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Investigations of vortex dynamics about two circular cylinders in a side-by-side arrangement help the understanding of flows around more complex structures, which are found to have many engineering applications. These applications involve offshore structures, power generation, micro-turbine engines, cooling towers, and paper machine forming fabrics, etc. Therefore, two-dimensional compressible laminar flows over two cylinders in side-by-side arrangement are numerically investigated at low Reynolds number. The high-order discontinuous Galerkin method is employed to simulate the flow, which combines the advantages associated with finite element and finite volume methods. As in classical finite element method, the spatial accuracy can be obtained by the high-order polynomial approximation within an element rather than by stencils as in finite volume method. The curved triangle is used to represent the wall boundary of cylinder to maintain the high-order accurate simulation. Then the characteristics of the wake flow are identified by capturing the vortex structure. After verifying the rationality of the method, the influences of gap spacing on vortex shedding and mechanical characteristics are analyzed. The results reveal that the flow depends to a large extent on the gap spacing between the two cylinders, which can change the vortex shedding pattern. At the gap spacing S*=1.1, wake flow pattern resembles the vortex street of a single bluff body. The flow in the gap is too weak to affect the wake pattern, leading to the complete suppression of vortices shed on the gap sides of both cylinders. At the gap spacing S*=1.4, the results reveal that the gap flow is deflected from one cylinder to another. Meanwhile, the wakes represent randomly flip-flopping between two states of the gap flow direction, which is called the flip-flopping wake pattern. The flow is no longer periodic but becomes drastically unsteady. Anti-symmetric flow pattern is predicted for gap spacing S*=2.5, indicating that two parallel vortex streets are anti-symmetric with respect to the centerline. With further increasing the gap spacing to S*=4, the symmetric flow pattern is observed. Furthermore, the flow preserves its structure very far downstream without any distortion. With the increase of the cylinder spacing, the average drag coefficients are declined significantly, and the absolute value of average lift coefficient decreases simultaneously. The Reynolds number has a little influence on the average drag coefficient. As the Reynolds number increases, the average lift coefficient decreases, while the vortex shedding frequency increases.
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Keywords:
- discontinuous Galerkin method /
- curved boundary /
- side-by-side cylinders /
- vortex shedding
[1] Chen Y, Fu S X, Xu Y W, Zhou Q, Fan D X 2013 Acta Phys. Sin. 62 064701 (in Chinese) [陈蓥, 付世晓, 许玉旺, 周青, 范迪夏 2013 62 064701]
[2] Huang Z, Olson J A, Kerekes R J, Green S I 2006 Comput. Fluids 35 485
[3] Williamson C H K 1985 J. Fluid Mech. 159 1
[4] Sumner D, Wong S S T, Price S J, Paidoussis M P 1999 J. Fluid. Struct. 13 309
[5] Zdravkovich M M 1977 J. Fluid. Eng. 99 618
[6] Meneghini J R, Saltara F, Siqueira C L R, Ferrari J A 2001 J. Fluid. Struct. 15 327
[7] Ding H, Shu C, Yeo K S, Xu D 2007 Int. J. Numer. Meth. Fl. 53 305
[8] Chen L, Tu J Y, Yeoh G H 2003 J. Fluid. Struct. 18 387
[9] Dong P, Feng S D, Zhao Y 2004 Chin. Phys. B 13 434
[10] Zhang W, Wang Y, Qian Y H 2015 Chin. Phys. B 24 064701
[11] Liang D W, Huang G P 2004 Gas. Turb. Exp. Res. 17 9 (in Chinese) [梁德旺, 黄国平 2004 燃气涡轮试验与研究 17 9]
[12] Liang C, Premasuthan S, Jameson A 2009 Comput. Struct. 87 812
[13] Reed W H, Hill T R 1973 Los Alamos Report 73 479
[14] Cockburn B, Shu C W 1991 Math. Model. Num. 25 337
[15] Bassi F, Rebay S 1997 J. Comput. Phys. 131 267
[16] Cockburn B, Shu C W 1989 Math. Comput. 52 411
[17] Peraire J, Persson P O 2008 Siam J. Sci. Comput. 30 1806
[18] Bassi F, Crivellini A, Rebay S, Savini M 2005 Comput. Fluids 34 507
[19] Yu J, Yan C 2010 Acta Mech. Sin. 5 962 (in Chinese) [于剑, 阎超2010 力学学报 5 962]
[20] Toro, Eleuterio F 2009 Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction (Netherlands: Springer Science Business Media) pp315-336
[21] Luo H, Baum J D, Lohner R 2008 J. Comput. Phys. 227 8875
[22] Luo H, Segawa H, Visbal M R 2012 Comput. Fluids 53 133
[23] Roshko A 1954 On the Drag and Shedding Frequency of Two-Dimensional Bluff Bodies (Washington DC: National Aeronautics and Space Administration) p129
[24] Nicolle A, Eames I 2011 J. Fluid Mech. 679 1
[25] Kim H J 1988 J. Fluid Mech. 196 431
[26] Zhou Y, Zhang H J, Yiu M W 2002 J. Fluid Mech. 458 303
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[1] Chen Y, Fu S X, Xu Y W, Zhou Q, Fan D X 2013 Acta Phys. Sin. 62 064701 (in Chinese) [陈蓥, 付世晓, 许玉旺, 周青, 范迪夏 2013 62 064701]
[2] Huang Z, Olson J A, Kerekes R J, Green S I 2006 Comput. Fluids 35 485
[3] Williamson C H K 1985 J. Fluid Mech. 159 1
[4] Sumner D, Wong S S T, Price S J, Paidoussis M P 1999 J. Fluid. Struct. 13 309
[5] Zdravkovich M M 1977 J. Fluid. Eng. 99 618
[6] Meneghini J R, Saltara F, Siqueira C L R, Ferrari J A 2001 J. Fluid. Struct. 15 327
[7] Ding H, Shu C, Yeo K S, Xu D 2007 Int. J. Numer. Meth. Fl. 53 305
[8] Chen L, Tu J Y, Yeoh G H 2003 J. Fluid. Struct. 18 387
[9] Dong P, Feng S D, Zhao Y 2004 Chin. Phys. B 13 434
[10] Zhang W, Wang Y, Qian Y H 2015 Chin. Phys. B 24 064701
[11] Liang D W, Huang G P 2004 Gas. Turb. Exp. Res. 17 9 (in Chinese) [梁德旺, 黄国平 2004 燃气涡轮试验与研究 17 9]
[12] Liang C, Premasuthan S, Jameson A 2009 Comput. Struct. 87 812
[13] Reed W H, Hill T R 1973 Los Alamos Report 73 479
[14] Cockburn B, Shu C W 1991 Math. Model. Num. 25 337
[15] Bassi F, Rebay S 1997 J. Comput. Phys. 131 267
[16] Cockburn B, Shu C W 1989 Math. Comput. 52 411
[17] Peraire J, Persson P O 2008 Siam J. Sci. Comput. 30 1806
[18] Bassi F, Crivellini A, Rebay S, Savini M 2005 Comput. Fluids 34 507
[19] Yu J, Yan C 2010 Acta Mech. Sin. 5 962 (in Chinese) [于剑, 阎超2010 力学学报 5 962]
[20] Toro, Eleuterio F 2009 Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction (Netherlands: Springer Science Business Media) pp315-336
[21] Luo H, Baum J D, Lohner R 2008 J. Comput. Phys. 227 8875
[22] Luo H, Segawa H, Visbal M R 2012 Comput. Fluids 53 133
[23] Roshko A 1954 On the Drag and Shedding Frequency of Two-Dimensional Bluff Bodies (Washington DC: National Aeronautics and Space Administration) p129
[24] Nicolle A, Eames I 2011 J. Fluid Mech. 679 1
[25] Kim H J 1988 J. Fluid Mech. 196 431
[26] Zhou Y, Zhang H J, Yiu M W 2002 J. Fluid Mech. 458 303
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