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Article

# Nusselt Numbers and Flow Structure on and Above a Shallow Dimpled Surface Within a Channel Including Effects of Inlet Turbulence Intensity Level

[+] Author and Article Information
P. M. Ligrani, N. K. Burgess, S. Y. Won

Convective Heat Transfer Laboratory, Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112-9208

J. Turbomach 127(2), 321-330 (Mar 01, 2004) (10 pages) doi:10.1115/1.1861913 History: Received October 01, 2003; Revised March 01, 2004

## Abstract

Experimental results from a channel with shallow dimples placed on one wall are given for Reynolds numbers based on channel height from 3,700 to 20,000, levels of longitudinal turbulence intensity from 3% to 11% (at the entrance of the channel test section), and a ratio of air inlet stagnation temperature to surface temperature of approximately 0.94. The ratio of dimple depth to dimple print diameter $δ∕D$ is 0.1, and the ratio of channel height to dimple print diameter $H∕D$ is 1.00. The data presented include friction factors, local Nusselt numbers, spatially averaged Nusselt numbers, a number of time-averaged flow structural characteristics, flow visualization results, and spectra of longitudinal velocity fluctuations which, at a Reynolds number of 20,000, show a primary vortex shedding frequency of $8.0Hz$ and a dimple edge vortex pair oscillation frequency of approximately $6.5Hz$. The local flow structure shows some qualitative similarity to characteristics measured with deeper dimples ($δ∕D$ of 0.2 and 0.3), with smaller quantitative changes from the dimples as $δ∕D$ decreases. A similar conclusion is reached regarding qualitative and quantitative variations of local Nusselt number ratio data, which show that the highest local values are present within the downstream portions of dimples, as well as near dimple spanwise and downstream edges. Local and spatially averaged Nusselt number ratios sometimes change by small amounts as the channel inlet turbulence intensity level is altered, whereas friction factor ratios increase somewhat at the channel inlet turbulence intensity level increases. These changes to local Nusselt number data (with changing turbulence intensity level) are present at the same locations where the vortex pairs appear to originate, where they have the greatest influences on local flow and heat transfer behavior.

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## Figures

Figure 6

Local Nusselt number ratio data from a channel with shallow dimples on one channel surface, and heating on one channel surface, for δ∕D=0.1, H∕D=1, Tu=0.069, and ReH=18,100

Figure 7

Local Nusselt number ratios along the test surface spanwise centerline, Z∕D=0.0, for different levels of channel inlet longitudinal turbulence intensity Tu from a channel with shallow dimples on one channel surface, and heating on one channel surface, for δ∕D=0.1, H∕D=1, and ReH=17,800–18,300

Figure 8

Local Nusselt number ratios along a line of constant X∕D=23.18, for different levels of channel inlet longitudinal turbulence intensity Tu from a channel with shallow dimples on one channel surface, and heating on one channel surface, for δ∕D=0.1, H∕D=1, and ReH=17,800–18,300.

Figure 9

Nusselt number ratios streamwise-averaged over one period of dimple surface geometry, for different levels of channel inlet longitudinal turbulence intensity Tu from a channel with shallow dimples on one channel surface, and heating on one channel surface, for δ∕D=0.1, H∕D=0, and ReH=17,800–18,300.

Figure 10

Ensemble-averaged spectrum of longitudinal velocity fluctuations measured at X∕D=6.27, Z∕D=0, and Y∕D=0.05, just downstream of the downstream edge of dimples in the seventh row, for ReH=20,000, δ∕D=0.1, H∕D=1, and Tu=0.033.

Figure 11

Ensemble-averaged spectrum of longitudinal velocity fluctuations measured at X∕D=6.27, Z∕D=0.5, and Y∕D=0.05, just downstream of the downstream edge of dimples in the seventh row, for ReH=20,000, δ∕D=0.1, H∕D=1, and Tu=0.033

Figure 12

Time sequence of flow images visualized in a spanwise-normal plane located at X∕D=12.14, which is just above the central part of the central dimple in the fifteenth row, for ReH=3,700, δ∕D=0.1, H∕D=1, and Tu=0.033

Figure 5

Local Nusselt number ratio data from a channel with shallow dimples on one channel surface, and heating on one channel surface, for δ∕D=0.1, H∕D=1, Tu=0.033, and ReH=17,800

Figure 13

Surveys of different time-averaged quantities measured in a spanwise-normal plane at X∕D=6.27, just downstream of the downstream edge of dimples in the seventh row, for δ∕D=0.1, H∕D=1, Tu=0.033, and ReH=20,000. (a) Normalized streamwise velocity. (b) Normalized total pressure. (c) Normalized static pressure. (d) Normalized normal velocity. (e) Normalized spanwise velocity. (f) Normalized streamwise vorticity. (g) Normalized Reynolds normal stress.

Figure 14

Dimpled channel friction factor ratios and globally averaged dimpled channel Nusselt number ratios, for different levels of channel inlet longitudinal turbulence intensity Tu from a channel with shallow dimples on one channel surface, and heating on one channel surface, for δ∕D=0.1, H∕D=1, and ReH=17,800–18,300

Figure 1

Schematic diagrams of: (a) The top and bottom dimpled test surfaces, and (b) cross-sectional view of the heated test surface. All dimensions are given in cm.

Figure 2

Schematic diagram of individual dimple geometry details for the present study. All dimensions are given in cm.

Figure 3

Baseline, constant property Nusselt numbers, measured with smooth channel surfaces and constant heat flux boundary condition, for a ratio of inlet stagnation temperature to surface temperature of 0.93–0.94, as dependent upon Reynolds number based on hydraulic diameter. Data are given for all four walls heated, and for one wall heated.

Figure 4

Apparatus employed to increase the magnitude of the longitudinal turbulence intensity in the channel

Figure 15

Globally averaged dimpled channel thermal performance parameters, for different levels of channel inlet longitudinal turbulence intensity Tu from a channel with shallow dimples on one channel surface, and heating on one channel surface, for δ∕D=0.1, H∕D=1, and ReH=17,800–18,300

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