Stability of air-cushion surge tanks with throttling

Abstract

The throttling orifice is introduced into air-cushion surge chambers to improve stability. The presence of the orifice adds another nonlinear term to the dynamic system, and its effect becomes predominant for oscillations with large displacements. By means of linearization, the type of singularities in the phase plane and their stability criteria in case of small oscillations are identified. The nonlinear analysis by direct numerical integration indicates that the system manifests itself as Hopf bifurcation with the surge-chamber size as its controlling factor. The bifurcation point corresponds to Svee's stability criterion. Before bifurcation, an unstable limit cycle may occur around the equilibrium state of practical interest, and it defines the domain of asymptotic stability. After bifurcation, two limit cycles may occur. Because of the existence of the stable one, the chamber size can be smaller than that specified by the Svee criterion. The orifice has stabilizing effect on surge motions.