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Research Papers: Forced Convection

# Heat Transfer and Pressure Drop Correlations for Square Channels With 45 Deg Ribs at High Reynolds Numbers

[+] Author and Article Information
Akhilesh P. Rallabandi, Huitao Yang

Department of Mechanical Engineering, Turbine Heat Transfer Laboratory, Texas A&M University, College Station, TX 77843-3123

Je-Chin Han

Department of Mechanical Engineering, Turbine Heat Transfer Laboratory, Texas A&M University, College Station, TX 77843-3123jc-han@tamu.edu

J. Heat Transfer 131(7), 071703 (May 14, 2009) (10 pages) doi:10.1115/1.3090818 History: Received June 23, 2008; Revised November 25, 2008; Published May 14, 2009

## Abstract

Systematic experiments are conducted to measure heat transfer enhancement and pressure loss characteristics on a square channel (simulating a gas turbine blade cooling passage) with two opposite surfaces roughened by 45 deg parallel ribs. Copper plates fitted with a silicone heater and instrumented with thermocouples are used to measure regionally averaged local heat transfer coefficients. Reynolds numbers studied in the channel range from 30,000 to 400,000. The rib height $(e)$ to hydraulic diameter $(D)$ ratio ranges from 0.1 to 0.18. The rib spacing $(p)$ to height ratio $(p/e)$ ranges from 5 to 10. Results show higher heat transfer coefficients at smaller values of $p/e$ and larger values of $e/D$, though at the cost of higher friction losses. Results also indicate that the thermal performance of the ribbed channel falls with increasing Reynolds numbers. Correlations predicting Nusselt number (Nu) and friction factor $(f¯)$ as a function of $p/e$, $e/D$, and Re are developed. Also developed are correlations for $R$ and $G$ (friction and heat transfer roughness functions, respectively) as a function of the roughness Reynolds number $(e+)$, $p/e$, and $e/D$.

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## Figures

Figure 5

Nusselt number ratios plotted along the channel for e/D=0.15: (a) p/e=5, (b) p/e=7.5, and (c) p/e=10

Figure 6

Nusselt number ratios plotted along the channel for e/D=0.18: (a) p/e=5, (b) p/e=7.5, and (c) p/e=10

Figure 12

(a) Variation in friction roughness (R) with roughness Reynolds number (e+) and (b) heat transfer roughness parameter G from current study plotted against roughness Reynolds number e+, compared with data from Refs. 20-21

Figure 2

(a) Values of Nu considered for averaging (x/D>4) for a ribbed channel (here shown on a typical Nu/Nu0 profile) and (b) normalized Nusselt number ratios for a smooth channel. Ratio approaches 1 in the highlighted fully developed region and (c) friction factor derived by fitting straight line to measured static pressure profile for x/D>4 for a ribbed channel.

Figure 3

(a) Fully developed ribbed-side average Nusselt numbers obtained in various test cases and (b) correlation for average Nu as a function of Re, rib height (e/D), and spacing (p/e)

Figure 4

Nusselt number ratios plotted along the channel for e/D=0.1: (a) p/e=5, (b) p/e=7.5, and (c) p/e=10

Figure 7

(a) Schematic of flow over inclined ribs indicating the effect of rib spacing for constant rib height and (b) schematic of flow over inclined ribs indicating effect of rib height (for constant p/e)

Figure 8

(a) Friction factors for various test cases and (b) correlation for friction factor as a function of e/D and p/e

Figure 9

(a) Comparison of current friction factor with raw data from Refs. 20-21 and (b) comparison of current friction roughness (R) with correlation published earlier (20-21)

Figure 10

(a) Ribbed side average Nusselt number enhancement ratio (compared with a smooth channel) plotted against friction factor penalty ratio for all cases and (b) thermal performance for all experimental cases. Performance is below 1 for most cases with Reynolds number exceeding 100,000, indicating a significant pressure loss penalty.

Figure 11

Correlations for R and G as a function of e/D and p/e

Figure 1

(a) Schematic of experimental setup, indicating flow meter, plenum, test section, and temperature measurement system and (b) detailed view of instrumented test section

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