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.     

Data-based estimation and simulation of compressible pulsating flow with reverse-flow through an orifice

Highly compressible pulsating flows are often encountered in devices where knowledge of the flow rate is required but elimination of pulsations is not an option. The current work is a continuation of a previous investigation that characterized the orifice discharge coefficient C_d as a function of dimensionless groups based on pulsation characteristics. The experimental apparatus has been rebuilt in the current work to mitigate temperature and vibration problems, allowing pressure and ΔP measurements to be made very close to the test section with 159-mm of nylon tubing. Data was acquired for 77 operating conditions spanning a range of pulsation frequencies, mass flow rates and system pressures. They confirm previously reported low C_d's in 0.20 range (calculated from time-averaged pressures) at some high-pressure low-flow operating conditions. Computational Fluid Dynamics (CFD) simulations of 12 of these data points suggest that the low C_d's result from reverse flow. Flow direction changed several times during each pulsation cycle closely tracking the orifice ΔP. A ‘core-and-sheath’ phenomena was observed for reverse-flow operating conditions: a positive core flow surrounded by a sheath of negative flow transitioned to a negative core and positive sheath several times during each pulsation cycle. The simulations also suggested that velocity profiles at the orifice stay stable and similar to steady-state profiles except for periods of rapid transitions. Based on these results a data-based quasi-steady method of estimating pulsating flow has been proposed. A pair of forward and reverse flow C_d's chosen by the data are used to predict instantaneous forward and reverse flows using the steady-state orifice discharge equation for compressible flow. The instantaneous values are then summed up over the pulsation cycle to estimate average mass flow rate. Average prediction errors were within 6%. A previously proposed method where regression was used to model C_d as a function of dimensionless groupings was shown to produce similar results. Both methods are designed to extract information from experimental data in order to overcome theoretical limitations and experimental error. The data is available upon request for further understanding of the flow physics.     

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.     

Discharge coefficient of pilot poppet valve at low Reynolds number

The discharge coefficient (C_q) is an important parameter that affects the flow capacity of hydraulic valve. Many researches of C_q focused on main stage poppet (half cone angle is 30°–45°), weather the results are suitable for pilot stage poppet (half cone angle is 10°–15°) is still uncertain. In this paper, the discharge coefficient of different pilot stage poppet valves are measured, and Fluid-Structure Interaction is used to analyze the influence of the orifice submerged jet on the discharge coefficient, visualization experiment is used to study the flow field at the tail of the valve port under different poppet structures. The results show that the stability of the flow field structure at the front of the valve port and the end of the valve port has an important influence on the discharge coefficient, and C_q of the pilot poppet valve still can be written as C_q = mRe^0.5 under the condition of low Reynolds number, however the proportional coefficient m been obviously smaller than poppet valve as main stage. In poppet valve with orifice, the m value of the C_q is between 0.04 and 0.05 of the flat-end poppet, and the variation range obviously smaller than ball-end poppet valve, the reason is that a stable annular vortex was formed at the flat-end poppet port front end, which made the pressure of the poppet surface insensitive to the flow change. While in poppet valve without orifice, the m value of the C_q is between 0.02 and 0.04 of the flat-end poppet, and the variation range obviously smaller than ball-end poppet valve, the reason is that the flow field presented various pattern at the ball-end poppet port back end, which drives the m value of the C_q under different working conditions fluctuate greatly.     

Experimental study of discharge coefficient for trapezoidal piano key weirs

Piano Key Weirs (PKW) have been invented in the last decade to increase discharge capacity of hydraulic structures. Despite extensive studies on this type of weir with a rectangular plan form (RPKW), there are only a few pieces of research addressing trapezoidal piano key weirs (TPKW). In this experimental study, geometrical parameters of TPKW models were varied under different flow conditions and effects on discharge coefficient (C_d) were investigated. The C_d values were found to be mostly influenced by L/W whereas W_i/W_o had the least effect. Results also showed that TPKW has higher discharge efficiency in comparison with RPKW. This was believed to be related to formation of an “interference wedge” over the TPKW. Finally, quantitative values for distinguishing three flow regimes (i.e. nappe, transition and submergence) as well as criteria for design of TPKW are proposed.     

Coordinating scheduling with batch deliveries in a two-machine flow shop

In the demanding world of supply chain management, traditional scheduling models which only address the optimization of production sequence at certain stage are often not globally optimized. Rather, the extension, including the distribution stage following the production, can bring a more holistic view to the decision makers. This research focuses mainly on a class of two-machine flow shop problem in which jobs need to be delivered to customers by vehicles after their production stages. Two performance measures—the sum of job completion times (∑C _j ) and the makespan (C _max)—are investigated separately. For the objective of ∑C _j , this study shows that it is strongly NP-hard whether the job sizes are assumed to be equal or not. On the other hand, with regard to the C _max objective, this paper concentrates only on the problem of different job sizes and provides a proof of its NP-hardness. A heuristic method that guarantees to contain a worst-case performance ratio of 2 is developed for the C _max problem.     

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%.     

Discharge coefficient in the combined weir-gate structure

The present study investigated the flow discharge coefficient (C_dt) in the combined rectangular broad crested weir-gate structure. To this end, the effect of the following dimensionless parameters on the C_dt were investigated: the width ratio of the central weir to the width of the total structure (B/B_o), the height ratio of the central weir to the height of the central weir floor (Z/P), the ratio of the gate width to the width of the total structure (b/B_o), the ratio of the gate opening height to the height of the central weir floor (d/P), and the ratio of the head on central weir to the total head behind the structure (h₁/H). The Flow-3D numerical model, artificial intelligence models such as linear multilayer perceptron (MLP), Canfis network (CNN), recurrent network (RNN), modular neural network (MNN), and regression equation, were used to estimate the C_dt. The results indicated that increasing d/P and b/B_o ratios led to a decline in this coefficient. In the case of h₁/H ≤ 0.4, an increase in B/B_o ratio resulted in decreasing the turbulence intensity and C_dt while the impact of enhancing the size of B/B_o was not significant if h₁/H > 0.4. Besides, increasing Z/P ratio caused an increase in resistance against the flow and thus a decline in C_dt. Further, the results of artificial intelligence models and regression equation demonstrated that the MNN model with an RMSE and R² of 0.03 and 0.97, respectively, could have an accurate estimate of the C_dt values.     

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.     

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.     

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.     

Effect of inner cone punch on metal flow in extrusion process

Using numerical simulation and experiment, the mechanical mechanisms of metal flow behavior were investigated in the extrusion process with inner cone punch. The characteristic variables, second invariant of the stress deviator J ₂ and the Lode’s coefficient μ were employed to partition the deformation region. It is shown that no metal flow interface occurred at the container bottom in the extrusion with inner cone punch and the dead zone disappeared completely. The strain types of the material in the plastic deformation area decreased from three types into a single type of tension and the homogeneity of metal deformation as well as metal flow was greatly improved. It was also indicated that inner cone punch was beneficial to the extrusion process and the promotion of product quality.     

A comparative study of flow rate characteristics of an averaging Pitot tube type flow meter according to H parameters based on two kinds of differential pressure measured at the flow meter with varying air temperature

A new averaging Pitot tube flow meter that has a shape similar to an Annubar® type flow meter was designed and its flow rate characteristic was evaluated. The air temperature supplied to the developed flow meter was maintained at a constant by controlling electric power supply to an electric heater during the calibration. Two kinds of differential pressure measured at the flow meter were used in calculating the H parameters, which represent characteristics of the developed flow meter. One H parameter (H_ΔP1) which was newly proposed in this research was calculated based on the difference between upstream pressure (stagnation pressure) at the flow meter and static pressure of the measured flow. The differential pressure is equivalent to the dynamic pressure of the flow. The other H parameter (H_ΔP2) which is used in a typical Annubar® type flow meter was calculated based on the difference between upstream and downstream pressure at the developed flow meters. Relationship curves between the two H parameters and the mass flow rate at the developed flow meter were obtained. The curves based on the H_ΔP2 parameter, which uses the difference between up and down stream pressure, show different gradients for varying the controlled air temperature. However, the other curve, based on the other H_ΔP1 parameter, which uses the dynamic pressure, can be represented by one linear curve even with varying air temperature.     

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%.     

Discharge equation for the gabion weir under through flow condition

A gabion weir is considered to be more environmentally friendly as compared to an impermeable weir, as its permeability allows substances and aquatic life to pass through it. Also, gabion weirs offer an alternative design with low afflux that could be adopted for flash flood mitigation. In the present study, a series of laboratory experiments were performed on flow through gabion weir of various sizes and for varying boulder sizes and discharges. Collected data were used to check the accuracy of the existing relationships between hydraulic gradient and flow velocity for highly porous material like gabion filled with boulders. It is found that Ergun's equation predicts the hydraulic gradient more accurately than the other available equation. Ergun's equation is extended to calculate the flow through the gabion weir. The derived discharge equation for flow through gabion weir was validated with the collected data. A qualitative performance of the present model indicates that it has the highest coefficient of correlation (R = 0.956) and the lowest MAPE (16.902), RMSE (0.002), AAD (15.52). It was found that the derived equation computes discharge within a maximum of ±10% error for almost all data sets, which can be considered satisfactory from practical consideration. Sensitivity analysis reveals that the discharge through the gabion weir is more sensitive to the boulders diameter and upstream depth as compared to the downstream depth of the gabion weir.     

Effects of flexible plate attached to the rear of the cylinder on flow structure

In this experimental study, the flow structure in the wake flow region was investigated with the Particle image velocimetry technique (PIV) by attaching elastic plates at different lengths behind the cylinder. The flow structure occurred at the wake flow region altered depending on the length of the flexible matter. In this experiment, the strips with the lengths of 75, 90, 120, 135 and 180 mm were used to control instabilities. Diameter of the cylinder (D) is 60 mm and the water height (h _w ) is 600 mm. Reynolds number was kept constant as 5000 based on cylinder diameter. The images were captured at mid-height of the cylinder (h _m ) which is 250 mm. As a result of experimental studies, attached flexible strip suppressed vortex shedding occurred in the behind of the cylinder and it is observed that effect of the length flexible of the strip is pretty much. Maximum level of flow characteristics such as Reynolds stress, fluctuation velocities and turbulent kinetic energy were decreased with flexible splitter plate and shifted through the downstream region.     

Estimating the uncertainty of discharge coefficient predicted for oblique side weir using Monte Carlo method

Side weir is a hydraulic structure, which is used in irrigation systems to divert some water from main to side channel. It is installed at the entrance of the side channel to control and measure passing water into the side channel. Many studies provided side weir water surface profile and coefficient of discharge to measure water discharge diverted into the side channel. These studies dealt with different side weir shapes (rectangular, trapezoidal, triangular and circular), which were installed perpendicular to the flow direction. Recently, some studies dealt with skew side weir, but these studies still need to more investigation. Here we report to investigate oblique side weir theoretically using statistical method to supported other studies in this case. Measurement uncertainty discharge coefficient C_d was obtained by two methods: analytical according to the ‘Guide to the expression of uncertainty in measurement’ and the Monte Carlo method. The results indicate that all experimental results are consistent with the analytical results. The relative expanded uncertainty of the discharge coefficient C_d does not exceed 2%.     

Coupled model of dual differential pressure (DDP) for two-phase flow measurement based on phase-isolation method

Phase-isolation is a novel ever-increasing multiphase separation technology, which can facilitate the multiphase fluid flowing concurrently with a substantially clear interface between two phases, and the phenomenon is promisingly employed for the separation and measurement of multiphase flows. Phase-isolation can be implemented by different kinds of lateral forces, of which the centrifugal force induced by the swirlers is the most convenient method. The radial pressure drop between pipe wall and pipe center, and the axial pressure drop along the pipe wall occurs at the downstream of the swirler. In the paper, the coupling model of dual differential pressure (DDP) including the radial-axial differential pressure and radial-radial differential pressure was built employing centrifugal phase-isolation for oil-water two-phase flow, and the theoretical measurement models were validated by our experimental data. At certain cross sections downstream of the swirler, the deviations between theoretical and experimental result of the volumetric oil fraction λ_o and mass flowrate Q_m were below ±7.16% and ±1.14% respectively when the radial-axial differential pressure was adopted, while the deviations between theoretical and experimental result of λ_o and Q_m were below ±6.91% and ±1.13% respectively using the radial-radial differential pressure. The acceptable deviation indicates that the DDP model can be the reference for the analysis and application of two-phase flow in the academic research and practical engineering.     

Characteristics of flow past a circular cylinder with a rectangular groove

In the present study, features of the flow past a circular cylinder with single longitudinal groove pattern placed on its surface were investigated. Six different rectangular groove sizes were tested for angular position of the groove from the forward stagnation point of the circular cylinder within 0°≤θ≤150°. The particle image velocimetry (PIV) technique were employed to measure flow field downstream of the cylinder immersed in a uniform flow field with the Reynolds number, Re=5000. Time-averaged flow data such as vorticity, 〈ω〉 streamline, 〈Ψ〉, streamwise, 〈u′u′〉 and transverse, 〈v′v′〉 Reynolds normal stresses, turbulent kinetic energy, TKE and RMS of streamwise, u_rms and transverse, v_rms velocity components were obtained from PIV data to demonstrate flow features. Moreover, frequency of Karman vortex shedding was explored using single point spectral analysis. It is concluded that presence of the groove on a cylinder surface significantly affects the near wake flow structure and turbulence statistics. Karman vortex shedding frequency, f_k strongly depends on the groove size. Moreover, the shear layer instability is induced on the grooved side with additional frequencies.     

Development of a new system for measuring the swirl ratio of an engine cylinder head under an unsteady flow condition

A new impulse-type swirl meter that measures the swirl ratio (R_s) and flow coefficient (C_fmean) during an intake air process for the intake port of an engine cylinder head under unsteady flow conditions was developed. The camshaft of the cylinder head was directly rotated by a step motor, allowing the valve lift to be adjusted automatically with the camshaft profile in the newly developed swirl measurement system. The measurements of the swirl ratio and flow coefficient were automated using a FPGA-DAQ board and a computer. The rotational speeds of the camshaft were held constant at steps of 90, 120, 150, 180 and 210 rpm during the measurement. As the camshaft rotation speed increased, the values of R_s tended to decrease while those of C_fmean tended to increase, implying that R_s and C_fmean depend on the engine speed. These results should be considered in the design of an intake port. With the newly developed swirl measurement system, it is possible to measure R_s and C_fmean repeatedly in a very short time. The repetitive measurement results of R_s and C_fmean were statistically processed. Through an uncertainty analysis, the values of the upper and lower bounds of R_s and C_fmean can be calculated for each camshaft rotation speed.