Lift analysis of a variable camber foil using the discrete vortex-blob method

Abstract

ECENT research activities in the area of active or smart material systems have generated significant interest to develop adaptive lifting surfaces for advanced aircraft and submarine structures. By using integrated actuators and sensors, advanced problems are being addressed in aeroelastic tailoring, vibration and attitude control, and high lift devices.16 For example, on submarine aftbodies, compliant attitude control appendages that utilize large out-of-plane foil deformation can provide enhanced lift with reduced wake disturbance compared to conventional full-flying and trailing-edge flapped designs.7~9 To quantify the performance improvements of such control surfaces, an analysis technique is required which can model separated flow at high Reynolds numbers and provide pressure distributions for structure and control system design. The purpose of this Note is to present use of a discrete vortex-blob method to compare lift performance between fixed and variable camber NACA 0012 foils at a Reynolds number of 1 x 10 7 for incompressible flow in two dimensions. The vortex method provides a natural and numerically efficient description of eddies and the vorticity they carry. Since a large number of discrete vortex blobs are used to produce a vorticity field in a Lagrangian reference frame, the method becomes grid free and allows modeling of unsteady flows10 even around multielement bodies of arbitrary shape (conformal mappings are not involved) in nonuniform motion or rotation. Formulation of the Discrete Vortex-Blob Method The discrete vortex-blob method, furthered by Spalart and coworkers11'12 at NASA Ames Research Center, and incorporated in the computer code KPD12, is based on a vorticity formulation of the Navier-Stokes equations for incompressible flow in two dimensions: