Discharge Coefficient Research Articles

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.

Experimental and numerical investigation of rectangular Labyrinth weirs in open channel

Labyrinth weirs are commonly used hydraulic structures to increase discharge efficiency in free-overflow discharges. These weirs provide higher discharge efficiency than conventional linear weirs at the same headwaters. This study investigated hydraulic performance of rectangular labyrinth weirs under different geometries and flow conditions experimentally and numerically. The numerical model was verified and validated using the grid convergence index method recommended in the literature and the experimental data. The numerical modelling results showed that the increase in performance of the labyrinth weir was caused by the distribution of lateral velocities in the inlet keys, while the nappe interference in the downstream keys was responsible for the decrease in performance at high headwater. Within the limitations of 1.5≤L/B≤2.33 and 0.1<Ho/P<0.61, a performance increase of 44% on average and a maximum of 67% for unit channel width was found for rectangular labyrinth weirs compared to linear weirs. For given limitations, two new empirical formulas with high correlation were derived to estimate the discharge coefficients of rectangular labyrinth weirs based on channel width (B) and weir crest length (L) for Ho/P>0.1 in which are widely used in practice. It is concluded that, when compared with some of the data in the literature, the empirical formulas give satisfactory results.

Numerical estimation of discharge coefficient for non-circular bottom intake racks

Current research presents a comprehensive numerical study on the performance of riverbed intake systems equipped with non-circular cross section racks. Three types of bottom racks, such as rhombus bars, rounded-edge rectangle bars, and circular bars, were numerically modeled using Flow3D software with different geometric and hydraulic parameter, all in super critical approaching flow in clear water condition. Subsequently, changes in diverted discharge ratio (DDR) of bottom racks and factors affecting its intensity and manner of changes, were studied using model results. The study reveals that the RNG k-ε turbulence model accurately represents the flow field around the bottom racks. The results indicated that the DDR changes are directly related to rack length changes but is inversely related to the rack slope and upstream flow discharge. Also, rhombus bars outperform circular and rounded bars, with 23.34% and 35.92% higher flow diversion, respectively, attributed to the formation of more negative pressures between bars. The main focus of the present study was on accurate and complete estimation of the diverted discharge coefficient (Cd) for racks with different bar shapes—especially non-circular bars using the results of the constructed numerical model. Proposed relations for the diverted discharge coefficient (DDC), especially for non-circular bars, were rigorously validated and showed high accuracy in predicting DDC under diverse hydraulic and geometric conditions.

Impacts of geometric configurations on performance of discharge coefficient and wall pressure of Venturi meter under high Reynolds number

The performance of discharge coefficient (Cd ) and wall pressure of Venturi meter under various convergent and divergent cone angles have been experimentally investigated. Several models of tubes have been examined, where the tubes have been manufactured with two convergent angles (20° and 40°) and three divergent angles (7°, 11° and 15°). A pipe system along with ten tapping points distributed along the Venturi meter wall has been utilised to measure the static pressure. The examinations have been done for wide ranges of Reynolds number (Re). Results of Cd have been compared with the empirical solutions and they show a good agreement between them with a relative difference less than 3.5%. As Re is increased until Re = 15000, the results of Cd is substantially increased. Results display that the convergent angle has a less impact on Cd and a major influence on pressure drop as compared to divergent angle. Divergent angle has an inversely impact on Cd . The best value of Cd has been obtained when using the tube that has a convergent angle of 7° and divergent angle of 20°. Present results clearly demonstrate the necessity of choosing the required geometric parameters accurately while designing Venturi meter to achieve the optimum performance

Water quality monitoring and modeling for an urban storm drainage channel in Thane, India.

The absence of a sewer system and inadequate wastewater treatment plants results in a discharge of untreated wastewater to the urban drainage channels and pollutes receiving waters. Field visits were carried out to observe water quality parameters such as dissolved oxygen (DO), biochemical oxygen demand (BOD), and chemical oxygen demand (COD) in an urban drainage system (Kolshet drain) in Thane City, Mumbai Metropolitan Region, India. Dye-tracing studies using rhodamine WT dye were used for computing the velocity, discharge, and dispersion coefficient of the drain. The data analysis shows that the BOD and COD values in the drain are higher than the permissible limits (30mg L-1 for BOD and 250mg L-1 for COD), which is not suitable for disposal to any receiving water body. Also, the DO was less than the permissible limit of a minimum of 3mg L-1 (for the survival of aquatic life). It is seen that the higher BOD load significantly reduced the DO throughout the drain. The Water Quality Analysis Simulation Program (WASP 8.32, 2019) developed by the US Environmental Protection Agency (USEPA) has been used for the simulation of the DO and BOD in the drainage channel. The model simulates an appropriate estimate of the expected variation of DO and BOD at points of interest. The modeling for the Kolshet drain is expected to enable better estimates of the wastewater parameters and the pollution transport in the drain for planning purposes.

Equations and methodologies of inlet drainage system discharge coefficients: A review

Abstract Accurate determination of grate inlet discharge coefficients is crucial in reducing modeling uncertainties and mitigating urban flooding hazards. This review critically examines the methods, equations, and recommendations for determining the weir/orifice discharge coefficients, based on the inlet parameters and flow conditions. Reviewing previous studies for inlets showed that the discharge coefficient of rectangular inlets under subcritical flow ranges from 0.53 to 0.6 for weirs and from 0.4 to 0.46 for orifices, while in grated circular inlets, it falls between 0.115 and 0.372 for weirs and between 0.349 and 2.038 for orifices. For circular non-grated inlets under subcritical flow, the weir and orifice coefficients are in the range of 0.493–0.587 and 0.159–0.174, respectively. However, the orifice discharge coefficients of grated and non-grated inlets with unknown Froude number range between 0.14–0.39 and 0.677–0.82, respectively. For supercritical flow, the weir and orifice discharge coefficients of grated and non-grated rectangular inlets are 0.03–0.47 and 1.67–2.68, respectively. Previous studies showed that it is recommended to correlate the discharge coefficients with the approaching flow and Froude number under subcritical and supercritical flows, respectively. Yet, additional studies are recommended for a better understanding of the limits and parameters governing the flow transitional stage between weir and orifice and between subcritical and supercritical conditions. Moreover, further research is required to determine the weir and orifice discharge coefficients of circular inlets under supercritical flow as well as the orifice discharge coefficient range of rectangular non-grated inlets under subcritical flow. Finally, it is recommended to increase the road surface roughness to reduce Froude number, and thereby, increase discharge coefficients of street inlets. The aim of this review is to help inlet designers and authorities promote sustainable cities with resilient urban drainage systems and reduce the environmental, economic, health, and social impacts of urban drainage failure.

Flow and spray characteristics of a gas–liquid pintle injector under backpressure environment

Both the flow and spray characteristics of a gas–liquid pintle injector element under the backpressure environment were investigated experimentally and numerically. The cold atomization tests were conducted with the backpressure range from 0.50 to 1.54 MPa. Both the interaction process between gas film and liquid jets and the detail distribution of the spray were obtained by the verified volume of fluid to discrete phase model. Results showed that there is a local high-pressure zone at the root of the liquid jets resulted by the collision of gas film and liquid jet. A semi-empirical model for predicting the discharge coefficient of the orifices is proposed considering the effect of local high-pressure zones based on the experiments. It was found that the discharge coefficient is mainly affected by the local momentum ratio (LMR) and ambient pressure. The discharge coefficient increases with the increase in LMR and ambient pressure. Before the primary breakup occurs, the liquid jets deform from rectangle jets to bow-shaped liquid films under the effect of the gas film. Then, both the gas and liquid mix in the range included by the gas passed by the windward surface and side of liquid jets. The droplet size is larger at the edges of the spray and the Sauter mean diameter (SMD) is beyond 100 μm. On the contrary, it is relatively small and uniform at the spray central, and the corresponding SMD is about 50 μm.

Submerged flow over various shapes of piano key weir

The weir, an essential element of dams utilized for floodwater management, plays a crucial role in human life. Over the years, nonlinear weirs have advanced into Piano Key Weirs (PKWs). These PKWs provide enhanced discharge efficiency, a reduced structural footprint, and heightened cost-effectiveness. PKWs possess a sophisticated structure defined by numerous geometric parameters. The impact of these parameters on the discharge capacity is of paramount significance. This study aims to experimentally investigate the hydraulic of submerged PKWs with different plan shapes, including triangular, trapezoidal, and rectangular, with apex width to cycle width ratio of (A/w) of 0, 0.25, and 0.5, and magnification ratio (B/w) of 1, 2, and 3, respectively. The results indicate that submergence depends on the shape and size of the PKW. Furthermore, the efficiency of the PKW increases as the ratio of approach flow head to weir height (Ho⁄P) decreases and B⁄w increases. The influence of the shape of the PKW on the performance of the weir is more pronounced at higher values of B/w. Additionally, the order of the highest discharge coefficient values follows a pattern from the trapezoidal to triangular and rectangular PKWs. Specifically, for B⁄w = 2, the trapezoidal PKW exhibits an approximate improvement of 6 and 15 % in the discharge efficiency compared to the triangular and rectangular PKWs, respectively. A new equation was developed to predict the discharge coefficient for different shapes of PKWs under various hydraulic conditions. Based on the experimental data, this study offers valuable insights into the hydraulic behavior and discharge coefficient of PKWs. This research significantly contributes to enhancing our understanding and optimizing the performance of submerged PKWs in water management systems.

Design of short Venturi flow meters for incompressible and isothermal flow applications

The Venturi flow meter offers a range of measurement options for liquids, gas, steam, and slurries in piped systems. The main criteria for assessing Venturi performance include permanent pressure loss, discharge coefficient, relative pressure loss coefficient, and measurement accuracy. However, the extended length of Venturis, relative to other flow rate measuring instruments, can present limitations in some applications. Furthermore, the manufacturing of shorter Venturis requires less material and energy. This study addresses the challenge by developing shorter Venturi meters that adhere to established performance standards. Previous studies show that cone angles, the ratio of throat diameter to inlet diameter (β-ratio), and the throat length impact the performance of a Venturi. The scope of this research considers single-phase, incompressible and isothermal flows. The investigation focuses on the effect of cone angles for flows with Reynolds numbers ranging from 5000 to 10,000,000. Two axisymmetric Venturis, with a β-ratio of 0.7, were designed and evaluated against an ISO-5167 classical Venturi with the same β-ratio. Despite the ISO-5167 Venturi outperforming the others across the key criteria, a Venturi designed with a 40-degree convergent cone angle and a 10-degree divergent cone angle was 24.9 % shorter than the classical design and demonstrated similar performance to the ISO-5167 Venturi across Reynolds numbers from 100,000 to 10,000,000.

Comment on “The hydraulic investigation of harmonic plan weirs” by A. Yıldız, A. İhsan Marti, M. Göğüş

In this paper, the stage-discharge equation of a harmonic plane weir is deduced applying both the classical approach of the discharge coefficient Cd and the Π- Theorem of dimensional analysis and the self-similarity theory. At first, using the laboratory measurements carried out by Yildiz et al. (2024), a new relationship for estimating Cd is proposed. This new empirical expression of the discharge coefficient (Eq. 15) allows for improving the performance of the stage-discharge equation (Eq. 13), which is characterized by errors in the discharge estimate E varying from – 7.7 to 7.7% and a mean square error MSE of 0.214. Then, applying the dimensional analysis, a new stage-discharge relationship was deduced and calibrated using the same dataset. This theoretical equation is characterized by errors E ranging from – 7.1 to 7.4 %, and a MSE of 0.193. In conclusion, the stage-discharge relationship deduced by dimensional analysis is characterized by the best performances in the discharge estimate and has also the advantage of working without the need of estimating the discharge coefficient.

Performance evaluation of film holes used for cooling the optical window of a sensor probe

In this paper, three types of film holes (namely cylindrical hole, round-to-slot hole, slot hole) are applied to provide cooling protection for a sensor probe’s optical window while considering the structural size limitations. The film cooling performance, discharge coefficients and pressure drop of three types of film holes are discussed and compared in terms of both the blowing ratios and the outlet heights of the film holes through numerical simulation. The results demonstrate that, compared to the cylindrical holes, the round-to-slot holes and slot holes exhibit significantly improved film coverage performance. Among these, the RTSH-0.6 hole exhibits the best comprehensive performance, the film cooling effectiveness of the RTSH-0.6 hole is higher than 0.99 under all three blowing ratios with the lowest pressure drop ratio less than 0.5.

Discussion of “A Reformed Empirical Equation for the Discharge Coefficient of Free-Flowing Type-A Piano Key Weirs”

Discussion of “A Reformed Empirical Equation for the Discharge Coefficient of Free-Flowing Type-A Piano Key Weirs”

CFD-EDEM simulations of droplets in an airless rotary spray coating process

Numerical simulations of airless rotary spray coating process are presented using CFD-EDEM with JKR contact model. The JKR model parameters are suggested according to the virtual test of accumulation angles in the funnel device. The reasonable droplet-wall surface energy is recommended from a relation of accumulation angles. The gas turbulence model is evaluated based on the comparisons of velocities and droplet number fractions using RNG k-ε, realizable k-ε and transition SST models. The simulated film thicknesses agree with measurements in literature. The correlation of exit droplet velocity of sprayer holes is proposed with a discharge coefficient of 2.27. The velocities and film thickness are predicted with changing rotation speeds. The normal force is an order of magnitude larger than the tangential force of droplet-wall collisions, and the ratio of the normal to tangential energy losses of droplet-wall collisions varies from 2.0 to 5.0 in airless rotary spray coating processes.

Discharge coefficient of vertical sluice gates with broad crested weir under free-submerged orifice flows using best subset regression.

Accurate calculation of flow discharge for sluice gates is essential in irrigation, water supply, and structure safety. The measurement of discharge with the requirement of distinguishing flow regimes is not conducive to application. In this study, a novel approach that considers both free and submerged flow was proposed. The energy-momentum method was employed to derive the coefficient of discharge. Subsequently, the discharge coefficient was determined through the experiment which was performed on the physical model of a vertical sluice gate with a broad-crested weir. Feature engineering, incorporating dimensional analysis, feature construction, and correlation-based selection were performed. The best subset regression method was employed to develop regression equations of the discharge coefficient with the generated features. The derived formula was applied to compute the discharge coefficient in the vertical sluice gate and determine the flow discharge. The accuracy of adopted method was assessed by comparing it with recent studies on submerged flow, and the results demonstrate that the developed approach achieves a high level of accuracy in calculating flow discharge. The coefficient of determination for the calculated flow rate is 0.993, and the root mean square percentage error is 5.04%.

Discharge performance of a submerged seawater intake in unsteady flows: Combination of physical models and decision tree algorithms

Developing impressive and cost-effective desalination technologies is crucial for addressing the increasing global demand for freshwater. In this regard, along with the process type and technology of desalination, the system's efficiency relies on the availability of a sufficient, constant, uniform, and high-quality discharge flow from the seawater intake structure. This investigation concerns the discharge flow performance of velocity caps, which serve as submerged seawater intake structures, in unsteady flows using physical models and decision tree algorithms. The observations indicate that the square caps are more prone to instability compared to the circular caps when exposed to waves. Additionally, circular caps can increase efficiency by about 12 % compared to square caps. Therefore, the circular velocity cap is more optimal than the square one. Results show that increasing wave height and period decreases the discharge through the intake due to increased interaction between wave and intake structure. Also, wave steepness leaves a significant reverse effect on seawater intake of about 40 %. The study also found that the optimal relative bottom height (w/h) is 1 for high flow depths and 0.5 for low flow depths, respectively. Finally, practical equations of discharge coefficients have been proposed based on decision tree algorithms with high accuracy. These high-accuracy equations show great potential for designing new desalination systems and optimizing existing ones.

Effect of Strip-Fin Height on Jet Impingement Heat Transfer in a Rectangular Channel at Two Jet-to-Target Surface Spacings

Abstract An experimental investigation of heat transfer performance in a rectangular impingement channel featuring staggered strip-fins was completed. Four configurations were considered to study the effects of varying the strip-fin height (H/d = 1.5 and 2.75) at two jet-to-target surface spacings (z/d = 3 and 6) on the heat transfer, pressure loss, and crossflow magnitude for a long impingement channel with in-line, 4 × 12 impinging jets. Also, the effect of the reference temperature choice, either jet inlet temperature or local bulk temperature, for calculating the local heat transfer coefficients was considered. The regionally averaged heat transfer coefficients were measured at seven Reynolds numbers, based on the jet diameter (10k–70k) utilizing the copper plate experimental method. The empirical correlations were expressed for the area averaged Nusselt number estimation of impingement channels with strip-fin or pin-fin roughness elements. The results showed that the long strip-fin channel with z/d = 3 provided the best thermal performance. The discharge coefficients are similar for all configurations between Rejet = 10k and 50k. The results are compared with the impingement channels with conventional pin-fins. They show that strip-fin channels provide lower pressure drop with marginally better heat transfer coefficients compared to the conventional pin-fin channels. However, when the channel weight is considered, strip-fins would increase the roughness material volume more than the conventional pin-fins.

Study on the impact of different hole shapes on liquefied gas leakage behavior

Accidental leakage of liquefied gas is a common occurrence during its storage, transportation, and usage. The shape of the leakage holes varies due to different causative factors. In this paper, we have established an experimental setup using R134a as the medium to simulate liquefied gas leakage. Different nozzle shapes are used to simulate the effect of various leakage hole shapes on the release process. The results indicate that, when the hole area (A) is constant, the discharge coefficient (Cd(exp)) decreases in the order of circular, square, and triangular holes. Simultaneously, based on dimensional analysis, we propose an empirical formula to predict the Cd(pre) for both circular and non-circular hole leakage. Notably, non-circular holes exhibit an axis-switching phenomenon during flash vaporization spray, leading to an asymmetric structure in the spray cone angle (θ) of triangular holes. The spray area of circular holes displays significantly larger lowest temperature and low-temperature regions compared to non-circular holes.

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.

Research on the Development of a Dispatching Scheme for Maneuvering the Filling and Drawdown Water Intake Gates of the Kaparas Reservoir

Purpose: The research aims to explore the laboratory hydraulic characteristics of the "Kapa-ras" water intake facility, specifically focusing on devising a control strategy for maneuvering gates amidst fluctuating flow rates and water levels in both the upstream and downstream ar-eas.
  
 Methods: Laboratory experiments were conducted to assess the performance of the water in-take facility under different gate opening schemes. These experiments included determining the capacity of the "Kaparas" reservoir intake for various gate configurations and establishing the discharge coefficient dependencies on the relative gate openings. Additionally, a series of experiments were conducted to ascertain the maximum allowable downstream depth without causing erosion to the attachment bottom, considering all potential gate opening scenarios.
  
 Results and conclusion: The main results yielded insights into the hydraulic behavior of the "Kaparas" water intake facility, enabling the determination of optimal gate control strategies for maintaining efficient water intake operations. Results indicated varying capacities for the reservoir intake under different gate configurations, and the dependence of discharge coeffi-cient on gate opening relative to the flow rates. Moreover, permissible downstream depths were identified to prevent erosion, ensuring the structural integrity of the attachment bottom. Consequently, these findings contribute to the effective management of water resources at the "Kaparas" facility.
  
 Research implications: The research outcomes provide valuable insights for enhancing the operational efficiency and sustainability of water intake facilities similar to "Kaparas." The findings can inform decision-making processes regarding gate control strategies and down-stream depth management, ultimately optimizing water resource utilization and mitigating po-tential environmental risks.
  
 Originality/value: This study contributes novel empirical data and analytical insights into the hydraulic behavior of water intake facilities, particularly in the context of gate maneuvering and downstream depth management. The research fills a gap in understanding the operational dynamics of such facilities and offers practical implications for hydroelectric complex man-agement, facilitating informed decision-making and resource optimization.

Influence of Inlet and Outlet Area Ratio on Intake Port Flow Capacity

The flow capacity of the intake port has a great influence on the charging efficiency of the internal combustion engine, affecting the engine’s performance, so it is critical to improve the intake port flow capacity. In this paper, the intake port numerical model was established, and the influence of the inlet and outlet area ratio on intake port flow capacity was studied. The results show that, under the same condition of relative pressure difference, the intake port discharge coefficient increases sharply and then slowly with an increase in area ratio. Under the same condition of area ratio, the discharge coefficient is only determined by relative pressure difference and decreases with an increase of relative pressure difference when the inlet and outlet area ratio>1. The optimal area ratio decreases and then converges with an increase in relative pressure difference. When the intake port is designed, the optimal area ratio under the working condition of a smaller relative pressure difference should be applied in order to ensure the discharge coefficient is optimal under all working conditions.