Search

In overbank flow due to the interaction mechanism between the main channel and floodplain, the flow property of the compound sections gets affected. The complexity is more when the compound channels have non-prismatic floodplains. Additional complexity occurs during the interaction between the subsections as well as due to non-uniformity of flow through converging parts of the compound channel. For prediction of flow, calculation of energy loss parameters from section to section is an important task for river engineers. In this paper, an experimental investigation for the energy losses of converging compound channels for different flow depths along the converging path is performed. The loss of energy due to contraction and compound geometry for a compound channel is evaluated, and the dependency of energy loss for such channels is analyzed. A generalized multivariable regression model has been developed to predict the energy slope with high accuracy. Using the expression of the energy loss concept, the discharge capacity in the converging compound is found to provide good results as compared to other standard model exists in the literature.

Channel fracturing technique (CFT) is a stimulation method which can promote the generation of high-fracture-conductivity open channels and get higher production and less cost in fracturing operation. This paper presents the numerical simulations of the gas-liquid two-phase flow in channel fracture packs by establishing a new model. To model the multi-phase flow in channel fracture pack, a two-fluid basic model is adopted and extended by including slip velocity and friction force in the closure relations. The flow in channel and in pillars are coupled by pressure and this model is solved using finite volume method. Also, a series of laboratory experiments were carried out to obtain the structure of channel fracture packs, and the measurement of fracture conductivity was carried out and the fracture productivity formula was used to validate the model. The simulation results of pressure, velocity and streamline are analyzed and discussed in this paper, and it shows that the main reason for the significant decrease in the actual production compared to the expected value in channel fracturing well is that ideal continuous channels which has high-fracture-conductivity are not formed, and the structure of pore-channels which complicates the flow laws are formed. The appearance of the structure of pore-channels will change the expected main flow pattern which is along the continuous open channels to a complicated flow which will bring much friction resistance. The flow laws in the channel fracture pack are primarily dominated by the number and distribution of pore-channels. Also, the factors such as bottom hole flowing pressure (BHFP), viscosity and density of the mixture in the formation, numbers of phase states and mass flow rate have impact on it, mainly in the aspect of velocity distribution. The natural gas and the formation water both have a similar behavior in pore-channels but have different flow trends in proppant packs, and their velocity in pore-channels are relatively higher than them in proppant packs, and compared to the velocity of natural gas, the velocity of formation water in pore-channels is relatively high. The original flowing trend in proppant pack changes and tends to show a sudden inrush to pore-channels which will bring a large amount of inlet, outlet and linear losses.

A free over-fall can be used as a flow metering hydraulic structure with a single depth measurement of the end. Due to that, theoretical and experimental research has been undertaken on free over-falls with various approaches for different cross-sectional shapes. This paper presents a new and relatively simple theoretical approach for computing the end depth ratio (EDR) and the end depth discharge (EDD) relationships for exponential and generalized trapezoidal channel cross-sections at free over-falls for sub-critical flow regime. The exponential channel is a general channel cross-section which is defined mathematically with a single exponential equation where five widely known prismatic shapes can be generated (rectangular, parabolic, semi-parabolic, triangular and semi-triangular). Similarly, the generalized trapezoidal channel is a geometric shape that is defined mathematically with the 2nd degree equation where seven widely known prismatic channel cross-sectional shapes can be generated (rectangular, triangular, semi-triangular, trapezoidal, semi-trapezoidal, inverted triangular (∆) and semi-inverted triangular). This suggested theoretical approach uses three velocity points at the end (brink) section and the continuity equation to obtain the EDR. To verify the proposed EDR and EDD relationships, relevant experimental and theoretical study results were gathered and statistically examined through the percentage difference and the correlation coefficient ( R 2 ). The computed results show very close agreements with the earlier works. For engineers in practice, simple equations are also generated to estimate the direct discharges ( Q ) using the end depth ( y e ) for each of the above mentioned channel cross-sections.

Presented are the results of flume experiments on the flow-retarding performance of baffle-post structures in openwater flow. Such structures consist of one to two parallel rows of unsubmerged posts that retard an approach flow, reducing flow velocity, increasing flow depth, and altering lateral distribution of flow. The results relate headloss and flow depth increase at the structure to lateral and streamwise variations in post spacing, post diameter, and approach flow conditions, and represent average velocities of flow through the structure. For given approach flows, the flow-retarding performance of baffle-post structures is shown to be much more sensitive to lateral spacing of posts and approach flow Froude number, than to streamwise spacing (for double row structures) and approach-flow depth relative to post diameter. Estimates are given for the percentage increase in water depth that baffle posts will produce. This information informs the design of baffle-post structures and evaluation of t...

A general solution is presented for elevation waves in a horizontal channel with a trapezoidal transverse cross-section. The procedural approach is based on the principles of the general theory of energy motion. Specific cases of the obtained solution are relations for rectangular and triangular cross-sections, as well as relations of simple form for waves of low height. The relation shows the dependence of the propagation velocity of long waves on the cross-sectional shape of the channel. The results agree completely with those obtained previously.

This paper presents a hybrid optimization method aiming to design the flow channel shape and reduce its flow resistance or pressure drop. The method combines flow pattern construction-based optimization with natural heuristic optimization. Firstly, an optimal flow field with minimum viscous dissipation is constructed. Then the channel shape is adapted by substituting the fluid cells that have lower dynamic pressure in the optimal flow field with solid cells. With solid cells being inserted into the flow domain, the channel volume decreases. This process (i.e. constructing optimal flow field and inserting solid cells to the flow domain) is repeated until the channel volume decreases to a certain value. As an intermediate result, a preliminary optimal channel shape is obtained. The second step of the hybrid optimization method is to further optimize the preliminary shape using the natural heuristic optimization. That is, the positions of the solid cells and fluid cells are exchanged stepwise. Ultimately, a streamlined channel shape is generated with reduced pressure drop. To demonstrate the validity of the method, a right-angle elbow, a straight tee channel and a multi-inlet channel are optimized, respectively.

The complexity of two-dimensional SKM model is to calibrate the three governing parameters (bed friction f, eddy viscosity coefficient λ or turbulent friction and secondary flow Г) before it can be applied to predict the depth-averaged velocity in an open channel flow. To quantify the secondary current, the factor k needs to be calibrated from reliable data-sets. The roughness parameter f is considered from the surface properties of the channel, whereas the eddy viscosity parameter λ is generally taken to be constant value. A computer program has been developed to solve the two-dimensional SKM model analytically so as to simulate the depth-averaged velocities from point to point along the lateral directions. The results reveal that the secondary flow factor k bears a specific relationship with flow depths over the constant depth domain and another relationship for variable depth domain. In this study, mathematical relationships have also been developed for accurate estimation of secondary flow coe...

The mechanical energy loss and the wall resistance are very important in practical engineering. These problems are investigated through theoretical analysis and numerical simulation in this paper. The results are as follows. (1) A new mechanical energy equation for the total flow is obtained, and a general formula for the calculation of the mechanical energy loss is proposed. (2) The general relationship between the wall resistance and the mechanical energy loss for the steady channel flow is obtained, the simplified form of which for the steady uniform channel flow is in consistent with the formula used in Hydraulics deduced by π theorem and dimensional analysis. (3) The steady channel flow over a backward facing step with a small expansion ratio is numerically simulated, and the mechanical energy loss, the wall resistance as well as the relationship between the wall resistance and the mechanical energy loss are calculated and analyzed.

Water transferring to the dam downstream creates high levels of kinetic energy. Stepped spillways are amongst the most effective spillways in reducing the kinetic energy of the flow moving towards the downstream. The geometry of the steps in stepped spillways can affect the reduction of kinetic energy of the flow transferring to the downstream. Therefore, in this study the effect of different number of steps and discharge on flow pattern especially energy dissipation were investigated. The VOF method was used to simulate the flow surface and the k-ε (RNG) turbulence model was used for flow turbulence simulation. Comparing the results obtained from the numerical simulation with the experimental data indicated an acceptable level of consistency. Comparing the obtained results showed that decreasing the number of the steps of pooled stepped spillways reduced flow velocity and increased the relative energy dissipation at the end of the spillway. Decreasing the number of steps increased the turbulent kinetic energy value. Also, the maximum turbulent kinetic energy was obtained near the step’s pool. Moreover the results indicated that the value of turbulent kinetic energy increased along the spillway.

We examine different aspects of energy conservation in the case of the analytical solution of Ritter for idealized dam break flow in a horizontal frictionless and dry channel. We detail the application of the unsteady Bernoulli equation in this case and highlight that the inertial effects cancel out when averaged over the whole flow region. We also show that the potential and kinetic contributions to the total mechanical energy in the flow region have a distinct and constant relative importance: potential energy accounts for 60%, and kinetic energy for 40% of the total mechanical energy. These properties of Ritter solution are rarely emphasized while they may be of practical relevance, particularly for the verification of numerical schemes with respect to their ability to ensure energy conservation.

2D surface flow models are useful to understand and predict the flow through breach, over a dyke or over the floodplains. This paper is aimed at the surface flows to study the behavior of flood waves. The open channel water flow in drains and rivers is considered in view of the fact that such flows are the source of flash flood. In order to predict and simulate the flood behavior, a mathematical model with the initial and boundary conditions is established using 2D Saint-Venant partial differential equations. Next, the corresponding model is discretized by using the explicit finite difference method and implemented on MATLAB. For the testing and implementation purpose a simple rectangular flow channel is considered. The output parameters like height or depth of water z (m), the fluid velocity u (m/s) and the volumetric flow rate Q (m3/sec) are simulated numerically and visualized for the different time steps. The initial simulation results are useful to understand and predict the flood behavior at different locations of flow channel at specific time steps and can be helpful in early flood warning systems. It is also suggested that the coupling of the subsurface flow with the surface flow may provide even better approximations for the flood circulation.

The protrusion of a hydraulic structure constructed in a river bed disturbs the flow and sediment transport. It is very important to investigate the changes on micro-flow behavior (turbulent) from sediment transport point of view. In this paper an attempt has been made to investigate the change in flow turbulent kinetic energy along the flow depth with and without Piano Key Weir (PKW; a type of labyrinth weirs) and try to establish a distribution pattern of turbulent kinetic energy with respect to relative depth. Here, relative depth is defined as ratio of depth of point of measurement and depth of flow. Flow resistance has been increased after introduction of PKW in channel. Turbulent kinetic energy has been fitted with Gaussian distribution of higher order as flow resistance increased. After introduction of PKW in channel, velocities slow down but shifting of centroid indicates relative ease of passing particles through sloping keys.

Active boundary layer flow control and boundary layer manipulation in the channel flow that was based on low temperature plasma were studied by means of a lattice Boltzmann method. Two plasma actuators were placed in a row to obtain the influence rule of their separation distance on the velocity profile at three locations and maximum velocity in the flow field. Two plasma actuators were placed symmetrically inside a channel to examine the effect of channel height and voltage on the velocity profile and flow rate. It was found that the channel height controls the distribution of flow velocity, which affected the flow rate and its direction. Increasing plasma voltage had a negative effect on the flow rate due to the generation of a larger and stronger flow vortex.

Mixed convection hydromagnetic flow of a viscous, incompressible, electrically and thermally conducting fluid in a rotating channel taking Hall current into account is studied. Fluid flow within the channel is induced due to an applied pressure gradient acting along the longitudinal axis of the plates of the channel. Exact solution of the governing equations is obtained in closed form. Expressions for the shear stress and critical Grashof number at the plates of the channel due to primary and secondary flows and mass flow rates in the primary and secondary flow directions are also derived. Asymptotic behavior of the solution for fluid velocity and induced magnetic field is analyzed for large values of rotation parameter K2 and magnetic parameter M2 to gain some physical insight into flow pattern. Heat transfer characteristics of fluid flow are considered taking viscous and Joule dissipations into account. Numerical solution of energy equation and numerical values of rate of heat transfer at the plates of the channel are computed with the help of MATLAB software. The numerical values of fluid velocity, induced magnetic field and fluid temperature are displayed graphically versus channel width variable η for various values of pertinent flow parameters whereas that of shear stress and critical Grashof number at the plates of the channel due to primary and secondary flows, mass flow rates in the primary and secondary flow directions and rate of heat transfer at the plates of the channel are presented in tabular form for various values of pertinent flow parameters.

The accuracy of discharge measurement in open channels using propeller current meters can be improved considerably by optimizing the number and locations of the current meters to be deployed for this purpose. The optimization is possible if the nature of the flow profile in the channel can be assessed. This paper reports development of a mathematical model of the flow velocity profile of rectangular open channels. One-dimensional velocity profile equation is taken as a sum of logarithmic and parabolic terms and used to determine the unit-width discharge profile across the width of the channel. The unit-width discharge equation comprises two logarithmic terms along with a beta function. The two equations together involve 10 mathematical parameters, which are linked to the physical conditions, geometry, and configuration of the channel. MATLAB code has been developed to account for these parameters and obtain the velocity profile of flow in any rectangular open channel. Flow under similar conditions...

The single-phase and multiphase Eulerian equations of change are derived by applying a suitable averaging procedure to the local instantaneous equations of change. In the present work, the local instantaneous equations of change for mass, species mass, momentum and energy are gross-scale averaged over the cross-sectional area. In particular, the internal energy equation is achieved by subtracting the kinetic energy equation from the total energy balance. Thus, two paths are to our disposal for deriving the cross-sectional averaged internal energy balance: (i) the averaged kinetic energy equation is subtracted from the averaged total energy equation, or (ii) the local instantaneous kinetic energy equation is subtracted from the local instantaneous energy equation and the resulting equation is averaged. The resulting Euler equations of change for internal energy are not identical for these two approaches. Approach (ii) is recommended because of its simplicity.

Although combining flows are common in natural streams, no comprehensive experimental data has been compiled to characterize the three-dimensional flow field within the compound channel confluence. The present study examines the time-averaged flow structure at confluence over a rigid bed. Current knowledge of channel confluence, based on laboratory observation indicates that cross flow interactions exert a significant influence on confluence events. Secondary current and turbulent stresses are reproduced well by the hydraulic model and found greater in the interface region as relative flow ratio decreases. Velocity fields in combining flow region arising from varying discharge ratios are presented. A zone of depression in surface elevation in compound channel junction is observed as well. The flow field in compound channel is seen to be moderately different from that of simple channel junction. This study contributes to a better knowledge of hydraulic key processes into fundamental aspect of combining flow dynamics.

Using primitive equation simulations, a zonally periodic channel is considered. The channel flow is forced by a combination of steady and high-frequency winds. The high-frequency forcing excites near-inertial motion, and the focus is on how this influences the low-frequency, nearly geostrophic part of the flow. In particular, this study seeks to clarify how Reynolds stresses exerted by the near-inertial modes affect the low-frequency kinetic energy. In the system considered, the near-inertial Reynolds stresses (i) serve as a sink term in the low-frequency kinetic energy budget and (ii) transfer low-frequency kinetic energy downward from the mixed layer. Transfer spectra show the bulk of this sink to occur at relatively small horizontal wavenumber (i.e., in the mesoscale, not the submesoscale). The presence of near-inertial motion can also affect the kinetic-to-potential energy exchanges, especially within the low-frequency band.

Diffuser channels with 90° rotation of the flow are used in a number of technical devices to slow down and turn the flow of the working fluid. Besides slowing down and turning of the flow at the outlet of the channels, it is necessary, as a rule, to possibly provide a uniform field of velocities. However, it is necessary to take into account the requirements for the compactness, which, in some cases, are crucial and lead to the need for nonoptimal channels in terms of aerodynamics, including wide-angle diffusers, which are highly likely to cause the flow breakaway with sharply uneven output velocity field. The results of experimental research method of alignment of the velocity field at the output of the wide-angle flat diffuser channel with 90° rotation of the flow by installing plates with round and square holes and varying degrees of perforation inside of the channel are presented in this paper. The studies were carried out on an open-type wind tunnel changing the dimensionless velocity at the inlet of the diffuser channel section in the range from 0.18 to 0.72. The values of the coefficients of the total energy loss in a channel were determined. Which of the installed perforated plates lead to the lowest increase of the energy loss was established. The optimal location of these plates within the duct was determined. The measurements of the velocity fields at the outlet of the channel were carried out. Simultaneously, the measurements of the pressure pulsations on the side wall at the outlet of the channel were carried out. It was shown that the minimal increase in energy losses due to the installation of plates can substantially equalize the output of the velocity field and reduce the dynamic loads on the walls. The obtained results allow us to recommend this method of aligning the output of the velocity field for real technical devices that require the simultaneous slowdown in the flow and its rotation.

Summary Is the energy equation for gradually-varied flow the best approximation for the free surface profile computations in river flows? Determination of flood inundation in rivers and natural waterways is based on the hydraulic computation of flow profiles. This is usually done using energy-based gradually-varied flow models, like HEC-RAS, that adopts a vertical division method for discharge prediction in compound channel sections. However, this discharge prediction method is not so accurate in the context of advancements over the last three decades. This paper firstly presents a study of the impact of discharge prediction on the gradually-varied flow computations by comparing thirteen different methods for compound channels, where both energy and momentum equations are applied. The discharge, velocity distribution coefficients, specific energy, momentum and flow profiles are determined. After the study of gradually-varied flow predictions, a new theory is developed to produce higher-order energy and momentum equations for rapidly-varied flow in compound channels. These generalized equations enable to describe the flow profiles with more generality than the gradually-varied flow computations. As an outcome, results of gradually-varied flow provide realistic conclusions for computations of flow in compound channels, showing that momentum-based models are in general more accurate; whereas the new theory developed for rapidly-varied flow opens a new research direction, so far not investigated in flows through compound channels.

Energy structure of MHD flow coupling with outer resistance circuit is studied to illuminate qualitatively and quantitatively the energy relation of this basic MHD flow system with energy input and output. Energy structure are analytically derived based on the Navier–Stocks equations for two-dimensional fully-developed flow and generalized Ohm's Law. The influences of applied magnetic field, Hall parameter and conductivity on energy structure are discussed based on the analytical results. Associated energies in MHD flow are deduced and validated by energy conservation. These results reveal that energy structure consists of two sub structures: electrical energy structure and internal energy structure. Energy structure and its sub structures provide an integrated theoretical energy path of the MHD system. Applied magnetic field and conductivity decrease the input energy, dissipation by fluid viscosity and internal energy but increase the ratio of electrical energy to input energy, while Hall parameter has the opposite effects. These are caused by their different effects on Bulk velocity, velocity profiles, voltage and current in outer circuit. Understanding energy structure helps MHD application designers to actively adjust the allocation of different parts of energy so that it is more reasonable and desirable.

It is well known that the energy transport of ocean waves propagates with the group velocity and that the energy decreases exponentially with depth. Expanding this theory, we will derive expressions for the energy transport as a function of depth and the total instantaneous transport's development over time for waves in waters of finite depth. Solutions to the Laplace equation are found for plane-parallel polychromatic waves with linearized boundary conditions. A time series of wave elevation collected at Uppsala University's wave energy research test site is chosen to present the results. Solutions for waters of both infinite and arbitrary depths are presented and compared. The solutions are convolution-type integrals with the wave elevation where we have found efficient ways to calculate the kernels. The difference in group velocity between finite depth and infinite depth and its impact on the energy transport is clearly seen in the results. The use of the deep-water approximation gives a too low energy transport in the time averaged as well as in the total instantaneous energy transport. We further show that the total instantaneous energy transport can actually have a direction that is opposite to the direction of the waves as observed from a reference frame fixed to the seabed.

Uniform flow distribution is an important and fundamental issue to miscellaneous devices. The present work studied the details of flow in a channel with a fundamental structure—a symmetric bifurcation of one flow channel into two sub-channels. The structure is designated to split one flow into two streams of even flow rate. Key geometric design factors of the flow channel are investigated regarding the effect to the development of a symmetric velocity profile after the flow channel bifurcation, as the symmetric velocity profile is critical to the even split of the flow into two streams in the next stage of flow channel bifurcation. The study is based on both two-dimensional and three-dimensional CFD analyses. Both laminar and turbulent flows are investigated. Commercial CFD software ANSYS FLUENT® was used. The numerical treatment of convection terms in governing equations was based on the QUICK scheme, and the SIMPLE algorithm was used to treat the coupling of pressure and velocity fields. The obtained results are of great significance to the design of flow distributors using cascade flow channel bifurcations.

The purpose of this study is to evaluate the behaviour and mechanism of debris flow on various slopes through numerical simulation. The numerical simulation was performed using the Finite Difference Element Method based on the equation of mass conservation and momentum conservation. In order to measure the behaviour of the debris flow, the debris flow of the straight rectangular channel slope and that of the one-stepped channel slope were compared. Firstly the water flow discharge, the water flow depth, and the sediment volume concentration at the slope downstream of the channel, depending on the different inflow water flow discharges at the upstream of the channel, were analyzed. The smaller the supply from the upstream of the channel, the water flow discharge and the water flow depth surged only at the point after the debris flow reached the downstream of the channel, and showed a tendency to decrease thereon after. On the other hand, when the supply at the upstream of the channel increased, the curve of the water flow discharge and the water flow depth was unsteadily high. Through the Root Mean Square ratio (RMS) comparison, the water flow discharge and water flow depth of the one-stepped channel slope was lower than that of the straight rectangular channel slope. Secondly, the water flow discharge, water flow depth, and sediment volume concentration depending on the change in the slope of the one-stepped channel slope were analyzed. The larger the slope, the larger the fluctuation in amplitude of the curve and this resulted in a higher water flow discharge distribution as well as in a wider fluctuation bandwidth. In the results of the study at each point, in the case of the straight rectangular channel, the water flow discharge and depth increased as it went downstream. This is because more erosion than deposition occurs when debris flow occurs at the upstream of the channel.

An experimentally study of water level changes at open channel junctions with angles of 30° and 60° for different flow conditions is presented. The experimental results were used to assess the equal water level assumption commonly adopted in confluence studies. The maximum value of the water depth at the confluence was assessed through comparison with the critical depth in the downstream channel. Additionally, the results were used to validate the generalization of a classical model for estimating the water depth in confluences with subcritical flows downstream from the junction, even in cases where one or both upstream channel flows were supercritical. The maximum average deviations between the model predictions and measurements were approximately 6%.

Flooding situation in river is a complex phenomenon and affects the livelihood and economic condition of the region. The modelling of such flow is primary importance for a river engineers and scientists working in this field. As a result of topography changes along the open channels, designing the converging compound channel is an essential. Fluvial flows are strongly influenced by geometry complexity and large overall uncertainty on every single measurable property, such as velocity distribution on different sectional parameters like width ratio, aspect ratio and hydraulic parameter such as relative depth. The geometry selected for this study is that of a non-prismatic compound channel having converging flood plain. For the research work the parameters, the water depth, incoming discharge of the main channel and floodplains were varied. Continuous variation of channel geometry along the flow path associated with secondary currents makes the depth averaged velocity computation difficult. In this paper the variations of depth average velocities for five different sections in between the convergence region of the converging compound channel are compared by taking two different flow depth conditions. And also shear stress distribution at the walls and on the bed of two stage converging compound channel is calculated by doing experimentation in laboratory as bed shear forces are useful for the study of bed load transfer whereas wall shear forces presents a general view of channel migration pattern. Then the numerical method is applied to analyse the flow conditions in non-prismatic compound channel configurations, the results of calculations show good agreement with the experimental data. As numerical hydraulic models can significantly reduce costs associated with the experimental models, an effort has been made through the present investigation to determine the different flow characteristics of a converging compound channel such as velocity distribution, depth averaged velocity distribution, boundary shear etc. In this paper a complete three dimensional and two-phase CFD model for flow distribution in a converging compound channel is investigated by using Large Eddy Simulation (LES) model for solving the turbulence equation. This study aims to validate CFD simulations of free surface flow or open channel flow by using Volume of Fluid (VOF) method by comparing the data observed in hydraulics laboratory of the National Institute of Technology, Rourkela.

This paper presents results of a modeled open channel flow through a porous media (River). In the model, we considered water as an incompressible fluid; the flow as steady and uniform; the system is assumed to be isothermal and the flow pattern is laminar. We have solved the resulting Brinkman equation using analytical method. By some mathematical operation, the momentum partial differential equation (PDE) was reduced to ordinary differential equation (ODE) and the resulting equations are solved analytically using the standard solution technique for a second order ODE. The analysis of the result was done and plotted on graph using MATLAB to show the effect of permeability on flow parameters such as velocity, pressure gradient and height of the channel. It is found that velocity of the open channel decreases with increase in permeability. Also, increase in the height of the open channel results in increase in velocity of flow in the open channel. We also found that an increase in the permeability of an open channel resulted in decrease in pressure.

To find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and the geometric mean. Also hydraulic averaging by means of conveyance is commonly used. In this study, water surface profiles numerically computed using different formulas for expressing the average slope were compared with exact analytical solutions of the differential energy equation. Maximum relative and mean square errors between numerical and analytical solutions were used as measures of the quality of numerical models. Experiments showed that all methods gave solutions useful for practical engineering purposes. For every method, the numerical solution was very close to the analytical one. However, from the numerical viewpoint, the differences between the methods were significant, as the errors differed up to two orders of magnitude.

This paper presents an analytical method for modeling the lateral depth-averaged velocity distribution along a half-meander in a curved compound channel. An equation is derived from the momentum equation and the flow continuity equation which contains a velocity term with both streamwise velocity variation and lateral secondary flow variation. A velocity variation parameter is proposed in the main channel and on the floodplain for a series of test sections. To study the validity of these equations experiments were conducted in a large scale meandering compound channel at Sichuan University, China. Based on the experimental data, the generation mechanism of secondary flow in the main channel along half a meander is analyzed. It is shown that the secondary current is enhanced by the centrifugal force and the floodplain flow. Due to the discontinuity of the flow depth and the effect of meandering in the main channel flow, a region divided method is adopted. A new boundary condition is proposed by introducing the angle between the main channel flow and the floodplain flow, and it is shown that this gives better modeling results in cross-over sections. The modeling results indicate that the proposed method, which uses the new boundary condition and includes both the streamwise velocity variation and the lateral secondary flow variation, can model the lateral depth-averaged velocity distributions more accurately. Finally, variations in the velocity term between the main channel and floodplain are discussed and analyzed.

Although, natural channels are rarely rectangular or trapezoidal in cross section, these cross sections are assumed for the computation of steady, gradually varied flow in open channel networks. The accuracy of the computed results, therefore, becomes questionable due to differences in the hydraulic and geometric characteristics of the main channel and floodplains. To overcome these limitations, an algorithm is presented in this paper to compute steady, gradually varied flow in an open-channel network with compound cross sections. As compared to the presently available methods, the methodology is more general and suitable for application to compound and trapezoidal channel cross sections in series channels, tree-type or looped networks. In this method, the energy and continuity equations are solved for steady, gradually varied flow by the Newton–Raphson method and the proposed methodology is applied to tree-type and looped-channel networks. An algorithm is presented to determine multiple critical depths in a compound channel. Modifications in channel geometry are presented to avoid the occurrence of multiple critical depths. The occurrence of only one critical depth in a compound cross section with modified geometry is demonstrated for a tree-type channel network.

This paper describes the measurement of the parameters of the experiment, the problems in the analysis of experimental data processing and experimental error. The flow pattern and pressure drop of flow boiling, heat flux and heat transfer coefficient of relations are studied by analysis of the experimental data. The test section were isolated three flow patterns, bubble-like flow, limited bubble-like flow and evaporated to dryness district. Only isolated bubble-like flow of a stream type such as channel width = 2.0mm thin channel, volume flow greater than 15.47L/h. For channel width =1.0mm thin channel, bubbly flows is limited bubbly flow changes corresponding volume flow 10.8L/h.

The recurring problem of calculating the normal depth in a trapezoidal open channel is easily solved by the rough model method. The Darcy-Weisbach relationship is applied to a referential rough model whose friction factor is arbitrarily chosen. This leads to establish the non-dimensional normal depth relationship in the rough model. Through a non-dimensional correction factor of linear dimension, the aspect ratio and therefore normal depth in the studied channel is deduced. Keywords: Rough model method, Trapezoidal channel, Normal depth, Turbulent flow, Discharge, Energy slope.

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.

Extensive experimental results conducted in a 10-m flume for various types of non-Newtonian fluids spanning a range of cross-sectional open channel shapes are presented and analysed in depth in this work. Open channel flow of non-Newtonian slurries is relevant in mining and chemical engineering applications. This database coupled with the literature data is used to develop the generalised friction factor–Reynolds number correlations in a unified fashion. Much confusion still exists in the literature regarding the definition of non-Newtonian Reynolds numbers. This difficulty is circumvented by considering two widely accepted definitions of the Reynolds number, namely due to Haldenwang et al. (Hydrotransport 15: 15th international conference on the hydraulic transport of solids in pipes, Banff, pp 755–768, 2002) for open channel flow and the modified Metzner–Reed pipe flow Reynolds number adapted for open channel flow. Three different types of purely viscous non-Newtonian fluids in rectangular, trapezoidal, triangular and semi-circular channel shapes were tested. The modelling procedure of Garcia et al. (Int J Multiph Flow 29:1605–1624, 2003) used for pipe flow predictions was extended to the present work. The logistic dose curves based on the Reynolds number proposed by Haldenwang et al. [14] performed better than those based on the adapted Metzner–Reed Reynolds number. Correlations developed can be used for the design of open channels of various shapes to transport non-Newtonian fluids.

Flow connection in channels is a phenomenon which frequently happens in rivers, water and drainage channels and urban sewage systems. The phenomenon appears to be more complex in rivers than in channels, especially at the y-junction bed joint that causes erosion and sedimentation at some areas resulting to morphological changes. Flow behavior at the channel junction area depends on variables such as channel geometry, discharge ratio, tributary width and y-junction connection angle of the channel, bed level changes at the bed joint, flow characteristic at the bed joint upstream and flow Froude number in different sections. In this research, fluent numerical model and junction angles of 30o, 45o& 60oare used to analyze and evaluate the effect of channel junction geometry on the flow pattern and the flow separation zone dimensions in different ratios of flow discharge (upstream channel discharge to total discharge of the flow). Results for two ratios of flow discharge are represented. Results are in agreement with earlier studies and it is shown that the change of the channel crossing angle affects the flow pattern in the main channel and also that the dimensions of the created separation zone in the main channel become larger when the crossing angle increases. This phenomenon can also be observed when the flow discharge ratio is lower. Analysis showed that the least dimension of the separation zone will be at the crossing angle of 45o.

The calculation of the mechanical energy loss is one of the fundamental problems in the field of Hydraulics and Engineering Fluid Mechanics. However, for a non-uniform flow the relation between the mechanical energy loss in a volume of fluid and the kinematical and dynamical characteristics of the flow field is not clearly established. In this paper a new mechanical energy equation for the incompressible steady non-uniform pipe flow of homogeneous fluid is derived, which includes the variation of the mean turbulent kinetic energy, and the formula for the calculation of the mechanical energy transformation loss for the non-uniform flow between two cross sections is obtained based on this equation. This formula can be simplified to the Darcy-Weisbach formula for the uniform flow as widely used in Hydraulics. Furthermore, the contributions of the mechanical energy loss relative to the time averaged velocity gradient and the dissipation of the turbulent kinetic energy in the turbulent uniform pipe flow are discussed, and the contributions of the mechanical energy loss in the viscous sublayer, the buffer layer and the region above the buffer layer for the turbulent uniform flow are also analyzed.

The paper reports about flow analysis in a wide compound channel. New experiments are conducted in a two stage compound channel having width ratio more than 11 and aspect ratio more than 5 under various over-bank conditions with relative depth varying between 0.08 and 0.43. These experiments are significant due to rarity of flow investigation in wide compound channel as evident from published literature. In the present work, new equations for predicting boundary shear stress distribution for a wide compound channel in terms of non-dimensional geometric and flow variables are developed. The model can be applied to predict the stage–discharge relation of compound channels of higher width ratio i.e. width ratio more than 6. The efficacy of the approach is tested in the experimental compound channel data-sets, data-sets from large channel facility [Flood Channel Facility channel] at Walling ford, UK, and natural compound river channel data having wide floodplains.

In this paper, the authors present experimental results of overbank flow in asymmetric rectangular compound channels considering both smooth and rough flumes. The mean velocity distributions in the main channel, floodplain, and the whole cross-section were measured for nine different test models constructed with variable main channel width and step height. The mean velocity measurements are then related to a dimensionless parameter called the relative depth defined as the ratio of the depth above the floodplain bed to the depth above the main channel bed. The variations and interactions of the three outlined mean velocities have been investigated with respect to relative depth. A set of single-variable regression models has been developed for estimating the three mean velocity types using relative depth as the only independent variable. Another set of multiple-variable regressions models has been derived using two additional dimensionless parameters which take into account the width dimensions of the constructed asymmetric compound channel. The application of several key statistics and validation procedures has indicated the high significance and reliability of the developed models in predicting the three mean velocity types. The predicted mean velocities can then be used to estimate the corresponding channel flow rate using the continuity equation.

The present study reports the effect of transcritical flow on velocity and shear stress distribution over a partially rough bed. Four series of runs have been performed in a right-angled open channel junction. Experimental data obtained from compound channel are used to compare with the simple ones. The physical size and geometry of roughness elements are chosen to encompass transcritical flow regimes. Using a small portion of the data recorded at each location using an acoustic Doppler velocimeter over a grid defined, an evaluation of transcritical flow in open channel junction is presented. The approach flow is subcritical followed by a transition to supercritical flow in the downstream branch channel is realized. Results show that the flow features around the junction are related to the strength of the secondary currents and turbulence quantities in shear layer increases with discharge ratio. Energy loss is associated with the bed shear stress exhibited is more in the simple channel than that of compou...

Smooth rectangular open channel flow is a benchmark for studying river hydraulics and sediment transport. Such a flow is more complicated than the classic boundary layer flow at least in two ways: (i) the maximum velocity occurs below the water surface, which is called the velocity-dip-phenomenon and (ii) the velocity distribution is affected not only by the channel bottom but also by the side-walls and the free surface. This fundamental flow is approximated herein by three hypotheses: (i) the velocity-dip-position shifts exponentially from the water surface to half flow depth as the width–depth ratio decreases from infinity to zero; (ii) the conventional wake-law for the centreline velocity distribution results from boundary shear stresses including the bottom, side-walls, and water surface in terms of secondary currents; and (iii) the cross-sectional velocity distribution is described by Guo and Julien's modified log-wake-law. These hypotheses are well supported by flume data.

Present paper investigates the steady criterion of the forced, isothermal, and incompressible capillary channel flow in both parallel plates and wedge-shaped channel, which has prominent application in liquid management technology in space. One-dimensional refined Bernoulli equation for parallel channel in Rosendahls work is modified mainly on geometric factors to establish algorithms for wedge-shaped channel. Liquid pressure loss theory is applied to explain the physical behavior of the flow collapse and critical volume flux is determined as a function of length of channels. Theoretical analysis of flow in both parallel and wedge-shaped channels demonstrates better liquid management performance in the wedge-shaped channel. Such results may be valuable in the capillary channel design for space liquid transport application.

The flow conditions in normal mode asymmetric flow field-flow fractionation are determined to approach the high retention limit with the requirement d≪l≪w, where d is the particle diameter, l the characteristic length of the sample exponential distribution and w the channel height. The optimal entrance velocity is determined from the solute characteristics, the channel geometry (exponential to rectangular) and the membrane properties, according to a model providing the velocity fields all over the cell length. In addition, a method is proposed for in situ determination of the channel height.

A methodology for determining the bathymetry of river cross-sections during floods by the sampling of surface flow velocity and existing low flow hydraulic data is developed . Similar to Chiu (1988) who proposed an entropy-based velocity distribution, the flow depth distribution in a cross-section of a natural channel is derived by entropy maximization. The depth distribution depends on one parameter, whose estimate is straightforward, and on the maximum flow depth. Applying to a velocity data set of five river gage sites, the method modeled the flow area observed during flow measurements and accurately assessed the corresponding discharge by coupling the flow depth distribution and the entropic relation between mean velocity and maximum velocity. The methodology unfolds a new perspective for flow monitoring by remote sensing, considering that the two main quantities on which the methodology is based, i.e., surface flow velocity and flow depth, might be potentially sensed by new sensors operating aboard an aircraft or satellite.

Weirs used for water discharge measurement in open-channel systems normally operate under free-flow conditions, for which the specific energy reaches a minimum at the weir crest. This type of transitional open-channel flow can be simulated using the ideal fluid flow theory. The traditional application of that theory requires the computation of the flow net over the weir. In this work, a potential flow model using a semi-inverse mapping is proposed in order to simulate potential flow over weirs. The model reduces the computation of the entire flow net to the determination of the streamlineflow pattern only. The computations are conducted numerically using a simple finite-difference technique, in which conservation of energy, momentum, and the critical flow condition with curvilinear streamlines is considered. The model is used to display parameters of engineering interest at the point of minimum specific energy. © 2013 American Society of Civil Engineers.

We introduce a mathematical model to study the transport of ions through ion channels. The system is derived in the framework of the energetic variational approach, taking into account the coupling between electrostatics, diffusion, and protein (ion channel) structure. The geometric constraints of the ion channel are introduced through a potential energy controlling the local maximum volume inside the ion channel. A diffusive interface (labeling) description is also employed to describe the geometric configuration of the channels. The surrounding bath and channel are smoothly connected with the antechamber region by this label function. A corresponding modified Poisson–Nernst–Planck channel system for ion channels is derived using the variational derivatives of the total energy functional. The functional consists of the entropic free energy for diffusion of the ions, the electrostatic potential energy, the repulsive potential energy for the excluded volume effect of the ion particles, and the potential energy for the geometric constraints of the ion channel. For the biological application of such a system, we consider channel recordings of voltage clamp to measure the current flowing through the ion channel. The results of one-dimensional numerical simulations are presented to demonstrate some signature effects of the channel, such as the current output produced by single-step and double-step voltage inputs. Copyright © 2013 John Wiley & Sons, Ltd.

The critical flow concept has many applications in open-channel flow problems. Determination of critical depths for canals and natural streams with different shapes is a classic task, but important for efficient hydraulic design. Generally, critical depth is used to classify the flow into subcritical and supercritical and may be used as a control point for computing water surface profiles in steady and unsteady gradually varied flows. For a given compound channel, the kinetic energy correction coefficient varies quite rapidly above the overbank level. In such a case, specific energy may have more than local minimum or maximum (multiple critical depth) for some combination of discharge and geometry. The compound channels are well documented in the literature, but occurrence condition of the multiple critical depth has not yet been determined. The first step in modeling critical depth is to determine whether multiple occurrences exist. In current research, symmetrical prismatic channels with two dif...

The paper presents the theoretical study of hydraulic jump in triangular channel section. Presuming the jump as one dimensional free shear layer with hydrostatic pressure distribution across it and using momentum equation, specific force equation is obtained. Using the specific force equation and eddy viscosity equation, analytical models for sequent depth, dimensionless profile, turbulent shear stress distribution and energy loss for various initial Froude numbers have been obtained. The proposed models for sequent depth and energy loss are also compared with the other developed models. The proposed energy loss model also provides the energy loss at any point along the jump, while this provision is not available in the models of other investigators. Newton–Raphson and Runge–Kutta methods are used for the solution of the proposed model. The outcome of this study can be used in the design of stilling basin floor and side walls on permeable foundations.

The flow of liquid in an annular channel with a partially shaded flow section is experimentally studied using the electrodiffusion method. The effect on the flow structure produced by a shutter closing one-quarter of the channel cross section is shown. An obstacle installed in the channel causes the flow to attain a 3D structure. The flow pattern in such channel differs significantly from that observed in undisturbed flow moving in an annular channel. It is revealed that the friction stress values measured on the channel’s inner wall depend essentially on the azimuth angle over the channel height. With distance away from the obstacle, the influence it has on the hydrodynamic flow structure tends to decrease, but the disturbance produced by it does not die out completely even at a distance of more than 600 mm from the obstacle. Data quantitatively characterizing the disturbance of flow structure in the studied channel are presented.

The mesh-free particle method has been successfully used in simulation of various types of flow. Small particle distance is typically used for representing the form of the simulation domain, requiring a large amount of computing time, accordingly, and, thus, seriously affecting the efficiency of the mesh-free method. In order to optimize the efficiency and accuracy of the mesh-free method in simulating open channel flow, a new approach based on the assigning velocity to ghost particles next to the solid boundary is developed. This ghost particle velocity correction also considers the bed roughness, the flow depth and the particle distance all together so that larger particle distance can be used in open channel flow simulations with the mesh-free method, requiring less simulation time, while the correct velocity distribution over depth is still maintained. Experimental cases are used to compare the numerical results to show the advantages of using this improved method.

Conventional approach in uniform open channel flow is to express the resistance coefficient in the Manning, Darcy-Weisbach or Chezy form. However, for practical cross-sections, including rectangular and trapezoidal ones, the governing equation is implicit in the uniform water depth. For these sections the water depth, corresponding to known values of the flow discharge, slope channel and resistance coefficient, is presently obtained by trial and error procedure. In this paper exact analytical solutions of uniform flow depth for rectangular and trapezoidal section have been obtained in the form of fast converging power series.