The hydraulics of parallel sluice gates under low flow delivery condition

In this paper the flow through parallel sluice gates under low flow conditions and with some of the gates closed resulting in symmetrical or asymmetrical gate installations was studied experimentally. The current stage–discharge formula for single sluice gates cannot be used for either free flowing or submerged parallel sluice gates. Then, on the basis of experimental observations, the effect of the closed gates was considered to develop a submergence distinguishing condition curve formula. For both free and submerged regimes, the Π-theorem along with the incomplete self-similarity concept was used to develop head–discharge formulas for symmetrical and asymmetrical gate installations. The proposed formulas were then calibrated using the compiled experimental data. The new approach is shown to be applicable within the entire range of operation, i.e. from free to submerged flow regimes as well as the transition zone.     

Effective parameters for calculating discharge coefficient of sluice gates

The present work demonstrates the characteristics of flow from sluice gates under free and submerged flow conditions using Energy and Momentum Equations (EMEs). The experimental data was used from the research works reported by different investigators to calibrate the proposed equations. An equation for estimation energy loss factor of sluice gate at free flow was presented and effect of this parameter on increasing discharge coefficient's accuracy was demonstrated. It was derived a theoretical equation for variations of sluice gate's discharge coefficient with relative opening and relative tailwater depth. Effects of energy loss factor on discharge coefficient and distinguishing limit were investigated. In this research the concepts of submergence limit of the gate and the submergence limit of hydraulic jump will be distinguished. By determining effective pressure on the gate and using EMEs, equations for variations of sluice gate's contraction coefficient with relative opening and relative submergence were presented. The result shows that at free flow condition, a minimum contraction coefficient obtained under a certain value of relative gate opening. At submerged flow condition, contraction coefficient would be either increased or decreased depending on the level of flow submergence. This paper carefully considered stage-discharge relationships for estimation gate discharge under free and submerged flow conditions.     

Distinguishing condition curve for radial gates

Identifying the free or submerged flow condition and the threshold between the two regimes is vital for accurate flow measurement through a gate. In this paper, analytical findings about distinguishing condition curve of radial gates are presented. The generality of the available calibration methods of the radial gates has been analyzed. Then, based on the assumption of starting the transition zone right at the interception point of the free and submerged flow relationships, a comprehensive equation is developed to distinguish the flow condition through a radial gate. Using ample high quality available experimental data, the accuracy of the proposed distinguishing curve was verified. The results indicated that the proposed distinguishing curve accurately identified observed flow condition data. Finally, by defining a suitable sensitivity index, the effects of downstream channel width, energy loss through the gate, Reynolds number, and contraction coefficient on the distinguishing condition curve have been evaluated. Also, the results promise the application of the proposed method for situations where only one of some parallel radial gates is operating under the submerged flow condition.     

Discharge estimation for submerged parallel radial gates

Seven hundred ninety-seven field-measured data points were collected to calibrate multiple parallel radial gates. Data were collected from three control structures (i.e., Al-Tawfiki, Al-Menoufi, and Abasi regulators), which are located in the Delta irrigation district of Egypt. Upstream and downstream water depths, gate opening size, and flow discharge was measured at each structure. Additionally, previous calibration methods were reviewed and evaluated. Dimensional analysis with application of the incomplete self-similarity concept demonstrated the best results for the study area. Based on the field measurement data, a simple formula that implicitly considers the discharge coefficient is proposed for estimating the flow rate through submerged parallel radial gates.     

Study and application of discharge calibration for submerged radial gates

Sophisticated stage-discharge rating curves for radial gates are essential to modernization efforts in water conservancy and irrigation projects. However, it is a challenging hydraulic issue to accurately determine discharges through radial gates, especially when subjected to highly submerged flow conditions. According to the variation trend of jet Froude number and the mechanism of energy dissipation subjected to submerged flows, a new criterion was proposed to subdivide submerged flow into partially submerged and totally submerged flows. Thus, the three stage-discharge equations were developed for free flow, partially submerged flow and totally submerged flow, respectively. With the aid of the experimental data of single radial gate and the field data of multi-radial gates, the proposed discharge calibration method, referred to as the identification method, was tested and verified. The results indicated the discharge prediction accuracies were satisfactory, in which the mean absolute percentage errors were less than 10%. The proposed method is feasible and easily programmed.     

Prediction of hydraulic jump characteristics in a closed conduit using numerical and analytical methods

The hydraulic jump is an economical alternative to dissipate energy in the conduit and to reduce erosion at the culvert outlet. In the literature, very limited studies have been reported on the performance of hydraulic jump in a closed conduit. The innovation of this research is to employ a numerical method for the estimation of the hydraulic jump characteristics in a closed conduit with different positive slopes (S₀). The analytical method was used to develop several equations for hydraulic jump and the provided results were compared with the numerical method. The results indicate that the numerical method predicts the flow depth ratio after conduit with higher accuracy (error less than 5%) in comparison to the analytical method (error less than 10%). Furthermore, in the slope of 0.00, the energy loss increases by 16% with increasing the Froude number from 4.617 to 5.562 while this value is 23% and 22% for slopes of 0.01 and 0.02, respectively. Finally, several equations were developed for the prediction of hydraulic jump characteristics in terms of Fr₁, S₀, and conduit depth (D).     

Application of the submerged experimental velocity profiles for the sluice gate's stage-discharge relationship

Sluice gates have been widely used and intensively studied, however their submerged flow conditions still call for in depth attention. A large scale experimental setup equipped with Acoustic Doppler Velocimetry, ADV, and electromagnetic flow-meter was used to thoroughly investigate various aspects of the hydraulics of submerged sluice gate. In this study, new experimental data sets are provided, that help better understand and quantify the flow features for submerged sluice gates. According to the experimental data generic fitting are provided for the velocity profiles from which the velocity correction factors can be obtained. Then, the experimentally obtained submerged head loss coefficient is presented and discussed. The results of this study showed that current classical Energy-Momentum methods (EM) failed to accurately determine the flow rate for the cases of highly submergences, while employing the interaction of the energy correction factors and head loss values in the EM model would result in more accurate head-discharge estimation. The new data set provided in this work can be used effectively for the validation of numerical modeling of submerged sluice gates.     

Correction of flow metering coefficients by using multi-dimensional non-linear curve fitting

Flow disturbances can significantly affect flow metering because the downstream flow of flow disturbances can become unstable and asymmetric, thus resulting in measurement errors in the flow meter. A clamp-on type ultrasonic flow meter is an example of a flow meter that is susceptible to flow disturbances given its diametrical configuration of ultrasonic paths. Several flow rate correction formulas have been suggested to mitigate the effect of flow disturbance for improved flow metering. As a novel method, a multi-dimensional non-linear correction formula is suggested to overcome limitations in flow metering that are attributed to the non-linearity of flow disturbances. The non-linear correction formula comprises n-th order polynomials with multiple variables. To validate the usefulness of the non-linear correction formula, the standard error of estimate (SEE) is introduced. Four types of flow configurations, namely, downstream of a contraction pipe, an expansion pipe, a single elbow joint, and a tee joint, are used to show the effect of the non-linear correction formula. The expanded uncertainty based on the SEE indicates estimated values of 1.29%, 11.14%, 1.07%, and 6.31% for the four upstream flow configurations, respectively. Thus, the effect of the non-linear correction formula is limited according to the upstream flow conditions. In the downstream flow of the contraction pipe and of the single elbow joint, the non-linear correction formula not only harmonizes the distribution of the flow rate deviations but also removes the biases of flow rate deviations with respect to the flow velocity, the installation location, and the diameter ratio.     

Comments on “Study and application of discharge calibration for submerged radial gates” by Guo X., Guo Y., Wang T., Fu H., Li J. Flow Meas. Instrum. 78 (2021) 101912, https://doi.org/10.1016/j.flowmeasinst.2021.101912

This paper discusses the capability of Guo et al.'s (2021) equations to determine the discharge of radial gates under submerged flow conditions. It was concluded that Guo et al.'s (2021) equations are associated with error reduction compared to the Incomplete Self-Similarity (ISS) theory and the calibration method. However, it does not have a significant advantage over Energy-Momentum (E-M) approach. Employing E-M principles, new equations were proposed to determine the discharge of radial gates, which has some advantages compared to Guo et al. (2021), such as (1) error reduction under partially and fully submerged flow conditions, (2) least dependence on the empirical constants, (3) uniformity of form over the entire submerged condition, and (4) no need to classify the submerged flow. Field calibration showed that the proposed equations in the present study for a single gate predict the discharge of parallel radial gates with a mean absolute error of less than 4.5% subject to the submerged operation of all open gates.     

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

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

Effect of the downstream transition region of a flow measurement flume of rectangular compound cross section on flow properties

In this study, the effect of the downstream expansion region of a flow measurement flume of rectangular compound cross section on some of the flow properties; such as the discharge coefficient, C_d, the approach velocity coefficient, C_v and the modular limit, ML were investigated. For this reason, extensive laboratory tests were conducted with nine models of different downstream transitions. The aforementioned hydraulic quantities were then related with the relevant parameters to obtain sets of curves from which one could decide which kind of downstream transition type would produce the highest modular limit. It was found that model type A yielded the highest modular limit with a downstream slope of about 1/7.     

Pressure measurement technique and installation effects on the performance of wafer cone design

The present study explores novel pressure averaging technique for wafer cone flowmeter design and its robustness in the presence of double 90° bend (out-of-plane) and gate valve as a source of upstream flow disturbance. The wafer cone flowmeter is tested in a circular pipe (inside diameter of 101 mm) with water as the working medium for the flow Reynolds number ranging from 1.19×10⁵ to 5.82×10⁵. Influence of the half cone angle (α) on the coefficient of discharge (C_d) of wafer cone flowmeter is studied with this new pressure averaging technique. Half cone angles considered in this study are 30° and 45° with a constant constriction ratio (β) of 0.75. The upstream static pressure tap is located at 1D upstream of the wafer cone. The downstream pressure averaging technique comprises eight circumferential holes of diameter 2 mm on the maximum diameter step of the wafer cone. The pressure taps are communicated through the support strut which serves as a downstream static pressure tap. The disturbance causing elements are individually placed at 1.5D, 5.5D, 9.5D and 13.5D upstream to the wafer cone flowmeter. The wafer cone flowmeter is also tested with gate valve opening of 25%, 50% and 75% for all the arrangements considered. The 30° cone is found to be better than 45° cone for the range of Reynolds number covered in the present study. The results show that the 30° wafer cone flowmeter with novel downstream pressure averaging technique is insensitive to the swirl flow created by a double 90° bend (out-of-plane) and requires an upstream length of 9.5D with a gate valve as a source of flow disturbance.     

Active control of impinging jet for modification of mixing

The objective of the present study is to modify mixing and heat transfer in impinging jets using a single-frequency excitation imposed at the jet exit. The excitation frequency is selected to be St _θ = fθ/U _J,max = 0.017 where θ is the jet-exit momentum thickness and U _J,max is the jet-exit maximum velocity. In free jets, this excitation results in turbulence suppression in a downstream location. On the other hand, in impinging jets, the effect of excitation significantly depends on the distance (H) between the jet exit and the impinging wall. For large H (e.g. H / D = 10, D is the jet exit diameter), the Nusselt number near the stagnation point (Nu _stag ) decreases due to turbulence suppression by the excitation. For small H (e.g. H / D = 2), Nu _stag is almost unchanged but the secondary peak much suppressed. On the other hand, Nu _stag increases for H / D = 6 due to turbulence enhancement by the excitation. The different behaviors of Nusselt number with respect to H / D are closely related to the changes in vortical structures by excitation.     

Effects of defects on the in-plane dynamic crushing of metal honeycombs

The effects of defects and their distributions on the in-plane dynamic crushing of honeycomb panels were studied using explicit finite element modeling. The influence of defect locations and ratios is investigated on the deformation modes and the plateau stresses with respect to the impact velocity. Numerical results show that the dynamic performance of honeycomb displays a high sensitivity on the defect location, especially under low and moderate impact velocities. By introducing a defect correction factor β_m and using the one-dimensional shock wave theory, an empirical formula is given for the variation of honeycomb’s plateau stress with respect to the impact velocity and the defect ratio.     

Structure and dynamics of the turbulent flow through a central baffle

Central baffle flume (CBF) can be utilized as a control structure to measure flow discharge in irrigation channels under free and submerged flow conditions. Stage-discharge relationship has been extensively studied for various geometrical parameters and flow conditions, whereas internal structure of the flow around a baffle has not been investigated in the literature. To address this need, the present work investigates the turbulent flow around a central baffle through high-resolution numerical simulations using an open source computational model. Velocity measurements were conducted in a laboratory flume to setup and validate the numerical model. Comparison of the numerical results with the experimental measurements proves that the present numerical model can predict water depth and velocity field. Longitudinal distance from the apex to the intersection point of water and critical depths can be estimated as L_xc = 2L_e, where L_e is the longitudinal length of the guide walls. A horseshoe vortex system identified in front of the baffle produces a significant bump on the free-surface and rib vortices generated from the baffle extend up to the sidewalls of the channel. The vertical separation layer observed downstream of the baffle results in a reverse flow and a vortex pair is formed by the impingement of the resulting reverse flow on the back of the baffle. Reverse flow, plunging flow structure, splash and rebounding wave events observed at the downstream produce substantial hydrodynamic effects on the baffle. Geometry of the central baffle was modified to suppress recirculation effects based on the insights into the complete flow structure around the baffle. Eventually, vortex structures were suppressed and the length of the recirculation zone was reduced by 76%.     

Experimental investigation of flow characteristics over asymmetric Joukowsky hydrofoil weirs for free and submerged flow

Weirs are one of the most common hydraulic structures used to regulate the upstream approach flow depth and measure the flow discharge. The hydrofoil weirs are a type of short-crested weirs that are designed based on the airfoil theory. These weirs have some merits compared to other types, such as a higher discharge coefficient, more stability, better submergence limiting condition, and lower fluctuations of the pressure and the free-surface profile. In the present study, experimental models of hydrofoil weirs with different relative eccentricities, cambers, angles of attack, and upstream slope angles are applied to investigate their hydraulic characteristics under free and submerged flow conditions. The longitudinal profiles of static pressure over different hydrofoil weirs are compared to circular-crested and ogee weirs. The results indicate that the maximum bed negative pressure belongs to the circular-crested weir, and the lowest bed pressure over the hydrofoil and ogee weirs are approximately the same. Applying a hydrofoil weir with an appropriate curvature and angle of attack instead of a circular-crested weir not only increases the structural weir height as well as the upstream water depth but also results in the lowest values of bed negative pressure, thereby reduces the potential of cavitation over the weir body, being safer hydraulic structures. The results also show that the discharge coefficient of hydrofoil weirs is greater than that of the broad- and short-crested weirs for the upstream approach flow depth relative to the weir crest to weir length h₁/L > 0.12 and is greater than that of the ogee weirs for 0.35 < h₁/L < 0.45. Furthermore, the derived relationships for the discharge coefficient, threshold submergence, and the discharge reduction factor due to submergence accurately predict the hydraulic characteristics of hydrofoil weirs compared to the available developed empirical relationships for these weirs and can be used efficiently for design purposes.     

Hydraulic jump and energy dissipation downstream stepped weir

Hydraulic jump can be defined as a sudden change or rise of water level because of changing the channel slope from steep to mild combined turbulent flow. This can be used for energy dissipation to reduce flow energy downstream hydraulic structure. Recent studies dealt with energy dissipation downstream hydraulic structures such as stepped weir by changing water level upstream and downstream to reduce flow energy. In this study, the focus was placed on the hydraulic jump formation downstream stepped weir and its characteristics, as well as used it as energy dissipation to reduce the residual energy that will be dissipated on stepped weir. 27 stepped weir models were tested with three different heights, slopes as well as changed number of steps for all models. It was found that the energy dissipation increased by increasing weir slope, the number of steps, and decreasing the height weir, by 20%, 20.6%, 21.8% respectively. It was also found that the energy dissipation increased when the hydraulic jump length increased, but this was not economy. The best model for energy dissipation in this study was that have lower height and greater slope and steps number. This model gives lower value of hydraulic jump length; this is more economy as it reduces the length of stilling basin which is reduces the cost of its construction downstream stepped weir or stepped spillway.     

Simulation of free surface flow over the streamlined weirs

The streamlined weirs are a special type of weirs, designed on the basis of airfoil theory. Because of their particular design, they have some merits compared to the other types of weirs, such as; high discharge coefficient, more stability of overflow and less fluctuations of water free surface. In the present study, a numerical simulation performed using an open source software namely, OpenFOAM, to give details about the flow structure over, up- and downstream of these weirs. Also, an experimentation setup was devised to evaluate the numerical results and determine the best numerical model. Analyzing the results of different turbulence models including; standard k-ε, realizable k-ε, RNG k-ε, k-ω SST, and Reynolds stress LRR, indicated that all the aforementioned models accurately estimate the flow field and hydraulic parameters. However, the k-ω SST model gives more accurate results, very close to the experimental data especially for the Reynolds stresses. Accordingly, the k-ω SST turbulence model was chosen as the best turbulence model for analyzing the flow over the streamlined weirs. Numerical results for different relative eccentricities show that, by increasing the relative eccentricity, the flow velocity over the crest of the weirs increases and accordingly the pressure in such section decreases. For a constant flow discharge upstream of different types of the streamlined weirs, the lowest bed pressure and the most probable potential of cavitation belongs to a circular-crested weir (a streamlined weir with a relative eccentricity of unity). Furthermore, the greatest bed shear stresses and the compressive forces occur downstream of the circular-crested weir. Thus, downstream of a circular-crested weir is responsible for larger potential of bed erosion. This is partly due to the formation of shock waves, reduction of the flow depth, and enhancement of the flow velocity downstream of a circular-crested weir. Moreover, the lowest bed shear stresses were observed upstream of the circular-crested weir. Therefore, upstream of a circular-crested weir shows the greatest potential of sedimentation. Finally, applying the streamlined weirs with an appropriate curvature, diminishes the unfavorable flow conditions, as observed for the circular-crested weir, being the safer and economic hydraulic structures.     

Effect of the pipe bend of the morning glory spillway on the cavitation number

Cavitation phenomena always threats the hydraulic structures with high velocity flow and suddenly varying the flow direction. It is assumed that the process of the flow depleting with high ratio through the morning glory spillway accompanied by suddenly varying the flow direction caused by the bend pipe can deteriorate the condition of the cavitation. Introducing the ratio R/D (diameter size of the vertical and horizontal shaft divided with radius of the bend pipe) can be beneficial to propose the novel design plan to avoid the cavitation caused by the bend pipe. Present study carried out a series experimental tests to validate a numerical model of the morning glory spillway with different R/D ratio to show the impacts of the suddenly varying the flow direction on the variation of the cavitation number. The cavitation values of the free, semi-submerged and submerged flow conditions showed that cavitation was mainly occurred on the internal arch of the bend pipe for free flow and the level of the danger for semi-submerged flow was the major danger level for internal arch of the bend pipe and due to submerged flow, the crest level at the entrance of the morning glory spillway was additionally threated by cavitation. To prevent from the cavitation, the values of the cavitation number due to different R/D as 0.55, 0.45, 0.35, and 0.25 were calculated by employing the validated numerical model due to high danger of the cavitation in semi-submerged condition. Results showed that due to D/R > 0.35, the possible cavitation damage is obtained for the internal and external arch of the bend pipe of the morning glory spillway; however, for D/R < 0.25, the bend pipe position is located in safe zone and the danger of the cavitation is negligible.     

Flow measurement using free over-fall in generalized trapezoidal channels based on one velocity point method

A free over-fall offers the possibility of being used as a flow measuring device in hydraulic structures with a single depth measurement of the end section. Due to its practical importance, considerable attention has been paid to investigate free over-falls for different channel cross-sections using various approaches. This paper presents a new theoretical approach for computing the end depth ratio (EDR) relationship for the generalized trapezoidal channel cross-sections at free over-falls in sub critical flow regimes from which the end depth discharge (EDD) can be computed. The generalized trapezoidal channel is a geometric shape that is defined mathematically with a single equation where five widely known prismatic channel cross-sectional shapes can be generated (trapezoidal, inverted triangular (Δ), rectangular, parabolic, and triangular). This suggested theoretical approach uses one velocity point at the geometric center of the end section based on the energy and the continuity equations. Relevant experimental and theoretical results were utilized in order to examine the suggested method through the statistical measuring indices (percentage difference and the correlation coefficient (R²)). The computed results show very close agreements with the earlier works. Furthermore, simple equations are also generated using the regression curve fitting technique in order to estimate the direct discharges (Q) using the end depth (y_e) for each of the above mentioned channel cross-sections.