Dynamics and control of flow in a thermal convection loop

Abstract

The dynamics of a thermal convection loop heated from below and cooled from above are investigated experimentally and theoretically. Three equations similar to the celebrated Lorenz equations are used to model and study the dynamics of the loop. In the absence of a controller, as the Rayleigh number (a quantity which is proportional to the heating rate) increases, the flow in the loop undergoes a sequence of transitions from a no-motion state to time-independent, unidirectional convection and then to chaos. The loss of stability of the time-independent motion occurs through a subcritical Hopf bifurcation. It is demonstrated experimentally and theoretically that through the use of an active (feedback) controller one can dramatically modify the nature of the flow in the loop. Linear feedback control, washout filter based feedback control, optimal control, and neural networks are used to delay the onset of chaotic convection. The performance of these control strategies is compared. The effect of time delay on the linear feedback control is investigated experimentally and theoretically. Nonlinear control is used to render the subcritical bifurcation supercritical and to replace the chaotic attractor with a periodic one. It is also demonstrated that control can be used to stabilize some of the otherwise non-stable periodic orbits embedded in the chaotic attractor