Predicting Cooling of Electronic Packaging Systems Using Computational Fluid Dynamics

by K.J. Hsieh and F.S. Lien
Department of Mechanical Engineering, University of Waterloo

sponsored by MMO/Nortel under MMO Project #DE708

Stage 1: Modeling Turbulent Forced Convective Heat Transfer in a Channel with Periodic Ribs

Stage 2: Modeling Turbulent Natural Convective Heat Transfer in a Tall Cavity

Stage 3: Modeling Turbulent Natural Convective Heat Transfer in a Square Cavity at Low Turbulence Level

Numerical Framework:

The CFD code STREAM [1] employs a general non-orthogonal fully collocated finite-volume strategy, incorporates the monotonic high-resolution approximation “UMIST” [2] for mean-flow as well as turbulence convection, uses the “SIMPLE” pressure-correction algorithm to satisfy mass conservation, and incorporates a range of turbulence models.

Ribbed Channel Geometry:




 

Configurations:
Drain and Martin [3]
Liou et al. [4]
Rib pitch to rib height ratio (Pi/H)
7.2
7.2
Channel height to rib height ratio (D/H)
5
5
Reynolds number
37200
12600

Turbulence Models:
 
Models employed
Compared with the base model

to investigate the effect of

Model LL + Yap
¾
Model LL
Yap correction
Model LL + Yap + NLSS
Non-linear stress-strain relation
HRN k-e model + wall functions
Wall function/ LL vs. LCL models
Model LCL + Yap

Mean-Flow Results:

Streamlines in a ribbed channel computed with model LL+Yap at Re=37200.


 

Mean velocity at four channel locations. (o) Experimental data; (—) model LL with Yap; (– –) model LL without Yap.


 

Mean velocity at four channel locations. (o) Experimental data; (—) model LL with Yap; (– –) model LL with Yap and NLSS.


 

Mean velocity at four channel locations. (o) Experimental data; (—) model LL with Yap; (– –) HRN k-e model with wall functions; (– –) model LCL with Yap.

Turbulence-Intensity Profiles:

Turbulence intensity at four channel locations. (o) Experimental data;(—) model LL with Yap; (– –) model LL without Yap.


 

Turbulence intensity at four channel locations. (o) Experimental data;(—) model LL with Yap; (– –) model LL with Yap and NLSS.


 

Turbulence intensity at four channel locations. (o) Experimental data;(—) model LL with Yap; (– –) HRN k-e model with wall functions; (– –) model LCL with Yap.


 

Nusselt Number:

The abscissa in the Nusselt number distributions figures, denoted by “s”, is defined along the rib faces and ribbed channel wall surface, where s=0 corresponds to the left-upper corner of the rib. The following figure illustrates the s-coordinate system along the surfaces.


 



Local Nusselt number distribution: (a) results from Manceau et al. [5]; (b) results from present study using model LL with Yap. (o) Experimental data;(—) computation with conjugate heat transfer; (– –) computation with imposed heat flux on the rib faces.

(a)

b)



 
Local Nusselt number distribution. (o) Experimental data];(—) model LL with Yap; (– –) model LL with Yap and NLSS.



 
Local Nusselt number distribution. (o) Experimental data; (—) model LL with Yap; (– –) HRN k-e model with wall functions; (– –) model LCL with Yap.

 
References:
  1. Lien, F.S. and Leschziner, M.A., “A General Non_orthogonal Finite-Volume Algorithm for Turbulent Flow at All Speed Incorporating Second-Moment Closure”, Comp. Meth. Appl. Mech. Eng., Vol. 114, pp. 123-148, 1994a.
  2. Lien, F.S. and Leschziner, M.A., “Upstream Monotonic Interpolation for Scalar Transport with Application to Complex Turbulent Flows”, Int. J. Num. Meth/ Fluids, Vol. 19, pp. 527-548, 1994b.
  3. Drain, L.E. and Martin, S. “Two-Component Velocity Measurements of Turbulent Flow in a Ribbed-Wall Flow Channel”, International Conference on Laser Anemometry - Advances and Applications”, Manchester, U.K., pp. 99-112, 1985.
  4. Liou, T.M. and Hwang, J.J, “Turbulent Heat Transfer Augmentation and Friction in Periodic Fully Developed Channel Flows”, Journal of Heat Transfer, Vol. 114, pp. 56-64, 1992.
  5. Manceau, R., Parneix, S., and Laurence, D., “Turbulent Heat Transfer Predictions Using the v2-f  Model on Unstructured Meshes”, International Journal of Heat and Fluid Flow, Vol. 21, pp. 320-328, 2000.
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