NUMERICAL ANALYSIS OF BULK DRAG COEFFICIENT IN DENSE VEGETATION BY IMMERSED BOUNDARY METHOD

Tomohiro Suzuki, Taro Arikawa

Abstract


In this paper, bulk drag coefficient in rigid dense vegetation is investigated mainly by using a three dimensional numerical simulation model CADMAS-SURF/3D by incorporating Immersed Boundary Method to calculate flow around the vertical cylinder in the Cartesian grid. Large Eddy Simulation is also incorporated as a turbulence model. Firstly, validation of the developed model is conducted with a single cylinder in the flow field based on literature. All the results obtained here (Re=300, 3,900 and 8,000) show good agreement with the reference data in literature. After the validation, multiple cylinders are allotted in three different densities (S/D=2.8, 2.0, 1.4) in a numerical wave tank and numerical simulations are conducted to investigate bulk drag coefficient. The result shows that the ratio of bulk drag coefficient to drag coefficient, which represents a reduction, is not just a function of density but a function of parameter 2a/S, in which 2a is stroke of the motion and S is cylinder distance. 2a is less than S, the effect of the density is neglected because the wake does not reach the other cylinders even when the density is high. On the contrary, it might affect the ratio of bulk drag coefficient to drag coefficient when the stroke of the motion is larger than the cylinder distance even when the density is low. In general, the ratio of bulk drag coefficient to drag coefficient decreases when 2a/S increases.

Keywords


bulk drag coefficient; drag coefficient; multiple cylinders; vegetation; Immersed Boundary Method; CADMAS-SURF/3D; Large Eddy Simulation

References


Arikawa, T., F. Yamada, M. Akiyama, 2005. Study of the Applicability of Tsunami Wave Force in a Three-Dimensional Numerical Wave Flume. Annual Journal of Coastal Engineering, JSCE, Vol.52: 46-50. (in Japanese) http://dx.doi.org/10.2208/proce1989.52.46

Arikawa, T., T. Yamano and M. Akiyama, 2007. Advanced Deformation Method for Breaking Waves by using CADMAS-SURF/3D, Annual Journal of Coastal Engineering, JSCE, Vol54: 71-75. (in Japanese) http://dx.doi.org/10.2208/proce1989.54.71

Augustin, L., Jennifer L. Irish, Patrick Lynett, 2009. Laboratory and numerical studies of wave damping by emergent and near-emergent wetland vegetation, Coastal Engineering 56 (2009) 332–340. http://dx.doi.org/10.1016/j.coastaleng.2008.09.004

Balaras, Elias, 2004. Modeling complex boundaries using an external force field on fixed Cartesian

grids in large-eddy simulations, Computers & Fluids 33 (2004) 375–404. http://dx.doi.org/10.1016/S0045-7930(03)00058-6

Blackburn, H. M. and Schmidt, S., 2001. Large eddy simulation of flow past a circular cylinder. In 14th Australasian Fluid Mechanics Conference.

Briscolini, M. and Santangelo, P., 1989. Development of the mask method for incompressible unsteady flows. Journal of Computational Physics, 84(1):57 – 75. http://dx.doi.org/10.1016/0021-9991(89)90181-2

Christensen, E.D., Deigaard, R., 2001. Large eddy simulation of breaking waves. Coastal Engineering 42: 53–86. http://dx.doi.org/10.1016/S0378-3839(00)00049-1

de Oude, R., D.C.M. Augustijn, F. D., Wijnberg, K., de Vries, M., and Suzuki, T., 2010. Modelling wave attenuation by vegetation in swan to determine a vegetation field for decreasing dike height in the noordwaard, the netherlands. ISEH 2010.

Fadlun, E. A., Verzicco, R., Orlandi, P., and Mohd-Yusof, J., 2000. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 161(1):35 – 60. http://dx.doi.org/10.1006/jcph.2000.6484

Goldstein, D., Handler, R., and Sirovich, L., 1993. Modeling a no-slip flow boundary with an external force field. Journal of Computational Physics, 105(2):354 – 366. http://dx.doi.org/10.1006/jcph.1993.1081

Heideman, J. and Sparpkaya, T., 1985. Hydrodynamic forces on dense arrays of cylinders. OTC1985.

Iimura, K., Tanimoto, K., Hien, N. X., Akagawa, Y., and Yutani, K., 2007. Numerical simulation of ship wave damping by emergent vegetation community. Annual Journal of Coastal Engineering, JSCE, 54:766–770. (in Japanese) http://dx.doi.org/10.2208/proce1989.54.766

Kobayashi N., Raichle A.W. & Asano, T., 1993. Wave attenuation by vegetation. J. Waterw. Port Coast. Ocean Eng. 119, 30-48. http://dx.doi.org/10.1061/(ASCE)0733-950X(1993)119:1(30)

Kravchenko, A. G., Moin, P., and Shariff, K., 1999. B-spline method and zonal grids for simulations of complex turbulent flows. J. Comput. Phys., 151(2):757– 789. http://dx.doi.org/10.1006/jcph.1999.6217

Lourenco, L. M. and Shih, C., 1993. Characteristics of the plane turbulent near wake of a circular cylinder; a particle image velocimetry study (data taken from Beaudan & Moin 1994).

Mendez F.M. & Losada I.J., 2004. An empirical model to estimate the propagation of random breaking and nonbreaking waves over vegetation fields. Coastal Engineering 51, 103-118. http://dx.doi.org/10.1016/j.coastaleng.2003.11.003

Mittal, R. and Balachandar, S., 1997. On the inclusion of three-dimensional effects in simulations of two-dimensional bluff body wake flows. In Proceedings of ASME Fluid Engineering Division Summer Meeting, Vancouver, BC, Canada.

Mohd-Yusof J. 1997. Combined immersed boundaries/B-splines methods for simulations of flows in complex geometries. CTR Annual Research Briefs, NASA Ames/Stanford University.

Narayan, S., 2009. The effectiveness of mangroves in attenuating cyclone- induced waves. Master's thesis, Delft University of Technology. Nepf., H. M., 1999. Drag, turbulence, and diffusion in flow through emergent vegetation, Water resources research, vol. 35, No. 2: 479-489.

Norberg, C., 1994. An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. Journal of Fluid Mechanics Digital Archive, 258(-1):287–316.

Ong, L. and Wallace, J., 1996. The velocity field of the turbulent very near wake of a circular cylinder. Experiments in Fluids, 20:441–453. http://dx.doi.org/10.1007/BF00189383

Peskin. C. S., 1972. Flow patterns around heart valves: A numerical method, Journal of Compt. Phys., 10-2, pp.252-271 http://dx.doi.org/10.1016/0021-9991(72)90065-4

Sarpkaya, T., 1976. Vortex shedding and resistance in harmonic flow about smooth and rough circular cylinders at high Reynolds numbers. Tech. Rep. No. NPS-59SL76021, Naval Postgraduate School, Monterey, CA.

SPM (Shore Protection Manual). 1984. Coastal Eng. Res. Center, U.S. Army Corps of Engineers, Washington, vol. I.

Sumer, B.M., J. Fredsøe, 2006. Hydrodynamics around cylindrical structures. Revised Edition, World Scientific.

Suzuki, T., T. Arikawa and Marcel J.F. Stive, 2009. Numerical modeling of hydrodynamics in a salt marsh. Proceedings of Coastal dynamics 2009, ASCE.

Suzuki, T., Okayasu, A., and Shibayama, T., 2007. A numerical study of intermittent sediment concentration under breaking waves in the surf zone. Coastal Engineering, 54(5):433 – 444. http://dx.doi.org/10.1016/j.coastaleng.2006.11.002

Yang, J. and Balaras, E., 2006. An embedded-boundary formulation for large eddy simulation of turbulent flows interacting with moving boundaries. Journal of Computational Physics, 215(1):12 – 40. http://dx.doi.org/10.1016/j.jcp.2005.10.035


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