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TECHNICAL PAPERS

Predicting Entropy Generation Rates in Transitional Boundary Layers Based on Intermittency

[+] Author and Article Information
Kevin P. Nolan

Stokes Research Institute, Department of Mechanical and Aeronautical Engineering, University of Limerick, Limerick, Irelandkevin.nolan@ul.ie

Edmond J. Walsh

Stokes Research Institute, Department of Mechanical and Aeronautical Engineering, University of Limerick, Limerick, Ireland

Donald M. McEligot

 Idaho National Laboratory (INL), P.O. Box 1625, Idaho Falls, ID 83415-38; University of Arizona, Tuscon, AZ 85721; and IKE, Universität Stuttgart, D-70550 Stuttgart, Germany

Ralph J. Volino

Department of Mechanical Engineering, United States Naval Academy, Annapolis, MD 21402

J. Turbomach 129(3), 512-517 (Jul 25, 2006) (6 pages) doi:10.1115/1.2720488 History: Received July 24, 2006; Revised July 25, 2006

Prediction of thermodynamic loss in transitional boundary layers is typically based on time-averaged data only. This approach effectively ignores the intermittent nature of the transition region. In this work laminar and turbulent conditionally sampled boundary layer data for zero pressure gradient and accelerating transitional boundary layers have been analyzed to calculate the entropy generation rate in the transition region. By weighting the nondimensional dissipation coefficient for the laminar conditioned data and turbulent conditioned data with the intermittency factor, the entropy generation rate in the transition region can be determined and compared to the time-averaged data and correlations for laminar and turbulent flow. It is demonstrated that this method provides an accurate and detailed picture of the entropy generation rate during transition in contrast with simple time averaging. The data used in this paper have been taken from conditionally sampled boundary layer measurements available in the literature for favorable pressure gradient flows. Based on these measurements, a semi-empirical technique is developed to predict the entropy generation rate in a transitional boundary layer with promising results.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Reθ predictions for favorable pressure gradient case: (▴) laminar conditioned data; (∎) turbulent conditioned data; (—) Thwaites’ method; and (- -), Buri’s method

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Figure 2

Predicted intermittency distribution: (∎) experimental data, Volino (19); and (- -) prediction, Eqs. 16,17,18

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Figure 3

Boundary layer data at Station 5: (∘) laminar-conditioned data; (▵) turbulent-conditioned data; (◆), turbulent-conditioned Reynolds shear stresses; (- -), Y+=U+; (—), von Kármán turbulent correlation; and (—, solid grey line) polynomial fit of turbulent-conditioned Reynolds shear stress data

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Figure 4

Entropy generation rate profiles at Station 5: (∘) laminar-conditioned data; (▵) viscous contribution to turbulent conditioned data; (—) Reynolds shear stress contribution to turbulent conditioned data; and (◻) turbulent-conditioned data

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Figure 5

Dissipation coefficient versus Reθ or experimental data: (∎) laminar-conditioned data; (•) turbulent-conditioned data; (▴) intermittency-weighted data; (▵) nonconditionally-sampled data; (—, solid grey line) laminar correlation; and (—) turbulent correlation

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Figure 6

Pohlhausen velocity profiles for laminar conditioned data: (•) laminar data, Volino (19); (—) zero pressure gradient, β=0.173(Λ=0); (- -), limits of Pohlhausen (Λ±12); and (—, solid grey line) β=0.27(Λ=21)

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Figure 7

Comparison of predicted and measured intermittency-weighted dissipation coefficient for favorable pressure gradient case: (∎) laminar-conditioned data; (▴), intermittency-weighted measurements; (•), turbulent-conditioned data; (—, solid grey line) laminar correlation, β=0.27(Λ=12); (—) turbulent correlation; (- -, broken grey line) prediction; (– –) Eq. 18.

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