Research on Hull Form Design and Numerical Simulation of Sinkage and Trim for a New Shallow-Water Seismic Survey Vessel

Abstract

When a ship sails in shallow water, it will show different hydrodynamic performance from that in deep water due to the limitations of water depth. The shallow water effect may lead to hull sinkage and trim, increasing the risk of bottoming or collision. In this study, a new design scheme of a shallow-water seismic survey vessel is proposed to solve the problems of traditional seismic survey vessels in shallow-water marine resources exploration and safety. The RANS (the Reynolds-Averaged Navier–Stokes) method combined with the Overset Mesh and DFBI (Dynamic Fluid Body Interaction) method is used for numerical simulation to analyze the influence of ship type, water depth, and speed on ship sinkage and trim, as well as the influence of the shallow-water ship’s attitude on resistance. The results show that with the decrease in water depth and the increase in speed, the pressure distribution around the hull becomes uneven, which leads to the aggravation of the sinkage and trim of the hull. In response to this problem, the shallow-water seismic survey vessel significantly improved the sinkage and trim of the hull in shallow water to ensure its safe navigation. The research also shows that navigation resistance can be effectively reduced by appropriately adjusting the ship’s attitude. Therefore, this study provides a reference for the development of shallow-water ships in the future.

1. Introduction

Seismic survey vessels are specialized operation ships designed for the exploration of offshore resources such as oil and natural gas [1,2]. As global exploration of ocean resources deepens, including studies in shallow-water zones, new oil and gas resources continue to be discovered in these regions, leading to an increasing international market demand for shallow-water seismic survey vessels. However, the existing seismic survey vessels in the world are tailored for deep-sea operations, characterized by heavy loads and deep draft, which makes them unsuitable for entering shallow-water areas to meet the demands of marine resource exploration there [3].

When ships operate in shallow-water areas, they encounter significantly different resistance performance compared to deep-water navigation [4], demonstrating a marked ‘shallow-water effect’ increase in resistance. Furthermore, as ships navigate in shallow waters, the water depth restricts the flow field between the ship and the seabed, leading to an increase in water flow speed. Part of the water flow beneath the ship is also pushed toward both sides of the ship, causing an increase in water flow speed along the sides of the ship as well. Changes in the surrounding flow field affect the navigation status and force conditions of the ship, resulting in trim and sinkage of the ship, posing risks of grounding or collision [5]. Hydrodynamic phenomena in restricted waters, especially the sinking of ships, pose a serious threat to the operational safety of the waterway, endangering the life and property of the crew [6].

When navigating in shallow waters, the performance of the ship is affected by the shallow-water effect, leading to changes in the attitude of the ship, including sinkage and trim. To prevent grounding and stranding, and ensure the safety of shallow-water seismic survey vessels during navigation and operations, a new type of shallow-water seismic survey vessel is proposed.

Jiang [7] calculated the amount of ship sinkage and trim in shallow waters and the applicable speed range of the ship from subcritical to supercritical speeds through numerical methods. Gourlay [8] investigated the case of a large, flat-bottomed ship, such as a bulk carrier, moving in close proximity to a flat sea floor. The flow beneath the ship could be modeled as a shear flow between two parallel plates, one of which is moving. It discussed the implications of these flow models on squat and viscous resistance. Krishna and Krishnankutty [9] conducted experimental and numerical studies on the trim and sinkage of high-speed catamaran vessels in shallow waterways, investigating the impact of under-keel clearance on safe navigation speed, as well as considering the effect of spacing between hulls on safe navigation speed. Shi et al. [10] analyzed the trim and sinkage of ship hulls under different speeds and water depths in shallow-water conditions using numerical simulations, providing references for the safe navigation of ships in shallow waters. Pavkov and Morabito [11] conducted model tests on the shallow-water effects of two different types of trimaran ships. A significant increase in hull resistance and sinking was observed at speeds close to the critical speed. Deng et al. [12] used the CFD method to calculate the calm water resistance and resistance components of a trimaran test model with and without appendages under different conditions. The calculations took into account the viscous effect and the presence of a free surface in order to investigate the effect of trim and sinkage on the resistance calculation. Ma et al. [13] explored the extent to which sinking and trim affect ship resistance using numerical simulation methods. They discussed how to effectively assess and optimize these effects to reduce resistance. Lungu [14] performed numerical simulations on the motion of a certain KRISO container ship in shallow water based on the CFD method, analyzing the impact of water depth on hull pressure, sinking, trim, and resistance. Bechthold and Kastens [15] analyzed the effects of different sailing speeds on ship trim and squat in shallow waters through numerical simulations, predicting the trim and sinking for Postpanmax container ships in very shallow waters. Feng et al. [16] conducted numerical simulations using full-scale and model-scale KCS as research objects to calculate ship resistance at different water depth/draft ratios, and discussed the hydrodynamic forces, sinkage, trim angle, and wave characteristics at different water depths. According to the research status on the sinking and trim of ships in shallow water, most of them solve the problem of ship attitude in shallow water by numerical simulation, and analyze the details of the flow field in the restricted water area, so as to provide some reference for the safe navigation of ships in shallow water.

In view of the fact that traditional seismic survey vessels cannot meet the needs of marine resources exploration in shallow waters, this study designs a new type of seismic survey vessel based on the original deep-water seismic survey vessel. Based on the RANS (the Reynolds-Averaged Navier–Stokes), combined with the Overset Mesh and DFBI (Dynamic Fluid Body Interaction) method, the numerical simulation of sinking and trim of the shallow-water seismic survey vessel is carried out, and the sinkage and trim during navigation are predicted. Initially, simulations of both the original and the modified new ship types in shallow-water conditions are compared to analyze changes in sinkage and trim. Subsequently, different water-depth scenarios are selected for new ship type, including H/T = INF (infinite water depth), H/T = 3 (medium water depth), and H/T = 1.7 (shallow water depth), for numerical simulations of sinkage and trim. The comparative analysis of sinkage and trim values under infinite, medium, and shallow water depths is conducted to evaluate the impact of ship type, water depth, and ship speed on the sinkage and trim of the ship. The numerical simulation of the sinkage and trim of the new ship type in shallow water has a certain reference value for the ship hull design of the shallow-water seismic survey vessel and the safe navigation of the shallow-water ship. At the same time, the ship model resistance of the sinkage and trim value simulation is recorded and compared with the resistance of the unopened sinkage and trim ship model test. Therefore, the research in this study provides a reference for the future development of shallow-water ships and the safety of shallow-water navigation.

2. Research on New Ship Design

2.1. Original Ship Type

Most existing seismic survey vessels are designed for deep-sea operations, with scant information available on the hull design of shallow-water survey vessels for reference. Given the operational characteristics of shallow-water survey vessels, which mainly operate in shallow waters of up to 5 m deep, they are severely restricted by shallow draft conditions. Therefore, based on the operational requirements of shallow-water survey vessels and the hull characteristics of existing deep-sea survey vessels, it was initially determined that the hull form of the shallow-water survey vessel should be a fat shallow draft ship. One of the challenges in designing the hull lines of a fat shallow draft ship lies in the design of the bow and stern sections, as well as ensuring a reasonable transition and alignment with the parallel mid-body.

The presence of a parallel mid-body can lead to excessive fullness in the bow and stern lines of a ship, manifesting primarily as follows: an overly steep bow entrance design may result in a pronounced shoulder bulge at the forward shoulder, generating a bow bilge vortex in that area; if the angle of run at the stern is too great, it can lead to flow separation at the aft of the ship. Conventional deep-sea seismic survey vessels often employ a small bulbous bow design to improve the flow field at the bow and minimize the bow bilge vortex [17]. Unlike deep-sea seismic survey vessels, shallow-water seismic survey vessels are constrained by the depth of water they operate in and have a shallower draft, which precludes them from using the small bulbous bow design of traditional deep-sea seismic survey vessels. Consequently, with consideration for these factors, this study originally proposes a hull form design for a shallow-water seismic survey vessel, as depicted in Figure 1.

To better observe the detailed distribution of the flow field around the hull, CFD numerical simulations are performed on the original ship type. The simulations assess the pressure distribution on the hull in deep water and identify any adverse flow phenomena such as flow separation (boundary layer separation). The computational results are shown in Figure 2 and Figure 3.

From the pressure distribution diagram in Figure 2, it can be seen that a high-pressure area (the red part) forms at the bow of the ship, and a low-pressure area (the blue part) forms at the forward shoulder, along the parallel mid-body, and near the stern. This uneven pressure distribution is caused by the plumper design of the bow and stern lines of the ship: the slower flow velocity at the bow leads to the formation of a high-pressure area; while in the low-pressure areas, increased flow velocity results in higher local frictional resistance. Such accelerations and decelerations of the water flow along the direction of the hull are normal, but if flow separation or backflow occurs around the hull, modifications and optimizations to the hull form are needed. Flow separation has a significant impact on hull resistance and flow loss, and it is a major consideration in the design of new hull forms. However, as can be seen from Figure 3, there are areas of flow separation or stagnation at the bow, forward shoulder, and stern (the blue part). In these areas, the flow cannot continue to advance along the hull in the direction of the flow, resulting in a large amount of water adhering to the hull due to viscous attachment, thus increasing hull resistance.

When the water flows across the bow, according to the Bernoulli principle, the flow velocity at the bow is the least, causing the water to stagnate at the bow. However, the water will accelerate again along the hull after passing the bow, so the stagnation at the bow does not pose a significant problem. However, due to the excessive curvature at the transition section between the bow and the parallel middle body, flow separation occurs at the forward shoulder. A similar flow separation occurs at the aft shoulder of the hull. In addition, flow separation also occurs at the stern due to excessively full curvature, which may lead to phenomena such as cavitation and vibration near the propeller, negatively affecting propeller performance.

2.2. Design of Hull Form

Based on the computational results obtained in deep water, it can be inferred that the phenomena of flow separation of the hull become more severe in shallow water. In order to minimize flow separation and energy losses, as well as reduce hull resistance, it was decided to make modifications to the original ship type.

• A proposal is made for a wide and flat bulbous bow, with the breadth exceeding the height, enabling the hull to navigate shallow waters effectively. This design not only mitigates the wave-making resistance encountered while sailing but also increases the proportion of displacement volume at the bow of the ship, which aids in enhancing the stability and sea-keeping of the ship.
• The curvature at the forward and aft shoulders of the hull is to be smoothed, aiming to minimize the phenomena of flow separation at these locations.
• Reducing the curvature and the angle of inclination at the stern, with the addition of deadwood to improve flow separation phenomena at the stern, is conducive to improved ship stability [18].

The comparison between the modified new ship type (indicated in red) and the original ship type (indicated in blue) is depicted in Figure 4.

In order to verify whether the modified new ship type can meet the operational requirements and to assess the improvement of the flow separation phenomenon, CFD calculations were first conducted for the modified ship type at 10 knots in deep water, and the results were compared with those of the original ship type, as shown in Figure 5. A comparison of the flow separation phenomenon between the original ship type and the modified ship type (Figure 3 and Figure 5) reveals significant improvement in flow separation for the modified ship type, particularly at the front and back shoulder of the hull where no flow separation occurred.

Due to the fact that the working water depth of this shallow-water seismic survey vessel is primarily in shallow waters of 5 m, operating at a speed of approximately 5 knots, CFD calculations were performed for the modified new ship type at a water depth of 5 m and a speed of 5 knots to analyze whether flow separation phenomenon would occur under working conditions. The calculation results, as shown in Figure 6, indicate a significant improvement in the flow separation phenomenon around the ship at a water depth of 5 m and a speed of 5 knots, meeting the operational requirements.

3. Numerical Simulation of Shallow-Water Performance

3.1. The Object of Calculation

The main ship design parameters of the modified shallow-water seismic survey vessel, including both the actual ship and the ship model at a scale of 11.641, are shown in

Table 1. Principal particulars of the shallow-water seismic survey vessel.

Particulars	Full Scale	Model
Length overall LOA (m)	88.234	7.58
Length on waterline LWL (m)	88.122	7.57
Length between perpendiculars Lpp (m)	84.8	7.28
Breadth B (m)	16.9	1.45
Depth D (m)	5.5	0.472
Draught T (m)	2.82	0.242
Wetted surface S (m2)	1869	13.79
Displacement volume ∇ (m3)	3727.8	2.363
Block coefficient CB	0.922	0.922

. The subsequent numerical simulation is carried out by the ship model.

3.2. Computational Domains and Mesh

In order to reduce the computational cost and take into account the symmetry of the shallow-water seismic survey vessel during navigation, only half of the computational domain is selected for CFD simulation using STAR-CCM+ 2021.1 (16.02.008-R8) software. Considering the necessity to simulate sinkage and trim motions at various water depths, the dimensions of this computational domain are as follows: the inlet is 1.0 Length Overall (L_pp) ahead of the bow, the outlet is 3.0L_pp aft of the stern, the top boundary is 1.0L_pp from the free surface, the side boundary distance from the longitudinal section of the hull is 2.0L_pp, and the bottom boundaries are located at 1.7 Draught (T), 3.0 T, and 1.0L_pp from the free water surface, as illustrated in Figure 7. The computational domain comprises two regions: the background domain, which is static and does not include the ship or move with it, and the motion domain, which includes the ship body and moves in unison with it.

In this study, the mesh of the computational domain was generated using a trimmed grid generator, with local refinement around the bow, stern, and periphery of the hull. The refinement of the volume mesh within the free surface and the wave-making turbulent regions was performed progressively, in accordance with the Kelvin wave system. Near the hull, a prism layer grid generator was employed to produce six boundary layers, with a prism layer growth rate of 1.2. In shallow-water areas, influenced by the bottom boundary, three boundary layers were formed at the bottom edge, with a prism layer growth rate of 1.5. The wall function approach was used to manage flow within the boundary layer, achieving appropriate near-wall thickness to ensure wall y+ values ranged between 30 and 60. In deep-water areas, due to the absence of bottom viscous effects, the treatment of the bottom boundary was consistent with the top boundary, both set as velocity inlets. To mitigate the impact of numerical uncertainties on the results, the original ship type and the new ship type maintained the same mesh size and refinement areas, as shown in Figure 8.

To investigate the sinkage and trim motions of a ship in calm water, the Overset Mesh method was chosen to solve the motion response of the ship. The DFBI model was employed to simulate realistic ship motions. In the DFBI model, the motion of the ship is simulated according to the acting forces induced by the flow [19]. In order to prevent low-quality interpolation or interpolation failure, which could lead to erroneous solutions when using the Overset Mesh method, the mesh in the coupling region between the background domain and the motion domain was refined for both the original and new ship types. This ensured that the mesh sizes in the background domain were comparable to those in the motion domain, and the boundary of the motion domain maintained a minimum of five layers of grids between itself and the hull. The meshes for the motion domains of the original and new ship types are illustrated in Figure 9.

3.3. Boundary Conditions and Solvers

The specific settings of the boundary conditions in the numerical simulation of each working condition are shown in

Table 2. Boundary condition settings.

Boundaries	Deep Water	H/T = 3
Inlet	Velocity inlet	Velocity inlet
Outlet	Pressure outlet	Pressure outlet
Top	Velocity inlet	Velocity inlet
Side	Velocity inlet	Velocity inlet
Bottom	Velocity inlet	No-slip wall
Hull	No-slip wall	No-slip wall
Symmetry	Symmetry plane	Symmetry plane
Overset boundary	Overset mesh	Overset mesh

.

To mitigate the effect of numerical uncertainties on the outcomes, both the original ship type and the modified new ship type were subjected to the same boundary conditions and setups. The boundary layer formed at the bottom of the water in shallow water may affect the flow between the ship and the water bottom, the bottom is designated as a no-slip wall surface. The VOF method is utilized in this study to model the free surface [20]. A three-dimensional unsteady implicit segregated solver was utilized, with the selection of the Eulerian two-phase flow model [21]. The turbulence model is the Realizable k-ε model, and the SIMPLE algorithm solver is used to solve the pressure–velocity coupling equation [22]. The convection term is discretized by the upwind scheme with second-order accuracy, the diffusion term is discretized by the central difference scheme, and the time term is discretized by the Euler implicit discrete scheme with first-order accuracy. The time step satisfies that the Courant number is less than one.

3.4. Numerical Verification Method

CFD uncertainty analysis can be categorized into two components: Verification and Validation. The process of verification is to evaluate the uncertainty of the numerical value, and the process of confirmation is to evaluate the uncertainty of the mathematical model. The uncertainty of the numerical method is verified based on the verification method proposed by Stern [23] and Wilson [24].

The convergence analysis of mesh size and time step is carried out under the condition of water depth draft ratio H/T = 1.7 and working speed Vm = 1.110 m/s, and the numerical discrete uncertainty is evaluated to verify the reliability of the numerical simulation method.

In the analysis of mesh convergence, three sets of grids S₁, S₂, and S₃ with mesh foundation size encryption ratio $r=\sqrt{2}$ are set for calculation. When generating the mesh, keep the time step t = 0.02 s and keep the mesh encryption area and other settings the same. In the time step convergence analysis, the medium mesh size S₂ is used and three different time steps T₁, T₂, and T₃ are set up with the growth rate of r = 2 for calculation, and other settings remain unchanged. The specific working conditions are set as shown in

Table 3. Numerical simulation cases for convergence analysis.

	Base Size (m)	Number of Background Domain Cells (106)	Number of Motion Domain Cells (106)	Number of Cells (106)	Time-Step (s)
S1	0.1025	6.53	2.89	9.42	0.02
S2	0.146	2.51	1.14	3.65	0.02
S3	0.205	0.96	0.46	1.42	0.02
T1	0.146	2.51	1.14	3.65	0.01
T2	0.146	2.51	1.14	3.65	0.02
T3	0.146	2.51	1.14	3.65	0.04

.

The results of grid convergence analysis and time step convergence analysis are shown in

Table 4. Results of convergence analysis.

	RG	PG	UG (%S2)	RT	PT	UT (%T2)
Sinkage	0.509	1.948	0.051	0.765	1.975	0.972
Trim	0.167	2.585	0.218	0.556	2.931	0.773

. The following conclusions can be obtained through the analysis of the results. The grid convergence rates R_G of sinkage and trim value are 0.509 and 0.167, which are monotonically convergent. The grid numerical discretization uncertainty U_G of the two is 0.051% S₂ and 0.218% S₂, and the numerical discretization uncertainty is small. The time step convergence rate R_T of the sinkage and trim value is 0.765 and 0.556, which are also monotonically convergent. The numerical dispersion uncertainty U_T of the time step is 0.972% T₂ and 0.773% T₂, both less than 1%, and the numerical dispersion uncertainty is small.

Based on the validated numerical results mentioned above, considering both numerical precision and computational efficiency, grid 2 and a time step t = 0.02 s were chosen for further numerical simulations. In grid 2, the base grid size was set at 0.146 m, resulting in a total of 3.65 million grid cells for the entire computational domain.

4. Analysis of the Influence of Hydrodynamic Performance

Based on the validated mesh partitioning and numerical simulation methods mentioned earlier, CFD simulations were conducted for the original ship type under shallow-water conditions and the modified new ship type under three different water depth conditions. The simulations aimed to analyze the sinkage and trim of the ships. The numerical simulation results were used to analyze the effects of hull form design, water depth, and sailing speed on the heavy motion of the ships. The objective was to assess whether the new seismic survey vessel design could meet the safety requirements for operating in shallow-water environments.

4.1. The Influence of Ship Type on Ship Sinkage and Trim

The numerical simulation results for the sinkage and trim of both the original and the modified new ship types under shallow-water conditions (H/T = 1.7) are presented in

Table 5. Numerical results of sinkage and trim in shallow water of two types of ships.

	Original Ship Type		New Ship Type		E (%)
Vm (m/s)	Sinkage (m)	Trim (deg)	Sinkage (m)	Trim (deg)	Sinkage	Trim
0.626	−0.0191	−0.1836	−0.0103	−0.1576	85.4	16.5
1.110	−0.0473	−0.2892	−0.0134	−0.2679	252.9	7.95
1.375	−0.0657	−0.4933	−0.0166	−0.4315	295.8	14.3
1.474	−0.1081	−0.6884	−0.0187	−0.5498	478.1	25.2

.

In this context, a positive sinkage indicates an upward movement of the hull, denoting a rise or buoyancy, whereas a negative value signifies a downward movement, representing a sinking occurrence. As for trim, a positive value indicates a trim by the head, while a negative value signifies a trim by the stern.

The sinkage and trim values for different ship types, as they vary with ship speed, are plotted in Figure 10 and Figure 11. These graphs reveal that in shallow-water conditions, the sinkage and trim values of both ship types increase with escalating sailing speeds. Both types of ships display a sinking tendency and a stern trim phenomenon.

As the sailing speed changes, the sinkage of the new ship type increases from −0.0103 m to −0.0187 m, an overall increase of 81.6%. In contrast, the original ship type exhibited a sharp increase in sinkage with changes in speed, from −0.0191 m to −0.1081 m, an increase rate of 465.97%. At the same speed, the change in hull form design has a maximum impact rate of 478.1% on the sinkage, which is more than fourfold, indicating that changes in hull form design significantly improve the sinkage phenomenon. However, the change in trim values between the two ship types is not particularly pronounced, with a maximum impact rate of 25.2%, and the trend in hull trim did not change.

Based on the content of the diagrams, it is observed that the wide and flat bulbous bow shape design of the new ship type increases the proportion of the displacement volume at the bow, effectively slows down the trim phenomenon of the ship. Compared to the original ship type, the new ship type is better at resisting the heaving motion, and across the full speed range of the ship, the maximum sinkage of the new ship type is only −0.0187 m, meeting the requirements for safe navigation without the risk of grounding.

4.2. Influence of Water Depth on Ship Sinking and Trim

The numerical simulation results for the sinkage and trim of the modified new ship under different water depths (H/T = INF, H/T = 3, H/T = 1.7) and various speeds are presented in

Table 6. Numerical results of sinkage and trim in different water depths.

Water Depth	Vm (m/s)	Sinkage (m)	Trim (deg)
H/T = INF	0.626	−0.0065	−0.1163
	1.110	−0.0076	−0.1509
	1.375	−0.0092	−0.2199
	1.474	−0.0105	−0.2719
H/T = 3	0.626	−0.0075	−0.1513
	1.110	−0.0105	−0.2112
	1.375	−0.0139	−0.2609
	1.474	−0.0151	−0.2877
H/T = 1.7	0.626	−0.0103	−0.1576
	1.110	−0.0134	−0.2679
	1.375	−0.0166	−0.4315
	1.474	−0.0187	−0.5498

.

In Table 6, a positive sinkage indicates an upward movement of the hull, denoting a rise or buoyancy, whereas a negative value signifies a downward movement, representing a sinking occurrence. As for trim, a positive value indicates a trim by the head, while a negative value signifies a trim by the stern.

The variation curves of the sinkage and trim of the ship with speed under different water depth conditions are shown in Figure 12 and Figure 13. The data presented in these Figures indicate that, at the same speed, the sinkage in shallow water is greater compared to that in deep and medium water depths, and this effect becomes more pronounced with an increase in speed. However, the trim in shallow water is also found to be greater than that in deeper waters, and it sharply increases with increased speed. At a speed of 1.474 m/s, the trim value in shallow water is 102.21% higher than that in deep water.

Analyzing the trends in sinkage and trim under different water depths reveals that, for the new ship type, the impact of shallow water on the trim is greater than its effect on the sinkage.

Figure 14 illustrates the axial velocity flow field distribution of a ship under the same speed in both deep and shallow-water conditions. From the diagram, it is evident that in deep water, the distribution of water flow is not restricted by water depth, with the flow primarily moving ‘downward’ as it passes beneath the hull, and only a small portion of the flow diverting toward the sides at the bow. In shallow water, however, the distance between the bottom of the hull and the seabed decreases, restricting vertical movement of the water flow when passing under the hull. This leads to an accelerated flow toward the sides of the hull, transitioning the water flow from a three-dimensional movement in deep water to a two-dimensional plane flow in shallow water. Due to the limitations imposed by the shallow-water depth, the velocity of the flow increases both beneath the hull and along its sides, causing a reduction in pressure at the bottom of the hull and generating a ‘suction force’ that results in the ship experiencing sinkage and trim. This alteration in the hydrodynamic performance of the hull, in turn, induces further sinkage and trim, exacerbating these phenomena. In severe cases, this can lead to grounding incidents.

4.3. The Influence of Speed on Ship Sinkage and Trim

From the analysis above, it is clear that with an increase in speed, both the sinkage and trim of the ship significantly increase, especially in shallow-water conditions, indicating that speed has a significant impact on the sinkage and trim of a ship in shallow waters. This section focuses on analyzing the impact of speed on the sinkage and trim of the ship through the distribution of pressure on the hull at different speeds.

Figure 15 illustrates the pressure distribution for the modified new ship type under shallow-water conditions, where H/T = 1.7. In shallow-water conditions, high-pressure zones are formed at both the bow and stern, while the forward shoulder and stern area, particularly near the deadwood, each develop into low-pressure zones. This results in a lower pressure at the mid-bottom of the hull compared to the bow and stern, leading to an uneven pressure distribution along the hull. Such a distribution induces sinkage and trim in the ship. At reduced speeds, the hull experiences less pressure. However, as speed increases, so does the velocity of water flow beneath the hull, which in turn amplifies the hull pressure and further aggravates the uneven distribution of pressure. Consequently, this leads to increased sinkage and trim of the ship. As the speed continues to rise, the high-pressure area at the bow expands further while the stern remains under lower pressure compared to the bow, causing greater sinking at the stern than the bow and resulting in a pronounced stern-down trim phenomenon.

4.4. The Influence of Shallow-Water Ship Attitude on Resistance

In this study, a hull sinkage and trim numerical simulation of the original ship type and the modified new ship type under different water depths is carried out. At the same time, the resistance of the new ship type under the open sinkage and trim state of each speed in the shallow-water environment is recorded. The numerical simulation calculation shows that the resistance of the new ship model in the free state is R_t1. In this study, the ship model resistance test without opening sinkage and trim is carried out in the shallow-water trailer towing tank of MARIN in the Netherlands. The resistance of the new type ship model test in the constrained state is R_t, and the specific test data are from Su et al. [25]. The results are presented in

Table 7. Ship model numerical simulation resistance in free state and ship model test resistance in constrained state.

Water Depth	Vm (m/s)	Trim	Rt1 (N)	Rt (N)	Resistance Change Rate (%)
H/T = 1.7	0.626	−0.1576	20.71	19.33	5.45%
	0.946	−0.2082	51.01	44.66	6.80%
	1.110	−0.2679	73.34	63.2	8.59%
	1.282	−0.3549	109.51	99.15	8.21%
	1.375	−0.4315	135.67	130.5	1.49%
	1.432	−0.4976	154.04	154.46	−2.06%
	1.474	−0.5498	173.71	181.74	−7.15%

.

At the same speed, the resistance of the ship model in a free state after open sinking and trimming showed significant changes compared to the constrained state. This is attributed to the motion of the ship causing stern-down trim, alterations in the ship’s wetted surface area, wave-making, and other factors, leading to changes in hull resistance. Across the entire speed range, the ships exhibited a stern-down trim condition, with the degree of trim increasing as speed increased. At speeds of 0.626 m/s, 0.946 m/s, 1.110 m/s, 1.282 m/s, and 1.375 m/s, the resistance of the ship model in a free state was greater than in a constrained state. The rate of resistance change increased with speed and the angle of trim before decreasing. At speeds of 1.432 m/s and 1.474 m/s, the resistance of the ship model in a free state was less than in a constrained state. This indicates that at smaller angles of stern trim, compared to the constrained state, the resistance of the ship model increases, however, as the angle of stern trim increases, the resistance tends to decrease. This suggests that changes in the posture of the ship have a significant impact on resistance, and a certain degree of stern trim can achieve a reduction in navigational resistance.

5. Conclusions

This research conducts numerical simulations of the sinkage and trim of both the original and the new modified hull forms under various water conditions. The resistance of the ship model in the free state is recorded in the numerical simulation process, and it is compared with the resistance of the ship model test in the restricted state. The respective results reveal:

Based on the numerical results of the original and new ship types in shallow water, it can be observed that in shallow-water conditions, compared to the original ship type, the new ship type can effectively improve hull sinkage and trim phenomena. Furthermore, within the full operational speed range, the new ship type does not experience grounding.

Through numerical simulations of sinkage and trim of the new ship type under varying water depths, it is evident that with decreasing water depth and increasing speed, the uneven distribution of hull pressure intensifies. The transition of flow around the hull from three-dimensional to two-dimensional planar flow due to water depth constraints exacerbates hull sinkage and trim.

By analyzing the resistance of the new ship type in shallow water under constrained and free conditions, it can be observed that changes in ship attitude significantly impact the sailing resistance of the ship. A certain stern trim angle during sailing can reduce sailing resistance effectively.

In this study, a new type of shallow-water seismic survey vessel is investigated, focusing on hull sinkage, trim, and resistance under shallow-water conditions. This research is valuable for designing shallow-water ships and ensuring safe navigation in shallow waters. However, the ship model resistance tests did not account for the sinkage and trim. This study lacks support from actual sinkage and trim tests, only conducting numerical simulations for both deep and shallow-water scenarios. Future research should consider opening these degrees of freedom in ship model tests to record and compare sinkage and trim with numerical simulation results.