Skip to main content Accessibility help

Large-eddy simulation of the compressible flow past a wavy cylinder

  • CHANG-YUE XU (a1), LI-WEI CHEN (a1) and XI-YUN LU (a1)


Numerical investigation of the compressible flow past a wavy cylinder was carried out using large-eddy simulation for a free-stream Mach number M = 0.75 and a Reynolds number based on the mean diameter Re = 2 × 105. The flow past a corresponding circular cylinder was also calculated for comparison and validation against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including drag reduction and fluctuating force suppression, shock and shocklet elimination, and three-dimensional separation and separated shear-layer instability, have been studied systematically. Because of the passive control of the flow over a wavy cylinder, the mean drag coefficient of the wavy cylinder is less than that of the circular cylinder with a drag reduction up to 26%, and the fluctuating force coefficients are significantly suppressed to be nearly zero. The vortical structures near the base region of the wavy cylinder are much less vigorous than those of the circular cylinder. The three-dimensional shear-layer shed from the wavy cylinder is more stable than that from the circular cylinder. The vortex roll up of the shear layer from the wavy cylinder is delayed to a further downstream location, leading to a higher-base-pressure distribution. The spanwise pressure gradient and the baroclinic effect play an important role in generating an oblique vortical perturbation at the separated shear layer, which may moderate the increase of the fluctuations at the shear layer and reduce the growth rate of the shear layer. The analysis of the convective Mach number indicates that the instability processes in the shear-layer evolution are derived from oblique modes and bi-dimensional instability modes and their competition. The two-layer structures of the shear layer are captured using the instantaneous Lamb vector divergence, and the underlying dynamical processes associated with the drag reduction are clarified. Moreover, some phenomena relevant to the compressible effect, such as shock waves, shocklets and shock/turbulence interaction, are analysed. It is found that the shocks and shocklets which exist in the circular cylinder flow are eliminated for the wavy cylinder flow and the wavy surface provides an effective way of shock control. As the shock/turbulence interaction is avoided, a significant drop of the turbulent fluctuations around the wavy cylinder occurs. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the passive control of the compressible flow past a wavy surface.


Corresponding author

Email address for correspondence:


Hide All
Adrian, R. J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure: homogeneous shear flow. J. Fluid Mech. 190, 531559.
Ahmed, A. & Bays-Muchmore, B. 1992 Transverse flow over a wavy cylinder. Phys. Fluids A 4, 19591967.
Ahmed, A., Khan, M. J. & Bays-Muchmore, B. 1993 Experimental investigation of a three-dimensional bluff-body wake. AIAA J. 31, 559563.
Anderson, E. & Szewczyk, A. 1997 Effects of a splitter plate on the near wake of a circular cylinder in 2 and 3-dimensional flow configurations. Exp. Fluids 23, 161174.
Arcas, D. & Redekopp, L. 2004 Aspects of wake vortex control through base blowing/suction. Phys. Fluids 16, 452456.
Barre, S., Quine, C. & Dussauge, J. P. 1994 Compressibility effects on the structure of supersonic mixing layers: experimental results. J. Fluid Mech. 259, 4778.
Batham, J. P. 1973 Pressure distributions on circular cylinders at critical Reynolds numbers. J. Fluid Mech. 57, 209228.
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539575.
Bogdanoff, D. W. 1983 Compressibility effects in turbulent shear layer. AIAA J. 21, 926927.
Bushnell, D. A. 2004 Shock wave drag reduction. Annu. Rev. Fluid Mech. 36, 8196.
Cai, J., Chng, T. L. & Tsai, H. M. 2008 On vortical flows shedding from a bluff body with a wavy trailing edge. Phys. Fluids 20, 064102.
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189214.
Chang, C.-C. & Lei, S.-Y. 1996 On the sources of aerodynamic forces: steady flow around a cylinder or a sphere. Proc. R. Soc. Lond. A 452, 23692395.
Chen, L.-W., Xu, C.-Y. & Lu, X.-Y. 2010 a Numerical investigation of the compressible flow past an aerofoil. J. Fluid Mech 643, 97126.
Chen, L.-W., Xu, C.-Y. & Lu, X.-Y. 2010 b Large-eddy simulation of opposing-jet-perturbed supersonic flow past a hemispherical nose. Mod. Phys. Lett. B 24, 12871290.
Choi, H., Jeon, W.-P. & Kim, J. 2008 Control of flow over a bluff body. Annu. Rev. Fluid Mech. 40, 113139.
Chorin, A. J. 1994 Vorticity and Turbulence. Springer.
Clemens, N. T. & Mungal, M. G. 1995 Large-scale structure and entrainment in the supersonic mixing layer. J. Fluid Mech. 284, 171216.
Deck, S. & Thorigny, P. 2007 Unsteadiness of an axisymmetric separating-reattaching flow. Phys. Fluids 19, 065103.
Delaunay, Y. & Kaiktsis, L. 2001 Control of circular cylinder wakes using base mass transpiration. Phys. Fluids 13, 32853302.
Desjardin, P. E. & Frankel, S. H. 1998 Large-eddy simulation of a non-premixed reacting jet: application and assessment of subgrid-scale combustion models. Phys. Fluids 10, 22982314.
Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C. & Poinsot, T. 1999 Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys. 152, 517549.
Freund, J. B., Lele, S. K. & Moin, P. 2000 Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate. J. Fluid Mech. 421, 229267.
Fureby, C. 1996 On subgrid-scale modelling in large eddy simulations of compressible fluid flow. Phys. Fluids 8, 13011311.
Garnier, E., Sagaut, P. & Deville, M. 2002 Large eddy simulation of shock/homogeneous turbulence interaction. Comput. Fluids 31, 245268.
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 17601765.
Gruber, M. R., Messersmith, N. L. & Dutton, J. G. 1993 Three-dimensional velocity field in a compressible mixing layer. AIAA J. 31, 20612067.
Hafez, M. & Wahba, E. 2007 Simulations of viscous transonic flows over lifting airfoils and wings. Comput. Fluids 36, 3952.
Hamman, C. W., Klewicki, J. C. & Kirby, R. M. 2008 On the Lamb vector divergence in Navier–Stokes flows. J. Fluid Mech. 610, 261284.
Herrin, J. L. & Dutton, J. C. 1995 Effect of a rapid expansion on the development of compressible free shear layers. Phys. Fluids 7, 159171.
Herrin, J. L. & Dutton, J. C. 1997 The turbulence structure of a reattaching axisymmetric compressible free shear layers. Phys. Fluids 9, 35023512.
Hill, D. J., Pantano, C. & Pullin, D. I. 2006 Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock. J. Fluid Mech. 557, 2961.
Howe, M. S. 1975 Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. J. Fluid Mech. 71, 625673.
Hwang, J. Y., Yang, K. S. & Sun, S. H. 2003 Reduction of flow-induced forces on a circular cylinder using a detached splitter plate. Phys. Fluids 15, 24332436.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Kawai, S. & Fujii, K. 2005 Computational study of supersonic base flow using hybrid turbulence methodology. AIAA J. 43, 12651275.
Knight, D., Zhou, G., Okong'o, N. & Shukla, V. 1998 Compressible large eddy simulation using unstructured grids. AIAA Paper 1998-0535.
Lam, K. & Lin, Y. F. 2008 Large eddy simulation of flow around wavy cylinders at a subcritical Reynolds number. Intl J. Heat Fluid Flow 29, 10711088.
Lam, K. & Lin, Y. F. 2009 Effects of wavelength and amplitude of a wavy cylinder in cross-flow at low Reynolds numbers. J. Fluid Mech. 620, 195220.
Lam, K., Wang, F. H., Li, J. Y. & So, R. M. C. 2004 a Experimental investigation of the mean and fluctuating forces of wavy (varicose) cylinders in a cross-flow. J. Fluids Struct 19, 321334.
Lam, K., Wang, F. H. & So, R. M. C. 2004 b Three-dimensional nature of vortices in the near wake of a wavy cylinder. J. Fluids Struct 19, 815833.
Lee, S., Lele, S. K. & Moin, P. 1991 Eddy shocklets in decaying compressible turbulence. Phys. Fluids A 3, 657664.
Lee, S. J. & Nguyen, A. T. 2007 Experimental investigation on wake behind a wavy cylinder having sinusoidal cross-sectional area variation. Fluid Dyn. Res. 39, 292304.
Lighthill, M. J. 1952 On sound generated aerodynamically. Part I. Proc. R. Soc. Lond. A 211, 564587.
Lighthill, M. J. 1963 Introduction of boundary layer theory. In Laminar Boundary Layers, (ed. Rosenhead, L.), pp. 46113, Oxford University Press.
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids 4, 633635.
Loginov, M. S., Adams, N. A. & Zheltovodov, A. A. 2006 Large-eddy simulation of shock-wave/turbulent-boundary-layer interaction. J. Fluid Mech. 565, 135169.
Lu, X.-Y., Wang, S. W., Sung, H. G., Hsieh, S. Y., & Yang, V. 2005 Large eddy simulations of turbulent swirling flows injected into a dump chamber. J. Fluid Mech. 527, 171195.
Lu, S. S. & Willmarth, W. W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60, 481551.
Lumley, J. L. 1967 Rational approach to relations between motions of differing scales in turbulent flows. Phys. Fluids 10, 14051408.
Macha, J. M. 1977 Drag of circular cylinders at transonic Mach numbers. J. Aircraft 14, 605607.
Mani, A., Moin, P. & Wang, M. 2009 Computational study of optical distortions by separated shear layers and turbulent wakes. J. Fluid Mech. 625, 273298.
Martin, M. P., Piomelli, U. & Candler, G. V. 1999 Subgrid-scale models for compressible large-eddy simulations. Theor. Comput. Fluid Dyn. 13, 361376.
Miserda, R. F. B. & Leal, R. G. 2006 Numerical simulation of the unsteady aerodynamic forces over a circular cylinder in transonic flow. AIAA Paper 2006–1408.
Moin, P., Squires, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 27462757.
Murthy, V. S. & Rose, W. C. 1978 Detailed measurements on a circular cylinder in cross flow. AIAA J. 16, 549550.
Nakamura, H. & Igarashi, T. 2008 Omnidirectional reductions in drag and fluctuating forces for a circular cylinder by attaching rings. J. Wind Engng Ind. Aerodyn. 96, 887899.
Oertel, H. & Affiliation, J. 1990 Wakes behind blunt bodies. Annu. Rev. Fluid Mech. 22, 539564.
Owen, J. C. & Bearman, P. W. 2001 Passive control of viv with drag reduction. J. Fluids Struct. 15, 597605.
Ozono, S. 1999 Flow control of vortex shedding by a short splitter plate asymmetrically arranged downstream of a cylinder. Phys. Fluids 11, 29282934.
Pantano, C. & Sarkar, S. 2002 A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329371.
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453477.
Peake, N. & Crighton, D. G. 2000 Active control of sound. Annu. Rev. Fluid Mech. 32, 137164.
Piomelli, U. 1999 Large-eddy simulation: achievements and challenges. Prog. Aerosp. Sci. 35, 335362.
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25. Phys. Fluids 16, 530545.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Prasad, A. & Williamson, C. H. K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375402.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layers. Annu. Rev. Fluid Mech. 23, 601639.
Rodriguez, O. 1984 The circular cylinder in subsonic and transonic flow. AIAA J. 22, 17131718.
Salvetti, M. V. & Banerjee, S. 1995 A priori test of a new dynamic subgrid-scale model for finite difference large-eddy simulations. Phys. Fluids 7, 28312847.
Samtaney, R., Pulin, D. I. & Kosović, B. 2001 Direct numerical simulation of decaying compressbilce turbulence and shocklet statistics. Phys. Fluids 13, 14151430.
Sandham, N. D. & Reynolds, W. C. 1991 Three-dimensional simulations of large eddies in the compressible mixing layer. J. Fluid Mech. 224, 133158.
Sandham, N. D., Yao, Y. F. & Lawal, A. A. 2003 Large-eddy simulation of transonic turbulent flow over a bump. Intl J. Heat Fluid Flow 24, 584595.
Sarkar, S. 1995 The stabilizing effect of compressibility in turbulent shear flow. J. Fluid Mech. 282, 163186.
Shvets, A. I. 1983 Pressure fluctuations during flow around blunt bodies. J. Appl. Mech. Tech. Phys. 24, 193199.
Simon, F., Deck, S., Guillen, P., Sagaut, P. & Merlen, A. 2007 Numerical simulation of the compressible mixing layer past an axisymmetric trailing edge. J. Fluid Mech. 591, 215253.
Smagorinsky, J. 1963 General circulation experiments with the privative equations. Part I. The basic experiment. Mon. Weath. Rev. 91, 99164.
Stanewsky, E. 2001 Adaptive wing and flow control technology. Prog. Aerosp. Sci. 37, 583667.
Thomas, J. L. & Salas, M. D. 1986 Far-field boundary conditions for transonic lifting solutions to the Euler equations. AIAA J. 24, 10741080.
Thombazis, N. & Bearman, P. W. 1997 A study of three-dimensional aspects of vortex shedding from a bluff body with a mild geometric disturbance. J. Fluid Mech. 330, 85112.
Thombi, L., Daisuke, H. & Yoshiaki, N. 2002 Passive separation control on a body at transonic speed. Trans. Japan Soc. Aerosp. Space Sci. 44, 229237.
Truesdell, C. 1954 The Kinematics of Vorticity. Indiana University Press.
Vreman, B., Kuerten, H. & Geurts, B. 1995 Shocks in direct numerical simulation of the confined three-dimensioal mixing layer. Phys. Fluids 7, 21052107.
Vreman, A. W., Sandham, N. D. & Luo, K. H. 1996 Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235258.
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 3948.
Wang, M., Freund, J. B. & Lele, S. K. 2006 Computational prediction of flow-generated sound. Annu. Rev. Fluid Mech. 38, 483512.
Wang, M. & Moin, P. 2000 Computation of trailing-edge flow and noise using large-eddy simulation. AIAA J. 38, 22012209.
Wang, S. W., Yang, V., Hsiao, G., Hsieh, S. Y., & Mongia, H. C. 2007 Large-eddy simulations of gas-turbine swirl injector flow dynamics. J. Fluid Mech. 583, 99122.
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413455.
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 6592.
Wu, J.-Z., Lu, X.-Y. & Zhuang, L.-X. 2007 Integral force acting on a body due to local flow structures. J. Fluid Mech. 576, 265286.
Wu, J.-Z., Ma, H.-Y. & Zhou, M.-D. 2006 Vorticity and Vortex Dynamics. Springer.
Xu, C.-Y., Chen, L.-W. & Lu, X.-Y. 2009 a Effect of Mach number on transonic flow past a circular cylinder. Chin. Sci. Bull 54, 18861893.
Xu, C.-Y., Chen, L.-W. & Lu, X.-Y. 2009 b Numerical simulation of shock wave and turbulence interaction over a circular cylinder. Mod. Phys. Lett. 23, 233236.
Yao, Y. F. & Sandham, N. D. 2002 Direct numerical simulation of turbulent trailing-edge flow with base flow control. AIAA J. 40, 17081716.
Yoshizawa, A. 1986 Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29, 21522164.
Zdravkovich, M. M. 1997 Flow Around Circular Cylinders. Oxford University Press.
Zhang, W., Dai, C. & Lee, S. J. 2005 PIV measurements of the near-wake behind a sinusoidal cylinder. Exp. Fluids 38, 824832.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Large-eddy simulation of the compressible flow past a wavy cylinder

  • CHANG-YUE XU (a1), LI-WEI CHEN (a1) and XI-YUN LU (a1)


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.