02actuator_disk

# 02actuator_disk - Actuator Disk stream tube assume...

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Actuator Disk u i n s p r e b t a m , D 0 A 0 (10.2) (10.3) (10.3a) (force = mass flow * delta velocity) V A , p 0 , D 0 V A + Δ v, D 1 p 0 V stream tube actuator disk A assume: propeller is a disk with diameter D and area A frictionless no rotation - upstream or downstream model propeller as thin "actuator disk" causing instantaneous increase in pressure A 1 , D 1 , V A + Δ v , DA , V V A , Thrust = T = A ⋅Δ p (10.1) continuity . .. ρ⋅ V A = constant m_dot = V A A 0 = ( V A ) VA + Δ v ρ A 1 V A D 0 2 2 ( Δ v ) 2 = VD + = V A D 1 = 2 V 2 2 V 2 D D D 0 D 1 = = V A V A + Δ v V V D 0 := D V A D 1 := D + Δ v Δ V A Δ _in_momentum = thrust_on_disk = T = m_dot out ( V A + Δ v ) m_dot in V A T = A 1 ( V A + Δ v ) 2 A 0 V A 2 2 2 (10.4) T := ρπ⋅ D 1 ( V A + Δ v ) 2 ρ π⋅ D 0 V A 2 4 4 1 2 T simplify ⋅ρπ⋅ using (10.3a) above (10.5) Δ v 4 now using Bernoulli equation p + 1 ⋅ρ⋅ v 2 = constant 2 on both sides of the disk (a force is applied at the disk) 9/8/2006 1 9/8/2006

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