Buoyancy-Driven Flow Transitions in Deep Cavities Heated From Below

Abstract

A numerical investigation has been conducted of flow transitions in deep three-dimensional cavities heated from below. The first critical Rayleigh number, RaI, below which the flow is at rest, and the second critical Rayleigh number, RaII, for transition from steady state to oscillatory flow, have been found for cavities of aspect ratios Ar in the range 1–5. Transition to chaos has also been examined for these cases. The results show that RaI=3583,2.545×104 and 5.5×105 and RaII=4.07×105,1.65×106 and 1.30×107 for aspect ratios of 1, 2, and 5 respectively. The route to chaos is PPeriodic→QP2(Quasi-periodic with two incommensurate frequencies)→QP3(Quasi-periodic with three incommensurate frequencies)→NChaotic for Ar=1 with the Rayleigh number varying from 4.07×105 to 4.89×105. The route is PPeriodic→P2(Periodic doubling)→I(Intermittent)→P(Periodic)→N(Chaotic) for Ar=2 over a Ra range of 1.65×106 to 1.83×106. The interval between periodic and chaotic flow is very short for Ar=5.

Simulations of the macroscopic and mesoscopic natural convection flows within rectangular cavities

“…9 at the mesoscopic scale. Overall, the results of the flow sequence from stationary unstable flow to periodic oscillatory flow presented in this study for the macroscopic scale (Kn = 10 À4 ) with AR = 1.5 and 2.0 are in good qualitative agreement with those reported in previous studies [3,4]. Furthermore, the current results demonstrate the importance of the Knudsen number, which represents the characteristics of the flow depend on the length scale of interest (e.g.…”

“…Furthermore, as the Rayleigh number increases, a flow bifurcation to a time-dependent flow motion with a single-frequency periodic oscillatory state is observed, namely the secondary instability. Moreover, as the Rayleigh number is increased yet further in the range of approximately Ra % 10 6 -10 8 [3,4], the flow finally transitions to a chaotic state. de Vahl Davis [1] provided a benchmark numerical solution for a square cavity heated on the left side, cooled on the right side, and with adiabatic boundary conditions on the upper and lower walls.…”

“…Previous investigations of natural convection within a cavity have shown that the primary flow instability, which represents a transition from diffusive thermal conduction to a stationary time-independent steady flow structure, occurs at critical Rayleigh numbers in the range Ra c = 10 3 -10 4 [3] which is dependent on the cavity aspect ratios. Furthermore, as the Rayleigh number increases, a flow bifurcation to a time-dependent flow motion with a single-frequency periodic oscillatory state is observed, namely the secondary instability.…”

Effect of surface radiation on RBC in cavities heated from below

“…Chunmei and Jayathi [3] carried out a numerical investigation of flow transitions in deep three-dimensional cavities heated from below to obtain the critical Rayleigh number for the onset of convection and the transition to turbulence in tall cavities with aspect ratio varying from 1 to 5. To determine the onset of convection, steady simulations were done starting with a Rayleigh number range across which the transition occurs.…”

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Variable Thermodynamic and Transport Properties

“…Numerical investigations have been conducted of flow transitions in Deep Cavities by Xia and Murthy [22]. Numerical investigation of turbulent natural convection in a square enclosure with localized heating from below and symmetrical cooling from the vertical side walls were carried out by Anil kumar Sharma et al [23].…”