Feedback stabilisation of two-dimensional non-uniform pool-boiling states

In this paper the feedback stabilisation of a two-dimensional pool-boiling system is discussed. The pool-boiling system is modelled by a so-called heater-only model, which consists of a Partial Differential Equation (PDE) which describes the heaters internal temperature field and its (nonlinear) boundary conditions given by the heat exchange between fluid and heater at the top and the heat supply at the bottom of the heater. The pool-boiling system is extended with an adjustable heat supply at the bottom of the heater, by which the unstable transition boiling regime is to be stabilised. Thereto, a feedback law, based on the Chebyshev-Fourier-cosine modes of the spectral discretisation of the temperature profile inside the heater, is applied to the system. The control parameters of this feedback law are designed such that satisfactory closed-loop dynamics are obtained. Using this specific feedback law, the control strategy is tested by simulations of the closed-loop pool-boiling system.