2017/11/12 by Anuj Kumar, Nidhil Mohamed A. R, Kumar, Anuj +5
Engineering · Environmental Science · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Wind and Air Flow Studies
paper · pdf · doi:10.48550/arxiv.1711.04278
openalex publication_date 2017/11/12 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28
We present an asymptotic theory for analytical characterization of the\nhigh-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free\ncircular cylinder. The viscosity-induced modifications to this flow are\nlocalized and except in the neighborhood of the rear stagnation point, behave\nlike a linear perturbation of the inviscid flow. Our theory gives a highly\naccurate description of these modifications by including the contribution from\nthe most significant viscous term in a correctional perturbation expansion\nabout an inviscid base state. We derive the boundary layer equation for the\nflow and deduce a similarity transformation that leads to a set of infinite,\nshear-free-condition-incompatible, self-similar solutions. By suitably\ncombining members from this set, we construct an\nall-boundary-condition-compatible solution to the boundary layer equation. We\nderive the governing equation for vorticity transport through the narrow wake\nregion and determine its closed-form solution. The near and far field forms of\nour wake solution are desirably consistent with the boundary layer solution and\nthe well-known, self-similar planar wake solution, respectively. We analyze the\nflow in the rear stagnation region by formulating an elliptic partial\nintegro-differential equation for the distortion streamfunction that\nspecifically accounts for the fully nonlinear and inviscid dynamics of the\nviscous correctional terms. The drag force and its atypical logarithmic\ndependence on Reynolds number, deduced from our matched asymptotic analysis,\nare in remarkable agreement with the high-resolution simulation results. The\nlogarithmic dependence gives rise to a critical Reynolds number below which the\nviscous correction term, counterintuitively, reduces the net dissipation in the\nflow field.\n