Graphical Abstract Figure
Abstract
Flows in compressors are extremely complex with various scales. Small-scale turbulence, middle-scale rotor–stator interaction (RSI), large-scale corner separation, and tip leakage flow should all be considered in the simulation of compressors. Recently, a new hybrid Reynolds-averaged Navier–Stokes-large eddy simulation (RANS-LES) strategy that modifies the turbulent viscosity equation based on the Kolmogorov energy spectrum, termed the grid-adaptive simulation (GAS) method, is proposed by our group to achieve high accuracy simulation using different grid resolutions. In this study, the GAS method with the shear stress transport (SST) turbulence model is employed to simulate the RSI just with RANS-like grid resolution in a single-stage transonic compressor TUDa-GLR open test case. Compared with experiments and other simulation methods (including RANS and delayed detached eddy simulation (DDES) methods), results show that the GAS method can significantly improve the prediction accuracy for stall margin and radial distribution of flow parameters. Then, the effect of RSI on the secondary flow structures is analyzed based on the unsteady flow field simulated by the GAS method. Results show that the incorrect prediction of rotor tip leakage vortex breakdown and the underestimation of mixing losses in the tip region of the rotor are blamed for the high prediction deviation of RANS. An intuitive total pressure fluctuation caused by wakes is observed in the stator inlet. The particle tracking shows that the wake from the suction surface of the rotor has a strong trend to transport into the tip region of the stator. Spectral proper orthogonal decomposition (SPOD) is also utilized. Unsteady temporal–spatial structures induced by local unsteadiness and RSI are distinguished by SPOD, which includes the reverse flow in the tip region of the rotor and the pressure wave generated from RSI. SPOD also found that the separation of the stator on the suction side exhibits an unsteady fluctuation with a frequency of 1.6 blade passing frequency (BPF).
References
1.
Greitzer
, E. M.
, Tan
, C. S.
, Wisler
, D. C.
, Adamczyk
, J. J.
, and Strazisar
, A.
, 1994
, “Unsteady Flow in Turbomachines: Where’s the Beef?
” Unsteady Flows Aero Propuls.
, 40
, pp. 1
–11
.2.
Adamczyk
, J. J.
, 1999
, “Aerodynamic Analysis of Multistage Turbomachinery Flows in Support of Aerodynamic Design
,” ASME J. Turbomach.
, 122
(2
), pp. 189
–217
. 3.
Smith
, L. H.
, Jr., 1966
, “Wake Dispersion in Turbomachines
,” ASME J. Basic Eng.
, 88
(3
), pp. 688
–690
. 4.
Adkins
, G. G.
, Jr., and Smith
, L. H.
, Jr., 1982
, “Spanwise Mixing in Axial-Flow Turbomachines
,” J. Eng. Power
, 104
(1
), pp. 97
–110
. 5.
Praisner
, T. J.
, Clark
, J. P.
, Nash
, T. C.
, Rice
, M. J.
, and Grover
, E. A.
, 2006
, “Performance Impacts Due to Wake Mixing in Axial-Flow Turbomachinery
,” ASME Paper No. 2006-GT-90666.6.
Nolan
, S. P. R.
, Botros
, B. B.
, Tan
, C. S.
, Adamczyk
, J. J.
, Greitzer
, E. M.
, and Gorrell
, S. E.
, 2010
, “Effects of Upstream Wake Phasing on Transonic Axial Compressor Performance
,” ASME J. Turbomach.
, 133
(2
), p. 021010
. 7.
Van de Wall
, A. G.
, Kadambi
, J. R.
, and Adamczyk
, J. J.
, 2000
, “A Transport Model for the Deterministic Stresses Associated With Turbomachinery Blade Row Interactions
,” ASME J. Turbomach.
, 122
(4
), pp. 593
–603
. 8.
Liu
, Y.
, Tang
, Y.
, Liu
, B.
, and Lu
, L.
, 2019
, “An Exponential Decay Model for the Deterministic Correlations in Axial Compressors
,” ASME J. Turbomach.
, 141
(2
), p. 021005
. 9.
Liu
, Y.
, Wei
, X.
, and Tang
, Y.
, 2023
, “Investigation of Unsteady Rotor–Stator Interaction and Deterministic Correlation Analysis in a Transonic Compressor Stage
,” ASME J. Turbomach.
, 145
(7
), p. 071004
. 10.
Zhong
, W.
, Liu
, Y.
, and Tang
, Y.
, 2024
, “Unsteady Flow Structure of Corner Separation in a Highly Loaded Compressor Cascade
,” ASME J. Turbomach.
, 146
(3
), p. 031003
. 11.
Sandberg
, R. D.
, and Michelassi
, V.
, 2022
, “Fluid Dynamics of Axial Turbomachinery: Blade- and Stage-Level Simulations and Models
,” Annu. Rev. Fluid Mech.
, 54
(1
), pp. 255
–285
. 12.
Sandberg
, R. D.
, Michelassi
, V.
, Pichler
, R.
, Chen
, L.
, and Johnstone
, R.
, 2015
, “Compressible Direct Numerical Simulation of Low-Pressure Turbines—Part I: Methodology
,” ASME J. Turbomach.
, 137
(5
), p. 051011
. 13.
Michelassi
, V.
, Chen
, L. W.
, Pichler
, R.
, and Sandberg
, R. D.
, 2015
, “Compressible Direct Numerical Simulation of Low-Pressure Turbines—Part II: Effect of Inflow Disturbances
,” ASME J. Turbomach.
, 137
(7
), p. 071005
. 14.
Pichler
, R.
, Sandberg
, R. D.
, Michelassi
, V.
, and Bhaskaran
, R.
, 2016
, “Investigation of the Accuracy of RANS Models to Predict the Flow Through a Low-Pressure Turbine
,” ASME J. Turbomach.
, 138
(12
), p. 121009
. 15.
Przytarski
, P. J.
, and Wheeler
, A. P. S.
, 2020
, “The Effect of Gapping on Compressor Performance
,” ASME J. Turbomach.
, 142
(12
), p. 121006
. 16.
Przytarski
, P. J.
, and Wheeler
, A. P. S.
, 2021
, “Accurate Prediction of Loss Using High Fidelity Methods
,” ASME J. Turbomach.
, 143
(3
), p. 031008
. 17.
Hodson
, H. P.
, and Howell
, R. J.
, 2005
, “Blade Row Interactions, Transition, and High-Lift Aerofoils in Low-Pressure Turbines
,” Annu. Rev. Fluid Mech.
, 37
(1
), pp. 71
–98
. 18.
Liu
, Y.
, Wang
, F.
, Zhao
, S.
, and Tang
, Y.
, 2024
, “A Novel Framework for Predicting Active Flow Control by Combining Deep Reinforcement Learning and Masked Deep Neural Network
,” Phys. Fluids
, 36
(3
), p. 037112
. 19.
Liu
, Y.
, Zhao
, S.
, Wang
, F.
, and Tang
, Y.
, 2024
, “A Novel Method for Predicting Fluid–Structure Interaction With Large Deformation Based on Masked Deep Neural Network
,” Phys. Fluids
, 36
(2
), p. 027103
. 20.
Wang
, D. X.
, 2014
, “An Improved Mixing-Plane Method for Analyzing Steady Flow Through Multiple-Blade-Row Turbomachines
,” ASME J. Turbomach.
, 136
(8
), p. 081003
. 21.
Rai
, M. M.
, 1989
, “Three-Dimensional Navier-Stokes Simulations of Turbine Rotor–Stator Interaction. Part I—Methodology
,” J. Propuls. Power
, 5
(3
), pp. 305
–311
. 22.
He
, L.
, 2010
, “Fourier Methods for Turbomachinery Applications
,” Prog. Aerosp. Sci.
, 46
(8
), pp. 329
–341
. 23.
Liu
, Y.
, Lu
, L. P.
, 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
. 24.
Liu
, Y.
, Yu
, X.
, and Liu
, B.
, 2008
, “Turbulence Models Assessment for Large-Scale Tip Vortices in an Axial Compressor Rotor
,” J. Propuls. Power
, 24
(1
), pp. 15
–25
. 25.
Yan
, H.
, Liu
, Y.
, and Lu
, L.
, 2019
, “Turbulence Anisotropy Analysis in a Highly Loaded Linear Compressor Cascade
,” Aerosp. Sci. Technol.
, 91
, pp. 241
–254
. 26.
Liu
, Y.
, Luo
, P.
, and Tang
, Y.
, 2024
, “Improved Prediction of Turbomachinery Flows Using Reynolds Stress Model With γ Transition Model
,” Aerosp. Sci. Technol.
, 144
, p. 108812
. 27.
Li
, W.
, and Liu
, Y.
, 2023
, “Study of Limits to the Rotation Function in the SA-RC Turbulence Model
,” Chin. J. Aeronaut.
, 36
(1
), pp. 246
–265
. 28.
Li
, W.
, and Liu
, Y.
, 2022
, “Numerical Investigation of Corner Separation Flow Using Spalart-Allmaras Model With Various Modifications
,” Aerosp. Sci. Technol.
, 127
, p. 107682
. 29.
He
, X.
, Zhao
, F.
, and Vahdati
, M.
, 2022
, “Detached Eddy Simulation: Recent Development and Application to Compressor Tip Leakage Flow
,” ASME J. Turbomach.
, 144
(1
), p. 011009
. 30.
He
, L.
, 2021
, “Averaging for High Fidelity Modeling—Toward Large Eddy Simulations in Multi-passage Multi-row Configurations
,” ASME J. Turbomach.
, 143
(2
), p. 021002
. 31.
Fard Afshar
, N.
, Möller
, F. M.
, Henninger
, S.
, Kožulović
, D.
, Morsbach
, C.
, Bechlars
, P.
, and Jeschke
, P.
, 2024
, “Assessment of the DDES-γ Model for the Simulation of a Highly Loaded Turbine Cascade
,” ASME J. Turbomach.
, 146
(1
), p. 011011
. 32.
Gao
, Y.
, and Liu
, Y.
, 2020
, “Modification of DDES Based on SST kω Model for Tip Leakage Flow in Turbomachinery
,” ASME Paper No. GT2020-14851.33.
Spalart
, P. R.
, 1997
, “Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach
,” Proceedings of First AFOSR International Conference on DNS/LES
, Louisiana Tech University, Ruston, LA
, Aug. 4–8
, Greyden Press, pp. 137
–148
.34.
Spalart
, P. R.
, Deck
, S.
, Shur
, M. L.
, Squires
, K. D.
, Strelets
, M. K.
, and Travin
, A.
, 2006
, “A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities
,” Theor. Comput. Fluid Dyn.
, 20
(3
), pp. 181
–195
. 35.
Liu
, Y.
, Yan
, H.
, Lu
, L.
, and Li
, Q.
, 2016
, “Investigation of Vortical Structures and Turbulence Characteristics in Corner Separation in a Linear Compressor Cascade Using DDES
,” ASME J. Fluids Eng.
, 139
(2
), p. 021107
. 36.
Liu
, Y.
, Zhong
, L.
, and Lu
, L.
, 2019
, “Comparison of DDES and URANS for Unsteady Tip Leakage Flow in an Axial Compressor Rotor
,” ASME J. Fluids Eng.
, 141
(12
), p. 121405
. 37.
Yan
, H.
, Liu
, Y.
, Li
, Q.
, and Lu
, L.
, 2018
, “Turbulence Characteristics in Corner Separation in a Highly Loaded Linear Compressor Cascade
,” Aerosp. Sci. Technol.
, 75
, pp. 139
–154
. 38.
Nikitin
, N. V.
, Nicoud
, F.
, Wasistho
, B.
, Squires
, K. D.
, and Spalart
, P. R.
, 2000
, “An Approach to Wall Modeling in Large-Eddy Simulations
,” Phys. Fluids
, 12
(7
), pp. 1629
–1632
. 39.
Piomelli
, U.
, Balaras
, E.
, Pasinato
, H.
, Squires
, K. D.
, and Spalart
, P. R.
, 2003
, “The Inner–Outer Layer Interface in Large-Eddy Simulations With Wall-Layer Models
,” Int. J. Heat Fluid Flow
, 24
(4
), pp. 538
–550
. 40.
Wang
, G.
, and Liu
, Y.
, 2022
, “A Grid-Adaptive Simulation Model for Turbulent Flow Predictions
,” Phys. Fluids
, 34
(7
), p. 075125
. 41.
Bakhtiari
, F.
, Wartzek
, F.
, Leichtfuss
, S.
, Schiffer
, H.-P.
, Goinis
, G.
, and Nicke
, E.
, 2015
, “Design and Optimization of a New Stator for the Transonic Compressor Rig at TU Darmstadt
,” DGLRK 2015-370225.42.
Berdanier
, R. A.
, and Key
, N. L.
, 2015
, “The Effects of Tip Leakage Flow on the Performance of Multistage Compressors Used in Small Core Engine Applications
,” ASME J. Eng. Gas Turbines Power
, 138
(5
), p. 052605
. 43.
Eitenmüller
, J.
, Wilhelm
, M.
, Gresser
, L.
, Ostrowksi
, T.
, Leichtfuss
, S.
, Schiffer
, H.-P.
, Lyko
, C.
, and Naik
, S.
, “Highly Accurate Delta Efficiency Measurements at the Large Scale Turbine Rig
,” ASME Paper No. GT2019-90294.44.
Brandstetter
, C.
, Jüngst
, M.
, and Schiffer
, H.-P.
, 2018
, “Measurements of Radial Vortices, Spill Forward, and Vortex Breakdown in a Transonic Compressor
,” ASME J. Turbomach.
, 140
(6
), p. 061004
. 45.
Klausmann
, F.
, Franke
, D.
, Foret
, J.
, and Schiffer
, H.-P.
, 2022
, “Transonic Compressor Darmstadt—Open Test Case Introduction of the TUDa Open Test Case
,” J. Global Power Propuls. Soc.
, 6
, pp. 318
–329
. 46.
He
, X.
, Zhu
, M.
, Xia
, K.
, Fabian
, K. S.
, Teng
, J.
, and Vahdati
, M.
, 2023
, “Validation and Verification of RANS Solvers for TUDa-GLR-OpenStage Transonic Axial Compressor
,” J. Global Power Propuls. Soc.
, 7
, pp. 13
–29
. 47.
Deng
, H.
, He
, X.
, Zhu
, M.
, Klausmann
, F.
, and Teng
, J.
, 2023
, “Unsteady Flow Phenomenon in the TUDa-GLR-OpenStage Compressor: URANS Observations
,” GPPS Conference Hong Kong
, GPPS-TC-2023-002.48.
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
. 49.
Liu
, Y.
, and Tang
, Y.
, 2019
, “An Elliptical Region Method for Identifying a Vortex With Indications of Its Compressibility and Swirling Pattern
,” Aerosp. Sci. Technol.
, 95
, p. 105448
. 50.
Xie
, N.
, Tang
, Y.
, and Liu
, Y.
, 2023
, “High-Fidelity Numerical Simulation of Unsteady Cavitating Flow Around a Hydrofoil
,” J. Hydrodyn.
, 35
(1
), pp. 1
–16
. 51.
Hou
, J.
, Liu
, Y.
, Zhong
, L.
, Zhong
, W.
, and Tang
, Y.
, 2022
, “Effect of Vorticity Transport on Flow Structure in the Tip Region of Axial Compressors
,” Phys. Fluids
, 34
(5
), p. 055102
. 52.
Hou
, J.
, and Liu
, Y.
, 2023
, “Evolution of Unsteady Vortex Structures in the Tip Region of an Axial Compressor Rotor
,” Phys. Fluids
, 35
(4
), p. 045107
. 53.
Valkov
, T. V.
, and Tan
, C. S.
, 1999
, “Effect of Upstream Rotor Vortical Disturbances on the Time-Averaged Performance of Axial Compressor Stators: Part 1—Framework of Technical Approach and Wake–Stator Blade Interactions
,” ASME J. Turbomach.
, 121
(3
), pp. 377
–386
. 54.
Greitzer
, E. M.
, Tan
, C. S.
, and Graf
, M. B.
, 2004
, Internal Flow: Concepts and Applications
, Cambridge University Press
, Cambridge
, Chapter 6
.55.
Lumley
, J. L.
, 1967
, “The Structure of Inhomogeneous Turbulent Flows,” Atmospheric Turbulence and Radio Wave Propagation
, A. M.
Yaglom
and V. I.
Tatarsky
, eds., Nauka
, Moscow
, pp. 166
–178
.56.
Nekkanti
, A.
, and Schmidt
, O. T.
, 2021
, “Frequency–Time Analysis, Low-Rank Reconstruction and Denoising of Turbulent Flows Using SPOD
,” J. Fluid Mech.
, 926
, p. A26
. 57.
He
, X.
, Zhao
, F.
, Rigas
, G.
, and Vahdati
, M.
, 2021
, “Spectral Proper Orthogonal Decomposition of Compressor Tip Leakage Flow
,” Phys. Fluids
, 33
(10
), p. 105105
. 58.
Towne
, A.
, Schmidt
, O. T.
, and Colonius
, T.
, 2018
, “Spectral Proper Orthogonal Decomposition and Its Relationship to Dynamic Mode Decomposition and Resolvent Analysis
,” J. Fluid Mech.
, 847
, pp. 821
–867
. 
