0
RESEARCH PAPERS: Forced Convection

# Discrete Green’s Function Measurements in a Serpentine Cooling Passage

[+] Author and Article Information
Charles W. Booten

Protonex Technology Corporation, Bloomfield, CO 80020booten@alum.mit.edu

John K. Eaton

Mechanical Engineering Department, Stanford University, Stanford, CA 94305eatonj@stanford.edu

J. Heat Transfer 129(12), 1686-1696 (Apr 16, 2007) (11 pages) doi:10.1115/1.2767749 History: Received October 04, 2006; Revised April 16, 2007

## Abstract

The inverse discrete Green’s function (IDGF) is a heat transfer coefficient that is valid for arbitrarily complex thermal boundary conditions. It was measured using a rapid experimentation technique in a generic serpentine turbine-blade cooling passage with rib turbulators for Reynolds numbers from 15,000 to 55,000. The model was designed to adhere closely to industry design practice. There were four square cross-section passages with ribs on two opposing walls at $45deg$ to the main flow. The rib pitch-to-height ratio was 8.5:1 and the blockage ratio was 0.1. The IDGF was measured with an element length of one rib pitch and was used to determine Nusselt numbers that were then compared to the literature. An increase in Nusselt number over thermally fully developed pipe flow of 2.5–3.0 is common in the literature and was consistent with the results in this work. The results showed that the heat transfer coefficient in such complex passages is weakly affected by the thermal boundary condition, which simplifies measurement of this quantity.

<>

## Figures

Figure 1

Turbine blade with serpentine cooling passages. Reproduced from Lindstrom (1).

Figure 2

Top view of the test section. Only the ribs on the top wall are visible. Dimensions are in millimeters.

Figure 3

Heated element locations. Each shaded element represents the location of the heated copper element in the instrumented plug.

Figure 4

Instrumented plug for straight sections of SGTIP model

Figure 21

Fully developed Nusselt numbers on corner elements versus Reynolds number

Figure 5

Dimensions of straight section plug in millimeters

Figure 6

End view of straight section instrumented plug. Dimensions are in millimeters.

Figure 7

Thermocouple numbers on the surface of instrumented plug. Only selected thermocouples are numbered for clarity. Numbers 1–8 are near the “upstream” side wall (column 1), 9–24 are in the centerline (column 2), and 25–32 are near the “downstream” side wall (column 3).

Figure 8

Comparison between mean velocity vectors from PIV (white) and MRV (black) in the centerplane of the first corner. Reproduced from Elkins (19).

Figure 9

The six corner measurement sections. Shaded areas represent copper elements; circles represent thermocouple locations.

Figure 10

Expanded view of corner plug in SGTIP model

Figure 11

Adiabatic wall temperature with respect to the fluid inlet temperature on surface mounted thermocouples. Thermocouple numbers are given in Fig. 7.

Figure 12

Experimental centerline temperature rise on element 33, Re=35,000

Figure 13

Comparison of the relative heat losses on the copper element and the corresponding heat gains on the adjacent upstream and two downstream elements on the pipe flow and for heating on element 2

Figure 14

G−1 in straight section locations, Re=15,000

Figure 15

G−1 in straight section locations, Re=55,000

Figure 16

Mean of measured elements in G−1Re=35,000

Figure 17

Fully developed Nusselt number. Values from this experiment, NuΔTaw and NuΔTbulk, are averages over all measured straight section elements.

Figure 18

Locations of “columns” of thermocouples in the square corner

Figure 19

Experimental temperature rise on the square corner, element 11 is heated, Reynolds number=35,000

Figure 20

G−1 for all measured locations, Re=35,000

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections