Flow Past a Circular Cylinder on Curved Surfaces

TL;DR

This study uses discrete exterior calculus to numerically analyze flow past a stationary cylinder on curved surfaces, finding that surface curvature has minimal impact on flow dynamics and related quantities.

Contribution

It demonstrates that the flow dynamics around a stationary cylinder are largely unaffected by the curvature of the embedding surface, highlighting a form of universality.

Findings

Surface curvature has minimal effect on drag and lift coefficients.

Flow dynamics are similar on spherical and cylindrical surfaces.

Flow characteristics are largely independent of surface geometry.

Abstract

We investigate the dynamics of flows past a stationary circular cylinder embedded on spherical and cylindrical surfaces at a fixed Reynolds number of 100. For flows on surfaces, it is convenient to express the Navier-Stokes equations in exterior calculus notation. We employ the discrete exterior calculus (DEC) method (Mohamed et al. (2016)) to numerically solve the equations. We explore the role played by curvature on dynamical quantities of interest: the drag coefficient (Cd), the lift coefficient (Cl), and the Strouhal number (St). Our simulations indicate that the effect of surface curvature on these quantities and the overall flow dynamics is somewhat insignificant thereby implying that the dynamics of the flow past a stationary circular cylinder exhibits universality, independent of the embedding surface geometry.