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Research Papers

Implicit Model Equation for Hydraulic Resistance and Heat Transfer including Wall Roughness

[+] Author and Article Information
Eckart Laurien

University of Stuttgart/Institute of Nuclear Technology and Energy Systems,
Pfaffenwaldring 31, D-70569 Stuttgart, Germany
e-mail: Laurien@ike.uni-stuttgart.de

Manuscript received May 12, 2015; final manuscript received October 13, 2015; published online February 29, 2016. Assoc. Editor: Thomas Schulenberg.

ASME J of Nuclear Rad Sci 2(2), 021016 (Feb 29, 2016) (6 pages) Paper No: NERS-15-1085; doi: 10.1115/1.4031948 History: Received May 12, 2015; Accepted October 13, 2015

Heat transfer to water at supercritical pressure within the core of a supercritical water reactor must be predicted accurately to ensure safe design of the reactor and prevent overheating of the fuel cladding. In the previous work (Laurien, 2012, “Semi-Analytic Prediction of Hydraulic Resistance and Heat Transfer for Pipe Flows of Water at Supercritical Pressure,” Proceedings of the International Conference on Advances in Nuclear Power Plants, ICAPP’12, Chicago, June 24–28), we have demonstrated that the wall shear stress and the wall temperature can be computed in a coupled way by a finite-difference method, taking the wall roughness into account. In the present paper, the classical two-layer model, consisting only of a laminar sublayer and a turbulent wall layer, is extended toward the same task. A set of implicit algebraic equations for the wall shear stress and the wall temperature is derived. It is consistent with the well-established Colebrook equation for rough pipes, which is included as a limiting case for constant properties. The accuracy of the prediction for strongly heated pipe flow is tested by comparison to experiments (Yamagata et al., 1972, “Forced Convective Heat Transfer to Supercritical Water Flowing in Tubes,” Int. J. Heat Mass Transfer, 15(12), 2575–2593) with supercritical water. The high accuracy and the generality of Laurien (2012) “Semi-Analytic Prediction of Hydraulic Resistance and Heat Transfer for Pipe Flows of Water at Supercritical Pressure,” Proceedings of the International Conference on Advances in Nuclear Power Plants, ICAPP’12, Chicago, June 24–28 are not achieved, but with the help of correction factors, the two-layer model has a potential for improved predictions of the hydraulic resistance and the heat transfer of pipe and channel flows at supercritical pressure.

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Figures

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Fig. 1

Nondimensional velocity profile in wall units for a smooth wall and with wall roughness ϵ in wall units, constant properties

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Fig. 2

Full line: curve-fit of the iterative solution (symbols) of Eq. (15) versus the nondimensional roughness ϵ+

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Fig. 3

Comparison of the present work Nu(Re) from Eq. (25), smooth, with Gnielinski’s correlation

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Fig. 4

Nu(Re) of the present work (Eq. 25) for Pr=1, smooth and rough wall

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Fig. 5

Wall shear stress using Eq. (36) for the experimental parameters of Ref. [20]. Dot-dashed line: constant properties (no heating); full lines: present work; dashed lines: results from Ref. [6] for the same qw

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Fig. 6

Symbols: Tw of the experiments [20]; large dashes: bulk temperature; small dashes: Tcs, full line Tw of the present work, qw=233  kW/m2

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Fig. 7

Symbols: Tw of the experiments [20]; large dashes: bulk temperature; small dashes: Tcs, full line Tw of the present work, qw=465  kW/m2

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Fig. 8

Symbols: Tw of the experiments [20]; large dashes: bulk temperature; small dashes: Tcs, full line Tw of the present work, qw=698  kW/m2

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