Skip to main content Accessibility help

The effect of aspect ratio on the wake structure of finite wall-mounted square cylinders

  • Yendrew Yauwenas (a1), Ric Porteous (a2), Danielle J. Moreau (a1) and Con J. Doolan (a1)


This paper presents a combined experimental and large-eddy simulation study to characterise the effect of aspect ratio on the near-wake structure of a square finite wall-mounted cylinder (FWMC). The cylinder aspect ratios (span $L$ to width $W$ ) investigated in the experiments were $1.4\leqslant L/W\leqslant 21.4$ and the oncoming boundary-layer thicknesses were $1.3W$ and $0.9W$ at a Reynolds number based on cylinder width of $1.4\times 10^{4}$ and $1.1\times 10^{4}$ , respectively. In complementary simulations, the cylinder aspect ratios investigated were 1.4, 4.3, 10 and 18.6. The cylinder wake structure was visualised in three-dimensional space using a vortex core detection method and decomposed to its oscillation modes using the spectral proper orthogonal decomposition (SPOD) technique. A parametric diagram is proposed to predict whether the time-averaged wake structure is a dipole or a quadrupole pattern, based on oncoming boundary-layer height and aspect ratio. Cellular shedding occurs when the aspect ratio is high with up to three shedding cells occurring across the span for aspect ratios $L/W>18$ . Each of these cells sheds at a distinct frequency, as evidenced by the spectral content of the surface pressure measured on the side face and the near-wake velocity. Amplitude modulation is also observed in the vortex shedding, which explains the amplitude modulation of the acoustic pressure emitted by square FWMCs. SPOD is shown to be a viable method to identify the occurrence of cellular shedding in the wake.


Corresponding author

Email address for correspondence:


Hide All
Becker, S., Hahn, C., Kaltenbacher, M. & Lerch, R. 2008 Flow-induced sound of wall-mounted cylinders with different geometries. AIAA J. 46 (9), 22652281.10.2514/1.34865
Behera, S. & Saha, A. K. 2019 Characteristics of the flow past a wall-mounted finite-length square cylinder at low Reynolds number with varying boundary layer thickness. J. Fluids Engng 141 (6), 061204–061204–17.
Bendat, J. S. & Piersol, A. G. 2010 Random Data: Analysis and Measurement Procedures, 4th edn. John Wiley and Sons.10.1002/9781118032428
Bourgeois, J. A., Sattari, P. & Martinuzzi, R. J. 2011 Alternating half-loop shedding in the turbulent wake of a finite surface-mounted square cylinder with a thin boundary layer. Phys. Fluids 23 (9), 095101.10.1063/1.3623463
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21 (2), 91108.
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1 (02), 191226.10.1017/S0022112056000135
Curle, N. 1955 The influence of solid boundaries upon aerodynamic sound. Proc. R. Soc. Lond. A 231 (1187), 505514.
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.10.1017/CBO9780511616938
Etzolt, F. & Fiedler, H. 1976 The near-wake structures of a cantilevered cylinder in cross flow. Z. Flugwiss. 24, 7782.
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 17601765.10.1063/1.857955
Hearst, R. J., Gomit, G. & Ganapathisubramani, B. 2016 Effect of turbulence on the wake of a wall-mounted cube. J. Fluid Mech. 804, 513530.10.1017/jfm.2016.565
Holman, J. 2010 Experimental Methods for Engineers. McGraw-Hill Education.
Hosseini, Z., Bourgeois, J. A. & Martinuzzi, R. J. 2013 Large-scale structures in dipole and quadrupole wakes of a wall-mounted finite rectangular cylinder. Exp. Fluids 54, 9.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.10.1017/S0022112095000462
von Kármán, T.1931 Mechanical similitude and turbulence. Technical Memorandum 611, NASA.
Kawamura, T., Hiwada, M., Hibino, T., Mabuchi, I. & Kumada, M. 1984 Flow around a finite circular cylinder on a flat plate (cylinder height greater than turbulent boundary layer thickness). Bull. Japan Soc. Mech. Engrs 27 (232), 21422151.10.1299/jsme1958.27.2142
Kim, S. E. 2004 Large eddy simulation using unstructured meshes and dynamic subgrid-scale turbulence models. In 34th AIAA Fluid Dynamics Conference and Exhibit, Portland, Oregon. AIAA Paper 2004-2548.
Lee, B. E. 1975 The effect of turbulence on the surface pressure field of a square prism. J. Fluid Mech. 69 (2), 263282.10.1017/S0022112075001437
Lee, L. 1997 Wake structure behind a circular cylinder with a free end. Proc. Heat Transfer Fluid Mech. Inst. 35, 241251.
Lilly, D. K. 1992 A proposed modification of the germano subgrid-scale closure method. Phys. Fluids A 4 (3), 633635.10.1063/1.858280
Mason, P. J. & Morton, B. R. 1987 Trailing vortices in the wakes of surface-mounted obstacles. J. Fluid Mech. 175, 247293.10.1017/S0022112087000387
Moreau, D. & Doolan, C. 2013 Flow-induced sound of wall-mounted finite length cylinders. AIAA J. 51, 24932502.10.2514/1.J052391
Okamoto, S. & Sunabashiri, Y. 1992 Vortex shedding from a circular cylinder of finite length places on a ground plane. Trans. ASME 114 (4), 512521.
Park, C. W. & Lee, S. J. 2000 Free-end effects on the near wake flow structure behind a finite circular cylinder. J. Wind Engng Ind. Aerodyn. 88 (2–3), 231246.10.1016/S0167-6105(00)00051-9
Passchier-Vermeer, W. & Passchier, W. F. 2000 Noise exposure and public health. Environ. Health Perspect. 108 (Suppl 1), 123131.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.10.1017/CBO9780511840531
Porteous, R.2016 The aeroacoustics of finite wall-mounted cylinders. PhD thesis, University of Adelaide.10.1017/jfm.2017.682
Porteous, R., Moreau, D. J. & Doolan, C. J. 2014 A review of flow-induced noise from finite wall-mounted cylinders. J. Fluids Struct. 51, 240254.10.1016/j.jfluidstructs.2014.08.012
Porteous, R., Moreau, D. J. & Doolan, C. J. 2017 The aeroacoustics of finite wall-mounted square cylinders. J. Fluid Mech. 832, 287328.10.1017/jfm.2017.682
Roache, P. J. 1997 Quantification of uncertainty in computational fluid dynamics. Annu. Rev. Fluid Mech. 29 (1), 123160.10.1146/annurev.fluid.29.1.123
Sakamoto, H. & Arie, M. 1983 Vortex shedding from a rectangular prism and a circular cylinder placed vertically in a turbulent boundary layer. J. Fluid Mech. 126, 147165.10.1017/S0022112083000087
Smagorinsky, J. 1964 Some aspects of the general circulation. Q. J. R. Meteorol. Soc. 90 (383), 114.10.1002/qj.49709038302
Sumner, D., Heseltine, J. L. & Dansereau, O. J. P. 2004 Wake structure of a finite circular cylinder of small aspect ratio. Exp. Fluids 37 (5), 720730.10.1007/s00348-004-0862-7
Tieleman, H. W. & Akins, R. E. 1996 The effect of incident turbulence on the surface pressures of surface-mounted prisms. J. Fluids Struct. 10 (4), 367393.10.1006/jfls.1996.0024
Tominaga, Y., Mochida, A., Yoshie, R., Kataoka, H., Nozu, T., Yoshikawa, M. & Shirasawa, T. 2008 AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. J. Wind Engng Ind. Aerodyn. 96 (10–11), 17491761.10.1016/j.jweia.2008.02.058
Towne, A., Schmidt, O. T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821867.10.1017/jfm.2018.283
Van Doormaal, J. P. & Raithby, G. D. 1984 Enhancements of the simple method for predicting incompressible fluid flows. Numer. Heat Transfer 7 (2), 147163.10.1080/01495728408961817
Wagner, C., Hüttl, T. & Sagaut, P. 2007 Large-Eddy Simulation for Acoustics. Cambridge University Press.10.1017/CBO9780511546143
Wang, H. & Zhou, Y. 2009 The finite-length square cylinder near wake. J. Fluid Mech. 638, 453490.10.1017/S0022112009990693
Wang, H., Zhou, Y., Chan, C. K. & Lam, K. S. 2006 Effect of initial conditions on interaction between boundary layer and a wall-mounted finite-length-cylinder wake. Phys. Fluids 18, 065106.10.1063/1.2212329
Wang, H. F., Cao, H. L. & Zhou, Y. 2014 POD analysis of a finite-length cylinder near wake. Exp. Fluids 55, 17901805.10.1007/s00348-014-1790-9
Welch, P. D. 1967 The use of fast Fouier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. AU‐15, 7073.10.1109/TAU.1967.1161901
Wilcox, D. C. 2006 Turbulence Modeling for CFD. DCW Industries.
Wolf, W. R. & Lele, S. K. 2012 Trailing-edge noise predictions using compressible large-eddy simulation and acoustic analogy. AIAA J. 50 (11), 24232434.10.2514/1.J051638
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed