Modeling of frictional gas flow effects in a piezoelectrically actuated low leak-rate microvalve under high-pressure conditions

Abstract

One-dimensional modeling of steady frictional radial flow of a perfect gas through a high-pressure piezoelectrically actuated microvalve under low leak-rate conditions is studied. Focusing on the micro-scale gap between the boss and seat plates, a model was developed for axisymmetric flow between two thermally insulated, parallel disks flowing radially toward an outlet hole at the center of the bottom disk. The fourth-order Runge–Kutta algorithm was utilized to integrate a system of nonlinear ordinary differential equations that govern the variations of flow properties. The most notable observation is that of a drastic increase in density and static pressure in contrast to a rather small increase in the Mach number (or velocity). The total pressure drop was also shown to be significant across the seat rings. A 2D Stokes flow model was also derived for incompressible, axisymmetric, radial flow between two concentric parallel disks in order to verify the trends of the flow property variations from the compressible radial flow model. The Stokes flow model trends for both static and total pressure concurred with the predictions of the radial compressible flow model. In addition, a comparison of Stokes flow values for both the static pressure rise and the total pressure drop to that of the numerical results demonstrates the necessity of accounting for compressibility effects.