Flow in a three-sided lid-driven cavity: parallel upward motion
Main Article Content
Abstract
This numerical investigation examines the flow dynamics within a three-sided lid-driven square cavity, characterized by two opposite horizontal walls translating independently to the right, an upward-moving left vertical wall, and a stationary right vertical wall. Two configurations are considered, each defined by equal Reynolds numbers (Re=100) for two moving walls, while the third wall operates at higher Reynolds numbers (Re=200, 400, 800, and 1600). The study analyzes the resulting flow fields, including primary and secondary vortex formation, vorticity distribution, velocity profiles, energy dissipation, and associated fluid characteristics. Particular emphasis is placed on the genesis and evolution of vortical structures, elucidating the complex interaction mechanisms inherent in this asymmetric boundary-driven system. The results demonstrate that variations in the Reynolds number of a single moving wall substantially alter the internal flow topology and energy, thereby contributing to a deeper understanding of three-sided lid-driven cavity flows under asymmetric forcing. Energy dissipation peaks near moving walls, scaling nonlinearly with Re. Insights can be provided for confined flow control in industrial applications.
Article Details
Section
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
-
ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
How to Cite
References
AbdelMigid TA, Saqr KM, Kotb MA, Aboelfarag AA. (2017). Revisiting the lid-driven cavity flow problem: Review and new steady-state benchmarking results using GPU accelerated code. Alexandria Eng J 2017;56(1):123–135. doi:10.1016/j.aej.2016.09.013.
Aidun CK, Triantafillopoulos NG, Benson JD. (1991). Global stability of a lid-driven cavity with throughflow: flow visualization studies. Phys Fluids A 1991;3:2081–2091. doi:10.1063/1.857891.
Albensoeder S, Kuhlmann HC, Rath HJ. (2001) Multiplicity of steady two-dimensional flows in two-sided lid-driven cavities. Theor Comput Fluid Dyn 2001;14:223–41. doi:10.1007/s001620050138.
Albensoeder S, Kuhlmann HC, Rath HJ. (2001). Three-dimensional centrifugal-flow instabilities in the lid-driven cavity problem. Phys Fluids 2001;13:121–135. doi:10.1063/1.1329908.
An B, Bergadà JM, Mellibovsky F, Sang WM. (2020). New applications of numerical simulation based on lattice Boltzmann method at high Reynolds numbers. Comput Math Appl 2020;79(6):1718–1741. doi:10.1016/j.camwa.2019.10.002.
Auteri F, Parolini N, Quartapelle L. (2002). Numerical investigation on the stability of singular driven cavity flow. J Comput Phys 2002;183:1–25. doi:10.1006/jcph.2002.7145.
Azzouz EA, Houat S, Dellil AZ. (2021). Numerical assessment of turbulent flow driving in a two-sided lid-driven cavity with antiparallel wall motion. Defect Diffus Forum 2021;406:133–148. doi:10.4028/www.scientific.net/DDF.406.133.
Azzouz EA, Houat S. (2020). Numerical analysis and explore of asymmetrical fluid flow in a two-sided lid-driven cavity. J Mech Eng Sci 2020;14(3):7269–7281. doi:10.15282/jmes.14.3.2020.26.0571.
Azzouz EA, Houat S. (2022) Numerical solutions of steady flow in a three-sided lid-driven square cavity. Int J Appl Comput Math 2022;8:118. doi:10.1007/s40819-022-01314-4.
Azzouz EA, Houat S. (2025). Bifurcation of antiparallel motion of the flow in a two-sided lid-driven cavity. Phys Fluids 2025;37:073623. doi:10.1063/5.0271758.
Azzouz, A., S. Houat, “Numerical Models' Effect in Asymmetrical Flow Driving in Tow-Sided Lid-Driven Cavity,” in Proceedings of the 24ème Congrès Français de Mécanique (CFM 2019), Association Française de Mécanique (AFM), 2019.
Azzouz, A., S. Houat, and O. Benhizia, “Numerical study of steady flow inside a lid-driven square cavity for Reynolds number up to 50000,” in Proceedings of the 23ème Congrès Français de Mécanique (CFM 2017), Association Française de Mécanique (AFM), 2017.
Bo AN, Mellibovsky F, Bergadà JM, Sang WM. (2020). Towards a better understanding of wall-driven square cavity flows using the lattice Boltzmann method. Appl Math Model 2020;82:469–486. doi:10.1016/j.apm.2020.01.057.
Botella O, Peyret R. (1998). Benchmark spectral results on the lid-driven cavity flow. Comput Fluids 1998;27(4):421–433. doi:10.1016/S0045-7930(98)00002-4.
Bruneau CH, Saad M. (2006). The two-dimensional lid-driven cavity problem revisited. Comput Fluids 2006;35(3):326–348. doi:10.1016/j.compfluid.2004.12.004.
Burggraf OR. (1966). Analytical and numerical studies of the structure of steady separated flows. J Fluid Mech 1966;24(1):113–151. doi:10.1017/S0022112066000545.
Canedo EL, Denson CD. (1989). Flow in driven cavities with a free surface. AIChE J 1989;35:129–138. doi:10.1002/aic.690350114.
Chen KT, Tsai CC, Luo WJ, Chen CN. (2013). Multiplicity of steady solutions in a two-sided lid-driven cavity with different aspect ratios. Theor Comput Fluid Dyn 2013;27:767–776. doi:10.1007/s00162-013-0296-z.
Erturk E. (2009). Discussions on driven cavity flow. Int J Numer Meth Fluids 2009;60:275–294. doi:10.1002/fld.1887.
Ferziger JH, Peric M. (2002). Computational Methods for Fluid Dynamics. 3rd ed. Berlin: Springer.
Gaskell PH, Innes GE, Savage MD. (1998). An experimental investigation of meniscus roll coating. J Fluid Mech 1998;355:17–44. doi:10.1017/S0022112097007398.
Ghia U, Ghia KN, Shin CT. (1982). High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J Comput Phys 1982;48:387–411. doi:10.1016/0021-9991(82)90058-4.
Gnanasekaran M, Manogaran, Satheesh A. (2024) Numerical analysis of turbulent flow characteristics with the influence of speed ratio in a double-sided cavity. MethodsX 2024;12:102594.
Gürcan F, Gaskell PH, Savage MD, Wilson MCT. (2003). Eddy genesis and transformation of Stokes flow in a double-lid driven cavity. Proc Inst Mech Eng C J Mech Eng Sci 2003;217:353–364. doi:10.1243/095440603762870018.
Kamel AG, Haraz EH, Hanna SN. (2020) Numerical simulation of three-sided lid-driven square cavity. Eng Rep 2020;2:e12151. doi:10.1002/eng2.12151.
Kuhlmann HC, Romanò F. (2018). The lid-driven cavity. In: Gelfgat A, editor. Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics. Vol. 50. Cham: Springer, p. 233–309. doi:10.1007/978-3-319-91494-7_8.
Kuhlmann HC, Wanschura M, Rath HJ. (1997). Flow in two-sided lid-driven cavities: non-uniqueness, instabilities and cellular structures. J Fluid Mech 1997;336:267–299. doi:10.1017/S0022112096004727.
Kusch HA, Ottino JM. Experiments on mixing in continuous chaotic flows. J Fluid Mech 1992;236:319–348. doi:10.1017/S0022112092001405.
Lemée T, Kasperski G, Labrosse G, Narayanan R. (2015) Multiple stable solutions in the 2D symmetrical two-sided square lid-driven cavity. Comput Fluids 2015;119:204–12. doi:10.1016/j.compfluid.2015.05.022.
McIlhany KL, Guth S, Wiggins S. (2011). Optimizing mixing in lid-driven flow designs through predictions from Eulerian indicators. Phys Fluids 2011;23:082005. doi:10.1063/1.3626022.
Meseguer A, Alonso A, Batiste O, An B, Mellibovsky F. (2024). Bifurcation analysis in the regularized four-sided cavity flow: equilibrium states in a D2-symmetric fluid system. Phys Fluids 2024;36:064104. doi:10.1063/5.0208089.
Murdock JR, Ickes JC, Yang SL. (2017). Transition flow with an incompressible lattice Boltzmann method. Adv Appl Math Mech 2017;9(5):1271–1288. doi:10.4208/aamm.OA-2016-0103.
Ramanan N, Homsy GM. (1994). Linear stability of lid-driven cavity flows. Phys Fluids 1994;6(8):2690–2701. doi:10.1063/1.868158.
Schreiber R, Keller HB. (1983). Driven cavity flows by efficient numerical techniques. J Comput Phys 1983;49:310–333. doi:10.1016/0021-9991(83)90129-8.
Shankar PN, Deshpande MD. (2000). Fluid mechanics in the driven cavity. Annu Rev Fluid Mech 2000;32:93–136. doi:10.1146/annurev.fluid.32.1.93.
Verma P, Das MK. (2024). Vortex structure and control in a lid-driven cavity with magnetic field. Phys Fluids 2024;36:121910. doi:10.1063/5.0242089.
Versteeg HK, Malalasekera W. (2007). An Introduction to Computational Fluid Dynamics: The Finite Volume Method. 2nd ed. India: Pearson.
Wahba EM. (2009). Multiplicity of states for two-sided and four-sided lid-driven cavity flows. Computers & Fluids 2009;38:247–253. doi:10.1016/j.compfluid.2008.02.001.