A method for calculating motion and wave loads of trimaran considering strong nonlinear loads

Abstract

The application discloses a trimaran motion and wave load calculation method considering strong nonlinear load, and relates to the field of ship hydrodynamic performance calculation. The method solves the problems that the traditional potential flow method is inaccurate in predicting strong nonlinear phenomena such as slamming and large amplitude motion, and the full viscous flow method is too high in calculation cost by coupling potential flow theory and viscous flow theory. The core comprises the following steps: a motion equation framework considering instantaneous wet surface change is constructed based on three-dimensional time domain potential flow theory; a viscous flow CFD method is used to accurately quantify the slamming load and identify the nonlinear damping caused by the entry and exit of a piece into water; and one-way / weak coupling is performed between a parameterized database and a potential flow model, so that the nonlinear load parameters are fed back to the motion equation for correction and rapid solution. The application considers both accuracy and efficiency, and is suitable for engineering design and analysis of various trimarans.

Description

Technical Field

[0001] This invention relates to the field of ship hydrodynamic performance calculation, specifically to a method for calculating the motion and wave loads of a trimaran that takes into account strong nonlinear loads, and in particular, a coupled calculation method that can simultaneously and efficiently take into account various weak and strong nonlinear loads such as wave impact, instantaneous wet surface changes, and first-order and second-order wave forces caused by large-scale motion of a high-speed trimaran. Background Technology

[0002] Trimaraners are widely used in the civilian sector due to their excellent speed, seakeeping, and spacious deck area. However, high-speed trimaran ships encounter complex nonlinear hydrodynamic phenomena when navigating in harsh sea conditions. For example, the violent motion of the hull (especially the slender hull and connecting bridge) in waves leads to frequent out-and-in of the water, triggering strong wave slamming loads; large-amplitude roll and pitch movements cause significant changes in the instantaneous wetted surface of the hull, significantly affecting restoring and damping forces; in addition, the rigid body motion caused by first-order wave forces and the low-frequency drift force caused by second-order wave forces work together to make the load environment extremely complex.

[0003] Currently, methods for predicting ship wave loads and motions mainly fall into two categories: methods based on potential flow theory and viscous flow methods based on computational fluid dynamics (CFD). Potential flow theory offers high computational efficiency and can easily handle first- and second-order wave forces, as well as consider steady or slowly varying wetted surfaces. However, it lacks the ability to capture strongly nonlinear viscous effects such as wave breaking, slamming, and turbulence. While fully viscous CFD methods (such as those using RANS equations) can accurately simulate these strongly nonlinear phenomena, their computational cost is extremely high, making them unsuitable for multi-scheme comparisons and preliminary engineering design stages.

[0004] Existing technical solutions (such as CN106709135A) focus on optimizing the trimaran hull layout to reduce drag through CFD analysis of wave-making flow fields, but do not systematically address the problems of strong nonlinear motion and load prediction in waves. Existing technical solutions (such as CN113656894A) focus on simulating the maneuverability or self-propulsion point of waterjet-propelled trimarans; although involving viscous CFD, their focus is not on the comprehensive calculation of wave loads. Other existing technical solutions (such as CN117875061A) perform model identification or prediction for roll and longitudinal motion respectively, but these are mostly based on linear or weakly nonlinear assumptions or rely on a large amount of experimental data, limiting their ability to handle transient strong nonlinear loads such as slamming loads.

[0005] Therefore, there is an urgent need to develop a method for calculating the motion and wave loads of high-speed trimaran ships that can maintain high computational efficiency while accurately taking into account the aforementioned strong nonlinear loads. Summary of the Invention

[0006] To address the aforementioned problems and technical requirements, the inventors have proposed a method for calculating the motion and wave loads of trimaran ships that considers strongly nonlinear loads. This method leverages the advantages of cleverly coupling potential flow theory and viscous flow theory to achieve comprehensive and efficient calculations of slamming loads, instantaneous wetted surface changes, nonlinear damping, and first / second-order wave forces.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads includes the following steps: S1: Establish a parametric geometric model of the trimaran and generate a surface mesh for potential flow calculation; S2: Based on the three-dimensional time-domain potential flow theory, the motion equation of the trimaran in waves is established, and the instantaneous wetted surface method is used to update the wetted surface of the hull in real time to calculate the weak nonlinear wave load. S3: CFD methods based on viscous flow theory identify and quantify strongly nonlinear loads, including wave impact loads and nonlinear damping caused by sheet entry and exit from water. S4: Integrate the strongly nonlinear load into the equation of motion to achieve coupling between potential flow and viscous flow; S5: Numerically solves the coupled motion equations in the time domain and synchronously outputs the hull motion response and wave load time history curves of key structural parts.

[0008] A further technical solution for S1 is to establish a parameterized geometric model of the trimaran (main hull, two hulls and connecting bridge), prepare appropriate ground element meshes for potential flow calculations, and refine the mesh near the waterline of the hull and in areas at risk of slamming (such as the bow of the main hull, the bow of the hull hull, and the lower surface of the connecting bridge) to ensure sufficient mesh density in areas with drastic changes in hull curvature (such as the bow, hull hull, and the lower surface of the connecting bridge).

[0009] A further technical solution for S2 is the establishment of a potential flow theory framework: based on three-dimensional time-domain potential flow theory, the motion equations of the trimaran in waves are established. These equations include: a) First-order wave excitation force, calculated based on incident and diffracted potentials, denoted as... .

[0010] b) Second-order average wave drift force and slow drift force, denoted as... .

[0011] c) Taking into account the weak nonlinear wave loads caused by large hull motion and wave rise. Its calculation methods include: Considering the interaction between the main hull and the two side panels of the trimaran, as well as the influence of the main hull and the two side panels on the liquid surface, based on the real-time updated instantaneous wetted surface of the trimaran, hydrodynamic pressure integration is carried out on the instantaneous wetted surface to obtain the nonlinear hydrostatic restoring force, nonlinear incident wave force and nonlinear diffracted wave force jointly caused by the coupling of the main panel and the coupling of the hull and the wave. The above force components are superimposed to obtain the weak nonlinear wave load.

[0012] Based on the above description, the equation of motion is specifically expressed as:

[0013] In the formula, For the mass matrix of the trimaran, To add a mass matrix, Additional quality matrix defined by the user; Here is the radiation damping matrix. For user-defined damping matrices, such as linear damping matrices; For first-order wave loads, For second-order wave loads, The weak nonlinear wave loads include hydrostatic restoring forces caused by transient wet surfaces, incident wave forces, and diffracted wave forces. For the weight of the trimaran; Impact load; It is a nonlinear damping force.

[0014] The further technical solution for S3 is as follows: a) Methods for identifying and quantifying wave slamming loads include: for wave slamming, a typical strong nonlinear transient event, local mesh refinement is performed on the slamming risk areas such as the bow of the main hull, the bow of the sheet hull, and the underside of the connecting bridge of the trimaran. A preset turbulence model combined with the VOF method is used to capture the free surface and conduct transient two-phase flow simulation to calculate and output the slamming pressure distribution and total slamming force time history curve under given working conditions.

[0015] The preset turbulence model is either the k-ω SST model or the LES large eddy simulation model.

[0016] b) Construct a slamming load prediction calculation model through a series of CFD calculation simulations covering multiple working conditions, which can be quickly invoked in coupled calculations; The model's input parameters include the trimaran's hull attitude, encountered wave conditions (wave height, encounter angle), and relative motion speed.

[0017] c) Methods for identifying and quantifying nonlinear damping include: for the significant nonlinear roll and pitch damping caused by the unique hull entry and exit of trimarans, CFD methods are used to simulate the free decay motion of the trimaran's roll or pitch, and the nonlinear damping coefficient is obtained by separating and fitting from the decay curve, and then the nonlinear damping force caused by the viscous effect during the trimaran's motion response is calculated.

[0018] A further technical solution for S4 is to integrate the strongly nonlinear loads (impact loads, nonlinear damping) obtained in S3 into the motion equations of S2. The coupling method can be unidirectional coupling or weak coupling, wherein: Unidirectional coupling involves calling a pre-calculated, strongly nonlinear load and adding it directly as a known input to the equation of motion. Weak coupling involves pausing the potential flow calculation at the moment when a slamming event may occur during the potential flow time-domain simulation. Based on the current motion of the hull and the wave condition, a pre-built slamming load prediction calculation model is invoked to correct the slamming load in real time. The correction result is then fed back to the motion equation, and the potential flow calculation continues.

[0019] A further technical solution for S5 involves numerically solving the coupled motion equations modified by S4 to obtain the time histories of the six-degree-of-freedom motion response (focusing on heave, pitch, and roll). Simultaneously, based on slice theory or three-dimensional hydroelasticity theory, the obtained hydrodynamic pressure distribution (derived from potential flow calculations and additional slamming pressure) is integrated along the ship's length to obtain the vertical wave moment, horizontal wave moment, and shear force distribution of the hull beams. This can be further combined with a structural model for quasi-static or dynamic structural response analysis.

[0020] The beneficial technical effects of this invention are: 1. Comprehensiveness: For the first time, this system comprehensively considers various sources of strong nonlinear loads that are crucial to high-speed trimarans, such as wave slamming loads, instantaneous wetted surface changes, nonlinear damping, and second-order wave forces, within a unified framework for calculating trimaran motion and wave loads.

[0021] 2. Balance between efficiency and accuracy: Based on the computationally efficient potential flow theory, CFD calculations (local simulation or pre-calculation models) with controllable computational costs are introduced only when dealing with strong nonlinear viscous effects, achieving a balance between accuracy and efficiency, and making it suitable for engineering applications.

[0022] 3. Wide applicability: In principle, this method is applicable to conventionally laid trimarans as well as adaptive trimarans with adjustable hull positions. It can perform motion response and wave load performance evaluation and comparative analysis under multiple speeds and sea states, providing a reliable basis for hull optimization and structural design. Attached Figure Description

[0023] Figure 1This is a flowchart of the overall calculation method provided in this application; Figure 2 This is a schematic diagram of the coupled calculation strategy of potential flow theory and viscous flow theory provided in this application; Figure 3 This is an instantaneous pressure cloud map and a schematic diagram of the free surface of the trimaran using the CFD method to simulate the slamming phenomenon of trimaran hulls. Figure 4 This is an example of the vertical and pitch motion response time-history curves of a trimaran in regular waves, calculated using the method of this invention. Detailed Implementation

[0024] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0025] Please refer to Figure 1 As shown, one embodiment of this application provides a method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads, including the following steps: S1: Trimaran Geometric Modeling and Potential Flow Mesh Generation. Specifically, a parametric geometric model of the target trimaran is established using 3D modeling software. The model is then imported into potential flow calculation preprocessing software or programmed manually to generate a surface mesh for 3D time-domain potential flow calculation. In this embodiment, the mesh needs to be appropriately refined near the waterline, the bow of the main hull, the bow of the hull sheet, and the underside (bottom) of the connecting bridge.

[0026] S2: A framework for calculating the motion and wave loads of a trimaran is constructed based on three-dimensional time-domain potential flow theory. Specifically, based on three-dimensional time-domain potential flow theory, the motion equations of the trimaran in waves are established, incorporating first-order and second-order wave forces. The instantaneous wetted surface method is used to update the wetted surface of the hull in real time to calculate the weakly nonlinear wave loads. For specific implementation details, please refer to the relevant content in the invention description.

[0027] In this embodiment, a potential flow solver is developed based on time-domain potential flow theory (e.g., using the impulse response function method to handle memory effects). Calculation conditions are set, including ship speed, wave parameters, and wave direction angle. The instantaneous wetted surface update option is enabled in the motion equations to capture instantaneous wetted surface changes caused by waves and motion.

[0028] S3: CFD pre-calculation of strongly nonlinear loads.

[0029] a) To address wave slamming loads, CFD software was first used to perform transient simulations of the trimaran in waves to calculate the wave slamming loads. Specifically, this included: accurately identifying the risk areas of wave slamming on the trimaran and collecting wave slamming characteristics, focusing on the bow of the main hull, the bow of the hull sheet, and the surface under the connecting bridge (wet deck area); and refining the local mesh in these risk areas to ensure the accuracy of the calculated slamming pressure and force. During the numerical simulation, a turbulence model adapted to the strongly nonlinear transient flow characteristics was selected, such as the k-ω SST model or the LES large eddy simulation model. Simultaneously, the VOF (Volume of Fluid) method was used to capture the gas-liquid free surface, accurately reproducing the actual physical state of free surface deformation and gas-liquid mixing during wave slamming. Based on the above mesh and model settings, transient two-phase flow numerical simulations were conducted in the risk areas of wave slamming on the trimaran. Key data such as the slamming pressure distribution and the total slamming force history were directly output through calculation, achieving accurate quantification of the wave slamming loads. The instantaneous pressure cloud diagram simulating the hull impact phenomenon of a trimaran using CFD methods is shown below. Figure 3 As shown in (a), the trimaran hull (orange portion) and the free surface are as follows: Figure 3 As shown in (b) of the diagram.

[0030] Secondly, based on the above methods, multi-condition calculations and analyses are conducted to obtain the wave slamming loads on each section of the trimaran under different hull attitudes, wave conditions (wave height, encounter angle), relative motion speeds, different entry angles, fluid densities, and other factors. The maximum slamming pressure, slamming force duration, and motion state (such as relative motion speed) at the time of slamming are recorded under each condition, thus constructing a trimaran whole-ship slamming load database. In addition, the free-fall method can also be used to calculate the slamming loads on sections, conducting multi-condition calculations and analyses of the slamming loads on sections under still water conditions and different wave conditions to obtain sufficient slamming load calculation results to expand the database.

[0031] Finally, the slamming load data in the database is analyzed and summarized. Dimensional analysis is used to establish a quantitative relationship between slamming load and hull attitude, relative speed, liquid level rise, entry angle, and fluid density. Alternatively, a neural network can be used to establish a mathematical calculation model for the slamming load of each compartment, ultimately forming a rapid prediction and calculation model for the entire trimaran's slamming load. ,in v rel The relative velocity between the trimaran and the fluid. ζ rel (This is due to a relative increase in liquid level).

[0032] b) To address the nonlinear damping caused by the entry and exit of the trimaran hull, a preset initial roll or pitch angle is set for the trimaran in a still water environment. A time-domain simulation of the free decay motion of roll / pitch without external wave excitation is conducted to accurately reproduce the viscous damping and flow separation characteristics during the entry and exit of the hull. The free decay motion time-history curves of the trimaran under different initial motion amplitudes are obtained through CFD calculations. Based on the amplitude decay method, energy method, or least squares method, data fitting and component separation are performed on the decay curves. After removing the linear damping component, the nonlinear damping coefficient at the corresponding motion amplitude is identified and quantified.

[0033] S4: Potential flow-viscous flow coupling calculation. Coupling methods are divided into two implementations: unidirectional coupling and weak coupling, such as... Figure 2 As shown, the strongly nonlinear load obtained in S3 is integrated into the potential flow solver. Specifically: One-way coupling: Viscous flow CFD calculations are pre-computed for typical sea states, speeds, and ship motion conditions to construct a database or mathematical model of slamming loads and nonlinear damping coefficients (i.e., S3-a); at each time step of the time-domain potential flow calculation, based on the currently calculated relative motion between the ship and the waves (such as bow sinking speed and relative wave height), the current wave slamming load is calculated from this database or mathematical model (if slamming is determined to occur) and incorporated into the equations of motion: the slamming load is added as an external load to the trimaran's equations of motion. In the process, the linear damping force and nonlinear damping force caused by viscous effect are calculated based on the linear damping coefficient and the nonlinear damping coefficient selected according to the real-time motion amplitude of the hull. The linear damping force can be added to the damping matrix in the equation of motion. In this context, nonlinear damping forces can be added to the equations of motion. This allows the impact loads and nonlinear damping effects to be considered when calculating the motion response of the trimaran. In this coupling method, the CFD module and the potential flow module do not interact in real time, resulting in a highly efficient and stable calculation process. In practical implementation, the above process can be integrated into an additional external force calculation module added to the source code of the potential flow solver.

[0034] Weak coupling: In each or several time steps of the time-domain potential flow iterative calculation, the probability of slamming is determined based on the current real-time motion attitude of the hull, relative wave height and other state parameters; when the triggering condition is met, a simplified CFD model or parameter database is temporarily called to complete the real-time load correction, and the correction result is fed back to the potential flow motion equation, and then the time-domain calculation is continued to advance, so as to realize the dynamic calibration of nonlinear load based on real-time state.

[0035] S5: Solution and Result Analysis. Run the coupled calculation program to solve the equations of motion in the time domain. After the calculation is complete, the output is as follows: Figure 4The motion response time-history curves shown in the figure are illustrated, with the solid red line representing the vertical motion response and the dashed line representing the pitching motion response. Simultaneously, based on the hydrodynamic pressure distribution on the hull surface (including potential flow pressure and additional wave impact pressure), the structural load is calculated by integrating along the ship's length, yielding the distribution of the vertical wave bending moment along the ship's length.

[0036] By following the steps above, we can quickly and accurately calculate the motion and wave loads of a high-speed trimaran in waves, taking into account strong nonlinear loads.

[0037] The above descriptions are merely preferred embodiments of this application, and the present invention is not limited to the above embodiments. It is understood that other improvements and variations derived directly by those skilled in the art without departing from the spirit and concept of the present invention, or those that can be appropriately adjusted according to the specific research object and computing resources to modify the scale and coupling strategy of CFD computation, should all be considered to be included within the protection scope of the present invention.

Claims

1. A method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads, characterized in that, The method includes: Establish a parametric geometric model of the trimaran and generate a surface mesh for potential flow calculation; Based on the three-dimensional time-domain potential flow theory, the motion equation of the trimaran in waves is established, and the instantaneous wetted surface method is used to update the wetted surface of the hull in real time to calculate the weak nonlinear wave load. CFD methods based on viscous flow theory identify and quantify strongly nonlinear loads, including wave impact loads and nonlinear damping caused by sheet entry and exit from water. The strong nonlinear load is integrated into the equation of motion to achieve coupling between potential flow and viscous flow; The coupled motion equations are numerically solved in the time domain, and the motion response of the hull and the wave load history curves of key structural parts are output simultaneously.

2. The method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads according to claim 1, characterized in that, The equation of motion is expressed as: In the formula, For the mass matrix of the trimaran, To add a mass matrix, To add an additional mass matrix; Here is the radiation damping matrix. This is a custom damping matrix; For first-order wave loads, For second-order wave loads, This refers to the weak nonlinear wave load; For the weight of the trimaran; Impact load; It is a nonlinear damping force.

3. The method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads according to claim 1, characterized in that, Methods for identifying and quantifying the wave impact load include: Local mesh refinement is applied to slam-prone areas such as the bow section of the main hull, the bow section of the hull, and the underside of the connecting bridge of the trimaran. A preset turbulence model combined with the VOF method is used to capture the free surface and conduct transient two-phase flow simulation to calculate and output the slamming pressure distribution and total slamming force time history curve under given working conditions.

4. The method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads according to claim 3, characterized in that, The preset turbulence model is either the k-ω SST model or the LES large eddy simulation model.

5. The method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads according to claim 3, characterized in that, The method further includes: A slamming load prediction calculation model is constructed through a series of CFD calculation simulations covering multiple working conditions, which can be quickly invoked in coupled calculations; The input parameters of the model include the trimaran's hull attitude, encountered wave conditions, and relative motion speed.

6. The method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads according to claim 1, characterized in that, Methods for identifying and quantifying the nonlinear damping include: The CFD method is used to simulate the free decay motion of the trimaran in roll or pitch, and the nonlinear damping coefficient is obtained by separating and fitting from the decay curve. The nonlinear damping force during the motion response of the trimaran is then calculated.

7. The method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads according to claim 1, characterized in that, The method for calculating weak nonlinear wave loads includes: Considering the mutual influence between the main hull and the two side panels of the trimaran, as well as the influence of the main hull and the two side panels on the liquid surface, based on the real-time updated instantaneous wetted surface of the trimaran, hydrodynamic pressure integration is carried out on the instantaneous wetted surface to obtain the nonlinear hydrostatic restoring force, nonlinear incident wave force and nonlinear diffracted wave force jointly caused by the coupling of the main panel and the coupling of the hull and the wave. The weak nonlinear wave load is obtained by superimposing the above force components.

8. The method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads according to claim 1, characterized in that, The coupling method for integrating the strongly nonlinear load into the equation of motion is either unidirectional coupling or weak coupling, wherein: The unidirectional coupling involves calling a pre-calculated, highly nonlinear load and adding it directly as a known input to the equation of motion. The weak coupling refers to the process where, during the potential flow time-domain simulation, at the moment when a slamming may occur, a pre-built slamming load prediction calculation model is invoked based on the current motion of the hull and the wave condition to make real-time corrections to the slamming load, and then the correction results are fed back to the motion equations.

9. The method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads according to claim 1, characterized in that, The method for outputting the wave load time history curve includes: Based on slice theory or three-dimensional hydroelasticity theory, the obtained hydrodynamic pressure distribution is integrated along the ship's length to obtain the vertical wave bending moment, horizontal wave bending moment and shear force distribution of the hull beam.

10. The method for calculating the motion and wave loads of a trimaran considering strongly nonlinear loads according to claim 1, characterized in that, When generating the surface mesh, the mesh is refined near the waterline of the hull and in areas at risk of slamming. The slamming risk area includes the bow of the main hull of the trimaran, the bow of the hull piece, and the lower surface of the connecting bridge.

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