A Method for Reconstructing Internal Temperature Distribution in Solid Structure
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A Method for Reconstructing Internal Temperature Distribution in Solid Structure You-An Shi1,2 · Dong Wei1 · Bin Hu3 · Lei Zeng1 · Yan-Xia Du1 · Ye-Wei Gui1 Received: 4 November 2018 / Accepted: 1 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, a method combining ultrasonic travel time measurement with inversion is proposed to reconstruct the solid temperature field. Based on the measured transient ultrasonic propagation time, the inverse problem of acoustic thermal coupling is solved directly, and the unknown equivalent heat flow is estimated. Then, the time and space distribution of the internal temperature field can be reconstructed accurately by calculating the corresponding heat conduction problems. Through the estimation of two typical heat flow function forms, the accuracy and influencing factors are simulated and analyzed. The feasibility and error of this method are analyzed through a transient verification experiment of a steel plate heated first and then cooled and a steady-state experiment in the literature. The results show that, compared with the previous methods, this method can predict the distribution of non-uniform temperature field more accurately and effectively. This method is expected to be an effective method for nondestructive testing of temperature distribution of solid structures. Keywords Reconstructing Internal Temperature Distribution · Acoustic-thermal coupled problem · Nondestructive measure · Ultrasonic · Validation experiment
List of Symbols tdelay V T a, b t k ρ Cp Q J i n
B
Ultrasonic travel time (s) Acoustic velocity (m/s) Temperature (K) Calibrated parameter Time (s) Heat conductivity coefficient (W/m.K) Density (kg/m3 ) Heat capacity ((J/kg K)) Heat flux (W/m2 ) Objective function Index Total measured number
Dong Wei [email protected]
1
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China
2
Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China
3
China Special Equipment Inspection and Research Institute, Beijing 100029, China
β γ P λ δ σ M Sdelay
Step size Conjugate coefficient Gradient of J Lagrange multiplier Kronecker symbol Standard deviation of measurement uncertainty Number of measurement point Sensitivity of ultrasonic travel time with temperature (s/K
1 Introduction Measuring the internal temperature in solid structure has widely played a fundamental and significant role in various fields of science and engineering. For example, in polymer injection molding process, on-line monitoring internal temperature variation is mostly related to productivity and quality [1, 2], as material properties depend primarily on temperature. Although the traditional thermocouple technique has been widely used in temperature measurement, it is not easy to obtain internal temperature owing to its limitation of installation. In addition, the well-known infrared technology, as a non-destruct
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