Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

Reynolds-averaged Navier–Stokes (RANS) simulations currently serve as the prevailing industrial method for simulating axial compressor flows, and this status is expected to persist in the foreseeable future. To evaluate the capabilities of contemporary RANS solvers for compressors, this article presents a statistical analysis of RANS simulation results submitted to the first and the second Global Power and Propulsion Society (GPPS) computational fluid dynamics (CFD) workshops, where blind tests on the TUDa-GLR-OpenStage transonic axial compressor were performed. The workshops were held online in December 2021 and in a hybrid format at Chania, Greece, in September 2022, which are the first primary turbomachinery CFD workshops following the 1994 International Gas Turbine Institute (IGTI) CFD blind test event on NASA Rotor 37. A total of 35 submissions were received from 12 distinct RANS solvers, contributed by 14 participants affiliated with 11 organizations across 5 countries. Participants include academic researchers, engineers from the turbomachinery industry, and developers of commercial CFD solvers. First, the grid convergence behavior exhibited by various solvers employing different turbulence models is examined. Afterward, the prediction accuracy of the ensemble of the simulation results is evaluated, and the representative simulation results are compared and analyzed in detail. The key factors that improve the prediction accuracy are identified. These results foster improved usage and further development of turbomachinery RANS solvers.

References

1.
Epstein
,
A. H.
,
2014
, “
Aeropropulsion for Commercial Aviation in the Twenty-First Century and Research Directions Needed
,”
AIAA J.
,
52
(
5
), pp.
901
911
.
2.
Sandberg
,
R. D.
, and
Michelassi
,
V.
,
2022
, “
Fluid Dynamics of Axial Turbomachinery: Blade- and Stage-Level Simulations and Models
,”
Annu. Rev. Fluid Mech.
,
54
, pp.
255
285
.
3.
Choi
,
H.
, and
Moin
,
P.
,
2012
, “
Grid-Point Requirements for Large Eddy Simulation: Chapman’s Estimates Revisited
,”
Phys. Fluids
,
24
(
1
), p.
011702
.
4.
Slotnick
,
J.
,
Khodadoust
,
A.
,
Alonso
,
J.
,
Darmofal
,
D.
,
Gropp
,
W.
,
Lurie
,
E.
, and
Mavriplis
,
D.
,
2014
, “CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences,” NASA Langley Research Center, Hampton, VA, NASA Report No. NASA/CR-2014-218178.
5.
Bush
,
R. H.
,
Chyczewski
,
T. S.
,
Duraisamy
,
K.
,
Eisfeld
,
B.
,
Rumsey
,
C. L.
, and
Smith
,
B. R.
,
2019
, “
Recommendations for Future Efforts in RANS Modeling and Simulation
,”
AIAA Scitech 2019 Forum
,
San Diego, CA
,
Jan. 7–11
.
6.
Casey
,
M.
,
2002
, “Validation of Turbulence Models for Turbomachinery Flows—A Review,”
Engineering Turbulence Modelling and Experiments 5
,
W.
Rodi
and
N.
Fueyo
, eds., Elsevier
,
Oxford
, pp.
43
57
.
7.
Horlock
,
J.
, and
Denton
,
J.
,
2005
, “
A Review of Some Early Design Practice Using Computational Fluid Dynamics and a Current Perspective
,”
ASME J. Turbomach.
,
127
(
1
), pp.
5
13
.
8.
Cumpsty
,
N. A.
,
2010
, “
Some Lessons Learned
,”
ASME J. Turbomach.
,
132
(
4
), p.
041018
.
9.
Van den Braembussche
,
R. A.
,
2008
, “Numerical Optimization for Advanced Turbomachinery Design,”
Optimization and Computational Fluid Dynamics
,
D.
Thévenin
and
G.
Janiga
, eds.,
Springer
,
Berlin, Heidelberg
, pp.
147
189
.
10.
Montomoli
,
F.
, and
Massini
,
M.
,
2019
, “Uncertainty Quantification Applied to Gas Turbine Components,”
Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines
,
F.
Montomoli
, ed.,
Springer
, London, pp.
157
193
.
11.
Sun
,
X.
,
Liu
,
X.
,
Hou
,
R.
, and
Sun
,
D.
,
2013
, “
A General Theory of Flow-Instability Inception in Turbomachinery
,”
AIAA J.
,
51
(
7
), pp.
1675
1687
.
12.
Denton
,
J.
,
1997
, “
Lessons From Rotor 37
,”
J. Therm. Sci.
,
6
(
1
), pp.
1
13
.
13.
Tinoco
,
E.
,
2023
, “
Summary Data From the Seventh AIAA CFD Drag Prediction Workshop
,”
AIAA AVIATION 2023 Forum
,
San Diego, CA and Online
,
June 12–16
.
14.
Rumsey
,
C. L.
,
Slotnick
,
J. P.
, and
Woeber
,
C. D.
,
2023
, “
Fourth High-Lift Prediction/Third Geometry and Mesh Generation Workshops: Overview and Summary
,”
AIAA J. Aircr.
,
60
(
4
), pp.
1160
1177
.
15.
Dunham
,
J.
,
1998
, “CFD Validation for Propulsion System Components,” Canada Communication Group Inc, Hull (Quebec), Canada, NATO Report No. AGARD-AR-355.
16.
Baldwin
,
B.
, and
Lomax
,
H.
,
1978
, “
Thin-Layer Approximation and Algebraic Model for Separated Turbulent Flows
,”
16th Aerospace Sciences Meeting
,
Huntsville, AL
,
Jan. 16–18
.
17.
Launder
,
B. E.
, and
Sharma
,
B. I.
,
1974
, “
Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc
,”
Lett. Heat Mass Transf.
,
1
(
2
), pp.
131
137
.
18.
Klausmann
,
F.
,
Franke
,
D.
,
Foret
,
J.
, and
Schiffer
,
H.-P.
,
2022
, “
Transonic Compressor Darmstadt—Open Test Case Introduction of the TCD Open Test Case
,”
J. Glob. Power Propuls.
,
6
, pp.
318
329
.
19.
He
,
X.
,
Zhu
,
M.
,
Xia
,
K.
,
Klausmann
,
F.
,
Teng
,
J.
, and
Vahdati
,
M.
,
2023
, “
Validation and Verification of RANS Solvers for TUDa-GLR-OpenStage Transonic Axial Compressor
,”
J. Glob. Power Propuls.
,
7
, pp.
13
29
.
20.
Müller
,
D.
,
2019
,
Zum Aerodynamischen Und Aeroelastischen Verhalten Des Axialverdichters An Der Stallgrenze
, Vol.
12
(
Forschungsberichte aus dem Institut für Gasturbinen, Luft- und Raumfahrtantriebe
),
Shaker Verlag
,
Düren
.
21.
Rumsey
,
C. L.
,
2007
, “
Apparent Transition Behavior of Widely-Used Turbulence Models
,”
Int. J. Heat Fluid Flow
,
28
(
6
), pp.
1460
1471
.
22.
Menter
,
F. R.
,
Kuntz
,
M.
, and
Langtry
,
R.
,
2003
, “Ten Years of Industrial Experience With the SST Turbulence Model,”
Turbulence, Heat and Mass Transfer 4
,
K.
Hanjalic
,
Y.
Nagano
, and
M.
Tummers
, eds.
Begell House
,
Ankara, Turkey
, pp.
625
632
.
23.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.
24.
Rumsey
,
C. L.
,
Allison
,
D. O.
,
Biedron
,
R. T.
,
Buning
,
P. G.
,
Gainer
,
T. G.
,
Morrison
,
J. H.
,
Rivers
,
S. M.
,
Mysko
,
S. J.
, and
Witkowski
,
D. P.
,
2001
, “CFD Sensitivity Analysis of a Modern Civil Transport Near Buffet-Onset Conditions,” NASA Langley Research Center, Hampton, VA, NASA Report No. NASA/TM-2001-211263.
25.
Shur
,
M. L.
,
Strelets
,
M. K.
,
Travin
,
A. K.
, and
Spalart
,
P. R.
,
2000
, “
Turbulence Modeling in Rotating and Curved Channels: Assessing the Spalart-Shur Correction
,”
AIAA J.
,
38
(
5
), pp.
784
792
.
26.
Menter
,
F. R.
,
Garbaruk
,
A. V.
, and
Egorov
,
Y.
,
2012
, “Explicit Algebraic Reynolds Stress Models for Anisotropic Wall-Bounded Flows,”
EUCASS Proceedings Series—Advances in AeroSpace Sciences
,
P.
Reijasse
,
D.
Knight
,
M.
Ivanov
, and
I.
Lipatov
, eds.,
EDP Sciences
,
Les Ulis, Paris, France
, Vol.
3
, pp.
89
104
.
27.
Dacles-Mariani
,
J.
,
Kwak
,
D.
, and
Zilliac
,
G.
,
1999
, “
On Numerical Errors and Turbulence Modeling in Tip Vortex Flow Prediction
,”
Int. J. Numer. Methods Fluids
,
30
(
1
), pp.
65
82
.
28.
Spalart
,
P.
, and
Allmaras
,
S.
,
1994
, “
A One-Equation Turbulence Model for Aerodynamic Flows
,”
Rech. Aerosp.
,
1
, pp.
5
21
.
29.
Smirnov
,
P. E.
, and
Menter
,
F. R.
,
2009
, “
Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart–Shur Correction Term
,”
ASME J. Turbomach.
,
131
(
4
), p.
041010
.
30.
Liu
,
Y.
,
Tang
,
Y.
,
Scillitoe
,
A. D.
, and
Tucker
,
P. G.
,
2020
, “
Modification of Shear Stress Transport Turbulence Model Using Helicity for Predicting Corner Separation Flow in a Linear Compressor Cascade
,”
ASME J. Turbomach.
,
142
(
2
), p.
021004
.
31.
Matsui
,
K.
,
Tani
,
N.
,
Perez
,
E.
,
Kelly
,
R. T.
, and
Jemcov
,
A.
,
2022
, “
Calibrated Rotation-Helicity-Quadratic Constitutive Relation Spalart-Allmaras (RH-QCR SA) Model for the Prediction of Multi-Stage Compressor Characteristics
,”
ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition
,
Rotterdam, Netherlands
,
June 13–17
.
32.
Liu
,
Y.
,
Lu
,
L.
,
Fang
,
L.
, and
Gao
,
F.
,
2011
, “
Modification of Spalart–Allmaras Model With Consideration of Turbulence Energy Backscatter Using Velocity Helicity
,”
Phys. Lett. A
,
375
(
24
), pp.
2377
2381
.
33.
Spalart
,
P. R.
,
2000
, “
Strategies for Turbulence Modelling and Simulations
,”
Int. J. Heat Fluid Flow
,
21
(
3
), pp.
252
263
.
34.
He
,
X.
,
Zhao
,
F.
, and
Vahdati
,
M.
,
2022
, “
A Turbo-Oriented Data-Driven Modification to the Spalart–Allmaras Turbulence Model
,”
ASME J. Turbomach.
,
144
(
12
), p.
121007
.
35.
Rumsey
,
C.
,
Carlson
,
J.-R.
,
Pulliam
,
T.
, and
Spalart
,
P.
,
2020
, “
Improvements to the Quadratic Constitutive Relation Based on NASA Juncture Flow Data
,”
AIAA J.
,
58
(
10
), pp.
4374
4384
.
36.
Hellsten
,
A.
,
2005
, “
New Advanced K-ω Turbulence Model for High-Lift Aerodynamics
,”
AIAA J.
,
43
(
9
), pp.
1857
1869
.
37.
Wilcox
,
D.
,
1998
,
Turbulence Modeling for CFD
, Vol.
2
,
DCW industries La Canada
,
CA
.
38.
Rumsey
,
C.
,
Smith
,
B.
, and
Huang
,
G.
,
2010
, “
Description of a Website Resource for Turbulence Modeling Verification and Validation
,”
40th Fluid Dynamics Conference and Exhibit
,
Chicago, IL
,
June 28–July 1
.
39.
Pope
,
S. B.
,
2000
,
Turbulent Flows
,
Cambridge University Press
,
Cambridge, UK
.
40.
Jameson
,
A.
,
Schmidt
,
W.
, and
Turkel
,
E.
,
1981
, “
Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge Kutta Time Stepping Schemes
,”
14th Fluid and Plasma Dynamics Conference
,
Palo Alto, CA
,
June 23–25
.
41.
Ni
,
R.
,
1982
, “
A Multiple-Grid Scheme for Solving the Euler Equations
,”
AIAA J.
,
20
(
11
), pp.
1565
1571
.
42.
Roe
,
P. L.
,
1981
, “
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
,”
J. Comput. Phys.
,
43
(
2
), pp.
357
372
.
43.
Edwards
,
J. R.
,
1997
, “
A Low-Diffusion Flux-Splitting Scheme for Navier-Stokes Calculations
,”
Comput. Fluids
,
26
(
6
), pp.
635
659
.
44.
ANSYS
,
2020
, “Ansys CFX–Solver Theory Guide,” Release 20.1, Canonsburg, PA.
45.
ANSYS
,
2018
, “Ansys Fluent–Solver Theory Guide,” Release 19.2, Canonsburg, PA.
46.
NUMECA International
,
2021
, “Theory Guide–Fine/Turbo and Fine/Design3D 14.2, ” Brussels. Belgium.
47.
Denton
,
J. D.
,
1992
, “
The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines
,”
ASME J. Turbomach.
,
114
(
1
), pp.
18
26
.
48.
Du
,
P.
, and
Ning
,
F.
,
2016
, “
Validation of a Novel Mixing-Plane Method for Multistage Turbomachinery Steady Flow Analysis
,”
Chinese J. Aeronaut.
,
29
(
6
), pp.
1563
1574
.
49.
Giles
,
M. B.
,
1990
, “
Nonreflecting Boundary Conditions for Euler Equation Calculations
,”
AIAA J.
,
28
(
12
), pp.
2050
2058
.
50.
Roache
,
P. J.
,
1998
,
Verification and Validation in Computational Science and Engineering
,
Hermosa Publishers
,
Albuquerque, NM
.
51.
Silverman
,
B. W.
,
1998
,
Density Estimation for Statistics and Data Analysis
,
Taylor & Francis Group
,
New York
.
52.
Denton
,
J. D.
,
1993
, “
The 1993 IGTI Scholar Lecture: Loss Mechanisms in Turbomachines
,”
ASME J. Turbomach.
,
115
(
4
), pp.
621
656
.
53.
Qiao
,
B.
,
He
,
X.
,
Vahdati
,
M.
,
Ju
,
Y.
, and
Zhang
,
C.
,
2023
, “
On the Over-Prediction of Centrifugal Compressor Pressure Ratio in the High Impeller Tip Mach Number Regime
,”
ASME J. Turbomach.
,
145
(
10
), p.
104502
.
54.
Xia
,
K.
,
He
,
X.
,
Zhu
,
M.
,
Klausmann
,
F.
,
Teng
,
J.
, and
Vahdati
,
M.
,
2023
, “
Endwall Geometric Uncertainty and Error on the Performance of TUDa-GLR-OpenStage Transonic Axial Compressor
,”
J. Glob. Power Propuls.
,
7
, pp.
113
126
.
55.
Klausmann
,
F. S.
,
Kilian
,
N.
,
He
,
X.
,
Spieker
,
D.
,
Schmidt
,
B.
, and
Schiffer
,
H. -P.
,
2024
, “
Transonic Compressor Darmstadt Open Test Case: Experimental Investigation of Stator Secondary Flows and Hub Leakage
,”
ASME J. Turbomach.
,
146
(
10
), p.
101007
.
56.
Shao
,
R.
,
He
,
X.
,
Zhu
,
M.
,
Klausmann
,
F.
, and
Teng
,
J.
,
2023
, “
Characterizing Shrouded Stator Cavity Flow on the Performance of a Single-Stage Axial Transonic Compressor
,”
ASME J. Turbomach.
,
145
(
11
), p.
111004
.
57.
Hall
,
E. J.
,
1998
, “
Aerodynamic Modelling of Multistage Compressor Flow Fields Part 1: Analysis of Rotor-Stator-Rotor Aerodynamic Interaction
,”
Proc. Inst. Mech. Eng., Part G
,
212
(
2
), pp.
77
89
.
58.
Yi
,
J.
, and
He
,
L.
,
2015
, “
Space–Time Gradient Method for Unsteady Bladerow Interaction–Part I: Basic Methodology and Verification
,”
ASME J. Turbomach.
,
137
(
11
), p.
111008
.
59.
Mayle
,
R. E.
,
1991
, “
The 1991 IGTI Scholar Lecture: The Role of Laminar-Turbulent Transition in Gas Turbine Engines
,”
ASME J. Turbomach.
,
113
(
4
), pp.
509
536
.
You do not currently have access to this content.