THEORY OF PROPULSION 6' Turbomachines

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THEORY OF PROPULSION6. Turbomachines

• P. M. SFORZA
• University of Florida

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Thermodynamics of a turbomachine
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Efficiency of adiabatic compression
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Work required for compression
Isentropic relation
Compressor work
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Turbojet cycle
General numbering system for the turbojet engine
Thermodynamic cycle for the turbojet engine
operating with a matched nozzle and constant
pressure combustor
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Adiabatic efficiency of expansion
Turbine work output
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Velocity components for a rotor
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Velocity in rotor and stator passages
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Forces and torque acting on the fluid
C3,u
r3
r2
C2,u
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Work depends on change in whirl
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The velocity triangle
Absolute velocity in laboratory coordinates
Relative velocity to an observer on the rotor
b
a
Linear velocity of rotation of the rotor
Tangential component of the absolute velocity
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Velocity component relations
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General Ideal Total Head Equation
Note the pressure head is the work done per
unit weight flow such that the units of W are
simply those of length, i.e., ft or m
Centrifugal effect increasing pressure by
increasing the radius of exit
Internal effect increasing pressure by diffusing
w2 inside the rotating passage
External effect increasing pressure by diffusing
c3 outside the rotor, i.e., in an external device
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Velocity triangles
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Combined velocity diagrams
b2
a2
b3
a3
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Pressure rise in axial compressors
Assume speeds are low subsonic and incompressible
relations are sufficiently accurate. Then
Pressure rise in the rotor
Pressure rise in the stator
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Static and stagnation pressure rise
Static pressure rise across stage
Stagnation pressure constant in stator ( no work
done, no losses)
Stagnation pressure rise across stage (pt changes
in rotor)
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Work and stagnation pressure
work per unit mass WcP/m in (N-m/s)/kg/s)J/k
g work per unit weight Wc P/w in
(ft-lb/s)/(lb/s)ft-lb/lbft orm
Incompressible flow
Compressible flow
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100 reaction stage
rotor
stator symmetrical
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50 reaction symmetric sections
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0 reaction stage the impulse stage
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Axial outlet stage c2gtc3 and rgt100
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Axial pressure through stages
hydraulic turbines use the impulse stage
impulse
p3
Swirl removed by axial exit stage
dp/dx is a minimum for the symmetric stage
symmetric
axial exit
100
p2
x
stator
rotor
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Stages necessary for fixed pressure gradient in
each stage
stage 1 stage 2 stage 3
stage 4
p3 p2
100
axial exit
symmetric
x
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Staging in turbomachines
conditions on pressure
chain rule for pressure rise
special case pressure rise is constant across
each stage
stator rotor stator
pit3pi1t2
ith stage
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Effect of staging on pressure ratio
Typical Range
(pt3/pt2)(i)
1.2
1.15
1.10
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Staging in turbomachines (cont.)
stage efficiency
stage temperature ratio
overall temperature ratio
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Efficiency for a staged turbomachine
Overall efficiency of adiabatic compression for n
stages of varying stage efficiency
But, for constant pressure rise in each stage
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Variation of work and efficiency with number of
stages
Stage efficiency h(i)ad,c constant
Wc the compressor work
had,c the efficiency of adiabatic compression
Overall pressure ratio pt3/pt2constant
Number of stages
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Variation of work and efficiency
overall efficiency had,cconstant
h(i) ad,c the stage efficiency of adiabatic
compression
overall pressure ratio pt3/pt2constant
Wc the compressor work
number of stages