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Research Papers: Experimental Techniques

# Novel Two-Dimensional Transient Heat Conduction Calculation in a Cooled Rotor: Ventilation Preheating—Blow-Down Flux

[+] Author and Article Information
J. P. Solano, G. Paniagua

Department of Turbomachinery and Propulsion, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo, 72 B1640 Rhode-Saint-Genèse, Belgium

J. Heat Transfer 131(8), 081601 (Jun 03, 2009) (9 pages) doi:10.1115/1.3122777 History: Received September 16, 2008; Revised January 13, 2009; Published June 03, 2009

## Abstract

This contribution presents an alternative to classical data reduction techniques to measure the heat transfer using thin-film gauges. A finite-element model of the two-dimensional unsteady heat conduction equation is solved in the cross-sectional area of a metallic airfoil bounded with a polyamide sheet on which thermal sensors are deposited. This novel methodology allows capturing all 2D heat conduction effects that are irremediably neglected with the 1D data reduction technique. The application of this technique in a compression tube facility allows an exact evaluation of the initial wall heat flux into cooled rotor blades. During the spinning-up period, the rotor is spun up to nearly its nominal speed (from 0 rpm to 6200 rpm) resulting in preheating due to drag losses. The long duration of this experiment $(∼450 s)$ and the magnitude of the wall temperature increase result in significant 2D conduction effects that are not accounted for using the 1D approach. In addition, short-duration experiments confirm the existence of 2D effects at smaller time scales $(∼0.5 s)$, as well as the influence of the initial nonuniform temperature distribution in the rotor blade. The resulting flux with such an initial condition appears to be the superposition of the wall heat flux at the end of the spinning up before the test and the flux due to the blow-down itself.

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Copyright © 2009 by American Society of Mechanical Engineers
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## Figures

Figure 14

(a) Comparison of two approaches for the computation of wall heat flux distribution: global computation and superposition of separate solutions and (b) relative error of the superposition procedure with respect to the global computation

Figure 15

(a) Wall heat flux evolution in the leading edge during the pretest rotation and (b) temperature distribution inside the leading edge substrate at the end of the pretest rotation (tr=450 s)

Figure 16

(a) Wall heat flux evolution during a 1D blow-down for different initial temperature distributions and (b) shifted temperature profiles at the end of the pretest rotation and blow-down processes

Figure 1

Thin-film gauges at 15% rotor blade height

Figure 2

Meridional view of the turbine facility

Figure 3

Typical testing sequence

Figure 4

Two-layered substrate thin-film gauges

Figure 10

(a) Temperature distribution at the end of the turbine pretest rotation (tr=450 s) and (b) parabolic fitting of the temperature evolution during the pretest rotation

Figure 11

Temperature field in the cross-sectional area of the two-layered rotor blade at tr=450 s

Figure 12

Wall heat flux distribution at the end of the nonuniform analytical blow-down (tf=0.5 s) versus initial wall heat flux distribution (tr=450 s)

Figure 13

Temperature history decomposition

Figure 5

Computational domain for the 1D approach

Figure 6

FEM mesh of the two-layered rotor blade

Figure 7

Analytical temperature evolution and wall heat flux reconstruction under 1D semi-infinite assumptions

Figure 8

(a) Temperature field in the cross-sectional area of the two-layered rotor blade at tf=0.5 s, (b) wall heat flux evolution in four control points, and (c) temperature profile in the four control locations at tf=0.5 s

Figure 9

(a) Wall heat flux distribution at tf=0.5 s in the rotor blade submitted to uniform 1D boundary conditions and (b) local error distribution with respect to expected 1D solution

Figure 17

(a) Experimental wall heat flux computation for uniform and nonuniform initial temperature distributions and (b) local error distribution referenced to uniform initial conditions

Figure 18

(a) Wall heat flux computation with two approaches: 2D and 1D and (b) local error distribution referenced to 1D results

Figure 19

(a) Wall heat flux computed with 2D approach and 1D approach corrected with Buttsworth and Jones’ (15) analytical expressions and (b) local error distribution referenced to 1D corrected results

## Errata

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