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L3-Fall+2011

# L3-Fall+2011 - MAE 14:650:474 Alternative Energy Systems...

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MAE 14:650:474 Alternative Energy Systems Lecture 3: Class Agenda o Turbo Machines square4 Axial and Radial Flow square4 Sample Problems 1 o Pre-test o Hydro power

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Definition and Classifications o turbomachine- device in which energy is transferred either to or from a continuous flowing fluid by the action of one or more moving blade rows. o examples: wind, hydroelectric, gas or combustion turbine MAE 14:650:474 Alternative Energy Systems 2 o classified as compressors (or pumps) and turbines o compressor (pump or fan) – energy is added to the fluid as the fluid traverses the rotor o turbine – energy is extracted from the fluid as the fluid traverses the rotor
Classifications o second way classifying turbo machines is by the path of fluid: radial, axial or mixed o radial flow – the path of the fluid is in the radial direction MAE 14:650:474 Alternative Energy Systems 3

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MAE 14:650:474 Alternative Energy Systems Analysis o control volume that will be used to develop the expressions for the turbines o control volume is rotating at an angular velocity, ω 4 o face 1 = inlet control surface o face 2 = exit control surface o V 1 = absolute velocity vector (inlet) o V 2 = absolute velocity vector (exit) o r 1 and r 2 = arbitrary radial distances o mutually perpendicular velocity components of are: V a = axial, V u = tangential, V m = radial
MAE 14:650:474 Alternative Energy Systems Analysis o conservation of angular momentum (for a control volume) o control volume is rotating at an angular velocity, ω o vector sum of moments 5

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MAE 14:650:474 Alternative Energy Systems Analysis o position vector: o velocity vector: 6 o cross product (moment about a point):
MAE 14:650:474 Alternative Energy Systems Analysis o simplest position vector to is o cross product (moment about a point): 1 V i r r ˆ = 7 o for component about axis: o assuming steady state, conservation of angular momentum:

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MAE 14:650:474 Alternative Energy Systems Analysis o torque as a function of mass flow rate, assuming (Euler Turbine/Pump Equation): o o 8 o if then angular momentum is added to the flow device is a pump o if then angular moment is extracted from the flow - turbine o turbomachine sign convention: so that expression is positive for a turbine and negative for a pump
MAE 14:650:474 Alternative Energy Systems Analysis o power is torque times the rotation rate: o r ω = U = tangential velocity of the rotor at a radius of r.

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