Abstract: 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_e, 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_e 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.

Key words: Liquid floated gyroscope (LFG); Annular channel; Roughness feature; Fluid drag

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