High-Reynolds-number flow past a shear-free circular cylinder

Anuj Kumar, Nidhil Mohamed A. R, Pritam Giri, Ratnesh K. Shukla

Published 2017-11-12Version 1

A semi-analytical study of the dynamics of incompressible flow of a Newtonian fluid past a circular cylinder with zero surface shear stress has been performed. Essentially, the modified flow field is considered to be a perturbed flow field over the irrotational flow description around a circular cylinder in an uniform cross flow. At finite Reynolds number, the perturbation over irrotational flow field is confined within a thin boundary layer, rear stagnation and wake regions. Equations governing the flow-field in boundary layer are linearized Navier-Stokes equations which is solved by adopting analytical route. Solution is shown to be superposition of infinite self-similar terms. Behind the circular cylinder, a stagnation region is formed where the perturbation and irrotational flow velocity components are shown to be of equal order. Vorticity produced in boundary layer is convected downstream through stagnation region to form a narrow wake. Similar to boundary layer analysis, governing equation in wake is also linearized to facilitate the analytical study. Solution in wake region is obtained by matching the solution from boundary layer near the stagnation region. Far wake solution is shown to be consistent with the leading order drag coefficient estimated from the momentum deficit in the far wake. Next, drag coefficient is estimated by calculating the net-dissipation over the entire flow field. Asymptotic expansion of drag coefficient in terms of boundary layer thickness is shown to have a logarithmic singularity. We show that at very high Reynolds number, flow past a circular cylinder with shear-free boundary will cause a net increase in dissipation of energy over the viscous irrotational flow, which stands in stark contrast to the case of spherical geometry (Moore[1]). Results from present analysis is validated against computational results.