The mechanical energy equation for total flow in open channels

The mechanical energy equation is a fundamental equation of a 1-D mathematical model in Hydraulics and Engineering Fluid Mechanics. This equation for the total flow used to be deduced by extending the Bernoulli＇s equation for the ideal fluid in the streamline to a stream tube, and then revised by considering the viscous effect and integrated on the cross section. This derivation is not rigorous and the effect of turbulence is not considered. In this paper, the energy equation for the total flow is derived by using the Navier-Stokes equations in Fluid Mechanics, the results are as follows：（1） A new energy equation for steady channel flows of incompressible homogeneous liquid is obtained, which includes the variation of the turbulent kinetic energy along the channel, the formula for the mechanical energy loss of the total flow can be determined directly in the deduction process.（2） The theoretical solution of the velocity field for laminar flows in a rectangular open channel is obtained and the mechanical energy loss in the energy equation is calculated. The variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are obtained.（3） The turbulent flow in a rectangular open channel is simulated using 3-D Reynolds averaged equations closed by the Reynolds stress model（RSM）, and the variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are discussed.     

《南水北调与水利科技》优先数字出版声明

The turbulent flows through the channels with abrupt cross-sectional changes are common and importantphysical process in nature.For a better prediction of the mean flow and turbulent characteristics for this problem,atwo-dimensional depth-averaged numerical model is developed.The model is robust and accurate in reproducing therecirculation flow behind a groyne and turbulent flows in channels with abrupt cross-sectional changes,when com-pared to the available experimental data of mean velocities and turbulence kinetic energy.Our results reveal that theabrupt cross-sectional change of a channel can affect the flow pattern significantly and introduces the complex turbu-lence characteristics.In particular,when the channel has an abrupt expansion,the mean flow pattern is mainly in lon-gitudinal direction with rather small transverse component.Meanwhile,a recirculating region forms behind the expan-sion position and the turbulence has very strong intensity within this region.For the flow in the channel with an ab-rupt contraction,the longitudinal component of the flow is decreased by the obstruction on one side and accelerated onthe other side,whereas the transverse velocity is small.The turbulence is extraordinarily strong in the regions adja-cent to the contraction wall in the narrow channel.In both cases of abrupt cross-sectional changes,the TKE is genera-ted dominantly by the shear of the longitudinal velocities.     

WALL EFFECTS ON FLOWS PAST TWO TANDEM CYLINDERS OF DIFFERENT DIAMETERS

Flows past two tandem cylinders of different diameters placed centrally in a channel with fixed centre-to-centre spacing 6D and diameter ratio are simulated based on the Lattice Boltzmann Method(LBM).In all the simulations,the diameter of the smaller cylinder is chosen as the characteristic length.The Reynolds number based on the average inflow velocity is 20-120 and studies are over the range of blockage ratio 2-8.In both Small-Big Arrangement(SBA)and Big-Small Arrangement(BSA),the effects of the channel width and Reynolds number on the flow structures and force coefficients are studied.Results show that the flows in BSA are more regular than those in SBA for the same flow fields.In BSA with and,the force coefficients all fluctuate with constant amplitudes and a coupled frequency,the coupled frequency becomes small as the blockage ratio decreases and by an exact test we give out the relation of the blockage ratio and Strouhal number.As the blockage ratio decreases to 2,there exist pitchfork bifurcations in both SBA and BSA,and results show that the critical Reynolds numbers of pitchfork bifurcations for SBA and BSA are both between 60 and 80.In SBA with,the flow structure has a static asymmetric mode.It is found that the channel width has also an effect on the critical spacing where the flow changes from single body mode into co-shedding mode.By an accurate survey on flows past two cylinders with equal diameters placed inside a channel with the width,the relation between channel width and the critical spacing is given and results show that the critical spacing increases as the channel width increases.     

Design and development of guide vane cascade for a low speed number Francis turbine

Guide vane cascade of a low speed number Francis turbine is developed for the experimental investigations.The test setup is able to produce similar velocity distributions at the runner inlet as that of a reference prototype turbine.Standard analytical methods are used to design the reference turbine.Periodic walls of flow channel between guide vanes are identified as the starting profile for the boundary of the cascade.Two alternative designs with three guide vanes and two guide vanes,without runner,are studied.A new approach,for the hydraulic design and optimization of the cascade test setup layout,is proposed and investigated in details.CFD based optimization methods are used to define the final layout of the test setup.The optimum design is developed as a test setup and experimental validation is done with PIV methods.The optimized design of cascade with one guide vane between two flow channels is found to produce similar flow conditions to that in the runner inlet of a low speed number Francis turbine.     

Estimation of discharge and its distribution in compound channels简

Results of research into a compound channel having width ratio(?)in excess of 11 are presented in the form of boundary shear distributions across the compound cross section.New relationship is derived between the percentage of shear carried by the flood plains(%)fp S and the percentage of area occupied by the flood plains(%)fp A.The equation so derived is taken as the basis to develop a new methodology to predict the stage discharge relationship specifically for wide compound channels using Darcy’s friction factor(f)for the main channel and flood plain regions.The methodology also is used for compound channels with smaller width ratios by applying the appropriate relation for%fp S derived earlier by different researchers and seems to work well.Next,as a corollary to the methodology,separate formulae are proposed to estimate flow distribution in main channel and flood plain regions.The proposed method and its corollary are tested for their validity against well-published small-scale data series of previous researchers along with some large-scale data series from EPSRC-FCF(A-Series)compound channel experiments and very good agreement is observed between the measured values and predicted values for total flow as well as zonal distribution of flow.The methodology is also applied to some compound river section data published in literature and is found to serve well the purpose of predicting flow in real world application.This new method gives the least RMS value of error for discharge prediction compared with some other well-known methods used for estimating stage-discharge relation in compound channels by considering all data sets.     

Effect of vegetated-banks on local scour around a wing-wall abutment with circular edges

Failure of bridges due to local scour in the vicinity of bridge abutments is a common occurrence. In this study, experiments under two different channel conditions were conducted to assess the impacts of vegetation on channel banks on local scour around a wing-wall abutment with circular edges. Some experiments were conducted in channel with vegetation on channel banks, and other experiments in channel without vegetation on channel bank. The flow velocity and Reynolds stress distributions in scour holes around a wing-wall abutment with circular edges were compared under these 2 different channel conditions. Results reveal that the vegetated-banks can reduce the time for achieving the equilibrium condition from 17 h to 9 h. Also, vegetated-bank channels can result in a significant decrease in the maximum scour depth from 0.084 m（for bare channel bank） to 0.00032 m. Additionally, around the abutment, vegetated-banks play a significant role in diminishing the Reynolds stress（RS） near the bed and removing negative values in RS distribution by weakening unfavorable pressure gradient and down-flow in the upstream of abutment.     

LARGE EDDY SIMULATION OF PULSATING TURBULENT OPEN CHANNEL FLOW

Pulsating turbulent open channel flow has been investigated by the u.se of I.arge Eddy Simulation (I.ES) technique coupled with dynamic Sub-Grid-Scale (SGS) model for turbulent SGS stress to closure the governing equations.Three-dimensional filtered Navier-Stokes equations are numerically solved by a fractional-- step method. The objective of this study is to deal with the behavior of the pulsating turbulent open channel flow and to examine the reliability of the I.ES approach for predicting the pulsating turbulent flow. In this study, the Reynolds number (Re,) is chosen as 180 based on the friction velocity and the channel depth, The frequency of the driving pressure gradient for the pulsating turbulent flow ranges low, medium and high value, Statistical turbulence quantities as well as the flow structures are analyzed.     

DEBRIS FLOW KINETIC CHARACTERISTICS UNDER NATURAL CONDITIONS

The study for debris flow kinetic characteristics can not be approached byexperiments due to their complexity and distransparency,etc.This paper is a picture of debrisflow kinetic characteristics based on the natural debris flow observation and experiments.Thekinetic characteristics of viscous debris flow are obtained by radar veloeimeter and ultrasoniclevel meter in jiangjia ravine.From those,the following are suggested:in natural channel,debris flow can be classified as three kinds of type:strong turbulent debris flow;turbulent debrisflow;weak turbulent debris flow:meanwhile the Reynolds number(Re)is chosen as an indexfor the classification.     

MODEL EXPERIMENT RESEARCH ON CROSS FRACTURE FLOW

This paper gives emphasis on the research of the problem of local head loss of cross fracture flow by a lot of model experiments,and a theoretical model of local head loss of cross fracture flow is founded by use of the momentum law of water flow.Through the correlation analysis between model experimental results and theoretical model,the correction coefficient of theoretical model is definite.The proposed calculation formula of local head loss of cross fracture flow can be used to analyze the problem of network fracture seepage.     

Spatial relationship between energy dissipation and vortex tubes in channel flow

The spatial relationship between the energy dissipation slabs and the vortex tubes is investigated based on the direct numerical simulation(DNS) of the channel flow. The spatial distance between these two structures is found to be slightly greater than the vortex radius. Comparison of the core areas of the vortex tubes and the dissipation slabs gives a mean ratio of 0.16 for the mean swirling strength and that of 2.89 for the mean dissipation rate. These results verify that in the channel flow the slabs of intense dissipation and the vortex tubes do not coincide in space. Rather they appear in pairs offset with a mean separation of approximately 10η.     

Delineating Capture Zone of a Pumping Well in a Slanting Regional Groundwater Flow to a Stream with a Leaky Layer

In this study, analytical and semi-analytical solutions are derived to delineate capture zone of a pumping well near a stream where a leaky layer exists between the aquifer and the stream. A groundwater regional flow is considered in the aquifer and allowed to have different angles with respect to the stream axis. Three critical pumping rates are introduced. At the first pumping rate, capture zone boundary tangents the interface between the aquifer and the leaky layer; called the in-homogeneity boundary. At the second pumping rate, capture zone boundary tangents the stream boundary and if the rate is increased, a part of pumped water would be withdrawn from the stream. The third pumping rate, which may be smaller or larger than the other two, is defined as the rate at which stream water begins to enter the leaky layer; it may or may not be captured by the pumping well. Four different capture zone configurations (cases) are analyzed for different values of pumping rates, groundwater flow directions, and leaky layer’s thickness and hydraulic conductivity. The first three cases analyze hydraulic situations whereby capture zone does not reach the stream, and hence, no pumped water is withdrawn from the stream. With the lowest pumping rate in the first case, no stream water enters the leaky layer. It enters the leaky layer but not the aquifer in the second, and enters the leaky layer and the aquifer in the third case. In the fourth case, where capture zone boundary intersects the stream, the fraction of pumped stream water to total pumped water is delineated.     

When does a stream become a river?

The distinction between a “stream” and “river” is imprecise and vague despite the popular usage of the terms across disciplines for describing flowing waterbodies. Based on an analysis of named flowing waterbodies in the continental United States, we suggest a bank-to-bank channel width of 15 m as a working threshold in defining smaller “streams” from larger “rivers.”     

台阶形陆架上孤立波传播的数值模拟

为了研究孤立波在带有陡升台地的陆架上的传播,用MAC方法求解了二维纳维尔-斯托克斯方程。本文在以下几点,改进了东京大学提出的修正的网格标记法:1.给出交错网格的新的标号系统;2.推导出自由表面上非规则星的新的压力迭代公式;3.对流函数、压力和速度使用了三值悬旗;4.把一维Burgers方程的部分守恒形式扩展用于二维N-S方程。这些使得程序更简单和精确。计算结果证卖,物理上很好地解释了孤立波的传播,入射波分成了反射波和透射波,然后开始分裂、破碎。 本文计算结果与线性波理论的结果很一致,但后者不能给出波运动的过程。     

Construction of a temporary protective embankment for eliminating a failure of a sewer inverted siphon

Translated from Gidrotekhnicheskoe Stroitel'stvo, No. 9, pp. 16–19, September, 1991.