Research Papers: Conduction

Analytical-Solution Based Corner Correction for Transient Thermal Measurement

[+] Author and Article Information
H. Jiang

University of Michigan-Shanghai
Jiao Tong University Joint Institute,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China
e-mail: jianghm188@163.com

W. Chen

University of Michigan-Shanghai
Jiao Tong University Joint Institute,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China
e-mail: chenwei_go@163.com

Q. Zhang

Department of Mechanical Engineering and Aeronautics,
School of Engineering
and Mathematical Sciences,
City University London,
Northampton Square,
London EC1V 0HB, UK
e-mail: Qiang.Zhang@city.ac.uk

L. He

Department of Engineering Science,
University of Oxford,
Parks Road, Oxford OX1 3PJ, UK
e-mail: li.he@eng.ox.ac.uk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 15, 2014; final manuscript received May 17, 2015; published online August 4, 2015. Assoc. Editor: Danesh / D. K. Tafti.

J. Heat Transfer 137(11), 111302 (Aug 04, 2015) (9 pages) Paper No: HT-14-1469; doi: 10.1115/1.4030980 History: Received July 15, 2014

The one-dimensional (1D) conduction analytical approaches for a semi-infinite domain, widely adopted in the data processing of transient thermal experiments, can lead to large errors, especially near a corner of solid domain. The problems could be addressed by adopting 2D/3D numerical solutions (finite element analysis (FEA) or computational fluid dynamics (CFD)) of the solid field. In addition to needing the access to a conduction solver and extra computing effort, the numerical field solution based processing methods often require extra experimental efforts to obtain full thermal boundary conditions around corners. On a more fundamental note, it would be highly preferable that the experimental data processing is completely free of any numerical solutions and associated discretization errors, not least because it is often the case that the main purposes of many experimental measurements are exactly to validate the numerical solution methods themselves. In the present work, an analytical-solution based method is developed to enable the correction of the 2D conduction errors in a corner region without using any conduction solvers. The new approach is based on the recognition that a temperature time trace in a 2D corner situation is the result of the accumulated heat conductions in both the normal and lateral directions. An equivalent semi-infinite 1D conduction temperature trace for a correct heat transfer coefficient (HTC) can then be generated by reconstructing and removing the lateral conduction component at each time step. It is demonstrated that this simple correction technique enables the use of the standard 1D conduction analysis to get the correct HTC completely analytically without any aid of CFD or FEA solutions. In addition to a transient infrared (IR) thermal measurement case, two numerical test cases of practical interest with turbine blade tip heat transfer and film cooling are used for validation and demonstration. It has been consistently shown that the errors of the conventional 1D conduction analysis in the near corner regions can be greatly reduced by the new corner correction method.

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Fig. 2

A schematic of the test section

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Fig. 1

Illustration of the corner conduction problem

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Fig. 3

Inlet temperature and surface temperature history during a typical transient thermal measurement

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Fig. 4

IR camera in situ calibration during a typical transient thermal measurement

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Fig. 5

HTC distributions with and without the assumption of semi-infinite 1D conduction and the percentage errors: (a) HTC distribution and (b) percentage errors introduced by the semi-infinite 1D conduction assumption near the corner region

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Fig. 6

An example of the 2D corner conduction: (a) 2D domain and (b) HTC variation with distance from the corner normalized by the domain length

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Fig. 7

General concept of the corner correction

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Fig. 11

Experimental HTC distribution obtained with and without new corner correction method and percentage errors: (a) corner HTC distributions and (b) percentage errors

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Fig. 8

Corner HTC distributions with and without the corner correction applied

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Fig. 9

Procedure flow chart for the new corner correction method

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Fig. 10

Application of the new corner correction approach for cases with nonuniform HTCs: (a) linear increase distribution and (b) triangle wave distribution

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Fig. 12

HTC of tip surface by processing transient temperature traces generated by a 3D conduction solver: (a) conventional 1D approach and (b) new correction approach (exact solution: HTC = 1500 W/m2 K)

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Fig. 13

HTC distributions: (a) baseline true values, used to generate transient surface temperature traces; (b) values by the standard 1D processing of the temperature transients; and (c) the corrected results after applying the new method

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Fig. 14

Percentage HTC errors from (a) the conventional 1D conduction approach and (b) the new correction approach

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Fig. 15

(a) Three-dimensional film cooling model employed and (b) true HTC distribution obtained near the cooling hole exit

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Fig. 16

(a) HTC contour directly calculated with the semi-infinite 1D assumption and (b) corrected HTC contour after applying the new corner correction approach

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Fig. 17

Percentage HTC errors from (a) the conventional 1D conduction approach and (b) the new correction approach



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