# zbMATH — the first resource for mathematics

Numerical modelling and passive flow control using porous media. (English) Zbl 1237.76189
Summary: The whole flow over a solid body covered by a porous layer is presented. The three main models used in the literature to compute efficiently the fluid flow are given: the reduction of the porous layer to a boundary condition, the coupling of Darcy equation with Navier-Stokes equations and the Brinkman-Navier-Stokes equations or the penalisation method. Numerical simulations on Cartesian grids using the latest model give easily accurate solutions of the flow around solid bodies with or without porous layers. Adding appropriate porous devices to the solid bodies, an efficient passive control of the two-dimensional incompressible flow is achieved. A strong regularisation of the flow is observed and a significant reduction of the vortex induced vibrations or the drag coefficient is obtained.

##### MSC:
 76S05 Flows in porous media; filtration; seepage 76D05 Navier-Stokes equations for incompressible viscous fluids 76D55 Flow control and optimization for incompressible viscous fluids 76M20 Finite difference methods applied to problems in fluid mechanics
Full Text:
##### References:
 [1] Angot, Ph.; Bruneau, Ch.-H.; Fabrie, P., A penalization method to take into account obstacles in incompressible viscous flows, Numer math, 81, (1999) · Zbl 0921.76168 [2] Bearman, P.W., Investigation of the flow behind a two-dimensional model with a blunt trailing edge with splitter plates, J fluid mech, 21, (1965) · Zbl 0123.21403 [3] Bearman, P.W.; Branković, M., Experimental studies of passive control of vortexinduced vibration, Eur J mech B/fluids, 23, (2004) · Zbl 1045.76500 [4] Bearman, P.W.; Harvey, J.K., Control of circular cylinder flow by the use of dimples, Aiaa j, 31, (1993) [5] Beavers, G.D.; Joseph, D.D., Boundary conditions at a naturally permeable wall, J fluid mech, 30, (1967) [6] Belov, E.B.; Lomov, S.V.; Verpoest, I.; Peeters, T.; Roose, D., Modelling of permeability of textiles reinforcements: lattice Boltzmann method, Compos sci tech, 64, (2004) [7] Breugem, W.P.; Boersma, B.J.; Uittenbogaard, R.E., The laminar boundary layer over a permeable wall, Transport porous media, 59, (2005) · Zbl 1157.76332 [8] Bruneau, C.-H.; Fabrie, P., Effective downstream boundary conditions for incompressible navier – stokes equations, Int J numer meth fluids, 19, (1994) · Zbl 0816.76024 [9] Bruneau, C.-H.; Mortazavi, I., Passive control of the flow around a square cylinser using porous media, Int J numer meth fluids, 46, (2004) [10] Bruneau, C.-H.; Mortazavi, I., Control of vortex shedding around a pipe section using a porous sheath, Int J offshore polar eng, 16, (2006) [11] Bruneau C-H, Gilliéron P, Mortazavi I, Passive control around the two-dimensional square back Ahmed body using porous devices, J Fluids Engg 2008, in press [12] Bruneau, C.-H.; Saad, M., The 2d lid-driven cavity problem revisited, Comp fluids, 35, (2006) · Zbl 1099.76043 [13] Caltagirone, J.-P., Sur l’interaction fluide-milieu poreux: application au calcul des efforts exercés sur un obstacle par un fluide visqueux, CR acad sci, 318, (1994), [série II] · Zbl 0795.76080 [14] Carbou, G., Brinkmann model and double penalization method for the flow around a porous thin layer, J math fluid mech, 8, (2006) [15] Carpenter, P.W.; Porter, L.J., Effects of passive porous walls on boundary-layer instability, Aiaa j, 39, (2001) [16] Das, D.B.; Nassehi, V.; Wakerman, R.J., A finite volume model for the hydrodynamics of combined free and porous flow in sub-surface regions, Adv environ res, 7, (2002) [17] Davies, C.; Carpenter, P.W., Instabilities in a plane channel flow between compliant walls, J fluid mech, 352, (1997) · Zbl 0903.76029 [18] Ehrenstein, U., On the linear stabilities of channel flow over ribelets, Phys fluids, 8, (1996) [19] Gilliéron P, Chometon F. Modelling of stationary three-dimensional detached airflows around an Ahmed Reference Body. In: ESAIM Proceedings; 1999. p. 7. [20] Hahn, S.; Je, J.; Choi, H., Direct numerical simulation of turbulent channel flow with permeable walls, J fluid mech, 450, (2002) · Zbl 1049.76561 [21] Hanspal, N.S.; Waghode, A.N.; Nassehi, V.; Wakeman, R.J., Numerical analysis of coupled Stokes/Darcy flows in industrial filtrations, Transport porous media, 64, (2006) · Zbl 1309.76195 [22] Hlomuka, J., The linearized non-stationary problem for the permeable boundary navier – stokes flows, Appl math comput, 158, (2004) · Zbl 1098.35118 [23] Jimenez, J.; Uhlmann, M.; Pinelli, A.; Kawahara, G., Turbulent shear flow over active and passive porous surfaces, J fluid mech, 442, (2001) · Zbl 1014.76027 [24] Jones, I.P., Low Reynolds number flow past a porous spherical shell, Proc Cambridge philos soc, 73, (1973) · Zbl 0262.76061 [25] Luchini, P., Asymptotic analysis of laminar boundary-layer flow over finely grooved surfaces, Eur J mech B/fluids, 14, (1995) · Zbl 0835.76024 [26] Miliou, A.; Sherwin, S.J.; Graham, J.M.R., Fluid dynamic loading on curved riser pipes, ASME J offshore mech artic eng, 125, (2003) · Zbl 1113.76420 [27] Nield, D.A.; Bejan, A., Convection in porous media, (1999), Springer · Zbl 0924.76001 [28] Ochoa-Tapia, J.A.; Whitaker, S., Momentum transfer at the boundary between a porous medium and a homogeneous fluid, Int J heat mass transfer, 38, (1995) · Zbl 0923.76320 [29] Pangrle, B.J.; Alexandrou, A.N.; Dixon, A.G.; Dibiasio, D., An analysis of laminar fluid flow in porous tube and shell systems, Chem eng sci, 46, (1991) [30] Perot, B.; Moin, P., Shear-free turbulent boundary layers. part 1. physical insights into near-wall turbulence, J fluid mech, 295, (1995) · Zbl 0869.76028 [31] Salinger, A.G.; Aris, R.; Derby, J.J., Finite element formulations for large-scale,coupled flows in adjacent porous and open fluid domains, Int J numer meth fluids, 18, (1994) · Zbl 0807.76039 [32] Silva, R.A.; de Lemos, M.J.S., Turbulent flow in a channel occupied by a porous layer considering the stress jump at the interface, Int J heat mass transfer, 46, (2003) · Zbl 1052.76068 [33] de Socio, L.M.; Marino, L.; Seminara, G., Stability and admittance of a channel flow over a permeable interface, Phys fluids, 17, (2005) · Zbl 1187.76120 [34] Vafai, K.; Tien, C.L., Boundary and inertia effects on flow and heat transfer in porous media, Int J heat mass transfer, 24, (1981) · Zbl 0464.76073 [35] Verleye, B.; Klitz, M.; Croce, R.; Roose, D.; Lomov, S.; Verpoest, I., Computation of the permeability of textiles, () [36] Wagner, C.; Friedrich, R., On the turbulence structure in solid and permeable pipes, Int J heat fluid flow, 19, (1998) [37] Whitaker, S., The method of volume averaging, (1999), Kluwer [38] Wiplier, O.; Ehrenstein, U., Numerical simulation of linear and nonlinear disturbance evolution in a boundary layer with compliant walls, J fluids struct, 14, (2000) [39] Wong, H.Y., A means of controlling bluff body separation, J ind aerodyn, 4, (1979) [40] Zadravkovich, M.M., Review and classification of various aerodynamic and hydrodynamic means for suppressing vortex shedding, J wind eng ind aerodyn, 7, (1981)
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.