Analytical solutions for transverse distributions of stream-wise velocity in turbulent flow in rectangular channel with partial vegetation

The theory of poroelasticity is introduced to study the hydraulic properties of the steady uniform turbulent flow in a partially vegetated rectangular channel. Plants are assumed as immovable media. The resistance caused by vegetation is expressed by the theory of poroelasticity. Considering the influence of a secondary flow, the momentum equation can be simplified. The momentum equation is nondimensionalized to obtain a smooth solution for the lateral distribution of the longitudinal velocity. To verify the model, an acoustic Doppler velocimeter （ADV） is used to measure the velocity field in a rectangular open channel partially with emergent artificial rigid vegetation. Comparisons between the measured data and the computed results show that the method can predict the transverse distributions of stream-wise velocities in turbulent flows in a rectangular channel with partial vegetation.

Debris cloud structure and hazardous fragments distribution under hypervelocity yaw impact

This study investigates how the debris cloud structure and hazardous fragment distribution vary with attack angle by simulating a circular cylinder projectile hypervelocity impinging on a thin plate using the finite element-smoothed particle hydrodynamics(FE-SPH)adaptive method.Based on the comparison and analysis of the experimental and simulation results,the FE-SPH adaptive method was applied to address the hypervelocity yaw impact problem,and the variation law of the debris cloud structure with the attack angle was obtained.The screening criterion of the hazardous fragment at yaw impact is given by analyzing the debris formation obtained by the FE-SPH adaptive method,and the distribution characteristics of hazardous fragments and their relationship with the attack angle are given.Moreover,the velocity space was used to evaluate the distribution range and damage capability of asymmetric hazardous fragments.The maximum velocity angle was extended from fully symmetrical working conditions to asymmetrical cases to describe the asymmetrical debris cloud distribution range.In this range,the energy density was calculated to quantitatively analyze how much damage hazardous fragments inflict on the rear plate.The results showed that the number of hazardous fragments generated by the case near the 35°attack angle was the largest,the distribution range was the smallest,and the energy density was the largest.These results suggest that in this case,debris cloud generated by the impact had the strongest damage to the rear plate.

用Velocity Verlet积分器改进HMC抽样方法

Hamilton Monte Carlo (HMC)方法是一种常用的快速抽样方法.在对哈密顿方程进行抽样时,HMC方法使用Leapfrog积分器,这可能造成方程的位置及动量的迭代值在时间上不同步,其产生的误差会降低抽样效率及抽样结果的稳定性.为此,本文提出了IHMC(Improved HMC)方法,该方法用Velocity Verlet积分器替代Leapfrog积分器,每次迭代时都计算两变量在同一时刻的值.为验证方法的效果,本文进行了两个实验,一个是将该方法应用于非对称随机波动率模型(RASV模型)的参数估计,另一个是将方法应用于方差伽马分布的抽样,结果显示:IHMC方法比HMC方法的效率更高、结果更稳定.

Group velocity distribution of Rayleigh waves and crustal and upper mantle velocity structure of the Chinese mainland and its vicinity

Based on the long period digital surface wave data recorded by 11 CDSN stations and 11 IRIS stations, the dispersion curves of the group velocities of fundamental mode Rayleigh waves along 647 paths, with the periods from 10 s to 92 s, were measured by multi-filter. Their distribution at 25 central periods within the region of 18~54N, 70~140E was inverted by Dimtar-Yanovskaya method. Within the period from 10 s to 15.9 s, the group velocity distribution is laterally inhomogeneous and is closely related to geotectonic units, with two low velocity zones located in the Tarim basin and the East China Sea and its north regions, respectively. From 21 s to 33 s, the framework of tectonic blocks is revealed. From 36.6 s to 40 s, the lithospheric subdivision of the Chinese mainland is obviously uncovered, with distinct boundaries among the South-North seismic belt, the Tibetan plateau, the North China, the South China and the Northeast China. Four cross-sections of group velocity distribution with period along 30N, 38N, 90E and 120E, are discussed, respectively, which display the basic features of the crust and upper mantle of the Chinese mainland and its neighboring regions. There are distinguished velocity differences among the different tectonic blocks. There are low-velocity-zones (LVZ) in the middle crust of the eastern Tibetan plateau, high velocity featured as stable platform in the Tarim basin and the Yangtze platform, shallow and thick low-velocity-zone in the upper mantle of the North China. The upper mantle LVZ in the East China Sea and the Japan Sea is related to the frictional heat from the subduction of the Philippine slab and the strong extension since the Himalayan orogenic period.

Sand particle lift-off velocity measurements and numerical simulation of mass flux distributions in a wind tunnel

Lift-off velocity of saltating sand particles in wind-blown sand located at 1.0 mm above the sand bed surface was measured using a phase Doppler particle analyzer in a wind tunnel. The results show that the probability distribution of lift-off velocity can be expressed as a lognormal function, while that of lift-off angle follows an exponential function. The probability distribution of lift-off angle conditioned for each lift-off velocity also follows an exponential function, with a slope that becomes steeper with increasing lift-off velocity. This implies that the probability distribution of lift-off velocity is strongly dependent on the lift-off angle. However, these lift-off parameters are generally treated as an independent joint probability distribution in the literature. Numerical simulations were carried out to investigate the effects of conditional versus independent joint probability distributions on the vertical sand mass flux distribution. The simulation results derived from the conditional joint probability distribution agree much better with experimental data than those from the independent ones. Thus, it is better to describe the lift-off velocity of saltating sand particles using the conditional joint probability distribution. These results improve our understanding of saltation processes in wind-blown sand.

Numerical investigation of velocity distribution of turbulent flow through vertically double-layered vegetation

The velocity structures of flow through vertically double-layered vegetation(VDLV)as well as single-layered rigid vegetation(SLV)were investigated computationally with a three-dimensional(3D)Reynolds stress turbulence model,using the computational fluid dynamics(CFD)code FLUENT.The detailed velocity distribution was explored with a varying initial Froude number(Fr),with consideration of the steady subcritical flow conditions of an inland tsunami.In VDLV flows,the numerical model successfully captured the inflection point in the profiles of mean streamwise velocities in the mixing-layer region around the top of short submerged vegetation.An upward and downward movement of flow occurred at the positions located just behind the tall and short vegetation,respectively.Overall,higher streamwise velocities were observed in the upper vegetation layer due to high porosity,with Pr=98%(sparse vegetation,where Pr is the porosity),as compared to those in the lower vegetation layer,which had comparatively low porosity,with Pr=91%(dense vegetation).A rising trend of velocities was found as the flow passed through the vegetation region,followed by a clear sawtooth distribution,as compared to the regions just upstream and downstream of vegetation where the flow was almost uniform.In VDLV flows,a rising trend in the flow resistance was observed with the increase in the initial Froude number,i.e.,Fr?0.67,0.70,and 0.73.However,the flow resistance in the case of SLV was relatively very low.The numerical results also show the flow structures within the vicinity of short and tall vegetation,which are difficult to attain through experimental measurements.

Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation

An analytical solution for predicting the vertical distribution of streamwise mean velocity in an open channel flow with submerged flexible vegetation is proposed when large bending occurs. The flow regime is separated into two horizontal layers： a vegetation layer and a free water layer. In the vegetation layer, a mechanical analysis for the flexible vegetation is conducted, and an approximately linear relationship between the drag force of bending vegetation and the streamwise mean flow velocity is observed in the case of large deflection, which differes significantly from the case of rigid upright vegetation. Based on the theoretical analysis, a linear streamwise drag force-mean flow velocity expression in the momentum equation is derived, and an analytical solution is obtained. For the free water layer, a new expression is presented, replacing the traditional logarithmic velocity distribution, to obtain a zero velocity gradient at the water surface. Finally, the analytical predictions are compared with published experimental data, and the good agreement demonstrates that this model is effective for the open channel flow through the large deflection flexible vegetation.

Velocity distribution of the flow field in the cyclonic zone of cyclone-static micro-bubble flotation column

Laboratory experiments have been conducted to study the flow field in a cyclone static micro-bubble flotation column. The method of Particle Image Velocimetry (PIV) was used. The flow field velocity distribution in both cross section and longitudinal section within cyclonic zone was studied for different circulating volumes. The cross sectional vortex was also analyzed. The results show that in cross section as the circulating volume increases from 0.187 to 0.350 m 3 /h, the flow velocity ranges from 0 to 0.68 m/s. The flow field is mainly a non-vortex potential flow that forms a free vortex without outside energy input. In the cyclonic region the vortex deviates from the center of the flotation column because a single tangential opening introduces circulating fluid into the column. The tangential component of the velocity plays a defining role in the cross section. In the longitudinal section the velocity ranges from 0 to 0.08 m/s. The flow velocity increases as does the circulating volume. Advantageous mineral separation conditions arise from the combined effects of cyclonic flow in cross and longitudinal section.

Velocity distribution of flow with submerged flexible vegetations based on mixing-length approach

By choosing a PVC slice to simulate flexible vegetation, we carried out experiments in an open channel with submerged flexible vegetation. A 3D acoustic Doppler velocimeter （micro ADV） was used to measure local flow velocities and Reynolds stress. The results show that hydraulic characteristics in non-vegetation and vegetation layers are totally different. In a region above the vegetation, Reynolds stress distribution is linear, and the measured velocity profile is a classical logarithmic one. Based on the concept of new-riverbed, the river compression parameter representing the impact of vegetation on river is given, and a new assumption of mixing length expression is made. The formula for time-averaged velocity derived from the expression requires less parameters and simple calculation, and is useful in applications.

PROBABILITY DISTRIBUTION FUNCTION OF NEAR-WALL TURBULENT VELOCITY FLUCTUATIONS

By large eddy simulation （LES）, turbulent databases of channel flows at different Reynolds numbers were established. Then, the probability distribution functions of the streamwise and wall-normal velocity fluctuations were obtained and compared with the corresponding normal distributions. By hypothesis test, the deviation from the normal distribution was analyzed quantitatively. The skewness and flatness factors were also calculated. And the variations of these two factors in the viscous sublayer, buffer layer and log-law layer were discussed. Still illustrated were the relations between the probability distribution functions and the burst events-sweep of high-speed fluids and ejection of low-speed fluidsIin the viscous sub-layer, buffer layer and loglaw layer. Finally the variations of the probability distribution functions with Reynolds number were examined.

In situ measurement on nonuniform velocity distributionin external detonation exhaust flow by analysis ofspectrum features using TDLAS

Instantaneous and precise velocity sensing is a critical part of research on detonation mechanism and flow evolution.This paper presents a novel multi-projection tunable diode laser absorption spectroscopy solution,to provide a real-time and reliable measurement of velocity distribution in detonation exhaust flow with obvious nonuniformity.Relations are established between overlapped spectrums along probing beams and Gauss velocity distribution phantom according to the frequency shifts and tiny variations in components of light-of-sight absorbance profiles at low frequencies analyzed by the fast Fourier transform.With simulated optical measurement using H2O feature at 7185.6 cm-1 carried out on a phantom generated using a simulation of two-phase detonation by a two-fluid model,this method demonstrates a satisfying performance on recovery of velocity distribution profiles in supersonic flow even with a noise equivalent absorbance up to 2×10^(-3).This method is applied to the analysis of rapidly decreasing velocity during a complete working cycle in the external flow field of an air-gasoline detonation tube operating at 25 Hz,and results show the velocity in the core flow field would be much larger than the arithmetic average from traditional tunable diode laser doppler velocimetry.This proposed velocity distribution sensor would reconstruct nonuniform velocity distribution of high-speed flow in low cost and simple operations,which broadens the possibility for applications in research on the formation and propagation of external flow filed of detonation tube.

Effect of number density on velocity distributions in a driven quasi-two-dimensional granular gas

The motion of mono-disperse spherical steel particles in a vibration driven quasi-two-dimensional （2D） square cell is studied. The cell is horizontally vibrated to eliminate the effect of gravity compaction. The velocity distributions at different particle number densities are studied and found to obey the form exp[-β（｜Vy｜/σy）α], in which Vy and （σy are velocity and its variance in the transverse direction, and α and β are fitting parameters. The value of α is found to decrease with the number density of particles increasing. To investigate the effect of the bottom plate, the molecular dynamics simulation without considering any bottom friction is performed. The accordance between the simulation result and the experimental result shows that the influence of bottom plate friction force on the high energy tail of the velocity distribution can be neglected.

Lateral Shear Layer and Its Velocity Distribution of Flow in Rectangular Open Channels

The lateral velocity distribution of flow in the shear layer of open channel is required to many problems in river and eco-environment engineering, e.g. distribution of pollutant dispersion, sediment transport and bank erosion, and aquatic habitat. It is not well understood about how the velocity varies laterally in the wall boundary layer. This paper gives an analytical solution of lateral velocity distribution in a rectangular open channel based on the depth-averaged momentum equation proposed by Shiono & Knight. The obtained lateral velocity distributions in the wall shear layer are related to the two hydraulic parameters of lateral eddy viscosity (λ) and depth-averaged secondary flow (Γ) for given roughened channels. Preliminary relationships between the above two parameters and the aspect ratio of channel, B/H, are obtained from two sets of experimental data. The lateral width (δ) of the shear layer was investigated and found to relate to the λ and the bed friction factor (f), as described by Equation (26). This study indicates that the lateral shear layer near the wall can be very wide (δ/H = 14.6) for the extreme case (λ = 0.6 and f = 0.01).

Prediction of boundary shear stress distribution in straight open channels using velocity distribution

Conventional methods for measuring local shear stress on the wetted perimeter of open channels are related to the measurement of the very low velocity close to the boundary.Measuring near-zero velocity values with high fluctuations has always been a difficult task for fluid flow near solid boundaries.To solve the observation problems,a new model was developed to estimate the distribution of boundary shear stress from the velocity distribution in open channels with different cross-sectional shapes.To estimate the shear stress at a point on the wetted perimeter by the model,the velocity must be measured at a point with a known normal distance to the boundary.The experimental work of some other researchers on channels with various cross-sectional shapes,including rectangular,trapezoidal,partially full circular,and compound shapes,was used to evaluate the performance of the proposed model.Optimized exponent coefficients for the model were found using the multivariate Newton method with the minimum of the mean absolute percentage error(MAPE)between the model and experimental data as the objective function.Subsequently,the calculated shear stress distributions along the wetted perimeter were compared with the experimental data.The most important advantage of the proposed model is its inherent simplicity.The mean MAPE value for the seven selected cross-sections was 6.9%.The best results were found in the cross-sections with less discontinuity of the wetted perimeter,including the compound,trapezoidal,and partially full circular pipes.In contrast,for the rectangular cross-section with an angle between the bed and walls of 90°,MAPE increased due to the large discontinuities.

Experimental Study on the Distribution of Velocity and Pressure near a Submarine Pipeline

As a transport means of oil and gas the submarine pipeline has many merits, such as continuous delivery, large conveying capacity, convenient management, etc. A tube was chosen in our study to simulate the submarine pipeline in the experiments. A high accuracy instrument ADV and high precision point-type pressure sensors were used to measure the parameters of the flow field, including the pressure distribution, velocities at seven cross sections near the submarine pipeline with five different clearance ratios, and twelve dynamic pressure values around the pipeline. The pressure distributions and velocity changes around the pipe under dif- ferent flow velocities and clearance ratios were analyzed. These results might be useful for further study of submarine pipeline ero- sion and protection.

rwo-phase pore-fluid distribution in fractured media, acoustic wave velocity vs saturation

关于声波速度与流体饱和度的关系已开展了大量实验工作,声波速度随饱和度的变化规律与孔隙流体在孔隙尺度范围分布的不均匀性有关,从理论上采用等效流体模型来定量表征通常存在着较大偏差。从弹性波动理论出发,以纵波震源作为激发震源项,采用时间域二阶和空间域八阶的交错网格有限差分方法对气水两相裂缝型介质的声波波场进行了数值模拟。通过计算不同孔隙流体分布模式下和不同饱和度情况下岩样的声波速度,分析了岩样在不同孔隙流体分布模式下声波速度随饱和度的变化规律,并对物理实验得出的声波速度随饱和度变化的规律从孔隙流体微观分布角度给出了合理解释。数值计算方法简单且精度高,对地震数据解释以及烃类开采过程中监测孔隙流体结构和组分变化有一定的指导作用。

Configuration of propagator method for calculation of electron velocity distribution function in gas under crossed electric and magnetic fields

This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v,θ and f. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.

Experimental study on upward bubble velocity and pierce length distributions in a water model of copper converter

The upward bubble velocity and the pierce length distributions in a sectionalwater model of the copper converter in Guixi Smelter in Jiangxi, China, were measured using atwo-contact electro-resistivity probe. In the case of using a single tuyere, the bubble velocitydistribution along longitudinal direction was similar to that derived from Guassian function. Beyondthe center of the longitudinal range, the bubble pierce length exhibited a sudden increase. Theupward bubble velocity at a specified location could go up to meters per second. Its probability ata fixed location obeys a lognormal function; the bubble pierce length there varies bellow a fewcentimeters. In the case of using multi-tuyeres, the upward bubble velocity was roughly uniformright above the tuyeres and showed a slow decrease beyond this region. The bubble pierce lengthwithin both of these two regions was roughly uniform. Its average value in the former region,however, was found to he somewhat lower than that in the later.

Measurement of oil volume fraction and velocity distributions in vertical oil-in-water flows using ERT and a local probe

This paper presents the use of a high performance dual-plane electrical resistance tomography (ERT) system and a local dual-sensor conductance probe to measure the vertical upward oil-in-water pipe flows in which the mean oil volume fraction is up to 23.1%. A sensitivity coefficient back-projection (SBP) algorithm was adopted to reconstruct the flow distributions and a cross correlation method was applied to obtain the oil velocity distributions. The oil volume fraction and velocity distributions obtained from both measurement techniques were compared and good agreement was found, which indicates that the ERT tech- nique can be used to measure the low fraction oil-water flows. Finally, the factors affecting measurement precision were discussed.

An Improved Analytical Model for Vertical Velocity Distribution of Vegetated Channel Flows

The existence of vegetation plays an important role to protect the ecosystem and water environment in natural rivers and wetlands, but it alters the velocity field of flow, consequently influencing the transport of pollutant and biomass. As a pre-requisite for the analysis of environmental capacity in a channel, the vertical velocity distribution of flows has attracted much research attention;however, there is yet lack of a good prediction model available. For the channel with submerged vegetation, the vertical velocity distribution in the lower vegetation layer will be different from that in the upper flow layer of non-vegetation. In this paper, after review on the most recent two-layer model proposed by Baptist et al., the author has proposed an improved two-layer analytical model by introducing a different mixing length scale (λ). The proposed model is based on the momentum equation of flow with the turbulent eddy viscosity assumed as a linear relationship with the local velocity. The proposed model is compared with the Baptist model for different datasets published in the literature, which shows that the proposed analytical model can improve the vertical velocity distribution prediction well compared with the Baptist model for a range of data. This study reveals that the λ is well related with the submergence of vegetation (H/h), as suggested by . When the constant β is taken as 3/100, the proposed model shows good agreement with a wide range of datasets studied: flow depth (H)/vegetation height (h) in 1.25 to 3.33, different vegetation densities of a in 1.1 to 18.5 m−1 (a defined as the frontal area of the vegetation per unit volume), and bed slopes in (1.38 - 4.0) × 10−3.