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# Turbulent Heat Transfer in Ribbed Coolant Passages of Different Aspect Ratios: Parametric Effects

[+] Author and Article Information
Arun K. Saha

Turbine Innovation and Energy Research (TIER) Center, Louisiana State University, Baton Rouge, LA 70803

Sumanta Acharya

Turbine Innovation and Energy Research (TIER) Center, Louisiana State University, Baton Rouge, LA 70803acharya@me.lsu.edu

J. Heat Transfer 129(4), 449-463 (Jun 08, 2006) (15 pages) doi:10.1115/1.2709653 History: Received January 16, 2005; Revised June 08, 2006

## Abstract

Turbulent flow and heat transfer in rotating ribbed ducts of different aspect ratios (AR) are studied numerically using an unsteady Reynolds averaged Navier–Stokes procedure. Results for three ARs (1:1, 1:4, and 4:1) and staggered ribs with constant pitch $(P∕e=10)$ in the periodically developed region are presented and compared. To achieve periodic flow behavior in successive inter-rib modules calculations are performed in a computational domain that extends to two or three inter-rib modules. The computations are carried out for an extended parameter set with a Reynolds number range of 25,000–150,000, density ratio range of 0–0.5, and rotation number range of 0–0.50. Under rotational conditions, the highest heat transfer along the leading and side walls are obtained with the 4:1 AR, while the 1:4 AR has the highest trailing wall Nu ratio and the lowest leading wall Nu ratio. The 1:4 AR duct shows flow reversal near the leading wall (leading to low Nu) at high rotation numbers and density ratios. For certain critical parameter values (low Re, high Ro, and/or DR), the leading wall flow is expected to become nearly stagnant, due to the action of centrifugal buoyancy, leading to conduction-limited heat transfer. The 4:1 AR duct shows evidence of multiple rolls in the secondary flow that direct the core flow to both the leading and trailing surfaces which reduces the difference between the leading and trailing wall heat transfer relative to the other two AR ducts.

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## Figures

Figure 1

(a) Schematic of a typical internal cooling strategy (5); and (b) a three-dimensional computational model of a periodic inter-rib module showing two ribs

Figure 2

Comparison of streamwise velocity and cross-stream velocity at (a) and (c) a streamwise location passing through the rib on the leading wall and (b) and (d) at a location in between the two consecutive ribs on leading and trailing wall

Figure 3

Effect of Reynolds number on (a) leading wall; (b) trailing wall; and (c) side wall at various AR ducts for Ro=0.12 and DR=0.13

Figure 4

Streamtraces and temperature contours at midtransverse plane for Re=25,000, Ro=0.12, and DR=0.13: (a)AR=1:1; (b)AR=1:4; and (c)AR=4:1

Figure 5

Streamtraces and temperature contours at mid transverse plane for Ro=0.12 and DR=0.13 and (a)Re=50,000 and (b)Re=100,000; AR=1:4

Figure 6

Secondary flow structures superimposed on temperature contours at x=0.5 for Ro=0.12, DR=0.13, Re=25,000 for various aspect ratios: (a)AR=1:1; (b)AR=1:4; and (c)AR=4:1. Bottom surface is the leading wall.

Figure 8

Axial variation of spanwise averaged Nusselt number on: (a) leading wall; and (b) trailing wall at various aspect ratios (AR) for Re=25,000 and 100,000 and Ro=0.12 and DR=0.13

Figure 9

Transverse variation of local Nusselt number on: (a) leading wall; and (b) trailing wall at various aspect ratios (AR) and Re=25,000 and 100,000 and Ro=0.12 and DR=0.13

Figure 10

Effect of rotation number on: (a) leading wall; (b) trailing wall; and (c) sidewall at various AR ducts and Re=25,000 and DR=0.13

Figure 11

Distribution of Nusselt number on sidewall at Re=25,000, Ro=0.25, and DR=0.13 at various aspect ratios: (a)AR=1:1; (b)AR=1:4; and (c)AR=4:1

Figure 12

Secondary flow structures superimposed on temperature contours at x=0.5 for Re=25,000, Ro=0.25, and DR=0.13 for various aspect ratios: (a)AR=1:1; (b)AR=1:4; and (c)AR=4:1

Figure 13

Contours of time-averaged Nusselt number for 1:4 AR duct on trailing wall at Re=25,000 and DR=0.13 for: (a)Ro=0.25; and (b)Ro=0.50

Figure 14

Axial variation of spanwise averaged Nusselt number on: (a) leading wall; and (b) trailing wall at various aspect ratios (AR) and Ro=0 and 0.25 (Re=25,000 and DR=0.13)

Figure 15

Effect of density ratio on: (a) leading wall; (b) trailing wall; and (c) sidewall at various AR ducts for Re=25,000 and Ro=0.12

Figure 16

Streamtraces (primary flow) and temperature contours at midtransverse plane and secondary vectors at x=1.0: (a)DR=0.0; and (b)DR=0.25 for AR=1:4 and at Re=25,000 and Ro=0.12

Figure 17

Axial variation of spanwise averaged Nusselt number on: (a) leading wall; and (b) trailing wall at various density ratios for 1:4 AR duct (Re=25,000 and Ro=0.12)

Figure 7

Distribution of Nusselt number on leading walls at Re=100,000, Ro=0.12, and DR=0.13: (a)AR=1:1; (b)AR=1:4; and (c)AR=4:1

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