Turbulence lecture 11

Turbulence lecture 11 - Turbulence Lecture 11 The Reynolds...

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Turbulence Lecture 11 The Reynolds Stresses There are three stresses in the Reynolds averaged mean momentum equation: - Viscous - Isotropic - Apparent j i ij i U U uP xxx ρ   +−   ∂∂∂   u u The apparent stress arises from momentum transferred by fluctuating the velocity field. Consider a Control Volume ( V ) With C.S., A , and outward normal . ˆ n Rate of gain of momentum in V is due to flow through of A . N () ˆ A M UU n d A t =− ∫∫ ±± i ± ²³´³µ momentum flow rate per unit per unit volume. area through A The j th component of the mean j M is ji j i j A i j i V i M uu ndA t uu dV x + + ∫∫∫ by the divergence theorem.
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So the Reynolds stress ij i uu x ρ comes from the mean momentum flux due to the fluctuating velocity on the boundary A () . iji uu n Tensor Properties Reynolds stress is a 2 nd order symmetry tensor.
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This note was uploaded on 06/07/2011 for the course EGM 6341 taught by Professor Mei during the Spring '09 term at University of Florida.

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Turbulence lecture 11 - Turbulence Lecture 11 The Reynolds...

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