On the Modeling and Control of Coupled Multi-Loop Thermosyphons

This paper presents a one-dimensional model for natural convection in coupled multi-loop thermosyphons. The physical model is governed by a system of Navier-Stokes equations, which are reduced to coupled systems of Lorenz equations via the Galerkin method. The simulations reveal different stages of flow of the Rayleigh number increases, e.g., from heat conduction, steady convective flow, to chaotic time-dependent flow. The control objective is either stabilized the flow in each loop at one its equilibrium points or track a reference signal in the chaotic range of the Rayleigh number. The controller design is based on proportional and integral (PI) control principles. The design can be easily implemented because the feedback state is measurable.