# zbMATH — the first resource for mathematics

Dynamics of tandem cylinders in the vicinity of a plane moving wall. (English) Zbl 1390.76072
Summary: We present dynamics of the flow around two cylinders in a tandem configuration along a moving plane wall. A spectral element method is employed to perform the simulations with high accuracy at Reynolds number $$\mathrm{Re} = 200$$. A moving wall with no-slip boundary is considered rather than a stationary wall to avoid the confusing interaction of the wall boundary layer and thus focus completely on the influence of wall proximity effects on the force and wake dynamics. The influence of the moving wall with gap ratio $$e / D = 0.2-5.0$$ and longitudinal center-to-center separation $$L / D = 1.5 - 8.0$$ on the unsteady force dynamics is examined for the two cylinder configuration. Through detailed analysis of the flow field dynamics, we observe early transition from reattachment to co-shedding behavior. At co-shedding separation distances, the combined wake interference and wall proximity effects lead to a parallel double-row of vortices for the tandem cylinders at $$\mathrm{Re} = 200$$ for $$e / D = 0.5$$. For a longitudinal separation of 4$$D$$, the ratio of the street width $$h$$ to distance between two adjacent vortices in the same row $$l$$ is in good agreement with that obtained from inviscid theory. Finally, we provide detailed flow visualizations, Strouhal number and force coefficient trends and investigate recovery of freestream behavior as the tandem cylinder configuration of varying $$L/D$$ is gradually distanced further from the moving plane wall.
##### MSC:
 76D17 Viscous vortex flows 76M10 Finite element methods applied to problems in fluid mechanics 76M22 Spectral methods applied to problems in fluid mechanics
Full Text:
##### References:
 [1] Taneda, S., Experimental investigation of vortex streets, J Phys Soc Jpn, 20, 1713-1721, (1965) [2] Bearman, P.; Zdravkovich, M., Flow around a circular cylinder near a plane boundary, J Fluid Mech, 89, 33-47, (1978) [3] Grass, A.; Raven, P.; R. J. Stuart, R.; Bray, J., The influence of boundary layer velocity gradients and bed proximity on vortex shedding from free spanning pipelines, ASME J Energy Resour Technol, 106, 70-78, (1984) [4] Taniguchi, S.; Miyakoshi, K., Fluctuating fluid forces acting on a circular cylinder and interference with a plane wall, Exp Fluids, 9, 197-204, (1990) [5] Lei, C.; Cheng, L.; Kavanagh, K., Re-examination of the effect of a plane boundary on force and vortex shedding of a circular cylinder, J Wind Eng Ind Aerodyn, 80, 263-286, (1999) [6] Buresti, G.; Lanciotti, A., Vortex shedding from smooth and roughened cylinders in cross-flow near a plane surface, Aeronaut Q, 30, 305-321, (1979) [7] Huang, W.; Hyung, J., Vortex shedding from a circular cylinder near a moving wall, J Fluids Struct, 23, 1064-1076, (2007) [8] Price, S.; Sumner, D.; Smith, J.; Leong, K.; Paidoussis, M., Flow visualization around a circular cylinder near to a plane walll, J Fluids Struct, 16, 2, 175-191, (2002) [9] Rao, A.; Thompson, M. C.; Leweke, T.; Hourigan, K., The flow past a circular cylinder translating at different heights above a wall, J Fluids Struct, 41, 9-21, (2013) [10] Stewart, B.; Thompson, M.; T. Leweke; Hourigan, K., The wake behind a cylinder rolling on a wall at varying rotation rates, J Fluid Mech, 648, 225-256, (2010) · Zbl 1189.76156 [11] Zdravkovich, M., The effects of interference between circular cylinders in cross flow, J Fluids Struct, 1, 239-261, (1987) [12] Igarashi, T., Characteristics of flow around two circular cylinders arranged in tandem, JSME, 24, 323-331, (1981) [13] Xu, G.; Zhou, Y., Strouhal numbers in the wake of two inline cylinders, Exp Fluids, 37, 248-256, (2004) [14] Zhou, Y.; Yiu, M., Flow structure, momentum and heat transport in a two-tandem cylinder wake, J Fluid Mech, 548, 17-48, (2005) [15] Mussa, A.; Asinari, P.; Luo, L., Lattice Boltzmann simulations of 2d laminar flows past two tandem cylinders, J Comput Phys, 228, 983-999, (2009) · Zbl 1157.76037 [16] Mittal, S.; Kumar, V.; Raghuvanshi, A., Unsteady incompressible flow past two cylinders in tandem and staggered arrangements, Int J Numer Methods Fluid, 25, 1315-1344, (1997) · Zbl 0909.76050 [17] Meneghini, J.; Saltara, F.; Siqueira, C.; Ferrari, J., Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements, J Fluids Struct, 15, 327-350, (2001) [18] Harichandan, A.; Roy, A., Numerical investigation of flow past single and tandem cylindrical bodies in the vicinity of a plane wall, J Fluids Struct, 33, 19-43, (2012) [19] Rao, A.; Thompson, M.; Leweke, T.; Hourigan, K., Dynamics and stability of the wake behind tandem cylinders sliding along a wall, J Fluid Mech, 722, 291-316, (2013) · Zbl 1287.76083 [20] Rao, A.; Stewart, B.; Thompson, M.; Lewele, T.; Hourigan, K., Flows past rotating cylinders next to a wall, J Fluids Struct, 27, 668-679, (2011) [21] Karniadakis, G.; Sherwin, S., Spectral/HP methods for computational fluid dynamics, (2005), Oxford University Press · Zbl 1116.76002 [22] Deville, M.; Fischer, P.; Mund, E., High-order methods for incompressible fluid flow, (2002), Cambridge University Press · Zbl 1007.76001 [23] Karniadakis, G.; Israeli, M.; Orszag, S., High-order splitting methods for the incompressible Navier-Stokes equations, J Comput Phys, 97, 414-443, (1991) · Zbl 0738.76050 [24] H. M., B.; S. J., S., Formulation of a Galerkin spectral elementfourier method for three-dimensional incompressible flows in cylindrical geometries, J Comput Phys, 197, 759-778, (2005) · Zbl 1106.76418 [25] Sengupta, T.; Bhumkar, Y.; Sengupta, S., Dynamics and instability of a shielded vortex in close proximity of a wall, Comput Fluids, 70, 166-175, (2012) · Zbl 1365.76041 [26] Gal, P. L.; Chauve, M.; Lima, R.; Rezende, J., Coupled wakes behind two circular cylinders, Phys Rev A, 41, 4566, (1990) [27] Williamson, C., Volution of a single wake behind a pair of bluff bodies, J Fluid Mech, 159, 1-18, (1985) [28] Lamb, H., Hydrodynamics, (1932), Dover New York · JFM 26.0868.02 [29] Milne-Thomson, L., Theoretical hydrodynamics, (1962), Macmillan · JFM 64.0848.12 [30] Sumer, B.; Fredsoe, J., Hydrodynamics around cylindrical structures, (2006), World Scientific · Zbl 1153.76003 [31] Drazin, P.; Reid, W., Hydrodynamic stability, (1981), Cambridge University Press Cambridge, UK · Zbl 0449.76027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.