Comparative study of two fluid model and dense discrete phase model for simulations of gas-solid hydrodynamics in circulating fluidized beds

Computational fluid dynamics(CFD)has become a valuable tool to study the complex gas-solid hydrodynamics in the circulating fluidized bed(CFB).Based on the two fluid model(TFM)under the Eulerian-Eulerian framework and the dense discrete phase model(DDPM)under the Eulerian-Lagrangian framework,this work conducts the comparative study of the gas-solid hydrodynamics in a CFB riser by these two different models.Results show that DDPM could be used to predict gas-solid hydrodynamics in the circulating fluidized bed,and there are differences between TFM and DDPM,especially in the radial distribution profiles of solid phase.Sensitivity analysis results show that the gas-solid drag model exhibits significant effects on the results for both the two models.The specularity coefficient and the restitution coefficient in the TFM,as well as the reflection coefficient and the parcel number in the DDPM,exhibit less impact on the simulated results.     

Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model

A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model.The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle,and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel.Several nominal variables are introduced to simplify the differential governing equation,integral constitutive equation,and boundary conditions.Rather than transforming the constitutive equation from integral to differential forms,the Laplace transformation is used directly to solve the integro-differential equations.The explicit expression for nominal torsional rotation and torque contains four unknown constants,which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation.A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped(CC)FGNT under torsional constraints and a clamped-free(CF)FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.     

Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are investigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability.Based on the Boltzmann transformation,an efficient semi-analytical method is proposed.The problem is then converted into a nonlinear equation in an integral form for the pressure field,and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed method has good convergence,and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature.Desorption,slippage,and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.     

Active control of multiscale features in wall-bounded turbulence

This study experimentally investigates the impact of a single piezoelectric(PZT)actuator on a turbulent boundary layer from a statistical viewpoint.The working conditions of the actuator include a range of frequencies and amplitudes.The streamwise velocity signals in the turbulent boundary layer flow are measured downstream of the actuator using a hot-wire anemometer.The mean velocity profiles and other basic parameters are reported.Spectra results obtained by discrete wavelet decomposition indicate that the PZT vibration primarily influences the near-wall region.The turbulent intensities at different scales suggest that the actuator redistributes the near-wall turbulent energy.The skewness and flatness distributions show that the actuator effectively alters the sweep events and reduces intermittency at smaller scales.Moreover,under the impact of the PZT actuator,the symmetry of vibration scales’velocity signals is promoted and the structural composition appears in an orderly manner.Probability distribution function results indicate that perturbation causes the fluctuations in vibration scales and smaller scales with high intensity and low intermittency.Based on the flatness factor,the bursting process is also detected.The vibrations reduce the relative intensities of the burst events,indicating that the streamwise vortices in the buffer layer experience direct interference due to the PZT control.     

Asymptotics for filtration of polydisperse suspension with small impurities

A model for deep bed filtration of a polydisperse suspension with small impurities in a porous medium is considered.Different suspended particles move with the same velocity as the carrier water and get blocked in the pore throats due to the size-exclusion mechanism of particle retention.A solution of the model in the form of a traveling wave is obtained.The global exact solution for a multiparticle filtration with one high concentration and several low concentrations of suspended particles is obtained in an explicit form.The analytic solutions for a bidisperse suspension with large and small particles are constructed.The profiles of the retained small particles change monotony with time.The global asymptotics for the filtration of a polydisperse suspension with small kinetic rates is constructed in the whole filtration zone.     

低温超导核磁共振陀螺仪模型

建立了单工作物质的三自由度3He低温超导核磁共振陀螺仪结构;利用了量子力学和经典动力学,经过严密的力学分析和数学演算,给出了三轴陀螺仪的工作原理和结构示意图;针对陀螺仪的交叉轴角速率耦合问题,给出了附加磁场线圈解耦法和冗余设计结构,最后建立了基于超导量子干涉仪探测磁矩,并采用最小二乘估计法来推导陀螺进动频率.陀螺仪测速范围可以达到10-9～103 rad/s,漂移为10-4 (°)/h.该陀螺仪结合低温超导技术具有高精度的前景.需要进一步对超导量子干涉磁矩检测仪的精度与陀螺性能进行研究.     

一种Cartesian气动网格的自适应划分算法

提出了针对空间Cartesian结构化网格的自适应划分算法,以满足飞机总体设计过程中进行多学科设计优化时根据方案变化生成CFD计算网格的需要,使气动特性能够得以自动化分析,并且保证优化迭代过程的顺利进行.分析了Cartesian网格划分过程中的两个关键问题,并给出了解决方法.在此基础之上,从理论上推导了能够自动适应飞机布局形式以及几何尺寸任意变化的Cartesian网格生成算法和实际划分步骤,并给出了其中部分主要的计算公式,同时论述了自适应划分过程中的若干重要问题.阐述了自适应划分所需的飞机及其部件特征尺寸的获取途径.最后展示了几个由自适应划分算法生成的Cartesian网格实例以说明其实际应用.     

DEM investigation of macro-and micro-mechanical properties of rigid-grain and soft-chip mixtures

We investigated the macro-and micro-mechanical properties of rigid-grain and soft-chip mixtures(GCMs)through numerical simulations using the discrete element method.We present a novel framework for the discrete modeling of soft chips and rigid grains in conjunction with calibration processes.Several numerical triaxial tests were also performed on GCMs with 0%,10%,20%,and 30%volumetric chip contents,P.The simulation results demonstrate that increasing P leads to higher GCM toughness,higher deviatoric peak stress,and higher corresponding shear strain.Higher P also contributes to more volume contraction and less dilation.The friction angles at both the peak and residual state significantly increase with increasing P.In view of the micro-mechanical features,strong contact force chains develop along the loading direction,which results in considerable anisotropy in the peak and residual states.Both the formation of strong force chains and rotation of grains decrease with increasing P,whereas the grain sliding percentage increases.The tensile force is mobilized with shearing and higher P leads to less mobilization of the tensile force.These findings are useful for better understanding the internal structure of GCMs with different soft-chip contents,especially in granular mixture mechanics and geomechanics.     

向蔡树棠先生学习什么——写在送别蔡先生这一天

题记蔡树棠教授离开我们已近半年,他的音容笑貌还时不时地浮现在我的脑海里.我刚从中国科学技术大学回来,蔡先生曾在该校工作多年,而那里的几位年青学子居然不知道蔡树棠这个名字,这使我有点悲哀.这里公布我写于送别他那天的短文<向蔡树棠先生学习什么>,希望大家记住这位曾在力学园地耕耘了半个多世纪的知名学者.     

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编辑部的同志要我写一点回忆,以纪念<力学与实践>创刊30年.往事悠悠,使我又回到20世纪70年代那动荡不安,却又是激情四射的年代.     

Complicated deformation simulating on temperature-driven 4D printed bilayer structures based on reduced bilayer plate model

The four-dimensional (4D) printing technology, as a combination of additive manufacturing and smart materials, has attracted increasing research interest in recent years. The bilayer structures printed with smart materials using this technology can realize complicated deformation under some special stimuli due to the material properties. The deformation prediction of bilayer structures can make the design process more rapid and thus is of great importance. However, the previous works on deformation prediction of bilayer structures rarely study the complicated deformations or the influence of the printing process on deformation. Thus, this paper proposes a new method to predict the complicated deformations of temperature-sensitive 4D printed bilayer structures, in particular to the bilayer structures based on temperature-driven shape-memory polymers (SMPs) and fabricated using the fused deposition modeling (FDM) technology. The programming process to the material during printing is revealed and considered in the simulation model. Simulation results are compared with experiments to verify the validity of the method. The advantages of this method are stable convergence and high efficiency, as the three-dimensional (3D) problem is converted to a two-dimensional (2D) problem. The simulation parameters in the model can be further associated with the printing parameters, which shows good application prospect in 4D printed bilayer structure design.

     

A robust hyper-elastic beam model under bi-axial normal-shear loadings

In this paper, a simple and robust constitutive model is proposed to simulate mechanical behaviors of hyper-elastic materials under bi-axial normal-shear loadings in the finite strain regime. The Mooney–Rivlin strain energy function is adopted to develop a two-dimensional (2D) normal-shear constitutive model within the framework of continuum mechanics. A motion field is first proposed for combined normal and shear deformations. The deformation gradient of the proposed field is calculated and then substituted into right Cauchy–Green deformation tensor. Constitutive equations are then derived for normal and shear deformations. They are two explicit coupled equations with high-level polynomial non-linearity. In order to examine capabilities of the developed hyper-elastic model, uniaxial tensile responses and non-linear stability behaviors of moderately thick straight and curved beams undergoing normal axial and transverse shear deformations are simulated and compared with experiments. Fused deposition modeling technique as a 3D printing technology is implemented to fabricate hyper-elastic beam structures from soft poly-lactic acid filaments. The printed specimens are tested under tensile/compressive in-plane and compressive out-of-plane forces. A finite element formulation along with the Newton–Raphson and Riks techniques is also developed to trace non-linear equilibrium path of beam structures in large defamation regimes. It is shown that the model is capable of predicting non-linear equilibrium characteristics of hyper-elastic straight and curved beams. It is found that the modeling of shear deformation and finite strain is essential toward an accurate prediction of the non-linear equilibrium responses of moderately thick hyper-elastic beams. Due to simplicity and accuracy, the model can serve in the future studies dealing with the analysis of hyper-elastic structures in which two normal and shear stress components are dominant.     

深部软岩新型相似模拟材料的研制

在总结以往相似模拟材料特点的基础上,结合深部软岩强度、变形特征,本着相似材料组分简单、模型制作便捷等原则,研制了仅以河砂为骨料,松香酒精溶液为粘结剂的深部软岩新型相似模拟材料。通过对不同配比试样进行单、三轴压缩、巴西劈裂试验,获得了不同配比条件下该相似模拟材料的强度、变形、破坏特征。研究表明,通过简单的配比调配,该相似模拟材料可以较好地模拟深部大多类型的软岩,且具有组分简单、模型制作便捷、力学性能稳定、无毒无污染、价格低廉、一定程度上可重复利用等特点。     

Modeling failure in cross-anisotropic frictional materials

Three-dimensional test results for frictional materials such as soils, concrete, and rock show that the shapes of their failure surfaces are influenced by the intermediate principal stress, shear banding, and cross-anisotropy (transverse isotropy). A general 3D failure criterion for cross-anisotropic soils for both non-rotating and rotating stresses is presented and compared with experimental results for sand, clay, and sea ice. The formulation relates the loading direction to the principal directions of the cross-anisotropic microstructure of the material. The criterion is based on a function of stress, previously used as the 3D failure criterion for isotropic frictional materials, which is set equal to a scalar that varies over a sphere. The formulation is specialized for true triaxial tests and torsion shear tests and determination of material parameters is demonstrated. The failure criterion is compared with experimental results from the literature to show that it is able to capture the conditions obtained in three-dimensional experiments without and with stress rotations. The limitations of the criterion are demonstrated by its failure to capture the behavior of some cross-anisotropic materials with particular micro-structures, and the reasons for the shortcomings are discussed.     

Transient and steady state behaviors of rapid granular shear flows

Rapid granular shear flow is a classical example in granular materials which exhibits fluid-like behavior solely or fluid-like and solid-like behaviors simultaneously. We have performed experiments on annular granular shear flows using monodisperse steel spheres with 2-mm and 3-mm diameters. We discuss some transient (static failure of material due to shear) and steady-state (completely sheared and partially sheared flows) features of rapid granular flows. Our results map out the boundary between overall compaction and dilation that characterizes multiphase behavior of the system. Dimensionless stresses rise as more material is loaded into the system. On the other hand, increasing the compressive force or shear rate is equal to easing the process of shearing by decreasing the ratio of shear to normal stress.     

沥青海砂作为软岩相似材料的实验研究

为了解决岩石工程相似模型实验中传统相似材料难以模拟深部软岩低强度、大变形和强流变的问题,本文选用70#沥青(产量大、成本低、粘弹性、易成型、易软化等)和海砂作为深部软岩的相似模拟材料.采用连续加压法对其进行了单轴压缩实验,对不同配比下试件的密度、抗压强度及初始弹性模量进行分析,得到了该相似材料有关的原始数据和规律.本文初步验证了使用该相似材料模拟深部软岩的可行性,并针对不足之处给出一些合理改进建议,为进一步模型模拟实验提供指导.     

3D printed,bio-inspired prototypes and analytical models for structured suture interfaces with geometrically-tuned deformation and failure behavior

Geometrically structured interfaces in nature possess enhanced, and often surprising, mechanical properties, and provide inspiration for materials design. This paper investigates the mechanics of deformation and failure mechanisms of suture interface designs through analytical models and experiments on 3D printed polymer physical prototypes. Suture waveforms with generalized trapezoidal geometries (trapezoidal, rectangular, anti-trapezoidal, and triangular) are studied and characterized by several important geometric parameters: the presence or absence of a bonded tip region, the tip angle, and the geometry. It is shown that a wide range (in some cases as great as an order of magnitude) in stiffness, strength, and toughness is achievable dependent on tip bonding, tip angle, and geometry. Suture interfaces with a bonded tip region exhibit a higher initial stiffness due to the greater load bearing by the skeletal teeth, a double peak in the stress–strain curve corresponding to the failure of the bonded tip and the failure of the slanted interface region or tooth, respectively, and an additional failure and toughening mechanism due to the failure of the bonded tip. Anti-trapezoidal geometries promote the greatest amplification of properties for suture interfaces with a bonded tip due the large tip interface area. The tip angle and geometry govern the stress distributions in the teeth and the ratio of normal to shear stresses in the interfacial layers, which together determine the failure mechanism of the interface and/or the teeth. Rectangular suture interfaces fail by simple shearing of the interfaces. Trapezoidal and triangular suture interfaces fail by a combination of shear and tensile normal stresses in the interface, leading to plastic deformation, cavitation events, and subsequent stretching of interface ligaments with mostly elastic deformation in the teeth. Anti-trapezoidal suture interfaces with small tip angles have high stress concentrations in the teeth and fail catastrophically by tooth failure, whereas larger tip angles exhibit a shear failure of the interfaces. Therefore, larger tip angles and trapezoidal or triangular geometries promote graceful failure, and smaller tip angles and anti-trapezoidal geometries promote more brittle-like failure. This dependence is reminiscent of biological systems, which exhibit a range of failure behaviors with limited materials and varied geometry. Triangular geometries uniquely exhibit uniform stress distributions in its teeth and promote the greatest amplification of mechanical properties. In both the bonded and unbonded cases, the predictions from the presented analytical models and experimental results on 3D printed prototypes show excellent agreement. This validates the analytical models and allows for the models to be used as a tool for the design of new materials and interfaces with tailored mechanical behavior.     

An extended strain energy density failure criterion by differentiating volumetric and distortional deformation

We extend Sih’s strain energy density criterion (Sih, 1974) for crack kinks and material failure by weighting differently the volumetric and distortional parts in the extended strain energy density factor. The work is inspired by the factor that failure by microscopic shearing governed by distortion and microscopic separation controlled by hydrostatic tension represent distinct deformation processes, and should be treated differently as we count their influences to material failure. With the weight parameter introduced to the extended strain energy density factor criterion, we explain satisfactorily several critical experiments which reported crack kink in samples subjected to mixed-mode loading. The extended strain energy density idea is also used to derive a generalized pressure-dependent yielding criterion, which supplies a theoretical basis for those novel strength criteria for materials like bulk metallic glasses. Corresponding methods to determine the two material parameters, the critical strain energy density factor and the weight parameter quantifying the relative contribution by distortion over volumetric deformation, are discussed.     

An analog experiment of magma fragmentation: behavior of rapidly decompressed starch sirup

Paper reports a result of analog experiments regarding the simulation of magma fragmentation. We filled a starch sirup foam, as an analog material, in a 117–240 mm long and a 50 mm diameter high pressure chamber and exposed it to a rapid decompression. The foam was prepared by mixing starch sirups of dynamic viscosities ranging from 5 to 10¹² Pa· s at temperatures ranging from 293 to 343 K with nitrogen at 2.5 MPa gauge pressure. In ejecting high-pressure foams into a low-pressure chamber, diagnostics of foam’s fragmentation process were pressure measurment and high-speed video recording. Prior to decompression experiments, we examined visco-elastic properties of foam specimens by using a rheometer. The foam deformation under decompression was found to be axial–symmetrical, and strongly coupled with bubble growth and coalescence. These effects contributed even more efficiently to fragmentation processes than previous laboratory experiments using other analog materials. Fragment shapes varied widely depending on the temperature and water concentration of starch sirup foams, which proved that fragmentation process was governed by not only ductile deformation but also brittle failure, and determined by the degree of visco-elasticities of starch sirup foams.      

聚酯纤维对透水沥青混凝土冲击压缩性能的影响

为研究聚酯纤维对透水沥青混凝土冲击压缩性能的影响，采用?74 mm钢质分离式霍普金森压杆装置对掺杂不同质量分数的聚酯纤维透水沥青混凝土进行冲击压缩实验。在静态和4个应变率下的实验结果表明，透水聚酯纤维沥青混凝土是应变率敏感性材料，具有较强应变率效应。透水聚酯纤维沥青混凝土具有较好的延展性，动态应力应变曲线分为3个阶段:弹性变形阶段、塑性变形阶段和破坏阶段。当应变率相同时，随着掺杂聚酯纤维质量分数的增大，透水沥青混凝土的冲击抗压强度呈现出先升高后降低的变化规律，掺杂聚酯纤维的质量分数为0.40%时，冲击抗压强度达到最大。冲击抗压强度约为静态抗压强度的8~13倍。