Similar articles

Abstract: We investigate the flow inside a 2D square cavity driven by the motion of two mutually facing walls independently sliding at different speeds. The exploration, which employs the lattice Boltzmann method (LBM), extends on previous studies that had the two lids moving with the exact same speed in opposite directions. Unlike there, here the flow is governed by two Reynolds numbers (Re_T, Re_B) associated to the velocities of the two moving walls. For convenience, we define a bulk Reynolds number Re and quantify the driving velocity asymmetry by a parameter α. Parameter α has been defined in the range α∈[-π/4,0] and a systematic sweep in Reynolds numbers has been undertaken to unfold the transitional dynamics path of the two-sided wall-driven cavity flow. In particular, the critical Reynolds numbers for Hopf and Neimark-Sacker bifurcations have been determined as a function of α. The eventual advent of chaotic dynamics and the symmetry properties of the intervening solutions are also analyzed and discussed. The study unfolds for the first time the full bifurcation scenario as a function of the two Reynolds numbers, and reveals the different flow topologies found along the transitional path.

双边反向驱动内流过渡流特性研究

[1]AlbensoederS, KuhlmannHC, 2002. Linear stability of rectangular cavity flows driven by anti-parallel motion of two facing walls. Journal of Fluid Mechanics, 458:‍‍153-180.

[2]AlbensoederS, KuhlmannHC, RathHJ, 2000. Multiple solutions in lid-driven cavity flows. I. Parallel wall motion. Zeitschrift fuer Angewandte Mathematik und Mechanik, 80(S3):S615-S616.

[3]AlexakisA, BiferaleL, 2018. Cascades and transitions in turbulent flows. Physics Reports, 767-769:1-101.

[4]AnB, BergadaJM, MellibovskyF, 2019. The lid-driven right-angled isosceles triangular cavity flow. Journal of Fluid Mechanics, 875:476-519.

[5]AnB, BergadàJM, MellibovskyF, et al., 2020a. New applications of numerical simulation based on lattice Boltzmann method at high Reynolds numbers. Computers & Mathematics with Applications, 79(6):1718-1741.

[6]AnB, MellibovskyF, BergadàJM, et al., 2020b. Towards a better understanding of wall-driven square cavity flows using the lattice Boltzmann method. Applied Mathematical Modelling, 82:469-486.

[7]AuteriF, ParoliniN, QuartapelleL, 2002. Numerical investigation on the stability of singular driven cavity flow. Journal of Computational Physics, 183(1):1-25.

[8]BoppanaVBL, GajjarJSB, 2010. Global flow instability in a lid-driven cavity. International Journal for Numerical Methods in Fluids, 62(8):827-853.

[9]FranjioneJG, LeongCW, OttinoJM, 1989. Symmetries within chaos: a route to effective mixing. Physics of Fluids A-Fluid Dynamics, 1(11):1772-1783.

[10]GuoZL, ShiBC, WangNC, 2000. Lattice BGK model for incompressible Navier-Stokes equation. Journal of Computational Physics, 165(1):288-306.

[11]GuoZL, ZhengCG, ShiBC, 2002. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chinese Physics, 11(4):366-374.

[12]HammamiF, Ben-CheikhN, Ben-BeyaB, et al., 2018. Combined effects of the velocity and the aspect ratios on the bifurcation phenomena in a two-sided lid-driven cavity flow. International Journal of Numerical Methods for Heat & Fluid Flow, 28(4):943-962.

[13]IwatsuR, IshiiK, KawamuraT, et al., 1989. Numerical simulation of three-dimensional flow structure in a driven cavity. Fluid Dynamics Research, 5(3):173-189.

[14]JiménezJ, 2012. Cascades in wall-bounded turbulence. Annual Review of Fluid Mechanics, 44:27-45.

[15]KalitaJC, GogoiBB, 2016. A biharmonic approach for the global stability analysis of 2D incompressible viscous flows. Applied Mathematical Modelling, 40(15-16):6831-6849.

[16]LeméeT, KasperskiG, LabrosseG, et al., 2015. Multiple stable solutions in the 2D symmetrical two-sided square lid-driven cavity. Computers & Fluids, 119:204-212.

[17]LeongCW, OttinoJM, 1989. Experiments on mixing due to chaotic advection in a cavity. Journal of Fluid Mechanics, 209:463-499.

[18]NewhouseS, RuelleD, TakensF, 1978. Occurrence of strange AxiomA attractors near quasi periodic flows on T^m, m≧3. Communications in Mathematical Physics, 64(1):35-40.

[19]NonE, PierreP, GervaisJJ, 2006. Linear stability of the three-dimensional lid-driven cavity. Physics of Fluids, 18(8):084103.

[20]NurievAN, EgorovAG, ZaitsevaON, 2016. Bifurcation analysis of steady-state flows in the lid-driven cavity. Fluid Dynamics Research, 48(6):061405.

[21]PerumalDA, DassAK, 2011. Multiplicity of steady solutions in two-dimensional lid-driven cavity flows by lattice Boltzmann method. Computers & Mathematics with Applications, 61(12):3711-3721.

[22]PrasadC, DassAK, 2016. Use of an HOC scheme to determine the existence of multiple steady states in the antiparallel lid-driven flow in a two-sided square cavity. Computers & Fluids, 140:297-307.

[23]QianYH, D’HumièresD, LallemandP, 1992. Lattice BGK models for Navier-Stokes equation. Europhysics Letters, 17(6):479-484.

[24]RomanòF, AlbensoederS, KuhlmannHC, 2017. Topology of three-dimensional steady cellular flow in a two-sided anti-parallel lid-driven cavity. Journal of Fluid Mechanics, 826:302-334.

[25]RomanòF, TürkbayT, KuhlmannHC, 2020. Lagrangian chaos in steady three-dimensional lid-driven cavity flow. Chaos, 30(7):073121.

[26]RuelleD, TakensF, 1971. On the nature of turbulence. Communications in Mathematical Physics, 20(3):167-192.

[27]ShankarPN, DeshpandeMD, 2000. Fluid mechanics in the driven cavity. Annual Review of Fluid Mechanics, 32:93-136.

[28]VassilicosJC, 2015. Dissipation in turbulent flows. Annual Review of Fluid Mechanics, 47:95-114.

[29]YangDX, ZhangDL, 2012. Applications of the CE/SE scheme to incompressible viscous flows in two-sided lid-driven square cavities. Chinese Physics Letters, 29(8):084707.

[30]YuPX, TianZF, 2018. An upwind compact difference scheme for solving the streamfunction-velocity formulation of the unsteady incompressible Navier-Stokes equation. Computers & Mathematics with Applications, 75(9):3224-3243.