Skip to main content
SpringerLink
Log in

On heat transfer and flow characteristics of jets impinging onto a concave surface with varying jet arrangements

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

The increase in hot gas temperature is helpful for the turbine efficiency improvement and energy-saving. The significantly curved leading edge suffers the highest thermal load in a turbine blade. Jet impingement is one of the popular heat transfer enhancement methods, which has been widely used in blade leading edge. In this study, the flow structure and heat transfer characteristics of jets impinging onto a curved surface with varying jet arrangements and Reynolds number (10,000–40,000) are numerically investigated. The relative jet-to-target spacing equals 1, and relative surface curvature equals 10. An array jets arrangement is provided as baseline. Concerning three array cases, jet holes are positioned in inline and staggered patterns with changing jet-to-jet spacing. In this work, streamlines of different sections, limiting streamlines near target wall and vortex, are obtained. Local Nusselt number contour, local Nusselt number curves and surface-averaged Nusselt number are also presented. Local heat transfer characteristics are analyzed with fluid flow. It is also shown that the heat transfer uniformity of both inline and staggered cases is significantly enhanced by comparing with an array jets case. The whole curved surface-averaged Nusselt number increases with increasing jet-to-jet streamwise spacing at inline arrangement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

\(d_{\text{jet}}\) :

Jet diameter, \({\text{mm}}\)

\(D\) :

Target wall diameter, \({\text{mm}}\)

\(D_{1}\) :

Upper surface diameter, \({\text{mm}}\)

\(f\) :

Friction factor

\(f_{\text{s}}\) :

Friction factor for an array jet

\(h\) :

Heat transfer coefficient, \({\text{W}}\, {{\text{m}}^{-2} \;{\text{K}^{-1}}}\)

\(l\) :

Flow length, \({\text{mm}}\)

\(L\) :

Jet-to-jet spacing between middle and adjacent side jets at Y direction, \({\text{mm}}\)

\({\text{Nu}}\) :

Nusselt number

\({\text{Nu}}_{\text{ave}}\) :

Averaged Nusselt number

\({\text{Nu}}_{{{\text{ave}},{\text{s}}}}\) :

Averaged Nusselt number for an array jet

P :

Jet-to-jet spacing for the same line jets at Y direction, \({\text{mm}}\)

\(P_{i}\) :

Inlet mass flow average total pressure, \({\text{Pa}}\)

\(P_{\text{o}}\) :

Outlet mass flow average total pressure, \({\text{Pa}}\)

\(q\) :

Heat flux, \({\text{W}} {\text{m}}^{-2}\)

\({\text{Re}}\) :

Jet Reynolds number

\(S\) :

Streamwise direction along the concave target surface

\(T_{\text{i}}\) :

Jet inlet temperature, \({\text{K}}\)

\(T_{\text{w}}\) :

Impingement wall temperature, \({\text{K}}\)

\(U_{\text{i}}\) :

Jet inlet velocity, \({\text{m}}\, {\text{s}^{-1}}\)

\(Z\) :

Jet-to-impingement surface spacing, \({\text{mm}}\)

\(\theta\) :

Degree between the middle array jets and side arrays, \(^\circ\)

\(\lambda\) :

Fluid thermal conductivity, \({\text{W}}\, {{\text{m}^{-1}}\;{\text{K}^{-1}}}\)

\(\mu\) :

Fluid dynamic viscosity, \({\text{Pa}}\;{\text{s}}\)

\(\rho\) :

Fluid density, kg m−3

References

  1. Han JC, Kwak JS. Heat transfer coefficients and film-cooling effectiveness on a gas turbine blade tip. ASME J Heat Transf. 2003;125(3):494–502.

    Article  Google Scholar 

  2. Sakakibara J, Hishida K, Phillips WRC. On the vortical structure in a plane impinging jet. J Fluid Mech. 2001;434(434):273–300.

    Article  Google Scholar 

  3. Anderson SL, Longmire EK. Particle motion in the stagnation zone of an impinging air jet. J Fluid Mech. 2006;299:333–66.

    Article  Google Scholar 

  4. HadŽIabdiĆ M, HanjaliĆ K. Vortical structures and heat transfer in a round impinging jet. J Fluid Mech. 2008;596:221–60.

    Article  Google Scholar 

  5. Dairay T, Fortuna V, Lamballais E. Direct numerical simulation of a turbulent jet impinging on a heated wall. J Fluid Mech. 2015;764:362–94.

    Article  CAS  Google Scholar 

  6. Lytle D, Webb BW. Air jet impingement heat transfer at low nozzle-plate spacings. Int J Heat Mass Transf. 1994;37:1687–97.

    Article  CAS  Google Scholar 

  7. Volkov KN. Interaction of a circular turbulent jet with a flat target. J Appl Mech Tech Phys. 2007;48(1):44–54.

    Article  Google Scholar 

  8. Attalla M, Salem M. Heat transfer from a flat surface to an inclined impinging jet. Heat Mass Transf. 2014;50(7):915–22.

    Article  CAS  Google Scholar 

  9. Agrawal C, Kumar R, Gupta A, Chatterjee B. Determination of rewetting velocity during jet impingement cooling of hot vertical rod. J Therm Anal Calorim. 2016;123(1):861–71.

    Article  CAS  Google Scholar 

  10. Matheswaran MM, Arjunan TV, Somasundaram D. Analytical investigation of exergetic performance on jet impingement solar air heater with multiple arc protrusion obstacles. J Therm Anal Calorim. 2019;137(1):1–14.

    Article  CAS  Google Scholar 

  11. Siavashi M, Rasam H, Izadi A. Similarity solution of air and nanofluid impingement cooling of a cylindrical porous heat sink. J Therm Anal Calorim. 2019;135(2):1399–415.

    Article  CAS  Google Scholar 

  12. Tong AY. On the impingement heat transfer of an oblique free surface plane jet. Int J Heat Mass Transf. 2003;46(11):2077–85.

    Article  Google Scholar 

  13. Xie Y. Flow and heat transfer characteristics of single jet impinging on dimpled surface. ASME J Heat Transf. 2013;135(5):052201.

    Article  Google Scholar 

  14. Weigand B, Spring S. Multiple jet impingement a review. Heat Transf Res. 2011;42(2):101–42.

    Article  Google Scholar 

  15. Behbahani AI, Goldstein RJ. Local heat transfer to staggered arrays of impinging circular air jets. ASME J Eng Gas Turbines Power. 1983;105(2):354–60.

    Article  Google Scholar 

  16. Huber AM, Viskanta R. Effect of jet-jet spacing on convective heat transfer to confined impinging arrays of axisymmetric air jets. Int J Heat Mass Transf. 1994;37(18):2859–69.

    Article  Google Scholar 

  17. Park J, Goodro M, Ligrani P, Fox M, Moon HK. Effects of mach number and Reynolds number on jet array impingement heat transfer. Int J Heat Mass Transf. 2007;50:367–80.

    Article  Google Scholar 

  18. Goodro M, Park J, Ligrani P, Fox M, Moon HK. Effects of hole spacing on spatially-resolved jet array impingement heat transfer. Int J Heat Mass Transf. 2008;51:6243–53.

    Article  Google Scholar 

  19. Goodro M, Park J, Ligrani P, Fox M, Moon HK. Effect of temperature ratio on jet array impingement heat transfer. ASME J Heat Transf. 2009;131(1):012201.

    Article  Google Scholar 

  20. Florschuetz LW, Truman CR, Metzger DE. Streamwise flow and heat transfer distributions for jet array impingement with crossflow. ASME J Heat Transf. 1981;103:337–42.

    Article  Google Scholar 

  21. San JY, Lai MD. Optimum Jet-to-jet spacing of heat transfer for staggered arrays of impinging air jets. Int J Heat Mass Transf. 2001;44:3997–4007.

    Article  Google Scholar 

  22. Xing Y, Spring S, Weigand B. Experimental and numerical investigation of heat transfer characteristics of inline and staggered arrays of impinging jets. ASME J Heat Transf. 2010;132(9):53–8.

    Article  Google Scholar 

  23. Shan Y, Zhang ZJ, Xie GN. Convective heat transfer for multiple rows of impinging air jets with small jet-to-jet spacing in a semi-confined channel. Int J Heat Mass Transf. 2015;86:832–42.

    Article  Google Scholar 

  24. Luo L. On the design method and heat transfer mechanism of high efficiency cooling structure in a gas turbine. PhD thesis. China: Harbin Institute of Technology; 2016 (in Chinese).

  25. Chupp RE, Helms HE, Mcfadden PW, Brown TR. Evaluation of internal heat-transfer coefficients for impingement-cooled turbine airfoils. J Aircr. 1969;6(3):203–8.

    Article  Google Scholar 

  26. Metzger DE. Impingement cooling of concave surfaces with lines of circular air jets. ASME J Eng Gas Turbines Power. 1969;91(3):149–55.

    Article  Google Scholar 

  27. Metzger DE, Bunker RS. Local heat transfer in internally cooled turbine airfoil leading edge regions: part i—impingement cooling without film coolant extraction. ASME J Turbomach. 1990;112(3):451–8.

    Article  Google Scholar 

  28. Kumar BVNR, Prasad BVSSS. Computational flow and heat transfer of a row of circular jets impinging on a concave surface. Heat Mass Transf. 2007;44(6):667–78.

    Article  Google Scholar 

  29. Katti V. Pressure distribution on a semi-circular concave surface impinged by a single row of circular jets. Exp Therm Fluid Sci. 2013;46:162–74.

    Article  Google Scholar 

  30. Calzada PDL, Alvarez JJ. Experimental investigation on the heat transfer of a leading edge impingement cooling system for low pressure turbine vanes. ASME J Heat Transf. 2010;132(12):122202.

    Article  CAS  Google Scholar 

  31. Patil VS, Vedula RP. Local heat transfer for jet impingement onto a concave surface including injection nozzle length to diameter and curvature ratio effects. Exp Therm Fluid Sci. 2018;92:375–89.

    Article  Google Scholar 

  32. Jung EY, Chan UP, Dong HL, Kim KM, Cho HH. Effect of the injection angle on local heat transfer in a showerhead cooling with array impingement jets. Int J Therm Sci. 2018;124:344–55.

    Article  Google Scholar 

  33. Fluent A. 12.0. Theory guide. 2009.

  34. Versteeg H, Malalasekera W. An introduction to computational fluid dynamics: the finite volume method. 2nd ed. London: Pearson Education; 2007.

    Google Scholar 

  35. Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 1994;32:1598–605.

    Article  Google Scholar 

  36. Wallin S, Johansson A. A complete explicit algebraic reynolds stress model for incompressible and compressible flows. J Fluid Mech. 2000;403:89–132.

    Article  Google Scholar 

  37. ANSYS ICEM CFD. 11.0 Help Manual. ANSYS Inc 2009.

Download references

Acknowledgements

The author acknowledges the financial support provided by the Natural Science Foundation of China (No. 51706051), China Postdoctoral Science Foundation funded Project (No. 2017M620116), Heilongjiang Postdoctoral Fund (No. LBH-Z17066) and the Fundamental Research Funds for the Central Universities (Grant No. HIT.NSRIF.2019061).

Author information

Authors and Affiliations

  1. School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China

    Dandan Qiu, Lei Luo, Songtao Wang, Zhiqi Zhao & Zhongqi Wang

  2. Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China

    Chenglong Wang

Authors
  1. Dandan Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chenglong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lei Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Songtao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhiqi Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhongqi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chenglong Wang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qiu, D., Wang, C., Luo, L. et al. On heat transfer and flow characteristics of jets impinging onto a concave surface with varying jet arrangements. J Therm Anal Calorim 141, 57–68 (2020). https://doi.org/10.1007/s10973-019-08901-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-019-08901-6

Keywords

Search

Navigation