Study of the ship resistance during swarm operation based on biomimetics

1 Study of the ship resistance during swarm operation based on biomimetics Jinhyeok Choi1 and Gisu Song1 * 1 National Korea Maritime and Ocean University, Busan, South Korea Abstract. In this study, the swarm operation of ships inspired by the natural behavior of a duck swarm is investigated through numerical simulation. The results show that swarm operation can be an alternative for reducing operating costs compared to operating individually. In nature, ducklings swim in positions where they experience less resistance by staying within the waves created by their mother. At these positions, ducklings experience reduced wave resistance and a wave riding effect. This allows ducklings to swim with less effort compared to swimming alone. In this study, this phenomenon was applied to ship operations. A KRISO Container Ship (KCS) and a fishing vessel in model scale were defined as a mother duck and a duckling, respectively. The simulation results showed that the fishing vessel experienced less resistance in all positions behind the KCS, and the amount of resistance reduction varied depending on the position. The best position for the fishing vessel is similar to where ducklings benefit most. When several fishing vessels were arranged like a group of ducks, the resistance reduction for the rear vessels became smaller but leveled out at a certain point. This study focuses on the hydrodynamic resistance performance of rear ships during swarm operation and also investigates the optimal swarm operation configurations. Keywords: Biomimetics, Swarm operation, Wave resistance, CFD, Duckling. 1 Introduction With the advent of the Fourth Industrial Revolution, technological trends in the marine transport industries and shipbuilding industries are rapidly developing. Among them, research related to autonomous and unmanned operation technologies that minimize accidents by human error and improve fuel efficiency is being actively conducted. As technologies for controlling such vessels developing, interest in controlling operating multiple ships as a swarm operation. Baek et al. [1] conducted a study on formation control techniques for autonomous navigation of unmanned surface vessels (USVs) based on potential fields. Operating multiple vessels in a swarm provides the advantage of performing missions more efficiently over a wider area compared to individual navigation. To maximize this advantage, studies have also been conducted on performing complex tasks that reflect dynamic, real-time environmental conditions. Kim et al. [2] developed small-scale USVs to verify swarm mission planning and autonomous navigation algorithms through real-sea experiments. And advanced control algorithms and navigation optimization technologies for the efficient operation of USV swarms are continuously being developed. To implement swarm navigation effectively, it is necessary not only to develop control technologies for multiple vessels, but also to understand the hydrodynamic interactions between each individual vessel in the swarm. Because each vessel in a swarm is exposed to a different hydrodynamic condition. Lee at al. [3] conducted numerical simulations with multiple vessels arranged in parallel. They confirmed that wave interference between ships in parallel formation causes changes in wave resistance depending on their distance and speed. Also, if multiple vessels are arranged longitudinally, the Kelvin wave generated by the leading vessel can affect the following vessels, such as their resistance characteristics. To maximize swarm navigation efficiency, it is essential to consider these hydrodynamic interactions when determining the optimal positions for trailing vessels, and to establish an optimal formation and spacing strategy accordingly. If the wave generated by the leading vessel is analyzed, the resistance of the following vessels can be reduced, thereby the overall energy consumption of the swarm can be minimized. In fact, the similar formation of vessel swarms is easily observed in nature, and this provide us valuable insights. For instance, the collective movement of birds and fish demonstrates the efficient formation. * Correspondence to: gisu.s[email protected]c.kr 16th International Symposium on Practical Design of Ships and Other Floating Structures PRADS 202 5 Ann Arbor, MI, USA, October 19th – 23rd 2025 2 The purpose of this study is to analyze the hydrodynamic resistance performance of vessels based on biomimetic approach. Among various examples in nature, ducks are known to form swarms on the free surface, similar to a ship. Yuan et al. [4] conducted a numerical study using velocity potential theory to investigate the resistance performance of ducklings following a mother duck. Inspired by this natural duck swarm, the ship swarm formation is mainly discussed in this study. We focused on how resistance changes according to the position of the rear ship and investigated the fundamental origin. 2 Numerical Method 2.1 Definition of target vessels The ships used in this study are the KCS (KRISO Container Ship) and a fishing vessel on model scale. Main particulars and geometries are given in Table 1 and Fig. 1, respectively. (a) KCS (b) Fishing ship Figure 1. Geometry of the KCS and the fishing ship Table 1. Main specifications of the KCS model and the fishing ship model Item KCS model (1/31.6) The fishing ship model (1/5.35) Length - LPP [m] 7.2786 1.768 Beam - BWL [m] 1.019 0.536 Depth - D [m] 0.6013 0.068 Draft – T [m] 0.3418 0.099 Displacement – Δ [m3] 1.649 0.07 Speed - U [m/s] 2.196 2.446 Froude number 0.26 0.59 To simulate a group of ducks, it is necessary to consider vessels with Froude numbers representative of a mother duck and her ducklings. In a previous study [4], the Froude numbers of the mother duck and duckling were 0.25 and 0.5, respectively. Since the Froude number of the KCS is defined as 0.26, which is close to that of the mother duck, the mother duck can be represented by the KCS. For the duckling, a fishing vessel was chosen in this study. If the KCS were to be scaled to match the duckling's Froude number, the resulting Froude number would be 0.52. However, since the KCS was designed with a bulbous bow for a Froude number of about 0.26, it is not suitable for representing the ducklings. For this reason, rather than scaling the KCS to match the duckling's Froude number, it was necessary to select a vessel for which experimental data is available at a Froude number close to 0.5-0.6 to represent the duckling. In the case of fishing vessels, several benchmark datasets have been made publicly available. Another important consideration in selecting the vessel to simulate the duckling is its length. To effectively observe the wave-riding phenomenon, the length of the vessel representing the duckling must be shorter than the wavelength of the waves generated by the vessel representing the mother duck. The wavelength (λ) is defined by Equation (1), and the wavelength of the KCS is evaluated as 3.09 m at a Froude number of 0.26. As shown in Table 1, the length of the fishing vessel in model scale is less than the wavelength. For these reasons, a fishing vessel was chosen to represent the duckling in this study. 𝜆= 2𝜋𝐹𝑟2𝐿𝑃𝑃 (1) As written above, this study was conducted in model scale, so the scale ratio of the KCS and the fishing vessel is different, respectively. This is because, in the process of selecting model ships that satisfy the Froude number and length conditions required to simulate a duck swarm, vessels with different scales were defined. Therefore, the length ratio between the KCS and the fishing vessel in full scale differs from that in model scale. As a result, 3 extrapolating the KCS and fishing vessel used in the simulations to full-scale ships would lead to a situation that different from the actual duck swarm. Additionally, as two different ships were used in this study, two characteristic lengths are involved. For consistency in data, all lengths shown in the following figures are based on the KCS model. To simulate the formation of a mother and duckling, KCS and the fishing vessel were arranged longitudinally, resembling a duck swarm, and numerical simulations were performed. The spacing between the KCS and the fishing vessel was defined using the wavelength (λ) generated by the forward positioned KCS. A total of eight numerical simulations were conducted with intervals from 1.50λ to 3.25λ, increasing by 0.25λ each case. The resistance reduction of the fishing vessel was represented using the CDR, which indicates the difference in resistance compared to obtained value when the fishing vessel is sailing alone. CDR is defined as in Equation (2), where RS is the resistance of the fishing vessel when sailing alone, and R is the resistance when the fishing vessel is positioned in the swarm operation. 𝐶𝐷𝑅 =(1 − 𝑅 𝑅𝑆)×100% (2) A negative CDR value indicates that the resistance of the fishing vessel in the formation is larger than in the alone condition, while a positive CDR indicates that the resistance has decreased compared with the alone condition. In other words, the larger the CDR, the more the resistance is reduced compared to the alone condition. 2.2 Numerical set-up Before simulating the duck swarm with KCS and fishing vessel, numerical simulations for each vessel were individually conducted to validate the numerical methodology through comparison with experimental data. The numerical simulations were carried out using the commercial CFD software, STAR-CCM+ ver. 16.06. The Reynolds-Averaged Navier-Stokes (RANS) equation with RSM (Reynolds Stress Model) turbulence model [5] was applied. To realistically describe the ship waves generated by a ship, the volume of fluid (VOF) method was applied, furthermore, the overset-mesh method was applied to allow for heave and pitch motions of target vessels. The computational domain used in present simulations is shown in Fig. 2. Considering the calculation efficiency of numerical simulation, simulation was performed for the fluid domain that included only half of the hull. To reduce the computational time and cost, total simulations were performed on half -body condition of the target vessels. The size of the computational domain was normalized based on length of target vessel and defined as 2.5LPP in the vertical direction, 7LPP in the streamwise direction, and 2LPP in the spanwise direction. Symmetry boundary conditions were applied left and right surfaces, velocity inlet boundary conditions were applied inlet, top and bottom surfaces, and pressure outlet boundary condition were applied outlet side. Figure 2. Computational domain The grid system for KCS used in this study is shown in Fig. 3 and Fig. 4. As shown in Fig. 3, an unstructured grid system called by Trimmer type was applied. To reduce the total number of cells, the wall function was employed, and Y1+ was set to 50. Considering that the fishing vessel will be positioned behind the KCS during the duck swarm simulation, the wave resolving mesh was extended sufficiently far downstream from the KCS. Top Bottom Right Inlet Outle t Left Overset boundary 7 LPP 2 LPP 2.5 LPP 4 (a) Side view (b) Top view Figure 3. Grid system of the KCS Table 2. Comparison of EFD and present simulation of the KCS EFD [5] Present Error [%] CTM.E+3 3.711 3.717 0.16 Trim [deg] -0.169 -0.167 -1.40 Sinkage [m] -0.0139 -0.0147 5.71 The experimental data used for comparing to numerical simulation is referred from the 2015 Tokyo CFD conference [6]. The comparison between the numerical simulation results and the experimental data at Froude number 0.26 is presented in Table 2. It was confirmed that there were no significant differences in resistance, trim and sinkage between the numerical simulation and experimental results. In the duck swarm simulation, the fishing vessel is located on the wave generated by the KCS. Therefore, it is important that the wave pattern around the KCS is generated similarly to the experiment in numerical simulation. To verify this, the simulated wave profiles around the KCS were compared with experimental data. As shown in Fig. 4, the experimental value of the wave profiles generated by KCS was obtained from previous study [7] and there was no significant difference. Figure 4. Wave pattern of the KCS (a) y/LPP = 0.0741 -0.01 -0.005 0 0.005 0.01 -0.2 0.3 0.8 1.3 1.8 2.3 2.8 z/LPP x/LPP EFD CFD Present EFD 5 (b) y/LPP = 0.1509 (c) y/LPP = 0.4224 Figure 5. Longitudinal wave cuts Figure 6. Wave profile on the KCS hull surface For more strict validation, a comparison of the wave profiles was conducted. Fig. 5 shows the comparison of wave profiles from CFD simulation and experiment at some specified positions where y/LPP is 0.0741, 0.1509, and 0.4224, respectively. The Y-axis and X-axis represents the normalized wave height the longitudinal position, respectively. Since the experimentally measured data exist only up to the position of x/LPP = 1.8, it was not possible to compare all the values from the numerica l simulation. As shown in Fig. 5, the wave profiles from the simulation are closely predicted to those of the measured data. Additionally, the wave profile on the KCS hull surface from the present simulation was also compared to experimental data in Fig. 6. Simulation results showed good agreement with measuring data. Based on numerical results compared above, it is confirm that the numerical setup for KCS is reliable. Next, the numerical method for the fishing vessel was also examined. The same numerical setup used for the KCS was equally applied. Similarly, the overset mesh method was employed for the fishing vessel to allow degrees of freedom in heave and pitch motions. The mesh around the fishing vessel was configured as shown in Fig. 7. The fishing vessel used in this study is the same geometry as that used in the experimental study by Park et al. [8] and the simulation results were compared with their experiment. As presented in Table 3, the resistance values showed minor differences. For the fishing vessel, comparison with model experiments was conducted at a speed of 2.446 m/s. However, when positioned behind the KCS, the fishing vessel must travel a t the same speed as the KCS, 2.196 m/s. Therefore, an additional simulation was conducted, as a result, a resistance of 72.34 N was obtained. This value was used as the resistance of the fishing vessel in the standalone condition for the present study. -0.01 -0.005 0 0.005 0.01 -0.2 0.3 0.8 1.3 1.8 2.3 2.8 z/LPP x/LPP EFD CFD -0.01 -0.005 0 0.005 0.01 -0.2 0.3 0.8 1.3 1.8 2.3 2.8 z/LPP x/LPP EFD CFD -0.008 -0.004 0.000 0.004 0.008 0.012 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z/Lpp x/Lpp CFD EFD 6 (a) (b) Figure 7. Grid system of the fishing vessel Table 3. Comparison of EFD and present simulation of the fishing vessel EFD [7] Present Error [%] RTM [N] 80.97 80.66 -0.38 3 Results 3.1 Wake field analysis Before consideration of KCS and the fishing vessel, the wake flow field behind the KCS alone was analyzed. Since previous study [4] was conducted by the potential simulation, the viscous effect could not be explained. Although this study was inspired by the duck formation in Yuan et al.’s study [4], the consideration of viscous effects is essential for the realistic analysis and understating of the flow field. The velocity normalized by ship speed behind the KCS is shown in Fig. 8. The wake region where the flow velocity is less than 95% of the KCS speed is clearly visualized. In other words, even the highest velocities in wake region are at least 5% slower than the ship speed of KCS. It was confirmed that the wake region extends longitudinally behind the KCS, and this is the area where the fishing vessel is located. Thus, even though ship speed of KCS and fishing vessel is same, the fishing vessel is exposed to lower actual inflow speed condition comparing to the operation alone condition and this situation significantly affects following vessel’s resistance. ssssss Figure 8. Wake region downstream of the KCS . 7 3.2 KCS & One fishing ship The duckling effect was simulated by placing a fishing vessel in a straight line behind KCS at various intervals. The position of the fishing vessel was defined from 1.50λ to 3.25λ with 0.25λ intervals. Fig. 9 shows the wave patterns obtained from each simulation case, and it was observed that the wave pattern varies according to the fishing vessel's location. Figure 9. Wave patterns of the KCS & the fishing vessel at each interval 1.5λ is defined as the base distance between the KCS and the fishing vessel. The height of the divergent waves generated by the fishing vessel at 1.75λ case is somewhat decreased comparing to base case. In case of 2.00λ, the transverse wave components were much diminished than those of base case. In case of 2.25λ, the divergent waves became amplified again. When the fishing vessel was located at 2.50λ, the overall wave distribution pattern is almost similar to those of 1.50λ case. The wave distributions behind fishing vessel in case of 2.75λ, 3.00λ, and 3.25λ were also almost same to those of 1.75λ, 2.00λ, and 2.25λ, respectively. Figure 10. Wave profile of the KCS and CDR of the fishing ship This repeating tendency is directly related to reduction of the resistance on a fishing vessel. Fig. 10 shows the fluctuation of CDR values along to distance from KCS. The starting point of x-axis (x/LPP = 0) means the KCS’s A.P. position. The CDR variation exhibited a clear periodic pattern with respect to wavelength. These results indicate that when two vessels are aligned in a straight line, the absolute distance between them is very important on the resistance and wave pattern of the rear vessel. In other words, it depends on the position on the phase of the wave generated by the forward vessel. As the swarm’s speed increases, the wavelength of the generated waves -10.00 0.00 10.00 20.00 30.00 40.00 50.00 -0.012 -0.008 -0.004 0.000 0.004 0.008 0.012 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 CDR [%] z/LPP x/LPP Wave profile (KCS alone) CDR (Fishing ship) Ａ Ｂ 8 also becomes longer as shown in Eq. (1). Consequently, the location at which the fishing vessel experiences minimum resistance shifts accordingly. To maintain optimal resistance reduction, the fishing vessel must adjust its distance from the KCS in response to change in wavelength. The CDR values for the fishing vessel were larger than zero (CDR > 0) at all positions, it indicates that the resistance was lower than that of sailing alone situation. Even if the KCS and the fishing vessel travel at the same speed while maintaining a fixed distance, the flow velocity experienced by each vessel is actually different. Since the fishing vessel is positioned in a region with a slower velocity than the KCS’s vessel speed, it experiences reduced resistance comparing to sailing alone at same speed. This confirms that the fishing vessel gains a resistance benefit simply by being positioned behind the KCS in resistance simulation. From the KCS wave profile in Fig. 10, it can be observed that the wave amplitude decreases progressively downstream. As the wave amplitude decreases, the CDR of the fishing vessel also tends to decrease further downstream. This is because the wave energy generated by the KCS decreases as it propagates downstream, leading to a reduction in wave amplitude. As a result, the interaction between the waves and the fishing vessel becomes weaker, which in turn reduces the resistance reduction effect obtained from the waves. According to Yuan et al.’s previous study [4], ducklings positioned behind the mother duck can even experience additional thrust, resulting in CDR values exceeding 100%. However, in realistic simulation with two vessels of KCS and fishing vessel, such high CDR values were not observed. Among several simulation cases, the contradictive wave patterns with respect to two different positions, A and B in Fig. 10 were compared in Fig. 11. Position A and B represent the maximum and minimum CDR position within one wavelength period. As wave elevation amplitude which is generated behind following vessel are smaller, the resistance of fishing vessel showed smaller resistance. Fig. 12 showed the wave amplitudes behind fishing vessel. In case of position A, it is relatively similar to that of isolation case. In contrast, the wave amplitude of position B is much less than that of isolation case. In case of position A, the bow of the fishing vessel is located at the wave crest generated by the KCS. At this point, the bow wave generated by the fishing vessel is superposed to the crest of the KCS generated wave, resulting amplified wave height. This amplification leads to larger waves around the fishing vessel and thus an increase in wave resistance. Ian contrast, at position B, the fishing vessel's bow wave superposition with the trough of the KCS generated wave, resulting wave damping. This leads to smaller waves around the vessel and reduces wave resistance. A ship’s total resistance consists of viscous resistance and wave resistance. For the fishing vessel positioned behind the KCS, the viscous resistance is expected to be similar at both positions A and B, as the flow velocities experienced at both positions are comparable due to their location within the KCS wake. Therefore, the difference in total resistance between positions A and B is primarily attributed to the difference in wave resistance. By comparing the wave heights around and downstream of the fishing vessel at positions A and B in Fig. 11 and Fig. 12, it was confirmed that the wave heights are smaller at position B where the resistance is significantly reduced indicating that the wave resistance of the fishing vessel is lowest at position B. Figure 11. Wave patterns of the KCS & the fishing vessel at A and B A B 9 Figure 12. Wave profiles downstream of the fishing vessel at y/LPP = 0 In previous study [4], the wave riding effect of a duckling was explained. When the duckling’s chest is positioned at the wave trough and its body at the wave crest, its resistance is minimized. This is called by the wave riding effect. This phenomenon occurs when the wave increases the pressure on the duckling’s abdomen, pushing it forward. At the same time, the low pressure on the duckling’s chest is generated at the wave trough. Thus the pressure difference between the chest and abdomen of the duckling induces the pressure drag, resultantly. . (a) Position A (b) Position B Figure 13. Pressure distribution of the fishing vessel at positions A and B Table 4. Comparison of trim and sinkage of the fishing vessel at positions A and B Fishing ship at position A Fishing ship at position B Trim [deg] -0.564 0.046 Sinkage [m] -0.017 -0.014 We would like to investigate whether the wave riding effect of duckling would be similarly repeated in the fishing vessel. To analyze clearly, the pressure distributions on fishing vessel at position A and B are given in Fig. 13. Based on the Fig. 13, it is clearly observed that higher pressure is distributed at the bow in case A comparing to that of case B. This is because the bow of the fishing vessel at position A is exposed to a wave crest. Conversely, higher pressure on stern in case B was simulated than that in case A. Through this comparison, it was confirmed that position B has a more advantageous pressure distribution for advance, with lower pressure at the bow and higher pressure at the stern comparing to those of position A. Additionally, this pressure distribution directly affects the trim of the fishing vessel. Table. 4 presents the trim and sinkage of the fishing vessel located in position A and B, respectively. A positive value indicates the bow trim and a negative value means the stern trim. In case of position A, the high pressure at the bow and low pressure at the stern led the stern trim. In case of position B, -0.004 -0.002 0.000 0.002 0.004 0.006 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 z/LPP x/LPP Fishing ship alone KCS & Fishing ship at A KCS & Fishing ship at B