Contents lists available at ScienceDirect Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng Hard sail optimization and energy efficiency enhancement for sail-assisted vessel Yong Ma a,b , Huaxiong Bi a , Mengqi Hu c , Yuanzhou Zheng a,b,∗ , Langxiong Gan a,b a School of Navigation, Wuhan University of Technology, Wuhan, Hubei, 430063, China b Hubei Key Laboratory of Inland Shipping Technology, Wuhan, Hubei, 430063, China c Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL, 60607, United States ARTICLE INFO Keywords: Sail-assisted vessel Arc-shaped sail Airfoil sail CFD EEDI ABSTRACT The shipping industry has valued wind energy in the last decades due to the global increasingly severe en- vironmental situation. The sail-assisted vessels have employed generous types of sails to exploit wind energy and reduce the energy consumption. To meet the ever-increasing energy saving requirements of sail-assisted vessels, this paper investigates the hard sail design optimization and energy efficiency enhancement problems for sail- assisted vessel. By using parametric section airfoil parametrization (PARSEC) method and particle swarm op- timization algorithm, we fulfill the optimization of the wingsail aerodynamic design. The performance of our optimized airfoil has been verified by multi-point theory, computational fluid dynamics (CFD) examination, and energy efficiency design index (EEDI) calculation. The maximum lift-to-drag ratio of the coupled wingsails has increased by 10% than that of the arc-shaped sail. And the vessel equipped with our coupled wingsails can remarkably reduce EEDI by 18.2% and 4% when compared to non-sails vessel, and the vessel equipped with variable-camber sail (VCS), respectively. 1. Introduction According to generous reports concerning shipping costs, fuel con- sumption accounts for − 30 % 55% of the total vessel managing capital depending on the types of vessel (Brouer et al. (2013); Jang and Choi (2016)). Like many other industries (Geertsma et al. (2017)), the shipping industry faces an enormous challenge in the last few years, taking into account the rise of fuel prices and the great pressure to reduce its environmental impact (Yuan and Ng (2017); Lan et al. (2015); Zhang and Wang (2013)). Therefore, green vessels that par- tially or entirely use clean energy such as solar and wind power are needed but missing (Li et al. (2015); Essia et al. (2016); Nguyen et al. (2013); Li et al. (2012)). Sail-assisted research has been a hot topic in the shipping industry due to the advantages of energy saving and being environmental friendly (He et al. (2015)). In this paper, we focus on improving the performance of hard sails and enhancing the energy ef- ficiency of sail-assisted vessels, which are major problems to be solved in sail-assisted navigation technology. To improve energy conservation and reduce emissions, sail-assisted technologies have been rapidly developed recently (He et al. (2015)). The existing mainstream sail can be divided into more than ten categories in terms of the sail shape and aerodynamic performance (Fujiwara et al. (2005a)). There are several typical sails including Square sails, skysails, Magnus roll sails and wingsails. Skysails are limited in a very narrow wind direction range. Mainly relying on drag force (He et al. (2015); Ebrahimi and Jahangirian (2014); Dadd et al. (2011)), wind energy utilization efficiency of square sails is low. Magnus roll sails have high reliability and high costs, and require ad- ditional power to rotate during navigation (Luyu et al. (2010); Sedaghat (2014)). A wingsail is a variable-camber aerodynamic structure that is fitted to a vessel in place of conventional sails in recent years. The aero- dynamic performance and stability of the wingsail are better than the conventional sails (Li et al. (2015); He et al. (2015); Rynne and von Ellenrieder (2010)). Referring to the multi-wingsail (Ouchi et al. (2013); Viola et al. (2015); Lee et al. (2016)), Ouchi et al. (2013) em- ployed numerical methods for examining its validity of the geometry structure and the aerodynamic performance. To find the optimum so- lution for multi-wingsail, Lee et al. (2016) developed a design optimi- zation framework by utilizing an evolutionary algorithm and the Kri- ging surrogate model. And its design results were validated through a three-dimensional CFD analysis. Viola et al. (2015) investigated the https://doi.org/10.1016/j.oceaneng.2019.01.026 Received 22 August 2018; Received in revised form 9 November 2018; Accepted 9 January 2019 ∗ Corresponding author. School of Navigation, Wuhan University of Technology, Wuhan, Hubei, 430063, China. E-mail addresses: myongdl@whut.edu.cn (Y. Ma), bihuaxiong96@gmail.com (H. Bi), mhu@uic.edu (M. Hu), zhengyuanzhou0909@163.com (Y. Zheng), glx701227@163.com (L. Gan). Ocean Engineering 173 (2019) 687–699 Available online 24 January 2019 0029-8018/ © 2019 Elsevier Ltd. All rights reserved. T