Dynamical behaviour of natural convection in a single-phase loop

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Abstract
A one-dimensional model is derived for natural convection in a closed loop. The physical model can be reduced to a set of nonlinear ordinary differential equations of the Lorenz type. The model is based on a realistic heat transfer law and also accounts for a non-symmetric arrangement of heat sources and sinks. A nonlinear analysis of these equations is performed as well as experiments to validate the model predictions. Both the experimental and the analytical data show that natural convection in a loop is characterized by strong nonlinear effects. Distinct subcritical regions are observed in addition to a variety of stable steady flow regimes. Thus, in certain ranges of the forcing parameter the flow stability depends significantly on the presence of finite perturbation amplitudes. An absolutely unstable range also exists which is characterized by a chaotic time behaviour of the flow quantities. It is also shown that the steady solutions are subject to an imperfect forward bifurcation if heating of the loop is performed non-symmetrically. In such a case one flow direction is preferred at the onset of convection and, moreover, the corresponding steady solution is more stable than a second, isolated, steady solution. The second solution has the opposite flow direction and is stable only in a relatively small, isolated interval. The preferred steady solution becomes unstable against time-periodic perturbations at a higher value of the forcing parameter. A backward- or a forward-directed bifurcation of the periodic solutions is found depending on the non-symmetry parameter of the system.