Airfoil Shape Optimization: Comparative Study of Meta-heuristic Algorithms, Airfoil Parameterization Methods and Reynolds Number Impact

Abstract

The aerodynamic efficiency in airfoil theory is defined as the ratio between the lift and drag force, which is the main objective function to be maximized in a wide kind of vehicle design due to its strong relationship between fuel consumption and range. This work employs the 4-digits NACA parameterization, a recently developed 6-parameters method, and the PARSEC technique with a correction of the matrices available in the literature, to compare the computational cost and the ability to achieved higher efficiency of these parameterizations. A genetic algorithm and particle swarm optimization routines are developed and implemented in Matlab, also a sine-cosine algorithm is tested, where Xfoil and the open-source computational fluid dynamic software OpenFOAM are coupled with the optimization algorithms. Finally, a Reynolds number impact study is performed related to the airfoil shape and the angle of attack which maximizes the aerodynamic efficiency. The results showed a faster convergence for the particle swarm optimization and the highest aerodynamic efficiency achieved by the 6-parameter method. Furthermore, with a higher Reynolds number, a higher angle of attack for the optimum lift-to-drag ratio as well a less camber is obtained.

Nature-Inspired Algorithms from Oceans to Space: A Comprehensive Review of Heuristic and Meta-Heuristic Optimization Algorithms and Their Potential Applications in Drones

“…Predictably PSO has been used for airfoil shape design as well as other algorithms. The results show better performance and convergence speed for PSO compared to GA [458]. Naumann et al have also used a modified version of CS to optimize airfoil shape in order to maximize the lift/drag ratio [459].…”

“…Publication Year Application Algorithm [455] 2018 Airfoil design GA, SA [456] 2001 Wing and blade airfoil design ES [457] 2019 Airfoil design FFO [458] 2021 Airfoil design PSO, GA [459] 2016 Airfoil design CS [460] 2015 Blade design ABC [461] 2017 Airfoil design GSA [462] 2022 Airfoil design HS [463] 2013 Aerodynamic shape optimization HS [382] 2016 Aerodynamic shape optimization SCA [466] 1999 Wing design GA [467] 2004 Wing design PSO [468] 2011 Wing design ACO [469] 2019 Wing design DE [470] 2019 Wing design FSO [471] 2017 Wing tip design ABC [474] 2016 Equipment placement in body GA [475] 2017 Equipment placement in body BA [476] 2017 Body shape design GA [478] 2017 Body shape design PSO [479] 2012 Body sizing DE…”

Aircraft Propeller Design through Constrained Aero-Structural Particle Swarm Optimization

“…One of the main inputs that composed the global model is the aerodynamic data associated with each airfoil located over the propeller span-wise section. Therefore, a parameterization method with a few parameters that are available to describe a wide range of geometries is required and that is the main reason why the 4-digit NACA method is selected for this study [10]. The 4-digit NACA airfoil shape is defined by the thickness t in chord hundredths, the maximum camber z in chord hundredths, and the maximum camber position x z p in chord tenths.…”

“…For the optimization method, a Particle Swarm Optimization (PSO) routine is developed, which guarantees the fulfilment of the target performance and the constraints, including the allowable stress where a structural model based on the Euler-Bernoulli beam theory is used to evaluate the structural viability of the candidate propellers. The PSO methodology has been employed for propeller optimization in different researches [6][7][8][9], and it also has been reported to be faster than other algorithms such as Generic Algorithms or sine-cosine optimizers [10,11].…”