Abstract: A simplified model of natural convection, similar to the Lorenz system, is compared to computational fluid dynamics simulations of a thermosyphon in order to test data assimilation (DA) methods and better understand the dynamics of convection. The thermosyphon is represented by a long time flow simulation, which serves as a reference ‘truth’. Forecasts are then made using the Lorenz-like model and synchronised to noisy and limited observations of the truth using DA. The resulting analysis is observed to infer dynamics absent from the model when using short assimilation windows. Furthermore, chaotic flow reversal occurrence and residency times in each rotational state are forecast using analysis data. Flow reversals have been successfully forecast in the related Lorenz system, as part of a perfect model experiment, but never in the presence of significant model error or unobserved variables. Finally, we provide new details concerning the fluid dynamical processes present in the thermosyphon during these flow reversals.
Abstract: Transient laminar natural convection regimes occurring in a thermal convection loop heated from below and cooled from above are investigated numerically for a wide range of Rayleigh numbers spanning the interval from 10^3 to 2.6 × 10^7. In the model system, the lower half of the loop is heated and maintained at a constant high temperature, while the upper half is cooled and maintained at a constant low temperature. A three-dimensional numerical model based on the finite volume method is used to solve the system of governing flow equations. Simulations are performed using water as the working fluid (Pr = 5.83) and detailed numerical results are presented and discussed for conduction, steady convection, and unsteady flow regimes. Although this subject has attracted researchers for decades, there have been no detailed three-dimensional numerical simulations of the dynamics of flow in the thermal convection loop. The objective of the present study is to fill this gap by presenting the temporal evolution of the velocity and temperature fields at key locations within the system. Emphasis is given to the analysis of dynamical behavior of the flow during the unsteady regime. The complexity of flow in the loop, which is characterized by vertical structures and flow recirculation, is visualized for the first time by performing detailed 3-D numerical simulations.
Abstract: This paper numerically investigates the nonlinear dynamics of the unstable convection regime of the thermal convection loop, an experimental analogue of the Lorenz model. The lower half of the toroidal loop is heated and maintained at a constant high temperature, while the upper half is cooled at a constant low temperature. Subject to the proper boundary conditions, the system of governing equations is solved using a finite volume method. The numerical simulations are performed for water corresponding to Pr = 5.83 and Rayleigh number varying from 1000 to 150,000. In the case of a loop heated from below and cooled from above, it has been demonstrated theoretically and experimentally in the literature that multiple flow regimes are possible. Numerical results in terms of streamlines, isotherms, and local heat flux distributions along the walls are presented for each flow regime. Although several studies have investigated the chaotic regime of convection loops, there have been no detailed numerical simulations of the dynamics of flow reversals. Fine-scale flow behavior during the transition from one flow direction to another is illustrated by the temporal evolution of temperature distribution, mass flow rate, and local heat flux at selected locations in the system. Issues related to the observed Kelvin–Helmholtz instabilities are discussed.