The compressible flows past a wavy-axis square cylinder are numerically carried out by means of the large-eddy simulation technique for two different free-stream Mach numbers ( and 0.85), which are less than the critical Mach number Mcr (). The Reynolds number based on the side-length of the wavy-axis square cylinder is chosen as . For comparison, the compressible flows around the corresponding normal square cylinder are also calculated. The control effects and mechanisms are systematically analyzed. Comparing the wavy-axis square cylinder with a normal square cylinder for and 0.85, about 23.5% and 8.1% drag reductions are acquired, respectively, and the fluctuating forces are suppressed significantly. Based on the analysis of drag decomposition, when , the drag reduction related to vortex force prevails over that relevant to compressible effect. Moreover, the wavy-axis square cylinder can also provide the effective control for type C moving shock. The effective drag reduction and suppression of fluctuating force obtained by the wavy-axis square cylinder are closely associated with the higher base-pressure and lower turbulent fluctuations in the near wake, which can be achieved by the strengthened compressibility and waviness effect of shear-layer. However, when approaches Mcr, the effective flow control from the wavy-axis square cylinder is attenuated due to the competition between strengthened compressibility and the waviness effect of the shear-layer.
References
1.
H.
Choi
, W. P.
Jeon
, and J.
Kim
, “Control of flow over a bluff body
,” Annu. Rev. Fluid Mech.
40
, 113
(2008
).2.
Y.
Oguma
, T.
Yamagata
, and N.
Fujisawa
, “Measurement of sound source distribution around a circular cylinder in a uniform flow by combined particle image velocimetry and microphone technique
,” J. Wind Eng. Ind. Aerodyn.
118
, 1
(2013
). 3.
B.
Chen
, X.
Yang
, G.
Chen
, X.
Tang
, J.
Ding
, and P.
Weng
, “Numerical study on the flow and noise control mechanism of wavy cylinder
,” Phys. Fluids
34
, 036108
(2022
).4.
D.
Gao
, Y.
Huang
, W. L.
Chen
, G.
Chen
, and H.
Li
, “Control of circular cylinder flow via bilateral splitter plates
,” Phys. Fluids
31
, 057105
(2019
).5.
A.
Mishra
, M.
Hanzla
, and A.
De
, “Passive control of the onset of vortex shedding in flow past a circular cylinder using slit
,” Phys. Fluids
32
, 013602
(2020
).6.
P.
Jüstel
, S.
Röhrborn
, P.
Frick
, V.
Galindo
, T.
Gundrum
, F.
Chindler
, F.
Stefani
, R.
Stepanov
, and T.
Vogt
, “Generating a tide-like flow in a cylindrical vessel by electromagnetic forcing
,” Phys. Fluids
32
, 097105
(2020
).7.
H.
Yu
, Z.
Xu
, and W. L.
Chen
, “Attenuation of vortex street by suction through the structured porous surface
,” Phys. Fluids
33
, 125101
(2021
).8.
C.
Zheng
, T.
Ji
, F.
Xie
, X.
Zhang
, H.
Zheng
, and Y.
Zheng
, “From active learning to deep reinforcement learning: Intelligent active flow control in suppressing vortex-induced vibration
,” Phys. Fluids
33
, 063607
(2021
).9.
H.
Du
, Q.
Zhang
, Q.
Li
, W.
Kong
, and L.
Yang
, “Drag reduction in cylindrical wake flow using porous material
,” Phys. Fluids
34
, 045102
(2022
).10.
C.
Xu
, L.
Zhao
, and J.
Sun
, “Large-eddy simulation of the compressible flow past a tabbed cylinder
,” Chin. Sci. Bull.
57
, 3203
(2012
).11.
J.
Cai
, T. L.
Chng
, and H. M.
Tsai
, “On vortical flows shedding from a bluff body with a wavy trailing edge
,” Phys. Fluids
20
, 064102
(2008
).12.
J. H.
Jung
and H. S.
Yoon
, “Large eddy simulation of flow over a twisted cylinder at a subcritical Reynolds number
,” J. Fluid Mech.
759
, 579
(2014
).13.
A.
Ahmed
and B.
Bays-Muchmore
, “Transverse flow over a wavy cylinder
,” Phys. Fluids A
4
, 1959
(1992
).14.
A.
Ahmed
, M. J.
Khan
, and B.
Bays-Muchmore
, “Experimental investigation of a three-dimensional bluff-body wake
,” AIAA J.
31
, 559
(1993
).15.
J. C.
Owen
, A. A.
Szewczyk
, and P. W.
Bearman
, “Suppression of Karman vortex shedding
,” Phys. Fluids
12
, S9
(2000
).16.
K.
Lam
, F. H.
Wang
, J. Y.
Li
, and R. M. C.
So
, “Experimental investigation of the mean and fluctuating forces of wavy (varicose) cylinders in a cross-flow
,” J. Fluids Struct.
19
, 321
(2004
).17.
K.
Lam
, F. H.
Wang
, and R. M. C.
So
, “Three-dimensional nature of vortices in the near wake of a wavy cylinder
,” J. Fluids Struct.
19
, 815
(2004
).18.
K.
Lam
and Y. F.
Lin
, “Large eddy simulation of flow around wavy cylinders at a subcritical Reynolds number
,” Int. J. Heat Fluid Flow
29
, 1071
(2008
).19.
K.
Lam
and Y. F.
Lin
, “Effects of wavelength and amplitude of a wavy cylinder in cross-flow at low Reynolds numbers
,” J. Fluid Mech.
620
, 195
(2009
).20.
K.
Lam
, Y. F.
Lin
, L.
Zou
, and Y.
Liu
, “Numerical simulation of flows around two unyawed and yawed wavy cylinders in tandem arrangement
,” J. Fluids Struct.
28
, 135
(2012
).21.
Y. F.
Lin
, H. L.
Bai
, M. M.
Alam
, W. G.
Zhang
, and K.
Lam
, “Effects of large spanwise wavelength on the wake of a sinusoidal wavy cylinder
,” J. Fluids Struct.
61
, 392
(2016
).22.
K.
Zhang
, H.
Katsuchi
, D.
Zhou
, H.
Yamada
, and J.
Lu
, “Large eddy simulation of flow over inclined wavy cylinders
,” J. Fluids Struct.
80
, 179
(2018
).23.
Y. Q.
Zhuang
, X. J.
Sun
, and D. G.
Huang
, “Numerical study of unsteady flows past a rotating wavy cylinder
,” Eur. J. Mech. B-Fluids
72
, 538
(2018
).24.
H. L.
Bai
, B.
Zhang
, and T. H.
New
, “The near wake of a sinusoidal wavy cylinder with a large spanwise wavelength using time-resolved particle image velocimetry
,” Exp. Fluids
60
, 15
(2019
).25.
H. L.
Bai
, M. M.
Alam
, N.
Gao
, and Y. F.
Lin
, “The near wake of a sinusoidal wavy cylinders: Three-dimensional POD
,” Int. J. Heat Fluid Flow
75
, 256
(2019
).26.
C. Y.
Xu
, L. W.
Chen
, and X. Y.
Lu
, “Large-eddy simulation of the compressible flow past a wavy cylinder
,” J. Fluid Mech.
665
, 238
(2010
).27.
C. Y.
Xu
and Z. Q.
Ni
, “Novel characteristics of wavy cylinder in supersonic turbulent flow
,” Eur. J. Mech. B-Fluids
67
, 158
(2018
).28.
C. Y.
Xu
, Y. T.
Zhang
, B.
Hou
, and J. H.
Sun
, “Numerical investigations of the compressible turbulent flow past wavy-axis cylinder
,” Fluid Dyn. Res.
51
, 055502
(2019
).29.
C. Y.
Xu
, B.
Hou
, Z.
Wang
, Y. T.
Zhang
, and J. H.
Sun
, “Effect of Mach number on the compressible flow past a wavy-axis cylinder
,” Aerosp. Sci. Technol.
104
, 105943
(2020
).30.
C. Y.
Xu
, L. W.
Chen
, and X. Y.
Lu
, “Effect of Mach number on transonic flow past a circular cylinder
,” Chin. Sci. Bull.
54
, 1886
(2009
).31.
H.
Jiang
and L.
Cheng
, “Flow separation around a square cylinder at low to moderate Reynolds numbers
,” Phys. Fluids
32
, 044103
(2020
).32.
S.
Murakami
, S.
Iizuka
, and R.
Ooka
, “CFD analysis of turbulent flow past square cylinder using dynamic LES
,” J. Fluids Struct.
13
, 1097
(1999
).33.
M.
Minguez
, C.
Brun
, R.
Pasquetti
, and E.
Serre
, “Experimental and high-order LES analysis of the flow in near-wall region of a square cylinder
,” Int. J. Heat Fluid Flow
32
, 558
(2011
).34.
F. X.
Trias
, A.
Gorobets
, and A.
Oliva
, “Turbulent flow around a square cylinder at Reynolds number 22000: A DNS study
,” Comput. Fluids
123
, 87
(2015
).35.
W.
Bai
, C. G.
Mingham
, D. M.
Causon
, and L.
Qian
, “Detached eddy simulation of turbulent flow around square and circular cylinders on Cartesian cut cells
,” Ocean Eng.
117
, 1
(2016
).36.
H.
Jiang
and L.
Cheng
, “Hydrodynamic characteristics of flow past a square cylinder at moderate Reynolds numbers
,” Phys. Fluids
30
, 104107
(2018
).37.
Y.
Cao
, T.
Tamura
, and H.
Kawai
, “Spanwise resolution requirements for the simulation of high-Reynolds-number flows past a square cylinder
,” Comput. Fluids
196
, 104320
(2020
).38.
T.
Nakagawa
, “Vortex shedding behind a square cylinder in transonic flows
,” J. Fluid Mech.
178
, 303
(1987
).39.
G. B.
Jacobs
, D. A.
Kopriva
, and F.
Mashayek
, “Compressible subsonic particle-laden flow over a square cylinder
,” J. Propul. Power
20
, 353
(2004
).40.
L.
Thombi
and Y.
Nakamura
, “Passive separation control on a square cylinder at transonic speed
,” Trans. Jpn. Soc. Aeronaut. Space Sci.
45
, 236
(2003
).41.
P. W.
Bearman
and J. C.
Owen
, “Reduction of bluff body drag and suppression of vortex shedding by the introduction of wavy separation lines
,” J. Fluids Struct.
12
, 123
(1998
).42.
R. M.
Darekar
and S. J.
Sherwin
, “Flow past a square-section cylinder with a wavy stagnation face
,” J. Fluid Mech.
426
, 263
(2001
).43.
W.
Xu
, L. Q.
Zhang
, and F.
Xu
, “Numerical study on the suppression of the oscillating wake of a square cylinder by a traveling wave wall
,” Int. J. Comput. Methods Eng. Sci. Mech.
20
, 48
(2019
).44.
Y.
Zheng
, H.
Rinoshika
, and A.
Rinoshika
, “Analyses on flow structures behind a wavy square cylinder based on continuous wavelet transform and dynamic mode decomposition
,” Ocean Eng.
216
, 108117
(2020
).45.
D.
Zhang
, A.
Rinoshika
, Y.
Zheng
, J.
Li
, and Y.
Zhang
, “Turbulent flow structures around a wavy square cylinder based on large eddy simulation
,” Fluid Dyn.
57
, 96
(2022
).46.
P.
Moin
, K.
Squires
, W.
Cabot
, and S.
Lee
, “A dynamic subgrid-scale model for compressible turbulence and scalar transport
,” Phys. Fluids A
3
, 2746
(1991
).47.
M. P.
Martín
, U.
Piomelli
, and G. V.
Candler
, “Subgrid-scale models for compressible large-eddy simulations
,” Theor. Comput. Fluid Dyn.
13
, 361
(2000
).48.
A.
Yoshizawa
, “Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling
,” Phys. Fluids
29
, 2152
(1986
).49.
L. W.
Chen
, C. Y.
Xu
, and X. Y.
Lu
, “Numerical investigation of the compressible flow past an aerofoil
,” J. Fluid Mech.
643
, 97
(2010
).50.
C. Y.
Xu
, T.
Zhou
, C. L.
Wang
, and J. H.
Sun
, “Applications of scale-adaptive simulation technique based on one-equation turbulence model
,” Appl. Math. Mech.
36
, 121
(2015
).51.
C. Y.
Xu
, Z.
Sun
, Y. T.
Zhang
, and J. H.
Sun
, “Improvement of the scale-adaptive simulation technique based on a compensated strategy
,” Eur. J. Mech. B-Fluids
81
, 1
(2020
).52.
C. Y.
Xu
and J. H.
Sun
, “Effect of von Karman length scale in scale adaptive simulation approach on the prediction of supersonic turbulent flow
,” Aerosp. Sci. Technol.
86
, 630
(2019
).53.
J. L.
Thomas
and M. D.
Salas
, “Far-field boundary conditions for transonic lifting solutions to the Euler equations
,” AIAA J.
24
, 1074
(1986
).54.
P.
Parnaudeau
, J.
Carlier
, D.
Heitz
, and E.
Lamballais
, “Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900
,” Phys. Fluids
20
, 085101
(2008
).55.
M.
Meyer
, S.
Hickel
, and N. A.
Adams
, “Assessment of implicit large-eddy simulation with a conservative immersed interface method for turbulent cylinder flow
,” Int. J. Heat Fluid Flow
31
, 368
(2010
).56.
J. Z.
Wu
, H. Y.
Ma
, and M. D.
Zhou
, Vorticity and Vortex Dynamics
(Springer-Verlag Press
, Berlin, Germany
, 2006
).57.
H.
Tijdeman
and R.
Seebass
, “Transonic flow past oscillating airfoils
,” Annu. Rev. Fluid Mech.
12
, 181
(1980
).58.
C. W.
Hamman
, J. C.
Klewicki
, and R. M.
Kirby
, “On the Lamb vector divergence in Navier-Stokes flows
,” J. Fluid Mech.
610
, 261
(2008
).59.
M. C.
Thompson
and K.
Hourigan
, “The shear-layer instability of a circular cylinder wake
,” Phys. Fluids
17
, 021702
(2005
).60.
S.
Pirozzoli
and F.
Grasso
, “Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M = 2.25
,” Phys. Fluids
18
, 065113
(2006
).61.
Y.
Na
and P.
Moin
, “The structure of wall-pressure fluctuations in turbulent boundary layers with adverse pressure gradient and separation
,” J. Fluid Mech.
377
, 347
(1998
).62.
W. K.
Blake
, Mechanics of Flow-Induced Sound and Vibration II
(Academic Press
, London, United Kingdom
, 1986
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
