C7_Isothermal_Interphase_Transport_part1

C7_Isothermal_Interphase_Transport_part1 - Interphase...

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Interphase Isothermal Momentum Transport Definition of friction factor for both laminar and turbulent flows Friction at fluid-solid surface K K F f AE = F K : the viscous force exerted by a fluid on the surface of an solid object A : the characteristic surface area E K : the kinetic energy of the fluid Examples Flow in a circular tube () 2 0 0 2 2 L rz K rz L rR PP RF R L P P R L τ πτ π == ⎛⎞ =⇒ = = ⎜⎟ ⎝⎠ ( ) ( ) 2 00 22 1 4 21 2 1 2 KK LL zz EE R D f L RL u u πρ ρ −− ±²³ ² ´± ² ³ ² ´ Viscous force Friction factor 2 1 2 Kz Eu = Characteristic surface area 2 A DL = =
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Interphase Isothermal Momentum Transport Friction at fluid-solid surface Flow around a sphere submerged in a fluid Viscous force in z-direction Friction factor () 33 3 Bouyant Gravitational 44 4 3 Ks s FR g R g R g π ρπ ρ =− = ±²³ ² ´± ²³ ²´ 22 2 14 1 3 12 s K F Dg f Ru u πρ ⎛⎞ == ⎜⎟ ⎝⎠ Characteristic area is usually taken as the projection of the sphere onto a plane perpendicular to the velocity of fluid approaching the sphere 2 A R =
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Developing velocity profile Laminar flow of incompressible and constant-viscosity fluids in circular tubes Friction factor as a function of dimensionless numbers 2 00 2 L Kr z rR L z FR d d z du Rd dz dr π τθ μ θ = = = ⎛⎞ =− ⎜⎟ ⎝⎠ ∫∫ Viscous force Friction factor () 2 2 21 2 L z z R dd z f RL u πρ = =
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C7_Isothermal_Interphase_Transport_part1 - Interphase...

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