L4-Fall+2011

# L4-Fall+2011 - MAE 14:650:474 Alternative Energy Systems...

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MAE 14:650:474 Alternative Energy Systems Lecture 4: Class Agenda o Turbo Machines Continued square4 Axial and Radial Flow square4 Sample Problems 1 o Pumps discussion (Graduate Student, Sean DeGennaro)

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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 turbomachine – o rotor
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. ( ) 2 1 2 1 u u V r V r m power ω ω τω - = = & ( ) ( ) V U V U m V r V r m power - = - = = & & ω ω τω 3 o head change = power/mass flow rate= o V = absolute velocity, U= tangential rotor velocity, V r = relative to rotor, α = nozzle angle and β = blade angle: r V U V + = 2 1 2 1 2 1 2 1 u u u u ( ) 2 u 2 1 u 1 V U V U m power H - = = &

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Turbo machinery o For axial flow turbomachines, the absolute velocity, V, can be broken into two components, V u and V a square4 turbine flow rate is controlled by the axial component square4 V is measured in the absolute, stationary observer MAE 14:650:474 Alternative Energy Systems X,V a 4 square4 β is the blade angle square4 U is tangential rotor velocity square4 velocity with respect to the rotor is V r o for an axial machine: the inlet and exit radii are ~equal; r=r 1 =r 2 , U=U 1 =U 2 and V a =V a1 =V a2
Turbo machinery o For radial flow, the absolute velocity, V can be broken into two components, V u and V m square4 turbine flow rate is controlled by the radial component square4 V is measured in the absolute, non-rotating reference, MAE 14:650:474 Alternative Energy Systems r,V m 5 i.e. a stationary observer square4 β is the blade angle square4 U is tangential rotor velocity square4 velocity with respect to the rotor is V r

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Definition and Classifications o radial device: the path of the fluid is in the radial direction. In this picture, the flow enters the rotor radially MAE 14:650:474 Alternative Energy Systems 6
Definition and Classifications o axial device: device where he path of the fluid in in the axial direction o in this illustration, the flow enters and leaves the rotor with axial velocity and very little radial velocity MAE 14:650:474 Alternative Energy Systems 7

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Definition and Classifications o mixed device: where fluid path is in the radial and axial direction MAE 14:650:474 Alternative Energy Systems 8
MAE 14:650:474 Alternative Energy Systems Example 1 Given an axial flow machine, where α 1 = β 2 =45 ° , α 2 = β 1 =30 ° , V 1 =V R2 & V 2 =V R1 Determine: 1) reaction, R and 2) whether the machine is a pump or turbine. oRECALL: for an axial machine: the inlet and exit radii are ~equal; r=r 1 =r 2 , U=U 1 =U 2 & V a =V a1 =V a2 V 1 V R1 9 o Note that when we draw the velocity triangles, they are symmetric.

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