Turbulence lecture 34

# Turbulence lecture 34 - Turbulence Lecture 34 Power Law...

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Turbulence Lecture 34 Power Law Profiles Simple: () 1 U n Uy xx δ  =   Where nn x = This is ok for U behavior at 0, yy == But 1 1 1 U 1 n n U y yn    = 1 U So that y n u y = = 1 1 n n 0 Where typically 7 in T.B.L. 1 0 n << 0 1 1 1 U 11 ! y n n u y = Which isn’t the ω τ slope that we expect, so this doesn’t model wall shear effect, though * 0 1 U U =− dy works out pretty well still. Piece wise Representation of Velocity Profile S e p a r a t i o n 1

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A. Inner region: 00 . 1 y δ ≤≤ Dimensional analysis perspective. () , , Uf y v u τ = 2 L LL L TT T u ω ρ = units of velocity called “friction velocity” (or ) * u 4, 2 nm == / \ variables dimensions 2 Π groups can be formed (Buckingham –Pi Theory) 1 wall coordinates yu u f uv uf y ++  =   = Consider now the B.L. equations as they apply in the near wall region where yx ∂∂ ± for everything Continuity U x 0 0 V V y += ⇒= since V= 0 at y= 0 2
X-momentum U U x V + 1 UP yx ρ ∂∂ =− 2 2 Uu v yy µ ′ ′ +− N N viscious turbulent stress stress 0 0 vt U

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Turbulence lecture 34 - Turbulence Lecture 34 Power Law...

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