THEORY OF PROPULSION 11' Component Matching

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THEORY OF PROPULSION 11. Component Matching

• P. M. SFORZA
• University of Florida

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Turbojet component matching case 1
Given M0, altitude, pt,2/pt,0, Tt,4, and
A6 Find N, A0, A7
Corrected weight flow in isentropic nozzle flow
is constant wq51/2/d5 constant pref(RTref/g
)-1/2A6(g1)/2-(g1)/2(g-1) Relating corrected
weight flows across the turbine yields
wq51/2/d5 (wq41/2 /d4) (pt,4/pt,5)(Tt5/Tt4)1/2
wq51/2/d5 (wq41/2 /d4)
(pt,4/pt,5)1-ht1-(pt,4/pt,5)(1-g)/g 1/2
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Correlation of corrected weight flow
pt,4/pt,5
Picking values of wq41/2/d4 for various values
of N/q41/2 yields a turbine efficiency and a
turbine pressure ratio
N/q41/2
ht decreasing
wq41/2/d4
wq41/2/d4
found
N/q41/2 increasing
Use maps to make a corrected weight flow
correlation
known
Chosen rpm
wq51/2/d5
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The matching condition
wq21/2/d2 (wq41/2/d4)(pt4/pt3)(pt3/pt2)(Tt2/Tt4
) C(pt3/pt2)
Known from given conditions
Known from previous step
Assume constant1
Matching condition Dht,t Dht,c and
NtNc Dht,c/q2 (Dht,t/q4)(Tt4/Tt2) Dht,c/q2
cpTrefhadc-1(pt3/pt2)(g-1)/g-1
On compressor map
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Compressor map
Surge or stall line (cL maximum)
pt,3/pt,2
Operating line
hadc constant
N/q21/2 N/q41/2(Tt4/Tt2)1/2
wq21/2/d2
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Matching the compressor and turbine
pt3/pt2
w2q21/2/d2 C(pt3/pt2)
Matching point new N matches power
w2q21/2/d2
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Capture area and nozzle exit area
inlet pressure recovery Tt0/Tt21 (adiabatic flow)
Free stream capture area required
Nozzle exit area required
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Sizing the engine
Tt4
M0 p0 T0
A0
Amin
A6
A7
Inlet performance given
1
1 A0/Amin
pt2/pt0
0
1 M
0 1 M
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Turbojet component matching case 2
Given M0, altitude, pt,2/pt,0, w, and N Find
Tt4, A6, A7
Calculate corrected weight flows, free stream
capture area and corrected rpm wq01/2/d0 and
wq21/2/d2
N/q21/2 A0 w(RTrefq0 )1/2gpref d0f(g,M0)-1
Tt2Tt0T010.5(g-1)M02 pt2pt0(pt2/pt0)
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Compressor map
Surge or stall line (cL maximum)
pt,3/pt,2
Operating line
hadc constant
N/q21/2 increasing
wq21/2/d2
Find pt3/pt2 and hadc
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The corrected weight flow
Dhtc/q2 cpTrefhadc-1(pt3/pt2)(g-1)/g - 1
Known from compressor map
Tt3/Tt2 1hadc-1(pt3/pt2)(g-1)/g -1
Determine corrected weight flow wq31/2/d3
(wq21/2/d2)(pt2/pt3)(Tt3/Tt2)1/2
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Determine the corrected weight flow
Across the (constant pressure) combustor assume
an exit temperature Tt4 Now find M4 from the
combustor equations Tt4/Tt3 f(g,M3, M4)
and pt4/pt3 g(g,M3,M4) Corrected weight flow
wq41/2/d4 (wq31/2/d3)(pt3/pt4)(Tt4/Tt3)1/
2
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Determine work required of the turbine
Work output of turbine Dht/q4
(Dhc/q2)(Tt2/Tt4) Corrected rpm N/q41/2
(N/q21/2)(Tt,2/Tt,4)1/2
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The matching point for work generated
Dht/q4
Locus of results for various Tt4
Matching point
wq41/2/d4
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Turbine performance map
pt,4/pt,5
N/q41/2 increasing
N/q41/2 increasing
g4 1.33 -(g4-1)/g4 -4
0 wq41/2/d4
maximum
wq41/2/d4
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Nozzle minimum and exit areas requirements
The stagnation temperature ratio is obtained
from Tt5/Tt4 ht1-(pt5/pt4)(g4-1)/g4
Corrected weight flow entering nozzle
wq51/2/d5 (wq41/2/d4)(Tt4/Tt5)1/2 Find A6
from wq51/2/d5 A6 (pref/Tref1/2)(gg/R)1/2(g
1) /2-(g1)/2(g-1) Nozzle exit area A7
A6(g-1)/21/2(g1)/2-(g1)/2(g-1)(p7/pt7)2/g
-(p7/pt7)(g1)/g 1/2
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Representative compressor map
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Representative turbine map
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Problem 14 Revised compressor map
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Corrected weight flow x (3.6)-1, lb/sec
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Sizing the engine
Tt4
M0 p0 T0
A0
Amin
A6
N
A7
Inlet performance given
1
1 A0/Amin
pt2/pt0
0
1 M
0 1 M
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Inlet-engine matching
A0 A1
Amin
For isentropic flow and g1.4 wq1/2/d
85.29AM(1M2/5)-3 const
For adiabatic flow (Ttconstant)
(wq1/2/d)min(wq1/2/d)0(pt0/pt,min)
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Inlet capture area
(wq1/2/d)2 (wq1/2/d)0(pt0/pt2)
85.29A0M0(1M2/5)-3/(pt2/pt0)
Compressor inlet
Free stream capture streamtube
Inlet pressure recovery
Assume the industry standard pressure
recovery (pt2/pt0)std 1-0.1(M0-1)1.5 Then the
capture area - weight flow relation is
A0 1-0.1(M0-1)1.5/85.29M0(10.2M02)-3(wq1/
2/d)2
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Capture streamtube area as function of Mach number
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Inlet requirements
A0 (A0/A1)(A1/Amin)Amin
capture streamtube contraction ratio minimum
area
Mlt1
Mlt1 Mgt1 Mlt1
Subcritical inlet flow influenced by engine
operation
Supercritical inlet flow independent of engine
operation
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Inlet performance as function of M
Inlet performance
Inlet operating below design pressure recovery
lowers A0 and therefore Fn and sfc will suffer
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Inlet performance as a function of M
Inlet performance
Excess weight flow
Excess mass flow must be spilled (a) A0
decrease, (b) internal bleed, or (c) spillage and
additive drag
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Effect of shock location in inlet
a b
a b
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Nozzle conditions and shock location
Turbine-fixed Burner fixed
Compressor fixed Inlet-fixed Flight
condition-fixed
Minimum area total pressure
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Effect of shock location on A6
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Effect of shock location on Tt6
Tt6(Tt5/Tt4)Tt4Tt4
Turbine inlet temperature