White papers

Antoine Reverberi

October 13, 2022

15 minutes

Antoine is a former naval architect at Damen with experience in ship design and optimization. He joined Extrality as a CFD engineer and brings his expertise in fluid dynamics to several projects with customers.

The objective of this study is to minimize the resistance of a ship at the target operational speed and to show that it can be done in a short time with few computing resources. First we will recall the context of the global shipping industry and a way to cut down emissions, then we will describe the procedure of hull form optimization and finally we will show how to effectively do it with Extrality Deep Learning Physics Platform.

In 2018, the International Maritime Organization (IMO) adopted an initial strategy to achieve decarbonization of international shipping that will require ships to reduce their greenhouse gas emissions (IMO, 2021). Therefore, it requires designers to improve their energy efficiency. One of the methods is to reduce ship resistance by optimizing the hull form. This reduction directly translates into fuel saving and lower greenhouse gasses emissions.

*Figure: The decarbonization of maritime transport can be achieved through the development and the combination of energy efficiency and clean solutions [**Shutterstock/studio concept**].*

As a ship moves through calm water, it creates both divergent waves, which spread outward from the ship and transverse waves, which travel at approximately the same speed as the ship. They generally consist of many wave systems, most prominently the bow and stern wave systems which interact with each other, either partially canceling the waves made by a ship (and reducing the wave-making resistance) or by adding and increasing the wave-making resistance. At low speeds the transverse waves have short wavelengths and several crests can be seen along the ship’s length. At high speeds, the wavelength increases resulting in some speeds with higher resistance due to interference. This fact causes the resistance curve to have “humps” and “hollows”.

*Figure (left): Theoretical resistance curve with “humps” and “hollows”. The figure shows a large increase in resistance at a Froude number of 0.40. This is the speed at which the length of the wave system generated by the ship is equal to the length of the ship. It is known as “hull speed,” which is the last efficient speed for a displacement ship.*

*Figure (right): Lord Kelvin (1887) showed that the waves travel at a constant angle of 19.47° behind the ship, no matter the speed of the vessel (Manen and Oossanen, 1988).*

However, when considering the forces acting, the total resistance is made up of the sum of the tangential shear (induced by the viscosity of the fluid) and normal pressure forces acting on the wetted surface of the vessel. After deducting from the total resistance the shear part, the remainder is called the residual resistance. Of this the wave-making resistance is the most important part.

The starting point of a good design is the development of a good curve of sectional areas. Bad wave interference can be avoided by using the specific wavelength (2π Fn^{2} L) to position the bulbous bow and the fore and aft shoulders in the curve of sectional areas. It is recommended if possible to position the fore and aft shoulders of the waterlines, causing a low pressure region, at a wave crest position of the specific wavelength. This will reduce the wave amplitude and hence the wave-making resistance. Next, local modifications can be applied to further improve the efficiency and quality of the hull:

- Fore body optimisation includes consideration in the design of the foremost part of the ship (including but not limited to bulb design, forward shoulder, and waterline entrance).
- Aft body optimisation deals with mitigation of the stern waves, avoiding eddies and improving the flow into the propeller. By improving the flow around the stern of the ship the hull resistance can be reduced.

*Figure: The procedure of hull form optimization can be split into three steps: 1) the LCB study, 2) fore body study and 3) aft body study.*

The longitudinal center of buoyancy (LCB) shows the distribution of the displacement along the hull and directly affects the wave produced by the vessel. This position is generally to be located in forward from midship for the low-speed vessels (Harvald, 1983). Determining the optimal position of the LCB during the early design phase plays an important role, but it is difficult work, especially for designers who do not have much experience.

(Lackenby, 1950) did research work on the variation of ship forms. The principle of his method is that the frames are shifted in longitudinal direction while the frame area and frame shape remain unchanged. A key quality of this method is that it also maintains the fairness of the hull to a very high degree during the transformation process.

In this study, it was assumed that the values of length, beam, draught and Cb are fixed and determined by external conditions such as cargo capacity, port limitation and routing of a ship. Hence, small shape modification is accomplished within a change in displaced volume of less than 1%. If the displacement is the only constraint, the length, beam, and draft can be automatically actualized to accommodate the redistributed volume.

*Figure: The Sectional Area Curve (SAC) of the baseline hull. Longitudinal positions on this curve represent sectional area values. The integrated area under the sectional area curve gives the displaced volume and the centroid of this area gives the center of volume of the ship (the longitudinal center of buoyancy LCB). The curve is extended over the ship’s length which is divided into three lengths namely: the entrance length, the length of the parallel middle body and the run length.*

*Figure: Lackenby transformation of LCB by +/-0,9% and its modified SAC plot. A positive value means forward shift, and a negative value implies a backward shift. Accordingly, the section area between stations 16 and 20 became fuller and the section area between stations 1 and 6 became more slender, and vice-versa.*

Most CAD tools provide the ability to perform this task conveniently. We use the CAD software Rhinoceros 3D (McNeel, 2010) to manipulate the geometry and we use Python and RhinoScript to automate Rhino operations.

*Figure: Python can be used all over Rhino to automate repetitive tasks.*

Computational Fluid Dynamics (CFD) often requires a lot of computation time and effort. This is especially true in the case of Reynolds-Averaged Navier-Stokes (RANS), needed to accurately assess the thick boundary layers in the aft part of hull shapes. Hence, CFD is often not directly applied in concept exploration studies, but rather for verification of a chosen design.

Extrality's platform of AI-powered simulations can predict physics behavior in just a few seconds thanks to a new algorithm mixing data and physical priors. This permits a drastic reduction of man–hours and computational time and thus exploration of a wider design space in the conceptual design phase. In the present case, an AI-model has been created leveraging a database of high-block coefficient ships simulations at different operational conditions (draught, speed). This platform was trained and validated versus CFD-obtained values, learning on full 3D volume information and made available on Extrality's platform. It is accessible directly from the web, without any installation needed. All simulations can be run in 3 clicks!

*Figure: 1) Upload the geometry, 2) Run the simulation with a single click and 3) Download the post-processing: volume, surface, evolution curves, coefficients.*

The baseline hull form to be optimized is a 1:2 scaled model of the Japan Bulk Carrier (JBC) hull (Larsson et al., 2015), whose main dimensions are listed in the table below.

*Figure: The JBC is a capesize bulk carrier designed jointly by National Maritime Research Institute (NMRI), Yokohama National University and Ship Building Research Center of Japan (SRC). No full scale ship exists. Geometry available at:* https://www.t2015.nmri.go.jp/jbc.html

*Table: Main dimensions of the JBC.*

As shown in the table below, the total resistance changes for different positions of the LCB. Since the Froude number is relatively low (Fn = 0.141), the portion of residual resistance in total resistance is low too, about 33%.

*Table: Comparison of resistance components. Results obtained with Extrality AI-powered simulations platform.*

This can be explained by the figure below showing the pressure distribution of the three ships. As the LCB position moves forward, the residuary resistance increases because of higher shoulder wave whereas aft-body pressure resistance is decreased by increase in pressure recovery of aft-body.

Conversely, as the LCB position moves backward, the residuary resistance decreases because of lower shoulder wave whereas aft-body pressure resistance is increased by decrease in pressure recovery of aft-body.

*Figure: Comparison of the hydrodynamic pressure force coefficient for the baseline (top), the LCB_mod01 (middle) and the LCB_mod02 (bottom). Results obtained with Extrality AI-powered simulations platform.*

This tendency is further supported by the figure showing the wave height along the hull. As expected at the bow and the stern, high pressure due to stagnation points result in a wave crest. On the other hand, the shoulders of the ship create low pressure which brings out a wave trough.

*Figure: Comparison of the wave height along the hull colored by the volume fraction water for the baseline (top), the LCB_mod01 (middle) and the LCB_mod02 (bottom). Results obtained with Extrality AI-powered simulations platform.*

Optimal results are shown in the figure below. Residual resistance has been calculated with multiple values of LCB and minimum residual resistance is achieved for the LCB located at -0,6% relative to its baseline.

Such a trend is not new and similar relationships have also been obtained in (Pak et al., 2020), (Szelangiewicz, 2009) and (Harries et al., 2001). However, it is interesting that Extrality properly reproduces the trends, all the more that the changes of the LCB are relatively small.

*Figure: Diagram showing the relation between resistance and LCB, which suggests existence of a minimum residual resistance for LCB value equal to -0,6% relative to its baseline.*

Minimum residual resistance equals 26,362 kN. Thus, compared with that of the original hull of 28,723 kN, the residual resistance of the new ship has decreased by more than 8%. However, residual resistance only accounts for about 33% of the total resistance so it can be predicted that the new hull will have about 3% reduction in total resistance compared to the original hull.

Hull form optimization has a large potential for fuel saving. With the Lackenby transformation, it is possible to calculate the shift of the frames to achieve a required LCB position while keeping the volume constant. This directly affects the wave produced by the vessel.

In this study, the vessel’s total resistance coefficient was calculated for different positions of the LCB and minimum resistance is achieved for the LCB located at -0,6% relative to its baseline.

While CFD often requires a lot of computation time and effort, with Extrality, it is possible to drastically reduce the amount of man–hours and computational time needed to optimize a hull form. This result can easily be obtained by one engineer within one working day!

Harries et al., 2001. Investigation on Optimization Strategies for the Hydrodynamic Design of Fast Ferries. *6th International Conference on Fast Sea Transportation (FAST 2001),* Southampton.

Harvald, 1983. Resistance and Propulsion of Ships. *John Wiley and Sons,* Toronto.

IMO, 2021. Further shipping GHG emission reduction measures adopted. Available online at: https://www.imo.org/en/MediaCentre/PressBriefings/pages/MEPC76.aspx

Lackenby, 1950. *On the systematic geometrical variation of ship forms.* Trans INA 92:289–316

Larsson et al., 2015. *Tokyo 2015: a Workshop on CFD in Ship Hydrodynamics*, vol. 1-3, NMRI (National Maritime Research Institute), Tokyo.

Manen and Oossanen, (1988). Principles of Naval Architecture, Volume 2. *Society of Naval Architects and Marine Engineers,* New Jersey.

McNeel, 2010. *Rhinoceros 3D, Version 6.0,* Robert McNeel & Associates, Seattle, WA.

Pak et al., 2020. Hull form design for resistance minimization of small-scale LNG bunkering vessels using numerical simulation. In *International Journal of Naval Architecture and Ocean Engineering 12.* pp. 856-867.

Szelangiewicz, 2009. Numerical analysis of influence of ship hull form modification on ship resistance and propulsion characteristics. *Polish Maritime Research 4 (62).* Vol 16. pp. 3-8.