Trimaran Hydrodynamics with Computational Fluid Dynamics

• The study focuses on the impact pressure and force characteristics on a trimaran section using Computational Fluid Dynamics (CFD).
• It notes the time domain features of slamming pressure and force correlated strongly with penetration depth, regardless of water entry methods.
• It analyzes the effects of velocity and acceleration on impact pressure and force.
• Initial impact of the main hull and wet-deck slamming are affected via entry velocities.
• Acceleration negligibly affects initial impact.
• Impact velocity had a quadratic relation with slamming pressure/forces.
• The link between acceleration and wet-deck slamming pressure/force was linear.
• These patterns are consistent with Wagner or MLM (Modified Logvinovich model) theories.
• Keywords: trimaran, Computational Fluid Dynamics (CFD), slamming, analytical method

Introduction

• Ships sailing in waves can cause the hull to slam, especially at the bow.
• Slamming has been a problem in Marine Hydrodynamics for a long time.
• The wet-deck structure of multihull ships provides more deck area but causes severe slamming under the wet-deck area.
• Multihull slamming involves the mutual influence of the adjacent hull water entry.
• Existing analytical models handle slamming for the side hull or main hull water entry, but the slamming event under the wet-deck area is beyond those models.
• Water rising caused by the entry of the main hull and side hull under the wet-deck area closes the gap and generates an impulsive force (i.e., slamming) on the structure.
• Model, full-scale experiments have been conducted for multihull slamming studies.
• Lavroff et al. studied wave impact of catamarans using a full-scale test of a 112 m INCAT wave-punch-catamaran and a model scale test of a 2.5 m sectional hydroelastic model.
• Jacobi et al. studied the impact behavior of large high-speed catamarans using full-size test data.
• Yu et al. conducted a model test of the hull slamming load of a trimaran in a seakeeping tank.
• Davis et al. studied a wave-piercing catamaran with an elastic segmented model under random wave conditions, developing empirical models for slam occurrence and loading.
• CFD techniques predict slamming pressure and force with violent free surface deformation and complex structural geometry.
• Panciroli et al. carried out experimental, numerical studies based on the SPH method about the hydroelastic response of a wedge structure in slamming.
• Iranmanesh et al. investigated the hydrodynamics of a horizontal circular cylinder during water entry under low Froude numbers.
• Vinod et al. used mesh-based CFD and the VOF (Volume Of Fluid) scheme to track the free surface to simulate the water impact and subsequent water inflow of three rigid axisymmetric objects (sphere and two cones).
• McVicar et al. studied slamming and bending of a large catamaran sailing at a high speed in waves using fluid-solid coupling simulation.
• Chen et al. proposed a three-dimensional, nonlinear time-domain hydroelastic method for ship hull response in oblique irregular waves.
• Two-dimensional simulation studies single hull slamming mechanisms because it simplifies computation and isolates the main flow pattern.
• Bilandi et al. used the finite volume method to simulate the uniform water entry of a two-dimensional symmetric wedge and an asymmetric wedge in calm water.
• Krastev et al. studied the hydrodynamic problem of two-dimensional wedge asymmetric water collision by numerical method.
• Hu et al. numerically studied the water entry of two-dimensional wedges with different tilt angles using the SPH method.
• Pure two-dimensional analysis of multihull slamming would mean the air trapped under the wet-deck after the side hull entry won't be an authentic reproduction of the wet-deck slamming process, because the air would escape during the gap closing.
• This study conducted quasi-two-dimensional analysis by choosing the length in the X direction of a three-dimensional trimaran model to maintain two-dimensionality as much as possible while ensuring air evacuation.
• The commercial software StarCCM+ was used for the simulation, based on mesh-type FVM (Finite Volume Method) for domain discretization and the VOF method for free surface capturing.
• The influence from trimaran hull motion on the slamming pressure and force characteristics were discussed via uniform velocity and acceleration.
• The slamming force on a trimaran body can be divided into two parts dependent on the body entry velocity and acceleration, inspired by analytical models derived for single symmetric blunt bodies.
• The basic assumption of the analytical model can be applied for complex slamming like trimaran.
• The velocity and acceleration dependent coefficients for trimaran can be extracted by the CFD solver.
• The slamming force under entry scenarios can be obtained by the superposition of the two pre-calculated coefficients to reduce the computational burden for slamming force prediction and shape optimization.

Numerical Models and Two-Dimensionality Verification

• Numerical simulation conducted by Star-CCM+ (v.12, Munich, Germany)
• Numerical models: standard k-e turbulence model, the Euler two phase flow model, and the VOF wave model.
• Fluid depth: 0.623 m, filled with water (density ≈ 997 kg/m³).
• Ship model is set 0.377 m above the water at simulation start.
• Boundary conditions: four sides, bottom set to non-slip wall, top set to pressure outlet.
• The trimaran geometry used is the same as in prior experimental work.
• The main mesh type used: structural mesh (hexahedral mesh)
• Basic size of the background mesh: 0.08 times the characteristic length, i.e., 0.8 m (minimum size of the water tank).
• The area around the free surface and the area through which the trimaran passes (labeled as "Refine background mesh area") was further refined with size 0.125 times that of the basic background mesh.
• The overset area moving with the trimaran used the same mesh size as the "Refine background mesh area."
• The close area around the trimaran was further refined with 0.25 times of the "Refined background mesh area.”
• The boundary layer of the trimaran was discretized in a body fitted manner instead of structural mesh.
• The basic size of the background mesh was 0.064 m; the mesh size of the refined area near free surface, the overset mesh area and the area through which the trimaran moves was 0.008 m; the size of the most refined area around the trimaran was 0.002 m.
• The total mesh count was 4.2 million with 3 million mesh within the overset mesh area.
• The CFL value used was 0.085, which meant the time step was 0.0001 s.
• Numerical models for the simulation were validated against a free dropping test and against another multihull dropping experiment.
• Details of validation cases can be found in ref. [16].

Two-Dimensionality Verification

• The special configuration of multihull ships like trimarans can mean the air cushion effect under the cross-sections affects pressure and overall force during slamming.
• A thicker section can mean air can’t escape during impact, affecting slamming ease.
• The study focuses on how slamming pressure and force are affected by motions when the air is free to escape, by figuring out the proper X-direction length of the section.
• Short length in the X direction facilitates effective ventilation under the cross-section and still allows the edge of the section not affect the middle plane significantly.
• The section length in the X direction needs to guarantee two-dimensionality of flow in the section's middle plane with the mini-mum effect of air.
• Two-dimensional simulation cannot fit this requirement since air will be trapped under the cross-section after the side hull enters the water.
• For this, three trimaran section cases free dropping with the length in the X direction of 0.2 m, 0.3 m, and 0.4 m were selected.
• The drop height was the same for these three cases, i.e., 0.1473 m (initial water entry velocity 1.7 m/s).
• The masses were were 3.013 kg, 4.52 kg, and 6.027 kg, (proportional to the length in the X direction).
• Five virtual pressure monitors were fitted the middle plane section of the structure.
• A virtual acceleration sensor was also fitted the body.
• Results showed pressure at all measuring points and acceleration were close.
• The difference between the three cases was around 10%.
• The 0.2 m case slightly deviated more and the other two cases were almost identical, meaning 0.3 m is long enough to eliminate the edge effect whilst still being thin enough for air to escape freely.
• The same experimental results were presented in filtered form, but unfiltered raw data are shown, with characteristics of the pressure and acceleration data very similar.
• Computational results match well with the raw data.
• The pressure distribution along the X direction was checked with a 0.3 m trimaran hull entering the water with constant velocity of 1.7 m/s.
• Monitoring points were arranged at the tip of the main hull and under the wet-deck along the X direction (The peak pressure decreases gradually along the X direction).
• The edge had limited affect on the flow under the main hull, with edges close to the edge dropping up to hald.
• The pressure maintained a constant distribution along the middle longitudinal section (within 0.025 m forward and backward).
• Pressure was integrated for vertical force analysis later.

Simulation Parameters

• The relationships between motions of the trimaran and hydrodynamic forces were studied.
• The variable separation method was used to determined the influence from entry velocity and acceleration.
• Constant velocity: V is -1.7 m/s
• Constant acceleration, five different accelerations were selected.
• The positive z-acis was set to be upward
• Velocity: 2V, i.e., -3.4 m/s (g is -9.81 m/s²).
• The computer used had Intel(R) Core(TM) i7-8700 (duo 3.2 GHz) CPU, RAM 32 GB.
• For a typical case, the computational time was about 10 CPU hours.

Pressure Analysis

• Pressure under the main hull and wet-deck were analyzed.
• Pressure time history under velocity and acceleration conditions was plotted against penetration depth.
• Two peaks in Figures 5a and 6a correlate to the initial slamming of the main hull and the subsequent wet-deck slamming.
• Pressure characteristics correlated strongly to the penetration depth, with increasing/decreasing patterns and peak positioning were the same under entry velocities and accelerations.
• Aligns with slamming prediction theories (Wagner's model or the MLM model).
• p(Υ,ξ) = ρξ Ρο(Υ,ξ) + ρξΡα(Υ,ξ)
• where is the penetration depth, and P, and Pa have different definitions in Wagner or MLM models.
• With constant entry velocities, pressure increases quadratically since acceleration parts were expected to be zero.
• Flow pattern is different compared to single hull water entry, as air gaps gradually close.
• The pressure peak on the side of the main hull and under the wet-deck also followed patterns predicted by the analytical models.
• The hydrodynamic mechanism behind these two types of slamming events is, to some extent, similar.
• Acceleration negligibly affects the pressure peak on the main hull.
• Wet-deck required the velocity dependent parts to be extracted from the total pressure value, using interpolation from pressure monitor, extracting from the total pressure value (acceleration and pressure peak showed linear dependency from the acceleration), where upward direction generates negative pressure distribution.
• Consistent figures showing a large peak pressure, and this is partially due the wet-deck with makes the slamming much stronger than just a single body.
• Pressure Spatial distribution/ free surface similar under under different entry depths, and values higher where velocities / accelerations also higher.
• Pressure distribution is strongly correlated with penetration depth of entry.