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Research Papers

# Impulse Response Processing of Transient Heat Transfer Gauge Signals

[+] Author and Article Information
M. L. Oldfield

Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK

J. Turbomach 130(2), 021023 (Mar 25, 2008) (9 pages) doi:10.1115/1.2752188 History: Received November 06, 2006; Revised December 23, 2006; Published March 25, 2008

## Abstract

A new, computationally efficient method is presented for processing transient thin-film heat transfer gauge signals. These gauges are widely used in gas turbine heat transfer research, where, historically, the desired experimental heat transfer flux signals, $q$, are derived from transient measured surface-temperature signals, $T$, using numerical approximations to the solutions of the linear differential equations relating the two. The new method uses known pairs of exact solutions, such as the $T$ response due to a step in $q$, to derive a sampled approximation of the impulse response of the gauge system. This impulse response is then used as a finite impulse response digital filter to process the sampled $T$ signal to derive the required sampled $q$ signal. This is computationally efficient because the impulse response need only be derived once for each gauge for a given sample rate, but can be reused repeatedly, using optimized MATLAB filter routines and is highly accurate. The impulse response method can be used for most types of heat flux gauge. In fact, the method is universal for any linear measurement systems which can be described by linear differential equations where theoretical solution pairs exist between input and output. Examples using the new method to process turbomachinery heat flux signals are given.

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## Figures

Figure 1

Early Macor blade showing fired platinum thin-film gauges on surface with gold leads

Figure 2

Kapton (polyimide) sheet with sputtered heat flux gauges wrapped round a metal nozzle guide vane with film cooling holes

Figure 3

Semi-infinite heat transfer gauge

Figure 4

First 50 points of Impulse response h[n] of impulse filter to convert T to q for semi-infinite heat transfer gauge

Figure 5

First 50 points of Impulse response h[n] of impulse filter to convert q to T for semi-infinite heat transfer gauge

Figure 6

Test result showing that the deviation from the ideal unit step in q when processing a parabola in T is less than ±6×10−14 over 10,000 points

Figure 7

Two layer heat transfer gauge

Figure 8

Two layer gauge test signal to ideally give step q output

Figure 9

Double-sided thin-film heat transfer gauge seen as a sum of differential and common mode gauges

Figure 10

Test signals for double sided gauge processing functions

Figure 11

Error of double sided method is less than 0.014%

Figure 12

Surface temperature trace from rotor tip direct heat transfer gauge for a complete run of the QinetiQ ILPF rotating turbine as described in Ref. 24

Figure 13

Heat transfer rate traces processed from the data shown in by three different methods: (a) new impulse response method as a double sided gauge; (b) Fourier transform method (16) as a two layer gauge; and (c) from temperature difference as a direct heat transfer gauge

Figure 14

Laser-cut semi-infinite thin-film gauge array to measure overtip time-resolved heat transfer signals. The rotor (not shown here) passes over the gauges (from Ref. 25).

Figure 15

Raw temperature trace with 200,000 points at 500,000samples∕s

Figure 16

Magnified section of temperature trace showing blade passing events

Figure 17

Heat flux signal processed by impulse method

Figure 18

Low pass filtered heat flux signal

Figure 19

Magnified section of heat flux traces showing blade passing events. New and old (27) processing agree excellently.

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