# Noncirculatory fluid forces on panels with porosity gradients

## TL;DR

This paper derives analytical expressions for unsteady non-circulatory forces on deforming panels with porosity gradients, advancing the understanding of aerodynamics for porous bodies and their stability.

## Contribution

It provides the first analytical solution for unsteady non-circulatory forces on deforming porous panels with variable porosity distributions.

## Key findings

- Analytical expression for non-circulatory pressure distribution.
- Influence of end conditions on force calculations.
- Application potential to bio-inspired propulsion and aeroelastic stability.

## Abstract

This Note determines the unsteady non-circulatory forces on an arbitrarily deforming panel with a Holder-continuous porosity distribution. An analytical expression for the non-circulatory pressure distribution is presented and evaluated for the special cases of uniform and variable-porosity panels undergoing harmonic deformations, where special attention is paid to the influence of the panel end conditions. These results constitute the first major step towards a complete linearized, unsteady aerodynamic theory for lifting porous bodies, which may have potential application to the performance estimation of biologically-inspired swimmers and fliers and to the future assessment of aeroelastic stability and flow noise production of porous airfoils.