Study on the Log-Linear Velocity Profile of Near-Bed Tidal Currentin Estuarine and Coastal Waters

Many observed data show that the near-bed tidal velocity profile deviates from the usual logarithmic law. The amount of deviation may not be large, but it results in large errors when the logarithmic velocity profile is used to calculate the bed roughness height and friction velocity （or shear stress）. Based on their investigation, Kuo et al. （1996） indicate that the deviation amplitude may exceed 100%. On the basis of fluid dynamic principle, the profile of the near-bed tidal velocity in estuarine and coastal waters is established by introducing Prandtl＇ s mixing length theory and Von Kannan selfsimilarity theory. By the fitting and calculation of the near-bed velocity profde data observed in the west Solent, England, the results are compared with those of the usual logarithmic model, and it is shown that the present near-bed tidal velocity profile model has such advantages as higher fitting precision, and better inner consistency between the roughness height and friction velocity. The calculated roughness height and friction velocity are closer to reality. The conclusions are validated that the logarithmic model underestimates the roughness height and friction velocity during tidal acceleration and overestimates them during tidal deceleration.

A New Model for Velocity Profiles in Estuarine Waters

Water motion in estuarine waters is the result of the action of various dynamic factors. Firstly, based on the hydro- dynamic characteristics in estuarine waters, neglecting the nonlinear effects of various flow hydrodynamic factors, the logarithm velocity profile of tidal current and the cubic velocity profile of Hansen and Rattray （1965） made for linear super- position at a sense of first order, a new model for velocity profile in estuarine waters is established. Then, by introducing the least square method combination of enumeration, the velocity profile data of wind-driven current measured in the laboratory and that observed at the North and the South Branches of the Yangtze Estuary are verified and compared with other formulas, all with satisfactory results. The results show that the new model not only considers the influences of various dynamic factors, such as tide, wind force, run-off and density pressure with high accuracy, but also provides reasonable boundary conditions on the bottom for hydrodynamics numerical simulation in estuarine waters. Thereby, the accuracy and credibility of numerical computation and prediction of water flow are improved. The research is theoretically important for the estuarine hydrodynamics.

Visualisation of air–water bubbly column flow using array Ultrasonic Velocity Profiler

In the present work, an experimental study of bubbly two-phase flow in a rectangular bubble column was performed using two ultrasonic array sensors, which can measure the instantaneous velocity of gas bubbles on multiple measurement lines. After the sound pressure distribution of sensors had been evaluated with a needle hydrophone technique, the array sensors were applied to two-phase bubble col- umn, To assess the accuracy of the measurement system with array sensors for one and two-dimensional velocity, a simultaneous measurement was performed with an optical measurement technique called particle image velocimetry （PIV）. Experimental results showed that accuracy of the measurement system with array sensors is under 10% for one-dimensional velocity profile measurement compared with PIV technique. The accuracy of the system was estimated to be under 20% along the mean flow direction in the case of two-dimensional vector mapping.

Simultaneous measurement of velocity profile and liquid film thickness in horizontal gas–liquid slug flow by using ultrasonic Doppler method

Horizontal gas-liquid two-phase flows widely exist in chemical engineering,oil/gas production and other important industrial processes.Slug flow pattern is the main form of horizontal gas-liquid flows and characterized by intermittent motion of film region and slug region.This work aims to develop the ultrasonic Doppler method to realize the simultaneous measurement of the velocity profile and liquid film thickness of slug flow.A single-frequency single-channel transducer is adopted in the design of the field-programmable gate array based ultrasonic Doppler system.A multiple echo repetition technology is used to improve the temporal-spatial resolution for the velocity profile.An experiment of horizontal gas-liquid two-phase flow is implemented in an acrylic pipe with an inner diameter of 20 mm.Considering the aerated characteristics of the liquid slug,slug flow is divided into low-aerated slug flow,high-aerated slug flow and pseudo slug flow.The temporal-spatial velocity distributions of the three kinds of slug flows are reconstructed by using the ultrasonic velocity profile measurement.The evolution characteristics of the average velocity profile in slug flows are investigated.A novel method is proposed to derive the liquid film thickness based on the instantaneous velocity profile.The liquid film thickness can be effectively measured by detecting the position and the size of the bubbles nearly below the elongated gas bubble.Compared with the time of flight method,the film thickness measured by the Doppler system shows a higher accuracy as a bubble layer occurs in the film region.The effect of the gas distribution on the film thickness is uncovered in three kinds of slug flows.

Accuracy analysis of predicted velocity profiles of laminar duct flow with entropy generation method

The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy generation. The analysis is concerned with the entropy generation rate in hydrodynamic, steady, laminar, and incompressible flow for Newtonian fluids in the insulated channels of arbitrary cross section. The entropy generation can be calculated from two local and overall techniques. Adaptation of the results of these techniques depends on the used velocity profile. Results express that in experimental works, whatever the values of local and overall entropy generation rates are close to each other, the results are more accuracy. In order to extent the subject, different geometries have been investigated. Also, the influence studied, and the distribution of volumetric geometries is drawn. of geometry on the entropy generation rate is local entropy generation rate for the selected geometries is drawn.

Numerical Simulation and Analysis on Velocity Profiles of Jet Projectile Charge

Jet projectile charge （JPC） is a relatively new type of perforating jet mainly used for defeating concrete targets. Velocity profile is an important parameter to investigate the penetration and performance of JPC. Since limited information such as X-ray radiographs and penetration depth can be obtained through the JPC experiment, the numerical simulation and further methodology are needed to depict the mechanism of JPC. This paper describes a mathematical approach based on Matlab to determine JPC velocity profile at various stand offs using three sets of jet data from numerical simulations. X-ray radiographs experimental results have been obtained at two time instants for two selected JPC design to verify the numerical accuracy. The velocity profiles by mathematical approach and simulation show good accordance. The number of experiments can be reduced by numerical simulation and analysis of velocity profiles. This approach can be generalized to any such system where explosive-metal interaction results in formation of jets.

Inversion Method for Sound Velocity Profile of Eddy in Deep Ocean

The modal wave number tomography approach is used to obtain sound speed profile of water column in deep ocean. The approach consists of estimation of the local modal eigenvalues from complex pressure field and use of these data as input to modal perturbative inversion method for obtaining the local sound speed profile. The empirical orthonormal function (EOF) is applied to reduce the parameter search space. The ocean environment used for numerical simulations includes the Munk profile as the unperturbed background speed profile and a weak Gaussian eddy as the sound speed profile perturbation. The results of numerical simulations show the method is capable of monitoring the oceanic interior structure.

Velocity profile of debris flow based on quadratic rheology model

The quadratic rheology model considers the yield stress,viscous stress,turbulent stress and disperse stress,so it is used in this study to derive the velocity profile of debris flows.The quadratic model with the parabolic eddy viscosity was numerically solved,and an analytical solution was derived for the quadratic model with a constant eddy viscosity.These two solutions were compared with the Arai-Takahashi model that excluded the viscous stress and the yield stress.The three models were tested by using 17 experiment cases of debris flows over rigid beds.The results prove that the quadratic model with parabolic and constant eddy viscosities is applicable to muddy and granular flows,whereas the Arai-Takahashi model tends to overestimate the flow velocity near the water surface if a plug-like layer exists.In addition,the von Karman constant and the zero-velocity elevation in the three models are related to sediment concentration.The von Karman constant decreases first and then increases as the sediment concentration increases.The zero-velocity elevation is below the bed surface,likely due to the invalidity of the non-slip boundary condition for the debris flows over fixed beds.

Effect of particle shape on packing fraction and velocity profiles at outlet of a silo

Many studies on how the particle shape affects the discharge flow mainly focus on discharge rates and avalanche statistics. In this study, the effect of the particle shape on the packing fraction and velocities of particles in the silo discharge flow are investigated by using the discrete element method. The time-averaged packing fraction and velocity profiles through the aperture are systematically measured for superelliptical particles with different blockinesses. Increasing the particle blockiness is found to increase resistance to flow and reduce the flow rate. At an identical outlet size, larger particle blockiness leads to lower velocity and packing fraction at the outlet. The packing fraction profiles display evidently the self-similar feature that can be appropriately adjusted by fractional power law. The velocity profiles for particles with different shapes obey a uniform self-similar law that is in accord with previous experimental results, which is compatible with the hypothesis of free fall arch. To further investigate the origin of flow behaviors, the packing fraction and velocity field in the region above the orifice are computed. Based on these observations, the flow rate of superelliptical particles is calculated and in agreement with the simulated data.

Modelling the temporal-varied nonlinear velocity profile of debris flow using a stratification aggregation algorithm in 3D-HBP-SPH framework

Estimation of velocity profile within mud depth is a long-standing and essential problem in debris flow dynamics.Until now,various velocity profiles have been proposed based on the fitting analysis of experimental measurements,but these are often limited by the observation conditions,such as the number of configured sensors.Therefore,the resulting linear velocity profiles usually exhibit limitations in reproducing the temporal-varied and nonlinear behavior during the debris flow process.In this study,we present a novel approach to explore the debris flow velocity profile in detail upon our previous 3D-HBPSPH numerical model,i.e.,the three-dimensional Smoothed Particle Hydrodynamic model incorporating the Herschel-Bulkley-Papanastasiou rheology.Specifically,we propose a stratification aggregation algorithm for interpreting the details of SPH particles,which enables the recording of temporal velocities of debris flow at different mud depths.To analyze the velocity profile,we introduce a logarithmic-based nonlinear model with two key parameters,that a controlling the shape of velocity profile and b concerning its temporal evolution.We verify the proposed velocity profile and explore its sensitivity using 34 sets of velocity data from three individual flume experiments in previous literature.Our results demonstrate that the proposed temporalvaried nonlinear velocity profile outperforms the previous linear profiles.

EXPERIMENTAL STUDY ON VELOCITY PROFILE OF SUBMERGED ABRASIVE SUSPENSION JET FLOW

Abrasive jet cutting, as a more efficient machining or cutting method, has emerged in recent years in mining and machining industries, but the knowledge about velocity profile of abrasive jet flow lacks in general. In practice, the Polyacrylamide (PAM) is generally applie d to jet fluid to increase the suspension of the abrasive particles. Als o, the effects of PAM on jet flow are not very clear. In this paper, velocity fi elds of both the abrasive particles and the fluid were systematically studied wi th the PIV technology. The slip velocity between the abrasive particle and the surrounding fluid was subtracted out to give a further description of abrasive suspension jet. Th e effects of polymer PAM on both the fluid flow and the movement of the suspendi ng abrasive particles were also measured. And it is found that the PAM is a prop er type of additive to improve velocity fields for both the abrasive particles and the fluid in a jet. The results of the PIV measurement can help give a bett er understanding about the basic physics of abrasive suspension jet flow, and a good guidance to validate and develop reliable computational models to describe the jet.

HEMODYNAMICS FOR ASYMMETRIC INLET AXIAL VELOCITY PROFILE IN CAROTID BIFURCATION MODEL

The asymmetric inlet velocity profile has been observed in phantom model using LDA and in health subjects using Magnet Resonance （MR）. The effects of asymmetric inlet axial velocity profile on the flow field and the Wall Shear Stress （WSS） of carotid bifurcation were numerically studied herein with the TF-AHCB model, The results show that the Wall Shear Stress Gradient （WSSG） in the front part of the sinus for inward-tilting inlet axial velocity profile is nearly 2 times of that for the symmetric one in the beginning of systole, the end of systole, and diastole, respectively. The area of WSS below 5× 10^-3 Pa at the outer wall of the sinus for outward-tilting inlet axial velocity profile is 1.5 times of that for the inward-tilting one during diastole of the cardiac cycle. The asymmetric inlet velocity profiles can reduce the flow velocity near the inner wall of the sinus, which has been normally considered a high velocity region. It is concluded that besides bifurcation geometry and flow waveform, the asymmetry of inlet velocity profile is probably a factor influencing atherosclerosis.

Simulation of Heat Transfer and Hydrodynamics over a Free Rotating Disk Using an Improved Radial Velocity Profile

The paper presents results of simulation of turbulent heat transfer and hydrodynamics over a free rotating disk using an integral method based on power-law velocity and temperature profiles and three different laws for the tangent of the flow swirl angle tan. It appeared that a quadratic correlation of tan is the most proper one for a free rotating disk. Resulting equation for the Nusselt number is in a better agreement with experimental data of different authors than known Dorfman formula.

AN APPROXIMATE METHOD FOR DETERMING THE VELOCITY PROFILE IN A LAMINAR BOUNDARY-LAYER ON FLAT PLATE

In this paper, using the integration method, it is sought to solve the problem for the laminar boundary_layer on a flat plate. At first, a trial function of the velocity profile which satisfies the basical boundary conditions is selected. The coefficients in the trial function awaiting decision are decided by using some numerical results of the boundary_layer differential equations. It is similar to the method proposed by Peng Yichuan, but the former is simpler. According to the method proposed by Peng, when the awaiting decision coefficients of the trial function are decided, it is sought to solve a third power algebraic equation. On the other hand, in this paper, there is only need for solving a linear algebraic equation. Moreover, the accuracy of the results of this paper is higher than that of Peng.

An estimation of the velocity profile for the laminar-turbulent transition in the plane jet on the basis of the theory of stochastic equations and equivalence of measures

The theory of stochastic equations and the theory of equivalence of measures previously applied to flows in the boundary layer and in the pipe are considered to calculate the velocity profile of the flat jet.This theory previously made it possible to determine the critical Reynolds number and the critical point for the flow of the plane jet.Here based on these results the analytical dependence for the index of the velocity profile is derived.Velocity profiles are calculated for a laminar-turbulent transition in the jet.This formula reliably reflects an increase of the energy transferred from a deterministic state to a random one with an increase of the index of the velocity profile.Results show satisfactory agreement with the known experimental data for the velocity profile of the flat jet.Using obtained results it is possible to determine the location of technical devices for laminarization of the flow in the jet.This is important both for reducing friction in the flow around aerodynamic vehicles and for maintaining the jet profile if it is necessary to ensure the stability of the flow characteristics.Also the obtained relations can be useful for researching of the processes in combustion chambers,in the case of welding and in other technical devices.

Velocity profiles description and shape factors inclusion in a hyperbolic,one-dimensional,transient two-fluid model for stratified and slug flow simulations in pipes

In a previous work it has been shown that a one-dimensional,hyperbolic,transient five equations twofluid model is able to numerically describe stratified,wavy,and slug flow in horizontal and nearhorizontal pipes.Slug statistical characteristics can be numerically predicted with results in good agreement with experimental data and well-known empirical relations.In this model some approximated and simplified assumptions are adopted to describe shear stresses at wall and at phase interface.In this paper,we focus on the possibility to account for the cross sectional flow by inserting shape factors into the momentum balance equations of the aforementioned model.Velocity profiles are obtained by a pre-integrated model and they are computed at each time step and at each computational cell.Once that the velocity profiles are known,the obtained shape factors are inserted in the numerical resolution.In this way it is possible to recover part of the information lost due to the one-dimensional flow description.Velocity profiles computed in stratified conditions are compared against experimental profiles measured by PIV technique;a method to compute the velocity profile during slug initiation and growth has been developed and the computed velocity distribution in the liquid phase was compared against the one-seventh power law.

VELOCITY PROFILES FOR AXIAL LAMINAR FLOW OF POWER-LAWFLUIDS THROUGH ECCENTRIC ANNULI

An analytical solution of velocity profiles for Non-Newtonian fluids described by the power-law equation in axial laminar flow through eccentric annuli is presented.The expressions of limit velocities and contours of equal velocity are obtained. The main approaches,claimed in this paper,are that the term T_(rz)/r in the differential equation of flow and the non-symmetrical velocity distribution about the geometric center of the radial clearance are considered.

A Computational Model for Velocity Separation in Shallow Sea

Based on the hydrodynamical feature and the theoretical velocity profiles of tidal flow and wind-induced flow in shallow sea, a computational model is established for the first time, which can separate observed velocity into tidal velocity and wind-induced velocity by use of the least square method. With the model, not only the surface. velocities of tidal. flow and wind-induced flow are obtained, but also the bed roughness height is determined and the wind velocity above the water surface is estimated. For verification of the model, the observed velocity in the Yellow River Estuary and the laboratory test is separated, then it is applied to the Yangtze River Estuary. All the results are satisfactory. The research results show that the model is simple in method, feasible in process and reasonable in result. The model is a valid approach to analysis and computation of field data, and can be applied to separate the observed velocity in shallow sea; at the same time, reasonable boundary conditions of the surface and bottom can be obtained for two- and three-dimensional numerical simulation.

Optimal transport of cold atoms by modulating the velocity of traps

This work experimentally demonstrates a new method of optimizing the transport of cold atoms via modulating the velocity profile imposed on a magnetic quadrupole trap.The trap velocity and corresponding modulation are controlled by varying the currents of two pairs of anti-Helmholtz coils.Cold 87Rb atoms are transported in a non-adiabatic regime over 22 mm in 200 ms.For the transported atoms their final-vibration amplitude dependences of modulation period number,depth,and initial phase are investigated.With modulation period n = 5,modulation depth K = 0.55,and initial phase φ = 0,cold atom clouds with more atom numbers,smaller final-vibration amplitude,and lower temperature are efficiently transported.Theoretical analysis and numerical simulation are also provided,which are in good agreement with experimental results.

Impact of Partially Covered Vegetation on the Lateral Velocity Distribution of Open Channel Flow

The vegetation affects the flow process and water environment, thus drawing increasing attention to river environment management. Previous research is mainly focused on flow through vegetation in a channel with fully covered single-layer vegetation. However, in natural rivers, different heights’ vegetation often co-exists along one or two sides of a river. This paper experimentally studies how the flow velocity distribution is affected by the two different-layered vegetation allocated along two sides of an open-channel. The vegetation was simulated by dowels of two heights, 10 cm and 20 cm, and arranged in a parallel pattern along two sides of a flume under partially submerged conditions. The velocities along a cross-section were measured by Acoustic Doppler Velocimetry (ADV). The results of lateral velocity distribution show that a strong shear layer exists between vegetation and non-vegetation zones, indicating the retarding effect of vegetation. Meanwhile, as the flow depth increases, the relative velocity in the free flow zone decreases compared with that in the vegetated region, indicating that vegetation resistance to the flow decreases as increasing depth under the same vegetation configuration. These ?ndings would help understand the role of multi-layered vegetation in riparian management.