Fluid kinematics around two circular cylinders moving towards impact

TL;DR

This paper develops a new formulation of the Navier-Stokes equations tailored for orthogonal space, and applies it to analyze the fluid flow around two cylinders moving towards impact, using bipolar transformation.

Contribution

It introduces a novel orthogonal space-based formulation of the Navier-Stokes equations and applies perturbation theory to study fluid kinematics around impacting cylinders.

Findings

Flow characteristics around cylinders are quantified.

The impact of cylinder motion on flow patterns is analyzed.

The bipolar transformation effectively parametrizes the problem.

Abstract

The scale factors of an arbitrary orthogonal space are a measure of its content of homogeneous orthogonal space. In the present study, it is shown, that their spatial and temporal rates of variation do not contribute to the differential calculus of arbitrary functions in orthogonal space. Based on this, the Navier-Stokes equations are formulated accordingly, to provide a method of studying the kinematics of fluid motion in orthogonal plane space. Employing this formulation and regular perturbation theory, the kinematic physical measures of the flow of an incompressible, viscous fluid around two identical circular cylinders, which move with equal and opposite velocity towards central impact are evaluated. For this case, the space is parametrised according to the bipolar transformation of the cartesian plane.