Streamwise velocity distribution in irregular shaped channels having composite bed roughness

Applications of the proposed model by Maghrebi which is able to predict the isovel contours quantitatively in a section of an open or closed channel both with irregular shapes and roughness, have been presented [Maghrebi MF, Rahimpour M. A simple model for estimation of dimensionless isovel contours in open-channels. Flow Meas Instrum 2005;16(6):347–52]. In the present paper, the model is applied to a flume with a composite roughness as well as to rivers with irregular cross section geometries. The obtained isovel contours in a flume section with nine cases of composite roughnesses are used for discharge estimations. Then, they are compared with measured ones. Model predictions are well correlated with the measured data. The isovel contours obtained by applications of the model to river sections are used to estimate the depth-average and surface velocities. Then they are compared with the measured data at the corresponding sections. The predicted results of water surface velocities are in good agreement with the measured data in a cross section of the River Unon in Japan. The result of the depth-average velocity shows, even better agreement with the measured data as well as the best analytical results for the River Severn in the UK.     

Prediction of stage–discharge curves in open-channels using a fixed-point velocity measurement

The single-point measurement method for discharge estimation, which was first introduced by Maghrebi, can be implemented to obtain the discharge at different stages of a river during a flood event. As an advantage of this method, discharge can be estimated automatically with a fixed measurement location in the river section or on the water surface, which is associated with minimum energy and cost consumptions. For the proposed model, we determine the isovel contours in a normalized form for the cross section of the flow. To do so, we need to apply the field or experimental data, concerning the cross sectional geometry at different stages and its roughness variation along the wetted perimeter to the model. Then we collect the data of the single fixed-point of velocity measurement at the flow section using a velocity current meter. To validate the method, it is applied to a flume with different cases of roughened walls. The obtained results of stage–discharge curves using the single point of measurement in comparison to the observed experimental ones show that this method can quickly and accurately estimate the flood discharges. The maximum deviation between the observed and calculated discharges for most of observations is less than 5%.     

Experimental study of simple flumes with trapezoidal contraction

There are different devices available for measuring the flow discharge. Static measuring devices such as weirs and flumes (without any moving parts) play a significant role in discharge measurement in open channels. Many researchers have focused on application of flumes in irrigation networks. This investigation set out to study the flow discharge through a trapezoidal cut-throated flume (TCTF). The flume is simply constructed by placing two triangular plates on either side of a rectangular open channel to form a trapezoidal throat. The channel cross section is rectangular while throat cross section of the flume is trapezoidal. The proposed flume is simple, low-cost, easy to install and does not require high maintenance. The present study was designed to determine the effect of different variables on the flume discharge. For this, an experimental study was carried out under free outflow conditions and under upstream subcritical flow regime to formulate the flume discharge. Three models are defined for flume discharge relation based on the Buckingham's theorem of dimensional analysis, and then calibrated using the experimental data collected during this study. The first discharge model has an average error of 1.81%, while the second and third improved models have average errors of 0.96% and 1.44% respectively. To reliably estimate the flume discharge, free-flow and submerged-flow conditions should be distinguished. For this, suitable equations with an average error less than 2.23% were presented to estimate the submergence threshold. The results of this study indicate that while the downstream wall slope influences the submergence threshold, the flume discharge is not influenced by this variable. The proposed models are simple and accurate and present appropriate estimation of discharge for flows through the TCTFs. The findings of this study will be of interest for practical hydraulic engineers.     

轮廓法测试残余应力中的数据处理

使用轮廓法测量铝合金T形构件淬火残余应力,重点研究了测量误差的数据处理。采用包络处理、左右轮廓平均、Gauss混合模型拟合以及节点插值处理后,得到最终轮廓值,并将其作为边界条件反向加载到应力重构有限元模型中,得到待测面应力场。使用X射线衍射法对待测面边界处应力进行修正。将测量结果和有限元模拟淬火结果进行对比,利用统计学方法分析对比结果。结果表明：轮廓法和X射线衍射法结合可以很准确地描述T形构件淬火残余应力场。T形构件淬火残余应力最大拉应力出现在筋条和腹板交界处,靠近腹板一侧。     

Experimental and theoretical modeling of a quarter-circular gate flow

Gates are important hydraulic structures and used for flow measurement, water delivery, and water level regulation in open channels and irrigation networks. In this study, the quarter-circular gate is introduced and investigated. The cross section of this gate consists of a quarter circular arc and the lip angle of the gate equals to zero. Discharge coefficient, variation of downstream flow depth, and velocity distribution at opening section of gate were experimentally measured. Using potential flow theory supported by dimensional analysis, equations for discharge coefficient and velocity distribution at gate opening section of quarter-circular gate were derived and then validated using experimental data. The mean percentage error (MPE) of obtained equation for discharge coefficient of quarter-circular gate was calculated as 2.24%, indicating the high precision of the proposed theory. Based on obtained results, downstream flow depth of quarter-circular gate is uniform. Also, velocity distribution at gate opening section is nearly uniform. Discharge coefficient of quarter-circular gate was averagely obtained 55% larger than that of sluice gate. It was also obtained larger than that of radial gate. Elimination of contraction section at downstream of gate opening, which is the main source for energy loss and therefore discharge capacity reduction, is the main reason for larger discharge coefficient of quarter-circular gate.     

Estimation of one-dimensional velocity distribution by measuring velocity at two points

The measurement of the velocity distribution and discharge in the open channels has always been an important issue in hydraulics. Unfortunately, flow measurement in the open channel is often expensive and sometimes produces poor results. There are many empirical methods to estimate the velocity distribution in a conduit, however, these methods are often applicable only to a narrow range of open channel conditions. In this paper, considering velocity as a random parameter, one-dimensional velocity distribution in open-channel has been derived based on the entropy concept and the principle of maximum entropy (POME). The entropy indexes (M, G, λ₂ and λ_*) are important parameters in entropy method to estimate velocity distribution and discharge in a conduit. A new approach is presented in this work for estimating the entropy parameters based on two-point velocity measurements. The approach for estimating the entropy parameters is tested for laboratory observations and velocity distribution and discharge are determined using Shannon, Renyi and Tsallis entropy methods. The present approach has shown good agreement with measured data. Also, the results showed that Tsallis entropy method is more accurate than other forms of entropy and the calculated values of NRMSE for estimated velocity profile and discharge are 7.86 and 8.8% respectively, showing a good simulation.     

Discharge prediction in flow measurement flumes with different downstream transition slopes

Experimental testing of 9 different rectangular compound cross-section flow measurement flumes with different downstream slopes was conducted to yield the coefficient of discharge and the approach velocity coefficient. The aim of the experimental research was the determination of stage–discharge relationship in compound cross-section flow measurement flumes with different downstream slopes. One empirical predictive model for each of the coefficient of discharge and the approach velocity coefficient for the 9 cross-sections have been derived using one dimensionless parameter for the coefficient of discharge and another one dimensionless parameter for the approach velocity coefficient as the single independent variable. This approach is preferred as it allows the estimation of discharge by only measuring the water depth at the head measurement section. All obtained predictive models statistics have indicated the high reliability of the derived models in estimating discharge in an open channel flume of a rectangular compound cross-section using the predicted coefficients.     

Weir velocity formulation for sharp-crested rectangular weirs

Discharge in open channels can be measured by sharp-crested rectangular weirs. Generally, measured head over the weir crest is substituted into an empirical formula derived from energy considerations to calculate the discharge. Assumptions made on the derivation are taken into account by defining a discharge coefficient that fits into the experimental data. In this study, a physical quantity, the average velocity over the weir section defined as ‘weir velocity’ is directly formulated as function of weir geometry and head over the weir. Weir velocity plotted against the weir head has a universal behavior for constant weir width to channel width ratio independent of the weir size. This unique behavior is described in terms of weir parameters to calculate the discharge without involving a discharge coefficient. Combining weir velocity data for variable weir widths provides a basis for direct formulation of discharge. The weir velocity exhibits simpler functional dependency on weir parameters in contrast to the discharge coefficient.     

Experimental investigation of flow characteristics of a magnetohydrodynamic (MHD) duct of fan-shaped cross section

Experiments along with numerical calculations are carried out to investigate the effect of the geometry of the cross section on flow characteristics of a MHD propulsion duct. A fan-shaped cross-section MHD thruster duct is chosen for comparison with a previously investigated rectangular cross section. Measurement of the velocity field is made using LDV (Laser Doppler Velocimetry) system with a fiber-optic cable and pressure distribution is measured with static pressure holes at the bottom surface. Comparison with rectangular cross section shows that the velocity profile is significantly influenced by the geometry of cross section while the axial pressure distribution is not so affected.     

Stage-discharge relationship for slide gates installed in partially full pipes

Sluice/slide gates are widely used for flow depth control and flow discharge measurements in open channels. The hydraulic behavior of the sluice gates located in the rectangular open channels is well documented in the literature. This study reports the results of an investigation conducted to establish the stage-discharge relationship for the sluice gates located in horizontal, circular open channels/pipes under free outflow conditions. Different stage-discharge models were proposed based on the Buckingham's theorem of dimensional analysis and orifice theory. A comprehensive series of laboratory experiments (729 runs) were performed to study the sluice gates located at the middle, and at the end of two circular pipes. Using the data collected from two circular open channels of nominal diameters 20 and 30 cm, the proposed models were calibrated. For the middle slide gates, the experimental results showed that the discharge prediction can be improved by introducing the Reynolds number. For the slide gates located at the middle of the channel, the best proposed model has an average error of 1.40% with a maximum error of 7.12%. For the slide gates located at the end of the channel, the Reynolds number has no significant effect and best proposed model has an average error of 2.47% with a maximum error of 6.59%. The results also showed that the flow discharge of the end slide gate (with unconfined free jet under gravity) is higher than the flow discharge of the middle slide gate for the same gate opening areas and upstream flow depths. The proposed sluice/slide gate for circular open channels offers a simple and reliable discharge measurement approach with acceptable accuracy.     

Application of large scale PIV in river surface turbulence measurements and water depth estimation

Large-Scale Particle Image Velocimetry (LSPIV) has emerged as a reliable technology to measure river surface flow velocity distribution and can be applied to estimate river discharge. Fewer studies have explored the capability of surface turbulence measurements using LSPIV. In this paper, LSPIV is applied to evaluate statistics of surface turbulence of a natural river. Turbulence measurements including velocity fluctuation, velocity spectra and the dissipation rate of turbulent kinetic energy (TKE) are validated by comparing with those measured by an Acoustic Doppler Velocimeter (ADV). Traditionally, estimation of stream discharge through LSPIV needs a secondary measurement to determine river bathymetry and water depth. A new method is presented here to demonstrate that for a fully developed and channel-controlled flow, the cross section geometry can be estimated from the combined measurements of surface mean velocity and the dissipation rate, following the Manning-Strickler formula. Therefore, river discharge can be estimated with LSPIV along with a calibrated Manning's roughness, without additional bathymetry survey. The proposed new method is applied to measure discharge in Milwaukee River (Milwaukee, Wisconsin, U.S.A.), which agreed well with data obtained from a nearby streamgage station.     

基于轮廓法测试焊接件内部残余应力

采用轮廓法测试低碳钢堆焊件和T形焊接结构的内部纵向残余应力。将焊接件沿垂直焊缝平面切割开,精确测试切割面的变形轮廓,然后将测试轮廓进行拟合,并将拟合结果作为有限元模型的边界条件进行弹性计算从而获得内部垂直切割平面的应力分布。比较不同曲面拟合方法拟合得到的切割面轮廓形貌;将轮廓法测试的焊接残余应力结果和热弹塑性三维有限元计算结果进行比较分析。研究结果表明:轮廓法能准确高效测试较厚焊接件内部整个截面上的纵向应力分布;由于线切割和轮廓测量误差造成轮廓法测得的应力在约2 mm厚表层区域的幅值和有限元计算结果相比误差较大,但轮廓法测试结果仍能反映出表层应力的分布趋势和特征;线切割断丝造成切割面的局部轮廓误差,会引起断丝区域测试应力出现突变。     

Study on the applicability of four flumes in small rectangular channels

Different experiments and numerical simulation research were carried out in order to explore the hydraulic characteristics and applicability of the cutthroat flume, NACA airfoil-shaped flume, airfoil pillar-shaped flume, and optimized airfoil-shaped flume in rectangular channels. The four flumes with contraction ratios of 0.4, 0.5, and 0.6 in rectangular channels were tested under 144 free-flow conditions. Based on the Fluent software, standard k-ε three-dimensional turbulence model and volume of fluid (VOF) method were utilized for numerical simulation in each working condition. The principle of critical flow was used to analyze the correlation between the discharge, the contraction ratio, and the upstream water depth. This correlation was used to obtain the discharge calculation formulas of the cutthroat flume, NACA airfoil-shaped flume, airfoil pillar-shaped flume, and optimized airfoil-shaped flume in rectangular channels. The Froude number in front of the flume, the backwater height, the critical submergence degree, the velocity distribution, the head loss, the discharge measurement formula, and the accuracy were studied and compared. It can be concluded from the results that the cutthroat flume, NACA airfoil-shaped flume, airfoil pillar-shaped flume, and optimized airfoil-shaped flume all have good applicability in rectangular channels. Moreover, the hydraulic characteristics of all the four flumes meet the water measurement specifications in the irrigation area. The upstream Froude number of the NACA airfoil-shaped flume is the smallest, whereas the backwater height and head loss of the cutthroat flume and optimized airfoil-shaped flume are the smallest. It is also worth noting that the critical submergence degree of the optimized airfoil-shaped flume is the highest, with an average value of 0.85. The discharge measurement formulas of the four flumes have been deduced using the correlation between the discharge, the contraction ratio, and the upstream water depth. It was found that the average errors between the calculated discharge and the measured discharge of the four flumes are 3.17%, 2.17%, 1.53%, and 2.29%, respectively, which are less than 5%, and therefore meet the discharge measurement requirements. In the agricultural irrigation system and flow monitoring system, the hydraulic characteristics of the four flumes can provide a reference and basis for the selection of flumes in the rectangular channel.     

Direct solution for discharge in generalized trapezoidal free overfall

In open channels, free overfall can be used as a discharge measuring structure by a single measurement of depth at the end of the channel. If the slope of channel is negative, zero or mild, the flow at upstream of end section will be critical and end depth value depends only on the shape of the approach channel and its critical depth. This research presents a theoretical end depth–discharge (EDD) relationship for free overfall (end section) in a horizontal open channel with generalized trapezoidal section. The generalized trapezoidal shape reduces to the commonly used trapezoidal section as well as to the Δ-shaped section. Two direct discharge equations in terms of end depth for subcritical flows are proposed by simulating free overfall as a weir without crest. Experimental data are then used to verify the proposed EDD relationships. The calculated discharges, using the proposed EDD relationships, show excellent agreement with the experimental data.     

Discharge formula for rectangular sharp-crested weirs

Sharp-crested rectangular weirs used for discharge measurement in channels and laboratories are experimentally investigated. Height and width of weir plate are the two parameters characterizing the head-discharge relationship. Laboratory experiments are conducted by measuring the discharge and the head over the weir for variable weir heights and widths. Applicability of various formulations for the discharge coefficient are investigated. Experiments indicate that discharge is independent of weir height, when the weir is operated within an appropriate discharge range. Average velocity over the weir plotted against the weir head displays universal characteristics such that it can be used in the expression of discharge over the weir, eliminating the need for a discharge coefficient. The head-discharge relationship for a rectangular weir has distinct features for the partially contracted weirs and for the fully contracted slit weirs.     

Non-intrusive measurements of shallow water discharge

Waste-water channels or physical hydraulic models often convey shallow water flows with depths around 5 cm. Such free surface flows can in principle be measured using standard measuring flumes or thin-plate weirs, but proper employment of these is often practically impossible, e.g. due to limited space. To avoid this, various flow meters with contact probes (i.e. »area-velocity« probes) are employed instead, but in reality this often results in inaccurate measured values of discharge. This paper presents an effective way to determine discharge of very shallow flow without intruding the flow. Our approach is based on computer aided visualization, namely on the quantification of the field of vectors representing local velocities on the water surface of the flow. In contrast to other studies, this method does not require complex measuring equipment, special lights or special devices for the seeding of particles. Experiments were conducted in 0.5 m and 1.06 m wide rectangular channels, made of glass and concrete, respectively, and they show that this method could be employed both in hydraulic laboratories and in the field. Measurements showed that velocity on the surface of the shallow water flow differs from theoretical average mean flow velocity in the observed cross section, and further that this difference increases with the decrease of water depth. This suggests that the assumption, which states that in shallow water flows the surface velocity is similar enough to the mean flow velocity, is not necessarily correct.     

Study of flow at side weir in narrow flume using visualization techniques

The purpose of the research was to quantify characteristics of a subcritical flow at a rectangular sharp-crested side weir in a rectangular main channel using non-invasive measuring techniques based on the visualization of the flow. Experiments were carried out in physical models, including nine different dimensions of the side weir and nine combinations of the inflow and tailwater level for each weir, amounting to 81 test runs. Velocity vector fields were measured in various horizontal planes along the side weir using a high speed digital camera and electrolysis-induced hydrogen bubbles as flow tracers. Recorded films were converted into sequences of images which were used for numerical calculation of local velocities. Components of velocity vectors were determined with great spatial and time resolution. Longitudinal profiles of water surface elevation at each side weir were determined using photos of laser-induced vertical section planes. Measured discharges and flow depths were used to formulate new equation for the side weir discharge coefficient using dimensional analysis. The principal results indicated that velocity distribution along the side weir was distinctly non-uniform, with various velocity ratios increasing along the crest. However, the calculated energy grade line was parallel to the main channel bed, indicating that only friction losses were present. The proposed equations for the side weir discharge coefficient gave results that were in good accordance with two other studies.     

基于ANSYS的轴向柱塞液压电机泵电磁场数值计算与分析

提出了一种新型轴向柱塞液压电机泵,简要介绍了其结构组成和工作原理。应用ANSYS/Emag模块对带有不同冷却流道的三种电机泵的定子模型对应的空载电磁场进行了数值计算。通过对计算结果进一步的分析和计算得到了电机泵电磁场的分布及油隙磁感应强度,并进行了对比分析。研究表明,带有12个条形冷却流道的定子结构的磁感应强度最大,带有24个圆形冷却流道的定子磁感应强度最低,带有8个条形冷却流道的定子结构的磁感应强度介于上述两种之间。所作研究为新型轴向柱塞液压电机泵定子的结构设计和优化提供了依据。     

Nonlinear forced vibrations and static deformations of 3D beams with rectangular cross section: The influence of warping, shear deformation and longitudinal displacements

The geometrically nonlinear vibrations of beams with rectangular cross section, which may experience longitudinal, torsional and bending deformations, in any plane, are investigated by the p-version finite element method. Two main models are used: one of them is based on Bernoulli-Euler theory for beam bending and the other is based on Timoshenko theory; both models assume that the cross section rotates as a rigid body and is free to warp in longitudinal direction, as in Saint-Venants’s theory for torsion. The geometrical nonlinearity is taken into account by considering Green’s strain tensor and the importance of the longitudinal displacements of quadratic order, which are most often neglected in the strain-displacement relation, is here examined. Generalized Hooke’s law is used and the equation of motion is derived by the principle of virtual work. The importance of the warping function is analysed for different rectangular cross sections, and it is shown that its consideration can be fundamental to obtain correct results. Then, it is shown that the linearization of the trigonometric functions related with the twist angle, which is usually applied in the displacement field in models based on Saint-Venant’s hypothesis, should be done in the strain-displacement relations. Comparisons of the models for 3D beams based on Bernoulli-Euler’s and Timoshenko’s theories is presented. It is shown that if the rotations along the transverse axes are directly approximated by the respective derivatives of the transverse displacement functions, as is assumed in the model presented here that is based on Bernoulli-Euler’s theory, the additional shear stresses that appear when the bending and torsion motions are coupled, lead to wrong results. Finally, taking into account accuracy and simplicity, a model is chosen and employed to investigate the nonlinear forced vibrations of beams using direct integration of the equations of motion in the time domain. Examples of bending-torsion couplings due to the nonlinear terms are presented in dynamical problems.     

The measurement of discharge using a commercial digital video camera in irrigation canals

This paper presents measurements of the discharge by image techniques on the surface velocity field and water stage in irrigation canals. The velocity and stage gauge are obtained from a commercial digital video camera. The time series of the surface velocity and stage were collected simultaneously. Particle image velocimetry (PIV) was used to determine the surface velocities in the irrigation canal. PIV proceeds by using bubbles floating on the water surface as tracer particles, and making a cross-correlation analysis between two continuous images. The whole surface velocity distribution in the irrigation canals can be obtained. The water stage of the canal is obtained from the digital video camera images by making use of image segments to separate the stage gauge and the background. The discharge is computed by using the surface velocities and water stage via open channel velocity distribution theory. Comparing the discharge measured using image techniques with Parshall flume data shows that the differences are less then 5%. The results suggest that the image measurement techniques developed can be used in applications to estimate the discharge in irrigation canals effectively.