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Heat and Mass Transfer

, Volume 46, Issue 1, pp 63–74 | Cite as

Optimization of a stepped circular pin-fin array to enhance heat transfer performance

  • Kwang-Yong KimEmail author
  • Mi-Ae Moon
Original

Abstract

A Stepped circular pin-fin array is formulated numerically and optimized with Kriging metamodeling technique to enhance heat transfer performance. The problem is defined by two non-dimensional geometric design variables composed of height of the channel, height of smaller diameter part of the pin-fins, and smaller diameter of the pin-fins, to maximize heat transfer rate compromising with friction loss. Ten designs generated by Latin hypercube sampling were evaluated by three-dimensional Reynolds-averaged Navier–Stokes solver and the evaluated objectives were used to construct the surrogate model. The predictions of objective function by Kriging model at optimum point show reasonable accuracy in comparison with the values calculated by RANS analysis. Optimum shape of pin-fins strongly depends on the weighting factor which measures importance of the friction loss term in the objective function. The thermal performances are much higher than that of the straight pin-fin at sampling optimum points with different weighting factors.

Keywords

Heat Transfer Design Variable Kriging Nusselt Number Heat Transfer Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

A

Areas of heat transfer surface

Ad,Ain

Areas of heat transfer surface and inlet plane, respectively

cp

Specific heat

D

Larger diameter of the pin-fins

Dh

Channel hydraulic diameter

d

Smaller diameter of the pin-fins

F

Objective function

f

Friction factor

f0

Reference friction factor

H

Height of the channel

h

Height of smaller diameter part of the pin-fins

k

Turbulence kinetic energy

N

Number of design variables

Nu

Local Nusselt number

Nu0

Reference Nusselt number

Nua

Average Nusselt number

\( \overline{Nu} \)

Endwall area-averaged Nusselt number

p, Δp

Pressure and pressure drop in a channel, respectively

\( \hat{p} \)

Periodic component of pressure

Pi

Pitch

Pr

Prandtl number

Prt

Turbulent Prandtl number

q0

Wall heat flux

Re

Reynolds number (= u b D h /ν)

S

Strain rate

T

Local mean temperature

Tw

Wall temperature

\( \hat{T} \)

Periodic component of temperature

ub

Average axial velocity

ui

Mean velocity components (i = 1, 2, 3)

W

Cross-streamwise distance between two neighbored pin-fins

xi

Rectangular coordinates (i = 1, 2, 3) or design variables (Eq. 12)

β

Weighting factor in objective function in Eq. 10 or model constant in Eq. 6

δij

Kronecker delta (i = 1, 2, 3)

γ

Pressure gradient in streamwise direction

μ, μt

Viscosity and turbulent viscosity, respectively

ν, νt

Kinematic viscosity and eddy viscosity, respectively

ρ

Fluid density

σ

Increasing rate of bulk temperature in axial direction (Eq. 4) or standard deviation of the population (Eq. 12)

σk, σω

Turbulence model constants in Eqs. 5 and 6, respectively

ω

Specific turbulence dissipation rate

Notes

Acknowledgments

This research was supported by ‘Multi-Phenomena CFD Engineering Research Center’ grant funded by National Research Foundation of Korea.

References

  1. 1.
    Azar K, Mandrone CD (1994) Effect of pin fin density of the thermal performance of unshrouded pin fin heat sinks. Trans ASME 116:306–309CrossRefGoogle Scholar
  2. 2.
    Chyu MK, Hsing YC, Shih TI-P, Natarajan V (1999) Heat transfer contributions of pins and endwall in pin-fin arrays: effects of thermal boundary condition modeling. J Turbomach 121:257–263CrossRefGoogle Scholar
  3. 3.
    Hwang JJ, Lui CC (2002) Measurement of endwall heat transfer and pressure drop in a pin-fin wedge duct. Int J Heat Mass Transf 45:877–889CrossRefGoogle Scholar
  4. 4.
    Ames FE, Dvorak LA, Morrow MJ (2004) Turbulent augmentation of internal convection over pins in staggered pin fin arrays. ASME Turbo ExpoGoogle Scholar
  5. 5.
    Jeng TM, Tzeng SC (2007) Pressure drop and heat transfer or square pin-fin arrays in in-line and staggered arrangements. Int J Heat Mass Transf 51:2364–2375CrossRefGoogle Scholar
  6. 6.
    Chyu MK (1990) Heat transfer and pressure drop for short pin-fin arrays with pin-endwall fillet. Trans ASME 112:926–932CrossRefGoogle Scholar
  7. 7.
    Armstrong J, Winstanley D (1988) A review of staggered array pin fin heat transfer for turbine cooling applications. J Turbomach 110:94–103Google Scholar
  8. 8.
    VanFossen GJ (1980) Heat-transfer coefficients for staggered arrays of short pin-fins. ASME J Heat Transf 102:44–50CrossRefGoogle Scholar
  9. 9.
    VanFossen GJ (1982) Heat transfer coefficient for staggered arrays of short pin fins. ASME J Eng Power 104:268–274CrossRefGoogle Scholar
  10. 10.
    Brigham BA, VanFossen GJ (1984) Length-to-diameter ratio and row number effects in short pin fin heat transfer. ASME J Eng Gas Turbines Power 106:241–246CrossRefGoogle Scholar
  11. 11.
    Metzger DE, Berry RA, Bronson JP (1982) Developing heat transfer in rectangular ducts with arrays of short pin fins. ASME J Heat Transf 104:700–706CrossRefGoogle Scholar
  12. 12.
    Metzger DE, Haley SW (1982) Heat transfer experiments and flow visualization of arrays of short pin fins. ASME Paper No. 82-GT-138Google Scholar
  13. 13.
    Metzger DE, Fan ZX, Sheppard WB (1982) Pressure loss and heat transfer through multiple rows of short pin fins. Heat Transf 3:137–142Google Scholar
  14. 14.
    Metzger DE, Sheppard WB (1986) Row resolved heat transfer variations in pin fin arrays including effects of non-uniform arrays and flow convergence. ASME Paper No. 86-GT-132Google Scholar
  15. 15.
    Goldstein RJ, Jabbari MY, Chen SB (1994) Convective mass transfer and pressure loss characteristics of staggered short pin-fin arrays. Int J Heat Mass Transf 37(Suppl 1):149–160CrossRefGoogle Scholar
  16. 16.
    Donahoo EE, Camci C, Kulkami AK, Belegundu AD (1999) A computational visualization of three-dimensional flow. ASME Turbo Expo, Indianapolis, IN, 99-GT-257Google Scholar
  17. 17.
    Andreini A, Carcasci C, Magi A (2004) Heat transfer analysis of a wedge shaped duct with pin fin and pedestal arrays. ASME Turbo Expo, Vienna, Austria, GT2004-53319Google Scholar
  18. 18.
    Saha AK, Acharya S (2004) Unsteady simulation of turbulent flow and heat transfer in a channel with periodic array of cubic pin-fins. Numer Heat Transf A 46:731–763CrossRefGoogle Scholar
  19. 19.
    Chen HT, Chen PL, Horng JT, Hung YH (2005) Design optimization for pin-fin heat sinks. J Electron Packag 127:397–406CrossRefGoogle Scholar
  20. 20.
    Park KW, Oh PK, Lim HJ (2005) Optimum design of a pin-fins type heat sink using the CFE and mathematical optimization. Int J Air Cond Refrig 13(2):71–82MathSciNetGoogle Scholar
  21. 21.
    Li Ping, Kim KY (2008) Multiobjective optimization of staggered elliptical pin-fin arrays. Numer Heat Transf A 53(4):418–431CrossRefMathSciNetGoogle Scholar
  22. 22.
    Husain A, Kim KY (2008) Shape optimization of a micro-channel heat sink for micro-electronic cooling. IEEE Trans Compon Packag Technol 31(2):322–330CrossRefGoogle Scholar
  23. 23.
    Raza W, Kim KY (2007) Evaluation of surrogate models in optimization of wire-wrapped fuel assembly. J Nucl Sci Technol 44(6):819–822CrossRefGoogle Scholar
  24. 24.
    Ansys CFX-11.0 (2006) Ansys IncGoogle Scholar
  25. 25.
    Liou WW, Huang G, Shih TH (2000) Turbulence model assessment for shock wave/turbulent boundary-layer interaction in transonic and supersonic flows. Comput Fluids 29:275–299zbMATHCrossRefGoogle Scholar
  26. 26.
    Bardina JE, Huang PG, Coakley T (1997) Turbulence modeling validation. AIAA Paper No. 1997–2121Google Scholar
  27. 27.
    Grag VK, Ameri AA (2001) Two-equation turbulence model for prediction of heat transfer on a transonic turbine blade. Int J Heat and Fluid Flow 22:593–602CrossRefGoogle Scholar
  28. 28.
    Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32:1598–1605CrossRefGoogle Scholar
  29. 29.
    Kim HM, Kim KY (2006) Shape optimization of three-dimensional channel roughened by angled ribs with RANS analysis of turbulent heat transfer. Int J Heat Mass Transf 49:4013–4022zbMATHCrossRefGoogle Scholar
  30. 30.
    Gee DL, Webb RL (1980) Forced convection heat transfer in helically rib-roughened tubes. Int J Heat Mass Transf 23:1127–1136CrossRefGoogle Scholar
  31. 31.
    Kim HM, Kim KY (2004) Design optimization of rib-roughened channel to enhance turbulent heat transfer. Int J Heat Mass Transf 47:5153–5168Google Scholar
  32. 32.
    Kim KY, Choi JY (2005) Shape optimization of a dimpled channel to enhance turbulent heat transfer. Numer Heat Transf A 48:1–15CrossRefGoogle Scholar
  33. 33.
    Petukhov BS (1970) Advances in heat transfer, vol 6. Academic Press, New York, pp 503–504Google Scholar
  34. 34.
    JMP® 5.1 (2004) SAS Institute, IncGoogle Scholar
  35. 35.
    Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4:409–435zbMATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Chang SW, Yang TL, Huang CC, Ching KF (2008) Endwall heat transfer and pressure drop in rectangular channels with attached and detached circular pin-fin array. Int J Heat Mass Transf 51:5247–5259zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringInha UniversityIncheonRepublic of Korea

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