Exact analysis of potential flow past bodies of irregular shapes

TL;DR

This paper introduces an exact analytical method for solving potential flow problems around irregularly shaped bodies using Heaviside functions and eigenfunction series, validated against standard solutions.

Contribution

It develops a novel analytical approach for potential flow past irregular shapes, expanding beyond standard geometries with a series solution and linear algebraic coefficient determination.

Findings

Excellent agreement with classical solutions

Accurate modeling of flow past complex geometries

Method effectively handles multiple irregular bodies

Abstract

Fluid flow past one or more solid bodies is a fundamental problem of much practical importance. Standard solutions of simplified problems involving incompressible inviscid irrotational flow past common geometries such as circular cylinders and airfoils are commonly available. This work presents exact analysis of a potential flow problem involving fluid flow past one or more bodies of irregular shapes. The problem is solved by expressing the shape of each body using Heaviside functions, and writing the potential function as an eigenfunction-based series. Using the properties of Heaviside functions, the series coefficients are determined by deriving a set of linear algebraic equations that govern the coefficients. Benchmarking of the analytical technique against well-known solutions of standard problems is carried out, showing excellent agreement. Good agreement with past work on the specific problem of potential flow past multiple circular cylinders further establishes the accuracy of the analytical technique. Illustrative problems of flow past complicated geometries are solved. Implementation aspects and limitations of the analytical technique are discussed.