【作者】 潘徐杰；

【导师】 张怀新；

【作者基本信息】 上海交通大学 ， 船舶与海洋结构物设计制造， 2009， 博士

【摘要】 自由表面是船舶与海洋工程领域的一个重要研究课题,对自由表面问题的模拟是船舶与海洋工程领域,计算流体力学的难点之一。虽然一些基于欧拉网格的自由表面处理方法在模拟带自由表面问题时能够取得不错的结果,但当遇到大变形自由表面、液面破碎、飞溅等问题时,基于欧拉网格的数值方法将使计算量增加并会遇到一定困难。移动粒子半隐式法(Moving-Particle Semi-Implicit Method, MPS)是最近兴起的一种基于拉格朗日(Lagrange)粒子的无网格法, MPS法中粒子的运动性使得该方法在自由表面尤其是大变形自由表面的模拟中有着出色的表现。研究表明,MPS法在船舶与海洋工程领域有着广阔的应用前景,但是鉴于该方法提出不久,算法自身仍有一些缺陷制约着MPS法的发展。因此,本文的目的在于研究MPS法理论基础,针对该方法目前比较突出的几点不足之处,讨论缓解或解决这些缺点的方法,进一步完善MPS法的理论,使其在船舶与海洋工程领域有着更好的适应能力,最后再结合大涡模拟,将MPS法应用至具有大变形自由表面的液体晃荡问题中。本文主要有以下几点内容和创新点:一、使用了一种防止粒子碰撞或穿越的人工修正步。MPS法中的拉格朗日粒子有着很强的运动随机性,使得在模拟过程中粒子之间相互碰撞以及粒子穿越边界条件的情况频繁发生,通过使用该人工修正步以避免上述情况的发生。数值实验表明,使用了该人工修正步后,模拟可以顺利进行,合适的修正距离可以保证粒子碰撞或穿越现象在整个模拟中出现的概率极低。二、讨论了不同核函数在不同类型模拟中的适用性。核函数是MPS法中的重要参数,也是MPS法中为数不多的可调参数之一,以往的研究中,往往通过调整不同的核函数来获取更好的模拟结果,但是没有针对核函数的特性进行系统的研究。通过讨论不同核函数在不同类型模拟中的适用性,可以指导在不同模拟中核函数的选取情况。三、研究了压力振荡现象,提出了以面积-时间平均为扩展的缓解方法,讨论了该方法对压力振荡现象的缓解效果。长期以来,压力振荡现象一直是制约MPS法广泛应用的最大原因,在早期MPS法的研究中,大多的注意力放在自由表面的表现上,压力问题因振荡现象而被忽视。通过使用面积-时间平均法,对不同的面积平均方式和不同的时间平均段进行讨论,选取合适的面积-时间平均方法,可将MPS法的压力结果缓解至工程实践可接受的范围之内,这为MPS法的进一步应用做好了准备,并且基于面积-时间的压力平均法也符合MPS法理论的实际意义。四、提出一种全新的基于邻居搜索的自由表面混合判别方法。通过粒子数密度来判别自由表面是MPS法在自由表面处理上的一大特色,该自由表面判别方法不但物理意义明确,而且基本不消耗计算资源,有着极高的效率。但是由于MPS法的算法流程问题,该方法会不可避免的产生自由表面的误判情况,这样不但会给模拟结果带来误差,还会加重模拟中的压力振荡现象,实际模拟表明这种自由表面误判的情况较为严重。新的自由表面判别方法由于是基于邻居搜索的,既而可以避免误判情况的发生,考虑到使用粒子数密度来判别自由表面的方法有着很高的效率,所以将基于邻居搜索的自由表面判别方法同基于数密度的自由表面判别方法结合使用,只在自由表面误判较为频繁的粒子数密度段使用邻居搜索,这样在不影响模拟效率的前提下,很大程度上避免了非自由表面粒子被误判的情况发生。五、基于大涡模拟的MPS法在具有大变形自由表面晃荡问题中的应用。工程中大部分问题都是湍流问题,而以往绝大多数的MPS法研究中均未考虑湍流,所以实现MPS的大涡模拟有着积极的意义。论文通过Smagorinsky涡粘模型,实现了MPS法的大涡模拟,讨论了大涡模拟中微分模型的合适作用距离。最后结合之前提出的方法,成功的模拟了3种不同情况下,具有大变形自由表面的晃荡问题,包括在二维水平方向上晃荡的共振方形液箱,二维平面内横摇的模型化的共振LNG液舱,以及在二维平面内3方向耦合运动的全尺寸共振LNG棱柱形液舱。上述不同方法在模拟中同时应用,均有很好的表现,模拟能够得到满意的结果。在具体的使用中,人工修正步能够很好的避免模拟中的碰撞和穿越问题;不同核函数的适用性能够准确的指导不同类型模拟的核函数选取;基于邻居搜索的混合自由表面判别方法能够准确的识别自由表面,并且对模拟的效率整体影响不大;而基于面积-时间平均的压力振荡缓解方法可以得到很好的压力结果,将原MPS法完全不能使用,幅度极大的振荡结果缓解至工程上可接受范围之内,并且压力结果同实验结果、其他数值模拟结果都极为接近,在晃荡的拍击压力上也有不错的表现。实践证明,提出的新技术或方法能够适应于MPS法的应用,并且很好的弥补了原MPS法在相关方面的不足。另外经过进一步完善MPS法大涡在大变形自由表面晃荡问题中有良好的表现,能够模拟出各种物理现象,这对工程实践有着重要的指导意义。更多还原

【Abstract】 Modeling free surface flows is of great significance in the field of ship and ocean engineering. However, these flows are difficult to simulate because the surface boundary conditions are specified on arbitarity moving surface. Some methods in Eulerian grid are flexible and robust to trace free surface in simulation, but with those method, Navier-Stokes equations are solved on a fixed grid, which brings the problem of numerical diffusion because the existence of the advection term in Navier-Stokes equations, especially when the deformation of free surface is very large and complicated or the free surface splashes. Moving-Particle Semi-Implicit Method (MPS) is a new meshless numerical method which bases on Lagrange particle, due to the advantage in free surface simulation, the MPS method plays more and more important role in numerical research. Studies show that the MPS method has broad prospects in the area of Naval Architecture and Ocean Engineering. But there are some deficiencies in its theory to restrict the development of MPS method. This paper studies deficiencies of MPS theory, and proposes some technologies for these deficiencies. With these technologies, the MPS method is coupled with a sub-particle scale (SPS) turbulence model to simulate sloshing problems with large deforming free surface. This paper has the following content andinnovations:1. Additional correction term for particles collision or pass through phenomena. Because the Lagrange behavior of particles, there are lots of particles collision phenomena in MPS simulation, some of these collision phenomena will pass through the boundary and lead to a serious consequence, but with the additional correction term and appropriate distance for correction, there are only few particles collision phenomena in simulations, and the probability of pass through phenomena is few.2. Behavior of kernel function in MPS method. Kernel function is a very important part in MPS theory, and it is one of the only a few adjustable parameters in MPS method. In early studies, better results are got by adjust kernel functions, but there has no systemic study on kerner functions’behavior. So the study on behavior of kernel function can help to select the kernel function for simulations.3. Pressure fluctuation phenomena, an area-time average method for pressure fluctuation phenomena, and the effect of the area-time average method. The unacceptable pressure fluctuation is an obvious defect in MPS method, and it has a negative influence to the development of MPS method. In most studies by MPS, more attention are putted on the free surface, pressure results are neglected because the fluctuation. An area-time average method is proposed in this paper, different area average type and different time average period are discussed. With different area-time average methods, the fluctuation of pressure is solved, the result is quit good and acceptable, and that makes MPS method more suitable for ocean engineering problem.4. A new mixed free surface traced method for MPS method, which based on neighbors search. MPS method uses the numerical density to trace the free surface, and it is efficiency. But due to the algorithm of MPS method, there are lots of non-free surface particles are traced as free surface particles. That will cause mistakes in simulation and make the pressure fluctuation more serious. The new mixed free surface traced method bases on neighbors search, so it solves the mistreatment problem in theory. Because its efficiency to use numerical density for free surface, the neighbors search method is mixed used with numerical density method, the neighbors search method is used when the mistreatment problem always happen, so the mixed free surface traced method solved the mistreatment problem with efficiency.5. Modified MPS-LES method for sloshing problem with violent surface. Most ocean engineering problems are problems with turbulence flow, and most of the early studies which bases on MPS method are laminar flow, so it is meanful to simulate the practical cases with turbulent flow. In this paper, the MPS method is extended to the large eddy simulation (LES) by coupled with a sub-particle-scale (SPS) turbulence model, the effect of the SPS turbulence is found as the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. 3 different sloshing problems are simulated by MPS-LES method successfully, these cases are a resonance sloshing rectangular tank, a modeled resonance rolling LNG tank longitudinal section and a full-scale resonance mix movement LNG tank transverse section.Results show, these new technologies or methods adapted to the MPS method and improved the original one. With these technologies, the modified MPS-LES method is good at the simulation of sloshing with large deforming free surface. The additional correction term make the modified MPS-LES method avoided nearly the entire pass through phenomena; behavior of kernel function is helpful to select a kernel function before simulation; the new mixed free surface traced method work well and no more mistreatment; different area-time average methods solved pressure fluctuation well, the pressure is good and very close to pressure of experiments or pressure by other methods.更多还原