The arbitrary boundary method to determine the performance of membrane-type restrictors

This paper presents a novel method to determine the flow rate and fluid resistance of membrane-type restrictors. The coupled fluid pressure and membrane deformation is solved utilizing a fluid and structure interaction algorithm. The arbitrary boundary condition of a membrane is properly handled by adding the displacement springs and torsion springs to the boundary nodes of the membrane, and the finite element method is used to calculate the membrane deformation. Three different methods are studied using several case studies: the arbitrary boundary method, the large deformation method, and the traditional method. The results are compared with the experimental data available in the literature. It has been found that among all three methods, the arbitrary boundary method offers the best results. The membrane deformations show a nonlinear relationship with different supply pressures. The results reveal the boundary condition of the membrane is not a fixed boundary or a simply supported boundary; it is an arbitrary boundary condition, which varies with respect to the supply pressure. By taking the statistical model into consideration in the design process, the proposed arbitrary boundary condition method offers the potential to accurately calculate the flow rate and improve the reliability of the designs for membrane-type restrictors.