**1. Introduction**

Nowadays, research on reducing wind resistance acting on ship hull to save fuel consumption and improve economic efficiency is still an attractive topic in the field of marine transportation. This is especially true for container ships with a large windward area, due to their high above-water superstructure and multi-external forms, resulting from the position of containers on the deck, where wind drag accounts for a large percentage of the total resistance. Therefore, researchers around the world are of the opinion that research on reducing wind drag acting on container ships as well as the ships with high superstructure and or large windward areas is more and more important.

It goes without saying that in recent years, a large number of studies on the reduction in wind drag acting on ships' hulls as well as on optimal aerodynamic hull forms, the effect of side covers and domes on wind drag, the interaction effect between hull and accommodation, the effect of strong wind on resistance, the safety of the ship in strong wind, and so on, have been published. A comprehensive review is given as follows:

There are many studies on applying commercial Computational Fluid Dynamics (CFD) to solve the aerodynamic performances of the ships. The most important point of the research is that: the CFD has been a popular and useful tool to solve ships' aerodynamic problems with fairly good accuracy. Using CFD modelling, various types of modified hull shapes with reduced wind drag acting on the ship have been developed [1–7].

Janssen, W.D. et al. (2017) presented a study on using both the commercial CFD code and wind tunnel model test to study aerodynamic performances and wind drag acting on a container ship hull. The 3D steady Reynolds Averaged Navier Stokes (RANS) CFD simulation method was used to solve the problem. The author concluded that CFD results were in good agreement with the experimental

ones and that the CFD could be used to develop a new hull shape with reduced wind drag acting on the ship. The average absolute difference of wind drag obtained in CFD simulation and tunnel test ranged from 37.9% for a box shaped representation of the ship to only 5.9% for a more detailed model. Modelling the spaces in between container stacks decreased the average total wind load considerably. The average absolute difference of total wind load was 10.4%. Using a slender ship hull instead of a blunt ship one decreased total wind load by up to 5.9%. Taking into account wind tunnel blockage following the approach of the engineering science data showed an underestimation of up to 17.5% for the lateral wind load, as shown by comparing the CFD results obtained in the narrow domain with those of the wider domain [1].

Andersen, I.M.V. (2013) presented a study that investigates the influence of the container configuration on the deck of a 900TEU container ship on wind drag by wind tunnel test with scale model of 1:450. The author concluded that the results serve as an indication that the magnitude of wind force acting on a large container ship depends on the container configuration on deck rather than the purpose of assessing the full scale wind resistance of a given container ship. For the reduced longitudinal force in relative wind, it was advantageous to make the container configuration as smooth as possible and streamlining could reduce the force in the head wind. However, streamlining of the configuration on the aft deck was a trade-off as it increased the yaw moment compared to full load on the aft deck. The high container stacks in the configuration appeared to increase the longitudinal force more than the low or empty container bays in the configuration. The transverse force of concern in beam wind depends largely on the side area of the ship, and for a fully loaded ship it could be reduced by reducing the stacking height of the outermost stacks. The yaw moment in relative wind could be reduced by achieving full load on the aft of the ship, and it is possible to reduce the resistance through a combination of drift and increased rudder angle. Moreover, the author gave a general recommendation that the external form of the ship should be made as smooth as possible. In addition, it is important that the center of gravity of the side area was as far from the aft as possible [2].

Fujiwara, T. et al. (2009) presented an experimental investigation on wind force for a container ship with various external forms due to different positions of containers on the desk, in order to study aerodynamic specifications. Based on the obtained experimental results, an estimation method for wind load acting on the container ship has been proposed. In the tunnel experiment, a scale model of 1.5 m long, a mean wind velocity of 25 m/s and a Reynolds number of about 2.4 <sup>×</sup> <sup>10</sup><sup>6</sup> have been selected. Under these conditions, the flow field was turbulent and the drag coefficients were independent of the Reynolds number. The authors have shown that a good agreement between their proposed estimation method the tunnel experimental test has been obtained. They also showed that the new method is important for the calculation of speed as well as other characteristics in the operation stage of container ships [3].

In a study presented by Kim, Y. et al. (2015), several design concepts and devices on the superstructure of a container ship have been suggested and tested in a wind tunnel to estimate the wind drag reduction. The authors have also used CFD with the RANS simulation method to estimate wind drag acting on the ship. The results show that the gap protectors between container stacks and visors in front of upper deck have been found to be the most effective means for reducing wind drag acting on the ship. The CFD results agreed with the experimental measurements in the wind tunnel, and the wind drag acting on the modified ships could be reduced by up to 56% in the wind direction angle from 0 to 50 degrees [4]. Other researchers [5–7] also presented results on using CFD and experimental tests to develop a modified hull shape with reduced wind drag acting on a container ship. The authors have proposed modified hull shapes with attached side covers, a center wall, a "T" center wall and a dome at the bow deck of the container ship to reduce wind drag. By using side covers and a center wall, the container ship could reduce wind drag by up to 40% in the head wind direction. A dome at the bow of the ship could reduce the total wind drag acting on the container ship by up to 30% at wind direction angles of less than 30 degrees.

Other available studies focused on the aerodynamic performances and wind drag acting on different types of ships and offshore using both the wind tunnel measurement and CFD simulation. Jun, S. et al. (2020) investigated the resistance performance of ships, using the air resistance correction method [8]. Wn ˛ek, A.D. et al. (2011, 2015) focused on the wind load acting on a LNG carrier with a specific geometrical hull shape [9,10]. Saydam, A.Z. et al. (2018) conducted an evaluation of wind load acting on ships by CFD analysis [11]. He, N.V. et al. (2013, 2016, 2019) presented research on the interaction effect between hull and accommodation on aerodynamic performances and wind drag acting on a wood chip carrier hull [12–14]. Sugata, K. et al. (2010) studied the reduction in wind drag acting on the hull of a Non Ballast water Ship (NBS) [15], and so on [16–19].

The mesh of computed domain effects on the CFD results of a ship has been reported in many previous published works. Viola, I.M. et al. (2009) tested two different mesh numbers of 1 million and 6.5 million tetrahedral elements. The obtained CFD results, i.e., the wind forces, have been compared with those of the experimental ones. It has been observed that the wind forces computed by the turbulent viscous model Realizable k-ε was in good agreement with the experimental results and the differences between computed results in the two mesh numbers were lower than 5% [20]. Wn ˛ek, A.D. et al. (2011, 2015) used two models of a floating LNG platform and an LNG carrier in the 1:400 scale to conduct an experimental tunnel test and CFD computation to investigate the wind forces acting on the models. The turbulent viscous model k-ω SST and three different mesh generation techniques, which were CFD hexa (y+ = 5), CFD tetra (no prism) and CFD tetra y+ (y+ = 0.1), were used for CFD computation. The CFD results of CFD tetra (y+ = 0.1) showed the best agreement with the experimental data obtained in the wind tunnel test and the tetrahedral mesh was shown to be of good quality for the meshing of complex geometric shapes [9,10]. Saydam, A.Z. et al. (2017) used the mesh numbers from 1 million to 5 million elements of unstructured tetrahedral mesh to test CFD results independent of mesh number for computed wind forces acting on the ships. It has been shown that the CFD results were in good agreement with the experimental data obtained in wind tunnel test, and mesh independence of wind forces was up to more than 2 million elements [11]. Watanabe, I. et al. (2016) and Trieu, N.V. et al. (2017a, 2017b) used unstructured tetrahedral mesh with three mesh numbers of 2.2 million, 2.6 million and 3.8 million elements, with y+ of less than 25, to test CFD results independent of mesh. They showed that the CFD results given were in good agreement with the experimental data, and about 2% of the wind drag coefficient was different from the mesh number [5,7,21]. In our previous paper [12–14], we used the same unstructured tetrahedral mesh to investigate the wind drag acting on a wood chip carrier. It has been shown that the CFD results were in good agreement with those of the experimental data obtained in the towing tank test conducted at Osaka Prefecture University, Japan.

In this paper, a commercial CFD code ANSYS-Fluent has been used to investigate the interaction effect between the hull and accommodation of a container ship on wind drag. By applying the CFD, aerodynamic performances and wind drag acting on a 1200 TEU container ship have been computed for two different cases, namely the hull with and without accommodation on its deck, to determine the interaction effect between the hull and accommodation of the ship. From the obtained results, several new hull shapes and frontal accommodation shapes, with reduced interaction effects between hull and accommodation on wind drag acting on the ship, have been proposed in this paper.

#### **2. Original Model and Computed Domain**

#### *2.1. Model Ship Used for Computation*

The full scale 1200 TEU container ship, which is designed with an accommodation located at the aft, has been used as the reference model for computation. The principal particulars of the ship are given in Table 1, and Figure 1 shows the designed hull form of the original model.


**Table 1.** Principal dimensions of the 1200TEU container ship.

**Figure 1.** Model of the ship and coordinate system.

#### *2.2. Computational Domain and Boundary Conditions*

In this research, all steps for the designed simulation domain, meshing and setting of the boundary conditions have been done as per the user guide published by the International Towing Tank Conference (ITTC) manual for using CFD, [22–26] and our previous publications [12–14]. In this study, the computational domain has been designed with 6.5 L, 2.2 L and 0.75 L instead of 1200 m length, 450 m breadth and 150 m height. Mesh of the computed domain has been used as unstructured mesh with a triple prism layer and y+ has been taken to be less than 5. The popular turbulent viscous model k-ε for unsteady flow has been used. The velocity inlet is given at the inlet as the wind velocity, the pressure outlet is given at the outlet of the computed domain. The bottom, top and sides are given at the walls. To meet realistic case pressure, the outlet makes the open air condition possible, the limited dimension of the computed domain must be designed to be large enough. However, the dimensions of the computed domain has an effect on the mesh number and also an effect on running time. If the top and side of the domain is far enough, the effects on the CFD result become small. Therefore, we must design an appropriate domain and boundary condition. In computation, the time size step is of 0.005 s and

6000 time steps. All cases have been done by an Intel Xeon Gold 6138 2.0 GHz computer, with 3.7 GHz Turbo, 20 C with 64 GB of RAM. Figure 2 shows computed domain and mesh used for simulation.

**Figure 2.** Computational domain and mesh.
