Numerical Study of the Three-Dimensional Laminar Flow around a Cubic Metal Foam Cell

Amroune, A.; Madani, B.

doi:10.47176/jafm.17.12.2562

Numerical Study of the Three-Dimensional Laminar Flow around a Cubic Metal Foam Cell

Document Type : Special Issue Manuscripts

Authors

Laboratory of Multiphase Transport and Porous Media (LTPMP), Faculty of Mechanical and Process Engineering (FGMGP)/ University of Sciences and Technology Houari Boumediene (USTHB), BP. 32, El Alia, 16111, Algiers, Algeria

10.47176/jafm.17.12.2562

Abstract

The present study examines numerically a three-dimensional (3D) laminar and stationary flow around an idealized metal foam cell shaped as an empty cube with cylindrical edges. The physical configuration adopted consists of an isolated cell placed inside a plane channel crossed by air as a working fluid. The numerical investigation is carried out using the dimensionless Navier-Stokes equations resolved by finite volume method. The flow configurations given for several Reynolds numbers are described entirely using 2D and 3D maps. The plane maps give streamlines at the side and top fiber planes: the vertical side of the cell is normal to the flow. In addition, the critical locations and zones characterizing the flow are also localized: the saddle points, separation nodes, attachment points, foci of the recirculation zones, and the attachment lines. For the Reynolds number in the range 75 ≤ Re≤ 500 , the results show that the topography of the streamlines at the vertical plane in the middle of the lateral fibers of the cell (z = 5,3 Dp ) is developed into arc-shaped vortex rollers in the gap. In the wake, two saddle points reveal the zones of influence of these spiral structures, formed by two vortices (Bt and Nw) and zones of upwash and downwash. At a high value of Re (Re = 500), the upwash weakens but does not disappear. Two recirculation bubbles are associated with the two saddles, in the gap and the wake of the upper fibers, parallel to the flow. At Re =500, the distribution flow loses its symmetry and displays matter transfer between the two recirculation. The displacement of the saddle point in the wake is 9.65 times that in the gap. No vortex shedding is observed in the wake of cell due to the nullity of the frequency shedding (f = 0) .The results indicate also that decreasing the pore diameter favors recirculation inside the cell gap. These recirculation lengths (L_r,z , L_r,y) located respectively in the wake of planes z = 5,3 Dp and y= Dp reduce the drag coefficient in equal proportion (51%) in the range 75 ≤ Re≤ 500 . It appears that the wake of the lateral fibers of the z=5.3D_p plane contributes better to the drag coefficient. We consider that the predominance of downwash associated with the instability of saddle point S.2 in the wake when Re increases leads to a decrease in the drag coefficient in the wake.

Keywords

Main Subjects

Boundary Layers

References

Abaidi, A., & Madani, B. (2020). Intensification of hydrogen production from methanol steam reforming by catalyst segmentation and metallic foam insert. International Journal of. Hydrogen Energy, 46(75), 37583-37598. https://doi.org/10.1016/j.ijhydene.2020.12.183

Abu-Qudais, M., Haddad, M. O., & Maqableh, M. A. (2001). Hydrodynamic and heat transfer characteristics of laminar flow past a parabolic cylinder with constant heat flux. Heat and Mass Transfer, 37, 299–308. https://doi.org/10.1007/s002310100199

Afgan, I., Kahil, Y., Benhamadouche, S., Ali, M., Alkaabi, A., Berrouk, S. A., & Sagaut, P. (2023). Cross flow over two heated cylinders in tandem arrangements at subcritical Reynolds number using large eddy simulations. International Journal of. Heat and Fluid Flow, 100(10), 109115. https://doi.org/10.1016/j.ijheatfluidflow.2023.109115

Backer, J. C. (1979). The laminar horseshoe vortex. Journal of Fluid Mechanics, 95(2), 347367. https://doi.org/10.1017/S0022112079001506

Behera, S., & Saha, K. A. (2019). Characteristics of the flow past a wall-mounted finite-length square cylinder at low Reynolds number with varying boundary layer thickness. Journal of Fluids Engineering, 141(6), 061204. https://doi.org/10.1115/1.4042751

Bhattacharya, A., Calmidi, V. V., & Mahajan, L. R. (2002) Thermophysical properties of high porosity metal foams. International Journal of Heat and Mass Transfer, 45(5), 1017-1031. https://doi.org/10.1016/S0017-9310(01)00220-4

Chen, W., Ji, C., Alam, M. Md., & Yan, M. (2022). Three-dimensional flow past two stationary side-by-side circular cylinders. Ocean Engineering, 244, 110379. https://doi.org/10.1016/j.oceaneng.2021.110379

Clift, R., Grace, J. R., & Weber, M. E. (2013). Bubbles, drops and particles. Dover Publications, Incorporated. ISBN 9780486788920, 048678892X

Ferfera, S. R., & Madani, B. (2020). Thermal characterization of a heat exchanger equipped with a combined material of phase change material and metallic foams. International Journal of. Heat and Mass Transfer, 148 (11), 119162. https://doi.org/10.1016/j.ijheatmasstransfer.2019.119162

Haupt, E. S., Zajaczkowski, J. F., & Peltier. J. L. (2011). Detached eddy simulation of atmospheric flow about a surface mounted cube at high reynolds number. Journal of Fluids Engineering, 133(3), 031002. https://doi.org/10.1115/1.4003649

Hu, J., Xuan, B. H., Kwok, S. C. K., Zhang, Y., & Yu, Y. (2018). Study of wind flow over a 6m cube using improved delayed detached Eddy simulation. Journal of Wind Engineering and Industrial Aerodynamics, 179, 463-474. https://doi.org/10.1016/j.jweia.2018.07.003

Hwang, Y. J., & Yang, S. K. (2004). Numerical study of vortical structures around a wall-mounted cubic obstacle in channel flow. Physics of Fluid, 16(7), 2382-2394. https://doi.org/10.1063/1.1736675

Islam, U. S., Rahman, H., Abbasi, S. W., Noreen, U., & Khan., A. (2014). Suppression of fluid force on flow past a square cylinder with a detached flat plate at low Reynolds number for various spacing ratio. Journal of Mechanical Science and Technology, 28 (12), 4969-4978. https://doi.org/10.1007/s12206-014-1118-y

Jiang, H., & Cheng, L. (2020). Flow separation around a square cylinder at low to moderate Reynolds numbers. Physics of Fluids, 32(4), 044103. https://doi.org/10.1063/5.0005757

Klotz, L., Durand, G. S., Rokicki, J., & Wesfreid, E. J. (2014). Experimental investigation of flow behind a cube for moderate Reynolds numbers. Journal of Fluid Mechanics, 750, 73-98. https://doi.org/10.1017/jfm.2014.236

Krajnović, S. (2011). Flow around a tall finite cylinder explored by large eddy simulation. Journal of fluid Mechanics, 676, 294-317. https://doi.org/10.1017/S0022112011000450

Kravchenko, G. A., & Moin, P. (2000). Numerical studies of flow over a circular cylinder at Re_D = 3900. Physics of Fluids, 12(2), 403-417. https://doi.org/10.1063/1.870318

Kumar, P., & Singh, S. K. (2019). Flow past a bluff body subjected to lower subcritical Reynolds number. Journal of Ocean Engineering and Science, 5(2), 173-179. https://doi.org/10.1016/j.joes.2019.10.002

Launay, G., Mignot, E., & Rivière, N. (2019). Laminar free-surface flow around emerging obstacles: Role of the obstacle elongation on the horseshoe vortex. European Journal of Mechanics - B/Fluids, 77, 71–78. https://doi.org/10.1016/j.euromechflu.2019.04.006

Li, J., Chambarel, A., Donneaud, M., & Martin, R. (1991). Numerical study of laminar flow past one and two circular cylinders, Computers & Fluids, 19(02), 155–170. https://doi.org/10.1016/0045-7930(91)90031-C

Liakos, A., & Malamataris, A. N. (2014). Direct numerical simulation of steady state, three dimensional, laminar flow around a wall mounted cube. Physics of Fluids, 26(5), 053603. https://doi.org/10.1063/1.4876176

Lu, J. T., Stone, A. H., & Ashby, F. M. (1998). Heat transfer in open-cell metal foams. Acta Materiala, 46(10), 3619-3635. https://doi.org/10.1016/S1359-6454(98)00031-7

Ma, Y., Rashidi, M. M., & Yang, Z. (2019). Numerical simulation of flow past a square cylinder with a circular bar upstream and a splitter plate downstream. Journal of Hydrodynamics, 31(5), 949-964. https://doi.org/10.1007/s42241-018-0087-5

Madani, B., Topin, F., Tadrist, T., & Rigollet, F. (2007). Flow laws in metallic foams: Experimental determination of inertial and viscous contributions. Journal of Porous Media, 10(1), 51-70. https://doi.org/ 10.1615/JPorMedia.v10.i1.40

Mishra, K. S., Sen, S., & Verma, A. (2021). Steady flow past a circular cylinder under large blockage. European Journal of Mechanics - B/Fluids, 87, 135–150. https://doi.org/10.1016/j.euromechflu.2021.01.014

Palau-Salvador, G., Stoesser, T., & Rodi, W. (2008). LES of the flow around two cylinders in tandem. Journal of Fluids and Structures, 24(8), 1304–1312. https://doi.org/10.1016/j.jfluidstructs.2008.07.002

Paterson, A. D., & Apelt, J. C. (1990). Simulation of flow past a cube in a turbulent boundary layer. Journal of Wind Engineering and Industrial Aerodynamics, 35, 149-176. https://doi.org/10.1016/0167-6105(90)90214-W

Richards, J. P., Hoxey, P. R., & Short, J. L. (2001). Wind pressures on a 6m cube. Journal of Wind Engineering and Industrial Aerodynamics, 89(14-15), 1553–1564. https://doi.org/10.1016/S0167-6105(01)00139-8

Saha, K. A. (2004). Three-dimensional numerical simulations of the transition of flow past a cube. Physics of Fluids, 16(5), 1630–1646. https://doi.org/10.1063/1.1688324

Shang, J., Zhou, Q., Alam, M. Md., Liao, H., & Cao, S. (2019). Numerical studies of the flow structure and aerodynamic forces on two tandem square cylinders with different chamfered-corner ratios. Physics of Fluids, 31(7), 075102. https://doi.org/10.1063/1.5100266

Sumner, D., Rostamy, N., Bergstrom, D. J., & Bugg, J. D. (2017). Influence of aspect ratio onthe mean flow field of a surface-mounted finite-height square prism. International Journal of Heat and Fluid Flow, 65, 1–20. https://doi.org/10.1016/j.ijheatfluidflow.2017.02.004

Visbal, R. M. (1991). Structure of laminar juncture flows. AIAA Journal, 29(8), 1273-1282. https://doi.org/10.2514/3.10732

Zhang, D., Cheng, L., An, H., & Zhao, M. (2017). Direct numerical simulation of flow around a surface mounted finite square cylinder at low Reynolds numbers. Physics of Fluids, 29(4), 045101. https://doi.org/10.1063/1.4979479

Zhang, X. F., Yang, J. C., Ni, M. J., Zhang, N. M., & Yu, X. G. (2022). Experimental and numerical studies on the three-dimensional flow around single and two tandem circular cylinders in a duct. Physics of Fluids, 34 (03), 033610. https://doi.org/10.1063/5.0084764.

Zhao, M., Al Mamoon, A., & Wu, H. (2021). Numerical study of the flow past two wall-mounted finite-length square cylinders in tandem arrangement. Physics of Fluids, 33(9), 093603. https://doi.org/10.1063/5.0058394

Zhou, Q., Alam, M. Md., Cao, S., Liao, H., & Li, M. (2019). Numerical study of wake and aerodynamic forces on two tandem circular cylinders at Re = 10³. Physics of Fluids, 31(4), 045103. https://doi.org/10.1063/1.5087221