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Research Papers: Fundamental Issues and Canonical Flows

Entropy Generation in a Boundary Layer Transitioning Under the Influence of Freestream Turbulence

[+] Author and Article Information
Edmond J. Walsh

 Stokes Research Institute, University of Limerick, Limerick, Ireland e-mail: Edmond.Walsh@ul.ie

Donald M. Mc Eligot

 Stokes Research Institute, University of Limerick, Limerick, Ireland;  Mechanical Engineering Department, University of Idaho, Idaho Falls, Idaho 83402;  Aero. Mech. Engineering Department, University of Arizona, Tucson, Arizona 85721

Luca Brandt, Phillip Schlatter

 Linne Flow Centre, KTH Mechanics, SE-100, 44 Stockholm, Sweden

J. Fluids Eng 133(6), 061203 (Jun 16, 2011) (10 pages) doi:10.1115/1.4004093 History: Received October 08, 2010; Revised April 20, 2011; Published June 16, 2011; Online June 16, 2011

The objective of the present research is to develop new fundamental knowledge of the entropy generation process in laminar flow with significant fluctuations (called pre-transition) and during transition prematurely induced by strong freestream turbulence (bypass transition). Results of direct numerical simulations are employed. In the pre-transitional boundary layer, the perturbations by the streaky structures modify the mean velocity profile and induce a “quasi-turbulent” contribution to indirect dissipation. Application of classical laminar theory leads to underprediction of the entropy generated. In the transition region the pointwise entropy generation rate (S′′′)+ initially increases near the wall and then decreases to correspond to the distribution predicted for a fully-turbulent boundary layer as the flow progresses downstream. In contrast to a developed turbulent flow, the term for turbulent convection in the turbulence kinetic energy balance is significant and can play an important role in some regions of the transitioning boundary layer. More turbulent energy is produced than dissipated and the excess is convected downstream as the boundary layer grows. Since it is difficult to measure and predict true turbulent dissipation rates (and hence, entropy generation rates) exactly other than by expensive direct numerical simulations, a motivation for this research is to evaluate approximate methods for possible use in experiments and design. These new results demonstrate that an approximate technique, used by many investigators, overestimates the dissipation coefficient Cd by up to seventeen per cent. For better predictions and measurements, an integral approach accounting for the important turbulent energy flux is proposed and validated for the case studied.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 3

Development of turbulence kinetic energy balance terms during bypass transition: (a) turbulent production and dissipation, (b) viscous diffusion and turbulent convection and (c) turbulent diffusion. All quantities are in wall coordinates

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Figure 4

Profiles of entropy generation rates in pre-transitional boundary layers at Rex 0.5 ≈ 350 for Tuin  = 4.7% and (Λ/δ*)in  = 5 as predicted from DNS results by both exact and approximate definitions

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Figure 5

Time- and spanwise-averaged total (S’’’)+ profiles at streamwise stations (Rex 0.5 ) in the transitional region, compared with the fully-turbulent DNS results of Schlatter and Örlü [65] for Reθ  = 3970. Numbers indicate streamwise stations in terms of Rex 0.5

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Figure 6

Predicted dissipation coefficients Cd from exact DNS results, Rotta approach, approximate technique and Blasius solution plus individual contributions of terms in Eq. 8

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Figure 7

Prediction of dissipation coefficient for the present example of bypass transition. NWMV = Emmons approach [46] for transitional flows and W & M = correlation of Walsh and McEligot [8] for fully-turbulent boundary layers at low Reynolds numbers

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Figure 2

Behavior of streamwise mean velocity: (a) comparison to Blasius prediction at Rex 0.5 ≈ 350 (Reθ ≈ 254) near the end of the pre-transitional laminar boundary layer and (b) evolution in wall coordinates

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Figure 1

Measures of evolution of the bypass transition process for the present example, Tuin  = 4.7% and (Λ/δ*)in  = 5; (a) Reynolds number based on momentum thickness, (b) skin friction coefficient and (c) intermittencies

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