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.

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.

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.

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.

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.

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.

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.

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.

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.

Prediction of Fluid Velocity Distribution near a Rising Bubble

A model is presented for predicting the fluid velocity distribution around a rising bubble which startsfrom rest on a distillation column tray by considering the unsteady fluid flow based on the method of streamfunction. Experimental measurement of the velocity distribution by using whole field digitized PIV (particle imagevelocimetry) method is briefly described. The velocity distribution predicted by the present model is in betteragreement with the measurements than the others models published in literature.

Analytical Models for Velocity Distributions in Compound Channels with Emerged and Submerged Vegetated Floodplains

The lateral distributions of depth-averaged velocity in open compound channels with emerged and submerged vegetated floodplains were analyzed based on the analytical solution of the depth-integrated Reynolds-Averaged Navier-Stokes equation with a term to account for the effects of vegetation.The three cases considered for open channels were two-stage rectangular channel with emerged vegetated floodplain,rectangular channel with submerged vegetated corner,and two-stage rectangular channel with submerged vegetated floodplain,respectively.To predict the depth-averaged velocity with submerged vegetated floodplains,we proposed a new method based on a two-layer approach where flow above and through the vegetation layer was described separately.Moreover,further experiments in the two-stage rectangular channel with submerged vegetated floodplain were carried out to verify the results.The analytical solutions of the cases indicated that the corresponding analytical depth-averaged velocity distributions agree well with the simulated and experimental prediction.The analytical solutions of the cases with theoretical foundation and without programming calculation were reasonable and applicable,which were more convenient than numerical simulations.The analytical solutions provided a way for future researches to solve the problems of submerged vegetation and discontinuous phenomenon of depth-averaged velocity at the stage point for compound channels.Understanding the hydraulics of flow in compound channels with vegetated floodplains is very important for supporting the management of fluvial processes.

Evolution of Electron Velocity Distribution during ECRH and Heating Effect Analysis

1 Electron velocity distributions and energy deposition of ECW Two set of soft X-ray spectra detection system consist of high performance sillicon drift detectors （SDD） , high speed A/D transform and processing software, software pulse height analyzer （SPHA）. They are installed at mid plane （ r=0 ） and undermid plane （ r=-16.4 cm ） of HL-2A tokamak respectively to measure the time evolution of soft X-ray spectra. According to spectrum, the thermal electron and superthermal electron temperatures are derived. Because of the ratio of peak counts to background counts is very high （p/b 〉1 400-3000 ） ,

Vertical distribution of the Kuroshio velocity in the Pollution Nagasaki section and its formative mechanism

The seasonal and interannual variations of the vertical distribution of the Kuroshio velocity and its formative mechanism were studied by analyzing the Global Ocean Reanalysis Simulation 2 （GLORYS2） dataset in the Pollution Nagasaki （PN） section （126.0°E-128.2°, at depths less than 1000 m）. The results indicated that： 1） the maximum transport in the PN section occurs in summer, followed by spring, and the minimum transport occurs in fall and winter; the maximum velocities are located at the subsurface in both winter and summer and velocities are relatively larger and at a shallower depth in summer; and the velocity core is located at the surface in spring and fall. The isopycnic line has a clear depression around the Kuroshio axis in winter. The depth of maximum velocity and the zero horizontal density gradients both exhibit substantial seasonal and interannual variations, and the interannual variations are larger. 2） The distributions of velocity and density are in accordance with the therma~ wind relation. Although Kuroshio transport is determined by the large-scale wind field and mesoscale motion in the Pacific Ocean; local heat flux and thermohaline circulation influence the density field, modify the vertical structure of the Kuroshio velocity, and adjust the allocation of water fluxes and nutrients transport. 3） Shelf-water offshore transport into the Kuroshio upper layer induced by southwest monsoons might contribute to the maximum velocity up to the surface in summer. Nonlinear and nongeostrophic processes are not considered in the present study, and the thermal wind relation accounts for part of the vertical structure of the Kuroshio velocity.

Influence of MBBR carrier geometrical properties and biofilm thickness restraint on biofilm properties,effluent particle size distribution,settling velocity distribution,and settling behaviour

The relatively poor settling characteristics of particles produced in moving bed biofilm reactor(MBBR)outline the importance of developing a fundamental understanding of the characterization and settleability of MBBR-produced solids.The influence of carrier geometric properties and different levels of biofilm thickness on biofilm characteristics,solids production,particle size distribution(PSD),and particle settling velocity distribution(PSVD)is evaluated in this study.The analytical Vi CAs method is applied to the MBBR effluent to assess the distribution of particle settling velocities.This method is combined with microscopy imaging to relate particle size distribution to settling velocity.Three conventionally loaded MBBR systems are studied at a similar loading rate of 6.0 g/(m^(2)·day)and with different carrier types.The AnoxK^(TM)K5 carrier,a commonly used carrier,is compared to so-called thickness-restraint carriers,AnoxK^(TM)Z-carriers that are newly designed carriers to limit the biofilm thickness.Moreover,two levels of biofilm thickness,200μm and 400μm,are studied using AnoxK^(TM)Z-200 and Z-400 carriers.Statistical analysis confirms that K5 carriers demonstrated a significantly different biofilm mass,thickness,and density,in addition to distinct trends in PSD and PSVD in comparison with Z-carriers.However,in comparison of thickness-restraint carriers,Z-200 carrier results did not vary significantly compared to the Z-400 carrier.The K5 carriers showed the lowest production of suspended solids(0.7±0.3 gTSS/day),thickest biofilm(281.1±8.7μm)and lowest biofilm density(65.0±1.5 kg/m^(3)).The K5 effluent solids also showed enhanced settling behaviour,consisting of larger particles with faster settling velocities.

VELOCITY DISTRIBUTION IN TRAPEZOID-SECTION OPEN CHANNEL FLOW WITH A NEW REYNOLDS-STRESS EXPRESSION

By considering that the coherent structure is the main cause of the Reynoldsstress, a new Reynolds stress expression was given. On this basis the velocity distribution in thetrapczoid-seclion open channel flow was worked out with the pseudo-spectral method. The results werecompared with experimental data and the influence of the ratio of length to width of thecross-section and the lateral inclination on the velocity distribution was analyzed. This model canbe used the large flux in rivers and open channes.

Effects of Tangential Velocity Distribution on Flow Stability in a Draft Tube

Numerical simulations of the flow in the draft tube of a Francis turbine are carried out in order to elucidate the effects of tangential velocity on flow stability.Influence of the location of the maximum tangential velocity is explored considering the equality of the total energy at the inlet of the draft tube.It is found that the amplitude of the pressure fluctuation decreases when the location of the maximum of the tangential velocity moves from the centre to the wall on the cross section.Thus,the stability of the flow in the draft tube increases with the moving of the location of the maximum tangential velocity.However,the relative hydraulic loss increases and the recovery coefficient of the draft tube decreases slightly.

Particle image velocimetry measurement of velocity distribution at inlet duct of waterjet self-propelled ship model

A vehicle-mounted three-dimensional underwater particle image velocimetry（PIV） device is used in a towing tank to measure the velocity distribution of the inlet duct of a waterjet ship model in a self-propulsion test. The following points are shown through a comparison of the influences of the stationary and free states of the ship model on the measured results：（1） during the test, the ship attitude will change, specifically, the ship model will heave and trim,（2） the degree of freedom disturbs the processing of the pixel images enough to distort the subsequent image processing,（3） the stationary state of the ship model is the optimal mode for measuring the velocity distribution using the PIV device, and（4） if the changes must be considered, the man-made heaving and trimming may be pre-applied, and be made a corrected stationary mode. In addition, the momentum effect coefficient and the energy effect coefficient are calculated in a non-uniform inflowing state, and the related factors affecting the two coefficients are analyzed. The test results show that the pumping action of the waterjet creates a transverse vector in the cross-sectional speed, which increases the non-uniformity of the inflow. These results could help to establish the design requirements for a waterjet-propelled ship type.

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.

Velocity distribution and scaling properties of wall bounded flow

The scaling and similarity of wall bounded turbulent flow were studied. The properties of such flows and the relationship between a power law and a logarithmic type of velocity distribution were investigated. Based on the physical mechanism involved, our results show that the power law and the logarithmic distribution are only different forms with the same hypothesis and hold only in the outer flow zone. Thus, a universal explanation for various empirical formulae of velocity distribution was obtained. Manning’s formula was studied to explain theoretically the experiential result that the roughness coefficient is only a comprehensive parameter of the whole system without a corresponding physical factor. The physical mechanism of the velocity distribution of parallel to wall bounded flow was explored, the results show that the parameters in the formula of velocity distribution are indices of the system responding to flowing environmental factors to represent general case of boundary roughness and the flowing state, corresponding physical mechanism is vortex motion.

The collision frequency of electron-neutralparticle in weakly ionized plasmas with non-Maxwellian velocity distributions

The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied.The average collision frequencies of electron-neutral-particle in plasmas are accurately derived.We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution,which will affect the transport properties of the charged particles in plasmas.Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.