舱室内液体晃荡的数值模拟及其与船体运动耦合作用的研究
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摘要
近年来，以液化天然气船（LNGC）为代表的液货船成为重要的海上运输装备。该类液货船在海上航行时，受海浪作用会产生船体摇荡运动，由于具有大体积的液舱，因此会引起液舱晃荡现象。在恶烈海况下，大幅船舶摇荡运动所引发的液体剧烈晃荡，会对液舱结构产生砰击，造成局部结构损坏，甚至还会恶化耐波性能严重影响运营作业安全。因此，开展液舱晃荡及其与船体的耦合运动研究就具有实际工程应用价值。
据此，本论文着重研究四个方面的问题：液舱晃荡的液面大变形现象模拟及其砰击压强计算；带防晃结构液舱的晃荡现象模拟，以及防晃结构效能对比分析；基于PIV技术的液舱晃荡流场测量及其模拟分析；液舱晃荡与船体的耦合运动模拟分析。
针对上述问题，本论文所开展的主要工作具体如下：
一、三维液舱晃荡运动控制方程及其数值计算方法
考虑到不同的晃荡激励形式，建立了三维液舱晃荡运动的控制方程，基于直角有限差分网格，对控制方程进行了数值离散，并采用超松弛高斯-赛德尔迭代法进行了速度和压强耦合求解。
二、三维液舱晃荡的PLIC-VOF方法数值模拟
基于直角有限差分网格，根据方向分裂算法以及Lagrange对流计算法求解流体体积分数控制方程，并结合控制方程的数值解法，发展了自由表面重构的PLIC-VOF法，并应用于模拟三维液舱的剧烈晃荡问题。
三、液舱晃荡的CLSVOF方法数值模拟
基于PLIC-VOF方法，考虑及Level-set方法隐式跟踪自由表面的性能，引入Level-set函数确定自由表面法向，结合PLIC-VOF良好的质量守恒性能，实现了PLIC-VOF方法与Level-set方法耦合的CLSVOF数值方法，并应用于液舱剧烈晃荡模拟等问题。
四、三维通度系数法结合PLIC-VOF法模拟带防晃结构的液舱晃荡问题
引入三维通度系数法，并修改了流动的控制方程，结合直角网格的PLIC-VOF方法，实现了三维带不同型式防晃结构的液舱晃荡数值模拟，并通过局部液面和压强时历对比探讨了防晃效果。
五、基于PIV技术的液舱晃荡流场精细测量与模拟
合理设计液舱及其平面运动机构，由伺服系统控制运动机构在直线方向的速度时历，考虑液舱的不同装载水平，设定共振频率下的横荡运动激励，应用PIV技术进行液舱晃荡流场的精细测量以及波形观察分析。应用PLIC-VOF方法，进行了液舱晃荡流场的数值模拟，以及PIV试验结果对比分析。
六、液舱晃荡的WC-MPS方法数值模拟
基于流体弱可压缩假定，提出了基于Tait状态方程的弱可压缩移动粒子半隐式法（WC-MPS）。该方法通过直接计算流体状态方程来快速获取流场压强，而没有求解计算耗时的压强Poisson方程，并应用该方法模拟了剧烈晃荡的自由表面大变形现象。
七、波浪中液舱晃荡与船体摇荡的耦合作用数值模拟
考虑到液舱晃荡与船体运动的耦合作用，建立了液货船的耦合运动方程，结合内流场粘性流体PLIC-VOF方法，确定液舱晃荡作用力以及力矩，由外流场二维切片方法确定波浪中船体频域水动力系数及波浪载荷，采用Newmark-β法进行耦合运动方程的时域求解，实现波浪中船体运动的数值模拟。
本论文研究的创新性可以总结为以下三个方面：
一、三维通度系数法结合PLIC-VOF方法模拟带防晃结构液舱的晃荡问题
基于三维通度系数法表达流场中的固体相，并修改流动的控制方程，与三维PLIC-VOF方法相结合，实现了带防晃结构的三维液舱晃荡模拟。
二、直角网格CLSVOF数值方法模拟液舱剧烈晃荡问题
基于PLIC-VOF方法的良好质量守恒性能，考虑及Level-set方法隐式跟踪自由表面的性能，针对每一时间步的Level-set函数重新初始化，由PLIC-VOF重构自由表面，通过确定邻近网格到自由表面网格的最近距离，进行Level-set函数的重新初始化，实现了耦合的CLSVOF数值方法，并应用于液舱剧烈晃荡模拟。
三、基于弱可压缩假定的WC-MPS方法模拟液舱剧烈晃荡问题
鉴于传统不可压缩移动粒子半隐式法（Fully Incompressible-MPS）通过求解Poisson方程获取压强，计算低效而耗时，因此基于流体弱可压缩假定，选用流体的Tait状态方程直接而快速求解流场压强，建立了弱可压缩移动粒子半隐式法（WeaklyCompressible-MPS），并应用于模拟剧烈晃荡问题。
Recent years, liquid cargo ships such as LNGC become an important facility fortransportation of liquefied cargoes. Navigating at sea, these ships will suffer from randomsea waves and ship motions. With the liquid tanks of large volumes, the liquid sloshing intanks occurs excited by ship motions. In severe sea states, the amplitudes of ship motionsare large and therefore arouse violent sloshing. This violent sloshing can pose greatimpulsive impact to the local tank structures, and cause their damage, and even harm safetynavigation and operation of LNG ships at sea. So it is of practical importance to study theviolent sloshing in tanks and its coupling effects with ship motions.
Based on above situations, in this thesis four related issues are focused on: thenumerical simulation of largely distorted free surface motions and computation ofimpulsive pressures during violent sloshing; the numerical simulation of liquid sloshing inbaffled tanks, and evaluation of effectiveness of different baffles; the measurements offlow fields during sloshing in liquid tanks and corresponding numerical simulations; thenumerical simulation and analysis of the coupled motions between tank sloshing and shipmotions.
Considering above issues, the work done in this thesis is as follow:
1. The governing equations and the corresponding numerical schemes for threedimensional sloshing in tanks
Considering the different kinds of sloshing excitations, the governing equations for3-D sloshing problem are established, and discretized numerically based on the cartesianstaggered grids by finite difference method, also the coupled velocity and pressure in theequations are solved by the over-relaxed Gauss-Seidel iteration scheme.
2. The PLIC-VOF method for three dimensional sloshing in tanks
In cartesian staggered grids, the governing equations for volume fractions are solvedbased on the directional splitting scheme and Lagrange convection algorithm. Applying the numerical algorithm for the governing equations, the PLIC-VOF method is developed toreconstruct free surface, and employed for the numerical simulation of the violent sloshingin tanks.
3. The CLSVOF method for the violent sloshing in tanks
Based on the PLIC-VOF method, the Level-set method is applied to determine thefree surface normal considering its excellent performance in tracking the free surfaceexplicitly. Because of the PLIC-VOF method with good property in mass conservation, theLevel-set method and the PLIC-VOF method are coupled to develop the CLSVOF method.Finally, this method is employed to simulate the violent sloshing in tanks.
4. The aperture technique coupled with the PLIC-VOF method in three dimensionsfor the numerical simulation of the liquid sloshing in tanks with the baffles
The3-D aperture approach is introduced, and therefore the governing equations aremodified to adapt to the change of the volume fraction in cells. Coupled with PLIC-VOFmethod, the sloshing problem in tanks with different type of the baffles is simulated, andthe effectiveness of the baffles are compared and evaluated according to the time historiesof the local pressures and wave elevations.
5. The detailed measurements of the flow fields in the tank with the sloshing problemby PIV technique and the numerical simulation correspondingly
The motion mechanism for the tank is rational designed, and its real-time velocity iscontrolled by the control systems. Considering different filling levels, the excitationfrequencies of the sway motion are set as the resonant frequencies under different fillingconditions. Based on these conditions, the PIV technique is applied to measure the flowfields and the flow patterns in the liquid tanks. Finally, the numerical simulation is carriedout by the PLIC-VOF method and compared with the PIV experimental results.
6. The WC-MPS method for the numerical simulation of the tank sloshing
With the weakly compressible assumption, a weakly compressible moving particlesemi-implicit method (WC-MPS) is introduced based on the Tait’s equation of state of thefluid. For this method, the pressure field is obtained directly by Tait’s equation of statewithout solving time-consuming Poisson’s equation. Employing this WC-MPS method, theviolent sloshing with highly-distorted free surface in tanks are simulated and validated withexperimental results.
7. The study on the coupling effects of tank sloshing and ship motion in waves
Considering the coupling effects of the tank sloshing and the ship motions, thecoupled motion equations of the liquid cargo ships are established. To obtain the force andmoment induced by the tank sloshing, the PLIC-VOF method for vicious fluid is applied.While, to determine the hydrodynamic coefficients and wave loads for the ships in waves,a two dimensional strip theory is applied in frequency domain. Taking advantage of theNewmark-β approach, the coupled motion is solved in time domain to simulate themotions of liquid cargo ships in waves.
The creativity of the studies in this thesis can be summarized as the flowing threeaspects:
1. The aperture technique coupled with the3-D PLIC-VOF method is developed andemployed to simulate the liquid sloshing in the baffled tanks.
The3-D aperture approach is introduced to express the solid phase in the flow field,and the governing equations are modified correspondingly coupled with the PLIC-VOFmethod. And this approach is used to simulate the sloshing problems in the baffled tanks.
2. The CLSVOF method in cartesian grids is developed and applied to simulate theviolent sloshing in tanks.
For the PLIC-VOF method has good property in mass conservation, and the Level-setmethod possesses excellent performance in tracking interface explicitly. Therefore, theLevel-set method and PLIC-VOF method are coupled to develop the CLSVOF method. Ineach time step, the reinitialization of Level-set function is based on the constructed freesurface by PLIC-VOF method, and the values of the Level-set function are obtained bydetermining the shortest distance from the neighboring cells to the free surface cells. Andthis coupled method is employed to simulate the violent sloshing in tanks.
3. The WC-MPS method based on weakly-compressible assumption is developed andapplied to simulate the violent sloshing in tanks.
For fully incompressible MPS method, the pressure field is obtained by solvingtime-consuming Poisson’s equation. With the weakly compressible assumption, a weaklycompressible moving particle semi-implicit method (WC-MPS) is introduced based on thepressure field computed directly by Tait’s equation of state of the fluid. Employing thisWC-MPS method, problems of the violent sloshing in tanks are simulated.
据此，本论文着重研究四个方面的问题：液舱晃荡的液面大变形现象模拟及其砰击压强计算；带防晃结构液舱的晃荡现象模拟，以及防晃结构效能对比分析；基于PIV技术的液舱晃荡流场测量及其模拟分析；液舱晃荡与船体的耦合运动模拟分析。
针对上述问题，本论文所开展的主要工作具体如下：
一、三维液舱晃荡运动控制方程及其数值计算方法
考虑到不同的晃荡激励形式，建立了三维液舱晃荡运动的控制方程，基于直角有限差分网格，对控制方程进行了数值离散，并采用超松弛高斯-赛德尔迭代法进行了速度和压强耦合求解。
二、三维液舱晃荡的PLIC-VOF方法数值模拟
基于直角有限差分网格，根据方向分裂算法以及Lagrange对流计算法求解流体体积分数控制方程，并结合控制方程的数值解法，发展了自由表面重构的PLIC-VOF法，并应用于模拟三维液舱的剧烈晃荡问题。
三、液舱晃荡的CLSVOF方法数值模拟
基于PLIC-VOF方法，考虑及Level-set方法隐式跟踪自由表面的性能，引入Level-set函数确定自由表面法向，结合PLIC-VOF良好的质量守恒性能，实现了PLIC-VOF方法与Level-set方法耦合的CLSVOF数值方法，并应用于液舱剧烈晃荡模拟等问题。
四、三维通度系数法结合PLIC-VOF法模拟带防晃结构的液舱晃荡问题
引入三维通度系数法，并修改了流动的控制方程，结合直角网格的PLIC-VOF方法，实现了三维带不同型式防晃结构的液舱晃荡数值模拟，并通过局部液面和压强时历对比探讨了防晃效果。
五、基于PIV技术的液舱晃荡流场精细测量与模拟
合理设计液舱及其平面运动机构，由伺服系统控制运动机构在直线方向的速度时历，考虑液舱的不同装载水平，设定共振频率下的横荡运动激励，应用PIV技术进行液舱晃荡流场的精细测量以及波形观察分析。应用PLIC-VOF方法，进行了液舱晃荡流场的数值模拟，以及PIV试验结果对比分析。
六、液舱晃荡的WC-MPS方法数值模拟
基于流体弱可压缩假定，提出了基于Tait状态方程的弱可压缩移动粒子半隐式法（WC-MPS）。该方法通过直接计算流体状态方程来快速获取流场压强，而没有求解计算耗时的压强Poisson方程，并应用该方法模拟了剧烈晃荡的自由表面大变形现象。
七、波浪中液舱晃荡与船体摇荡的耦合作用数值模拟
考虑到液舱晃荡与船体运动的耦合作用，建立了液货船的耦合运动方程，结合内流场粘性流体PLIC-VOF方法，确定液舱晃荡作用力以及力矩，由外流场二维切片方法确定波浪中船体频域水动力系数及波浪载荷，采用Newmark-β法进行耦合运动方程的时域求解，实现波浪中船体运动的数值模拟。
本论文研究的创新性可以总结为以下三个方面：
一、三维通度系数法结合PLIC-VOF方法模拟带防晃结构液舱的晃荡问题
基于三维通度系数法表达流场中的固体相，并修改流动的控制方程，与三维PLIC-VOF方法相结合，实现了带防晃结构的三维液舱晃荡模拟。
二、直角网格CLSVOF数值方法模拟液舱剧烈晃荡问题
基于PLIC-VOF方法的良好质量守恒性能，考虑及Level-set方法隐式跟踪自由表面的性能，针对每一时间步的Level-set函数重新初始化，由PLIC-VOF重构自由表面，通过确定邻近网格到自由表面网格的最近距离，进行Level-set函数的重新初始化，实现了耦合的CLSVOF数值方法，并应用于液舱剧烈晃荡模拟。
三、基于弱可压缩假定的WC-MPS方法模拟液舱剧烈晃荡问题
鉴于传统不可压缩移动粒子半隐式法（Fully Incompressible-MPS）通过求解Poisson方程获取压强，计算低效而耗时，因此基于流体弱可压缩假定，选用流体的Tait状态方程直接而快速求解流场压强，建立了弱可压缩移动粒子半隐式法（WeaklyCompressible-MPS），并应用于模拟剧烈晃荡问题。
Recent years, liquid cargo ships such as LNGC become an important facility fortransportation of liquefied cargoes. Navigating at sea, these ships will suffer from randomsea waves and ship motions. With the liquid tanks of large volumes, the liquid sloshing intanks occurs excited by ship motions. In severe sea states, the amplitudes of ship motionsare large and therefore arouse violent sloshing. This violent sloshing can pose greatimpulsive impact to the local tank structures, and cause their damage, and even harm safetynavigation and operation of LNG ships at sea. So it is of practical importance to study theviolent sloshing in tanks and its coupling effects with ship motions.
Based on above situations, in this thesis four related issues are focused on: thenumerical simulation of largely distorted free surface motions and computation ofimpulsive pressures during violent sloshing; the numerical simulation of liquid sloshing inbaffled tanks, and evaluation of effectiveness of different baffles; the measurements offlow fields during sloshing in liquid tanks and corresponding numerical simulations; thenumerical simulation and analysis of the coupled motions between tank sloshing and shipmotions.
Considering above issues, the work done in this thesis is as follow:
1. The governing equations and the corresponding numerical schemes for threedimensional sloshing in tanks
Considering the different kinds of sloshing excitations, the governing equations for3-D sloshing problem are established, and discretized numerically based on the cartesianstaggered grids by finite difference method, also the coupled velocity and pressure in theequations are solved by the over-relaxed Gauss-Seidel iteration scheme.
2. The PLIC-VOF method for three dimensional sloshing in tanks
In cartesian staggered grids, the governing equations for volume fractions are solvedbased on the directional splitting scheme and Lagrange convection algorithm. Applying the numerical algorithm for the governing equations, the PLIC-VOF method is developed toreconstruct free surface, and employed for the numerical simulation of the violent sloshingin tanks.
3. The CLSVOF method for the violent sloshing in tanks
Based on the PLIC-VOF method, the Level-set method is applied to determine thefree surface normal considering its excellent performance in tracking the free surfaceexplicitly. Because of the PLIC-VOF method with good property in mass conservation, theLevel-set method and the PLIC-VOF method are coupled to develop the CLSVOF method.Finally, this method is employed to simulate the violent sloshing in tanks.
4. The aperture technique coupled with the PLIC-VOF method in three dimensionsfor the numerical simulation of the liquid sloshing in tanks with the baffles
The3-D aperture approach is introduced, and therefore the governing equations aremodified to adapt to the change of the volume fraction in cells. Coupled with PLIC-VOFmethod, the sloshing problem in tanks with different type of the baffles is simulated, andthe effectiveness of the baffles are compared and evaluated according to the time historiesof the local pressures and wave elevations.
5. The detailed measurements of the flow fields in the tank with the sloshing problemby PIV technique and the numerical simulation correspondingly
The motion mechanism for the tank is rational designed, and its real-time velocity iscontrolled by the control systems. Considering different filling levels, the excitationfrequencies of the sway motion are set as the resonant frequencies under different fillingconditions. Based on these conditions, the PIV technique is applied to measure the flowfields and the flow patterns in the liquid tanks. Finally, the numerical simulation is carriedout by the PLIC-VOF method and compared with the PIV experimental results.
6. The WC-MPS method for the numerical simulation of the tank sloshing
With the weakly compressible assumption, a weakly compressible moving particlesemi-implicit method (WC-MPS) is introduced based on the Tait’s equation of state of thefluid. For this method, the pressure field is obtained directly by Tait’s equation of statewithout solving time-consuming Poisson’s equation. Employing this WC-MPS method, theviolent sloshing with highly-distorted free surface in tanks are simulated and validated withexperimental results.
7. The study on the coupling effects of tank sloshing and ship motion in waves
Considering the coupling effects of the tank sloshing and the ship motions, thecoupled motion equations of the liquid cargo ships are established. To obtain the force andmoment induced by the tank sloshing, the PLIC-VOF method for vicious fluid is applied.While, to determine the hydrodynamic coefficients and wave loads for the ships in waves,a two dimensional strip theory is applied in frequency domain. Taking advantage of theNewmark-β approach, the coupled motion is solved in time domain to simulate themotions of liquid cargo ships in waves.
The creativity of the studies in this thesis can be summarized as the flowing threeaspects:
1. The aperture technique coupled with the3-D PLIC-VOF method is developed andemployed to simulate the liquid sloshing in the baffled tanks.
The3-D aperture approach is introduced to express the solid phase in the flow field,and the governing equations are modified correspondingly coupled with the PLIC-VOFmethod. And this approach is used to simulate the sloshing problems in the baffled tanks.
2. The CLSVOF method in cartesian grids is developed and applied to simulate theviolent sloshing in tanks.
For the PLIC-VOF method has good property in mass conservation, and the Level-setmethod possesses excellent performance in tracking interface explicitly. Therefore, theLevel-set method and PLIC-VOF method are coupled to develop the CLSVOF method. Ineach time step, the reinitialization of Level-set function is based on the constructed freesurface by PLIC-VOF method, and the values of the Level-set function are obtained bydetermining the shortest distance from the neighboring cells to the free surface cells. Andthis coupled method is employed to simulate the violent sloshing in tanks.
3. The WC-MPS method based on weakly-compressible assumption is developed andapplied to simulate the violent sloshing in tanks.
For fully incompressible MPS method, the pressure field is obtained by solvingtime-consuming Poisson’s equation. With the weakly compressible assumption, a weaklycompressible moving particle semi-implicit method (WC-MPS) is introduced based on thepressure field computed directly by Tait’s equation of state of the fluid. Employing thisWC-MPS method, problems of the violent sloshing in tanks are simulated.
引文
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