ESTIMATION OF FLOW CHARACTERISTICS IN MICRO-GEOMETRIES

摘要

The estimation of gaseous flow characteristics in micro-geometries is important for MEMS (Micro Electro Mechanical Systems) as a non-testing method. Therefore, the methodology to estimate the gaseous flow characteristics in micro-geometries for a wide flow range from no-slip to slip flow (Kn<0.01) and from incompressible and compressible flow using a f·Re (the product of friction factor and Reynolds number) correlation is developed and proposed. A f·Re correlation as a function of Mach number and incompressible slip f·Re, f·Re_(inc,slip) was obtained for micro-channels whose cross-sections are parallel, circular and annular. Then, incompressible slip f·Re, f·Re_(inc,slip) is a function of Knudsen number and incompressible no-slip f·Re, f·Re_(inc,no-slip) where f·Re_(inc,no-slip) is a function of channel geometry. The flow characteristics through micro-geometries can be predicted by a f·Re correlation. A f·Re correlation obtained here is applicable to micro-channels whose cross-sections are parallel, circular, rectangular and annular. The detail of the procedure how to apply the f·Re correlation is also documented. In the developed methodology, the forth-order Runge-Kutta method was employed to integrate the nonlinear ordinary differential equation for the pressure and the regular-Falsi method was also employed to find the inlet Mach number. The present results are compared with both available numerical simulations and experimental measurements. The results are in excellent agreement with them.