Abstract

Turbomachines are an integral part of society, with global trends demanding more efficient designs while staying within structural limits. Fan blade designs must be designed for both steady and vibratory structural responses. Design space exploration (DSE) of turbomachinery blades allows improved designs to be found. DSE requires samples of vibratory responses. Traditionally, analysis to obtain these samples is too computationally expensive for thorough DSE. This work develops a simplified analysis method based on Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) and harmonic mode superposition (HMS) finite element analysis (FEA). This reduces the computational cost and allows for enough samples to create surrogate models. This work also develops a surrogate method which indirectly emulates the vibratory responses to accurately handle the large spikes in vibratory stress found throughout the design space. It was found that combining these methods allows for accurate emulation of a fan blade design space while accounting for vibratory stress. The surrogates with improved accuracy allow better designs to be found while ensuring that those designs meet structural requirements.

References

1.
Soderquist
,
D. R.
,
2019
,
“Analysis of Distortion Transfer and Generation Through a Fan and a Compressor Using Full-Annulus Unsteady Rans and Harmonic Balance Approaches,” Master's thesis, Brigham Young University, Provo, UT
.
2.
Bakhle
,
M.
,
Reddy
,
T.
,
Herrick
,
G.
,
Shabbir
,
A.
, and
Florea
,
R.
,
2012
, “
Aeromechanics Analysis of a Boundary Layer Ingesting Fan
,”
48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
, AIAA 2012–3995.
3.
Cousins
,
W. T.
,
Voytovych
,
D.
,
Tillman
,
G.
, and
Gray
,
E.
,
2017
, “
Design of a Distortion-Tolerant Fan for a Boundary-Layer Ingesting Embedded Engine Application
,”
53rd AIAA/SAE/ASEE Joint Propulsion Conference
,
Atlanta, GA
,
July 10–12
.
4.
Heinlein
,
G.
,
Bakhle
,
M.
, and
Chen
,
J.
,
2019
, “
Aeromechanic Response of a Coupled Inlet-Fan Boundary Layer Ingesting Distortion-Tolerant Fan
,”
ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition
,
Phoenix, AZ
,
June 17–21
.
5.
Provenza
,
A. J.
,
Duffy
,
K. P.
, and
Bakhle
,
M. A.
,
2019
, “
Aeromechanical Response of a Distortion-Tolerant Boundary Layer Ingesting Fan
,”
ASME J. Eng. Gas Turbines Power
,
141
(
1
), p.
011011
. 10.1115/1.4040739
6.
Kang
,
E.
,
Jackson
,
E.
, and
Schulte
,
W.
,
2011
. “An Approach for Effective Design Space Exploration,”
Foundations of Computer Software. Modeling, Development, and Verification of Adaptive Systems. Monterey Workshop 2010. Lecture Notes in Computer Science
,
R.
Calinescu
and
E.
Jackson
, eds., Vol.
6662
,
Springer
,
Berlin, Heidelberg
.
7.
Bunnell
,
S.
,
Thelin
,
C.
,
Gorrell
,
S.
,
John
,
S.
,
Ruoti
,
C.
, and
Hepworth
,
A.
,
2018
, “
Rapid Visualization of Compressor Blade Finite Element Models
,”
ASME Turbo Expo 2018: Turbine Technical Conference and Exposition
,
American Society of Mechanical Engineers
, Paper No. GT2018–77188.
8.
Bunnell
,
S. R.
,
Gorrell
,
S.
,
Salmon
,
J.
,
Thelin
,
C.
, and
Christopher
,
R.
,
2020
, “
Structural Design Space Exploration Using Principal Component Analysis
,”
ASME J. Comput. Inf. Sci. Eng.
,
20
(
6
), p.
061014
. https://doi.org/10.1115/1.4047428
9.
Thelin
,
C.
,
Bunnell
,
S.
,
Salmon
,
J.
, and
Gorrell
,
S.
,
2019
, “
Difference Modeling for Design Space Exploration and Comparison of Three-Dimensional Structural Simulation Results
,”
Inf. Visual.
,
18
(
4
), pp.
455
470
. 10.1177/1473871619862791
10.
Javed
,
A.
,
Pecnik
,
R.
, and
Van Buijtenen
,
J.
,
2016
, “
Optimization of a Centrifugal Compressor Impeller for Robustness to Manufacturing Uncertainties
,”
ASME J. Eng. Gas Turbines Power
,
138
(
11
), p.
112101
. 10.1115/1.4033185
11.
Benamara
,
T.
,
Breitkopf
,
P.
,
Lepot
,
I.
,
Sainvitu
,
C.
, and
Villon
,
P.
,
2017
, “
Multi-Fidelity POD Surrogate-Assisted Optimization: Concept and Aero-Design Study
,”
Struct. Multidiscipl. Optim.
,
56
(
6
), pp.
1387
1412
. 10.1007/s00158-017-1730-4
12.
Brown
,
J. M.
,
Beck
,
J. A.
,
Carper
,
E. B.
, and
Kaszynski
,
A. A.
,
2019
, “
Emulation of As-Manufactured Transonic Rotor Airfoil Modal Behavior and the Significance of Frequency Veering
,”
ASME
, Paper No. GT2019–91670.
13.
Knapke
,
C. J.
,
Wolff
,
M.
, and
Johnston
,
D. A.
,
2019
, “
Blended Fan Blade Effects on Aerodynamic Forces
,”
AIAA Scitech 2019 Forum
,
San Diego, CA
,
Jan. 7–11
.
14.
He
,
Z.
,
Epureanu
,
B. I.
, and
Pierre
,
C.
,
2007
, “
Parametric Study of the Aeroelastic Response of Mistuned Bladed Disks
,”
Comput. Struct.
,
85
(
11–14
), pp.
852
865
. 10.1016/j.compstruc.2007.01.007
15.
Laxalde
,
D.
, and
Pierre
,
C.
,
2011
, “
Modelling and Analysis of Multi-Stage Systems of Mistuned Bladed Disks
,”
Comput. Struct.
,
89
(
3–4
), pp.
316
324
. 10.1016/j.compstruc.2010.10.020
16.
Philippe
,
J.
,
Thouverez
,
F.
,
Blanc
,
L.
, and
Gruin
,
M.
,
2018
, “
Vibratory Behavior Prediction of Mistuned Stator Vane Clusters: An Industrial Application
,”
Comput. Struct.
,
196
, pp.
12
23
. 10.1016/j.compstruc.2017.11.003
17.
Forrester
,
A.
,
Sobester
,
A.
, and
Keane
,
A.
,
2008
,
Engineering Design via Surrogate Modelling: A Practical Guide
,
John Wiley & Sons
,
Hoboken, NJ
.
18.
Goodman
,
T.
, and
Spence
,
R.
,
1978
, “
The Effect of System Response Time on Interactive Computer Aided Problem Solving
,”
ACM SIGGRAPH Comput. Graph.
,
12
(
3
), pp.
100
104
. 10.1145/965139.807378
19.
Simpson
,
T.
,
Iyer
,
P.
,
Rothrock
,
L.
,
Frecker
,
M.
,
Barton
,
R.
,
Barron
,
K.
, and
Meckesheimer
,
M.
,
2005
, “
Metamodel-Driven Interfaces for Engineering Design: Impact of Delay and Problem Size on User Performance
,”
46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
,
Austin, TX
,
Apr. 18–21
.
20.
Simpson
,
T. W.
,
Barron
,
K.
,
Rothrock
,
L.
,
Frecker
,
M.
,
Barton
,
R. R.
, and
Ligetti
,
C.
,
2007
, “
Impact of Response Delay and Training on User Performance With Text-Based and Graphical User Interfaces for Engineering Design
,”
Res. Eng. Des.
,
18
(
2
), pp.
49
65
. 10.1007/s00163-007-0033-y
21.
Huang
,
Z.
,
Wang
,
C.
,
Chen
,
J.
, and
Tian
,
H.
,
2011
, “
Optimal Design of Aeroengine Turbine Disc Based on Kriging Surrogate Models
,”
Comput. Struct.
,
89
(
1–2
), pp.
27
37
. 10.1016/j.compstruc.2010.07.010
22.
Tedesco
,
J.
,
McDougal
,
W. G.
, and
Ross
,
C. A.
,
2000
,
Structural Dynamics
,
Pearson Education
,
London, UK
.
23.
Wennerstrom
,
A. J.
, and
Frost
,
G. R.
,
1976
,
“Design of a 1500 ft/sec, Transonic, High-Through-Flow, Single-Stage Axial-Flow Compressor with Low Hub/Tip Ratio,” Tech. Rep., Air Force Aero Propulsion Laboratory, AFAPL-TR-76-69, Wright-Patterson AFB, OH
.
24.
Law
,
C.
, and
Puterbaugh
,
S.
,
1988
,
“Parametric Blade S Test Report Rotor Configuration No. 4,” Tech Rep., Air Force Aero Propulsion Laboratory, AFWAL-TR-88-2110, Wright-Patterson AFB, OH
.
25.
Snyder
,
L.
, and
Burns
,
D.
,
1988
,
“Forced Vibration and Flutter Design Methodology,” Tech. Rep., U.S. Department of Energy, AGARD Manual on Aeroelasticity in Axial-Flow Turbomachines, Volume 2: Structural Dynamics and Aeroelasticity, AGARDAG-298
.
26.
Saravanamuttoo
,
H.
,
Rogers
,
G.
, and
Cohen
,
H.
,
2001
,
Gas Turbine Theory
,
Prentice Hall
,
Upper Saddle River, NJ
.
27.
Nicholas
,
T.
,
1999
, “
Critical Issues in High Cycle Fatigue
,”
Int. J. Fatigue
,
21
(
1
), pp.
S221
S231
. 10.1016/S0142-1123(99)00074-2
28.
Nicholas
,
T.
, and
Zuiker
,
J.
,
1996
, “
On the Use of the Goodman Diagram for High Cycle Fatigue Design
,”
Int. J. Fract.
,
80
(
2–3
), pp.
219
235
. 10.1007/BF00012670
29.
Cowles
,
B.
,
1996
, “
High Cycle Fatigue in Aircraft Gas Turbines—An Industry Perspective
,”
Int. J. Fract.
,
80
(
2–3
), pp.
147
163
. 10.1007/BF00012667
30.
Hughes
,
T. J.
,
2012
,
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
,
Courier Corporation
,
North Chelmsford, MA
.
31.
Thelin
,
C.
,
2019
,
“Application and Evaluation of Full-Field Surrogate Models in Engineering Design Exploration,”Master's thesis, Brigham Young University, Provo, UT
.
32.
Kamaraj
,
A. V.
,
2016
,
“Stress Prediction in Turbine Blades Under Forced Excitation,” Ph.D. thesis, San Diego State University, San Diego, CA
.
33.
Pingle
,
P.
, and
Avitabile
,
P.
,
2011
,
Linking Models and Experiments
,
Springer
,
New York City, New York
, pp.
187
200
.
34.
List
,
M. G.
,
2016
,
“Numerical Quantification of Interaction Effects in a Closely-Coupled Diffuser-Fan System,” Ph.D. thesis, University of Cincinnati, Cincinnati, OH
.
35.
Soderquist
,
D. R.
,
Gorrell
,
S. E.
, and
Custer
,
C. H.
,
2018
, “
Analysis of Distortion Transfer and Generation Through a Compressor Using the Harmonic Balance Approach
,”
2018 AIAA Aerospace Sciences Meeting
,
Kissimmee, FL
,
Jan. 8–12
.
36.
Soderquist
,
D. R.
,
Orme
,
A. D.
,
Gorrell
,
S. E.
, and
List
,
M. G.
,
2019
, “
Radial Variation in Distortion Transfer and Generation in a Highly Loaded Fan Stage From Nearstall to Choke
,”
ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition
, Paper No. GT2019–91753.
37.
Kou
,
H.-J.
,
Lin
,
J.-S.
, and
Zhang
,
J.-H.
,
2016
, “
Numerical Study on Vibration Stress of Rotating Fan Blade Under Aerodynamic Load at Critical Speed
,”
Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng.
,
230
(
6
), pp.
1044
1058
. 10.1177/0954410015603071
38.
Kou
,
H.-J.
,
Lin
,
J.-S.
,
Zhang
,
J.-H.
, and
Fu
,
X.
,
2017
, “
Dynamic and Fatigue Compressor Blade Characteristics During Fluid-Structure Interaction: Part I-Blade Modelling and Vibration Analysis
,”
Eng. Fail. Anal.
,
76
, pp.
80
98
. 10.1016/j.engfailanal.2017.02.002
39.
Montomoli
,
F.
,
Hodson
,
H.
, and
Lapworth
,
L.
,
2011
, “
RANS–URANS in Axial Compressor, a Design Methodology
,”
Proc. Inst. Mech. Eng. Part A J. Power Energy
,
225
(
3
), pp.
363
374
. 10.1177/2041296710394267
40.
Mondal
,
P.
, and
Mathew
,
J.
,
2017
, “
Large Eddy Simulation of a Compressor Stage
,”
ASME 2017 Gas Turbine India Conference
,
Bangalore, India
,
Dec. 7–8
.
41.
Danforth
,
C. E.
,
1975
, “
Distortion-Induced Vibration in Fan and Compressor Blading
,”
J. Aircr.
,
12
(
4
), pp.
216
225
. 10.2514/3.59819
42.
Wallace
,
R. M.
,
2003
,
“Modal Response of a Transonic Fan Blade to Periodic Inlet Pressure Distortion,” Ph.D. thesis, Virginia Tech, Blacksburg, VA
.
43.
Peterson
,
M. W.
,
Gorrell
,
S. E.
,
List
,
M. G.
, and
Custer
,
C.
,
2016
, “
Implementation of Fourier Methods in CFD to Analyze Distortion Transfer and Generation Through a Transonic Fan
,”
52nd AIAA/SAE/ASEE Joint Propulsion Conference
,
Salt Lake City, UT
,
July 25–27
.
44.
Peterson
,
M. W.
,
2014
,
“Implementation of Fourier Methods in CFD to Analyze Distortion Transfer and Generation Through a Transonic Fan,” Master's thesis, Brigham Young University, Provo, UT
.
You do not currently have access to this content.