Dynamics of buoyancy-driven microflow in a narrow annular space

This paper aims to investigate the dynamics of buoyancy-driven microflow in a narrow annular space inside a liquid floated gyroscope (LFG). Several theoretical models with a non-uniform thermal boundary for fluid flow in annular channels are given to analyze the effects of various parameters, such as the clearance size h, roughness height r _c, and rough density ε, on the flow and temperature profiles as well as on the fluid-drag torque. In the narrow annular regime, the relationship between the temperature and the angular displacement of the outer wall is defined as a cosine function, and the surface roughness of the inner wall is structured as a series of surface protrusions with a circular shape. With the increase of clearance size h, the flow velocity gradually increases to a stable level, and the drag torque increases initially and then decreases to a stable level. Furthermore, the increase of roughness height r _c and roughness density ε intensifies the frictional effect of fluid on the inner-wall surface. However, these two parameters have no significant effect on the flow velocity. This study can provide theoretical references for precision manufacturing and precision improvement of gyro instruments.