Bifurcations from steady to quasi-periodic flows in a laterally heated cavity filled with low Prandtl number fluids

Medelfef, Abdessamed; Henry, Daniel; Bouabdallah, A.; Kaddeche, Slim

doi:10.1017/jfm.2018.912

Cited by 5 publications

(11 citation statements)

References 33 publications

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“…All these symmetries, however, can be broken when the value of Gr is increased. Details on the evolution of such symmetries in a 4×2×1 cavity for different convection levels (increase of Gr) and different Prandtl numbers can be found in [27]. As will be explained thereafter, these symmetries can also be kept or lost depending on the direction of the applied vibration.…”

Section: Reference Buoyant Casementioning

confidence: 95%

Three-dimensional effect of high frequency vibration on convection in silicon melt

et al. 2020

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Using the Chebyshev spectral method, the effect of high frequency (HF) vibrations on a cubic cell heated from the side and containing a liquid metal is investigated. This study extends the numerical and theoretical two-dimensional results presented in the authors' past work [Phys. Fluids 31, 043605 (2019)] about the influence of HF vibration direction on the flow structure in a rectangular crucible filled with a liquid metal. The vibration direction can now be three dimensional, and not limited to the main flow plane. In practice, the study considers that the vibration vector is contained in one of the three principal planes of the cavity (xz, xy, and yz planes). Two different cases, i.e., under weightlessness and gravity conditions, are considered for each type of vibration to better understand the separate effect of both vibration and buoyancy forces and also their combined effects. Each type of vibration has its own features and affects the flow intensity and patterns differently.

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Section: Reference Buoyant Casementioning

confidence: 95%

Three-dimensional effect of high frequency vibration on convection in silicon melt

et al. 2020

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“…For transient computations or unsteady flow simulations, an accurate time stepping of the equations discretized on the spectral element mesh is performed using the third-order accurate time integration scheme proposed by Karniadakis, Israeli & Orszag (1991). Finally, for the specific calculation of periodic orbits (or cycles), we used the cycle continuation method developed by Medelfef et al (2019), but originally proposed by Sánchez et al (2004) and already successfully used in a Rayleigh-Bénard problem by Puigjaner et al (2011). The method is still based on a Newton-Krylov approach in which the periodic states of (2.1)-(2.3) are obtained as fixed points of a Poincaré map.…”

Section: Numerical Methods and Tests Of Accuracymentioning

confidence: 99%

“…The trajectories in the phase space used to approach the periodic state are computed with the time integration scheme at second or third order with a small time step t. The method is found to work well with a convergence generally obtained with a few Newton-Krylov steps (3 to 7), each Newton-Krylov step requiring 1 to 4 generalized minimal residual algorithm (GMRES) iterations for a prescribed precision of 10 −2 . The stability of these periodic solutions is further investigated in the framework of the Floquet theory using an Arnoldi method (Medelfef et al 2019). In our previous work (Medelfef et al 2019), a time integration scheme at third order was always used.…”

Section: Numerical Methods and Tests Of Accuracymentioning

confidence: 99%

Steady and oscillatory flows generated by Eckart streaming in the two-dimensional Rayleigh–Bénard configuration

et al. 2022

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This paper presents a detailed analysis of the flows induced in a long two-dimensional cavity heated from below in the presence of streaming due to ultrasound acoustic waves emitted by a source. The problem is tackled by using performing spectral element codes, allowing continuation of steady solutions, bifurcation points and periodic cycles. For a given dimensionless source size, the governing parameters are the acoustic streaming parameter $A$ which modulates the acoustic force generating the Eckart streaming and the Rayleigh number ${\textit {Ra}}$ which quantifies the buoyant force responsible for the convection. The streaming flow, which goes to the right along the horizontal axis and returns along the lower and upper boundaries, influences the instability thresholds, which are first strongly stabilized above the pure Rayleigh–Bénard threshold ${\textit {Ra}}_0$ when $A$ is increased, before a destabilization to reach the pure streaming threshold $A_c$ at ${\textit {Ra}}=0$ . The steady multi-roll convective flow generated without streaming is replaced by periodic waves when $A$ is increased, forward waves for moderate $A$ and backward waves for large $A$ . The transition between these waves induces a specific dynamics involving steady flows, which has been elucidated. The waves also eventually disappear for a sufficient increase of the Rayleigh number, replaced by steady multi-roll flows hardly influenced by the streaming flow. A very rich dynamics is thus observed with the competition between the waves and the steady flows.

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“…3 The buoyancy-driven flow (1) displays the following two symmetries in the general case Gr > 0. 22,27 Reflectional symmetry about the mid-plane y = 1 2 (denoted P b hereafter):…”

Section: B Double-lid-driven Flowmentioning

confidence: 99%

“…The objective in several of these studies is the understanding of the onset and the development of timedependent flows focusing on low Pr fluids. 27,28 A large body of literature has investigated fundamental aspects in 2D and 3D rectangular cavities, see e.g., Refs. 29-32 and references therein.…”

Section: Introductionmentioning

confidence: 99%

Topological equivalence between two classes of three-dimensional steady cavity flows: A numerical-experimental analysis

et al. 2019

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The present study concerns Lagrangian transport and (chaotic) advection in threedimensional (3D) flows in cavities under steady and laminar conditions. The main goal is to investigate topological equivalences between flow classes driven by different forcing; streamline patterns and their response to nonlinear effects are examined. To this end we consider two prototypical systems that are important in both natural and industrial applications: a buoyancy-driven flow (differentially-heated configuration with two vertical isothermal walls) and a lid-driven flow governed by the Grashof (Gr) and the Reynolds (Re) numbers, respectively. Symmetries imply fundamental similarities between the streamline topologies of these flows. Moreover, nonlinearities induced by fluid inertia and buoyancy (increasing Gr) in the buoyancy-driven flow versus fluid inertia (increasing Re) and single-or double-wall motion in the lid-driven flow cause similar bifurcations of the Lagrangian flow topology. These analogies imply that Lagrangian transport is governed by universal mechanisms and differences are restricted to the manner in which these phenomena are triggered. Experimental validation of key aspects of the Lagrangian dynamics is carried out by particle image velocimetry (PIV) and 3D particle-tracking velocimetry (PTV).

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Bifurcations from steady to quasi-periodic flows in a laterally heated cavity filled with low Prandtl number fluids

Cited by 5 publications

References 33 publications

Three-dimensional effect of high frequency vibration on convection in silicon melt

Three-dimensional effect of high frequency vibration on convection in silicon melt

Steady and oscillatory flows generated by Eckart streaming in the two-dimensional Rayleigh–Bénard configuration

Topological equivalence between two classes of three-dimensional steady cavity flows: A numerical-experimental analysis

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