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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

Energy Balance in Turbulent Flow

The Reynolds equation is given as

(1)

Multiplying (1) by  and rearranging terms, one finds

(2)

where

 = convection,

 = diffusion by turbulence,

 = viscous diffusion,

 = direct viscous dissipation,

 = fluctuation energy production.

Equation (2) is the statement of balance of mean mechanical energy for the mean motion.

Subtracting (1) from the Navier-Stokes equation, it follows that

(3)

Multiplying (3) by  and taking expected value, we find the equations of balance turbulence energy fluctuation. i.e.,

(4)

where  is the fluctuation kinetic energy and

 = convection

 = production

 = turbulent diffusion

 = viscous diffusion

 = dissipation



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