Aerodynamic Simulation of A Containership to Evaluate Cargo Configuration Effect on Frontal Wind Loads

Fuel consumption has always been a matter of concern for ships propulsion. In this research we aim to develop computer models of several containership cargo stacking configurations and discuss an optimal configuration at a constant front wind speed. The paper presents the simulation results by using ANSYS CFX for a 1:4 scale Post- Panamax 9000 TEU containership. The ship is modelled in a cubic domain that contains unstructured mesh with details, in such a way that can demonstrate the influence of the container configuration on wind force. Also the numerical results are verified versus wind tunnel test data. An optimal stack configuration led to about 25% reduction in air resistance. It is proposed that in order to reduce the wind drag force and consequently reduce the fuel consumption and pollutant emissions, empty spaces between the cargo containers and unbalanced cargo distribution over the deck should be inhibited. Also, it is advised to make the cargo distribution on the most forward and aftward deck areas more streamlined.


Introduction
Generally, in calm sea state, wind resistance comprises 3% to 5% of the total ship resistance (Moonesun, 2010) but for containerships which possess large windage area, wind resistance comprises significant amount of total resistance about 2% to 10% (Minsaas and Steen, 2008). The wind forces on a ship generally influence the ship by increasing the induced resistance. The longitudinal force generally constitutes the largest part of the total wind induced resistance. The transverse force causes yaw, drift and deviation of vessel from the desired course, which can cause the added resistance in two ways: (i) the ship's heading will not be aligned with the steered course which leads to great resistance; (ii) the drift must be compensated for, which means that the rudder angle must be increased repeatedly. Increasing the rudder angle will also increase resistance; this leads to wearing out of steering gear system and increase of fuel consumption and gas emission, especially during extended periods of execution. Magnitude of resistance compared with the longitudinal force is discussed by Andersson (1978) and van Berlekom (1981). According to Andersson (1978), the induced resistance from the increased rudder angle plays an insignificant role, while according to van Berlekom (1981), it can be of the same magnitude as the longitudinal force for stronger winds. Generally, the longit-udinal force is of greatest importance for the propulsion resistance. Its share in the total resistance has been discussed by van Berlekom (1981) and Aage (1968). According to van Berlekom (1981), the wave and wind resistance are of the same magnitude. However, Aage (1968) stated that the wind resistance rarely contributed to more than 10% of the total resistance. For the first time it was concluded by Blendermann (1997) that the wind forces are influenced by container stacking configuration. Blendermann (1997) stated that the uneven bay heights increase the wind resistance. A ship with randomly stacked containers on deck compared with a fully stacked ship experiences significantly higher longitudinal force, smaller transverse force, smaller roll moment, and smaller yaw moment (Blendermann, 1997). Andersson's (1978) test results for the longitudinal force are summarized as (i) less significant effect between empty ship and a ship which only carries containers on the aft deck; (ii) a significant effect due to container configuration on the fore deck; (iii) irregularities such as many empty bays have a significant effect of up to 70%-100% increased force compared with the fully stacked reference ship; (iv) full load on the fore deck and streamlining of the aft deck is the most favorable one of the 19 tested configurations. Andersen (2012aAndersen ( , 2012b presented experiments with streamlined versus uneven container configurations. Wind tunnel test model was developed by increasing the number of stacking configuration from 6 to 16, while the longitudinal force and yaw moment were investigated. Minimum amount of longitudinal forces were experienced when containers in aft and forward deck were streamlined. Under the streamlined condition, reduction of yaw moment was experienced in fore deck while the maximum yaw moment was experienced for aft deck configuration. In full stack configuration, the longitudinal force was extensively increased. Hassan et al. (2012) investigated the effect of container configuration on wind resistance of containership in association with the longitudinal and lateral forces along with pressure contours and velocity streamlines through computational fluid dynamics approach. Furthermore, 14 different stacking configurations were investigated from 0° to 90°w ind directions. Finally, the alteration of wind resistance force and its effect on fuel consumption and gas emission was investigated. The natural sea conditions were simulated; in other words, simulation domain and boundary conditions were selected so as to meet the natural sea conditions for a container vessel. A 2800 TEU containership of 221.65 m in overall length was modelled. Steady state condition with three million mesh cells and k-ε turbulence model were considered for the solver set-up. The study, however, lacked any extensive verification with experimental data. Validation of numerical result was confined to the customary empirical formula.
To analyze aerodynamic performance of a Post-Panamax containership with different container stacking configuration models on deck, by means of CFD along with comparison of the achieved results against experimental data, and to analyze wind force under alteration of container stacking configurations are the most important goals of the present study. In addition, to check the challenges of a numerical investigation of the above subject, such as the flow turbulence pattern and its influence on wind force, comprises the subsidiary targets of the present study. Pressure contours and velocity streamlines at critical locations as the containers loading vary on the deck are investigated.

Computational fluid dynamics
In this study, CFD is employed for computation of the mass conservation, momentum and energy equation around the vessel's body. By splitting up (discretizing) the nominated area for analysis into the smaller parts and applying of the boundary conditions over boundary nodes with exerting approximation, a linear equation system is obtained to solve which, the velocity and pressure field will be attained over the assigned domain. To this point, ANSYS CFX is used which is recognized as one of the most powerful fluid flow analysis packages. A finite volume method (FVM) is used by the software (ANSYS, 2009).
An exclusive feature of the software is to use one unit for all steps of the simulation process including the geometry and grid generation, physical definition of the model state, solver and post solver process. Diverse types of grid are producible by the software including the triangular and tetrahedron mesh element for 2D geometries and tetrahedron, hexahedron, pyramidal and wedge for 3D geometries. The present study employs a 3D grid. Also the software provides the ability of the grid size alteration in boundaries and the required area of geometries for the operator. This feature causes precise optimization of the vortex and eddies region i.e. inner part of the boundary layers.

Assumptions
Owing to high amount of computation, the following simplified assumptions have been considered in this study.
(1) Only the above waterline ship's body has been inspected for the effect of wind analysis.
(2) The fluid flow is 3D and for turbulence effect determination, k-ω and SST model have been used.
(3) The ship's geometry is symmetrical in length, therefore the symmetry condition has been considered and the demi-body of the model is inspected.
(4) The ship is supposed to be fixed with zero heel and trim.
(5) Owing to the computing conservation, the nearest practical scale of ship has been adopted for simulation.
(6) Wind has transient nature but with respect to the studied forces, it has been supposed under the steady state condition.

Analysis method
Excessive dimension of the solving domain, particularly in wind tunnel simulation that lateral boundaries negatively affect the solution condition is very important. On the other hand, by considering the excessive domain, it intensively increases the calculation grid and eventually increases the solving time. Therefore, attaining an appropriate computational optimal domain requires trials and experience. In the present study, the optimal computational domain has been considered with respect to test space dimensions (Table 1) (Andersen, 2012a(Andersen, , 2012b. To prevent software computational error and prepare proper conditions for software solver, the prototype domain was scaled one to four. Incidentally, in order to decrease the volume of calculation, noting a negligible effect of over-extending domain cross-sec- Hamed MAJIDIAN, Farhood AZARSINA China Ocean Eng., 2018, Vol. 32, No. 2, P. 196-205 tion on final results, the width and height of the domain were kept to the minimum. So regarding the above and frugality in calculation time, the dimensions of domain has been selected according to Table 2. Whereas the limitation of boundary layers on the model body in wind tunnel does not exist in a computer model, so the length of domain has been extended long enough.

Simulation of Post-Panamax containership
For wind force study on Post-Panamax containership with respect to the different stacking configuration on deck, ship's body above waterline, superstructure, aft and fore deck and finally the loaded containers on deck have been simulated; the container size was 40-feet (Shipsbusiness, 2016). As illustrated in Fig. 2, a right-handed Cartesian coordinate system is used and then fixed across the intersection of base line passing through deck and an imaginary line passing athwart ship through deck over L pp /6. The axis direction has been adopted from ITTC (1993). Moreover, the drag force assumed in positive direction of X axis which means the angle between ship advance and the wind flow direction was 180°. Incidentally, it must be noted for domain meshing due to the complication of ship's geometry, unstructured mesh is chosen that extensively improves the precision of analysis results. Density of mesh in different parts is adjusted according to the simulation importance (Fig. 3). For this purpose, the mesh density for surface parts of vessel's hull and containers which have significant importance in equation solving, are selected in the range of 0.1 m. Mesh density inside boundary layers was up to five times inflated and in regions of high pressure exposure, particularly at the outer body of ship hull and containers, the mesh density was intensively increased (see Fig. 4). For decreas-ing the volume of computation, moving from the ship's hull toward the domain's wall, the density of mesh decreases respectively to the mesh size of 0.5 m. The total number of seven million meshes in two million nodes has been computed over solving domain which has proved the results more reliable. It must be noted that the gaps of bays were assumed to be 1.0 m.

Boundary condition
The aim of boundary condition in computational fluid dynamics is to converge the discretized equations for solving the specified framework in accordance with the defined flow specification around the computational domain boundaries.
For this purpose, the boundary condition of the case is to choose the wind velocity inlet profile assigned as the inlet condition (Fig. 5). For simulation relative to the real condi-      (Andersen, 2012b). For comparison of numerical with test results, non-dimensional drag force is employed. To prevent a reverse flow, the outlet boundary is considered of the pressure outlet where the magnitude of the pressure is zero. Application of the pressure outlet boundary condition, in simulations that a reverse flow occurs during iterations, results in a proper convergence rate. Owing to the symmetry of ship's geometry, in order to reduce the computational efforts, the symmetry condition through the entire domain is considered with respect to XZ plane. Wall boundary condition is applied where the fluid is surrounded by solid. Two-phase fluid investigation was not the subject of the present study. Hence, the sea surface is assigned as a fixed wall resembling conditions of the wind tunnel boundary condition as no-slip wall. In reality, however, the sea surface will have a surface velocity and wave elevation.
Grid density grew up due to the importance of the area where wind strikes the ship surface. However, the far field wall considered the free slip wall as it was so far from the flow field and the equation solving has little or no effect there. Consideration of y+ on walls supports the flow contribution by reduction of computations. For lateral walls of the domain, this boundary condition has been chosen due to the symmetrical plan which is assumed as a free slip wall too.
It must be noted that the computational domain was considered large enough to minimize the effect of the lateral boundaries on vessel.

Convergence of results
Aim at approaching fine range of convergence, respect to software and hardware performance, 10 to 50 cycles of iteration is considered which has been stopped when the difference between two successive RMS becomes smaller than 0.0001 that determining the convergence range which has been shown in Fig. 6.

Non-dimensional coefficients
The measured forces and moments are post-processed into non-dimensional coefficients to make the results independent of wind velocity and ship size. The results are normalized using the flow velocity wind profile, U, the density of the air, ρ, and the ship's length between the perpendiculars (L pp ) in a suitable exponent: (1) The description of coefficients are convenient if different configurations of the same ship are to be compared because they are normalized using L pp .

Container configurations
Ten different container stacking configurations are investigated. Stacking details are shown in Appendix 1. Stacking configurations are divided to three categories generally. The first category includes systematic configuration, the second category includes the streamlined, and the third group includes random stacking configuration.
Many considerations are taken into account when loading containers on board of a ship (IMO, 2012;DNV, 2001). Some are: • Reefer containers must be placed where the power supply for the refrigeration is located.
• Hazardous goods containers have designated locations.
• Containers are loaded for unloading in the right order at different ports of call.
• Heel, trim and stability are taken into consideration when loading the ship.
• The line of sight from the bridge must be 500 m or two ship lengths whichever are smaller, i.e. it must be possible to see the sea surface from the bridge 500 m in front of the ship, which dictates how high the containers in front of the bridge can be stacked (IMO, 2012). Furthermore stated by class that the view of the sea surface from the coning position shall not be obscured by more than two ship lengths, or 500 m, whichever are smaller, forward of the bow to 10° on either side under all condition of draught, trim and deck cargo (DNV, 2001).
For 0° wind blowing angle of attack which could be assumed as the head wind or air resistance against ship motion, wind counters and wind velocity passing through the model have been investigated at different container configurations. Fluid flow separation and vortex contribution  Hamed MAJIDIAN, Farhood AZARSINA China Ocean Eng., 2018, Vol. 32, No. 2, P. 196-205 around the containership with diverse stacking configurations area remarkable part of the present research.

Results for containership's aerodynamics investigation
In the following, due to limitation exposed by page numbers of the present study, only the loading conditions No. 1, 4, 7 and 10 (According to Appendix 1) are explained.

Full stack loading
Deck has been loaded by maximum container stacking capacity. It is distinctively shown in Fig. 7 that the maximum amount of pressure contour is experienced in the forward part of ship's body where the wind profile impacted to ship's body. Over the last bay of containers in debut, the pressure particularly increases on the upper tier corners. Note that bays are numbered from ship aft to fore. As the exposed cross section is directly impacted by wind, the maximum pressure is experienced in this area. Here, the minimum wind speed would be expected. This does not mean wind losing power, though, and after retrieving energy, pressure increases along the ship's length. The minimum pressure occurs on the top of container tiers surface where wind velocity increases as shown in Fig. 8. It is observable that the wind velocity strongly decreases after passing over the ship astern and the largest vortex is contributed. Other than that, the homogenous shape of container layout through stacked bays prevented any contribution of vortex between stacked bays. This is advantageous for drag force reduction.

Streamlined loading through entire deck
Regarding to gradual increase of containers tiers height through bays, wind pressure is gently distributed over all bays at fore deck which possesses the minimum spot pressure over all bays in comparison with other stacking configuration (see Fig. 9).
Pressure decreased through bays toward superstructure which could signify that the wind pressure gradually increased along the bays (see Fig. 10).
Gradual decrease of container bays from superstructure toward astern prevents the generation of vortex and eddy current in this area which leads to attaining optimum aerodynamic shape of configuration.
The minimum flow turbulence and vortex contribution is experienced in this configuration. Owing to gradual reduction of tiers height toward forward of vessel, wind flow velocity does not slow down until the middle bays over fore deck.
Late flow separation over mid bays is very effective in drag force reduction. In addition, the shape of superstructure in aft bays in conjunction with a stern, effectively min-   imized the formation of large vortices. Velocity reduction in wake is also minimized. Streamlined configuration is most favorable of aerodynamic loading condition.

Random stacking with maximum seven containers in height
In this configuration, multiple changes in bay heights along the ship length cause the added exposed cross sections which eventually lead to the growth of high pressure region in front of container bays. These high pressure regions are especially observed in the top tier corners which are directly exposed to wind flow around ship's body (see Fig. 11). Vortex formation is observable at locations where bay heights change (see Fig. 12). Whereas the loading configuration is non-homogenous, disordered wind velocity alteration occurs between bays, which leads to vortex formation between bays that has great effect on the increasing drag force. The empty spaces between bays result in the air getting enough space to regain its energy before hitting the next bay and thereby increase the resistance. Several random stacking configurations (according to Appendix 1) show similar trends in velocity and pressure behavior.

Pyramid stacking configuration with one container less
in each bay on each side As shown in Fig. 13, elimination of one container from the outer side of each bays has no significant effect on pressure contours. However, the area that is exposed to free wind flow on outer bays is partially reduced, therefore the drag force is reduced.
The maximum pressure is observable at ship stem and the vicinity area over water surface.
Large magnitude of ship forward cross sectional area intensifies the turbulence of wind flow that is traced in numerical solution outputs as sudden increase in drag amount (Fig. 15).
In the next part, numerical results are compared versus wind tunnel experimental results in order to determine the precision of numerical method.

Aerodynamic drag force results
For numerical approach a Core i7 quad core CPU with 8GB Ram system has been employed. The run time of the     system for grid generation was about 45 minutes and for the process about 120 minutes for each configuration.

Verification of results
A containership similar to the one which was employed in wind tunnel test (Andersen, 2012b) was used for numerical simulation. The non-dimensional numerical results are compared with the wind tunnel test results. The blockage correction is ignored for simulation (Maciejewski and Osmólski, 2002). Achieved results have been adopted for 0°w ind angle of attack (head wind) in order to compare the results in certain situation. The results of CFD solution of 5266.2 N drag force for full stack condition have been attained. Normalized drag force is 0.0084 (non-dimensional). Whilst the obtained non-dimensional drag force for the same configuration of experimental test is 0.01 which implies the reliability of the achieved numerical results.
On the other hand, results by CFD method depicted approximately the same difference for other stacking configurations. Moreover the CFD results show the same relative magnitude compared with experimental results. Also, results for different stacking configurations are presented in the diagram of Fig. 16 which shows a rational order.
In order to verify the precision in numerical results, drag coefficients for each configuration are compared with the normal drag coefficient of containership which exists between 0.55 to 0.8 (Minsaas and Steen, 2008). While the simulations were performed for half of model, the results were doubled and presented in Fig. 17. Generally, the differences between the numerical and wind tunnel test results are about 20% which imply the reliability of the method.
Wind drag force may also be calculated using class rules such as DNV and ABS (Hsu, 1984). The typical equation is in the following form: where V yt is the average wind speed above sea surface, C is the shape factor, A is the frontal surface area in square meters, and α is the wind angle of incidence. Inserting the respective values of 1.185 kg/m 3 for air density, 12.85 for wind speed, 84.7 m 2 for frontal area in a full stack condition (configuration #1 in Appendix 1), and also assuming a shape factor of unity, results in a wind force of 8286.6 N while the simulated value is 5266.2 N for full stack condition. This suggests that a unity shape factor for the hull and cargo overpredicts the wind force. Instead a value of about C=0.65 can precisely correct the formula. In the case of streamlined configurations, although the frontal area to be used in Eq.
(2) for seven tiers cargo is the same as a full stack, the shape factor must be further reduced. With this additional check the numerical results are verified and the CFD performance indicates well conformity.

Effect of wind velocity on drag force
Wind speed is defined as input and drag coefficient as output for full stack configuration. Results are shown in Table 3. Different speeds were selected from beafurt scale. Respectively sea force of 4, 5, 6, 7 and 8 were selected. Air density is considered 1.185 kg/m 3 and L pp assumed 80 m. The results are non-dimensionalized by Eq. (1) and presented in Fig. 18.

Summary of results
In comparison with drag force in streamlined stacking condition, a full stack condition increased drag force by 9.5%, a deck with empty bays 18.2%, and a random stacking configuration 24%.
Difference of drag force between full streamlined stacking configuration versus full stacking in aft deck, while streamlined stacking in fore deck, was increased by 2.6% . Also the difference of drag force between random full stack-  ing on aft deck versus random stacking with maximum five containers in height was 5%.
In ten investigated stacking configurations, the difference of drag force between the fully streamlined stacking and full stack condition (which supposed as reference condition) was 10%.
Moreover, the difference of drag force between the fully streamlined stacking configuration (which supposed as optimum condition) and fore deck streamline and aft deck full load was 2.6% which indicates the minimum difference among all the stacking configurations with optimum condition. Also it was 5% with pyramid stacking condition. These three loading configurations are favorable stacking due to the drag force reduction (see Table 4).
In this way the difference of drag force between fully streamlined configuration and random stacking with five containers in height was 24% and with random stacking with seven containers in height was 19% that implies the random stacking configurations are unfavorable stacking conditions due to the drag force reduction.
Difference of fully streamlined stacking with even bays empty was 14.6% and with randomness was 24% that implies as far as possible for loading the even container stacking in height is more effective than random stacking configuration for drag force reduction (see Table 5).

Conclusions
A Post-Panamax containership has been simulated by using ANSYS CFX software in order to compare the achieved longitudinal force with wind tunnel test results as the container stacking configuration varies over deck. Generally, the effect of container stacking configuration on drag force at head winds could be concluded as the following .
Every change of stacked configuration on deck has direct influence on drag force. The drag force depends on both the ship cross sectional area, as well as the amount of ship's longitudinal surface over which wind passes. In fact, the latter has a more significant effect.
From summary of results, it could be concluded that every empty bay caused additional flow turbulence. Thus, as far as possible loading with empty bays must be avoided during ship voyage due to the effect of random stacking and empty bays on drag force increase. It is revealed that change of stacking configuration on aft deck led to the increase of drag force. Regarding to the attained results the fore deck stacking configuration does have the main significant role in change of drag force, while, the aft deck stacking configuration also alters the drag force. Fore and aft deck streamlined is the optimum stacking configuration. Fully streamlined, aft deck full stack while fore deck streamlined, and pyram-   id stacking condition are three favorable stacking configurations for the drag force reduction. As a general instruction for drag force reduction, any unevenness and random stacking must be avoided during loading of container on deck. Also during seakeeping, the same configuration instruction could be advantageous due to the resistance reduction.
It is proposed that in order to reduce the wind drag force and consequently reduce the fuel consumption and pollutant emissions, empty spaces between the cargo containers should be inhibited and unbalanced cargo distribution over deck should be prohibited. Also, it is advised to make the cargo distribution more streamlined on the most forward and aftward deck areas .