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RESEARCH PAPERS: Experimental Techniques

A Periodic-Transient Method for High-Resolution Heat Transfer Measurement on Two-Dimensional Curved Surfaces

[+] Author and Article Information
M. Röger

German Aerospace Center (DLR), Institute of Technical Thermodynamics, Solar Research, Pfaffenwaldring 38-40, D-70569 Stuttgart, Germanymarc.roeger@dlr.de

J. Heat Transfer 129(12), 1638-1654 (Mar 28, 2007) (17 pages) doi:10.1115/1.2767677 History: Received August 11, 2006; Revised March 28, 2007

Abstract

Measurement of heat transfer distribution is frequently required in engineering. However, some heat transfer techniques are not able to measure accurately on two-dimensional curved surfaces. In this field, periodic-transient measurement methods are advantageous. This paper describes the development of a periodic-transient technique for high-resolution heat transfer measurement and its application to multiple air-jet cooling of a concave solar receiver window. In contrast to other measurement techniques, the periodic-transient technique requires neither homogenous heating nor quantitative measurement of surface or fluid temperatures. The heat transfer coefficient is determined by periodically heating the substrate and evaluating the phase shift between the heat flux penetrating the substrate and the resulting temperature response. Equations for a hollow-sphere and flat-plate substrates are derived. The curved window surface is periodically heated by a simple device with standard light bulbs. A procedure for taking the transient heating characteristic into consideration is described. The distribution of surface temperature fluctuation is measured nonintrusively by thermography. For the sample application of air-jet cooling, a detailed uncertainty estimation is presented. The relative measurement uncertainty of the local, convective heat transfer coefficient ranges from $−2.4%$ to $+14.1%$ for $h=10W∕(m2K)$ and from $−2.3%$ to $+9.7%$ for $h=200W∕(m2K)$. The uncertainty of the spatially averaged heat transfer coefficient lies between $+2.0%$ and $+9.8%$ for $hm=10W∕(m2K)$ and between $+0.7%$ and $+6.7%$ for $hm=200W∕(m2K)$. The periodic-transient method described complements established techniques for high-resolution heat transfer measurements on two-dimensional curved surfaces.

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Figures

Figure 1

Measurement principle and relevant quantities

Figure 2

System representation

Figure 3

Amplitude A(ω) and phase response φ(ω) for different Bi numbers (hollow sphere, r1=0.310m, r2=0.315m)

Figure 4

Schematic graph of input and output signals (Xin(t), Xout(t)) and phase shift φ

Figure 5

Characteristic curves for heat transfer coefficient determination by phase response evaluation (hollow sphere, r1=0.310m, r2=0.315m, fused silica, λ=1.40W∕(mK), ρ=2203kg∕m3, cp=754J∕(kgK))

Figure 6

The way from the measurement task to the experimental layout

Figure 7

Measurement setup (TC=thermocouple, Δp=differential pressure gage, HFS=heat flux sensor)

Figure 8

Window-cooling designs and coordinate systems with nozzle orientation (center)

Figure 9

Energy flows and heat fluxes on the heated side of the substrate

Figure 10

(a) Electric heating power. (b)–(d) Heat fluxes at points A and B on the heated side for heat transfer coefficients hA=22W∕m2K and hB=128W∕m2K. Vertical lines point out the phase angles. Simulation: flat plate, δ=0.005m, fused silica, λ=1.40W∕(mK), ρ=2203kg∕m3, cp=754J∕(kgK), Tper=1000s(ω=0.0063s−1).

Figure 11

Characteristic heating curve (Pel=380±260W, Tper=1000s)

Figure 12

Evaluation procedure for finding the heat transfer coefficient

Figure 13

Phase shift ∣φ∣ found from measured phase shift ∣φmeas∣ and correction phase shifts φcorr,heat and φcorr,paint (measurement)

Figure 14

Heat transfer distribution measured on the window surface with symmetric air-jet cooling (six round-type nozzles; d=0.008m; ϑ=0deg; φ=0deg; V̇0=51m3∕h; w=47m∕s; Re=23,200; Trot=∞; h in W∕m2K(25°C)). Periodic-transient method, left; stationary method, right.

Figure 15

Heat transfer with asymmetric air-jet cooling (5 of 18 slot-type nozzles; dh=0.0159m; ϑ=0deg; φ=0deg; V̇0=245m3∕h; w=68m∕s; Re=65,800; h in W∕m2K(25°C)). Nonpulsating cooling (Trot=∞).

Figure 16

Heat transfer distribution with asymmetric air-jet cooling. Pulsating cooling (Trot=22s; for other parameters, see Fig. 1).

Figure 17

Relative measurement uncertainty of convective heat transfer coefficient

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