An approximate computational method for the fluid stiction problem of two separating parallel plates with cavitation

Stiction forces exerted by a fluid in a thin, quickly widening gap to its boundaries can become a strongly limiting factor of the performance of technical devices, like compressor valves or hydraulic on-off valves. In design optimization such forces need to be properly and efficiently modelled. Cavitation during parts of a stiction process plays a strong role and needs to be taken into account to achieve a meaningful model. The paper presents an approximate calculation method which uses qualitative solution properties of the non cavitating stiction problem, in particular of its level curves and gradient lines. In this method the formation of the cavitation boundaries is approximated by an elliptic domain. The pressure distribution along its principle axis is described by a directly integrable differential equation, the evolutions of its boundaries is guided just by pressure boundary conditions when the cavitation zone expands and by a nonlinear differential equation when it shrinks. The results of this approximate model agree quite well with the solutions of a Finite Volume model for the fluid stiction problem with cavitation.