Three-dimensional Numerical Simulation On Flow State Multiplicity And Pattern Evolution Of Rayleigh-bénard Convection In Cylindrical Containers

Rayleigh-Bénard convection driven by the buoyancy in the confined cavity heatedfrom below has received considerable attention not only for its applications in manyengineering and science fields, but also for its fundamental aspects as the richdynamical behavior and the complex pattern formation determined by the nonlineareffect of the system. At present, the research activities of Rayleigh-Bénard convectionare mainly forcused on the Boussinesq fluid, whose density changes as a linear functionof temperature. However, there are only a few studys about the water near its densitymaximum in cylindercal container heated from below, especially for the patternformation in this configuration. This paper conducted a three-dimensional numericalsimulation to study the steady states multiplicity and non-linear flow evolution of theBoussinesq fluild and cold water in cylindrical Rayleigh-Bénard convection,respectively. The Prandtl number of the Boussinesq fluid is7, and for cold waterPr=11.57. The governing equations are solved by a finite volume method and the effectof initial condition and control parameter are taken into account. For the Boussinesqfluid, we obtained a rich variety of convection patterns, such as single-roll, two-roll andaxisymmetric pattern, we also determined the stability range of all the steady patternswe obtained and the bifurcate sequence of different flow states. For the cold water, wesuccessfully observed many stable steady convection patterns under different densityinversion parameters. We also observed the hysteresis phenomenon in cold waterconvection.It is found that, the coexisting phenomenon of multiple steady flow states in thesame Rayleigh number is observed both in the Boussinesq fluid and cold water. Ourresearch demonstrates that the flow initial condition has a significant effect on thepattern formation and evolution, under different initial condition, the final bifurcatesequence also is different. The density inversion parameter mhas a great influence onthe cold water Rayleigh-Bénard convection. For small m, the flow structure in coldwater is similar with the flow state in the Boussinesq fluids, they are all exhibit the bigconvection roll. However, for the larger m, the flow pattern mainly shows severalseparately up-flows, especially for m>0.5, their also observed the statified flowphenomenon. The results also show that the aspect ratio of the cylinder has an importantinfluence on the multiplicity of the steady flow states, the decrease of the aspect ratio will restrict the increase of the number of rolls in the system.