Modeling of Frictional Gas Flow in a Piezoelectrically Actuated High-Pressure Microvalve for Flowrate Control
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One-dimensional modeling of frictional compressible gaseous flow through a high-pressure piezoelectrically-actuated microvalve is studied. Focusing on the micro-scale gap between the boss and seat plates, variations of flow properties were predicted using two 1-D models: 1. Channel Flow Model, 2. Radial Flow Model. Both models utilized a 4th order Runge-Kutta algorithm to integrate a respective system of nonlinear ordinary differential equations. A channel flow model was developed for steady, compressible flow of a perfect gas between two infinite insulated parallel plates. This model served the purpose of benchmarking the numerical code against analytical expressions for the properties of flow through a constant-area channel. Additionally, utilizing this model, the total pressure loss through the outlet tube was found to be negligible in comparison to that of total pressure loss across the seat rings. The radial flow model was developed for steady, axisymmetric, compressible flow of a perfect gas between two insulated, parallel disks flowing radially toward an outlet hole at the center of the bottom disk. This model was implemented to determine the variation of properties of flow between the boss and seat plates of a JPL microvalve. The most notable conclusion from the flow property trends is that of a drastic increase in density and static pressure in contrast to a rather small increase in the Mach number. Also of importance, the total pressure drop was shown to be significant across the seat rings. A 2-D Stokes flow model was derived for incompressible, axisymmetric, radial flow between two concentric parallel disks. The results of this model were used to verify the flow property variations from the radial flow model. In particular, for the Stokes flow model, relations for radial velocity, average velocity, Darcy friction factor, volumetric flowrate, static pressure rise, and total pressure drop were derived. The Stokes flow model trends for both static and total pressure were in accord with the radial compressible flow model trends. 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.