Airfoil Parameterization Techniques: A Review

The selection of suitable shape parameterization technique is one of the significant factors affecting the fidelity of the solution found during aerofoil shape optimization process. This paper investigates the effect of shape parameterization on an automated aerofoil shape optimization problem. Four well known shape parameterization techniques were considered for study; Bezier curves, Class-Shape function Transformation, Hicks-Henne " Bump " function and polynomial method. A boundary layer panel code was coupled with a surrogate-based multi-objective evolutionary algorithm and implemented within an automatic design loop. The optimization problem was formulated for NACA 0012 aerofoil at 5 degree angle of attack. The main criteria for comparison were based on the number of parameters required by each method for accurate representation of the aerofoil, the ability to find the aerofoil with the best performance within the constrained design space and also the computational cost. Preliminary results show that the optimization process was able to increase the lift-to-drag ratio of the aerofoil by 30%. Class-Shape Transformation and Hicks-Henne Bump function were able to find the best aerofoil shape within the design space effectively.

The potential influence of different combinations of parameterization methods and optimization strategies on the attainable optimum and the optimization cost is evaluated by comparisons of the optimized airfoils. The optimization strategies consist of a single-objective metamodel assisted Genetic Algorithm and multi-objective Differential Evolution both assisted and non-assisted. Bspline and Bézier formulations are used together with a direct and standard description of the airfoil shape. The multi-point optimizations are applied to airfoils in 2D cascades corresponding to propeller geometries. Nomenclature B i,q (.) Basis function c Airfoil chord C(.) Curve coordinate vector C d Airfoil drag coefficient C l Airfoil lift coefficient C p Pressure coefficient dD Elemental drag dL Elemental lift dT Elemental thrust dU Elemental torque force f 1 , f 2 Weighting factor J Advance ratio M ∞ Free-stream Mach number n, N, q Variables r Radius R tip Propeller tip radius u Running coordinate v ∞ Free-stream velocity w. Weight X Coordinate vector α Local angle of attack β Local blade angle ε, γ Angle η el Elemental efficiency Σ Overall performance τ Constraint penalty Ω. Objective function ω Angular velocity ρ Air specific mass Abreviations ANN Artificial Neural Network DOE Design Of Experiments GA Genetic Algorithm MODE Multi-Objective Differential Evolution RANS Reynolds Averaged Navier-Stokes

Aerospace Science and Technology, 2007

The effect of airfoil shape parameterization on optimum design and its influence on the convergence of the optimization process are investigated. A new method for airfoil shape parameterization is presented which takes into consideration the characteristics of viscous transonic flow particularly around the trailing edge. The method is then applied to airfoil shape optimization at high Reynolds number turbulent flow conditions using a Genetic Algorithm. An unstructured grid Navier-Stokes flow solver with a two-equation K−ε turbulence model is used to evaluate the fitness function. The aerodynamic characteristics of the optimum airfoil obtained from the proposed parametric method are compared with those from alternative methods. It is concluded that the new method is capable of finding efficient and optimum airfoils in fewer number of generations.

2006

More and more complex optimisation techniques play an increasing role in todays industry. Different techniques like gradient based methods or evolutionary search techniques are coupled (hybridisation, memetic algorithms [1]), enhanced by methods to fasten objective function evaluations (fitness approximation, metamodel assisted optimisation [2, 3]), or applied to more complex tasks with more than one objective function (multi-objective optimisation [4, 5]). Each of these enhanced techniques is able to improve ...

Proceedings of the 5th International Conference on Mechanical Engineering, Materials and Energy (5th ICMEME2016), 2016

Nowadays, Airfoil shape optimization are developed by many researchers. Especially, evolutionary method is taken to find out the shape of airfoil. The main objective work is finding the shape of airfoil that get the aerodynamic properties which good for lift and drag of the aircraft wing. PSO is the evolutionary method that used for this work. The work are combination between the CFD analysis as Reynolds number 550,000 and optimization technique to get the airfoil shape that maximum lift to drag ratio. The result is compared with the standard NACA 2412 airfoil. The optimization airfoil has improved lift to drag ratio compared to the standard NACA 2412 airfoil for 53.22%. Airfoil shape optimization Airfoil shape profile. The airfoil profile can be generated by setting the point variables and make it continuously by using the spline interpolation. The NACA2412 airfoil shape is created by using the seven points as shown in the Fig. 1. The four points at the lower and upper part of airfoil are assigned as the seven of design variables. The leading and tailing edge are fixed in the same y direction that equal to zero and x direction are assigned equal one and zero, respectively. The spline interpolation is

As shape parameterization defines the design variables for the optimization of some object (geometric knowledge representation), it is very important to apply parameterizations with a low number of control points in order to reduce the dimensionality of the search space. A parameterization for 2D and 3D geometries based on piecewise Bezier curves and surfaces is proposed here. The requested C 1 inter-segment continuity is accomplished by automatically generating additional control points without increasing the number of optimization variables. The computational procedure takes the initially given complex surface or points cloud (2D or 3D), adaptively splits the domain into 2D or 3D patches and iteratively tries to reduce the necessary number of control points while satisfying the requested modeling accuracy. This adaptive parameterization procedure can serve as a geometric data-set compression utility and fits well into evolutionary optimization.

This paper is the second part of a short course on the utilisation of Evolutionary Algorithms as an e ective means to solve the Aerofoil Design Problem in Aerodynamics. In it their application to both Direct and Inverse Aerofoil Design Problem is described, and results are given. Finally, several possible parallel models for Evolutionary Algorithms are discussed, and the results of the application of one of them to the above problem are presented.

A new method for airfoil shape parameterization is presented. This method is then applied to Genetic Algorithm for airfoil shape optimization. Considered objective function is L/D at transonic speed and viscous Navier-Stokes equations are solved by double time implicit method. This method profits by the merits of explicit methods to accelerate the convergence by solving the residual equation explicitly in a pseudo time, however it solves the original equations implicitly and therefore it has not the limitations of explicit methods. With the aid of this new method and spring analogy for grid movement, the computation of objective function and optimization process is decreased. Results from usual PARSEC and new parameterization method for airfoil shape parameterization are compared to show the efficiency of the method with respect to the PARSEC method.

Multi Mission Unmanned Aerial Vehicle (RC-MM-UAV) emerging design concept involves morphing wings with mission segment based airfoils. To identify the appropriate planform, the Direct Numerical Optimization (DNO) methodology is applied in the design. The DNO comprises of two phases; a) Airfoil shape parameterization method to develop candidate shapes; and b) Validated flow solver to compute the aerodynamic forces. The design parameterization study involves testing the accuracy and flexibility of five shape functions by measuring the geometrical difference between a set of benchmark airfoils and the approximated solution through the shape functions. A Particle Swarm Optimizer (PSO) was utilized and with the integration of a local line search algorithm, geometrical convergence is established. The second phase of DNO examined the validity of a high fidelity flow solver by comparing computed data against experimental solutions. A Reynolds Average Navier Stokes (RANS) model with a multi-zonal fluid grid was developed to duplicate flow transition, and provided lift and drag variance of 3% and 4% respectively over an angle-of-attack range -1° to 12°. Further research will involve integration of the above results to support the design decision of RC-MM-UAV airfoils.

Modelling and Simulation in Engineering, 2012

The method of optimization algorithms is one of the most important parameters which will strongly influence the fidelity of the solution during an aerodynamic shape optimization problem. Nowadays, various optimization methods, such as genetic algorithm (GA), simulated annealing (SA), and particle swarm optimization (PSO), are more widely employed to solve the aerodynamic shape optimization problems. In addition to the optimization method, the geometry parameterization becomes an important factor to be considered during the aerodynamic shape optimization process. The objective of this work is to introduce the knowledge of describing general airfoil geometry using twelve parameters by representing its shape as a polynomial function and coupling this approach with flow solution and optimization algorithms. An aerodynamic shape optimization problem is formulated for NACA 0012 airfoil and solved using the methods of simulated annealing and genetic algorithm for 5.0 deg angle of attack. T...