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Research Papers

Inverse Prediction of Temperature Through Time Rescaling of High-Temperature Experimental Data

[+] Author and Article Information
J. A. Myrick

Department of Mechanical, Aerospace
and Biomedical Engineering,
The University of Tennessee,
1512 Middle Drive,
Knoxville, TN 37996-2210
e-mail: jmyrick2@vols.utk.edu

M. Keyhani

Fellow ASME
Professor
Department of Mechanical, Aerospace
and Biomedical Engineering,
The University of Tennessee,
1512 Middle Drive,
Knoxville, TN 37996-2210
e-mail: keyhani@utk.edu

J. I. Frankel

Professor
Department of Mechanical,
Aerospace and Biomedical Engineering,
The University of Tennessee,
1512 Middle Drive,
Knoxville, TN 37996-2210
e-mail: jfranke1@utk.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received December 8, 2015; final manuscript received June 21, 2016; published online July 27, 2016. Assoc. Editor: Samuel Sami.

J. Thermal Sci. Eng. Appl 8(4), 041005 (Jul 27, 2016) (12 pages) Paper No: TSEA-15-1348; doi: 10.1115/1.4034093 History: Received December 08, 2015; Revised June 21, 2016

This paper presents experimental data from a two-layer test sample made up of a copper layer and an AISI type 316 stainless steel (SS) layer that was heated with a laser power source. Experiments were conducted to generate high-temperature benchmark data that ranged from room temperature to 820 °C. The concept of time rescaling was employed to account for the dependence of thermal diffusivity on temperature in order to utilize the calibration integral equation method (CIEM). The future time regularization method was used to obtain a stable prediction for the surface temperature. An estimate for the future time regularization parameter was acquired through analysis of the in-depth calibration test thermocouple (TC) response. Results for three test cases consisting of selected pairs of calibration data and reconstruction data (to be predicted) are presented and discussed. Four different values of the future time regularization parameter were employed in the three test cases. The proposed nonlinear (NL) formulation improved the prediction accuracy when compared to the constant properties formulation of the CIEM. It should be emphasized that no knowledge of TC probe depth or TC response properties is required.

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Figures

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Fig. 1

Schematic of the one-dimensional domain with an in-depth TC

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Fig. 2

Details of the test sample: (a) sketch of the test sample and insulation and (b) side view of the actual sample with the two type N TCs shown

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Fig. 3

Experimental setup assembly in the laser test facility at the University of Tennessee-Knoxville. Inset shows the square laser beam profile.

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Fig. 4

Webcam pictures of the sample: (a) anodized copper surface before laser on, (b) sample surface when the laser threshold is on (laser is off), (c) during heating, and (d) glowing of the anodized copper surface at about 700 °C (laser is off)

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Fig. 5

Test case 1–4 measured experimental data: (a) laser heat flux and (b) TC temperatures

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Fig. 6

Test case 1–4 temperature data in the original time domain and the rescaled (stretched) time domain to account for temperature-dependent thermal diffusivity: (a) TC1 data and (b) TC2 data

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Fig. 7

Estimation of the future time regularization parameter, γest, using TC2 data from test 1

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Fig. 8

Test case 1–4 results: (a) comparison between the TC1 prediction with the measured data and (b) temperature prediction error versus time

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Fig. 9

Test case 2–5 measured experimental data: (a) laser heat flux and (b) TC temperatures

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Fig. 10

Test case 2–5 results: (a) comparison between the TC1 prediction with the measured data and (b) temperature prediction error versus time

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Fig. 11

Test case 3–6 measured experimental data: (a) laser heat flux and (b) TC temperatures

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Fig. 12

Test case 3–6 results: (a) comparison between the TC1 prediction with the measured data and (b) temperature prediction error versus time

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