A coupled WC-TL SPH method for simulation of hydroelastic problems

A coupled weakly compressible (WC) and total Lagrangian (TL) smoothed particle hydrodynamics (SPH) method is developed for simulating hydroelastic problems. The fluid phase is simulated using WCSPH method, while the structural dynamics are solved using TLSPH method. Fluid and solid components of the method are validated separately. A sloshing water tank problem is solved to test the WCSPH method while oscillation of a thin plate and large deformation of a cantilever beam are simulated to test the TLSPH method. After validating each component, the coupled WC-TL SPH scheme is used to simulate two benchmark hydroelastic problems. The first test case shows the evolution of water column with an elastic boundary gate, and the second one investigates the breaking water column impact on elastic structures. The agreement between WC-TL SPH results and literature data shows the ability of the proposed method in simulating hydroelastic phenomena.     

A new approach for the limit to tree height using a liquid nanolayer model

Liquids in contact with solids are submitted to intermolecular forces inferring density gradients at the walls. The van der Waals forces make liquid heterogeneous, the stress tensor is not any more spherical as in homogeneous bulks and it is possible to obtain stable thin liquid films wetting vertical walls up to altitudes that incompressible fluid models are not forecasting. Application to micro tubes of xylem enables to understand why the ascent of sap is possible for very high trees like sequoias or giant eucalyptus.      

基于表面力模型的液滴冲击弹性基底SPH模拟

采用光滑粒子动力学SPH方法建立液滴冲击弹性基底的流固耦合数值模型,给出描述粘性流体和弹性固体运动的SPH离散方程和数值处理格式,引入人工耗散项来抑制标准SPH方法的数值震荡。为模拟液滴的表面张力效应,通过精确检测边界粒子,采用拉格朗日插值方法计算表面法向量和曲率,结合界面理论中的连续表面力CSF方法,建立了适用于自由表面液滴的表面力模型,方形液滴变形的模拟结果与拉普拉斯理论解吻合较好。随后,采用SPH流固耦合模型模拟1.0 mm直径水滴以不同速度(0.2 m/s～3.0 m/s)冲击两种薄板型基底,分析了基底弹性变形对液滴铺展、收缩以及回弹行为的影响。     

改进SPH方法在陶瓷材料层裂数值模拟中的应用

为了探讨铝飞片撞击陶瓷材料时的层裂现象,采用改进SPH方法模拟应力波在陶瓷材料中的传播。结果表明,当离散粒子分布不均匀时,数值模拟计算的自由面速度时程曲线与实测曲线吻合良好。对比CSPM方法,改进SPH方法的精度更高。提出适用于数值模拟的陶瓷材料损伤演化方程,对脉冲载荷下陶瓷/钢层合板层裂的破坏过程进行数值模拟,结果表明,由于陶瓷的波阻抗高于钢的,且抗压强度远高于抗拉强度,因此拉应力引起的层裂破坏是主要的。即使在材料内部传播的只是弹性压缩波,当弹性波到达材料界面时,由界面反射引起的卸载波也能导致陶瓷发生层裂破坏。     

Oldroyd-B黏弹性液滴弹跳行为的改进SPH模拟

基于光滑粒子流体动力学SPH(Smoothed Particle Hydrodynamics)方法对Oldroyd-B黏弹性液滴撞击固壁面产生的弹跳行为进行了模拟与分析。首先,为了解决SPH模拟黏弹性自由表面流出现的张力不稳定性问题,联合粒子迁移技术提出了一种改进SPH方法。然后,对Oldroyd-B黏弹性液滴撞击固壁面产生的铺展行为进行了改进SPH模拟,与文献结果的比较验证了方法的有效性。最后,通过降低Reynolds数捕捉到了液滴的弹跳行为;并在此基础上,分析了液滴黏度比、Weissenberg数和Reynolds数对液滴弹跳行为的影响。结果表明,改进SPH方法可有效地模拟黏弹性自由表面流问题;液滴黏度比、Weissenberg数和Reynolds数对液滴最大回弹高度均有显著的影响。     

A single degree of freedom ‘lollipop’ model for carbon nanotube bundle formation

Current carbon nanotube (CNT) synthesis methods include the production of ordered, free-standing vertically aligned arrays, the properties of which are partially governed by interactions between adjacent tubes. Using material parameters determined by atomistic methods, here we represent individual CNTs by a simple single degree of freedom ‘lollipop’ model to investigate the formation, mechanics, and self-organization of CNT bundles driven by weak van der Waals interactions. The computationally efficient simple single degree of freedom model enables us to study arrays consisting of hundreds of thousands of nanotubes. The effects of nanotube parameters such as aspect ratio, bending stiffness, and surface energy, on formation and bundle size, as well as the intentional manipulation of bundle pattern formation, are investigated. We report studies with both single wall carbon nanotubes (SWCNTs) and double wall carbon nanotubes (DWCNTs) with varying aspect ratios (that is, varying height). We calculate the local density distributions of the nanotube bundles and show that there exists a maximum attainable bundle density regardless of an increase in surface energy for nanotubes with given spacing and stiffness. In addition to applications to CNTs, our model can also be applied to other types of nanotube arrays (e.g. protein nanotubes, polymer nanofilaments).     

A modified averaging scheme with application to the secondary Hopf bifurcation of a delayed van der Pol oscillator

In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator.     

A corrected symmetric SPH method to simulate viscoelastic free surface flows based on the PTT model

In this work, a corrected symmetric and periodic density reinitialized SPH (CSPDR‐SPH) method is proposed and extended to simulate the viscoelastic free surface flows based on the Phan–Thien–Tanner model. The improvements mainly lie in deriving a corrected symmetric kernel gradient, and combining it with a periodic density reinitialization procedure. In addition, a simple artificial viscosity and a simple artificial stress form are adopted. Thus, the CSPDR‐SPH method has higher accuracy and better stability than the SPH method, and conserves both linear and angular momentums. The consistency and convergence of the CSPDR‐SPH method are justified by approximating a function in one and two dimensions. The merits of CSPDR‐SPH method are demonstrated by several benchmarks. The simple flow in a two‐dimensional channel is investigated to show the capability of the CSPDR‐SPH method to simulate the viscoelastic free surface flow. Then the CSPDR‐SPH method is extended to simulate the impacting drop problem. Numerical results show that the CSPDR‐SPH method can precisely capture the viscoelastic free surface. The Reynolds number, Weissenberg number and elongation parameter have remarkable effect on the flows. Copyright © 2012 John Wiley & Sons, Ltd.     

A novel method to calculate the pressure interaction between dust and fluid using SPH

Unstable behavior of smoothed particle hydrodynamics (SPH) dust particles, such as clumping or fingering under certain conditions, has been reported by several researchers who have conducted studies on dusty fluid SPH. The simulation results in this study show that this instability is numerical, and the instability is mainly attributable to the ill‐interpolated pressure gradient in the interaction term between 2 phases. In this paper, we introduce a new method to calculate the pressure force interaction term between dust and fluid particles. The key idea is to first interpolate the pressure gradient at SPH fluid particles and then use the values to calculate the pressure gradient at SPH dust particles, in a consecutive manner. To compare the new method with the existing method, we first conducted an interpolation of pressure gradient at hydrostatic equilibrium under gravity to estimate any error. The results show that the new method is more accurate. We then conducted additional numerical tests, namely, dust‐liquid counterflow, sedimentation in a confined tank, and sedimentation in the presence of turbulence. The unphysical unstable behavior of SPH dust particles such as clumping or fingering was significantly reduced in the new method. The results also show that the instability becomes more significant when using the existing method especially for the case when simulating a flow with relatively high concentration of dust or for the case in which inertia dominates the dynamics of dust particles. Especially, in those cases, the existing method should be avoided, and the newly proposed method is highly recommended.     

Large‐scale SPH simulations of droplet impact onto a liquid surface up to the consequent formation of Worthington jet

In this study, the whole process of liquid droplet impact onto a liquid surface up to the consequent formation of the central column was simulated using the smoothed particle hydrodynamics method (SPH), and compared with an experiment using a high‐speed video camera. The surface tension tensor for the particle‐based expression was adequately included as the gradient of the surface tension and that enabled the simulation leading to the formations of crater and crown as well as the consequent central column. The simulated time series of the crater depth and diameter and crown height corresponded quantitatively well with the experimental result up to the rebound motion while discrepancies remained as a lower central column height in the simulation, and this seemed to be ascribed to the difficulty in realizing the complex surface structure that inevitably appeared in the fast rebound motion. Copyright © 2009 John Wiley & Sons, Ltd.     

基于SPH法的二维矩形液舱晃荡研究

液体晃荡是一种复杂的流体运动现象,自由液面的存在使得该现象具有很强的非线性和随机性。针对二维矩形液舱在不同振幅水平激励下的纵荡问题,应用SPH法对其进行了数值研究。首先计算了小振幅激励下的纵荡,计算结果分别与线性理论解、文献VOF法结果及文献SPH法结果作了比较分析,以验证所建数值模型的合理性;然后计算了液舱在大振幅水平激励下的纵荡,着重分析了不同振幅下液体晃荡的速度向量图、液面波动时程、压强波动时程、动量波动时程以及波动的频谱图,并将计算所得液面波动结果与小振幅激励下的液面波动结果作了比较。分析结果表明,在大振幅水平激励下,液面波动的波峰值较小振幅下的结果有较为明显的增大,而波谷值则无过大的变化,总体波动幅值比小振幅下的结果大;随着激励幅值的增大,液面波动幅值呈现明显增大的趋势,压强的整体波动幅值也呈增大趋势,动量波动的均值亦有明显增大;波动能量随着激励幅值的增大而增大并向第一阶频率区域集中。SPH法对处理液体大幅晃荡这种具有自由表面大变形的问题有十分优越的特性。     

INVESTIGATION OF THE DYNAMIC BUCKLING OF DOUBLEWALLED CARBON NANOTUBE SUBJECTED TO AXIAL PERIODIC DISTURBING FORCES

IntroductionThediscoveryofthefirstcarbonnanotubes[1]hasattractedwideattentionandstimulatedextensivestudies[2 - 5 ].Thestudiesshowedthatthecarbonnanotubesexhibitsuperiormechanical,electronicandchemicalproperties.Onthemechanicalbehavior,thecarbonnanotubespossessexceptionallyhighstrength ,stiffnessandelasticmodulus.Theestimatemodulusofthecarbonnanotubemayreachashighas 1TPa.Itisthelargestofallknownmaterials.Thestrengthorstiffnessishigherthananyknownfiber[3].Thecarbonnanotubeareusedascompositemat…     

SPH 方法在聚能装药射流三维数值模拟中的应用

采用有限元软件LS-DYNA中的SPH 算法实现聚能装药射流形成过程的三维数值模拟。将SPH方法和FEM 方法与理论计算结果相比较。研究结果表明:SPH 数值模拟计算过程十分稳定,避免了有限元数值模拟过程中的网格扭曲、缠绕和物质穿透等问题,而且计算精度比有限元方法更高;采用SPH 方法计算的射流速度、射流长度与有限元计算结果和理论计算结果的误差均小于5%,因此该方法对于模拟诸如聚能装药等多介质、大变形问题十分有效;初始相邻粒子数N 的最佳取值范围为600~1800,在该范围内计算结果的误差小于3%,且计算效率高。     

Mind the Gap: The Shape of the Free Surface of a Rubber-Like Material in Proximity to a Rigid Contactor

Extending Andreussi and Gurtin's [1] pioneering work on the wrinkling of a free surface, we investigate the wrinkling stability of an incompressible elastic-like half-space whose surface is proximate to a contactor. Assuming a plane-strain deformation and accounting for both surface prestress and curvature dependence of the surface free-energy density, we impose balances of forces and torques both in the bulk and on the surface. From the resulting linearized bulk and superficial equations, we derive a quintic dimensionless dispersion relation and perform a parametric study to see when stable or unstable behavior of the free surface is manifested. When compared with the quadratic dispersion relation of Andreussi and Gurtin [1], we see here that the combined effects associated with surface prestress, curvature-dependence of the surface free-energy density, and the interactions between the surface and the proximate contactor always lead to an increased number of linearly stable wrinkled configurations.     

土体颗粒物流动物质点法模拟的弹塑性和非牛顿流体本构模型比较研究

土体颗粒物流动是一种典型的大变形破坏,具有非牛顿流体的流动特征。准确模拟土体颗粒物的流动及冲击过程,对滑坡和泥石流等地质灾害的防治具有重要意义。物质点法是一种无网格粒子类方法,已在各类大变形问题中得到了广泛应用。以往土体颗粒物流动的模拟,通常采用弹塑性本构模型,但缺乏对非牛顿本构模型的模拟分析。本文引入非牛顿本构模型的模拟分析,旨在为土体颗粒物流动模拟提供一种新的方法与思路。非牛顿本构模型的模拟分析是将非牛顿广义Cross模型引入三维物质点法,通过人工阻尼力模拟颗粒间的摩擦力,对土体颗粒物的坍塌、沿斜面滑动以及冲击障碍物等问题进行了动态模拟,研究了其运动全过程,并与弹塑性本构模型的模拟结果进行了对比验证。结果表明,基于非牛顿流体本构模型的物质点法可以较好地模拟土体颗粒物加速、减速到再次稳定的流动全过程及其对障碍物的冲击效应。     

The contribution of internal degrees of freedom to the non-Newtonian rheology of model polymer fluids

We report non-equilibrium molecular dynamics simulations of rigid and non-rigid dumbbell fluids to determine the contribution of internal degrees of freedom to strain-rate-dependent shear viscosity. The model adopted for non-rigid molecules is a modification of the finitely extensible nonlinear elastic (FENE) dumbbell commonly used in kinetic theories of polymer solutions. We consider model polymer melts — that is, fluids composed of rigid dumbbells and of FENE dumbbells. We report the steady-state stress tensor and the transient stress response to an applied Couerte strain field for several strain rates. We find that the rheological properties of the rigid and FENE dumbbells are qualitatively and quantitatively similar. (The only exception to this is the zero strain rate shear viscosity.) Except at high strain rates, the average conformation of the FENE dumbbells in a Couette strain field is found to be very similar to that of FENE dumbbells in the absence of strain. The theological properties of the two dumbbell fluids are compared to those of a corresponding fluid of spheres which is shown to be the most non-Newtonian of the three fluids considered.Symbol Definition b dimensionless time constant relating vibration to other forms of motion - F force on center of mass of dumbbell - F _i force on bead i of dumbbell - F force between center of masses of dumbbells and - F _ij force between beads i and j - h vector connecting bead to center of mass of dumbbell - H dimensionless spring constant for dumbbells, in units of / ² - I moment of inertia of dumbbell - J general current induced by applied field - k _B Boltzmann's constant - L angular momentum - m mass of bead, (= m/2) - M mass of dumbbell, g - N number of dumbbells in simulation cell - P translational momentum of center of mass of dumbbell - P pressure tensor - P _xy xy component of pressure tensor - Q separation of beads in dumbbell - Q _eq equilibrium extension of FENE dumbbell and fixed extension of rigid dumbbell - Q ₀ maximum extension of dumbbell - r _ij vector connecting beads i and j - r position vector of center of mass dumbbell - R vector connecting centers of mass of two dumbbells - t time - t ^* dimensionless time, in units of m/ - T ^* dimensionless temperature, in units of /k - u potential energy - u velocity vector of flow field - u _x x component of velocity vector - V volume of simulation cell - X general applied field - strain rate, s^–1 - ^* dimensionless shear rate, in units of /m ² - general transport property - Lennard-Jones potential well depth - friction factor for Gaussian thermostat - shear viscosity, g/cms - ^* dimensionless shear viscosity, in units of m/ ² - ^* dimensionless number density, in units of ^–3 - Lennard-Jones separation of minimum energy - relaxation time of a fluid - angular velocity of dumbbell - orientation angle of dumbbell      

应用基于GPU的SPH方法模拟二维楔形体入水砰击问题

光滑粒子流体动力学(SPH)法是一种无网格的拉格朗日效值方法,广泛应用于计算流体领域模拟复杂自由表面流问题.SPH方法的主要缺点就是计算量过大,而基于GPU的并行计算方法可使SPH计算得到有效加速.本文应用基于GPU的SPH并行计算方法研究了二维楔形体的入水砰击问题.数值计算结果与文献中对应的解析解比较一致,验证了基于GPU的SPH方法的精度和可靠性.仿真结果同时显示基于GPU的并行计算方法可使SPH计算速度得到显著提高.     

Transportation of heat through Cattaneo-Christov heat flux model in non-Newtonian fluid subject to internal resistance of particles

Thermal conduction which happens in all phases(liquid,solid,and gas) is the transportation of internal energy through minuscule collisions of particles and movement of electrons within a working body.The colliding particles comprise electrons,molecules,and atoms,and transfer disorganized microscopic potential and kinetic energy,mutually known as the internal energy.In engineering sciences,heat transfer comprises the processes of convection,thermal radiation,and sometimes mass transportation.Typi...     

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。     

A diffuse-interface approach to two-phase isothermal flow of a Van der Waals fluid near the critical point

A novel numerical method for simulations of isothermal, compressible two-phase flows of one fluid component near the critical point is presented on the basis of a diffuse-interface model and a Van der Waals equation of state. Because of the non-convexity of the latter, the nature of the set of governing equations is mixed hyperbolic–elliptic. This prevents the application of standard numerical methods for compressible flow. Moreover, the Korteweg capillary stress tensor, characteristic for the diffuse-interface approach, introduces third-order spatial derivatives of mass density in the Navier–Stokes equation, resulting in a dispersive behavior of the solution. Our computational method relies on a transformation of the conserved variables, which controls dispersion, stabilizes the numerical simulation and enables the use of coarser grids. A one-dimensional simulation shows that this method provides better stability and accuracy than without transformation of variables. Two- and three-dimensional simulations for isothermal liquid–vapor flows, in particular the retraction of a liquid non-spherical drop in vapor and the binary droplet collision in vapor, show the applicability of the method. The surface tension calculated from the numerical results is in good agreement with its theoretical value if the computational grid is sufficiently fine.