Experimental investigation of particle velocity distributions in windblown sand movement

With the PDPA (Phase Doppler Particle Analyzer) measurement technology, the probability distributions of particle impact and lift-off velocities on bed surface and the particle velocity distributions at different heights are detected in a wind tunnel. The results show that the probability distribution of impact and lift-off velocities of sand grains can be expressed by a log-normal function, and that of impact and lift-off angles complies with an exponential function. The mean impact angle is between 28° and 39°, and the mean lift-off angle ranges from 30° to 44°. The mean lift-off velocity is 0.81–0.9 times the mean impact velocity. The proportion of backward-impacting particles is 0.05–0.11, and that of backward-entrained particles ranges from 0.04 to 0.13. The probability distribution of particle horizontal velocity at 4 mm height is positive skew, the horizontal velocity of particles at 20 mm height varies widely, and the variation of the particle horizontal velocity at 80 mm height is less than that at 20 mm height. The probability distribution of particle vertical velocity at different heights can be described as a normal function. Supported by the National Natural Science Foundation of China (Grant No. 10532030) and the National Basic Research Program of China (Grant No. G2000048702)     

A probability density function of liftoff velocities in mixed-size wind sand flux

With the discrete element method (DEM), employing the diameter distribution of natural sands sampled from the Tengger Desert, a mixed-size sand bed was produced and the particle-bed collision was simulated in the mixed-size wind sand movement. In the simulation, the shear wind velocity, particle diameter, incident velocity and incident angle of the impact sand particle were given the same values as the experimental results. After the particle-bed collision, we collected all the initial velocities of rising sand particles, including the liftoff angular velocities, liftoff linear velocities and their horizontal and vertical components. By the statistical analysis on the velocity sample for each velocity component, its probability density functions were obtained, and they are the functions of the shear wind velocity. The liftoff velocities and their horizontal and vertical components are distributed as an exponential density function, while the angular velocities are distributed as a normal density function. Supported by the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)     

风沙运动的DPM数值模拟

采用离散颗粒模型对风沙气固两相流动进行了数值计算．在该模型中,采用体平均的Navier-Stokes方程来描述气相的运动,对离散颗粒采用拉格朗日方法模拟,求解颗粒运动方程．采用硬球模型描述颗粒问碰撞作用．计算结果表明,沙粒平均水平速度廓线在0．02 m以上高度可以表示为按对数函数或幂函数规律增加,在0．02 m以下则发生偏离;在大于0．02 m的高度,输沙通量随高度按指数规律衰减,而在地面附近由于颗粒蠕移的影响发生偏离,这与已有文献结果一致。本文的模拟有助于风沙运动规律的研究与掌握。     

Double exposure, multiple-field particle image velocimetry for turbulent probability density

A particle image velocimeter method is described in which double exposed fields of particles moving in a two-dimensional slice of a steady turbulent flow are photographed repeatedly to build up a statistical ensemble of flow field realizations on a single photographic plate. Each interrogation spot on the plate contains a sample of the probability density function of the two components of velocity that lie in the photographic object plane, assuming paraxial photography. Theory is developed showing how this sample can be measured by two-dimensional spatial correlation analysis, followed by deconvolution to remove the effects of finite particle image size. The probability density measurements are biased inherently against large velocities, but these effects can be minimized and/or corrected.     

三维混合沙输运数值模拟

采用计算流体力学和颗粒离散元耦合的方法模拟了三维混合沙输运过程。采用体平均的Navier-stokes方程来描述气相运动,考虑了气相和颗粒相的相互作用。颗粒运动通过求解牛顿运动方程来求解,采用硬球模型描述颗粒和颗粒及颗粒和壁面的碰撞。本模型中,颗粒运动是三维的而气相运动是二维的。计算结果表明:总输沙率沿高度方向在大于2cm以上按照指数衰减,在2 cm以下则偏大;各粒径颗粒具有不同的输沙率分布,粗粒径颗粒按指数规律衰减,其它粒径颗粒输沙率随高度先指数增加后减少;各粒径颗粒平均水平速度随高度对数函数增加且同高度时随粒径增大而减小,1 cm高度以下则相反;沙粒平均粒径沿高度线性递减,2 cm以下粒径偏大。     

基于矢量水听器的深海直达波区域声传播特性及其应用

对于深海近水面声源产生的声场, 处于较大深度处的接收器在一定水平距离范围内能接收到直达波. 2014年在某深海海域进行的水声考察实验中, 应用深度为140 m的拖曳声源发射实验信号, 布放在水下3146 m深处的矢量水听器成功地接收到了直达波信号. 本文应用射线理论, 分析了深海直达波区域声场的传播特性, 得出了水平振速与垂直振速的传播损失与声线到达接收点处的掠射角以及收发水平距离之间的关系. 在以上分析的基础上, 提出了一种利用水平振速与垂直振速的能量差估计声源距离的方法, 并结合2014年实验数据对实验中两条航线上8 km范围内的目标声源进行了测距, 测距结果与目标的GPS数据符合得较好.     

Lift-off characteristics of triple flame with concentration gradient

The concentration gradient and uniform mean velocity of a triple flame in a mixing layer were studied using a multi-slot burner, which can stabilize the lift-off flame especially at a very small concentration gradient. Flame stabilization conditions were examined, and the lift-off heights of the triple flame were measured for methane and propane flames. A hot-wire anemometer was used to measure the velocity distributions. Mass spectroscopy (for methane) and Rayleigh scattering (for propane) were used to measure the concentration gradients. OH radical distribution was measured by laser-induced fluorescence (LIF), and in-stream velocity variation was measured with particle-image velocimetry (PIV). Maximum in-stream temperatures were measured using the coherent anti-Stokes Raman scattering (CARS) technique. Lift-off heights of triple flames have minimum values during the increase of concentration gradient, and the propagation velocity of triple flames reaches its maximum at a critical concentration gradient. This is caused by three factors: velocity distribution upstream, flammable limit of premixed gas, and reaction of diffusion flame. The critical concentration gradient, which maximizes the propagation velocity is suggested as a new criterion of transition from a premixed flame to a triple flame.     

Dynamics of drag and force distributions for projectile impact in a granular medium

Our experiments and molecular dynamics simulations on a projectile penetrating a two-dimensional granular medium reveal that the mean deceleration of the projectile is constant and proportional to the impact velocity. Thus, the time taken for a projectile to decelerate to a stop is independent of its impact velocity. The simulations show that the probability distribution function of forces on grains is time independent during a projectile's deceleration in the medium. At all times the force distribution function decreases exponentially for large forces.     

Velocity statistics in excited granular media

We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3-8 times the gravitational acceleration), the probability distribution P(v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P(v) approximately exp(-mid R:v/v(c)mid R:(1.5)), in agreement with a recent theory. The characteristic velocity v(c) is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy. (c) 1999 American Institute of Physics.     

Simulations of turbulent lifted jet flames with two-dimensional conditional moment closure

Simulations of H₂ air lifted jet flames are presented, obtained in terms of two-dimensional, first-order conditional moment closure (CMC). The unsteady CMC equation with detailed chemistry is solved without the need for operator splitting, while the accompanying flow field is determined using commercial CFD software employing a k − ε turbulence model. Computed lift-off heights and Favre-averaged species mole fractions are found to be very close to values obtained experimentally for a wide range of jet velocities and fuel–air mixtures. Simulations for which the initial condition is an attached flame and the jet velocity gradually increased do not result in lift-off, a result fully consistent with experimental observation and capturing the hysteresis behaviour of lifted flames. The stabilisation mechanism is explored by quantifying the balance of terms comprising the CMC in the lift-off region. In line with experimental data, it is found that the scalar dissipation rate at the stabilisation height is well below the extinction value, and that axial transport and molecular diffusion play a major role. The radial components of spatial convection and diffusion are always small, fully justifying the alternative approach of employing a cross-stream averaged CMC.     

风沙稳定输运中起跳沙粒运动状态分布函数

本文用气固二相流模型模拟了风沙稳定输运过程。若起跳沙粒运动状态分布函数采用由实验得到的正态分布函数形式时,计算出的水平质量流量通量随高度的变化规律与实验结果不同。经深入分析,本文提出一新的起跳沙粒运动状态分布函数形式。其中初始起跳角的分布仍采用正态分布函数形式,而对初始起跳速度则采用指数函数和正态分布函数的分段函数形式。计算结果表明本文提出的起跳沙粒运动状态分布函数与实际情况吻合较好。     

基于辅助粒子滤波算法的红外目标跟踪

针对红外目标在跟踪中计算复杂的问题,构建辅助粒子滤波算法。利用贝叶斯重要性采样算法,在权值大的粒子基础上引入辅助粒子变量,然后重新定义重要采样分布函数,防止重采样后粒子概率密度变化。两次加权计算,使粒子权值比仅用重采样的粒子权值变化更稳定,采样点最接近真实状态;同时不同权值粒子的概率阈值可作为粒子滤波是否完成的判断准则。在二维平面构造红外运动目标模型中,系统为零均值高斯白噪声。仿真数据表明:该算法在x,y方向的均方误差、画面处理时间、RM SE性能上优于粒子滤波算法和重采样粒子滤波算法。     

基于相场方法的孔隙尺度油水两相流体流动模拟

基于真实岩心颗粒粒径分布,利用过程法构建疏松砂岩油藏的三维孔隙结构模型,利用相场方法建立两相流体流动数学模型并利用有限元方法进行求解,研究驱替速度、流体性质、润湿性对剩余油分布以及采出程度的影响.结果表明：驱替速度的增大和油水粘度比的减小会导致较大的毛管数,进而有利于采出程度的提高;就润湿性而言,水湿条件下毛管力是水驱油的动力,而在油湿条件下是阻力,因此水湿岩心采出程度更高.同时,从孔隙尺度对油水渗流机理及剩余油分布机理进行揭示,结果表明：由于多孔介质的复杂孔隙结构,流体在流经不同孔隙时呈现不同的流动特征,进而对油水两相流整体的压力分布、流速分布造成重要影响.     

Statistics of particle pair relative velocity in the homogeneous shear flow

Small scale clustering of inertial particles and relative velocity of particle pairs have been fully characterized for statistically steady homogeneous isotropic flows. Depending on the particle Stokes relaxation time, the spatial distribution of the disperse phase results in a multi-scale manifold characterized by local particle concentration and voids and, because of finite inertia, the two nearby particles have high probability to exhibit large relative velocities. Both effects might explain the speed-up of particle collision rate in turbulent flows. Recently it has been shown that the large scale geometry of the flow plays a crucial role in organizing small scale particle clusters. For instance, a mean shear preferentially orients particle patterns. In this case, depending on the Stokes time, anisotropic clustering may occur even in the inertial range of scales where the turbulent fluctuations which drive the particles have already recovered isotropy. Here we consider the statistics of particle pair relative velocity in the homogeneous shear flow, the prototypical flow which manifests anisotropic clustering at small scales. We show that the mean shear, by imprinting anisotropy on the large scale velocity fluctuations, dramatically affects the particle relative velocity distribution even in the range of small scales where the anisotropic mechanisms of turbulent kinetic energy production are sub-dominant with respect to the inertial energy transfer which drives the carrier fluid velocity towards isotropy. We find that the particles’ populations which manifest strong anisotropy in their relative velocities are the same which exhibit small scale clustering. In contrast to any Kolmogorov-like picture of turbulent transport these phenomena may persist even below the smallest dissipative scales where the residual level of anisotropy may eventually blow-up. The observed anisotropy of particle relative velocity and spatial configuration is suggested to influence the directionality of the collision probability, as inferred on the basis of the so-called “ghost collision” model.     

Suspension and fall of heavy particles in random two-dimensional flow

We investigate the settling of heavy particles in a steady, two-dimensional random velocity field, and find instances in which particle suspension occurs. This leads to a bimodal velocity distribution that may explain some apparently conflicting results reported in the literature. The bimodal distribution is typically smeared out by a time dependence of the ambient flow but, if the time variation is slow, the settling rates of some particles will be as well. The resulting broadbanded velocity distribution of the settling particles will have significance for processes such as rain drop formation, in which the spread of particle velocities affects the statistics of particle collisions.     

基于频带分解和距离加权的单矢量水听器浅海被动测距方法研究

本文针对浅海环境下中低频宽带脉冲声源被动测距问题, 提出了一种声压和水平振速联合处理的被动测距方法. 在浅海波导中, 声压和质点振速的自相关函数卷绕(warping)谱具有稳定的频率特征. 声压和水平振速的自相关卷绕谱具有相同的准线谱特征, 垂直振速自相关卷绕谱具有宽谱叠加线谱的特征, 与声压自相关卷绕谱相比, 其尖峰个数比更多, 且尖峰宽度更宽. 利用引导源, 本文提出了基于频带分解和距离加权的声压和水平振速联合被动测距方法. 利用该方法对2008年冬季青岛海域综合实验中单矢量水听器接收的气枪信号进行处理, 结果表明, 该方法能够实现气枪声源的有效测距. 与传统单声压水听器被动测距方法相比, 该方法可以有效减小代价函数的主瓣宽度、提高测距精度.     

Relation between the probability density and other properties of a stationary random process

We consider the Pope-Ching differential equation [Phys. Fluids A 5, 1529 (1993)] connecting the probability density p(x)(x) of a stationary, homogeneous stochastic process x(t) and the conditional moments of its squared velocity and acceleration. We show that the solution of the Pope-Ching equation can be expressed as n(x), where n(x) is the mean number of crossings of the x level per unit time and is the mean inverse velocity of crossing. This result shows that the probability density at x is fully determined by a one-point measurement of crossing velocities, and does not imply knowledge of the x(t) behavior outside of the infinitesimally narrow window near x.     

壁面粗糙度对水平后台阶气粒两相流动影响的PDPA实验研究

用相位多普勒颗粒测速仪(PDPA)测量了颗粒的平均与脉动速度,研究了壁面粗糙度对水平后台阶气粒两相流动的影响。研究结果表明,壁面粗糙度减小颗粒纵向平均速度,增大颗粒纵向和横向脉动速度。壁面粗糙度对流场中不同位置处颗粒运动影响的强弱不同,其中逆流区处较弱,下游处较强。壁面粗糙度对不同粒径颗粒运动影响的强弱不同,其中对细颗粒的影响较弱且被局限在壁面附近,对粗颗粒的影响较强且扩散到整个流场。     

Improvement of the pressure algorithm of the stand-alone PDF method to treat unsteady three-dimensional turbulent reacting flows

This paper deals with the particle-mesh probability density function (PDF) method. It shows how an existing but less precise pressure algorithm for the stand-alone method can be improved. The present algorithm is able to handle the general case of an unsteady three-dimensional turbulent reacting flow. The transport equation of the joint PDF of velocity and composition is solved with a particle method. Open boundary conditions are realized and for statistical reasons a simple but effective particle splitting procedure is applied.

Based on a simple configuration, the properties of the presented improved pressure algorithm are analysed. It is shown which numerical condition must be taken care of so that the algorithm is able to correct the particle positions such that the normalization condition is fulfilled as accurately as specified.

To verify the algorithm the combustion of a methane–air mixture enclosed in an open simulation volume is calculated. It is shown that the simple particle splitting algorithm works very effectively in the studied case. The behaviour of the improved pressure algorithm is examined by different calculations. To analyse the convergence of the algorithm, the particle number per cell and the grid spacing are varied. To demonstrate the accuracy, a statistically stationary inflow/outflow configuration is used and the numerical solution is compared to an analytical one. For a less symmetric test case, the previous unsteady combustion problem is simulated, including an additional mean velocity in one direction.

The presented improved pressure algorithm provides the opportunity to calculate unsteady three-dimensional turbulent reacting flows with a stand-alone method, and offers an alternative to the complex hybrid finite-volume/particle PDF method.     

Equipartition of rotational and translational energy in a dense granular gas

Experiments quantifying the rotational and translational motion of particles in a dense, driven, 2D granular gas floating on an air table reveal that kinetic energy is divided equally between the two translational and one rotational degrees of freedom. This equipartition persists when the particle properties, confining pressure, packing density, or spatial ordering are changed. While the translational velocity distributions are the same for both large and small particles, the angular velocity distributions scale with the particle radius. The probability distributions of all particle velocities have approximately exponential tails. Additionally, we find that the system can be described with a granular Boyle's law with a van?der?Waals-like equation of state. These results demonstrate ways in which conventional statistical mechanics can unexpectedly apply to nonequilibrium systems.