14-Integral_2 - Module 14 Integral Method-II Professor S.M....

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Module 14 ME 6302 Integral Method-II Professor S.M. Ghiaasiaan G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0405
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Module 14 ME 6302 2 Example: Turbulent, 2-D Incompressible, Constant- Property Flow Over a Flat Plate • The integral method can be applied to turbulent boundary layers. However: – 1. The velocity in turbulent boundary layers varies approximately as: – 2. The approximate velocity profile fails very close to the wall, where the universal law-of-the- wall should be used. The wall shear stress should be related to the velocity profile using the law-of- the-wall. 1 7 vy
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Module 14 ME 6302 3 Example: Turbulent, 2-D Incompressible, Constant- Property Flow Over a Flat Plate • Start with: y x u δ Y s v v () 2 21 (1) ss Uv dd U UU dx dx τ ρ δδ ∞∞ + +=
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Module 14 ME 6302 4 Example: Turbulent, 2-D Incompressible, Constant- Property Flow Over a Flat Plate 2 0 1 0 1 1 Y Y uu dy UU u dy U δ ∞∞ ⎛⎞ =− ⎜⎟ ⎝⎠
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Module 14 ME 6302 5 Example: Turbulent, 2-D Incompressible, Constant- Property Flow Over a Flat Plate • Assume • Assume no wall injection , and use the following approximation for the logarithmic law-of-the-wall velocity profile (Kays and Crawford, 1993): •w h e r e ( ) 1 7 1 2 1 8 7 72 u y U δ =⇒ = = (0 ) s v = 1 7 8.75 (2) uy + + = * * s yU y v U τ ρ + = = * u u U + =
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Module 14 ME 6302 6 Universal Velocity Profile
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This note was uploaded on 05/22/2010 for the course ME 6302 taught by Professor Mostafaghiaasiaan during the Spring '10 term at Georgia Institute of Technology.

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14-Integral_2 - Module 14 Integral Method-II Professor S.M....

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