NUMERICAL EXPLORATION OF VISCOUS FLOW REGIMES: INSIGHTS FROM POISEUILLE, COUETTE AND TAYLOR-COUETTE FLOWS

Abstract

We present a numerical study for Poiseuille and Couette as well as Taylor- Couette swirling flows. The governing equations of momentum and energy are transformed into coupled and nonlinear ordinary differential equations using similarity transformation and then solved numerically. We critically evaluate the effect of dimensionless pressure gradients on fluid velocity and observed that the velocity increases as the dimensionless pressure gradient increases. Couette flows are simulated in different scenarios, including top plate moving, bottom plate moving, and top plate moving in adverse pressure gradient conditions. In a third scenario, the flow velocity profile revealed a backflow regime (BFR). A simple schematic model is, therefore, proposed to explain the presence of BFR in the flow’s profile. Numerical and analytical solutions around the circular cylinder are presented. The marginal discrepancy between the analytical and numerical profiles is maximum at ~ 900 and 2700 degrees, which indicates that the chosen method is suitable and capable of reproducing engineering problems. Velocity magnitude and vector diagrams show that the cylinder shape was found to have a significant effect on the flow field. The velocity at the top and bottom of the cylinder is twice the velocity that seen away from the cylinder.

Keywords

• analytical and numerical solutions
• poiseuille flow
• couette flow
• pressure gradient force
• flow around a circular cylinder
• velocity profile