C6_Isothermal_Turbulent_Flow

C6_Isothermal_Turbulent_Flow - Turbulent Isothermal Flow...

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Turbulent Isothermal Flow Turbulent versus laminar flow Observation of turbulent and laminar flows in circular tube Unsteady state Steady state
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Turbulent Isothermal Flow Turbulent versus laminar flow Observation of turbulent and laminar flows in circular tube 2 max 0 4 45 1/7 7/4 1/4 0 19/ 4 Re 2100 1 1 2 8 10 4 5 2 0. For and For a 08 nd 19 z z zz L z z L u u r uR u L PP w R u u r uRu L P Pw R µ πρ < ⎛⎞ =− = ⎜⎟ ⎝⎠ −= << ≈− −≈
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Turbulent Flow Turbulent flow Time-smoothed equations of change for incompressible fluids Reynolds decomposition of velocity 0 0 /2 0 1 ( ) tt xxx x x uuu u u s d s t + =+ = 2 0 =0 = = xx x x x x x x y x uu u u u u u u u u p p p ∂∂ ′′ ⇒= = ≠= + Equation of continuity () ( ) . .0 0 0 . yy zz xyz ∂∂∂ ′′′ ∇=⇔ + + ∇= + = = u
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Turbulent Flow Turbulent flow Time-smoothed equations of change for incompressible fluids x-component of the equation of motion for constant μ (y- and z- components can be similarly written) 2 xx x y x yx x x zx uu u u u u u tx y z p ug xz x y ρρ ρ µ ⎛⎞ ∂∂∂∂ =− + + ⎜⎟ ⎝⎠ ∂∂∂ ′′ −+ ++ + ∂∂ Define () Reynolds stress tt t x x y xy x z x τρ ′ ′ == = ±²²²²²²²²³²²²²²²²²´ [] ( ) .. tv p t ⎡⎤ =− ∇
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C6_Isothermal_Turbulent_Flow - Turbulent Isothermal Flow...

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