Abstract
In the present study, 2-D large eddy simulations (LES) are conducted for flow past a porous circular array with a solid volume fraction (SVF) of 8.8%, 15.4% and 21.5%. Such simulations are relevant to understanding flow in natural streams and channels containing patches of emerged vegetation. In the simulations discussed in the paper, the porous cylinder of diameter D contains a variable number of identical solid circular cylinders (rigid plant stems) of diameter d = 0.048D. Most of the simulations are conducted at a Reynolds number of 2 100 based on the diameter D and the velocity of the steady uniform incoming flow. Though in all cases wake billows are shed in the regions where the separated shear layers (SSLs) forming on the sides of the porous cylinder interact, the effect of these wake billows on the mean drag is different. While in the high SVF case (21.5%), the total drag force oscillates quasi-regularly in time, similar to the canonical case of a large solid cylinder, in the cases with a lower SVF the shedding of the wake billows takes place sufficiently far from the cylinder such that the unsteady component of the total drag force is negligible. The mean amplitude of the oscillations of the drag force on the individual cylinders is the largest in a streamwise band centered around the center of the porous cylinder, where the wake to wake interactions are the strongest. In all cases the maximum drag force on the individual cylinders is the largest for the cylinders directly exposed to the flow, but this force is always smaller than the one induced on a small isolated cylinder and the average magnitude of the force on the cylinders directly exposed to the flow decreases monotonically with the increase in the SVF. Predictions of the global drag coefficients, Strouhal numbers associated with the wake vortex shedding and individual forces on the cylinders in the array from the present LES are in very good agreement with those of 2-D direct numerical simulations conducted on finer meshes, which suggests LES is a better option to numerically investigate flow in channels containing canopy patches, given that LES is computationally much less expensive than DNS at high Reynolds number. To prove this point, the paper also discusses results of 2-D LES conducted at a much higher Reynolds number, where the near-wake flow is strongly turbulent. For the higher Reynolds number cases, where the influence of the turbulence model is important, the effect of the sub-grid scale model and the predictive capabilities of the unsteady Reynolds averaged Navier-Stokes (RANS) approach to predict flow past porous cylinders are discussed.
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References
Ricardo A. M., Franca M. J., Ferreira R. M. L. Turbulent flows within random arrays of rigid and emergent cylinders with varying distribution [J]. Journal of Hydraulic Engineering, ASCE, 2016, 142(9): 04016022.
Ricardo A. M., Koll K., Franca M. J. et al. The terms of turbulent kinetic energy budget within random arrays of emergent cylinders [J]. Water Resources Research, Water Resources Research, 2014, 50(5): 4131–4148.
Salinas-Vazquez M., de la Lama M. A., Vicente W. et al. Large eddy simulation of a flow through circular tube bundle [J]. Applied Mathematical Modelling, 2011, 35(9): 4393–4406.
Lam K., Li J. Y., So R. M. C. Force coefficient and Strouhal numbers of four cylinders in cross flow [J]. Journal of Fluids and Structures, 2003, 18(3): 305–324.
Hassan Y. A., Barsamian H. R. Tube bundle flows with the large eddy simulation technique in curvilinear coordinate [J]. International Journal of Heat and Mass Transfer, 2004, 47(14): 3057–3071.
Prasad A., Williamson C. H. K. The instability of the shear layer separating form a bluff body [J]. Journal of Fluid Mechanics, 1997, 333: 375–402.
Zong L., Nepf H. Vortex development behind a finite porous obstruction in a channel [J]. Journal of Fluid Mechanics, 2012, 691: 1–24.
Nicolle A., Eames I. Numerical study of flow through and around a circular array of cylinder [J]. Journal of Fluid Mechanics, 2011, 679: 1–31.
Pierce C. D., Moin P. Progress variable approach for large eddy simulation of large eddy simulation of turbulence combustion [R]. Palo Alto, USA: Stanford University, 2001, Report TF-80
Pierce C. D., Moin P. Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion [J]. Journal of Fluid Mechanics, 2004, 504: 73–97.
Lilly D. K. A proposed modification of the Germano subgrid scale closure problem [J]. Physics of Fluids A, 1992, 4(3): 633–635.
Smagorinsky J. General circulation experiments with primitive equations. I: The basic experiment [J]. Monthly Weather Review, 1963, 91(3): 99–164.
Chang K., Constantinescu G., Park S. Analysis of the flow and mass transfer processes for the incompressible flow past an open cavity with a laminar and a fully turbulent incoming boundary layer [J]. Journal of Fluid Mechanics, 2006, 561: 113–145.
Chang K., Constantinescu G. Coherent structures in flow over two-dimensional dunes [J]. Water Resources Research, 2013, 49(5): 2446–2460.
Tokyay T., Constantinescu G., Meiburg E. Lock exchange gravity currents with a high volume of release propagating over an array of obstacles [J]. Journal of Fluid Mechanics, 2011, 672: 570–605.
Chen Z., Ortiz A., Zong L. et al. The wake structure behind a porous obstruction and its implications for deposition near a finite patch of emergent vegetation [J]. Water Resources Research, 2012, 48(9): W09517.
Singh S. P., Mittal S. Flow past a cylinder: shear layer instability and drag crisis [J]. International Journal for Numerical Methods in Fluids, 2005, 47(1): 75–98.
Park J., Kwon K., Choi H. Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160 [J]. KSME International Journal, 1998, 12(6): 1200–1205.
Sumner D., Price S. J., Paidoussis M. P. Flow-pattern identification for two staggered circular cylinders in cross-flow [J]. Journal of Fluid Mechanics, 2000, 411: 263–303.
Lee K., Yang K., Yoon D. Flow-induced forces on two circular cylinders in proximity [J]. Computers and Fluids, 2009, 38(1): 111–120.
Akbari M. H., Price S. J. Numerical investigation of flow patterns for staggered cylinder pairs in cross-flow [J]. Journal of Fluids and Structures, 2005, 20(4): 533–554.
Acknowledgements
The authors would like to thank the National Center for High Performance Computing (NCHC) in Taiwan and the TRACC facility at the Argonne National Laboratory for providing the computational resources needed to perform the simulations. We also acknowledge the financial support from the Ministry of Science, ICT and Future Planning, subjected to the project EDISON (Education-research Integration through Simulation On the Net, NRF-2011-0020560).
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Biography: Kyoungsik Chang (1977-), Male, Ph. D., Assistant Professor
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Chang, K., Constantinescu, G. & Park, S. 2-D eddy resolving simulations of flow past a circular array of cylindrical plant stems. J Hydrodyn 30, 317–335 (2018). https://doi.org/10.1007/s42241-018-0030-9
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DOI: https://doi.org/10.1007/s42241-018-0030-9