近场水下爆炸瞬态强非线性流固耦合无网格数值模拟研究

近场水下爆炸涉及多相流体的掺杂耦合以及结构的大变形、损伤和断裂等瞬态强非线性现象, 传统的网格算法在模拟近场水下爆炸时面临结构网格畸变、多相界面捕捉精度不足等难题, 鉴于此, 本文建立了完全无网格的近场水下爆炸冲击波和气泡全物理过程瞬态强非线性流固耦合动力学模型. 流体采用基于黎曼求解器的光滑粒子流体动力学(SPH)方法求解, 结构采用重构核粒子法(RKPM)求解, 并基于法向通量边界条件实现流固耦合. 为提高SPH对流场间断的求解精度, 引入黎曼问题思想并结合MUSCL重构算法, 为解决流场粒子体积变化剧烈导致的精度下降问题, 应用了自适应粒子分割与合并方法. 为模拟水下爆炸对结构造成的损伤断裂, 基于退化实体几何表述, 采用Lemaitre损伤算法, 建立了RKPM壳结构断裂损伤模型. 依据所建立的SPH-RKPM流固耦合模型, 对近场水下爆炸冲击波传播、气泡脉动与射流以及结构毁伤进行了模拟, 将得到的冲击波载荷、气泡演化以及结构响应与实验值和其他数值解对比, 验证了当前建立的SPH-RKPM流固耦合模型的有效性和精度, 并给出了水下爆炸载荷特性及其对结构的流固耦合毁伤机制与规律, 旨在为近场水下爆炸载荷预报提供理论和基础性技术支撑, 为毁伤威力评估和舰船防护结构设计提供参考.      

一种基于黎曼解处理大密度比多相流SPH的改进算法

多相流界面存在密度、黏性等物理场间断,直接采用传统光滑粒子水动力学(smoothedparticle hydrodynamics,SPH)方法进行数值模拟,界面附近的压力和速度存在震荡.一套基于黎曼解能够处理大密度比的多相流SPH计算模型被提出,该模型利用黎曼解在处理接触间断问题方面的优势,将黎曼解引入到SPH多相流计算模型中,为了能够准确求解多相流体物理黏性、减小黎曼耗散,对黎曼形式的SPH动量方程进行了改进,又将Adami固壁边界与黎曼单侧问题相结合来施加多相流SPH固壁边界,同时模型中考虑了表面张力对小尺度异相界面的影响,该模型没有添加任何人工黏性、人工耗散和非物理人工处理技术,能够反应多相流真实物理黏性和物理演变状态.采用该模型首先对三种不同粒子间距离散下方形液滴震荡问题进行了数值模拟,验证了该模型在处理异相界面的正确性和模型本身的收敛性;后又通过对Rayleigh--Taylor不稳定、单气泡上浮、双气泡上浮问题进行了模拟计算,结果与文献对比吻合度高,异相界面捕捉清晰,结果表明,本文改进的多相流SPH模型能够稳定、有效的模拟大密度比和黏性比的多相流问题.      

一种基于黎曼解处理大密度比多相流SPH的改进算法

多相流界面存在密度、黏性等物理场间断,直接采用传统光滑粒子水动力学(smoothed particle hydrodynamics, SPH)方法进行数值模拟,界面附近的压力和速度存在震荡.一套基于黎曼解能够处理大密度比的多相流SPH计算模型被提出,该模型利用黎曼解在处理接触间断问题方面的优势,将黎曼解引入到SPH多相流计算模型中,为了能够准确求解多相流体物理黏性、减小黎曼耗散,对黎曼形式的SPH动量方程进行了改进,又将Adami固壁边界与黎曼单侧问题相结合来施加多相流SPH固壁边界,同时模型中考虑了表面张力对小尺度异相界面的影响,该模型没有添加任何人工黏性、人工耗散和非物理人工处理技术,能够反应多相流真实物理黏性和物理演变状态.采用该模型首先对三种不同粒子间距离散下方形液滴震荡问题进行了数值模拟,验证了该模型在处理异相界面的正确性和模型本身的收敛性;后又通过对Rayleigh–Taylor不稳定、单气泡上浮、双气泡上浮问题进行了模拟计算,结果与文献对比吻合度高,异相界面捕捉清晰,结果表明,本文改进的多相流SPH模型能够稳定、有效的模拟大密度比和黏性比的多相流问题.     

完全拉格朗日SPH在冲击问题中的改进和应用

光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)在模拟固体大变形、破碎和裂纹扩展等问题中有天然的优势, 但SPH固有的拉伸不稳定缺陷是SPH在计算固体力学领域进一步应用的一大障碍. 完全拉格朗日SPH (total Lagrangian-SPH, TL-SPH)方法是一种有效的改善拉伸不稳定的措施, 但其仍面临边界区域精度低、界面条件难以施加、损伤裂纹难以模拟等缺陷. 因此, 首先将可达到二阶精度的高阶SPH方法与TL-SPH耦合, 为了节省高阶方法的计算量, 进一步简化粒子选取模式, 提出TL-SFPM (TL-simplified finite particle method)方法; 其次, 将可提高界面精度的DFPM (discontinuous finite particle method)方法与TL-SPH结合, 并提出一种基于黎曼解的界面接触算法, 通过在不同材料粒子间建立黎曼模型求解不同材料间的相互作用, 分别应用于流体?固体接触和固体?固体接触中; 再者, 为了捕捉固体受外载荷后的损伤程度及破坏模式, 提出一种完全拉格朗日框架下的粒子损伤破坏模型; 最后, 通过流?固冲击的带弹性挡板溃坝算例和固?固冲击的子弹撞击靶板算例验证提出的TL-SFPM方法、界面接触算法和损伤破坏模型的合理性和精确性, 进一步扩展TL-SPH方法在计算固体冲击问题中的应用.      

含液颗粒材料液固耦合分析的离散颗粒模型及特征线SPH法

对含液颗粒材料流固耦合分析建议了一个基于离散颗粒模型与特征线SPH法的显式拉格朗日-欧拉无网格方案。在已有的用以模拟固体颗粒集合体的离散颗粒模型[1]基础上,将颗粒间间隙内的流体模型化为连续介质,对其提出并推导了基于特征线的SPH法。数值例题显示了所建议方案在模拟颗粒材料与间隙流相互作用的能力和性能以及间隙流体对颗粒结构承载能力及变形的影响。     

流固耦合破坏分析的多分辨率PD-SPH方法

流固耦合破坏是一类涉及结构变形与破坏以及复杂自由表面现象的强非线性力学问题. 结合近场动力学(peridynamics, PD)与光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)各自的优势并考虑其计算效率问题, 提出一种适用于分析流?固耦合破坏问题的多分辨率PD-SPH混合方法. 分别采用SPH和PD方法以不同的空间和时间分辨率对流体和结构进行离散与求解, 利用具有与流体粒子相同光滑长度的虚粒子处理流?固界面, 以高精度满足界面边界条件. 通过两个经典算例: 液柱静压力下弹性板的变形和溃坝流体冲击弹性闸门的变形问题, 表明提出的多分辨率PD-SPH方法兼具较高的计算精度和计算效率; 对含裂缝的Koyna重力坝水力劈裂问题进行模拟计算, 所得裂缝扩展路径与文献结果吻合, 说明该方法适用于涉及结构破坏的流固耦合问题仿真. 最后尝试采用该方法进行流体冲击作用下含裂纹混凝土板崩塌过程数值仿真, 准确描述混凝土板的断裂破坏和全过程中的流体运动. 多分辨率PD-SPH混合方法或可为流?固耦合作用下的结构损伤破坏仿真提供一种新选择.      

基于SPH的动力松弛法

光滑质点流体动力学方法(SPH;Smoothed Particle Hydrodynamics)是一种新的纯Lagrangian方法,由于该方法在计算空间导数的时候不需要借助于网格,从而避免了Lagrangian网格在处理大变形问题时的缠结和扭曲问题.传统上,SPH方法主要用来模拟天体问题以及流体或固体的动力问题.动力松弛法(DR;Dynamic Relax-ation)通过采用虚拟质量和虚拟阻尼将一个静力问题转化为动力问题,最早用于解决潮汐问题.DR方法从数学的角度来说是一种求解线性方程组的方法,并不涉及连续结构的离散.所以采用网格方法离散时,DR方法同样受到网格变形导致计算精度下降的困扰.论文采用SPH离散连续体,然后用DR方法求解结构的平衡状态,并根据SPH的特点,提出一种加速收敛的新型计算方法.     

光滑粒子动力学方法的发展与应用

光滑粒子动力学(smoothed particle hydrodynamics,SPH)是一种拉格朗日型无网格粒子方法,已经成功地应用到了工程和科学的众多领域.SPH使用粒子离散及代表所模拟的介质,并且基于粒子体系估算和近似介质运动的控制方程.本文分析和综述了SPH模拟方法的发展历程、数值方法与应用进展.介绍了SPH方法的基本思想;从连续性、边界处理、稳定性和计算效率4个方面阐述了SPH方法的研究现状;介绍了SPH方法近年来在可压缩流动、不可压缩流动以及弹塑性材料高速变形与失效方面的一些典型应用;并对SPH方法的发展与应用进行了预测与展望.      

基于ALE,CEL和SPH方法的球形破片高速冲击充液结构对比研究

为研究ALE,CEL和SPH方法在高速冲击流固耦合动力学数值分析中的差异性,开展球形破片高速冲击充液结构数值模拟研究。建立经文献资料验证的ALE,CEL和SPH三种动力学模型,研究了流体压力变化、形成的空腔尺寸、破片速度衰减变化和充液结构变形等模拟精度,并分析相应的计算成本。结果表明,ALE,CEL和SPH三种方法均能有效模拟破片高速冲击充液结构的流固耦合动力学过程;ALE方法预测的空腔尺寸精度较高;CEL方法预测的流体压力、破片速度衰减和充液结构变形精度较高;SPH方法预测的空腔尺寸、破片速度衰减精度较高;当网格尺寸一致时, SPH方法计算时长约为ALE和CEL方法的两倍,但SPH方法前后处理更加简便。     

SPH方法Delaunay三角刨分与自由液面重构

光滑粒子法(SPH)作为一种拉格朗日型无网格方法,兼具欧拉网格方法和拉格朗日网格方法的优势,已经成功应用于科学和工程的众多领域。SPH方法后处理一般基于无规则分布的粒子,不如网格类方法后处理简便、直接。另外,SPH方法模拟自由液面流动等问题时,通过粒子位置难以重构自由液面的准确位置。发展一种基于Delaunay三角刨分的SPH后处理方法,即先基于SPH粒子位置利用Delaunay三角刨分建立三角网格,然后将粒子信息转化成网格单元/节点信息,从而可以在三角网格上进行后处理,实现基于网格方法的后处理功能,并可以在三角网格上直接提取或重构自由液面。将本文的方法应用到液滴碰撞和溃坝流SPH模拟结果的后处理中,得到了非常好的结果,表明本文的方法有效可靠。     

Simulating bubble dynamics in a buoyant system

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid–based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge.     

Numerical simulation for the air entrainment of aerated flow with an improved multiphase SPH model

Aerated flow is a complex hydraulic phenomenon that exists widely in the field of environmental hydraulics. It is generally characterised by large deformation and violent fragmentation of the free surface. Compared to Euler methods (volume of fluid (VOF) method or rigid-lid hypothesis method), the existing single-phase Smooth Particle Hydrodynamics (SPH) method has performed well for solving particle motion. A lack of research on interphase interaction and air concentration, however, has affected the application of SPH model. In our study, an improved multiphase SPH model is presented to simulate aeration flows. A drag force was included in the momentum equation to ensure accuracy of the air particle slip velocity. Furthermore, a calculation method for air concentration is developed to analyse the air entrainment characteristics. Two studies were used to simulate the hydraulic and air entrainment characteristics. And, compared with the experimental results, the simulation results agree with the experimental results well.     

An SPH pressure correction algorithm for multiphase flows with large density ratio

In this paper, we propose an interfacial pressure correction algorithm for smoothed particle hydrodynamics (SPH) simulation of multiphase flows with large density ratios. This correction term is based on the assumption of small deformation of the interface, and derived from perturbation expansion analysis. It is also proven to be applicable in cases with complex interfaces. This correction algorithm helps to overcome the discontinuities of the pressure gradient over the interfaces, which may cause unphysical gap between different phases. This proposed correction algorithm is implemented on a recent multiphase SPH model, which is based on the assumption of pressure continuity over the interfaces. The coupled dynamic solid boundary treatment is used to simulate solid walls; and a cut‐off pressure is applied to avoid negative particle pressure, which may cause computational instabilities in SPH. Three numerical examples of air–water flows, including sloshing, dam breaking, and water entry, are presented and compared with experimental data, indicating the robustness of our pressure correction algorithm in multiphase simulations with large density ratios. Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling and computation of cavitation in vortical flow

The paper presents an investigation of Euler–Lagrangian methods for cavitating two-phase flows. The Euler–Euler methods, widely used for simulations of cavitating flows in ship technology, perform well in regions of moderate flow changes but fail in zones of strong, vortical flow. Reasons are the strong approximations of cavitation models in the Euler concept. Alternatively, Euler–Lagrangian concepts enable more detailed formulations for transport, dynamics and acoustic of discrete vapor bubbles. Test calculations are performed to study the influence of different parameters in the equations of motion and in the Rayleigh–Plesset equation for bubble dynamics. Results confirm that only Lagrangian models are able to describe correctly the bubble behavior in vortices, while Eulerian results deviate strongly. Lagrangian formulations enable additionally the determination of acoustic pressure of cavitation noise. Two-way coupling between the phases is required for large regions of the vapor phase. A new coupling concept between continuous fluid flow and discrete bubble phase is developed and demonstrated for flow through a nozzle. However, the iterative coupling between the phases via volume fractions is computationally expensive and should therefore be applied only in regions where Eulerian treatment fails. A corresponding local concept for combination with an Euler–Euler method is outlined and is in progress.     

An improved SPH model for multiphase flows with large density ratios

This paper presents a new smoothed particle hydrodynamics (SPH) model for simulating multiphase fluid flows with large density ratios. The new SPH model consists of an improved discretization scheme, an enhanced multiphase interface treatment algorithm, and a coupled dynamic boundary treatment technique. The presented SPH discretization scheme is developed from Taylor series analysis with kernel normalization and kernel gradient correction and is then used to discretize the Navier‐Stokes equation to obtain improved SPH equations of motion for multiphase fluid flows. The multiphase interface treatment algorithm involves treating neighboring particles from different phases as virtual particles with specially updated density to maintain pressure consistency and a repulsive interface force between neighboring interface particles into the pressure gradient to keep sharp interface. The coupled dynamic boundary treatment technique includes a soft repulsive force between approaching fluid and solid particles while the information of virtual particles are approximated using the improved SPH discretization scheme. The presented SPH model is applied to 3 typical multiphase flow problems including dam breaking, Rayleigh‐Taylor instability, and air bubble rising in water. It is demonstrated that inherent multiphase flow physics can be well captured while the dynamic evolution of the complex multiphase interfaces is sharp with consistent pressure across the interfaces.     

An improved KGF‐SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows

The kernel gradient free (KGF) smoothed particle hydrodynamics (SPH) method is a modified finite particle method (FPM) which has higher order accuracy than the conventional SPH method. In KGF‐SPH, no kernel gradient is required in the whole computation, and this leads to good flexibility in the selection of smoothing functions and it is also associated with a symmetric corrective matrix. When modeling viscous incompressible flows with SPH, FPM or KGF‐SPH, it is usual to approximate the Laplacian term with nested approximation on velocity, and this may introduce numerical errors from the nested approximation, and also cause difficulties in dealing with boundary conditions. In this paper, an improved KGF‐SPH method is presented for modeling viscous, incompressible fluid flows with a novel discrete scheme of Laplacian operator. The improved KGF‐SPH method avoids nested approximation of first order derivatives, and keeps the good feature of ‘kernel gradient free’. The two‐dimensional incompressible fluid flow of shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, the original KGF‐SPH and improved KGF‐SPH. The numerical results show that the improved KGF‐SPH with the novel discrete scheme of Laplacian operator are more accurate than SPH, and more stable than FPM and the original KGF‐SPH. Copyright © 2015 John Wiley & Sons, Ltd.     

Direct-forcing immersed boundary lattice Boltzmann simulation of particle/fluid interactions for spherical and non-spherical particles

The lattice Boltzmann method (LBM) is a useful technique for simulating multiphase flows and modeling complex physics. Specifically, we use LBM combined with a direct-forcing (DF) immersed boundary (IB) method to simulate fluid–particle interactions in two-phase particulate flows. Two grids are used in the simulation: a fixed uniform Eulerian grid for the fluid phase and a Lagrangian grid that is attached to and moves with the immersed particles. Forces are calculated at each Lagrangian point. To exchange numerical information between the two grids, discrete delta functions are used. The resulting DF IB-LBM approach is then successfully applied to a variety of reference flows, namely the sedimentation of one and two circular particles in a vertical channel, the sedimentation of one or two spheres in an enclosure, and a neutrally buoyant prolate spheroid in a Couette flow. This last application proves that the developed approach can be used also for non-spherical particles. The three forcing schemes and the different factors affecting the simulation (added mass effect, corrected radius) are also discussed.     

Development and elaboration of numerical method for simulating gas–liquid–solid three-phase flows based on particle method

A numerical method for simulating gas–liquid–solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas–liquid two-phase problem, and the latter is a gas–liquid–solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.     

SPH simulation of oblique shocks in compressible flows

The Lagrangian smoothed particle hydrodynamics (SPH) method is used to simulate shock waves in inviscid, supersonic (compressible) flow. It is shown for the first time that the fully Lagrangian SPH particle method, without auxiliary grid, can be used to simulate shock waves in compressible flow. The wall boundary condition is treated with ghost particles combined with a suitable repulsive potential function, whilst corners are treated by a novel ‘angle sweep’ technique. The method gives accurate predictions of the flow field and of the shock angle as compared with the analytical solution. The study shows that SPH is a good potential candidate to solve complex aerodynamic problems, including those involving rarefied flows, such as atmospheric re‐entry. Copyright © 2016 John Wiley & Sons, Ltd.