A modified SPH method to model the coalescence of colliding non-Newtonian liquid droplets

This paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non-Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas-to-liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head-on binary collision of vdW liquid droplets. Both Newtonian and non-Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off-center binary collision of non-Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non-Newtonian liquid droplets without tensile instability.     

Kinetics of microcrack blunting ahead of macrocrack approaching shear wave speed

The fracturing of glass and tearing of rubber both involve the separation of material but their crack growth behavior can be quite different, particularly with reference to the distance of separation of the adjacent planes of material and the speed at which they separate. Relatively speaking, the former and the latter are recognized, respectively, to be fast and slow under normal conditions. Moreover, the crack tip radius of curvature in glass can be very sharp while that in the rubber can be very blunt. These changes in the geometric features of the crack or defect, however, have not been incorporated into the modeling of running cracks because the mathematical treatment makes use of the Galilean transformation where the crack opening distance or the change in the radius of curvature of the crack does not enter into the solution. Change in crack speed is accounted for only via the modulus of elasticity and mass density. For this simple reason, many of the dynamic features of the running crack have remained unexplained although speculations are not lacking. To begin with, the process of energy dissipation due to separation is affected by the microstructure of the material that distinguishes polycrystalline from amorphous form. Energy extracted from macroscopic reaches of a solid will travel to the atomic or smaller regions at different speeds at a given instance. It is not clear how many of the succeeding size scales should be included within a given time interval for an accurate prediction of the macroscopic dynamic crack characteristics. The minimum requirement would therefore necessitate the simultaneous treatment of two scales at the same time. This means that the analysis should capture the change in the macroscopic and microscopic features of a defect as it propagates. The discussion for a dual scale model has been invoked only very recently for a stationary crack. The objective of this work is to extend this effort to a crack running at constant speed beyond that of Rayleigh wave. Developed is a dual scale moving crack model containing microscopic damage ahead of a macroscopic crack with a gradual transition. This transitory region is referred to as the mesoscopic zone where the tractions prevail on the damaged portion of the material ahead of the original crack known as the restraining stresses, the magnitude of which depends on the geometry, material and loading. This damaged or restraining zone is not assumed arbitrarily nor assumed to be intrinsically a constant in the cohesive stress approach; it is determined for each step of crack advancement. For the range of micronotch bluntness with 0 < β < 30° and 0.2 σ_∞/σ₀ 0.5, there prevails a nearly constant restraining zone size as the crack approaches the shear wave speed. Note that β is the half micronotch angle and the applied stress ratio is σ_∞/σ₀ with σ₀ being the maximum of the restraining stress. For σ_∞/σ₀ equal to or less than 0.5, the macrocrack opening displacement COD is nearly constant and starts to decrease more quickly as the crack approaches the shear wave speed. For the present dual scale model where the normalized crack speed v/c_s increases with decreasing with the one-half microcrack tip angle β. There prevails a limit of crack tip bluntness that corresponds to β 36° and v/c_s 0.15. That is a crack cannot be maintained at a constant speed if the bluntness is increased beyond this limiting value. Such a feature is manifestation of the dependency of the restraining stress on crack velocity and the applied stress or the energy pumped into the system to maintain the crack at a constant velocity. More specifically, the transitory character from macro to micro is being determined as part of the unknown solution. Using the energy density function dW/dV as the indicator, plots are made in terms of the macrodistance ahead of the original crack while the microdefect bluntness can vary depending on the tip geometry. Such a generality has not been considered previously. The macro-dW/dV behavior with distance remains as the inverse r relation yielding a perfect hyperbola for the homogeneous material. This behavior is the same as the stationary crack. The micro-dW/dV relations are expressed in terms of a single undetermined parameter. Its evaluation is beyond the scope of this investigation although the qualitative behavior is expected to be similar to that for the stationary crack. To reiterate, what has been achieved as an objective is a model that accounts for the thickness of a running crack since the surface of separation representing damage at the macroscopic and microscopic scale is different. The transitory behavior from micro to macro is described by the state of affairs in the mesoscopic zone.     

相移数字云纹测量系统

介绍了一种相位移数字云纹变形测量系统．测试系统采用ＣＣＤ摄像系统记录光栅图像，控制采样的空间频率大约为光栅线密度的整数倍，对试件栅进行采样后用数字信号处理的方法，实现空间相位移及进行实时数字云纹条纹显示，并对相移误差及光栅信号的高阶谐波的影响进行了校正     

An improved particle shifting technique for incompressible smoothed particle hydrodynamics methods

The smoothed particle hydrodynamics (SPH) method is one of the powerful Lagrangian tools for modeling free surface flows. However, it suffers from particle disorder, which leads to interpolation and numerical errors. To overcome this problem, several techniques have been introduced until now, among which the particle shifting technique (PST) based on Fick's law is an efficient one. The current form of this method needs tuning parameters to fulfill numerical stability criteria. In this study, to eliminate calibration factors, a new shifting coefficient is derived theoretically based on particle positions before and after shifting, regardless of other parameters such as velocity, pressure, time step intervals, etc. The only required input is particle positions, and the main concern is conserving particle densities in their updated positions. In addition to the proposed PST, a new distribution index (DI) is introduced for measuring the spatial uniformity of particles. Furthering the research, some novel treatments are also studied to improve particle movements near free surface boundary. The proposed idea is only assessed for ISPH method in this study, and its performance in other SPH schemes needs more investigations. Following this innovative method, it is validated by modeling different cases including dam break flow, paddle movement, and elliptical water drop. In all cases, particle arrangements have been improved by means of the modified shifting method. In that sense, good agreements between simulation results with experimental data, analytical solutions, and other numerical methods approve the ability of the developed method in simulating free surface flows.     

水面舰艇编队的最佳防空队形探讨

最佳防御队形以编队对来袭导弹的可探测面积尽可能大为前提,并以"抗饱和攻击能力"为衡量标准.各方向的可拦截批次受两方面因素限制:一是来袭导弹被发现时其与指挥舰的距离,一般距离越大,防御准备就越充分,可拦截批次就越大;二是护卫舰到来袭导弹轨迹的距离,一般距离越小,单次拦截时间就越短,可拦截批次就越大.定义以概率1可拦截批次最小的方向为最危险方向,经计算初始队形各方向可拦截的批次不等,通过"削峰补谷"的方式予以均衡和优化.若以拦截批次的期望为标准,最危险方向与以概率1可拦截的批次为标准的结果相同.如果得到空中预警机的信息支援,在最危险方向上编队就可更早地对距离指挥舰148.4km远的导弹发起拦截,增大编队的抗饱和攻击能力,但由于防空导弹射程限制,预警机提供的信,息支援无法得到充分利用,此时限制编队抗饱和攻击能力的主要矛盾转向防空导弹的射程.     

Aligning retention time shifts in HPLC three‐dimensional spectra by icoshift approach combined with data arrangement methods and the release of a graphical user interface

High‐performance liquid chromatography coupled with photodiode array detection has been extensively applied in many fields and the peaks among the analyzed samples can be shifted due to the variations of instrumental and experimental conditions. In multivariate analysis, retention time alignment is an important pretreatment step. Hence, the shifted peaks in high‐performance liquid chromatography coupled with photodiode array detection three‐dimensional spectra should be aligned for further analysis. Being motivated by this purpose, the interval correlated shifting method combined with the proposed data arrangement methods are recommended and employed on high‐performance liquid chromatography coupled with photodiode array detection data as a demonstration. We validate the alignment performance of the proposed method through comparison the consistency of the retention time before and after alignment. The obtained results demonstrated that the proposed method is capable of successful aligning the employed data. Additionally, the interval correlated shifting method combined with the data arrangement modes is implemented in an easy‐to‐use graphical user interface environment and so can be operated easily by users not familiar with programming languages.     

Collisional broadening and shifting of the 211-202 transition of H2O, H2O, H2O by atmosphere gases

Broadening and shifting of the 2₁₁-2₀₂ transition of H₂¹⁶O, H₂¹⁷O, H₂¹⁸O by pressure of water, nitrogen and oxygen were precisely measured at room temperature using spectrometer with radio-acoustic detection of absorption. Shift parameters for all studied lines as well as broadening parameters of H₂¹⁷O, H₂¹⁸O lines were measured for the first time. Comparison of obtained results with previously known experimental and theoretical data is presented.     

结构光测量相位波动误差补偿方法研究

在计算机仿真分析投影仪伽马非线性特性对包裹相位波动误差影响的基础上,提出一种面向相移结构光测量的相位波动误差补偿方法.该方法采用二次多项式最小二乘拟合的方法近似输出条纹光强分布,实现包裹相位波动误差的补偿,减小投影仪非线性导致的系统测量误差.此方法简单,运算量小,不依赖环境光源及投影仪、摄像机具体参数,具有很强的通用性...     

Uniqueness and stability of slowly oscillating periodic solutions of delay equations with bounded nonlinearity

We study slowly oscillating periodic solutions of delay equations with small parameters. When the nonlinearity has finite and nonzero limits at infinities, the appearance of these solutions and their periods can be found though asymptotic analysis. Under further natural assumptions on the nonlinearity, we prove that slowly oscillating periodic solutions are unique and asymptotically stable when parameters are sufficiently small.