Chaotic flow in a 2D natural convection loop with heat flux boundaries

Chaotic natural convection in a toroidal thermosyphon with heat flux boundaries

“…And second, as the forcing in the system increases, there is not a well defined, dominant oscillatory frequency but rather a broad-band power spectra is observed which weakens only at very high frequencies. This is a notable disparity from prior 2D simulations detailed in Louisos et al [25] where the dominant oscillatory frequency is more pronounced at higher forcing. We now turn our attention to a comparison of 2D and 3D thermosyphon results wherein both the similarities and disparities are explored in further detail.…”

“…In this work, we numerically simulate the first 10; 000þ s of flow time (P 40; 000 time-steps) in order to analyze flow-field from start-up at time t ¼ 0 (i.e., thermal equilibrium throughout the domain at a temperature of 300 K and no flow) to the point where the low regime is able to be well characterized. The efficacy of this computational strategy as it pertains to this model of the thermosyphon has been demonstrated in the previous works by Ridouane et al [22,23] and Louisos et al [24,25] …”

“…And second is the fact that flow reversals were not found in 3D isothermal simulations [23] but are known to occur in experiments with heat flux boundary conditions. In an earlier works by Louisos et al [24,25] a chaotic flow regime with flow reversals was found in 2D simulations with heat flux boundary conditions. We thus seek to extend this prior work by examining a 3D thermosyphon with toroidal geometry and heat flux boundaries.…”

“…This definition of the Rayleigh number in terms of a heat flux boundary has been validated over a large range of forcing conditions (i.e., gravity, heat flux) in prior work [24,25]. Variations of the Rayleigh number are achieved by adjusting the value of the heat flux ð1:0 6 q 00 6 1:0 Â 10 4 W=m 2 Þ with the gravitational acceleration ð0:5 m=s 2 < g < 9:8 m=s 2 Þ in order to yield Rayleigh numbers ranging from 1:45 Â 10 3 6 Ra 6 2:8 Â 10 8 .…”

“…The typical progression of flow regimes with increased forcing is as follows: (1) pure-conduction and/or quasi-conduction characterized by no bulk circulation and weak, localized mixing at the ±heat flux discontinuity; (2) stable convection with continuous, unidirectional bulk mass-flow (i.e., no flow reversals); (3) Lorenz like chaotic flow characterized by oscillations that grow in amplitude with time and result in flow reversals where the bulk mass flow transitions from CCW to CW and back to CCW many times throughout a given simulation; and (4) high-Rayleigh, stable convection characterized by unidirectional flow with high frequency, low amplitude, aperiodic oscillations centered about a particular mass flow rate [25]. However, for the lowest Rayleigh numbers considered in this study, neither the pure-conduction nor quasi-conduction flow regime was observed.…”