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Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics
Review of Turbulence and Turbulence Modeling

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The National Science Foundation
ME 637 The National Science Foundation
  Review of Turbulence & Turbulence Modeling
Features of Turbulence | Reynolds Equation and Mixing Length Model | Energy Equations | Correlations and Scales | Vorticity Transport | Two-Equation Model | Stress Transport Models | Rate-Dependent Models | PDF Models |

Reynolds Equation and Mixing Length Model

Turbulent Flow Between Two Parallel Plates

Equation (3) now becomes
, (6)

Integrating (6) and noting that , we find

, (7)

At the centerline , equation (7) implies

, (8)

Eliminating  between (7) and (8), the result is

, (9)

Introducing the dimensionless variable , equation (9) may be restated as

, (10)

where

, and . (11)

Alternatively introducing , equation (9) becomes

, (12)

For high Reynolds number flows as , equations (10) and (12) imply

, (as ,   (core region)). (13)

, (as ,   (surface layer)). (14)



Dr. Goodarz Ahmadi | Turbulence & Multiphase Fluid Flow Laboratory | Department of Mechanical & Aeronautical Engineering
Copyright © 2002-2005 Dr. Goodarz Ahmadi. All rights reserved.
Potsdam, New York, 13699
ahmadi@clarkson.edu