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TECHNICAL PAPERS: Forced Convection

# Computation of Flow and Heat Transfer in Rotating Rectangular Channels $(AR=4:1)$ With Pin-Fins by a Reynolds Stress Turbulence Model

[+] Author and Article Information
Guoguang Su, Je-Chin Han

Turbine Heat Transfer Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843

Hamn-Ching Chen

Ocean Engineering Program, Department of Civil Engineering, Texas A&M University, College Station, TX 77843

J. Heat Transfer 129(6), 685-696 (Aug 17, 2006) (12 pages) doi:10.1115/1.2717935 History: Received July 05, 2005; Revised August 17, 2006

## Abstract

Computations with multi-block chimera grids were performed to study the three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with staggered arrays of pin-fins. The channel aspect ratio (AR) is 4:1, the pin length to diameter ratio $(H∕D)$ is 2.0, and the pin spacing to diameter ratio is 2.0 in both the stream-wise $(S1∕D)$ and span-wise $(S2∕D)$ directions. A total of six calculations have been performed with various combinations of rotation number, Reynolds number, and coolant-to-wall density ratio. The rotation number and inlet coolant-to-wall density ratio varied from 0.0 to 0.28 and from 0.122 to 0.20, respectively, while the Reynolds number varied from 10,000 to 100,000. For the rotating cases, the rectangular channel was oriented at $150deg$ with respect to the plane of rotation to be consistent with the configuration of the gas turbine blade. A Reynolds-averaged Navier-Stokes (RANS) method was employed in conjunction with a near-wall second-moment turbulence closure for detailed predictions of mean velocity, mean temperature, and heat transfer coefficient distributions.

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## Figures

Figure 1

Geometry and conceptual view of the rotating channel for the rectangular duct (AR=4:1) with pin-fins

Figure 2

Numerical grid for (a) full channel and (b) one-half channel

Figure 3

Grid refinement study for channel B at (a) Re=10,000, Ro=0.0 and (b) Re=100,000, Ro=0.0

Figure 4

Velocity vectors and dimensionless temperature [θ=(T−Ti)∕(Tw−Ti)] contours in the middle plane of symmetry of the nonrotating channel (Re=10,000, Δρ∕ρ=0.122)

Figure 5

Dimensionless temperature [θ=(T−Ti)∕(Tw−Ti)] contours close to the pin-fins and the trailing surface of nonrotating channel (Re=10,000, Δρ∕ρ=0.122)

Figure 6

Horseshoe vortices and dimensionless temperature [θ=(T−Ti)∕(Tw−Ti)] contours around pin-fins in the nonrotating channel (Re=10,000, Ro=0.0, Δρ∕ρ=0.122)

Figure 7

Comparison between the calculated and measured Nusselt number ratios for the nonrotating duct with 12 rows of pin-fins (Re=104, Δρ∕ρ=0.122)

Figure 8

Nusselt number ratio contours on (a) the leading surface, (b) the trailing surface, and (c) the pin-fin surface for lower Reynolds number (Re=10,000) cases

Figure 9

Comparison between the calculated and measured Nusselt number ratios for the nonrotating and rotating ducts: (a) Re=10,000, Ro=0; (b) Re=10,000, Ro=0.14; and (c) Re=20,000, Ro=0

Figure 10

Effect of rotation on spanwise-averaged Nusselt number ratios for the lower Reynolds number (Re=10,000) cases

Figure 11

Nusselt number ratio contours on (a) the leading surface, (b) the trailing surface, and (c) the pin-fin surface for high Reynolds number (Re=100,000) cases

Figure 12

Effect of Reynolds number on spanwise-averaged Nusselt number ratios for a nonrotating duct (Ro=0.0, Δρ∕ρ=0.122)

Figure 13

Effects of rotation and density ratio on spanwise-averaged Nusselt number ratios for high Reynolds number (Re=100,000) cases

Figure 14

Effect of Reynolds number on friction factor ratios for nonrotating pin-fin channels

Figure 15

Comparison of predicted friction coefficients with experimental correlations for nonrotating pin-fin channels

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