Studying the relationship between the hydraulic and geometry characteristics of labyrinth weirs based on the historical memory of reported data

One of the effective ways to increase the efficiency of weirs is to use nonlinear weirs, such as labyrinth weir, which increases the flow capacity by increasing the length of the weir at a fixed width. Given the importance of precisely estimating the flow discharge coefficient of this type of weir and its impact on supplying the safety of water structures, in the present study, the flow coefficient of labyrinth weirs was estimated using data-driven models of Extreme Learning Machine (ELM), Classification And Regression Tree (CART), Chi-square Automatic Interaction Detector (CHAID), and Multiple Linear Regression (MLR). After the modeling process, the predicted results were compared with the observed values using statistical measures and diagnostic analysis. In this study, three input combinations of hydraulic parameters, including the total upstream hydraulic head of weir (H_T), weir discharge (Q), and head to weir height (H_T/P) were used as input vectors. In order to evaluate the accuracy of the models, the statistical indicators of Coefficient of Efficiency (CE), RMSE, MDE, and RSD were employed. The final results showed that the ELM method created with all potential input parameters (H_T, Q, and H_T/P) was highly accurate in determining flow discharge coefficient. Due to having the lowest error (CE = 0.8815, RMSE = 0.0370), it was selected as the superior model.     

Effect of the inlet-to-outlet key width ratio of Piano Key Weir on its hydraulic behaviour

The Piano Key Weir (PKW) is an ungated type of spillway, i.e., a novel evolution over the traditional labyrinth weir. It allows the reservoirs to operate with elevated supply levels without causing any damage to the dam structures, thereby providing additional storage. It is designed to improve the hydraulic performance of linear weirs by increasing pass discharge and energy dissipation. In this study, an experimental investigation has been carried out to assess the effect of the inlet-to-outlet width ratio (W_i/W_o) on PKW hydraulic behaviours viz hydraulic efficiency and energy dissipation. To this end, nine different width proportions (1 ≤ W_i/W_o ≤ 2) type-A PKW models were tested and examined. The findings revealed that the W_i/W_o ratio significantly impacts the hydraulic performance of PKW, and the results indicate that the efficiency of the PKW increases as the width ratio increases at a certain limit and then starts decreasing. The discharge coefficient was the highest for the given discharge and head, resulting in the best hydraulic performance with a W_i/W_o ratio between 1.25 and 1.30. However, the energy dissipation across the PKW decreases as the width ratio increases. Moreover, the discharge coefficient of different width ratios (W_i/W_o) ranging between 1.28 and 1.30 is 7–17% higher than W_i/W_o = 1 and 8–13% higher than W_i/W_o = 2.0. However, the energy dissipation across the weir for W_i/W_o = 2.0 indicates 15–29% less energy dissipation than W_i/W_o = 1. It means the energy dissipation across the weir decreases as the W_i/W_o ratio increases.     

Experimental analysis of flow characteristics over hydrofoil weirs

The rounded crested weirs are commonly used for discharge measurements and this overflow structures have advantages such as stable overflow pattern and good accuracy. Hydrofoil weirs with streamlined properties are similar to the ogee weirs and can be used as a spillway profile. The hydraulic features of flow over hydrofoil weirs created by the NACA0018, NACA0021 and NACA0024 hydrofoil geometry placed in an open channel are investigated experimentally under free-flow conditions. The velocity field of hydrofoil weir flows are measured by one-dimensional Laser Doppler Anemometer. Experimental velocity profiles are measured along the middle section of the channel, especially around the weir structure, to determine the boundary layer separation. According to the determination of optimum weir structure the free surface profiles, pressure distributions on weir surfaces, experimental discharge coefficients and head losses over weir structures are determined for different structure and flow conditions. Pressure distributions over the hydrofoil weir are presented. In addition, the relationships between discharge coefficient (C_d) and flow rate (Q), specific total head (H/R), relative weir height (P/H), relative total head (H/P) and dimensionless total energy head upstream of the weir (H/L) are investigated.     

A new approach for oblique weir discharge coefficient prediction based on hybrid inclusive multiple model

One type of long-crested weir is oblique weir. Oblique weirs are longer than standard weirs. Therefore, they can pass more discharge capacity than weirs at the given channel width. The main objective of the present study was to investigate the efficacy of several intelligent models including multiple linear regression (MLR), Gaussian process regression (GPR), artificial neural network (ANN) and multiple models driven by ANN (MM-ANN) methods in estimating oblique weir discharge coefficient (C_d). Different input combinations were predicted using the variables of H/P, P/L_e, and W/L_e and the output coefficient of discharge. Prediction models were analyzed by statistical index, including root mean square error (RMSE), correlation coefficient (R), error percentage chart, relative error (RE%) plot, Kling-Gupta efficiency (KGE), probability density function (PDF) plot, scatter plot, scatter plot of error residuals and Taylor's diagram. Obtained results showed that the ANN model performed best by combining the inputs of the three variables (i.e., H/P, P/L_e, and W/L_e) with R = 0.746 and RMSE = 0.065 among the standalone models. Eventually, the proposed hybrid model MM-ANN was most accurate in estimating the oblique weir C_d by improving the prediction results of the implemented models.     

Investigation of the influence of various process parameters on the radial forging processes by the finite element method (FEM)

In this study, the finite deformation theory was used to develop a large rigid-plastic deformation finite element program which could simulate the radial forging process of work-hardening materials. First, experiments were carried out to confirm the accuracy of the program. Then we investigated the influence of each parameter on the forging process. The parameters adopted in this study are die corner radius (R), ring gap height (H), friction factor (m), and work-hardening coefficient (n). The effects of parameters on the flange thickness ratio (h/H) and the outer protruding shape ratio (D/D ₀) are also obtained. The relationship between the process parameters and the deformation behaviours under radial forging is obtained through simulation. When the radius of die corner and the ring gap height are larger, the flange thickness ratio (h/H) becomes larger, but the outer protruding shape ratio (D/D ₀) decreases. The value of friction factor (m) doesn’t seem to affect the flange thickness ratio (h/H) much, but the outer protruding shape ratio (D/D ₀) decreases upon increasing the friction factor . When the work-hardening coefficient (n) is larger, the flange thickness ratio (h/H) is also larger, but the outer protruding shape ratio (D/D ₀) decreases. The results of this study offer some advanced knowledge about finding the best designs of process and die in radial forging process.     

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 (C_d) changes proportionally with h/L ratio, maintaining an average range of C_d 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 C_d 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.     

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.     

Sensitivity analysis of the factors affecting the discharge capacity of side weirs in trapezoidal channels using extreme learning machines

Side weirs are installed on the side walls of main channels to control and regulate flow. In this study, sensitivity analysis is planned using Extreme Learning Machines (ELM) to recognize the factors affecting the discharge coefficient in trapezoidal channels. A total of 31 models with 1 to 5 parameters are developed. The input parameters are ratio of side weir length to trapezoidal channel bottom width (L/b), Froude number (Fr), ratio of side weir length to flow depth upstream of the side weir (L/y₁), ratio of flow depth upstream of the side weir to the main channel bottom width (y₁/b) and trapezoid channel side wall slope (m). Among the models with one input parameter, the model including Froude number modeled the discharge coefficient more accurately (MAPE=4.118, R²=0.835). Between models with two input parameters, the model using Fr and L/b produced MAPE and R² values of 2.607 and 0.913 respectively. Moreover, among the models with four input parameters, the model containing Fr, L/b, L/y₁ and y₁/b was the most accurate (MAPE=2.916, R²=0.925).     

Experimental study of discharge coefficient of trapezoidal arced labyrinth weirs of widened middle cycle

Arced labyrinth weir is a certain type of nonlinear weirs with a very high discharge capacity. Thanks to the increased effective length and the ensuing increased discharge capacity of these weirs, they can be used in dam spillways and water regulating structures. This study focused on trapezoidal Arced labyrinth weirs (TALW) of widened middle cycle. Various experiments were performed to evaluate the effect on discharge coefficient of various geometric parameters, including the ratio of inside apex width of the end cycles to that of the middle cycle (w₂/w₁) and the ratio of the length of labyrinth weir (Apron) in flow direction to the width of the middle cycle (B/w₁). Results of this study showed that with a decrease in w₂/w₁ from 0.42 to 0.30, discharge coefficient (C_d) would increase by 13–33%.     

Experimental study of effect of creating an additional cycle along the lateral crest of the labyrinth weirs

One of the practical and economical ways to enhance the discharge capacity is to use labyrinth weirs. The longer crest length in labyrinth weirs than in linear weirs has caused these weirs to have both a higher discharge coefficient and water discharge capacity than a linear weir. In the present study, the discharge coefficient of trapezoidal and triangular labyrinth weirs was investigated by creating an additional cycle along the lateral crest of the weir. By constructing 10 physical models of labyrinth weirs, tests were performed in the hydraulic and sediment laboratory of the Khuzestan Water and Power Authority (KWPA). Dimensional analysis by the Buckingham method revealed the discharge coefficient (Cd) as a function of variable parameters such as the total hydraulic head to weir height ratio (Ht/P) and weir shape factor (Sf). The results of experimental tests showed that at the hydraulic head ratio (Ht/P) of 0.1, the TP weir had a higher discharge coefficient of 3.5% than the TPTPO weir and 2.5% than the TPTRO weir. However, at a hydraulic head ratio of 0.12, the TR weir had a lower discharge coefficient of 4.6% than the TRTPO weir and 6.9% compared to the TRTRO weir. For the hydraulic head ratio of 0.14, the TRTPI weir was 5.8% and the TRTRI weir was 9.4% higher than the TR weir. Statistical analysis using SPSS indicated that TRTPO and TPTRO weirs had the highest correlation with the cubic model.     

Influence of crest geometric on discharge coefficient efficiency of labyrinth weirs

Labyrinth type weirs are structures that, due to their geometry, allow the discharge capacity to be increased compared to linear weirs. They are a favorable option for dam rehabilitation and upstream level control. There are various geometries of labyrinth type weirs such as trapezoidal, triangular or piano key as well as different types of crest profiles. Geometric changes are directly related to hydraulic efficiency. The objective of this work was to analyze the hydraulic performance of a labyrinth type weir, by simulating several geometries of the apex and of the crest using Computational Fluid Dynamics (CFD). For model validation, experimental studies reported in the literature were used. Tests were carried out with trapezoidal and circular apexes and four types of crest profiles: sharp-crest, half-round, quarter-round and Waterways Experiment Station (WES). The results revealed a determination coefficient of R² = 0.984 between experimental and simulated data with CFD, which provides statistical agreement. Simulations showed that circular-apex weirs are more efficient than those with trapezoidal apex, because they have a higher discharge coefficient (4.7% higher). Of the four types of crest profiles analyzed, the half-round and the WES crest profiles had similar discharge coefficients and were generally greater than those of the sharp-crest and the quarter-round (5.26% y 8.5% higher) profiles. Nevertheless, to facilitate a practical construction process, it is recommended to use a half-round profile. For hydraulic heads with H_T/P > 0.5 ratio, all profiles generated sub-atmospheric pressures on the side walls of the weir. However, when H_T/P ≈ 0.8 ratio the half-round crest generated a higher negative pressure (−1500 Pa), while the sharp-crest profile managed to increase the pressure by 76% (−350 Pa), but with a greater area of negative pressure. On the other hand, the WES profile reduced the negative-pressure area by 50%.     

Investigation of flow characteristics and energy dissipation over new shape of the trapezoidal labyrinth weirs

Labyrinth weirs are mainly used to increase the discharge capacity. The current study adds a new performance to labyrinth weirs as an energy dissipator. The labyrinth weirs' zigzag shape and flow behaviour could benefit energy dissipation. Therefore, the present study aims to investigate the hydraulic characteristics and energy dissipation of the compound labyrinth weir. Sixteen models were used for different sidewall angles (α°) of 6–35 and 90 (linear weir for comparison). The results demonstrated the highest values of the compound coefficient of discharge, C_dc, for a sidewall angle of 35°, and the lowest value of the compound coefficient of discharge for a sidewall angle of 6°. The C_dc increased initially at low H՛_t/P՛ values, and the C_dc showed a decreasing trend for higher values of H՛_t/P՛. For sidewall angles (α°) ranging from 6 to 35, the compound coefficient of discharge C_dc does not significantly change as it approaches a value of H՛_t/P՛ = 1.0. Furthermore, for the range of the relative critical head (y_c/P՛) between 0.07 and 0.95, the results showed that the compound labyrinth weirs could dissipate the energy of flow by 93%, 92%, 89%, 85%, 83%, 79%, and 75% for α° = 6, 8, 10, 12, 15, 20°, and 35, respectively. The amount of improvement in energy dissipation over a compound labyrinth weir was better than a linear weir by 17%, 15%, 14%, 12%, 11%, 10%, and 8% for α° = 6, 8, 10, 12, 15, 20, and 35, respectively. The residual energy (E₁/E_min) at the base of downstream compound labyrinth weirs was closer to the minimum potential amount of residual energy as y_c/P՛ increased. For a given value of y_c/P՛, the relative residual energy at the base of compound labyrinth weirs increased as the sidewall angle (α) increased. An empirical equation has been provided to predict the compound coefficient of discharge when relative energy dissipation data is available.     

CFD analysis of the performance of elbow-meter with high concentration coal ash slurries

Elbow meter is a simple flow measuring device and its characteristics for the flow of single-phase fluids are reasonably well understood and the functional dependence of elbow meter coefficient (C_k) on parameters like Reynolds Number, radius ratio, pipe roughness etc. Is well documented in literature. Elbow meters are also being used for solid liquid flow in many industries. The present study aims to establish the characteristics of an elbow meter for high concentration coal ash slurry pipelines using validated CFD. High concentration coal ash slurries are known to behave as homogeneous fluids exhibiting behavior as Bingham plastic fluids. The validated CFD methodology has been used to predict the values of C_k for the flow of Bingham plastic fluid and establish its dependence on radius ratio, Hedstrom Number and Bingham Reynolds Number. Further, for the flow of high concentration fly ash slurry flows, C_k for any given radius ratio is observed to be independent of Hedstrom Number (over the range investigated He ≤ 10⁵). Further, in fully turbulent flows, beyond a critical Reynolds number (Re_B ≥ 5.3 × 10³), C_k remains constant and is dependent only on the radius ratio.     

Pareto genetic design of group method of data handling type neural network for prediction discharge coefficient in rectangular side orifices

The powerful method of Group Method of Data Handling (GMDH) was used for estimating the discharge coefficient of a rectangular side orifice. First, the existing equations for calculating the discharge coefficient were studied making use of experimental results. On the first hand, the factors affecting the discharge coefficient were determined, then five models were constructed in order to analyze the sensitivity in achieving accuracy by using different parameters. The results, obtained using statistical indexes (MARE=0.021 and RMSE=0.017), showed that one model out of the five models, on estimation using the dimensionless parameters of the ratio of depth of flow in main channel to width of rectangular orifice (Y_m/L), Froude number (Fr), the ratio of sill height to width of rectangular orifice (W/L) and width of main channel to width of rectangular orifice (B/L), presented the best results.     

On the Determination of Friction Forces in Turbulent Lubrication

The mixing length theory, used previously for the determination of the velocity profiles and pressure distributions in turbulent films is now employed in order to determine the friction stresses T_o, T_h on the two lubricated surfaces and their dependence on the Reynolds number and on the pressure distribution. Thus, it results that the curves τ_o(B_xτ and –τ_h(B_x) are antisymmetric and that the derivatives τ_o/τB_x, τ_h/τB_x at B_x = 0 have constant values, independent of the Reynolds number. These results allow the determination of simple analytical formulas for the friction stresses τ_o.h as functions of the Reynolds number and of the parameter B_x, by using a linearization procedure, valid for small and moderate variations of the film thickness.

The obtained formulas are then used for the calculation of the friction forces and friction torques in journal bearings and slider bearings.     

Process compensation and printed circuit board manufacture

The analysis of the current method of transferring data between the designer and the manufacturer of printed circuit boards has suggested that the use of a manufacturing workstation in the manufacturing process can result in the production of higher quality circuit boards. In order to transmit the design between the workstation and the production database, a neutral format is suggested. The various production processes change the physical and electrical properties of the boards, use of the neutral format allows the manufacturer to take into account the idiosyncrasies of his production line and produce boards to a higher standard. By using a generic representation of the machine languages used to drive the tools (along with the neutral format), the manufacturer should be able to add new machines to the production line quickly and easily.Nomenclature Symbol Value Units Meaning - C F capacitance between two tracks - l m length of a track - h m height of a general track - H 2.7×10^–6 m height of a track. This is equal to the amount of copper plate on the board - t m distance between two tracks - dC F capacitance of a thin strip of the track - k None gradient of the line used as an approximation to the true shape of the track - t _o m distance between the two tracks at the base of the tracks after etching - dh m height of a thin strip of the copper track - R resistance of a track - m resistivity of the copper used to make the track - w m width of a track - w _b m width of a track at the base - w _t m width of a track at the top - ₀ 8.85×10^–12 F m^–1 permittivity of free space - _t 1.0005 None relative permittivity of air     

Numerical and experimental modelling of flow at Tyrolean weirs

In this study, a small-scaled Tyrolean weir model was constructed in the laboratory environment and a series of experiments were conducted on it, for two different rack inclinations (θ₁ = 18° and θ₂ = 25°) and three different bar spacings (e₁ = 3 mm, e₂ = 6 mm and e₃ = 10 mm) for a range of upstream flow discharges. The flow rates passing through the racks and going downstream over the racks were measured. Empirical equations for the discharge coefficient and water capture capacity of the Tyrolean weirs were determined by applying dimensional analysis to the parameters involved in the phenomenon. The related dimensionless parameters were presented with graphs and empirical equations for discharge coefficients were derived, coefficient of determination R² of equations for θ₁ = 18° and θ₂ = 25° are found 0.838 and 0.825 respectively. According to results obtained from experimental data, C_d increases as the Froude number ((F_r)_e) between bars increases and water capture capacity [(q_w)_i/(q_w)_T] of the racks decreases with increasing ((F_r)_e). Also, a numerical model of the Tyrolean weir was generated by using Flow-3D software and it was shown that the results of the numerical analysis were very consistent with the physical model results at large bar spacing such as e = 10 mm. As the bar spacing (e) reduces, the success of the numerical model giving consistent results with physical model is decreasing.     

Effect of carbide volume fraction on erosive wear behaviour of hardfacing cast irons

The present work reports the effect of carbide volume fraction on erosive wear behaviour of hardfacing cast irons. Five different grades of weld hardfacing cast irons were selected for the present investigation. The solid particle erosion experiments were carried out with blast furnace sinter, silica sand and alumina particles under mild (53–75 μm, 25 m s⁻¹), moderately severe (125–150 μm/100–150 μm, 50 m s⁻¹) and under severe erosion conditions (300–425 μm, 90 m s⁻¹) at impingement angles of 30 and 90°. The variation in erosion rate with carbide volume fraction was observed to be strong function of the erodent particle hardness, impingement angle and the impact velocity. Under mild erosion conditions, erosion rate decreased with increasing carbide volume fraction (CVF), whereas erosion rate increased with CVF under moderately severe erosion condition with alumina particles. With silica sand particles under moderately severe erosion conditions the beneficial effect of large volume fraction of carbides could only be observed at 30°, whereas at normal impact erosion rate increased with increasing CVF. The erosion rate showed power law relationship with ratio of hardness of erodent particle to that of the target material (H_e/H_t) and expressed as E=c(H_e/H_t)^p.With increasing severity of erosion conditions erosion rate showed stronger dependence on H_e/H_t as compared to those under mild and moderately severe erosion conditions. The mechanism of materials removal from the carbides involved Hertzian fracture with softer sinter particles, whereas harder alumina particles could plastically indent and cause gross fracture of the carbides.