direct-transfer pre-swirl system: performance modelling, validation and optimisation · 2009. 4....
TRANSCRIPT
-
1Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Laboratory of Thermal TurbomachinesNational Technical University of Athens
Direct-Transfer Pre-Swirl System:Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
-
2Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Paper Objectives
Ø Construct a model of a gas turbine direct-transfer pre-swirl air system using models of its individual components
Ø Validate the modelling against experimental results from 3 different publicly available test cases
Ø Optimise the design of such a system on its own and as part of a complete engine performance model
-
3Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
qMODELLING PHILOSOPHY
qMODEL VALIDATION
o Test Case 1
o Test Case 2
o Test Case 3
q DESIGN OPTIMISATION
o System Level
o Engine Level
q CONCLUSION
Contents
-
4Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Direct Transfer Pre-Swirl Air System
Pre-swirlNozzle
ReceiverHole
InnerLabyrinth
Seal
OuterLabyrinth
Seal
Cover-plate
Pre-swirlChamber
To BladeCooling Passage
Pre-swirlNozzle
ReceiverHole
InnerLabyrinth
Seal
OuterLabyrinth
Seal
Cover-plate
Pre-swirlChamber
To BladeCooling Passage
Important ParametersRelative Total Temperature
Tt,rel,RH
Discharge Coefficient
CD,RH
Swirl Ratio
β = Vφ / Ω rΩ
(RH)
(PN)
-
5Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Modelling Philosophy
1 2 3 4
5
8
6
7Pre-swirlNozzle
ReceiverHole
Pre-swirlChamber
InnerLabyrinth
Seal
OuterLabyrinth
Seal
12
3
4
5
8
6
7
Connected components communicate through their external interfaces by exchanging a pre-defined set of variables. For describing flow conditions, these variables are mass flow, total temperature, total pressure and swirl angle. The exit flow conditions of a component are linked to the corresponding inlet ones through the conservation equations for mass, energy, axial and angular momentum, the component characteristics and appropriate empirical correlations.
-
6Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Cavity Component Model
Ø Arbitrary geometry (discs, cones, cylinders)Ø J Input flows and N output flowsØ Fully mixed flowØWork and heat transfer from surrounding K surfacesØMixing pressure losses
Ω
rK, AKrm
r
zin outrN, AN
rJ, AJ
mixSTATOR
ROTOR
Q
-
7Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Orifice Component Model
α
Ω
L
rf
U
V
Vrel
φ
z1
2
d
Vφ
ir
α
Ω
L
rf
U
V
Vrel
φ
z1
2
d
Vφ
ir
Ø Axial & radial holesØ Rotating & stationary
Discharge Coefficient CD corrected through correlations for:ü Hole Reynolds numberü Inlet corner radiusü Hole lengthü Pressure ratioü Incidence angle
( ) i:DRe:D3'dL,2dr,21D CC1ffff1C f ∆+−⋅⋅⋅⋅−=
α−
α⋅
−= φ−
cosVVU
taniis
1,1
Incidence Angle Definition
-
8Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Labyrinth Seal Component Model
Ω
1 2
cp
STATOR
ROTOR
FIN
Ω
1 2
cp
STATOR
ROTOR
FIN
)PR1ln(nPR1
TR
PCAm
t
2t
1,t
1,tD +
−⋅
⋅⋅Γ⋅⋅=&
02.0pcpc
n1n1
1
+⋅
−−
=Γ
For flow through straight, staggered and stepped labyrinth seals
CD = 0.71 for 1.3 < c/t < 2.3
-
9Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
qMODELLING PHILOSOPHY
qMODEL VALIDATION
o Test Case 1
o Test Case 2
o Test Case 3
q DESIGN OPTIMISATION
o System Level
o Engine Level
q CONCLUSIONS
Contents
-
10Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Validation Test Case 1: Geis et al. (2004)
0.98
0.99
1
1.01
1.02
1.03
0 0.5 1 1.5 2 2.5 3 3.5βmix
T t,r
el,R
H /
T t,P
N
-0.2
-0.1
0
0.1
0.2
0.3
MR [N
m]
Geis et al. (2004) Measured Temparatures
Present Work Predicted Temparatures
Present Work Predicted Moments
Tt,rel,RH
Tt,PN
-
11Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Validation Test Case 2: Lewis et al. (2006) - I
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0.0 0.5 1.0 1.5 2.0 2.5 3.0
βin
Θ
Present WorkTheoreticalComputed
Pre-swirlNozzles
ReceiverHoles
Pre-swirlChamberPre-swirl
Nozzles
ReceiverHoles
Pre-swirlChamber
( )2RH
2RH,rel,tPN,tP
rTTC2
⋅Ω
−⋅⋅=Θ
2RH
S
2
RH
PNin rm
M21rr2
⋅Ω⋅⋅
−−
⋅β⋅=Θ
&
Theoretical Value of Θ
-
12Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Validation Test Case 2: Lewis et al. (2006) - II
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8βmix
CD
Present WorkCFDMeasured
Pre-swirlNozzles
ReceiverHoles
Pre-swirlChamberPre-swirl
Nozzles
ReceiverHoles
Pre-swirlChamber
-
13Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Validation Test Case 2: Lewis et al. (2006) - III
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0.0 0.5 1.0 1.5 2.0
βmix
Θ
( )
⋅⋅Ω−=Θ
P
2RH
2
RH,rel,tPN,t C2rTT
1P
2RH
2
P
2RH
2
mixC2
rC2
r=β
⋅⋅Ω
⋅⋅Ω⋅Θ=Θ′
-
14Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Validation Test Case 3: Chew et al. (2003)
-0.5
0
0.5
1
1.5
0 0.5 1 1.5
βmix
Θ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Present WorkMeasured
Pre-swirlNozzles
ReceiverHoles
Pre-swirlChamber
Inner Labyrinth
Seal
Outer Labyrinth
Seal
Pre-swirlNozzles
ReceiverHoles
Pre-swirlChamber
Inner Labyrinth
Seal
Outer Labyrinth
Seal
CD
Θ'
CD
-
15Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
qMODELLING PHILOSOPHY
qMODEL VALIDATION
o Test Case 1
o Test Case 2
o Test Case 3
q DESIGN OPTIMISATION
o System Level
o Engine Level
q CONCLUSIONS
Contents
-
16Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Optimisation: System Level
0
1
2
3
4
5
6
7
0 0.5 1 1.5 2 2.5 3 3.5 4βin,RH
Θ
0.3
0.4
0.5
0.6
0.7
0.8
0.9
CD,RH
CD Θ
-
17Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Optimisation: Engine Level - I
H.P. CompressorBurner
H.P.Turbine
Pre-SwirlSystem
H.P.Compressor
Pre-SwirlSystem
H.P.Turbine
Burner
-
18Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Optimisation: Engine Level - II
0.9
0.95
1
1.05
-5 0 5 10Change in Pre-swirl Nozzle Angle (deg)
β mix
-2
-1
0
1
2
3
4
Inci
denc
e A
ngle
i (d
eg)
-
19Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Optimisation: Engine Level - III
0.87
0.92
0.97
1.02
Fuel Flow
Θ
βmix=1 at design
βmix=1.01 at design
-
20Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
qMODELLING PHILOSOPHY
qMODEL VALIDATION
o Test Case 1
o Test Case 2
o Test Case 3
q DESIGN OPTIMISATION
o System Level
o Engine Level
q CONCLUSIONS
Contents
-
21Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Conclusions
Ø A generic approach for modelling direct-transfer pre-swirl air systems using object-oriented simulation principles is presented. Ø Three components (orifice, cavity and labyrinth seal) are combined together to simulate different experimental pre-swirl systems found in the open literature. The predicted results are consistent with the experimental data and computational results reported in the relevant references. Ø The ease with which the proposed approach allows different pre-swirl system configurations to be constructed and evaluated, both on their own and as part of a complete engine performance model is demonstrated. Ø Since the approach presented allows components to be represented in varied levels of detail, it is possible to create more realistic models early in the engine design process.
-
22Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
-
23Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Cavity Component Equations (I)
( )∑ ∑= =
φφ =⋅⋅−⋅⋅J
1j
K
1kkj,in,j,inj,inmix,mmix MVrmVrm &&
( )mix,kmix,kmixkkk,mk VrVrArC5.0M φφ −⋅Ω⋅−⋅Ω⋅ρ⋅⋅⋅⋅=
( )∑ ∑= =
⋅Ω+=⋅⋅−⋅⋅J
1j
K
1kkj,in,tj,pj,inmix,tmix,pmix MQTCmTCm &&
Angular Momentum Conservation Equation → Vφ,mix
Energy Conservation Equation → Tt,mix
Moment exerted by fluid on each surrounding surface, Mk (from drag force equation):
-
24Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Friction Coefficients
( ) 2.05
o
i8.0m Rer
r1sin07288.0C −ϕ− ⋅
−⋅θ⋅=
fm CrL2C ⋅⋅π⋅=
( )[ ] 2f10f 6.0CRelog07.4C −ϕ −⋅⋅=
For free disks or cones with non-zero inner radius and half angle θ:
For a smooth cylinder of length L:
where
-
25Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Cavity Component Equations (II)
Mixing total pressure, Pt,mix
( )refSSav TTAhQ −⋅⋅=
Axial momentum equation → Ps,mix:
Convective heat transfer, Q:
( ) ( )( )
ζ+
⋅−⋅ζ−⋅=
−γγ
1
mix,s
Pmixmix,tmix,smix,t T
CmQT1PP
&
( )( )mix,tis,mix,t
mix
mix,zmix
J
1jj,inj,in,sj,in,zj,in
mix,s PPA
VmAPVmP −−
⋅−⋅+⋅=
∑=
&&
-
26Direct-Transfer Pre-Swirl System: Performance Modelling, Validation and Optimisation
A. Alexiou & K. Mathioudakis
Orifice Component Equations
( )
21
22,1,12,2
1
1,t
2,s
1,t
1,t1
1,t
2,s1,this
VVrVr2
PP
1P
12
PP
Am
−⋅−⋅⋅Ω⋅+
−⋅
ρ⋅
−γ
γ⋅⋅
⋅ρ⋅=
φφφ
γ−γ
γ
&
1-D, isentropic, compressible expansion of a perfect gas from the upstream total pressure to the downstream static pressure and considering the work transfer to the fluid: