Unsteady Lift Prediction with a Higher-Order Potential Flow Method

Julia A Cole,Goetz Bramesfeld,Mark D Maughmer,Michael Kinzel,Michael Melville

doi:10.3390/aerospace7050060

Julia A Cole, Goetz Bramesfeld + Show 3 more

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An unsteady formulation of the Kutta–Joukowski theorem has been used with a higher-order potential flow method for the prediction of three-dimensional unsteady lift. This study describes the implementation and verification of the approach in detail sufficient for reproduction by future developers. Verification was conducted using the classical responses to a two-dimensional airfoil entering a sharp-edged gust and a sinusoidal gust with errors of less than 1% for both. The method was then compared with the three-dimensional unsteady lift response of a wing as modeled in two unsteady vortex-lattice methods. Results showed agreement in peak lift coefficient prediction to within 1% and 7%, respectively, and mean agreement within 0.25% for the full response.

Highlights

In order to support the use of the unsteady formulation of the Kutta–Joukowski theorem, it is helpful to begin with a broader discussion of approaches to the calculation of unsteady lift
A relation exists between the two approaches in that the indicial response can be found via pressure integration, but the actual method itself is independent of the way that the response is developed
To achieve numerical convergence of the method, a constraint is necessary on the ratio of the distance traversed by a single point on the wing over a time-step is defined by ∆xw and the length of an surface DVEs (SDVEs) is dictated by ∆xc :

Summary

Introduction

The classical solution for a step change in angle of attack of an airfoil in an incompressible flow is the Wagner function [14], which assumes the circulatory unsteady lift response (including vorticity on the surface and shed into the wake) based on unsteady two-dimensional thin airfoil theory. This solution can be superimposed over time in order to estimate the two-dimensional, circulatory, unsteady-lift response that is due to a series of changes in angle of attack using the Duhamel integral. A relation exists between the two approaches in that the indicial response can be found via pressure integration, but the actual method itself is independent of the way that the response is developed

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