Optimization, Control and Morphing of Airfoils for Minimum Drag-to-Lift Ratio Using Particle Swarm Optimization of PARSEC Parameters

Abstract

The need for efficient designs of aircraft structures is very important, with the airfoil design being a primary contributor to it. The optimum airfoil design is different for different flow conditions. It is desirable to be able to maintain optimum shape of an airfoil throughout the changing conditions. This work presents a Particle Swarm Optimization (PSO) of a two-dimensional airfoil as a first step towards using Shape Memory Alloy (SMA) actuators to morph the airfoil into the optimum shape based on flight conditions. An SMA constitutive model was used and a feedback controller was designed to control the actuators. The airfoil is constructed using the PARSEC parameterization method. The PARSEC parameters are the control variables in the optimization process. In PSO, each particle is a set of control variables that represents PASREC parameters. For each particle, these are passed to the CFD solver to construct the airfoil geometry and calculate the fitness function, in each iteration. Both the standard PSO and constriction PSO variants were studied. The constriction PSO airfoil shape optimization gave better results. COMSOL Multiphysics was used to construct the geometry, generate grid, apply boundary conditions and solve the fluid dynamics problem. The Spalart-Allmaras turbulence model was used. LiveLink™ for MATLAB version of COMSOL was used to integrate the CFD fitness evaluator and the PSO algorithm, which was executed using a series of MATLAB subroutines.The four-digit NACA airfoil series was used as the pool of available airfoils. The PSO gave optimum airfoil shapes (PASREC parameters) at different Reynolds numbers. The resulting shapes had optimum lift-to-drag values at the respective Reynolds numbers. The designed controller moves between these optimum shapes based on the input. The methodology is very general and can be seamlessly applied to any design and optimization process