A 2-D numerical study of chaotic flow in a natural convection loop

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. ! 2009 Elsevier Ltd. All rights reserved.