transfer distributions. NASA Contractor report 3373, Department of Mechanical Engineering, Arizona State University, Tempe

  4. 4.

    Bailey JC, Bunker RS (2002) Local heat transfer and flow distributions for impinging jet arrays of dense and sparse extent. In: Proceedings of the ASME Turbo Expo 2002

  5. 5.

    Katti V, Prabhu SV (2008) Influence of spanwise pitch on local heat transfer for multiple jets with crossflow. J Thermophys Heat Transf 22(4):654–668

    Article  Google Scholar 

  6. 6.

    Brevet P, Dejeu C, Dorignac E, Jolly M, Vullierme JJ (2002) Heat transfer to a row of impinging jets in consideration of optimization. Int J Heat Mass Transf 45:4191–4200

    Article  Google Scholar 

  7. 7.

    Van Treuren K (1994) Impingement flow heat transfer measurements of turbine blades using a jet array. PhD Thesis, University of Oxford, pp 1–269

  8. 8.

    Van Treuren K, Wang Z, Ireland P, Jones I, Kohler S (1996) Comparison and prediction of local and average heat transfer coefficients under an array of inline and staggered impinging jets, 96-GT-163. IGTI Congress and Exhibition, Birmingham

  9. 9.

    Zuckerman N, Lior N (2005) Impingement heat transfer: correlations and numerical modeling. Trans ASME 127:544–552

    Article  Google Scholar 

  10. 10.

    Huang Y, Ekkad SV, Han J-C (1998) Detailed heat transfer distributions under an array of orthogonal impinging jets. J Thermophys Heat Transf 12(1):73–79

    Article  Google Scholar 

  11. 11.

    Gao L (2003) Effect of jet hole arrays arrangement on impingement heat transfer. Masc. Thesis, Louisiana State University, pp 1–73

  12. 12.

    Gao L, Ekkad SV, Bunker RS (2005) Impingement heat transfer, part I: linearly stretched arrays of holes. J Thermophys Heat Transf 19(1):57–65

    Article  Google Scholar 

  13. 13.

    Andrews GE, Durance J, Hussain CI, Ojobor SN (1987) Full coverage impingement heat transfer: influence of the number of holes. J Turbomach 109:557–563

    Article  Google Scholar 

  14. 14.

    Garimella S, Nenaydykh B (1996) Nozzle-geometry effects in liquid jet impingement heat transfer. Int J Heat Mass Transf 39(4):2915–2923

    Article  Google Scholar 

  15. 15.

    Fabbri M, Jiang S, Dhir VK (2005) A comparative study of cooling of high power density electronics using sprays and microjets. Trans ASME 127:38–48

    Article  Google Scholar 

  16. 16.

    Phalnikar KA, Alvi FS, Shih C (2001) Behavior of free and impinging supersonic microjets. In: AIAA, pp 1–15

  17. 17.

    Leland JE, Ponnappan R, Klasing KS (2002) Experimental investigation of an air microjet array impingement cooling device. J Thermophys Heat Transf 16:187–192

    Article  Google Scholar 

  18. 18.

    Behnia M, Parneix S, Shabany Y, Durbin PA (1999) Numerical study of turbulent heat transfer in confined and unconfined impinging jets. Int J Heat Fluids Flow 20:1–9

    Article  Google Scholar 

  19. 19.

    Cooper D, Jackson D, Launder B, Liao G (1993) Impingement jet studies for turbulence model assessment-I. Flow-field experiments. Int J Heat Mass Transf 36:2675–2684

    Article  Google Scholar 

  20. 20.

    Coussirat M, Van Beeck MJ, Mestres M, Egusguiza E, Buchlin JM, Escaler X (2005) Computational fluids dynamics modeling of impinging gas-jet systems: 1, assessment of eddy viscosity models. J Fluids Eng 127:691–703

    Article  Google Scholar 

  21. 21.

    De Paz ML, Jubran BA (2010) A numerical study of an impingement array inside a three dimensional turbine vane. In: ASME Paper # GT2010-22270, Proceedings of ASME turbo expos 2010 conference, Glasgow, 14–18 June, 2010

  22. 22.

    Kumar BVNR, Prasad BVSSS (2008) Computational flow and heat transfer of a row of circular jets impinging on a concave surface. Heat Mass Transf 44:667–678

    Article  Google Scholar 

  23. 23.

    El-Gabry LA, Kiminski DA (2005) Numerical investigation of jet impingement with cross flow—comparison of Yang–Shih and standard K–E turbulence models. Numer Heat Transf A 441–469

  24. 24.

    Halila EE, Lenahan DT, Thomas TT (1982) Energy efficient engine: high pressure turbine test hardware detailed design report. In: NASA, NAS3-0643, pp 1–194

  25. 25.

    FLUENT Inc. (2003) Fluent 6.1 users guide. FLUENT Inc., Lebanon

    Google Scholar 

  26. 26.

    Roache P (1998) Verification and validation in computational science and engineering. Hermosa Publishers, Albuquerque

    Google Scholar 

  27. 27.

    Roache P (1998) A method for uniform reporting of grid refinement studies, quantification of uncertainty in computational fluid dynamics. FED (ASME) 20:109–120, 199. In Computational Fluid Dynamics. FED (ASME) 20:109–120, 199

  28. 28.

    Logan E, Roy R (2003) Handbook of turbomachinery—chapter 4: selection of a gas turbine system, 2nd edn. CRC, Boca Raton

    Google Scholar 

  29. 29.

    Menter FR (1992) Improved two-equation k-! Turbulence models for aerodynamic flows. NASA TM 103975

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The authors would like to extend their thanks to the Natural Science and Engineering Research Council of Canada and the Province of Ontario for their funding towards this research. Special thanks are also due to the High Performance Computing Virtual Laboratory for their financial support and extensive resources.

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Correspondence to B. A. Jubran.

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De Paz, M.L., Jubran, B.A. Numerical modeling of multi micro jet impingement cooling of a three dimensional turbine vane. Heat Mass Transfer 47, 1561–1579 (2011).

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  • Heat Transfer
  • Target Spacing
  • Average Nusselt Number
  • Local Heat Transfer
  • Suction Surface