Large-eddy simulations of flow normal to a circular disk at \(\mathit{Re} = 1.5 \times 10^5\). (English) Zbl 1390.76227
Summary: Numerical simulations of the flow normal to a circular disk have been carried out using the large-eddy simulation (LES) method with Smagorinsky subgrid scale model. The Reynolds number Re based on the free stream velocity and the diameter of the disk is \(1.5\times 10^{5}\). The thickness to diameter ratio of the disk is 0.02. The instantaneous vortical structures in wake of the disk are revealed. Toroidal vortices are formed along the disk edges due to Kelvin-Helmholtz instability. The toroidal vortices break up as the flow goes downstream and then hairpin-like vortices are formed. Worm-like vortices parallel to the axis of the disk are observed in the center region of the medium wake. Two distinct vortex spreading modes in the far wake are observed: one has a main shedding plane; the other has not. Three dominant frequencies at the Strouhal number \(\mathrm{St}_1 = 0.01\), \(\mathrm{St}_n = 0.148\) (corresponding to the natural frequency) and \(\mathrm{St}_{3} 0.8-1.35\), characterizing that the wake instability mechanisms are found through frequency analysis. The time and azimuth averaged statistics, e.g., streamlines, pressure, vorticity and profiles of velocity and kinetic energy, are also presented and discussed.
MSC:
| 76F65 | Direct numerical and large eddy simulation of turbulence |
| 65Y15 | Packaged methods for numerical algorithms |
| 76-04 | Software, source code, etc. for problems pertaining to fluid mechanics |
Software:
OpenFOAMReferences:
| [1] | Auguste, F.; Fabre, D.; Magnaudet, J., Bifurcations in the wake of a thick circular disk, Theor Compu Fluid Dyn, 24, 1, 305-313, (2010) · Zbl 1191.76045 |
| [2] | Auguste, F.; Magnaudet, J.; Fabre, D., Falling styles of disks, J Fluid Mech, 719, 388-405, (2013) · Zbl 1284.76130 |
| [3] | Berger, E.; Scholz, D.; Schumm, M., Coherent vortex structures in the wake of a sphere and a circular disk at rest and under forced vibrations, J Fluids Struct, 4, 3, 231-257, (1990) |
| [4] | Breuer, M., Large eddy simulation of the subcritical flow past a circular cylinder: numerical and modeling aspects, Int J Numer Methods Fluids, 28, 9, 1281-1302, (1998) · Zbl 0933.76041 |
| [5] | Breuer, M., A challenging test case for large eddy simulation: high Reynolds number circular cylinder flow, Int J Heat Fluid Flow, 21, 5, 648-654, (2000) |
| [6] | Chrust, M.; Bouchet, G.; Dušek, J., Parametric study of the transition in the wake of oblate spheroids and flat cylinders, J Fluid Mech, 665, 199-208, (2010) · Zbl 1225.76090 |
| [7] | Chrust, M.; Bouchet, G.; Dušek, J., Effect of solid body degrees of freedom on the path instabilities of freely falling or rising flat cylinders, J Fluids Struct, 47, 55-70, (2014) |
| [8] | Ern, P.; Risso, F.; Fabre, D.; Magnaudet, J., Wake-induced oscillatory paths of bodies freely rising or falling in fluids, Ann Rev Fluid Mech, 44, 97-121, (2012) · Zbl 1355.76019 |
| [9] | Fabre, D.; Auguste, F.; Magnaudet, J., Bifurcations and symmetry breaking in the wake of axisymmetric bodies, Phys Fluids, 20, 051702, (2008) · Zbl 1182.76238 |
| [10] | Fage, A.; Johansen, F. C., On the flow of air behind an inclined flat plate of infinite span, Proc R Soc London Series A, Containing Papers of a Mathematical and Physical Character, 116, 773, 170-197, (1927) · JFM 53.0810.22 |
| [11] | Fernandes, P. C.; Risso, F.; Ern, P.; Magnaudet, J., Oscillatory motion and wake instability of freely rising axisymmetric bodies, J Fluid Mech, 573, 479-502, (2007) · Zbl 1108.76310 |
| [12] | Gallardo, J. P.; Andersson, H. I.; Pettersen, P., Turbulent wake behind a curved circular cylinder, J Fluid Mech, 742, 192-229, (2014) |
| [13] | Garnier, E.; Sagaut, P.; Deville, M., Large eddy simulation of shock/homogeneous turbulence interaction, Comput Fluids, 31, 2, 245-268, (2002) · Zbl 1059.76032 |
| [14] | Hunt, J. C.R.; Wray, A. A.; Moin, P., Eddies, streams, and convergence zones in turbulent flows, Center for turbulence research report CTR-S88, 193-208, (1988), NASA USA |
| [15] | Johnson, T.; Patel, V., Flow past a sphere up to a Reynolds number of 300, J Fluid Mech, 378, 19-70, (1999) |
| [16] | Kuo, Y. H.; Baldwin, L. V., The formation of elliptical wakes, J Fluid Mech, 27, 02, 353-360, (1967) |
| [17] | Lamballais, E.; Silvestrini, J.; Laizet, S., Direct numerical simulation of flow separation behind a rounded leading edge: study of curvature effects, Int J Heat Fluid Flow, 31, 3, 295-306, (2010) |
| [18] | Marshall, D.; Stanton, T. E., On the eddy system in the wake of flat circular plates in three dimensional flow, Proc R Soc London Series A, Containing Papers of a Mathematical and Physical Character, 130, 813, 295-301, (1931) |
| [19] | Meliga, P.; Chomaz, J. M.; Sipp, D., Global mode interaction and pattern selection in the wake of a disk: a weakly nonlinear expansion, J Fluid Mech, 633, 159-189, (2009) · Zbl 1183.76721 |
| [20] | Michael, P., Steady motion of a disk in a viscous fluid, Phys Fluids, 9, 466, (1966) · Zbl 0139.21501 |
| [21] | Najjar, F. M.; Balachandar, S., Low-frequency unsteadiness in the wake of a normal flat plate, J Fluid Mech, 370, 101-147, (1998) · Zbl 0932.76015 |
| [22] | Narasimhamurthy, V. D.; Andersson, H. I., Numerical simulation of the turbulent wake behind a normal flat plate, Int J Heat Fluid Flow, 30, 6, 1037-1043, (2009) |
| [23] | OpenFOAM, The open source CFD toolbox, programmer’s guide, version 1.6, (2009), OpenCFD Limited Boston, MA, USA |
| [24] | Rimon, Y., Numerical solution of the incompressible time-dependent viscous flow past a thin oblate spheroid, Phys Fluids, 12, II–65-75, (1969) · Zbl 0207.26405 |
| [25] | Rivet, J. P.; Henon, M.; Frisch, U.; d’Humieres, D., Simulating fully three-dimensional external flow by lattice gas methods, Europhys Letters, 7, 231, (1988) |
| [26] | Roberts, J. B., Coherence measurements in an axisymmetric wake, AIAA J, 11, 1569-1571, (1973) |
| [27] | Roos, F. W.; Willmarth, W. W., Some experimental results on sphere and disk drag, AIAA J, 9, 285-291, (1971) |
| [28] | Shenoy, A. R.; Kleinstreuer, C., Flow over a thin circular disk at low to moderate Reynolds numbers, J Fluid Mech, 605, 253-262, (2008) · Zbl 1191.76047 |
| [29] | Shenoy, A. R.; Kleinstreuer, C., Influence of aspect ratio on the dynamics of a freely moving circular disk, J Fluid Mech, 653, 463-487, (2010) · Zbl 1193.76035 |
| [30] | Smagorinsky, J., General circulation experiments with the primitive equations, Mon Weather Rev, 91, 3, 99-164, (1963) |
| [31] | Tao, L.; Thiagarajan, K., Low KC flow regimes of oscillating sharp edges I. vortex shedding observation, Appl Ocean Res, 25, 1, 21-35, (2003) |
| [32] | Tao, L.; Thiagarajan, K., Low KC flow regimes of oscillating sharp edges II. hydrodynamic forces, Appl Ocean Res, 25, 2, 53-62, (2003) |
| [33] | Tchoufag, J.; Fabre, D.; Magnaudet, J., Global linear stability analysis of the wake and path of buoyancy-driven disks and thin cylinders, J Fluid Mech, 740, 278-311, (2014) |
| [34] | Tian, X.; Ong, M. C.; Yang, J.; Myrhaug, D., Large-eddy simulation of the flow normal to a flat plate including corner effects at a high Reynolds number, J Fluids Struct, 49, 149-169, (2014) |
| [35] | Van Driest, E. R., On turbulent flow near a wall, J Aero Sci, 23, 1007-1011, (1956) · Zbl 0073.20802 |
| [36] | Weller, H. G.; Tabor, G.; Jasak, H.; Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput Phys, 12, 620-631, (1998) |
| [37] | Willmarth, W. W.; Hawk, N. E.; Harvey, R. L., Steady and unsteady motions and wakes of freely falling disks, Phys Fluids, (1964) · Zbl 0116.18903 |
| [38] | Xu, C. Y.; Chen, L.; Lu, X., Large-eddy simulation of the compressible flow past a wavy cylinder, J Fluid Mech, 665, 238-273, (2010) · Zbl 1225.76174 |
| [39] | Yang, D.; Pettersen, B.; Andersson, H. I.; Narasimhamurthy, V. D., Vortex shedding in flow past an inclined flat plate at high incidence, Phys Fluids, 24, 8, 084103, (2012) |
| [40] | Yang, J.; Liu, M.; Wu, G.; Liu, Q.; Zhang, X., Low-frequency characteristics in the wake of a circular disk, Phys Fluids, 27, 6, 064101, (2015) |
| [41] | Yang, J.; Liu, M.; Wu, G.; Zhong, W.; Zhang, X., Numerical study on coherent structure behind a circular disk, J Fluids Struct, 51, 172-188, (2014) |
| [42] | Yang, J.; Tian, X.; Li, X., Hydrodynamic characteristics of an oscillating circular disk under steady in-plane current conditions, Ocean Eng, 75, 53-63, (2014) |
| [43] | Yang, J.; Wu, G.; Zhong, W.; Liu, M., Numerical study on bifurcations in the wake of a circular disk, Int J Comput Fluid Dyn, 28, 5, 187-203, (2014) |
| [44] | Zhong, H. J.; Lee, C. B., The wake of falling disks at low Reynolds numbers, Acta Mech Sin, 28, 1-5, (2012) · Zbl 1288.76003 |
| [45] | Zhong, W.; Liu, M.; Wu, G.; Yang, J.; Zhang, X., Extraction and recognization of large-scale structures in the turbulent near wake of a circular disc, Fluid Dyn Res, 46, 1, 1-21, (2014) |
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