A planar duct flow configuration with a cross-flow injected from a longitudinal slit close to the upper wall of the duct is studied by using a direct numerical simulation approach to explore the underlying flow mechanism in relation to the tip-leakage vortex (TLV), which is one of the most important flow phenomena in turbomachinery. Major characteristics of TLV in a rotor of turbomachinery are identified in the current flow model. The analysis of mean and instantaneous flow fields reveals that the interaction between the main (axial) flow and jet (cross) flow is the primary source of the generation of the TLV. The evolution of the TLV is then investigated, and a vortex breakup phenomenon is identified. The evolution of TLV can be divided into three phases, i.e., the formation phase, the breakup phase, and the diffusion phase. Mean streamlines and turbulence kinetic energy (TKE) budgets are analyzed, showing that the high TKE central spot in the formation phase is due to the interaction between highly swirling vortex filaments and mean velocity gradient. In the outer part of the TLV, the TKE is mainly produced in the shear-layer and transported toward the center by the turbulence transport.
REFERENCES
1.
J. D.
Denton
, “Some limitations of turbomachinery CFD
,” in ASME Turbo Expo 2010: Power for Land, Sea, and Air
(American Society of Mechanical Engineers
, 2010
), pp. 735
–745
.2.
T. C.
Booth
, P. R.
Dodge
, and H. K.
Hepworth
, “Rotor-tip leakage: Part I—Basic methodology
,” J. Eng. Gas Turbines Power
104
(1
), 154
–161
(1982
).3.
M.
Inoue
, M.
Kuroumaru
, and M.
Fukuhara
, “Behavior of tip leakage flow behind an axial compressor rotor
,” J. Eng. Gas Turbines Power
108
(1
), 7
–14
(1986
).4.
C. T.
Hsiao
and G. L.
Chahine
, “Scaling of tip vortex cavitation inception noise with a bubble dynamics model accounting for nuclei size distribution
,” J. Fluids Eng.
127
(1
), 55
–65
(2005
).5.
J. J.
Adamczyk
, M. L.
Celestina
, and E. M.
Greitzer
, “The role of tip clearance in high-speed fan stall
,” J. Turbomach.
115
(1
), 28
–39
(1993
).6.
C. S.
Tan
, I.
Day
, S.
Morris
, and A.
Wadia
, “Spike-type compressor stall inception, detection, and control
,” Annu. Rev. Fluid Mech.
42
, 275
–300
(2010
).7.
Z.
Xie
, Y.
Liu
, X.
Liu
, D.
Sun
, L.
Lu
, and X.
Sun
, “Computational model for stall inception and nonlinear evolution in axial flow compressors
,” J. Propul. Power
34
(3
), 720
–729
(2017
).8.
J.
Wells
, A.
Salem-Said
, and S. A.
Ragab
, “Effects of turbulence modeling on RANS simulations of tip vortices
,” in 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
(AIAA
, 2010
), p. 1104
.9.
M.
Furukawa
, M.
Inoue
, K.
Saiki
, and K.
Yamada
, “The role of tip leakage vortex breakdown in compressor rotor aerodynamics
,” J. Turbomach.
121
(3
), 469
–480
(1999
).10.
Y.
Liu
, X.
Yu
, and B.
Liu
, “Turbulence models assessment for large-scale tip vortices in an axial compressor rotor
,” J. Propul. Power
24
(1
), 15
–25
(2008
).11.
12.
Y.
Gao
, Y.
Liu
, L.
Zhong
, J.
Hou
, and L.
Lu
, “Study of the standard k-ε model for tip leakage flow in an axial compressor rotor
,” Int. J. Turbo Jet-Engines
33
(4
), 353
–360
(2016
).13.
X.
Yu
and B.
Liu
, “Stereoscopic PIV measurement of unsteady flows in an axial compressor stage
,” Exp. Therm. Fluid Sci.
31
(8
), 1049
–1060
(2007
).14.
H.
Du
, X.
Yu
, Z.
Zhang
, and B.
Liu
, “Relationship between the flow blockage of tip leakage vortex and its evolutionary procedures inside the rotor passage of a subsonic axial compressor
,” J. Therm. Sci.
22
(6
), 522
–531
(2013
).15.
R. L.
Miorini
, H.
Wu
, and J.
Katz
, “The internal structure of the tip leakage vortex within the rotor of an axial waterjet pump
,” J. Turbomach.
134
(3
), 031018
(2012
).16.
H.
Wu
, R. L.
Miorini
, D.
Tan
, and J.
Katz
, “Turbulence within the tip-leakage vortex of an axial waterjet pump
,” AIAA J.
50
(11
), 2574
–2587
(2012
).17.
Y.
Li
, C.
Huang
, and J.
Katz
, “Measurements and characterization of turbulence in the tip region of an axial compressor rotor
,” J. Turbomach.
139
(12
), 121003
(2017
).18.
J.
Decaix
, G.
Balarac
, M.
Dreyer
, M.
Farhat
, and C.
Münch
, “RANS and LES computations of the tip-leakage vortex for different gap widths
,” J. Turbul.
16
(4
), 309
–341
(2015
).19.
Y.
Liu
, L.
Lu
, L.
Fang
, and F.
Gao
, “Modification of Spalart–Allmaras model with consideration of turbulence energy backscatter using velocity helicity
,” Phys. Lett. A
375
(24
), 2377
–2381
(2011
).20.
K. B.
Lee
, M.
Wilson
, and M.
Vahdati
, “Validation of a numerical model for predicting stalled flows in a low-speed fan—Part I: Modification of Spalart–Allmaras turbulence model
,” J. Turbomach.
140
(5
), 051008
(2018
).21.
D.
You
, M.
Wang
, P.
Moin
, and R.
Mittal
, “Effects of tip-gap size on the tip-leakage flow in a turbomachinery cascade
,” Phys. Fluids
18
(10
), 105102
(2006
).22.
D.
You
, M.
Wang
, P.
Moin
, and R.
Mittal
, “Large-eddy simulation analysis of mechanisms for viscous losses in a turbomachinery tip-clearance flow
,” J. Fluid Mech.
586
, 177
–204
(2007
).23.
D.
You
, M.
Wang
, P.
Moin
, and R.
Mittal
, “Vortex dynamics and low-pressure fluctuations in the tip-clearance flow
,” J. Fluids Eng.
129
(8
), 1002
–1014
(2007
).24.
A.
Pogorelov
, M.
Meinke
, and W.
Schröder
, “Cut-cell method based large-eddy simulation of tip-leakage flow
,” Phys. Fluids
27
(7
), 075106
(2015
).25.
S. M. A.
Moghadam
, M.
Meinke
, and W.
Schröder
, “Analysis of tip-leakage flow in an axial fan at varying tip-gap sizes and operating conditions
,” Comput. Fluids
183
(15
), 107
–129
(2019
).26.
J.
Boudet
, A.
Cahuzac
, P.
Kausche
, and M. C.
Jacob
, “Zonal large-eddy simulation of a fan tip-clearance flow, with evidence of vortex wandering
,” J. Turbomach.
137
(6
), 061001
(2015
).27.
J.
Boudet
, J.
Caro
, B.
Li
, E.
Jondeau
, and M. C.
Jacob
, “Zonal large-eddy simulation of a tip leakage flow
,” Int. J. Aeroacoust.
15
(6-7
), 646
–661
(2016
).28.
Y.
Liu
, L.
Zhong
, and L.
Lu
, “Comparison of DDES and URANS for unsteady tip leakage flow in an axial compressor rotor
,” J. Fluids Eng.
141
(12
), 121405
(2019
).29.
X.
Su
, X.
Ren
, X.
Li
, and C.
Gu
, “Unsteadiness of tip leakage flow in the detached-eddy simulation on a transonic rotor with vortex breakdown phenomenon
,” Energies
12
(5
), 954
(2019
).30.
P.
Moin
and K.
Mahesh
, “Direct numerical simulation: A tool in turbulence research
,” Annu. Rev. Fluid Mech.
30
, 539
–578
(1998
).31.
D. A.
Rains
, “Tip clearance flows in axial flow compressors and pumps
,” Ph.D. thesis, California Institute of Technology
, Pasadena, CA
, 1954
.32.
B.
Lakshminarayana
, “Methods of predicting the tip clearance effects in axial flow turbomachinery
,” J. Basic Eng.
92
(3
), 467
–480
(1970
).33.
G. T.
Chen
, E. M.
Greitzer
, C. S.
Tan
, and F. E.
Marble
, “Similarity analysis of compressor tip clearance flow structure
,” J. Turbomach.
113
(2
), 260
–269
(1991
).34.
A. P. S.
Wheeler
and R. D.
Sandberg
, “Direct numerical simulations of a transonic tip flow with free-stream disturbances
,” in ASME 2013 Turbine Blade Tip Symposium
(ASME
, 2013
), Paper No. V001T01A002
.35.
A. P. S.
Wheeler
, R. D.
Sandberg
, N. D.
Sandham
, R.
Pichler
, V.
Michelassi
, and G. M.
Laskowski
, “Direct numerical simulations of a high pressure turbine vane
,” J. Turbomach.
138
(7
), 071003
(2016
).36.
A. P. S.
Wheeler
and R. D.
Sandberg
, “Numerical investigation of the flow over a model transonic turbine blade tip
,” J. Fluid Mech.
803
, 119
–143
(2016
).37.
I. Z.
Naqavi
, J. C.
Tyacke
, and P. G.
Tucker
, “Direct numerical simulation of a wall jet: Flow physics
,” J. Fluid Mech.
852
, 507
–542
(2018
).38.
A. R.
Karagozian
, “The jet in crossflow
,” Phys. Fluids
26
(10
), 101303
(2014
).39.
L.
Zhu
, W.
Zhang
, J.
Kou
et al., “Machine learning methods for turbulence modeling in subsonic flows around airfoils
,” Phys. Fluids
31
(1
), 015105
(2019
).40.
Z.
Wang
, K.
Luo
, D.
Li
et al., “Investigations of data-driven closure for subgrid-scale stress in large-eddy simulation
,” Phys. Fluids
30
(12
), 125101
(2018
).41.
Y.
Gao
, Y.
Liu
, and L.
Lu
, “Investigation of turbulence characteristics in a tip leakage flow model using large-eddy simulation
,” in ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition
(ASME
, 2019
), Paper No. GT2019-90844.42.
Y.
Gao
and Y.
Liu
, “A flow model for tip leakage flow in turbomachinery using a square duct with a longitudinal slit
,” Aerosp. Sci. Technol.
95
, 105460
(2019
).43.
J.
Fang
, Y.
Yao
, Z.
Li
, and L.
Lu
, “Investigation of low-dissipation monotonicity-preserving scheme for direct numerical simulation of compressible turbulent flows
,” Comput. Fluids
104
, 55
–72
(2014
).44.
J.
Fang
, Y.
Yao
, A. A.
Zheltovodov
, Z.
Li
, and L.
Lu
, “Direct numerical simulation of supersonic turbulent flows around a tandem expansion-compression corner
,” Phys. Fluids
27
, 125104
(2015
).45.
W.
Ni
, L.
Lu
, C.
Le Ribault
, and J.
Fang
, “Direct numerical simulation of supersonic turbulent boundary layer with spanwise wall oscillation
,” Energies
9
(3
), 154
(2016
).46.
J.
Fang
, Y.
Yao
, A. A.
Zheltovodov
, and L.
Lu
, “Investigation of three-dimensional shock wave/turbulent-boundary-layer interaction initiated by a single fin
,” AIAA J.
55
(2
), 509
–523
(2017
).47.
W.
Ni
, L.
Lu
, J.
Fang
, C.
Moulinec
, and Y.
Yao
, “Large-scale streamwise vortices in turbulent channel flow induced by active wall actuations
,” Flow, Turbul. Combust.
100
(3
), 651
–673
(2017
).48.
W.
Ni
, L.
Lu
, J.
Fang
, C.
Moulinec
, D. R.
Emerson
, and Y.
Yao
, “Flow separation control over a rounded ramp with spanwise alternating wall actuation
,” Phys. Fluids
31
(1
), 015101
(2019
).49.
S. K.
Lele
, “Compact finite difference schemes with spectral-like resolution
,” J. Comput. Phys.
103
, 16
–42
(1992
).50.
J.
Fang
, F.
Gao
, C.
Moulinec
, and D. R.
Emerson
, “An improved parallel compact scheme for domain-decoupled simulation of turbulence
,” Int. J. Numer. Method Fluids
90
(10
), 479
–500
(2019
).51.
N. D.
Sandham
, Q.
Li
, and H. C.
Yee
, “Entropy splitting for high–order numerical simulation of compressible turbulence
,” J. Comput. Phys.
178
(2
), 307
–322
(2002
).52.
D. V.
Gaitonde
and M. R.
Visbal
, “Pade-type higher-order boundary filters for the Navier-Stokes equations
,” AIAA J.
38
(11
), 2103
–2112
(2000
).53.
S.
Gottlieb
and C. W.
Shu
, “Total variation diminishing Runge-Kutta schemes
,” Math. Comput.
67
(221
), 73
–85
(1998
).54.
P.
Sagaut
, “Theoretical background: Large-eddy simulation
,” in Large-Eddy Simulation for Acoustics
, 1st ed. (Cambridge University Press
, Cambridge, UK
, 2007
), pp. 89
–127
.55.
E.
Lenormand
, P.
Sagaut
, and L. T.
Phuoc
, “Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number
,” Int. J. Numer. Methods Fluids
32
(4
), 369
–406
(2000
).56.
J. D. H.
Rudy
and J. C.
Strikwerda
, “A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations
,” J. Comput. Phys.
36
(1
), 55
–70
(1980
).57.
J. W.
Kim
and D. J.
Lee
, “Generalized characteristic boundary conditions for computational aeroacoustics
,” AIAA J.
38
(11
), 2040
–2049
(2000
).58.
P.
Orlandi
and S.
Pirozzoli
, “DNS of transitional and turbulent flows in rectangular ducts
,” e-print arXiv:1907.07987v1.59.
R. D.
Moser
, J.
Kim
, and N. N.
Mansour
, “Direct numerical simulation of turbulent channel flow up to Reτ=590
,” Phys. Fluids
11
(4
), 943
–945
(1999
).60.
J.
Zhou
, R. J.
Adrian
, S.
Balachandar
, and T. M.
Kendall
, “Mechanisms for generating coherent packets of hairpin vortices in channel flow
,” J. Fluid Mech.
387
, 353
–396
(1999
).61.
S.
Pirozzoli
, M.
Bernardini
, and F.
Grasso
, “Characterization of coherent vortical structures in a supersonic turbulent boundary layer
,” J. Fluid Mech.
613
, 205
–231
(2008
).62.
S. J.
Kline
, W. C.
Reynolds
, and F. A.
Schraub
, “The structure of turbulent boundary layers
,” J. Fluid Mech.
30
, 741
–773
(1967
).63.
S. G.
Ruben
and P. K.
Khosla
, “Polynomial interpolation methods for viscous flow calculations
,” J. Comput. Phys.
24
, 217
–244
(1977
).64.
U.
Ghia
, K. N.
Ghia
, and C. T.
Shin
, “High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
,” J. Comput. Phys.
48
, 387
–411
(1982
).65.
M.
Dreyer
, J.
Decaix
, C.
Münch
, and M.
Farhat
, “Mind the gap—A new insight on the tip leakage vortex using stereo PIV
,” Exp. Fluids
55
(11
), 1849
(2014
).© 2019 Author(s).
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