Assessment of Viscous Flows in High-Speed Micro Rotating Machinery for Energy Conversion Applications

This paper investigates the characteristics of viscous flow in the micron-scale clearances surrounding high-speed micro-rotors currently being developed for miniature energy conversion applications. Analysis and experimental results from 4 mm diameter microfabricated rotors operated above 1 million rpm are used to describe the viscous flow characteristics, and provide guidelines for system-level design. To first order, the flow is characterized as fully developed shear flow (Couette flow) across the small gaps, induced by the rotor motion. However, secondary flows are induced perpendicular to the direction of rotor motion when externally applied pressure gradients exist along the small gaps. The developing flow in the entrance region of the small gaps in this secondary flow direction impacts the shear flow profile, hence affecting the drag on the disk. The effect of other inertial forces, such as Coriolis and centrifugal forces, are investigated analytically and numerically and found to affect the shear flow profile on the fluid in the motor gap at high rotational speeds. Since viscous losses are prevelant in microsystems, appropriate modeling is necessary for system-level design.