Analysis of an Unsteady Incompressible Crossflow on a Stationary Circular Cylinder at Reynolds number 3,900 Using Refined Potential Flow Theory

Abstract The motion of a fluid around a circular cylinder presents interesting phenomena including flow separation, wake and turbulence. The physics of these are enshrined in the continuity equation and the Navier-Stokes Equations (NSE). Therefore, their studies are important in mathematics and physics. They also have engineering applications. These studies can either be carried out experimentally, computationally, or theoretically. Theoretical studies of a cylinder flow using classical potential flow theory (CPT) have some gaps when compared to experiments. Attempting to bridge these gaps, this article introduces refined potential flow theory (RPT) and employs it on a stationary circular cylinder incompressible crossflow at Reynolds number 3,900. It leverages experimental observations, physical deductions and some agreements between CPT and experiments in the theoretical development. This results in the incompressible Eulerian Kwasu function which is a quasi-irrotational stream function that satisfies the governing equations and boundary conditions. It captures vorticity, boundary layer, shed wake vortices, three-dimensional effects, and static unsteadiness. The Lagrangian form of the function is exploited for the flow pathlines that are used to incorporate dynamic unsteadiness. A gravity analogy is used to predict the separation, transition, and reattachment points. The analogy introduces the perifocal frame of fluid motion. The forces are obtained in this frame with a change of variable. The drag prediction is within the error bound of measured data. The RPT pressure distribution, separation point and Strouhal number are also within acceptable ranges. Energy spectra analyses of the wake velocity display Kolmogorov’s Five-Thirds law of homogeneous isotropic turbulence.