16100lecture6_cg

16100lecture6_cg - Compressible Viscous Equations Also...

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Compressible Viscous Equations Also known as the compressible Navier-Stokes equations: Mass: () 0 = + j j v x t ρ Momentum: , 1,2,3 i ij i j ji j p i tx x x ρν ρν ν τ ∂∂ += + = Energy: 22 11 j j ev v ρρ ++ + j i j jjj p q xxx ντ ν =− + + ∂∂∂ ± ,, ( ) j ik ij ij k j xx x q k e e p state relationship ideal gas x νν τµ δ λ  =+ +   ∂Τ == Τ ± Incompressible Viscous Equations In this case, we assume . const = Mass: 0 = j j x Momentum: + + = + i j j i j i j i j i x x x x p x t µ Usually, Τ = . Often, when temperature variations are small, =const. is assumed. 0 j jj ii i j j j i i x x x µµ =  ⇒+ = +   = ²³´
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16.100 2 Usual form of momentum for incompressible flow: j j i i j i j i x x v x p v v x t v +
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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16100lecture6_cg - Compressible Viscous Equations Also...

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