Modelling and control of rectangular natural circulation loops

Abstract

The aim of this paper is to address the problem of suppressing unstable dynamics occurring in rectangular natural circulation loops on the base of a reliable model-based controller. The first part of the study is devoted to define a high order model, through the reduction by truncation of the Fourier series expansion of the functions describing the loop geometry of Navier–Stokes infinite-dimensional partial differential equations describing the flow, the heating conditions and the temperature distribution of the fluid. The first three modes were considered so that a closed model of seven ordinary differential equations was obtained. The model was then integrated and simulations compared with experimental data, confirming its ability to address the description of the dynamical behaviour of rectangular natural circulation loops. The satisfactory performances of the model lead to use it for the design and experimental testing of model-based feedback control strategies. In particular, a traditional proportional-derivative control approach has been applied to the model linearised around its equilibrium points. The flow velocity or an opportunely selected temperature difference between given points of the loop were chosen as feedback variables. Accordingly, the target of the control action was to drive the feedback variable to its stationary value, computed by means of the mathematical model. Experimental validation of the proposed model-based strategies satisfactorily demonstrated the capability of the approach in stabilising the system dynamics.