Lecture.13

# Lecture.13 - AE 1350 Lecture Notes#13 Topics to be...

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AE 1350 Lecture Notes #13

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Topics to be discussed Propellers Gas Turbines Turbojet Turboprop Turbofan Rockets
How does a propeller work? It captures a stream of air molecules, adds energy to the particles. Particles approach the propeller with low velocity. They leave with higher velocity, and energy. This change in momentum of the particles is caused by the rearward force exerted by the propeller on the particles. There is an equal and opposite reaction - the particles exert a forward force on the blades. This is called thrust.

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As the propeller turns. . V V +v V +2v Streamlines contract as they approach the propeller. Velocity of the particles steadily increases.
Thrust Generated V V +v V +2v Mass flow rate = ρ A (V +v) where A is the propeller disk area. Momentum flow rate = mass flow rate times velocity Thrust = Rate at which Momentum flows out- Rate at which momentum flows in = ρ A(V +v) (V +2v) - ρ A (V +v) V = 2 ρ A(V +v)v Thrust is increased if the disk area A is large, and/or if the excess velocity v is large.

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Power Consumed V V +v V +2v Mass flow rate = ρ A (V+v) where A is the propeller disk area. Energy flow rate = 1/2 times (mass flow rate) times (velocity squared) Rate at which energy is added to the fluid = Rate at which energy flows out- Rate at which momentum flows in = 1/2 ρ A(V +v) (V +2v) 2 - 1/2 ρ A (V +v) V 2 = 2 ρ A(V + v) 2 v = T(V +v) Notice that power consumed will be high for a given thrust T and forward velocity V , if v is high.
Propeller Thrust vs. Power Consumed

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Lecture.13 - AE 1350 Lecture Notes#13 Topics to be...

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