Bifurcation analysis of steady natural convection in a tilted cubical cavity with adiabatic sidewalls

Torres, Juan F.; Henry, Daniel; Komiya, Atsuki; Maruyama, Shigenao

doi:10.1017/jfm.2014.448

Cited by 30 publications

(16 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In this study, we keep the same cubical configuration, system of coordinates, and notation as described in Ref. [25]. For RBC in noncubical cavities (aspect ratio A = 1) an uneven shear stress exerted from the sidewalls favors certain groups of solutions [26].…”

Section: Problem Descriptionmentioning

confidence: 99%

“…1, is still a fundamental physics problem whose mechanism is not fully understood [18][19][20][21][22][23][24]. In an attempt to explain this transition, we previously conducted a preliminary, but detailed, bifurcation analysis for water (Prandtl number Pr = 5.9) in a cubical enclosure and reported several critical angles where stable solutions cease * torres.jf@outlook.com, felipe.torres@toshiba.co.jp to exist [25]. It is well-known, however, that the dynamics of RBC in an enclosure is greatly dependent on the Prandtl number, i.e., the ratio of momentum diffusivity to thermal diffusivity expressed as Pr = ν/α, where ν and α are the kinematic viscosity and thermal diffusivity, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

et al. 2015

View full text Add to dashboard Cite

The transition from the complex Rayleigh-Bénard convection to the simple heated-from-the-sides configuration in a cubical cavity filled with a Newtonian fluid is numerically studied. The cavity is tilted by an angle θ around its lower horizontal edge and is heated and cooled from two opposite tilted sides. We first analyze the effect of a marginal inclination angle on quasi-Rayleigh-Bénard convection (θ≈0∘), which is a realistic physical approximation to the ideal Rayleigh-Bénard convection. We then yield the critical angles where multiple solutions that were initially found for θ≈0∘ disappear, eventually resulting in the single steady roll solution found in the heated-from-the-sides configuration (θ=90∘). We confirm the existence of critical angles during the transition θ:0∘→90∘, and we demonstrate that such angles are a consequence of either singularities or collisions of bifurcation points in the Rayleigh-number-θ parameter space. We finally derive the most important critical angles corresponding to any Newtonian fluid of Prandtl number greater than that of air.

show abstract

Section: Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Other geometries have also been considered. Torres et al [17] study the transition from Rayleigh-Bénard convection to the heated-from-the-sides configuration in a closed parallelepiped. Convective patterns arising in a tilted cylinder at much larger rates of heating and for angles covering the Rayleigh-Bénard case are shown in [18].…”

Section: Introductionmentioning

confidence: 99%

Effect of small inclination on binary convection in elongated rectangular cells

et al. 2019

View full text Add to dashboard Cite

We analyze the effect of a small inclination on the well-studied problem of two-dimensional binary fluid convection in a horizontally extended closed rectangular box with a negative separation ratio, heated from below. The horizontal component of gravity generates a shear flow that replaces the motionless conduction state when inclination is not present. This large scale flow interacts with the convective currents resulting from the vertical component of gravity. For very small inclinations the primary bifurcation of this flow is a Hopf bifurcation that gives rise to chevrons and blinking states similar to those obtained with no inclination. For larger but still small inclinations this bifurcation disappears and is superseded by a fold bifurcation of the large scale flow. The convecton branches, i.e., branches of spatially localized states consisting of counterrotating rolls, are strongly affected, with the snaking bifurcation diagram present in the non-inclined system destroyed already at small inclinations. For slightly larger but still small inclinations we obtain small amplitude localized states consisting of corotating rolls that evolve continuously when the primary large scale flow is continued in the Rayleigh number. These localized states lie on a solution branch with very complex behavior strongly dependent on the values of the system parameters. In addition, several disconnected branches connecting solutions in the form of corotating rolls, counterrotating rolls, and mixed corotating and counterrotating states are also obtained.

show abstract

“…Subramanian et al [26] analyze in extended layers the rich variety of spatiotemporal patterns that had been observed experimentally by Daniels et al [27,28] when varying the inclination angle. Torres et al [29] study the transition from the Rayleigh-Bénard convection to the heated-from-the-sides configuration in parallelepipedic cavities. Both works cover a wide range of inclination angles, from quasi-Rayleigh-Bénard convection to the heated from the side configuration.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent patterns in quasivertical cylindrical binary convection

2018

View full text Add to dashboard Cite

This paper reports on numerical investigations of the effect of a slight inclination α on pattern formation in a shallow vertical cylindrical cell heated from below for binary mixtures with a positive value of the Soret coefficient. By using direct numerical simulation of the three-dimensional Boussinesq equations with Soret effect in cylindrical geometry, we show that a slight inclination of the cell in the range α≈0.036rad=2^{∘} strongly influences pattern selection. The large-scale shear flow (LSSF) induced by the small tilt of gravity overcomes the squarelike arrangements observed in noninclined cylinders in the Soret regime, stratifies the fluid along the direction of inclination, and produces an enhanced separation of the two components of the mixture. The competition between shear effects and horizontal and vertical buoyancy alters significantly the dynamics observed in noninclined convection. Additional unexpected time-dependent patterns coexist with the basic LSSF. We focus on an unsual periodic state recently discovered in an experiment, the so-called superhighway convection state (SHC), in which ascending and descending regions of fluid move in opposite directions. We provide numerical confirmation that Boussinesq Navier-Stokes equations with standard boundary conditions contain the essential ingredients that allow for the existence of such a state. Also, we obtain a persistent heteroclinic structure where regular oscillations between a SHC pattern and a state of nearly stationary longitudinal rolls take place. We characterize numerically these time-dependent patterns and investigate the dynamics around the threshold of convection.

show abstract

Bifurcation analysis of steady natural convection in a tilted cubical cavity with adiabatic sidewalls

Abstract: International audienceno abstrac

Cited by 30 publications

References 43 publications

Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

Effect of small inclination on binary convection in elongated rectangular cells

Time-dependent patterns in quasivertical cylindrical binary convection

Contact Info

Product

Resources

About