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Research Papers

# Unsteady Analysis of Blade and Tip Heat Transfer as Influenced by the Upstream Momentum and Thermal Wakes

[+] Author and Article Information
Ali A. Ameri

Department of Aerospace Engineering, Ohio State University, Columbus, OH 43210

David L. Rigby

ASRC Aerospace, NASA Glenn Research Center, Cleveland, OH 44135

A and E Consulting, Westlake, OH 44140

James Heidmann, John C. Fabian

NASA Glenn Research Center, Cleveland, OH 44135

J. Turbomach 132(4), 041007 (Apr 29, 2010) (7 pages) doi:10.1115/1.3213549 History: Received August 28, 2008; Revised February 09, 2009; Published April 29, 2010; Online April 29, 2010

## Abstract

The effect of the upstream wake on the time averaged rotor blade heat transfer was numerically investigated. The geometry and flow conditions of the first stage turbine blade of GE’s $E3$ engine with a tip clearance equal to 2% of the span were utilized. The upstream wake had both a total pressure and temperature deficit. The rotor inlet conditions were determined from a steady analysis of the cooled upstream vane. Comparisons between the time average of the unsteady rotor blade heat transfer and the steady analysis, which used the average inlet conditions of unsteady cases, are made to illuminate the differences between the steady and unsteady calculations. To help in the understanding of the differences between steady and unsteady results on one hand and to evaluate the effect of the total temperature wake on the other, separate calculations were performed to obtain the rotor heat transfer and adiabatic wall temperatures. It was found that the Nusselt number distribution for the time average of unsteady heat transfer is invariant if normalized by the difference in the adiabatic and wall temperatures. It appeared though that near the endwalls the Nusselt number distribution did depend on the thermal wake strength. Differences between steady and time averaged unsteady heat transfer results of up to 20% were seen on the blade surface. Differences were less on the blade tip surface.

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## Figures

Figure 1

Total pressure and temperature at the exit

Figure 2

Grid on blade hub and surfaces

Figure 3

Blade surface heat flux at four equally spaced times in a period of wake-passing; top row shows the suction side, and the bottom row shows the pressure side

Figure 4

Distribution of the average wall heat flux on the blade surface (w/o thermal wake)

Figure 5

Distribution of the average adiabatic wall temperature over the blade surface (w/o thermal wake)

Figure 6

Average heat transfer coefficient distribution over the blade surface (w/o thermal wake)

Figure 7

Distribution of the average wall heat flux on the blade surface (with thermal wake)

Figure 8

Distribution of the average adiabatic wall temperature over the blade surface (with thermal wake)

Figure 9

Average heat transfer coefficient distribution over the blade surface (with thermal wake)

Figure 10

Percent difference between the unsteady average and steady computation of the heat flux

Figure 11

Figure 12

Figure 13

Average of the unsteady heat flux

Figure 14

Figure 15

Average of the unsteady Nusselt number

Figure 16

Percent deviation from the average of the unsteady Nusselt number

Figure 17

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