THEORY OF PROPULSION 9' Axial Turbines

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THEORY OF PROPULSION 9. Axial Turbines

• P. M. SFORZA
• University of Florida

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Blade element forces
w, relative velocity
L, lift
b2
b4
b2
i
Fu, turning force
Fa, axial force
b2
D, drag
chord line
u, compressor
u, turbine
g
stagger angle
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Airfoil characteristics and angle relationships
w
b4
cL,max
b2
cL cD
sinb4sinb2 cosb4 - cosb2
1 0
0 p b
i0 0 is i
Airfoil lift and drag curves
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Turning force based on blade element aerodynamics
aerodynamic efficiency ecD/cL
turning force
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Turbine work aerodynamic analysis
Introducing the aerodynamic coefficients
c4
cA
w4
b4
u
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The corrected flow variables
wmg
Equation of state
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Aerodynamic operating regimes of turbines and
compressors
compressor operating range
turbine operating range
cL
cL
sin b
0 p/2 p
b
i0 0 is i
c
g-ip-b4
wq41/2/d4 increasing with N/q41/2 constant
w
u
g
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Lift curve for a blade
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Drag curve for a blade
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Turbine work for fixed N
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Weight flow through turbine
Corrected weight flow a maximum when entrance to
turbine is choked
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Turbine performance map
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Turbine performance map
g1.33 -(g-1)/g -4
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Compressor performance
weight flow increasing
weight flow increasing weight flow
decreasing
weight flow increasing
w
c
w
c
cL
CL
u
u
sinb2
sinb2 1
For fixed c2 direction increased weight flow
increases b2 and decreases i
0 b p/2
0 b p/2
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Compressor map
Surge or stall line (cL maximum)
Wc/q2 or pt,3/pt,2
Operating line
hadc constant
N/q21/2 increasing
wq21/2/d2
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Similarity parameters by dimensional analysis
pt3f(pt,2,Tt,2, m, gR, w,m, d) 8 primary
variables and 4 dimensions (L, t, M, T) 4
dimensionless groupings P1pt,3/pt,2 P2m(gRTt,2)
1/2/pt,2d2 P3wd/(gRTt,2)1/2 P4m/mdrAcA/mdrdcA/
mRe (Reynolds number) Therefore P1f(P2, P3,
P4)
w
d
m
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Dimensional analysis for compressor
mrAcArpd2cA/4rd2cA P1pt,3/pt,2 P2m(gRTt,2)1/
2/pt,2d2wq21/2/d2d2 P3wd/(gRTt,2)1/2dN/q21/2
P4m/mdr2A2c2,A/md(p2/T2)d(MAT21/2)/mdd2/f2q21
/2
Corrected weight flow
Corrected rpm
Reynolds number index
For a given compressor d is a common factor
and pt,3/pt,2f(wq21/2/d2, N/q21/2, d2/f2q21/2)
Weak dependence