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Research Papers

Unsteady Conjugate Heat Transfer Modeling

[+] Author and Article Information
L. He, M. L. G. Oldfield

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

J. Turbomach 133(3), 031022 (Nov 29, 2010) (12 pages) doi:10.1115/1.4001245 History: Received September 29, 2009; Revised October 06, 2009; Published November 29, 2010; Online November 29, 2010

The primary requirement for high pressure turbine heat transfer designs is to predict blade metal temperature. There has been a considerable recent effort in developing coupled fluid convection and solid conduction (conjugate) heat transfer prediction methods. They are, however, confined to steady flows. In the present work, a new approach to conjugate analysis for periodic unsteady flows is proposed and demonstrated. First, a simple model analysis is carried out to quantify the huge disparity in time scales between convection and conduction, and the implications of this for steady and unsteady conjugate solutions. To realign the greatly mismatched time scales, a hybrid approach of coupling between the time-domain fluid solution and frequency-domain solid conduction is adopted in conjunction with a continuously updated Fourier transform at the interface. A novel semi-analytical harmonic interface condition is introduced, initially for reducing the truncation error in finite-difference discretization. More interestingly, the semi-analytical interface condition enables the unsteady conjugate coupling to be achieved without simultaneously solving the unsteady temperature field in the solid domain. This unique feature leads to a very efficient and accurate unsteady conjugate solution approach. The fluid and solid solutions are validated against analytical solutions and experimental data. The implemented unsteady conjugate method has been demonstrated for a turbine cascade subject to inlet unsteady hot streaks.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 4

Surface Nu distribution (NGV, MT1)

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Figure 1

Nusselt number for flat plate laminar boundary layer

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Figure 2

Computational mesh for a transonic NGV

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Figure 3

Surface pressure distribution (NGV, MT1)

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Harmonic temperature distribution (1D slab): (a) in-phase harmonic component A, and (b) out-phase harmonic component B

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Figure 5

Mesh for steady conduction (cylinder)

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Fluid-solid domain interface

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Radial temperature distribution (cylinder)

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Heat transfer in corner region: (a) normal flux only and (b) normal and tangential fluxes

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Temperature amplitude (corner solution): (a) semi-analytical BC and (b) finite-difference BC

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Radial temperature harmonics

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Mesh-dependence of wall temperature: (a) 100 Hz and (b) 1000 Hz

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Unsteady heat flux in time (with and without unsteady wall temperature)

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Cooled blade configuration (subject to Incoming hot streak)

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Computational mesh (conjugate solution)

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Instantaneous unsteady total temperatures (inlet total temperature amplitude, AT=0.2)

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Solution convergence characteristic: (a) heat flux (time-domain fluid solution) and (b) harmonic wall temperature amplitude (frequency-domain solution)

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Time averaged surface heat flux: (a) 10% and (b) 20% hot streak amplitudes

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Total temperature contours (steady versus time-averaged unsteady): (a) steady and (b) time-averaged

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Instantaneous stream-traces: (a) hot and (b) cold portion impinging

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Time traces of fluid temperatures: (a) 10% and (b) 20% hot streak amplitudes

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Figure 21

Impinging hot and cold flow patterns

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