Analytical Analysis of Recirculating Flow in Single-Screw Extruders

Current analytical theories of recirculating flow in single-screw extruders consider only cross-channel flow in channels of infinite width with only one exception. Proper analysis of recirculating flow requires inclusion of normal velocities and the effect of finite channel width. More broadly, this paper presents an analytical description of lid-driven cavity flow—one of the most frequently studied flows in fluid dynamics. Expressions for velocities and flow rates for Newtonian fluids are obtained that satisfy the balance equations. These expressions have been compared to results of numerical analyses with good agreement. Flow rates and velocities are displayed with 3D surface plots and contour plots. These plots provide better insight into the flow behavior than 2D graphs. We have analyzed flow in slit channels with width much greater than the height ($W>>H$) and flow in a square channel ($W=H$). The vortex center (stagnation point) in a slit channel is located at normal coordinate $\psi =2/3$. The vortex center in a square channel is located at $\psi =0.76$. These analytical results allow for the development of better analytical models for melt temperature distribution, mixing, and devolatilization in single-screw extruders.