A classical remark on the compatibility of inlet velocity and pressure singularities: Finite-element visualization

Abstract

In this article we consider a smooth channel with infinite length. A circular cylinder is placed in the channel as an obstacle. A fluid satisfying Newton’s law of viscosity is taken in the channel with two different classes of velocity profiles at the inlet namely, a linear (constant) velocity profile and a parabolic profile. The mathematical model is structured by using the fundamental laws involved in the field of fluid rheology. Since the flow-describing differential equations are nonlinear in nature, a computational scheme is executed to report the primitive flow field quantities that is the pressure and the velocity. The numerical method used in this case is the finite-element method. The obtained outcomes are given by way of graphical trends. For a clear insight both the contour plots and line graphs are added. Further, the benchmark quantities namely, the drag and the lift coefficients are evaluated around the outer surface of the obstacle through the line integration. For accuracy the numerical data subject to both the drag and the lift coefficients is recorded up to nine different refinement mesh levels. Finally, the findings are concluded with the potential remark that the flow in a channel (having no-slip condition at both the lower and upper walls) with the parabolic velocity profile initiated at the inlet is the more realistic approach as compared to the linear (constant) profile being considered at the inlet.