Weir Geometry Research Articles

Characterisation of a continuous blender: Impact of physical properties on mass holdup behaviour

Continuous blenders are a key unit operation in Continuous Direct Compaction, a route to solid oral dosage forms that is receiving significant interest. Mass holdup in these blenders is a crucial variable; understanding how it is influenced by material properties, equipment configuration and process settings is key. The present work evaluated a Gericke GCM-450 blender for range of outlet weir aperture geometries (angled or horizontal), material properties (pure components and blends) and process settings (throughput and impeller speed). Results show opposing mass holdup behaviour depending on weir choice, material density and flowability, likely linked to the propensity of the material to form an inclined powder surface that matches – or does not – the chosen weir geometry. The present work underscores the need for fundamental process phenomena understanding, especially when insight is sought for how blender performance varies across multiple dimensions (throughput, impeller speed, material properties) and discrete equipment choices (weir geometry).

Investigation of the impact of surface roughness on the flow characteristics of a broad-crested weir

ABSTRACT Weirs are a common hydraulic structure. The broad-crested weir's effectiveness depends on its height and surface roughness. The present study investigates the coefficient of discharge (Cd) for various broad-crested weirs in a laboratory flume. Two types of weir geometry were used and outfitted with three types of surface roughness (cement, boulders, and gravel) and the coefficient of discharge. The outcomes showed that the coefficient of discharge reduces as the surface roughness of the broad-crested weir increases for a given (H/H + P). The average value of the discharge coefficient for Group 1 (models 1, 2, and 3) was 0.66, 0.65, and 0.64, respectively. For comparison between models 1 and 2 and between models 1 and 3, the decrease in the coefficient of discharge was approximately 2 and 3.5%, respectively. Group 2 (models 4, 5, and 6) had an average value of the discharge coefficient of 0.63, 0.62, and 0.61, respectively. The decrease in the coefficient of discharge for comparison between models 4 and 5 and between models 4 and 6 was around 1.75 and 3%, respectively. Empirical equations were obtained to accurately fit the data. This study can inform the design of weirs, allowing for improved control and flow regulation in hydraulic systems.

Flow Patterns Modeling over Spillway: Review Study

A spillway dam, constructed concurrently with concrete or masonry, is a vital infrastructure designed to provide the controlled release of surplus water that surpasses the dam's storage capacity. Since the Ogee spillway is among the best and most well-known worldwide, it deserves study. Weir flow, inertia, and gravity are crucial in many open-channel applications. Consequently, hydraulic performance data between model and prototype structures are commonly scaled using Froude similitude. As the upstream head decreases in a weir flow, the surface tension and viscosity forces become more important, perhaps to the point where Froude scaling fails to achieve complete model-prototype similarity. Size-scale effects are responsible for various alterations to the head-discharge connection, the nappe trajectory, and air entrainment. Hydraulic parameters were explored in this work utilizing Flow3D software to find weir geometry optimization using the CFD method. In addition, this study attempted to evaluate flow on various parts of crested weirs in three different models.

An experimental and numerical investigation of hydraulic performance of in-channel triangular labyrinth weir for free overflow

ABSTRACT Labyrinth weirs are well known for their superiority in providing higher flow capacity for a given hydraulic head, especially in areas where space is limited. This study presents an experimental and numerical study to determine the hydraulic efficiency of triangular labyrinth weirs. The discharge coefficient of a weir was determined in two different ways, depending on the width of the channel (C d ) and the length of the crest of the weir (C L ). Although the crest length is the most important factor in increasing the discharge coefficient per unit channel width, the discharge coefficient per unit crest length decreases with increasing the crest length for a given head. It can be said that the main reason for the reduction in weir efficiency, particularly at high headwater, is nappe interference and therefore local submergence between cycles. From the results of systematic analyses, some new highly correlated multiple regression equations calculating these two coefficients in relation to the weir geometries and the flow conditions were obtained. As a result of the literature comparison, although they were found to be generally compatible with the results of similar studies in the literature, the reasons for the differences between them were discussed.

Impact of downstream obstructions on ogee weir efficiency: a regression analysis

ABSTRACT This study delves into the impact of downstream obstruction angles on the discharge coefficient (Cd) over ogee weirs within open channel flows, a critical factor for accurate flow rate predictions in hydraulic engineering. Employing a series of detailed laboratory experiments, the influence of various obstruction angles on Cd was scrutinized applying a suite of regression analysis to develop predictive models. The analysis was enriched by considering hydraulic parameters such as flow rate, water level, and weir geometry. Despite the established importance of Cd in hydraulic designs the nuanced effects of downstream obstructions have received limited attention, highlighting a critical research gap. The findings highlight a strong correlation between obstruction angles and Cd, with developed regression models demonstrating notable predictive strength. Remarkably the models exhibited varying levels of accuracy, with the Random Forest regressor achieving an exceptionally low root mean square error (RMSE) of 0.005, indicating superior predictive performance. Conversely, traditional models like Decision tree and XG BOOST reflected higher RMSE values of 0.60, suggesting less predictive accuracy in this context. LASSO, Bayesian Ridge, and OMP regressors stood out with an RMSE of zero, denoting perfect predictions under the study's specific conditions.

Discharge Coefficient of Symmetrical Stepped and Triangular Labyrinth Side Weirs in a Subcritical Flow Regime

The labyrinth side weir structure is an optimal solution to regulate and divert excess flows across rivers, and irrigation and drainage channels when the opening length of the side weir is limited. Changing the geometry of the side weir is considered one way to improve its efficiency. The present study investigates the hydraulic effects of stepped labyrinth side weirs to increase their discharge capacity. To estimate the outflow over symmetrical stepped labyrinth side weir, the discharge coefficient needs to be determined. Normal triangular labyrinth side weir in one cycle mode has been modified by increasing the crest path using different steps. A total of 417 experiments were conducted on normal and stepped side weirs for various weir opening lengths, weir heights, internal head angles, and hydraulic conditions. The results were analyzed and compared. It was found that efficiency improved, and the discharge coefficient increased as the number of the steps decreased. Furthermore, the water surface profile becomes more uniform with decreasing number of steps. A lower number of steps, smaller head angle, and high weir length produce a higher discharge coefficient by approximately 15%–35% compared to a normal triangular labyrinth side weir; in addition, the Knope length decreases by approximately 40%–70% for the same effective length. Additionally, a reliable equation to estimate the discharge coefficient of the stepped labyrinth side weir was presented. The results of this study can be used to design side weirs with high hydraulic performance when the weir-included angle selected is small or there is a lack of space.

Estimation Of Disharge Coefficient On Weir Configuration Based On Flow Rate And Velocity

The development of water treatment and water resources considers the flow rate adjusted using a weir. Weir is designed with many hydraulic factors, including the coefficient of discharge (Cd). Characteristics of the value of Cd show a decreasing trend on triangular and rectangular weirs. The value of Cd varies based on the flow's characteristics and the channel's geometry. Estimation of the best Cd value in flow discharge engineering and sediment deposition is necessary to know the accuracy of weir geometry. Some plans in water treatment and water resource building sometimes assume a Cd value based on literature. This study aims to estimate the value of Cd based on variations in flow rate and was conducted on a laboratory scale with weir shape limitations in the form of triangles and rectangles. The water sample was discharged by a water pump into an open channel. The angle of the weir opening was determined for the rectangular and triangular weir of 90°. Flow monitoring included flow discharge through the use of a current meter. Water was recycled in each measurement with a total of 60 cycles. The Cd values in a triangular weir were greater than in a rectangular weir. The Cd values for the rectangular weir ranged from 0.068 to 0.089, while the Cd values for the triangular weir ranged from 0.557 to 0.598. This value indicated that the greater the flow rate, the lower the Cd value. Therefore, weir configuration of water discharged using a triangular weir was better than a rectangular weir at low flow rates, less than 0.05 m3/s.

A review of hydraulic performance and design methods of labyrinth weirs

Abstract Labyrinth weirs are complex hydraulic structures. They have been widely used as a water regulator and to increase discharge in channels and spillway dams. Labyrinth weirs are an economical and effective method to pass large floods. In addition, they are used to reduce the requirements of the structural footprint. These features make them an interesting and appropriate choice to increase the capacity of discharge. Several factors affect the discharge capacity and the hydraulic performance of labyrinth weirs, including water level to crest height ratio, angle of sidewalls, apex width, conveyance channel conditions, and vertical aspect ratio. The present paper aims to summarise the most relevant knowledge of the hydraulic characteristics of the labyrinth weirs reported in previous articles. The importance of the present study is to provide a better understanding of how these weirs operate, in addition to which future studies deserve further investigation. The results demonstrated that some parameters still need further investigation. Also, energy dissipation over the labyrinth weir needs further investigation with different weir geometry. Furthermore, the results showed that common design equations did not take into account all parameters affecting labyrinth weir performance, including geometries, flow conditions, site conditions, and scale effect. In addition, machine learning techniques need further study.

Discharge Estimation over Piano Key Weirs: A Review of Recent Developments

The piano key (PK) weir has advanced over the labyrinth weir to increase the discharge capacity. Piano key weirs exhibit nonlinear flow behavior and are easy to place on the existing spillway or newly constructed dam with less base area. Various investigators are given equations to calculate the discharge coefficient for free and submerged flow conditions. The study focuses on reviewing the impacts of the PK weir geometry on the weir flow discharge coefficient, including weir length and height, upstream and downstream key widths, and apex overhangs. In this study, all possible aspects of PK weirs were briefly reviewed. From sensitivity analysis, it is observed that the discharge coefficient of the PK weir is more sensitive for the L/W dimensionless ratio followed by the B/P ratio. L is total length of the weir crest, W is width of the weir, B is total width of PK weir and P is height of the weir. This review paper is intended to serve as an accessible resource for hydraulic structures researchers and hydraulic engineering professionals alike interested in the hydraulics of PK weirs.

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.

Experimental and numerical analysis of weir structures in open channel flows

Weirs are important water structures used to hold water in dams and canals and to safely transfer water from upstream to downstream. Due to these features, these structures, which have been used for years, have many different designs. In this study, a rectangular labyrinth weir and an inclined-bed rectangular weir were studied experimentally and numerically. The weir geometries used in the experiment were produced in a 3D printer and transferred to the numerical simulation with the same dimensions. The discharge and discharge coefficients corresponding to five different upstream heights obtained from the experiment and numerical simulation were obtained and the data were compared.

Developing a model for multi-objective optimization of open channels and labyrinth weirs: Theory and application in Isfahan Irrigation Networks

Finding an optimal design for hydraulic structures and devices, which work together in irrigation networks, can be formulated as a multi-objective optimization problem. In this paper, a novel framework is proposed for simultaneous optimization of an open channel section and a labyrinth weir geometry. A recently proposed optimizer called Multi-Objective Multi-Verse Optimization (MOMVO) algorithm is employed and its results are compared with Pareto Envelope-based Selection Algorithm II (PESA-II) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) using five metrics, including spacing (SP), Maximum Spread (MS), Non-uniformity of Pareto Front (NPF), Mean Ideal Distance (MID), and Coverage Measure (CM). The first objective function is defined to minimize the construction costs per unit length of the open channel, and the second one is to minimize total concrete volume of the labyrinth weir. The results showed significant differences between MOMVO Pareto optimal solutions and the other two algorithms. The least values of SP, NPF, and MID metrics were provided by MOMVO, which meant its solutions had better conditions regarding uniformity and the closeness to the ideal point. To optimize irrigation network as a system, penalty functions were applied to satisfy hydraulic conditions (flow velocity, Froude number, and nappe interference). Results showed that if the proposed model had been employed in Isfahan Irrigation Networks (IINs) design, it would have reduced the construction costs of open channel and labyrinth weir approximately 11% and 74%, respectively. It can be reported that the most cost-effective design has the least channel wetted perimeter, channel cross-section top width, cross-sectional area, and labyrinth apex length; and the highest channel depth, and weir sidewall angles.

FEM analysis of water surface profile using VOF Method

The prediction of water surface elevation in open channels is important for evaluation and determination of the heights of side wall of structures in open channel systems. At present empirical equations are basically used for the purpose. In the early half of the 19th century experimental approach was mainly used but it had the drawbacks of laborious data collection and instrument operation limitation. The 3D flow behavior or some complex turbulent structure which is the nature of any open channel flow, cannot be effectively captured through experiments, so in these circumstances, computational approach can be adopted to overcome these obstacles. In comparison to experimental studies computational approach is repeatable, can simulate at full scale, can generate the flow taking all the data points into consideration. The motive of the present work is to use the simple geometry of the rectangular broad crested weir to test the commercial CFD software ANSYS-CFX in order to test its feasibility for implementation in more complex open channel flows. The experimental results of Hager & Schwalt’s are validated and then the analysis has been done for weirs with different slopes.

A laboratory investigation on the potential of computational intelligence approaches to estimate the discharge coefficient of piano key weir

The piano key weir (PKW) is a type of nonlinear control structure that can be used to increase unit discharge over linear overflow weir geometries, particularly when the weir footprint area is restricted To predict the outflow passing over a piano key weir, the discharge coefficient in the general equation of weir needs to be known. This paper presents the results of laboratory model testing of a piano key weir located on the straight open channel flume in the hydraulic laboratory of Bu-Ali Sina University. The discharge coefficient of piano key weir is estimated by using four computational intelligence approaches, namely, feed forward back-propagation neural network (FFBPN), an extension of genetic programming namely gene-expression programming (GEP), least square support vector machine (LSSVM) and extreme learning machine (ELM). For this purpose, 70 laboratory test results were used for determining discharge coefficient of piano key weir for a wide range of discharge values. Coefficient of determination (R2), Nash-Sutcliffe efficiency coefficient (NS), root mean square error (RMSE), mean absolute relative error (MARE), scatter index (SI) and BIAS are used for measuring the models’ performance. Overall performance of the models shows that, all the studied models are able to estimate discharge coefficient of piano key weir satisfactorily. Comparison of results showed that the ELM (R2=0.997 and NS= 0.986) and LSSVM (RMSE=0.016 and MARE=0.027) models were able to produce better results than the other models investigated and could be employed successfully in modeling discharge coefficient from the available experimental data.

Effects of weir geometry on scour development in the downstream of Piano Key Weirs

Abstract Scouring in the downstream of all weirs, including Piano Key Weirs (PKWs), can have major safety implications. Since the research on downstream scouring of PKWs is very limited, and the weir geometry is also known to have an impact on downstream scouring, this study investigated scouring in the downstream of PKWs with rectangular and trapezoidal geometries and two different heights. The scour hole measurements showed that in both rectangular and trapezoidal models, scour hole parameters increased both with the increase in discharge rate and the increase in weir height. Under similar discharge conditions, the scour depth downstream from the rectangular model was greater than that downstream from the trapezoidal model. The dimensionless maximum scour depth, the distance of maximum scour depth from the weir toe, and the scour hole length for the trapezoidal PKW were, on average, 6, 13, and 11% lower than the corresponding ones for the rectangular PKW, respectively. However, these differences decreased with the increase in falling height. For both weir geometries, the maximum scour depth was aligned with the outlet keys. In addition, the maximum scour depth under the outlet keys was 13% greater than the one under the inlet keys.

Hydraulics of sharp-crested weir culverts with downstream ramps in free-flow, partially, and fully submerged-flow conditions

Laboratory experiments were conducted to investigate the hydraulics and discharge characteristics of sharp-crested weir culverts with downstream ramps for hydraulically smooth wall boundary and for free, partially submerged, and fully submerged-flow conditions. Four weir-culvert models were tested with different weir heights, ramp lengths, and culvert heights. The partially submerged-flow conditions were created when a slight increase in tailwater caused the headwater to rise due to partial submergence of the culvert. In this flow regime, supercritical flow over the ramp interacted with culvert outflow and this flow regime was classified as Supercritical Jet Interaction Regime or SJIR. Once tailwater reached the weir crest, the weir flow regime became submerged indicating fully submerged-flow condition. Based on the variations of water surface profiles, submerged flows were further classified into Surface Jump Regime (SJR), Surface Wave Regime (SWR), and Deeply Submerged Regime (DSR) and the boundaries between each flow regime were defined by regime plots. To predict discharge of weir culverts with downstream ramps, variations of discharge coefficient with weir geometry and flow regimes were studied and empirical formulations were developed. In addition, free and partially submerged flow discharges were predicted by implementing the interaction factor. It was found that the interaction factor was independent of the Froude number in SJR, while it correlated with the Froude number in SJIR. Under submerged-flow conditions, evaluation of the discharge characteristics of the proposed weir-culvert model showed correlations with water surface flow regimes and a three-stage prediction formula was proposed for estimation of submerged flow. The energy losses over weir-culvert models were also calculated and it decreased with submergence.

Experimental study for measuring discharge through compound broad crested weir

This paper deals with a new compound broad crested weir for measurement of discharge. Calibration of broad crested weir is mainly dependent upon the length of the weir crest (L), weir height and upstream water head over weir crest (h). Hence measurement of discharge varies as per change in the flow characteristics due to change in the geometry of weir for a given flume. Based on experimental analysis, past researchers have shown that discharge coefficient (Cd) changes proportionally with h/L ratio, maintaining an average range of Cd for various h/L values. In the present study a novel approach towards design of compound broad crested weir is proposed which can effectively measure wide range of discharges thereby maintaining a constant discharge coefficient irrespective of the head over weir. Experimentation has been carried out in a laboratory horizontal tilting flume 2.5 m long, 20 cm wide and 30 cm deep. The investigation is carried out for discharge ranging from 10 lps to 2 lps. In the earlier experimentation conducted Cd was varying in the range from 0.518 to 0.648, after which the broad crested weir model is modified for suiting best results thereby resulting in the reformed discharge coefficient values of 0.546–0.599 which is in close proximity to the design input value of 0.6.

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.

Numerical analysis of the hydraulic characteristics of modified labyrinth weirs

Labyrinth weirs increase the discharge rate by increasing the effective length of the weir within a confined width. In this paper, an attempt was made to improve the hydraulic performance of labyrinth weirs by both notching the weir wall and inclining the weir crest edge. To simulate the free flow surface, the volume of fluid (VOF) method, and the turbulence, the RNG k-e model was adopted in the FLOW-3D software. To validate the numerical model with the experimental data, the results indicate that the maximum relative error is 4.8%, which confirms that the numerical model is fairly well to predict the specifications of flow over on the labyrinth weir. Numerical simulation results showed that for low HT/P ratios (HT: approach flow head, P: weir height), modifying the geometry using either methods improved the discharge coefficient and discharge capacity over the labyrinth weir compared to a conventional weir. By increasing lc/wc (lc: the weir cycle length and wc: the weir cycle width) for low ratios of HT/P, the flow magnification ratio Q/Qn (Q: weir discharge, Qn: conventional weir discharge) increases. By increasing the HT/P ratio, the flow magnification ratio and the flow rate both decrease significantly, that is because of the vortex flow formation, the rejection of the flow upstream, and local submergence of entry cycles with a high HT/P ratio. Therefore, modifying the labyrinth weir geometry at low HT/P ratios (HT/P < 0.2) results in a better hydraulic performance, a higher discharge coefficient, and larger discharge values.

Geometry of polygonal hydraulic jumps and the role of hysteresis

An experimental study shows that polygonal hydraulic jumps, which are formed when a liquid jet impacts a target plate, can exhibit modal hysteresis, yet the normalized jump geometry $A/P\phantom{\rule{0}{0ex}}H$ is unaffected by the flow history and has a weak dependence on the weir geometry. All experimental data collapses upon scaling with the downstream Weber number, illustrating the role of surface tension in mode selection.