Energy and Momentum Velocity Coefficients for Calibrating Submerged Sluice Gates in Irrigation Canals

There is renewed interest in developing calibration methods for gates operating in submerged conditions in irrigation canals. In the present study, a new method based on a generalization of the standard energy-momentum method that accounts for variations in the energy and momentum velocity coefficients is proposed, for the following reasons. First, it was found that the assumption of uniform submerged jet velocity to account for the kinetic energy head and momentum flux is in reality equivalent to assuming a parabolic relationship between the Coriolis and Boussinesq coefficients. Second, literature investigations showed that the coefficients for the downstream side of submerged gates are notably greater than unity, and the implicit parabolic relationship between these coefficients in the standard energy-momentum method is inadequate, at least for high submergence conditions. The proposed energy-momentum method was evaluated using the data obtained from four gates operating in an irrigation canal in Southern Spain. Improvements in accuracy compared to the standard energy-momentum method (with a constant contraction coefficient Cc = 0.61) were obtained. The results indicate that the calibration of coefficient approach provides a means to improve the energy-momentum method by (indirectly) accounting more accurately for nonuniform velocity effects in the energy-momentum equations.     

Benchmark of Discharge Calibration Methods for Submerged Sluice Gates

Real accuracy of several calibration methods for sluice gates working in the submerged orifice flow condition was determined considering water discharge from water levels and gate openings. Data were taken from three gates of the same laboratory canal covering a large operational range. Using accurate hydraulic data, most of the methods produce errors of up to ±10%. However, errors can rise up to ±40% with methods using typically recommended calibration values or constant discharge coefficients. The best results were obtained by a method based on dimensional analysis and the incomplete self-similarity theory proposed recently in the literature. Calibration with field data, in this case, produced errors not higher than ±3%. On the other side, when the gate discharge data are not available, the use of a contraction value of 0.611 within a good theoretical formulation gives very good results.     

Transitional Flow between Orifice and Nonorifice Regimes at a Rectangular Sluice Gate

The hydraulic transition between nonorifice and orifice flow regimes at a rectangular sluice gate was analyzed to determine the value of a coefficient (Co) used to define the threshold between the two regimes. The transition coefficient was defined as the ratio of vertical gate opening to upstream water depth. Several dozen data sets were collected in a hydraulic laboratory, each including the measurement of upstream and downstream water depth for five different vertical gate openings, and 17 different steady-state discharges from 0.02?to?0.166?m3/s. Various approaches were tested to define the limits of the nonorifice-to-orifice regime transition, but the one presented herein uses the specific-energy equation for open-channel flow. After the transition limits were defined, an estimation of the nonorifice-to-orifice transition coefficient, Co, was made. The experimental results indicate that orifice flow always exists when Co is less than 0.83, and nonorifice flow always exists when Co is greater than 1.00. A procedure was developed to determine the flow regime and the discharge at a rectangular gate in the range 0.83相似文献   

Flow Upstream of Orifices and Sluice Gates

Potential flow solutions of a point/line sink are extended to study the velocity field upstream of a finite-size orifice and sluice gate. It is found that, in the “near field” zones, the iso-velocity surfaces appear to be semiellipsoidal; while in the “far field” zones they become hemispheres. The shape and size of the orifice/sluice gate were found to be of no effect on the flow behavior beyond a certain distance. The development of velocity profile away from the orifice and sluice gate is examined, and the effects of water depth are studied. The results of this study compare very well with other numerical and experimental studies, and provide a general understanding of the flow field upstream of orifices and sluice gates.     

Refined Energy Correction for Calibration of Submerged Radial Gates

The energy-momentum (E-M) method for calibrating submerged radial gates was refined using a large laboratory data set collected at the Bureau of Reclamation hydraulics laboratory in the 1970s. The original E-M method was accurate in free flow, and when the gate significantly controls submerged flow, but for large gate openings with low head loss through the gate, discharge prediction errors were sometimes large (approaching 70%). Several empirical factors were investigated with the laboratory data, including the combined upstream energy loss and velocity distribution factor and the submerged flow energy correction. The utility of the existing upstream energy loss and velocity distribution factor relation was extended to larger Reynolds numbers. The relation between the relative energy correction and the relative submergence of the vena contracta was shown to be sensitive to the relative jet thickness. A refined energy correction model was developed, which significantly improved the accuracy of submerged flow discharge predictions. Although the focus of this work was radial gates, the energy correction concept and these refinements potentially have application to all submerged sluice gates.     

Conversion from Discharge to Gate Opening for the Control of Irrigation Canals

The paper reviews several methods to convert discharge into gate opening. A control algorithm for one or several reaches of an irrigation canal sometimes uses a discharge as the control action variable even though the device to be manipulated is a gate or a weir. In this case a slave controller has to convert the discharge into a gate opening or a sill elevation in the case of a weir. This is usually done by inverting the static relation between discharge and gate opening. An improved method can be based on the characteristics theory to estimate the deviations of the water levels. However, both methods underestimate the gate opening deviations required to deliver a desired discharge deviation, because water levels vary continuously over time when the gate is operated. The paper proposes a method to take into account this dynamic behavior of the pool-gate interaction by using a simple linear model for the pools’ dynamics, the integer delay zero model. The proposed method enables us to better estimate the gate opening necessary to get a desired average discharge. The method is evaluated in simulation and on a gate of the Gignac Canal, located in the South of France. A dimensionless analysis of the problem is finally performed to evaluate the methods’ applicability.     

Role of Energy Loss on Discharge Characteristics of Sluice Gates

A theoretical method was used to derive an equation for the discharge coefficient of sluice gates in rectangular channels under orifice-flow (both free and submerged) conditions. The proposed equation allows for the effects of energy dissipation between the upstream section of the gate and the vena contracta. The hydraulic energy loss in the upstream pool is attributable to the induced turbulence by the recirculating region and to the growth of bottom boundary layer. For the submerged-flow condition, turbulent shear-layer entrainment is also responsible for the energy loss. This energy loss is introduced into the equations through a coefficient k that has been conventionally assumed to be negligible. Experimental data from the literature were used to validate the equation, which showed good agreement with the measured values. It is also shown that the magnitude of the energy-loss factor is a function of the geometry of the gate and can modify the discharge coefficient. An equation for the distinguishing condition between free and submerged flows is also presented. The new equations can be used to predict the performance of sluice gates with different edge shapes under free- and submerged-flow situations.     

Calculation of Contraction Coefficient under Sluice Gates and Application to Discharge Measurement

The contraction coefficient under sluice gates on flat beds is studied for both free flow and submerged conditions based on the principle of momentum conservation, relying on an analytical determination of the pressure force exerted on the upstream face of the gate together with the energy equation. The contraction coefficient varies with the relative gate opening and the relative submergence, especially at large gate openings. The contraction coefficient may be similar in submerged flow and free flow at small openings but not at large openings, as shown by some experimental results. An application to discharge measurement is also presented.     

General Characteristics of Solutions to the Open-Channel Flow, Feedforward Control Problem

A dimensionless formulation of the open-channel flow equations was used to study the feedforward control problem for single-pool canals. Feedforward inflow schedules were computed for specified downstream demands using a gate-stroking model. The analysis was conducted for various design and operational conditions. Differences in the shape of the computed inflow hydrographs are largely related to the volume change resulting from the transient, the time needed to supply this volume, and the time needed by the inflow perturbation to travel down the canal. The gate-stroking method will fail to produce a solution or the solution will demand extreme and unrealistic inflow variations if the time needed to supply the canal volume change is much greater than the travel time of the upstream flow change. As an alternative, a simple feedforward-control flow schedule can be developed based on this volume change and a reasonable delay estimate. This volume compensating schedule can deliver the requested flow change and keep water levels reasonably close to the target under the range of conditions tested.     

Flow through Side Sluice Gate

The hydraulic characteristics of a side sluice gate were studied experimentally. It was found that the specific energy remains constant along the side sluice gate. The coefficient of discharge for the side sluice gate is related to the main channel Froude number and the ratio of upstream depth of flow to sluice gate opening for free flow. It also depends on an additional parameter: the ratio of tailwater depth to the gate opening for submerged flow. Suitable equations for discharge coefficient are obtained.     

Multiple-Model Optimization of Proportional Integral Controllers on Canals

Canals or open channels that convey water often consist of pools in series separated by control structures. Successful implementation of water-level control with these structures using decentralized proportional integral (PI) controllers depends heavily on the tuning of the control parameters. These parameters are hard to determine due to the interactions between the pools and the varying flow conditions in the canal. This paper presents a procedure for tuning any linear controller (including decentralized PI controllers) that guarantees stability of the controlled canal. It minimizes a cost function that weights the water-level deviations from the target level against control efforts at both low- and high-flow conditions. The procedure is tested on a model of the Umatilla Stanfield Branch Furnish Canal in Oregon. The tests show the capability of the procedure to deal with the pool interactions. The results of a realistic turnout schedule applied to the controlled canal show the high performance of the controllers (small water-level deviations in all pools) over varying flow conditions.     

Cutthroat Measurement Flume Calibration for Free and Submerged Flow Using a Single Equation

A series of detailed laboratory measurements were made under steady-state flow conditions through a 0.914-m (3-ft) Cutthroat flume in an attempt to more accurately define transition submergence for four standard throat widths. It was found that the change from free to submerged flow, and vice versa, is gradual and that there is no easily observable transition point. The gradual transition between the flow regimes suggested a new calibration approach in which a single equation could more elegantly and more accurately fit the laboratory measurements, eschewing the need for separate free- and submerged-flow equations, and obviating the need to define transition submergence. Such an equation was found, providing greater calibration accuracy up to 95% submergence in 0.914-m Cutthroat flumes.     

Influence of Sluice Gate Contraction Coefficient on Distinguishing Condition

Sluice gates are widely used for flow control in open channels. Flow through the gate may be free or submerged depending on tailwater depth. One may determine whether the flow will be free or submerged by determining the maximum tailwater level that permits free flow. This is called the distinguishing condition. This paper derives a theoretical equation for the distinguishing condition including the contraction coefficient as a parameter, based on the basic equations for free flow and the hydraulic jump. The equation is investigated using experimental data from two different gate types. The results show that the contraction coefficient varies with gate type and that this affects the distinguishing condition. The results also show that for a given upstream depth, tainter gates (radial gates) are less likely to become submerged than vertical gates due to larger contraction coefficients. The present study results are useful in the design and operation of sluice gates.     

Open Channel Flow through Different Forms of Submerged Flexible Vegetation

Laboratory experiments are used to explore the effect of two forms of flexible vegetation on the turbulence structure within a submerged canopy and in the surface flow region above. The two simulated plant forms involve flexible rods (stipes) of constant height, and the same rods with a frond foliage attached. These plant forms were arranged in a regular staggered configuration, set at the same stipe density. The plant geometry and its mechanical properties have been scaled from a real aquatic plant using Froudian similarity, and the methods used for quantifying the bending stiffness, flexural rigidity, and drag force–velocity relationship of the vegetation are outlined. Experimental results reveal that within the plant layer, the velocity profile no longer follows the logarithmic law profile, and the mean velocity for the rod/frond canopy is less than half of that observed for the simple rod array. In addition to the mean flow field, the turbulence intensities indicate that the additional superficial area of the fronds alters the momentum transfer between the within-canopy and surface flow regions. While the frond foliage induces larger drag forces, shear-generated turbulence is reduced due to the inhibition of momentum exchange by the frond surface area. It is known that the additional drag exerted by plants reduces the mean flow velocity within vegetated regions relative to unvegetated ones, but this research indicates that plant form can have a significant effect on the mean flow field and, therefore, potentially influence riverine and wetland system management strategies.     

Structure of Flow Upstream of Vertical Angled Screens in Open Channels

This paper presents the results of a laboratory study of the structure of flow in a diversion structure with a vertical angled wedge-wire fish screen. This screen had a 10×25?mm mesh and was tested at three angles of 10.4, 17.5, and 26.8°, to the direction of the approaching flow, for two mean velocities of 0.5 and 0.8?m/s, with a depth of flow of about 0.75?m. In this water and fish diversion (channel or) structure, it was found that the depth of flow at any section is approximately constant with a drop at the screen on the side of the canal and decreased towards the bypass located at the downstream end. The distribution of the velocity component u in the direction of the approaching flow as well as the perpendicular component w and the resultant velocity V was uniform in the vertical direction. The depth averaged mean velocity for different verticals at any section in the diversion structure increased with the longitudinal distance x and was correlated with the relative width, bs/b (in the diversion structure) for all five experiments. Correlations have been found for the depth averaged transport velocity and the impinging velocity on the screen in terms of the approach velocity U. A general relation has also been developed for the attack angle of the flow on the screen. The downstream part of the screen carried more flow into the canal compared to the upstream part as a result of the uniform mesh size used in this study. The results of this hydraulic study should be useful, particularly for freshwater adult fish, in designing screens in irrigation canals and for micro-hydro sites that use diversion canals.     

Flow Resistance Law in Channels with Flexible Submerged Vegetation

In this paper, experimental data collected in a straight flume having a bed covered by grasslike vegetation have been used to analyze flow resistance for flexible submerged elements. At first, the measurements are used to test the applicability of Kouwen’s method. Then, a calibration of two coefficients appearing in the semilogarithmic flow resistance equation is carried out. Finally, applying the Π-theorem and the incomplete self-similarity condition, a flow resistance equation linking the friction factor with the shear Reynolds number, the depth-vegetation height ratio and the inflection degree is deduced.     

Closed-Form Expression of the Response Time of an Open Channel

Computing accurately the response time of an open channel is of extreme importance for management operations on canal networks, such as feed-forward control problems. The methods proposed in the literature to approximate the response time do not always account for the influence of a cross structure at the downstream end of a canal pool, which may have a significant impact on the response time. This paper proposes a new approach to compute the response time, accounting explicitly for the backwater and the feedback effects due to the downstream cross structure. The method provides a distributed analytical expression of the response time as a function of the characteristics of the canal (geometry, roughness) and of the downstream cross structure. A test canal with a weir or a gate at the downstream end is used to compare the new method with some of the others. Results show that the proposed expression accurately reproduces the response time for various backwater and downstream boundary conditions.     

Dimensionless Stage–Discharge Relationship in Radial Gates

Dimensional analysis was used to obtain stage–discharge relationships under submerged and free flow conditions in radial gates to develop a management tool. Experimental data from a laboratory flume and the indicial method of dimensional analysis were used for this purpose. The resulting equation relates the discharge (or critical depth) to upstream and downstream water depth and gate opening. These equations were then validated by experimental data obtained from field radial gates and compared with the conventional gate equation. Results showed that there was a good agreement between dimensionless equations and field and laboratory data under submerged or free flow conditions. Dimensionless equations are more general and accurate than the conventional ones when there is not an accurate estimation of discharge coefficients.     

Volume Compensation Method for Routing Irrigation Canal Demand Changes

This paper examines the problem of routing known water demands through gate-controlled, open-channel irrigation delivery systems. Volume-compensation principles were used to route multiple demands in multiple-pool canal systems. The volume-compensation method schedules each demand change individually under the assumption of a series of steady states and superimposes the individual results. Volume-compensation routing schedules were computed for two of the test cases proposed by the ASCE Task Committee on Canal Automation. Alternative routing schedules were computed with the gate-stroking method, which is an inverse solution of the unsteady-flow equations. Both solutions were tested through unsteady-flow simulation. While not as effective as gate-stroking solutions, volume-compensation solutions performed satisfactorily under ideal flow control conditions. When subjected to realistic operational constraints, specifically constraints on the flow regulation interval, and also to incorrect canal hydraulic roughness information, both methods performed similarly.