Stability maps for rectangular circulation loops

This study aims to define a methodology for the construction of stability maps of rectangular natural circulation loop. The interest for these maps derives from their ability to present in synthetic form the results of stability analysis. In fact, the proposed methodology is based on the linear stability analysis around equilibrium points of a high order nonlinear mathematical model describing the dynamical behaviour of the non-dimensional flow velocity and temperature inside the loop. Imposed heat flux at the loop walls has been assumed at the boundaries; in particular, it has been considered that the fluid is heated and cooled during its passage in the horizontal sections, respectively, at bottom and top of the loop, whereas the vertical legs are supposed adiabatic. Hence, the stability analysis was performed considering the effect of the variation of the modified Grashof number, Grm, for a wide range of loop geometrical configurations, assuming various aspect ratios (ratio of the vertical to the horizontal length of the tube) and inner tube diameters.