Experimental analysis of sand particles＇ lift-off and incident velocities in wind-blown sand flux

The probability distributions of sand particles' lift-off and incident velocities in a wind-blown sand flux play very important roles in the simulation of the wind-blown sand movement. In this paper, the vertical and the horizontal speeds of sand particles located at 1.0 mm above a sand-bed in a wind-blown sand flux are observed with the aid of Phase Doppler Anemometry (PDA) in a wind tunnel. Based on the experimental data, the probability distributions of not only the vertical lift-off speed but also the lift-off velocity as well as its horizontal component and the incident velocity as well as its vertical and horizontal components can be obtained by the equal distance histogram method. It is found, according to the results of the χ ²-test for these probability distributions, that the probability density functions (pdf's) of the sand particles' lift-off and incident velocities as well as their vertical components are described by the Gamma density function with different peak values and shapes and the downwind incident and lift-off horizontal speeds, respectively, can be described by the lognormal and the Gamma density functions. These pdf's depend on not only the sand particle diameter but also the wind speed.     

Probability of rebound and eject of sand particles in wind-blown sand movement

When incident particles impact into a sand bed in wind-blown sand movement, rebound of the incident particles and eject of the sand particles by the incident particles affect directly the development of wind sand flux. In order to obtain rebound and eject lift-off probability of the sand particles, we apply the particle-bed stochastic collision model presented in our pervious works to derive analytic solutions of velocities of the incident and impacted particles in the post-collision bed. In order to describe randomness inherent in the real particle-bed collision, we take the incident angle, the impact position and the direction of resultant action of sand particles in sand bed on the impacted sand particle as random variables, and calculate the rebound and eject velocities, angles and coefficients (ratio of rebound and eject velocity to incident velocity). Numerical results are found in accordance with current experimental results. The rebound and eject lift-off probabilities versus the incident and creeping velocities are predicted. The project was supported by the National Natural Science Foundation of China (10532040, 10601022). The English text was polished by Yunming Chen.     

Analysis of sand particles’ lift-off and incident velocities in wind-blown sand flux

In the research of windblown sand movement,the lift-off and incident velocities of saltating sand particles play a significant role in bridging the spatial and temporal scales from single sand particle’s motion to windblown sand flux.In this paper,we achieved wind tunnel measurements of the movement of sand particles near sand bed through improving the wind tunnel experimental scheme of paticle image velocimetry(PIV) and data processing method.And then the influence of observation height on the probability distributions of lift-off and incident velocities of sand particles was analyzed.The results demonstrate that the observation height has no obvious influence on the distribution pattern of the lift-off and incident velocities of sand particles,i.e.,the probability distribution of horizontal and vertical velocities of lift-off and incident sand particles follow a Gaussian distribution and a negative exponential distribution,respectively.However,it influences the center of the Gaussian distribution,the decay constant and the amplitude of the negative exponential distribution.     

风沙两相流跃移层中沙粒相的速度分布

从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Boltzmann方程，对风沙流研究中几种不同的分布函数及其相应的统计平均值等基本概念给出了严密的数学定义，指出了不同分布函数之间的区别和联系，在略去铅垂方向空气阻力的情况下，给出了沙粒相速度分布函数沿铅垂方向的边缘分布，作为风沙流中跃移理论的主要基础之一。利用结果对前人在风沙流研究中发现的某些重要规律和现象进行了解释。     

Effect of thermal diffusion and electrostatic force on evolution of wind-blown sand flow

A theoretical model is suggested to mathematically describe the effect of thermal diffusion from a sand-bed on evolution of a wind-blown sand flow.An upward wind field is engendered by the thermal diffusion and the coupling interaction among the horizontal and upward wind flow,saltating grains,and a kind of electrostatic force exerted on the grains are considered in this theoretical model.The numerical results show that the effect of the thermal diffusion on the evolution process of wind-blown grain flow is quite obvious and very similar to the effect of the electrostatic force on the evolution.Not only the time for the entire system to reach a steady state(called the duration time),the transport rate of grains,the mass-flux profiles and the trajectory of saltating grains are affected by the thermal diffusion and the electrostatic force exerted on saltating grains, but also the wind profiles and the temperature profiles at the steady state are affected by the wind-blown sand flow.     

Simultaneous PIV and PTV measurements of wind and sand particle velocities

Wind-blown sand is a typical example of two-phase particle-laden flows. Owing to lack of simultaneous measured data of the wind and wind-blown sand, interactions between them have not yet been fully understood. In this study, natural sand of 100–125 μm taken from Taklimakan Desert was tested at the freestream wind speed of 8.3 m/s in an atmospheric boundary layer wind tunnel. The captured flow images containing both saltating sand and small wind tracer particles, were separated by using a digital phase mask technique. The 2-D PIV (particle imaging velocimetry) and PTV (particle tracking velocimetry) techniques were employed to extract simultaneously the wind velocity field and the velocity field of dispersed sand particles, respectively. Comparison of the mean streamwise wind velocity profile and the turbulence statistics with and without sand transportation reveal a significant influence of sand movement on the wind field, especially in the dense saltating sand layer (y/δ < 0.1). The ensemble-averaged streamwise velocity profile of sand particles was also evaluated to investigate the velocity lag between the sand and the wind. This study would be helpful in improving the understanding of interactions between the wind and the wind-blown sand.     

风沙运动的沙粒带电机理及其影响的研究进展

土壤风蚀以及沙尘暴是人类面临的重大自然环境灾害之一,它直接关系着人类的生存环境和生活质量.许多国家和政府以及科学家们对此一直十分关注并开展了大量研究.由于大气和地表条件的多样性以及地表沙粒的运动与风场作用的相互耦合,导致风沙运动问题研究的复杂性.除此之外,伴随着对风沙运动机理的研究和对沙尘暴的观测,人们发现在风沙跃移运动和沙尘暴中的沙粒带有电荷并形成风沙电场.沙粒的运动不仅导致沙粒带电和风沙电场形成,而且也直接受到沙粒带电和风沙电场的影响.为了弄清风沙电的起因以及揭示其影响规律,研究人员对此进行了野外观测、实验室测量和理论推测等.本文将就这一问题重点介绍有关风沙运动中沙粒带电的机理、风沙电场分布规律、沙粒带电对风沙运动的微宏观物理量以及沙尘暴中沙粒带电对电磁波散射的影响等方面的实验和理论研究的基本概况和进展以及作者等人在此方面的研究工作.主要包含内容有:沙粒带电及其电场的基本实验测量,粒带电对风沙运动的影响,沙尘暴对电磁波衰减的影响研究以及有关风沙起电的机理研究等.同时,对这一研究领域中目前关注与存在的主要问题给予评述.图6参81      

风沙影响下铁路道碴变形模量的离散元数值分析

针对风沙区有碴铁路道床的结构特性,对其在细沙贯入下的有效变形模量研究有助于理解风沙影响下的道床动力特性。采用离散单元模型对道碴碎石和细沙颗粒进行数值建模,并对不同含沙率γ下的有效变形模量进行了数值分析。结果表明,在低含沙率下(γ<30%)沙石混合体的变形模量基本保持不变,在高含沙率下(γ>30%),变形模量随含沙率的增加呈线性降低,以上变形模量随含沙量的变化规律与试验结果相一致。基于离散单元模型的数值模拟,在细观尺度上对沙石混合体的力链强度、空间分布及配位数进行了分析,揭示了沙石混合体有效变形模量随含沙量变化的内在机理。本文工作对风沙区有碴铁路道床力学行为的研究具有一定的借鉴意义,有助于促进风沙影响下有碴铁路道床的结构设计和沙害治理。     

地表温度对颗粒跃移轨迹的影响

为了研究由地表温度变化引起的向上的垂向气流对沙粒跃移运动的影响,本文给出了考虑近地表温度变化和水平来流风场作用下的沙粒的跃移运动。在定量给出不同时刻的近地表温度和垂向风速的基础上,计算了由于太阳辐射所引起的近地表层垂向气流对沙粒跃移运动的影响,发现:垂向风速在午后可达到1.5m/s并使得沙粒跃移轨迹的最大高度和长度分别增加55.56%和73.68%;同时,与不考虑温度效应的情况不同的是,沙粒跃移轨道最大高度将随粒径变化。     

Discrete particle simulation of mixed sand transport

An Eulerian/Lagrangian numerical simulation is performed on mixed sand transport. Volume averaged Navier–Stokes equations are solved to calculate gas motion, and particle motion is calculated using Newton's equation, involving a hard sphere model to describe particle-to-particle and particle-to-wall collisions. The influence of wall characteristics, size distribution of sand particles and boundary layer depth on vertical distribution of sand mass flux and particle mean horizontal velocity is analyzed, suggesting that all these three factors affect sand transport at different levels. In all cases, for small size groups, sand mass flux first increases with height and then decreases while for large size groups, it decreases exponentially with height and for middle size groups the behavior is in-between. The mean horizontal velocity for all size groups well fits experimental data, that is, increasing logarithmically with height in the middle height region. Wall characteristics greatly affects particle to wall collision and makes the flat bed similar to a Gobi surface and the rough bed similar to a sandy surface. Particle size distribution largely affects the sand mass flux and the highest heights they can reach especially for larger particles.     

Sand particle dislodgement in windblown sand

The incipient motion of sand particle from sand bed plays a very important role in the prediction of windblown sand.In this paper,we proposed a new method for predicting the incipient motion of sand particle based on wind speed fluctuation as follows,when the wind speed is larger than the critical wind speed,if the total impulse on sand particle is larger than the critical impulse,incipient motion of sand particle would take place,otherwise if not.Furthermore,from the analysis of entrainment in the rolling and lifting modes,we come to the following conclusion.When the average wind speed is smaller than the critical wind speed,if the average wind speed is used to judge the incipient motion of sand particle,one will underestimate the number of sand particles jumping from the bed,if the instantaneous wind speed is used to judge incipient motion of sand particle,one will overestimate the number of sand particles jumping from the bed;When the average wind speed is larger than the critical wind speed,either the average or the instantaneous wind speeds is used to judge the incipientmotion of sand particles,one will overestimate the number of sand particles jumping from the bed.     

Computational studies of inertia-gravity waves radiated from upper tropospheric jets

The generation and physical characteristics of inertia-gravity waves radiated from an unstable forced jet at the tropopause are investigated through high-resolution numerical simulations of the three-dimensional Navier–Stokes anelastic equations. Such waves are induced by Kelvin–Helmholtz instabilities on the flanks of the inhomogeneously stratified jet. From the evolution of the averaged momentum flux above the jet, it is found that gravity waves are continuously radiated after the shear-stratified flow reaches a quasi-equilibrium state. The time–vertical coordinate cross-sections of potential temperature show phase patterns indicating upward energy propagation. The sign of the momentum flux above and below the jet further confirms this, indicating that the group velocity of the generated waves is pointing away from the jet core region. Space–time spectral analysis at the upper flank level of the jet shows a broad spectral band, with different phase speeds. The spectra obtained in the stratosphere above the jet show a shift toward lower frequencies and larger spatial scales compared to the spectra found in the jet region. The three-dimensional character of the generated waves is confirmed by analysis of the co-spectra of the spanwise and vertical velocities. Imposing the background rotation modifies the polarization relation between the horizontal wind components. This out-of-phase relation is evidenced by the hodograph of the horizontal wind vector, further confirming the upward energy propagation. The background rotation also causes the co-spectra of the waves high above the jet core to be asymmetric in the spanwise modes, with contributions from modes with negative wavenumbers dominating the co-spectra. Dedicated to the memory of our colleague Dr. Binson Joseph     

Wave-induced liquefaction of a saturated sand layer

The paper presents a theoretical study of the dynamic liquefaction of a saturated sand layer. The motion of the sand is induced by a periodic disturbance at the lower boundary of the layer, which simulates the influence of a plane excitation wave coming from below. The initial boundary value problem is solved numerically with the use of the hypoplastic constitutive equation for particular sand. Both horizontal and vertical disturbances are considered. The repeated deformation caused by a strong dynamic disturbance results in the reduction of the effective pressure and in the liquefaction of the sand. The degree of liquefaction as a function of the depth is nonuniform. The liquefaction patterns produced by vertical and horizontal disturbances are completely different. Received February 22, 2000     

Weighted averaged equations for modeling velocity profiles of 1D steady open channel flows

A new mathematical algorithm is proposed to address the essential details of vertical distributions of horizontal velocity for one‐dimensional steady open‐channel flow. This new algorithm comprises a system of weighted averaged equations developed from corresponding Reynolds equations by performing weighted average operations instead of conventional depth average operations. It is the system of weighted averaged equations, instead of the vertical grids, that allows for more hydraulic coefficients identifiable. It can be thought of as an extension of the St. Venant equations to address the vertical distributions of horizontal velocities, as well as the water surface profiles. To avoid the difficult expansion of governing partial differential equations in high order, an indirect scheme is proposed to solve hydraulic variables through their weighted average values. The governing partial differential equations are generated by using a variety of weight functions, and the weighted averages of relevant hydraulic variables are taken as the unknown independent variables to be solved first. Then, on the basis of the values and polynomial expansions of these weighted averaged velocities, a system of linear algebraic equations is generated and the unknown hydraulic variables or their coefficients are easily solved. Note that the new model is not proposed to compete with any three‐dimensional models in modeling accuracy or accommodation ability to all conditions. It just provides a valuable option to study the vertical structure of flow in open channels where only essential detail and reasonable accuracy of vertical distributions are required, and the data availability and other conditions limit the application of fully three‐dimensional models. The performance of the model is evaluated with experimental data of flows in two different flumes. It is shown that the model well predicted the velocity profiles of sections along the centerlines of these flumes with reasonable accuracy and essential details of vertical distributions of horizontal velocity. Copyright © 2013 John Wiley & Sons, Ltd.     

Shear wave velocity in sand considering the effects of frequency based on particle contact theory

Since the shear waves involved in in-situ and laboratory measurement methods vary significantly in terms of the frequency range, it is necessary to consider the effects of frequency on the shear wave velocity. In this study, sand particles are assumed to be spherical solid particles with an equal radius and identical material properties, and sand skeletons are regarded as granular aggregations generated through the random packing of sand particles. It is also assumed that the sand particles only undergo elastic deformation during shear wave propagation. Based on a spherical particle model, a formula is obtained for calculating the shear wave velocity in sand, with the shear wave frequency as an extra influencing parameter. The quantitative calculations demonstrate that the shear wave velocity decreases with an increase of sand porosity, and accelerates with increases of vertical effective stress and elastic modulus of the sand particles. It is also indicated that both the particle density and Poisson’s ratio of the sand particles have negligible effects on the shear wave propagation. The frequency dispersion characteristics of shear wave propagating in sand are also discussed. Moreover, the critical frequency is defined and its analytical expression is derived. The calculation results obtained using the proposed equations agree well with the in-situ measurement results and bender element test data.     

SEMI-IMPLICIT FINITE VOLUME SHALLOW-WATER FLOW AND SOLUTE TRANSPORT SOLVER WITH k–ε TURBULENCE MODEL

A 3D semi-implicit finite volume scheme for shallow- water flow with the hydrostatic pressure assumption has been developed using the σ-co-ordinate system, incorporating a standard k–ε turbulence transport model and variable density solute transport with the Boussinesq approximation for the resulting horizontal pressure gradients. The mesh spacing in the vertical direction varies parabolically to give fine resolution near the bed and free surface to resolve high gradients of velocity, k and ε. In this study, wall functions are used at the bed (defined by the bed roughness) and wind stress at the surface is not considered. Surface elevation gradient terms and vertical diffusion terms are handled implicitly and horizontal diffusion and source terms explicitly, including the Boussinesq pressure gradient term due to the horizontal density gradient. The advection terms are handled in explicit (conservative) form using linear upwind interpolation giving second-order accuracy. A fully coupled solution for the flow field is obtained by substi- tuting for velocity in the depth-integrated continuity equation and solving for surface elevation using a conjugate gradient equation solver. Evaluation of horizontal gradients in the σ-co-ordinate system requires high-order derivatives which can cause spurious flows and this is avoided by obtaining these gradients in real space. In this paper the method is applied to parallel oscillatory (tidal) flow in deep and shallow water and compared with field measurements. It is then applied to current flow about a conical island of small side slope where vortex shedding occurs and velocities are compared with data from the laboratory. Computed concentration distributions are also compared with dye visualization and an example of the influence of temperature on plume dispersion is presented. © 1997 John Wiley & Sons, Ltd.     

Single-beam gamma densitometry measurements of oil–water flow in horizontal and slightly inclined pipes

Gamma densitometry is a frequently used non-intrusive method for measuring component volume fractions in multiphase flow systems. The application of a single-beam gamma densitometer to investigate oil–water flow in horizontal and slightly inclined pipes is presented. The experiments are performed in a 15 m long, 56 mm diameter, inclinable stainless steel pipe using Exxsol D60 oil (viscosity 1.64 mPa s, density 790 kg/m³) and water (viscosity 1.0 mPa s, density 996 kg/m³) as test fluids. The test pipe inclination is changed in the range from 5° upward to 5° downward. Experimental measurements are reported at three different mixture velocities, 0.25, 0.50 and 1.00 m/s, and the inlet water cut is varied from 0 to 1. The gamma densitometer is composed of radioactive isotope of Am-241 with the emission energy of 59.5 keV, scintillation detector [NaI(Tl)] and signal processing system. The time averaged cross-sectional distributions of oil and water phases are measured by traversing the gamma densitometer along the vertical pipe diameter. Based on water volume fraction measurements, water hold-up and slip ratio are estimated. The total pressure drop over the test section is measured and frictional pressure drop is estimated based on water hold-up measurements. The measurement uncertainties associated with gamma densitometry are also discussed. The measured water hold-up and slip ratio profiles are strongly dependent on pipe inclination. In general, higher water hold-up values are observed in upwardly inclined pipes compared to the horizontal and downwardly inclined pipes. At low mixture velocities, the slip ratio decreases as the water cut increases. The decrease is more significant as the degree of inclination increases. The frictional pressure drop for upward flow is slightly higher than the horizontal flow. In general, there is a marginal difference in frictional pressure drop values for horizontal and downwardly inclined flows.     

平面激波加载下砂墙结构的冲击响应特性

砂墙结构在爆炸安全防护领域具有广泛应用,为了研究激波加载下砂墙结构的冲击响应特性,基于水平激波管实验装置,开展平面激波冲击砂墙结构系列实验,采用高速纹影摄像系统捕捉流场中激波波系的演化过程和砂墙结构的运动过程。入射激波马赫数为1.827~2.413,相应入射激波载荷强度为0.378~0.724 MPa。砂墙结构利用铁砂、矾土、石英砂3种实验用砂制备,所制备砂墙结构孔隙度分别为56.6%、69.3%、56.6%。高速纹影照片显示:平面激波冲击砂墙结构发生反射和透射,伴随入射激波和透射激波的传播,在百微秒内,砂墙未产生显著运动,表现出显著的类固体动力学响应特性。基于冲击理论,确定了铁砂墙、矾土砂墙、石英砂墙的线性冲击关系,冲击关系中线性常数λ值量级为100,根据凝聚介质实用状态方程推断:较低强度载荷冲击作用下,砂墙主要产生体积变形,而由冲击引起的热能效应则可以忽略。     

Effects of viscous dissipation on a power-law fluid over plate embedded in a porous medium

The present study is devoted to investigate the influences of viscous dissipation on buoyancy induced flow over a horizontal or a vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained with prescribed variable surface temperature (PT) or with prescribed variable surface heat flux (PHF) for the horizontal plate case. While, the similarity solutions are obtained with prescribed variable surface heat flux for the vertical plate case. Different similar transformations, for each case, are used. Numerical results for the details of the velocity and temperature profiles are shown on graphs. Nusselt number associated with temperature distributions and excess surface temperature associated with heat flux distributions which are entered in tables have been presented for different values of the power-law index n and the exponent as well as Eckert number.     

砂土初始孔隙比空间变异性对其力学特性及破坏模式的影响分析

现有研究大多采用简单的摩尔库伦模型针对土的空间变异性对边坡或基础的安全系数或失效概率做计算分析.事实上临界状态本构模型,如SIMSAND,能更准确地反映土的应力-应变关系.为此,本文采用SIM-SAND模型,针对砂土初始孔隙比的空间变异性对其力学特性及破坏模式的影响做详细分析,算例采用简单的室内平面应变双轴试验,分为松砂排水、密砂排水、松砂不排水和密砂不排水四种情况.每一种情况均采用蒙特卡罗方法进行初始孔隙比的随机分布生成,并做大量计算,以此来分析初始孔隙比的不均匀性对剪切带生成和破坏模式和竖向承载力发展及其概率密度分布的影响.