THEORY OF PROPULSION 8' Axial Flow Compressors

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THEORY OF PROPULSION8. Axial Flow Compressors

• P. M. SFORZA
• University of Florida

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Linear, or 2-D, Cascade
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Circulation about a single blade
For a stationary cascade
B
C D
A
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Circulation about a single blade
These terms cancel each other
The circulation is proportional to the amount the
flow is turned
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The tangential force component
constant
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The axial force component
For incompressible flows caconstant Thus there
is no net external axial force acting on the
fluid, that is, Fa0 for incompressible flow
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Compressibility effect
In a gas compressor the ideal process is an
isentropic compression where p rk and thus
Note For a pressure ratio of 1.2 and k1.4,
c3a/c2a0.88 The pressure rise causes a density
rise, in turn requiring a 12 decrease in the
axial velocity component.
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Forces on the control volume
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Forces in the control volume
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Incompressible flow in the cascade
Bernoullis equation
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The lift forces in terms of circulation
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Forces and equivalent velocity field
u
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Compressible flow in the cascade
Bernoullis equation for compressible flow
Momentum equation along a streamline
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Compressible flow result
Then
The integrated momentum equation is then
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Momentum equation terms defined
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Axial component of the lift force
For incompressible flow M0 and r2r3 the
previous result is recovered
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Velocity triangles
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Combined velocity diagrams
b2
a2
b3
a3
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Pressure rise through axial flow stages
Incompressible flow
Pressure rise in the rotor
low subsonic speeds, Mlt0.6
Pressure rise in the stator
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pressure rise across rotor stator
Across rotor
Across stator
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Static and stagnation pressure rises across an
axial stage
Static pressure rise across stage was shown to be
Stagnation pressure constant in stator ( no work
done, no losses)
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Static and stagnation pressure rises across an
axial stage (cont.)
Stagnation pressure rises across stage because
work done on fluid raises pt in the rotor
Static pressure rise across stage
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Relationship between 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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Work required for different processes
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Work in lightly loaded stages
neglect
Like incompressible flow with an average density
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Degree of reaction
Stagnation pressure rise
Static pressure rise
Degree of reaction ratio of static to total
pressure rise
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100 reaction stage
All the pressure rise occurs in the rotor
rotor
stator symmetrical
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50 reaction stage symmetric sections
Half the pressure rise in the rotor and half in
the stator
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0 reaction stage the impulse stage
All the pressure rise in the stator
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Axial outlet stage c2gtc3 and rgt100
Whirl velocity is removed from the exit flow
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Axial pressure variation through the different
types of stages
hydraulic turbines use the impulse stage
impulse
p3
dp/dx is a minimum for the symmetric stage
symmetric
Swirl removed by axial exit stage
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 overall pressure ratio
Typical Range
(pt3/pt2)(i)
1.2
1.15
1.10
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Staging in turbomachines (continued)
stage efficiency
stage temperature ratio
overall temperature ratio
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Efficiency of adiabatic compression
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 with number of
stages
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