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

Abstract

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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Notes

  1. 1.

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

Abbreviations

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

GCI:

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

Y+:

Non-dimensional wall distance

Z :

Vertical length coordinate—from nozzle to target plate

β:

Flow distribution parameter, Eq. 4

ρ:

Density

μ:

Viscosity

γ:

Ratio of specific heats

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Acknowledgments

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). https://doi.org/10.1007/s00231-011-0819-3

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Keywords

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