Journal of Aerodynamics

Volume 2014, Article ID 931232, 11 pages

http://dx.doi.org/10.1155/2014/931232

## Shape Optimization of an Airfoil in Ground Effect for Application to WIG Craft

^{1}Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO 63130, USA^{2}Institute of Fluid Mechanics, Beijing Institute of Aeronautics and Astronautics, Beijing 100191, China^{3}Washington University in St. Louis, St. Louis, MO 63130, USA

Received 31 May 2014; Accepted 19 October 2014; Published 8 December 2014

Academic Editor: Jian-han Liang

Copyright © 2014 Yilei He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper employs a multiobjective genetic algorithm (MOGA) to optimize the shape of a widely used wing in ground (WIG) aircraft airfoil NACA 4412 to improve its lift and drag characteristics, in particular to achieve two objectives, that is, to increase its lift and its lift to drag ratio. The commercial software ANSYS FLUENT is employed to calculate the flow field on an adaptive structured mesh generated by ANSYS ICEM software using the Reynolds-Averaged Navier-Stokes (RANS) equations in conjunction with a one equation Spalart-Allmaras (SA) turbulence model. The results show significant improvement in both the lift coefficient and lift to drag ratio of the optimized airfoil compared to the original NACA 4412 airfoil. It is demonstrated that the performance of a wing in ground (WIG) aircraft can be improved by using the optimized airfoil.

#### 1. Introduction

Ground effect is an aerodynamic phenomenon that occurs on an aircraft during take-off and landing when the aircraft is in close vicinity of the ground. The close proximity of the ground alters the flow of air around the wing causing an increase in the lift and a reduction in the induced drag of the wing. Wing in ground effect (WIG) craft is a type of aircraft which takes-off and lands with very small ground clearance compared to other transport aircrafts. WIG craft is more fuel efficient than other general aviation and transport aircrafts and has relatively very short take-off distance [1]. These advantages make WIG craft attractive for many military and civil applications which require take-off and landing from aircraft carriers from and to water surface, respectively. Therefore, it is of interest to optimize airfoils for the wings of WIG craft for superior performnace by increasing lift as well as the lift to drag ratio.

When flying in the proximity of the ground, the flow around an aircraft is forced to be parallel to the ground due to ground effect; thus, the aerodynamics in ground effect is significantly different from that in out of ground effect in unbounded flow. The aerodynamic analysis requires an additional bounday condition to simulate the effect of the ground [2, 3]. In the realm of ground effect aircraft, most studies have focused on two kinds of ground effect—the steady ground effect (SGE) wherein the flying altitude does not vary with time and the dynamic ground effect (DGE) wherein the flying altitude varies continuously with time [4–11]. However, to date, neither SGE nor DGE have considered the airfoil optimization in the presence of ground.

The focus of this paper is on optimization of one of the most well-known airfoil used for wing in ground effect (WIG) craft—the NACA 4412 airfoil. The goal is to optimize the shape of this airfoil by employing a multiobjective genetic algorithm (MOGA) to improve its aerodynamic performance compared to the original NACA 4412 airfoil. The commercially available software ANSYS FLUENT is used for calculation of the flow field using the Reynolds-Averaged Navier-Stokes (RANS) equations in conjunction with a one equation Spalart-Allmaras (S-A) turbulence model. Using MOGA, globally optimal NACA 4412 airfoil shape is obtained for a typical cruising speed and angle of attack. The two optimization objectives are considered—maximization of the lift coefficient and the lift to drag ratio. These two parameters are indicators of an aircraft’s aerodynamic efficiency. The results for the NACA 4412 airfoil optimized in ground effect are compared with those of the optimized NACA 4412 airfoil in the free stream. This comparison is used to assess what is the best airfoil for WIG craft—the one optimized for ground effect or the one optimized for free-stream. Among various possible heights above the ground, which height can yield the best overall performance for optimization of the airfoil at all heights including the free-stream?

#### 2. Brief Description of the Genetic Algorithm and Airfoil Parameterization

##### 2.1. Single Objective Genetic Algorithm (SOGA)

Genetic algorithms are a class of stochastic optimization algorithms inspired by the biological evolution. In GA, a set or generation of input vectors, called individuals, is iterated over, successively combining traits (aspects) of the best individuals until a convergence is achieved. In general, GA employs the following steps [12, 13].(1)* Initialization*: randomly create individuals.(2)* Evaluation*: evaluate the fitness of each individual.(3)* Natural selection*: remove a subset of the individuals. Often the individuals that have the lowest fitness are removed; although culling, the removing of those individuals with similar fitness, is sometimes performed.(4)* Reproduction*: pick pairs of individuals to produce an offspring. This is often done by roulette wheel sampling; that is, the probability of selecting some individual for reproduction is given by
A crossover function is then performed to produce the offspring. Generally, crossover is implemented by choosing a crossover point on each individual and swapping alleles—or vector elements as illustrated in Figure 1.(5)* Mutation*: randomly alter some small percentage of the population.(6)* Check for Convergence*: if the solution has converged, return the best individual observed. If the solution has not yet converged, label the new generation as the current generation and go to Step (2). Convergence occurs after a certain number of generations when the shape of the optimized airfoil does not change from one generation to next.