Searching optimal shape in viscous flow: its dependence on Reynolds number

TL;DR

This paper investigates how the optimal shape of a 2D body in viscous flow varies with Reynolds number, using a transformation-based method to analyze cubic profiles under geometrical constraints.

Contribution

It introduces a novel analysis linking the optimal shape of a body in viscous flow to Reynolds number through cubic profile constraints.

Findings

Optimal shape depends on the cubic's leading coefficient and Reynolds number

Derived a transformation method for analyzing shape optimization

Established relationship between shape parameters and flow conditions

Abstract

In this work a simple problem on 2D optimal shape for body immersed in a viscous flow is analyzed. The body has geometrical constraints and its profile would be found in the class of cubics which satisfy those conditions. The optimal profile depends on the leading coefficient of these cubics and its relation with the Reynolds number of the system is found. The solution to the problem uses a method based on a suitable transformation rule for the cartesian reference.