고점성 유체의 슬로싱 유동 해석

Analysis of Sloshing Flow in Highly-Viscous Fluids

A sloshing motion of highly viscous fluid in a rigid rectangular box with free surface is considered. The flow is generated by the motion of container being in harmonic motion in time along the horizontal axis normal to gravity, where the container velocity externally imposed is u=cos(2πt). Matched asymptotic method is invoked to elucidate flow visualization results such as linear profile of free surface and thin film flow on the vertical sidewall. Theoretical solution and physical reasoning are given to confirm that no-slip condition could be satisfied through near wall boundary layer of the thickness of l~O($F_r\sqrt{R_e}$), where F_r and R_e denotes, respectively, Froude and Reynolds number.