Abstract

Accurate uncertainty quantification of compressor performance arising from blade geometric deviations is conducive to blade optimization design, blade error verification, etc. In order to investigate the impact of actual blade geometric deviations on compressor performance, this study initially conducted measurements of geometric deviations on three sections of 100 blades. Then, the probability density distributions of various geometric deviations were obtained through kernel density estimation. Subsequently, combining data-driven nonintrusive polynomial chaos with Halton sequence, the distribution of sampling points and the construction approach of the response model were determined. Based on the parameterization of a subsonic rotor geometric model, blade samples with different geometric features were generated. Utilizing numerical simulation results of the aerodynamic performance of each sample, the impact of blade geometric deviations on compressor performance was quantified, and sensitivity analysis was conducted using Sobol' index. It was observed that the total pressure ratio was most sensitive to the stagger angle deviation at 50% blade height, while the sensitivity of the isentropic efficiency to each geometric deviation varied with operating conditions. Then, the flow field was divided into five regions based on different flow loss mechanisms, and a viscous loss coefficient was introduced to quantify the flow losses in each region. It was found that various geometric deviations at 50% span section, as well as leading edge radius deviation and stagger angle deviation at 95% span section, have a significant impact on the flow field losses.

References

1.
An
,
G.
,
Kang
,
J.
,
Zou
,
Y.
,
Zhang
,
L.
,
Lang
,
J.
,
Yuan
,
W.
, and
Zhang
,
Q.
,
2023
, “
Investigation of the Unsteady Flow in a Transonic Axial Compressor Adopted in the Compressed Air Energy Storage System
,”
J. Energy Storage
,
63
, p.
106928
.10.1016/j.est.2023.106928
2.
Zhang
,
L.
,
Yang
,
F.
,
An
,
G.
,
Lang
,
J.
,
Yuan
,
W.
, and
Zhang
,
Q.
,
2024
, “
Investigation of a Rotating Stall in a Supercritical CO2 Centrifugal Compressor
,”
Phys. Fluids
,
36
(
5
), p.
054102
.10.1063/5.0207917
3.
Garzon
,
V. E.
, and
Darmofal
,
D. L.
,
2003
, “
Impact of Geometric Variability on Axial Compressor Performance
,”
ASME J. Turbomach.
,
125
(
4
), pp.
692
703
.10.1115/1.1622715
4.
Guo
,
Z.
,
Chu
,
W.
,
Zhang
,
H.
,
Liang
,
C.
, and
Meng
,
D.
,
2023
, “
Statistical Evaluation of Stability Margin of a Multi-Stage Compressor With Geometric Variability Using Adaptive Polynomial Chaos-Kriging Model
,”
Phys. Fluids
,
35
(
7
), p.
076114
.10.1063/5.0158821
5.
Bammert
,
K.
, and
Sandstede
,
H.
,
1976
, “
Influences of Manufacturing Tolerances and Surface Roughness of Blades on the Performance of Turbines
,”
ASME J. Eng. Gas Turbines Power
,
98
(
1
), pp.
29
36
.10.1115/1.3446107
6.
Suder
,
K. L.
,
Chima
,
R. V.
,
Strazisar
,
A. J.
, and
Roberts
,
W. B.
,
1995
, “
The Effect of Adding Roughness and Thickness to a Transonic Axial Compressor Rotor
,”
ASME J. Turbomach.
,
117
(
4
), pp.
491
505
.10.1115/1.2836561
7.
Roberts
,
W. B.
,
Armin
,
A.
,
Kassaseya
,
G.
,
Suder
,
K. L.
,
Thorp
,
S. A.
, and
Strazisar
,
A. J.
,
2002
, “
The Effect of Variable Chord Length on Transonic Axial Rotor Performance
,”
ASME J. Turbomach.
,
124
(
3
), pp.
351
357
.10.1115/1.1459734
8.
Lange
,
A.
,
Voigt
,
M.
,
Vogeler
,
K.
,
Schrapp
,
H.
,
Johann
,
E.
, and
Gümmer
,
V.
,
2012
, “
Impact of Manufacturing Variability and Nonaxisymmetry on High-Pressure Compressor Stage Performance
,”
ASME J. Eng. Gas Turbines Power
,
134
(
3
), p.
032504
.10.1115/1.4004404
9.
Lange
,
A.
,
Voigt
,
M.
,
Vogeler
,
K.
,
Schrapp
,
H.
,
Johann
,
E.
, and
Gümmer
,
V.
,
2012
, “
Impact of Manufacturing Variability on Multistage High-Pressure Compressor Performance
,”
ASME J. Eng. Gas Turbines Power
,
134
(
11
), p.
112601
.10.1115/1.4007167
10.
Schnell
,
R.
,
Lengyel
,
K. T.
, and
Nicke
,
E.
,
2014
, “
On the Impact of Geometric Variability on Fan Aerodynamic Performance, Unsteady Blade Row Interaction, and Its Mechanical Characteristics
,”
ASME J. Turbomach.
,
136
(
9
), p.
091005
.10.1115/1.4027218
11.
Angelo
,
M. A.
,
Salvatore
,
S.
, and
Salvatore
,
R.
,
2003
, “
Stochastic Response Surface Method and Tolerance Analysis in Microelectronics
,”
COMPEL
,
22
(
2
), pp.
314
327
.10.1108/03321640310459234
12.
Ghanem
,
R.
,
1998
, “
Scales of Fluctuation and the Propagation of Uncertainty in Random Porous Media
,”
Water Resour. Res.
,
34
(
9
), pp.
2123
2136
.10.1029/98WR01573
13.
Ma
,
C.
,
Gao
,
L.
,
Cai
,
Y.
, and
Li
,
R.
,
2017
, “
Robust Optimization Design of Compressor Blade Considering Machining Error
,”
ASME
Paper No. GT2017-63157.10.1115/GT2017-63157
14.
Guo
,
Z.
,
Chu
,
W.
, and
Zhang
,
H.
,
2022
, “
Uncertainty Analysis of Global and Local Performance Impact of Inflow and Geometric Uncertainties Using Sparse Grid-Based Non-Intrusive Polynomial Chaos
,”
Proc. Inst. Mech. Eng., Part A
,
236
(
7
), pp.
1239
1256
.10.1177/09576509221086709
15.
Mazzoni
,
C. M.
,
Ahlfeld
,
R.
,
Rosic
,
B.
, and
Montomoli
,
F.
,
2018
, “
Uncertainty Quantification of Leakages in a Multistage Simulation and Comparison With Experiments
,”
ASME J. Fluids Eng.
,
140
(
2
), p.
021110
.10.1115/1.4037983
16.
Luo
,
J.
,
Xia
,
Z.
, and
Liu
,
F.
,
2019
, “
Quantification of Performance Uncertainty for a Transonic Compressor Rotor Using an Adaptive NIPC Method
,”
ASME
Paper No. GT2019-90316.10.1115/GT2019-90316
17.
Xia
,
Z.
,
Luo
,
J.
, and
Liu
,
F.
,
2019
, “
Statistical Evaluation of Performance Impact of Flow Variations for a Transonic Compressor Rotor Blade
,”
Energy
,
189
, p.
116285
.10.1016/j.energy.2019.116285
18.
Xia
,
Z.
,
Luo
,
J.
, and
Liu
,
F.
,
2019
, “
Performance Impact of Flow and Geometric Variations for a Turbine Blade Using an Adaptive NIPC Method
,”
Aerosp. Sci. Technol.
,
90
, pp.
127
139
.10.1016/j.ast.2019.04.025
19.
Xiu
,
D.
, and
Karniadakis
,
G. E.
,
2003
, “
Modelling Uncertainty in Flow Simulations Via Generalized Polynomial Chaos
,”
J. Comput. Phys.
,
187
(
1
), pp.
137
167
.10.1016/S0021-9991(03)00092-5
20.
Ju
,
Y.
,
Liu
,
Y.
,
Jiang
,
W.
, and
Zhang
,
C.
,
2021
, “
Aerodynamic Analysis and Design Optimization of a Centrifugal Compressor Impeller Considering Realistic Manufacturing Uncertainties
,”
Aerosp. Sci. Technol.
,
115
, p.
106787
.10.1016/j.ast.2021.106787
21.
Schlüter
,
L.
,
Voigt
,
P.
,
Voigt
,
M.
,
Mailach
,
R.
,
Schmidt
,
R.
,
Rostamian
,
M.
, and
Becker
,
B.
,
2022
, “
The Validation of a Parametric Leading Edge Model for Probabilistic CFD Analyses of Post-Service Compressor Airfoils
,”
ASME
Paper No. GT2022-78309.10.1115/GT2022-78309
22.
Prots
,
A.
,
Schlüter
,
L.
,
Voigt
,
M.
,
Mailach
,
R.
, and
Meyer
,
M.
,
2022
, “
Impact of Epistemic Uncertainty on Performance Parameters of Compressor Blades
,”
ASME
Paper No. GT2022-82579.10.1115/GT2022-82579
23.
Guo
,
Z.
,
Chu
,
W.
,
Zhang
,
H.
,
Liang
,
C.
, and
Meng
,
D.
,
2023
, “
Aerodynamic Evaluation of Cascade Flow With Actual Geometric Uncertainties Using an Adaptive Sparse Arbitrary Polynomial Chaos Expansion
,”
Phys. Fluids
,
35
(
3
), p.
036122
.10.1063/5.0144937
24.
Ahlfeld
,
R.
, and
Montomoli
,
F.
,
2017
, “
A Single Formulation for Uncertainty Propagation in Turbomachinery: SAMBA PC
,”
ASME J. Turbomach.
,
139
(
11
), p.
111007
.10.1115/1.4037362
25.
Guo
,
Z.
,
Chu
,
W.
, and
Zhang
,
H.
,
2022
, “
A Data-Driven Non-Intrusive Polynomial Chaos for Performance Impact of High Subsonic Compressor Cascades With Stagger Angle and Profile Errors
,”
Aerosp. Sci. Technol.
,
129
, p.
107802
.10.1016/j.ast.2022.107802
26.
Ahlfeld
,
R.
,
Belkouchi
,
B.
, and
Montomoli
,
F.
,
2016
, “
SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos
,”
J. Comput. Phys.
,
320
, pp.
1
16
.10.1016/j.jcp.2016.05.014
27.
Guo
,
Z.
, and
Chu
,
W.
,
2022
, “
Stochastic Aerodynamic Analysis for Compressor Blades With Manufacturing Variability Based on a Mathematical Dimensionality Reduction Method
,”
Proc. Inst. Mech. Eng., Part C
,
236
(
10
), pp.
5719
5735
.10.1177/09544062211062452
28.
Oladyshkin
,
S.
, and
Nowak
,
W.
,
2012
, “
Data-Driven Uncertainty Quantification Using the Arbitrary Polynomial Chaos Expansion
,”
Reliab. Eng. Syst. Saf.
,
106
, pp.
179
190
.10.1016/j.ress.2012.05.002
29.
Wang
,
W.
,
Chu
,
W.
,
Zhang
,
H.
, and
Kuang
,
H.
,
2017
, “
Experimental and Numerical Study of Tip Injection in a Subsonic Axial Flow Compressor
,”
Chin. J. Aeronaut.
,
30
(
3
), pp.
907
917
.10.1016/j.cja.2017.04.004
30.
Chi
,
Z.
,
Chu
,
W.
,
Zhang
,
Z.
, and
Zhang
,
H.
,
2022
, “
Research on the Stability Enhancement Mechanism of Multi-Parameter Interaction of Casing Treatment in an Axial Compressor Rotor
,”
Proc. Inst. Mech. Eng., Part G
,
236
(
12
), pp.
2405
2419
.10.1177/09544100211063079
31.
Chi
,
Z.
,
Chu
,
W.
,
Zhang
,
Z.
, and
Zhang
,
H.
,
2023
, “
Stall Margin Evaluation and Data Mining Based Multi-Objective Optimization Design of Casing Treatment for an Axial Compressor Rotor
,”
Phys. Fluids
,
35
(
8
), p.
086117
.10.1063/5.0161142
32.
Chi
,
Z.
,
Chu
,
W.
,
Zhang
,
H.
, and
Luo
,
B.
,
2022
, “
Unsteady Effects of Casing Treatment on Tip Flow Structures in a Subsonic Compressor Rotor
,”
ASME
Paper No. GT2022-82342.10.1115/GT2022-82342
33.
Zhang
,
H.
,
Liu
,
W.
,
Wang
,
E.
,
Wu
,
Y.
, and
Yao
,
W.
,
2019
, “
Mechanism Investigation of Enhancing the Stability of an Axial Flow Rotor by Blade Angle Slots
,”
Proc. Inst. Mech. Eng., Part G
,
233
(
13
), pp.
4750
4764
.10.1177/0954410019829272
34.
Zhang
,
H.
,
Li
,
Q.
,
Dong
,
F.
, and
Chu
,
W.
,
2021
, “
Mechanism of Affecting the Performance and Stability of an Axial Flow Compressor With Inlet Distortion
,”
J. Therm. Sci.
,
30
(
4
), pp.
1406
1420
.10.1007/s11630-021-1489-1
35.
Liu
,
B.
,
Liu
,
J.
,
Yu
,
X.
, and
An
,
G.
,
2022
, “
A Novel Decomposition Method for Manufacture Variations and the Sensitivity Analysis on Compressor Blades
,”
Aerospace
,
9
(
10
), p.
542
.10.3390/aerospace9100542
36.
Wang
,
J.
,
Wang
,
B.
,
Yan
,
H.
,
Sun
,
Z.
,
Zhou
,
K.
, and
Zheng
,
X.
,
2023
, “
Compressor Geometric Uncertainty Quantification Under Conditions From Near Choke to Near Stall
,”
Chin. J. Aeronaut.
,
36
(
3
), pp.
16
29
.10.1016/j.cja.2022.10.012
37.
Piantadosi
,
J.
,
Howlett
,
P.
, and
Boland
,
J.
,
2007
, “
Matching the Grade Correlation Coefficient Using a Copula With Maximum Disorder
,”
J. Ind. Manage. Optim.
,
3
(
2
), pp.
305
312
.10.3934/jimo.2007.3.305
38.
Rosenblatt
,
M.
,
1956
, “
Remarks on Some Nonparametric Estimates of a Density Function
,”
Ann. Math. Stat.
,
27
(
3
), pp.
832
837
.10.1214/aoms/1177728190
39.
Blatman
,
G.
, and
Sudret
,
B.
,
2011
, “
Adaptive Sparse Polynomial Chaos Expansion Based on Least Angle Regression
,”
J. Comput. Phys.
,
230
(
6
), pp.
2345
2367
.10.1016/j.jcp.2010.12.021
40.
Babacan
,
S. D.
,
Molina
,
R.
, and
Katsaggelos
,
A. K.
,
2010
, “
Bayesian Compressive Sensing Using Laplace Priors
,”
IEEE Trans. Image Process.
,
19
(
1
), pp.
53
63
.10.1109/TIP.2009.2032894
41.
Sobol
,
I. M.
,
2001
, “
Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates
,”
Math. Comput. Simul.
,
55
(
1
), pp.
271
280
.10.1016/S0378-4754(00)00270-6
42.
Chu
,
W.
,
Ji
,
T.
,
Chen
,
X.
, and
Luo
,
B.
,
2023
, “
Mechanism Analysis and Uncertainty Quantification of Blade Thickness Deviation on Rotor Performance
,”
Proc. Inst. Mech. Eng., Part A
,
237
(
6
), pp.
1188
1202
.10.1177/09576509231162143
43.
Li
,
X.
,
Dong
,
J.
,
Chen
,
H.
, and
Lu
,
H.
,
2022
, “
The Control of Corner Separation With Parametric Suction Side Corner Profiling on a High-Load Compressor Cascade
,”
Aerospace
,
9
(
3
), p.
172
.10.3390/aerospace9030172
44.
Ji
,
T.
,
Chu
,
W.
,
Liang
,
C.
, and
Meng
,
D.
,
2023
, “
Uncertainty Quantification on the Influence of Blade Thickness Deviation at Different Rotational Speeds Based on Flow Dissipation Analysis
,”
Phys. Fluids
,
35
(
6
), p.
066126
.10.1063/5.0155693
45.
An
,
G.
,
Kang
,
J.
,
Wang
,
L.
,
Zhang
,
L.
,
Lang
,
J.
, and
Li
,
H.
,
2023
, “
Decoupling and Reconstruction Analysis in a Transonic Axial Compressor Using the Dynamic Mode Decomposition Method
,”
Phys. Fluids
,
35
(
8
), p.
084120
.10.1063/5.0160392
You do not currently have access to this content.