Head-discharge Relationship Research Articles

Effects of Bottom-Up Blockage on Entrance Loss Coefficients and Head-Discharge Relationships for Pipe Culvert Inlets: Comparisons of Theoretical Methods and Experimental Results

Effects of Bottom-Up Blockage on Entrance Loss Coefficients and Head-Discharge Relationships for Pipe Culvert Inlets: Comparisons of Theoretical Methods and Experimental Results

Parametric study of flow at circular piano-key inlets over the vertical shaft spillways

Swirling flow at vertical shaft spillways results in flow fluctuations, reduces hydraulic system efficiency, and causes structural damage. Optimizing the shape of the inlet is a practical means to decrease the swirling flow strength. In the present study a comprehensive experimental investigation was performed to examine the effects of a new type of inlet over vertical shaft spillways, namely the circular piano-key (CPK) inlet, for free, orifice and full-pipe or black water flow regimes. Head-discharge relationships, threshold and critical submergence depths and the effects of different geometrical parameters of the CPK inlets on the spillway flow discharge coefficient were assessed. Results reveal that increases in the height of the inlet and outlet keys increase the released capacity of the shaft spillway. Given its increased total crest length and the effects of the radially placed walls of a CPK against the swirling flow, angles of the inlet and outlet keys of the CPK are found to significantly affect the spillway flow discharge. The effect of inlet and outlet overhangs on the efficiency of CPK inlets is not noteworthy, being negligible. Considering the destructive effects of swirling flow, the CPK inlets significantly decrease the range of submergence for an unfavourable swirling flow regime condition, increasing the threshold submergence depth and decreasing the critical submergence depth. The flow discharge through the CPK inlets is higher than those of the other circular-type spillways. The present modified CPK inlets more effectively divert water, serving as an economical alternative to the conventional circular spillways.

Numerical study on scroll vortex intake with partially or fully sealed cover of vortex chamber

When installed in deep tunnel systems, the cover of the vortex dropshaft may be partially or fully sealed. With air exchange restricted through the cover, the air supply to the dropshaft through the inflow channel might not be adequate. Hence, further investigation is required to examine the effect of the restricted air passage through the cover on the flow regimes and hydraulic performance of the scroll vortex dropshaft. This study aims to quantify the head-discharge relationship, air-water distribution, and minimum air core size with different cover opening conditions. The 3D model of a fully open scroll vortex dropshaft is constructed, and numerical simulations are carried out and validated using experiment data. The results show that the effect is generally small when the ratio of the opening and dropshaft area is larger than 1%. When the cover is fully sealed, the minimum air core size reduces by ~5% of the dropshaft area which can have a serious implication to the design of the scroll vortex dropshaft. The present study provides a practical evaluation of the effect of the opening condition in the cover of the vortex chamber on the performance of scroll vortex dropshafts for underground water drainage systems..

Support vector machine (SVM) approach to develop the discharge prediction model for triangular labyrinth weir

Abstract Most of the studies on labyrinth weir were carried out in the laboratory, and regression models have been developed for discharge coefficient in terms of pertinent independent parameters. It is difficult to obtain an exact analytical solution to the head discharge relationship due to the existence of 3D flow. Consequently, various forms of soft computing techniques are used as an appropriate alternative to achieve greater accuracy in developing a discharge prediction model. In the present study, support vector regression (SVR) has, therefore, been implemented to develop a discharge coefficient prediction model for a triangular labyrinth (TL) weir using a sizeable amount of laboratory data available in the literature. An attempt has also been made to obtain a simple discharge coefficient equation using the same data based on the non-linear regression (NLR) approach for field application. A comparative study has been carried out to assess the accuracy of the discharge coefficient models obtained in the present study and those reported in the literature. Sensitivity analysis has been made to study the influence of individual parameters on the discharge coefficient. The accuracy of different discharge coefficient prediction models was also tested for the data of prototype labyrinth weir and appropriate models were recommended for the field application.

Flow characteristics of a tangential vortex intake with steep-slope tapering section

Abstract Tangential vortex intakes are compact hydraulic structures commonly used in water supply, drainage and sewerage systems to convey water from high to low elevations efficiently. For certain intake design, due to the complex three-dimensional (3D) flow transition, hydraulic jump and shock waves may form. This paper presents an experimental and 3D computational fluid dynamics (CFD) modeling of the flow in a tangential vortex intake with a steep-slope (sloping angle = 45°) tapering section. Swirling velocity field was measured using laser Doppler anemometry (LDA) for discharges with typical flow features. CFD predictions were most encouraging in the good agreement with measured head-discharge relationship, air core size and velocity. It was found that the flow regimes are determined by the hydraulic controls at different sections under different discharges, forming a complex flow transition with an inclined hydraulic jump at the tapering section. While the swirling flow in the dropshaft is highly asymmetrical, the local tangential velocity is similar to that of a stable tangential intake with Rankine vortex behaviour. Flow energy dissipation is caused by the hydraulic jump at the tapering section and the friction loss at the dropshaft. The present study offers comprehensive insights to the design of tangential vortex intake structures. HIGHLIGHTS Tangential vortex intake flow with steep-slope tapering section elucidated first time. Comprehensive flow profiles and velocity field measured for a range of discharges. 3D CFD predictions are in good agreement with the measurements. Flow regimes are determined by the hydraulic controls at different sections. Flow energy dissipation is caused by hydraulic jump and dropshaft friction loss.

Hydraulics of flow over full-cycle cosine and rectangular sharp-crested weirs

Laboratory experiments were carried out to investigate the hydraulic characteristics of full-cycle cosine and rectangular sharp-crested weirs in free flow condition. The head–discharge relationships of full-cycle cosine weirs were determined theoretically and the discharge coefficients were correlated with weir geometry for both rigid and erodible bed conditions. The proposed model showed higher discharge coefficients in full-cycle cosine weirs in comparison with rectangular sharp-crested weirs. The three-dimensional velocity profiles of full-cycle cosine and rectangular weirs were measured by an acoustic Doppler velocimeter probe. The effects of weir geometry on mean flow and local erosion upstream of the weirs were studied for two sediment sizes of 0.7 mm and 1.2 mm. The time-averaged velocity profiles exhibited strong three-dimensional flow in full-cycle cosine weirs. The strength of the upper eddy in the crest location of full-cycle cosine weirs decreased by increasing the weir gap opening and the jet stream deflected upward due to uneven eddy sizes. The maximum streamwise velocity of cosine weirs increased by four times the average velocity at the crest level of the weir and the transverse velocity profiles captured strong vortices in the vertical plane closest to the weir. The effect of weir gap opening of full-cycle cosine weirs on the total scour volume was studied for two sediment sizes. It was found that the scour volume in the upstream region of cosine weirs was higher than the scour volume formed upstream of a rectangular weir with the same opening.

Insights from three-dimensional computational fluid dynamics modelling of a scroll vortex intake

ABSTRACT Scroll vortex intakes are commonly used in water supply, drainage and sewerage systems. Water flows into the intake via an eccentric approach channel, forming a swirling vortex flow with a stable air core along the dropshaft. Previous design theories have largely been based on unjustified assumptions on the velocity and pressure distributions of the vortex flow at the intake bellmouth. To clarify these assumptions, a validated three-dimensional computational fluid dynamics model has been developed. Model predictions compare well with independent measurements of flow profile, velocity and air core size. While the vortex flow in the scroll chamber can be described by a free vortex with constant circulation equal to that at the inlet, the tangential velocity and the pressure distribution at the bellmouth outlet have to be approximated by a forced vortex. A revised theory is proposed, providing significant improvement to the prediction of air core sizes and head–discharge relationship.

A hybrid gene expression programming model for discharge prediction

The head–discharge relationship of an overflow weir is a prerequisite for flow measurement. Conventionally, it is determined by regression methods. With machine learning techniques, data-driven modelling becomes an alternative. However, a standalone model may be inadequate to generate satisfactory results, particularly for a complex system. With the intention of improving the performance of standard gene expression programming (GEP), a hybrid evolutionary scheme is proposed, which is coupled with grey system theory and probabilistic technique. As a gene filter, grey relational analysis (GRA) eliminates noise and simulated annealing (SA) reduces overfitting by optimising the gene weights. The proposed GEP-based model was developed and validated using experimental data of a submerged pivot weir. Compared with standalone GEP, the GRA–GEP–SA model was found to generate more accurate results. Its coefficients of determination and correlation were improved by 3.6% and 1.7%, respectively. The root mean square error was lowered by 24.8%, which is significant. The number of datasets with an error of less than 10% and 20% was increased by 15% and 12%, respectively. The proposed approach outperforms classic genetic programming and shows a comparative error level with the empirical formula. The hybrid procedure also provides a reference for applications in other hydraulic issues.

Emitter Clogging and Hydraulic Performance of Drip System under Different Water Qualities and Placement Techniques

The present study was conducted at the Indian Agricultural Research Institute, New Delhi, India, to evaluate the effect of sand-disc filters, pressure compensating (bioline) and non-pressure compensating (inline) emitters, and surface and subsurface placement of laterals on emitter clogging using wastewater and groundwater for irrigation. Results of this study revealed that besides water quality, the type of emitter, placement of laterals, and emitter position on laterals affected emitter's clogging. The major cause of clogging was associated with the precipitated substance accumulated at the emitter inlet concurrently close the micro-pore channels of the emitter, consequently reduce the emitter discharge. The major substances that took part in the clogging of emitter were EC, pH, HCO3, Turbidity, total solid, Escherichia coli (E. coli), and total coliform. It was observed that these substances (HCO3, Turbidity, total solid, E. coli, and total coliform) of groundwater and wastewater were categorized with a medium risk of clogging except for magnesium (low risk of clogging). Pressure compensating drip emitter showed better performance against clogging as compared to non-pressure compensating drip emitter. Sub-surface placement of drip emitter was more prone to clogging under both wastewater and groundwater. It was observed a significant (p ≤ 0.05) effect of lateral placement, emitter types, and the interaction between these factors on emitter's clogging under both types of water. Emitter flow rate decreased with the increasing time of operation of the drip systems at normal operating pressure, because of clogging of emitters. By flushing operation, it was observed a 3 to 5% higher flow rate in inline drip emitter than bioline (1-2%). The R2 value, which precisely describes the head-discharge relationship, was high (0.99) in most of the bioline treatments. This study also observed and recommended that pressure compensating emitter would be the most appropriate technique to reduce the clogging while using wastewater for irrigation. Flushing effectively controlled the emitter's clogging thus improved the emitter's water discharge rate.

Effects of modern marguerite-shaped inlets on hydraulic characteristics of swirling flow in shaft spillways

This study used model experiments to investigates hydraulic characteristics of flow at marguerite-shaped inlets with holes at the bottom of their lobes, known as modern marguerite-shaped inlets. This innovation reduces the swirling flow strength and improves the hydraulic performance of simple shaft spillways. Head–discharge relationships, flow circulation, threshold and critical submergence depths, and discharge coefficients are detailed for different flow regimes. The findings suggest that flow discharges through this type of inlet were approximately six, three, and two times greater than flow discharges through a simple shaft spillway, a circular piano key inlet, and a simple marguerite-shaped inlet, respectively. Increasing the outer length and height of inlets also uniformly distributed the flow around shaft spillways. The best hydraulic performance was observed in the inlets with an outer height of 1.25D and an outer length of 3.75D, where D is the diameter of the shaft spillway. Different equations, with high correlations and low errors, were derived to determine the threshold and critical submergence depths and the discharge coefficients for free and orifice flow regimes.

Study of flow over piano key weir of different plan shapes with free and partially submerged outlet conditions

Abstract Piano key weirs are being increasingly used for better flood passage downstream, both as a new structure or on top of hydraulic structures like a dam, to increase their discharging capacity as well as reservoir storage. Much research has been done on rectangular plan-form, while other plan-forms warrant attention. The present study focuses on two different plan geometries of PKW, i.e., rectangular (RPKW) and trapezoidal with angle α equal to 9 degrees (TPKW9) for their head-discharge relation in a wide channel of 0.984 m width under free-flow condition. Since the role of CFD is increasingly becoming prominent in present times, a numerical study using ANSYS-FLUENT was also carried out to ascertain its relevance in predicting flows around complex structures like PKW. Further, the tailgate was closed to render the PKW's outlet from partial to fully submerged conditions. The effect of these submerged outlets was studied for any changes in the discharging capacity of the PKW. The study shows RPKW to be more hydraulically efficient than TPKW9 for the model geometry. Further, the study finds that under partial to full submergence of PKW outlets, both PKW units' discharging capability remains unchanged.

Hydraulic characteristics of swirling flow at shaft spillways with the marguerite-shaped inlets

ABSTRACT Hydraulic characteristics of swirling flow at shaft spillways with an innovative inlet, namely the marguerite-shaped inlet, is investigated based on model experimentation. Detailed measurements of head–discharge relationship, flow regimes, water free-surface profiles, flow circulation, discharge coefficient and threshold and critical submergence depths were performed for shaft spillways with marguerite-shaped inlets. Results indicate that the strength of swirling flow through a marguerite-shaped inlet is significantly lower than that of a simple shaft and a morning glory spillway. Marguerite-shaped inlets increase the developed crest length by at least 6 times the global size of the original shaft spillway. Therefore, they produce exceptional hydraulic performances in increasing the weir overflow length without changing the global size of the shaft spillway, thereby increasing the flow discharge up to 6, 4 and 1.5 times the simple shaft, morning glory and circular piano-key spillways, respectively. Finally, based on the detailed experimental data, different empirical correlations are derived for estimating the threshold and critical submergence depths and discharge coefficient of the marguerite-shaped inlets for different flow regimes using regression analysis.

Geometric Effects on Discharge Relationships for Labyrinth Weirs

Published labyrinth weir design methods, along with specific site constraints, are typically used to develop an appropriate labyrinth weir geometry (footprint, weir height, wall thickness, apex dimensions, sidewall length, sidewall angle, number of cycles, crest shape, etc.) for the desired head-discharge relation. When a proposed labyrinth weir geometry deviates from the underlying design data, uncertainty in hydraulic performance increases and may merit additional guidance or numerical or physical modeling. This study quantifies the effects of systematic variations (apex dimensions, sidewall length, channel width, and weir height) on labyrinth weir hydraulic performance. After considering hydraulic performance, constructability, and economics, an optimum apex width was identified. Hydraulic efficiency was found to decrease with increasing cycle number (for a constant-width channel), and upstream apex geometries were more significant than downstream geometries with respect to hydraulic efficiency. The impact of weir height on hydraulic efficiency was variable, with an overly short weir showing a negative impact and taller weirs being beneficial but only up to a certain height.

Hydraulic performance of circular crested oblique weirs

Abstract The present study attempted to improve the discharge capacity of oblique weirs by rounding their crests. Twenty-four oblique weir models have been tested in which oblique angle (α), weir height (P) and crest diameter (D) were changed. Analysis of the results shows that the discharge (QOC) increases with the increase of effective head above crest (He). Values of discharge coefficient (CD) are found decreasing slightly with the increase of (He/P) and (He/D) values and weirs of small oblique angles give lower values of CD. An empirical expression is presented to determine CD in terms of He/P, He/D and α (in radian) with a correlation coefficient of 0.90 and a standard error of 0.01. The highest discharge capacity is obtained from a weir having α = 20°, P = 20 cm, D = 4 cm and D/P ratio = 0.2 in which the percentage increase in discharge is ranging between 147% and 175% compared to sharp crested normal weir. Comparison of the present study results with those of other investigations shows that circular crested oblique weirs offer higher discharge capacity compared with some other weir shapes. A simple design method is recommended through which the lasting dimensions and the head-discharge relationship of the weir can be predicted.

Half-Round Circular Crested Weir: On Hysteresis, Instabilities, and Head–Discharge Relationship

AbstractWaters flowing over rounded weirs experience a rapidly accelerated flow region near the crest. The head-discharge relationship of a half-round crested weir was tested physically under caref...

Scale Effects in Free-Flow Nonlinear Weir Head-Discharge Relationships

AbstractUsing similitude relationships, laboratory-scale models have been used for decades to predict and confirm prototype hydraulic structure performance. For free-flow weir discharge conditions,...

Discharge Coefficient of a Round-Crested Weir

A model experimental study was conducted for the discharge capability of different shapes of the crest of a weir. The flow rate and the head over the weir measured by laboratory experiments were used as two parameters for characterizing the head discharge relationship. Experiments indicated that the head discharge relationship for different radii located upstream and downstream of the crest of the weir had different features. A series of detailed experiments investigated the effects of different upstream rounding radii on the discharge capability when the downstream rounding radius was constant and the round ratio between the radius of the rounded upstream corner to the weir breath in the direction of flow was equal to 1.00. Experimental results showed that the rounded upstream corner could increase the discharge capability. The discharge capability increased as the upstream round ratio became larger and did not change when the round ratio varied from 0.10 to 0.30 and from 0.75 to 1.00 in this experiment. Based on the experimental data distribution, the empirical formula for the discharge coefficient was fitted with the round ratio as the group parameter.

Optimised Triangular Weir Design for Assessing the Full-Scale Performance of Green Infrastructure

Conventional triangular weirs have been originally developed to measure, divert, and control surface water. However, a special application of these weirs, such as for low flow measurements in full-scale monitoring of Green Infrastructure (GI), is not well investigated. Available head-discharge relationships for triangular sharp-crested weirs are only valid under a free-flow regime. Literature focusing on the V-notch weir usage for GI assessment suggests that it is necessary to calibrate the head-discharge relationship before its use. This study focuses on understanding the effects of site constraints on the measurement performance of a V-notch weir at low flow rates, and the validity of equations derived for similar applications that can be found in the literature. The variation of discharge coefficient in various flow regimes was investigated experimentally based on calibration runs covering flow rates between 0.054 l/s and 7 l/s. The results show that for 30° and 45° V-notch weirs, three flow regimes can be identified. It was observed that literature equations to calculate the discharge coefficient are valid for partially-contracted triangular weirs only at heads greater than vertex distance from the channel. However, for low flows that are expected to occur when estimating the full-scale performance of GI, the equations available from the literature for similar site conditions underestimated the flow rate between 85% and 17%. This emphasises the need for accurate calibration of a V-notch device under the site conditions to achieve the necessary level of accuracy in GI performance estimation. The procedure outlined in this work can be easily replicated to determine the optimal monitoring system configuration. Alternatively, if the site conditions would match those described in this study, the computed discharge using the proposed relations, in combination with the general V-notch weir equation, provides a significant improvement in the accuracy of measurements, expands the head applicability range of V-notch weirs, and enables better understanding of GI performance at the full scale.

A Performance Comparison of Machine Learning Algorithms for Arced Labyrinth Spillways

Labyrinth weirs provide an economic option for flow control structures in a variety of applications, including as spillways at dams. The cycles of labyrinth weirs are typically placed in a linear configuration. However, numerous projects place labyrinth cycles along an arc to take advantage of reservoir conditions and dam alignment, and to reduce construction costs such as narrowing the spillway chute. Practitioners must optimize more than 10 geometric variables when developing a head–discharge relationship. This is typically done using the following tools: empirical relationships, numerical modeling, and physical modeling. This study applied a new tool, machine learning, to the analysis of the geometrically complex arced labyrinth weirs. In this work, both neural networks (NN) and random forests (RF) were employed to estimate the discharge coefficient for this specific type of weir with the results of physical modeling experiments used for training. Machine learning results are critiqued in terms of accuracy, robustness, interpolation, applicability, and new insights into the hydraulic performance of arced labyrinth weirs. Results demonstrate that NN and RF algorithms can be used as a unique expression for curve fitting, although neural networks outperformed random forest when interpolating among the tested geometries.

Head discharge relationship for inclined non-rectangular notches

Experimental results on the discharging capacity of inclined sharp crested weirs are presented. Three non-rectangular notch shapes such as parabolic, semi-circular and inverted semicircular notches were considered in the study. It is found that the theoretical discharge increases nonlinearly with an increase in flow depth over the crest of the notch and inclination of the notch with vertical. The regression equations are developed between the non-dimensional theoretical discharge and non-dimensional flow depth over the crest. The regression coefficients are found to be the function of the angle of inclination of the notch. Further, the actual discharge varies linearly with the theoretical discharge, with coefficient of discharge being the function of angle of inclination of the notch with vertical. The average coefficient of discharge for parabolic, semi-circular and inverted semicircular is found to be 0.638, 0.796 and 0.77, respectively. In addition, the discharging index for the inclined notches are defined which increases with an increase in inclination of the notch with vertical.