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ISSN Online: 2377-424X

International Heat Transfer Conference 12
August, 18-23, 2002, Grenoble, France

An ordinary differential model for single-phase rectangular natural circulation loops

Get access (open in a dialog) DOI: 10.1615/IHTC12.1920
6 pages

要約

This paper aims to propose a reliable mathematical model of the dynamics of rectangular natural circulation loops. This is necessary in the design of a control system, which might be even a simple system commanding the heat power supply with a proportional action either on the velocity or on the temperature. The aim of such a controller would be the damping of the unstable oscillations that may arise for high values of the heat power supplied in the heating section, which can lead the system to dangerous chaotic motion and flow reversals. The model definition started from the Navier-Stokes balance equations of the system, in the hypothesis of one dimensional motion and of validity of Boussinesq approximation. The Fourier series expansion of the functions describing the geometry of the loop, the boundary conditions and the fluid temperature distribution, allowed the reduction of the set of three partial differential equations, which are infinite dimensional, to an infinite set of ordinary differential equations, in which each thermal mode is decoupled from the others. Therefore, in order to reduce the model to a finite number of equations in closed form, it was sufficient to choose the number of modes to be considered for a good approximation. The Fourier expansion, in this study, was stopped at the third mode and led to a reduced model of seven ordinary differential equations. The model simulations were compared with those obtained from a real system during an experimental phase. The comparisons confirmed the ability of the model to address the dynamic description of the rectangular natural circulation loop.