Increase In Discharge Coefficient Research Articles

Hydraulic performance analysis of piano key weirs with curvilinear keys: a numerical and experimental study

ABSTRACT A significant number of dams worldwide are very old and thus require a reassessment of maximum flood discharges due to siltation and climate change effects. The Piano Key Weir (PKW) is a relatively new labyrinth-type weir that has emerged as a viable solution for dam rehabilitation and new projects with space constraints. While various studies have been conducted in the past to investigate the influence of geometrical parameters of PKW, there is a lack of information regarding the effect of non-linear slope profile of keys on the discharge efficiency. In this paper, ogee profiles have been introduced in the outlet keys to study their influence on the discharge coefficient. The experiments were performed at the Hydraulics Laboratory, IIT Roorkee, India, using a flume 15 m long, 0.39 m wide and 0.52 m deep. These experiments involved four PKW models with different slope profiles in the outlet key. The results of the laboratory studies and RANS model simulations indicate that the PKW models with ogee shaped outlet keys are more efficient than the linear shaped counterpart for heads higher than their design head. The maximum increase in discharge coefficient for the PKW models with curvilinear outlet keys was 9%.

The discharge coefficient of sharp triangular weir pierced by orifices

Although triangular sharp-crested weirs have less discharge-passing ability compared to rectangular weirs, they have greater accuracy and sensitivity for measuring discharge. In order to enhance the passing-discharge and the discharge coefficient from a sharp-crested-triangular weir, an orifice was created in the weir. In this research, for the first time, several square orifices were created in the weir of the sharp crested triangular weir with different numbers and dimensions. The results of the discharge-passage investigation revealed that by creating one orifice, the discharge passage rose by 41.3%; with the increase of each orifice, the discharge passage increases by 37.2 % on average. It was also observed that upon increasing the relative dimensions (the ratio of the side-square-orifice length to the flume width) by 0.033, the discharge passage grew by 36% in average. Also, the results of discharge-coefficient investigations-showed that with creation of one orifice, it increased by 5.1% in average. But based on the novelty of this research, by increasing one orifice from 2 to 4, the discharge coefficient increases by 1.92 percentage. By upstream velocity measurement in control weir (weir without orifice) and combined weirs (weirs with orifices), a noticeable change in the lateral and depth velocity-profiles was observed, and these changes led to increase in the passing-discharge and also an increase in the discharge coefficient. Finally, an equation was presented to determine the discharge coefficient with high accuracy.

On the effect of flow regime and slope of the channel bed on the hydraulic performance of the sharp-crested rectangular side weir: a numerical simulation

The aim of this study is to numerically investigate the effect of bed slope on the hydraulic performance of side weirs in supercritical and subcritical flow regimes. Increasing the bed slope decreases the weir efficiency and discharge coefficient in the subcritical flow regime up to 14.54% and in the supercritical flow regime up to 9.26%. By examining the longitudinal velocity distribution, it was observed that in the subcritical flow regime, the maximum longitudinal velocity occurs at the beginning of the upstream of the side weir, and by moving towards the downstream of the weir, the flow velocity decreases and increases again after leaving the length of the weir. In the supercritical flow regime, it has an increasing trend when the flow enters from the upstream of the side weir. The increase in discharge coefficient with the increase of the weir height varied between 4.6% and 7.8%. With increase of the slope of the channel bed, the velocity along the length of the weir increases by 10.88% and 6.17%, respectively, in the subcritical and supercritical regimes, and the transverse velocity along the transverse direction for the subcritical and supercritical flow regimes decreased by 22.23% and 4.80%, respectively.

Effects of in-nozzle liquid fuel vortex cavitation on characteristics of flow and spray: Numerical research

The current work studies the dynamics of vortex cavitation under various conditions, including the pressure and orifice number, and their effects on the nozzle flow and spray characteristics using a modified cavitation model considering the swirling flow. Its validation against experimental data has demonstrated a high precision of the code in terms of vortex cavitation inside the nozzles. The higher the inlet pressure, the higher the mass flow rate and discharge coefficient, but the weaker the vortex cavitation; while the vortex cavitation intensity decreases, the discharge coefficient increases and the mass flow rate is almost constant with increasing back pressure. Moreover, under the influence of vortex cavitation, the primary jet liquid spreading angle, spray penetration, and spray volume coefficient increase first and then decrease with increasing inlet pressure; with an increase of back pressure, however, the primary jet liquid spreading angle increases, the spray penetration vice versa. Additionally, once the inner well-organized large-scale longitudinal vortices are destroyed, the vortex cavitation will not incept, which induces a larger discharge coefficient and spray penetration, but a smaller primary jet liquid spreading angle as a result. The swirling flow in the multi-hole nozzle is inhibited; hence, vortex cavitation is difficult.

Discharge coefficients formulae of grate inlets of complicated conditions for urban floods simulation and urban drainage systems design

With the acceleration of climate change and urbanization, all over the world is widely facing serious urban flooding problems. Grate inlets are key elements for the discharge exchange of surface flows and underground sewer flows in urban floods, so the accurate calculation of the overflow discharges of the grate inlets is related to the accurate simulation of the urban flood evolution process, which also plays an important role in the design of sustainable urban drainage systems. This study investigated the discharge coefficients of six types of grate inlets under different approaching discharges, transverse and longitudinal road slopes through 285 indoor 1:1 tests, mainly focusing on the supercritical flow conditions with less attention before. The experimental results show that: (1) With all other parameters being equal, as the interception discharge Q increases, the discharge coefficient increases. When the approaching Froude number increases, the discharge coefficient also decreases. The performance of parallel grate inlets in terms of discharge coefficients is not significantly different from that of vertical grate inlets. (2) Using Buckingham’s theorem of dimensional analysis, 12 groups of accurate grate inlets discharge coefficient calculation formulae were creatively proposed. The average relative errors of the 12 groups of formulae are 0.37% ∼ 5.41%, indicating that the calculated values of the formulae and the measured values are in good agreement. (3) The discharge coefficients of grate inlets were found to show a strong dependence on the Froude number of the approaching discharge, being in agreement with previous study result. But the relative error of individual data in this method is large, so the use of equations with more influencing parameters is recommended. A novel and effective method was also proposed to calculate the interception discharge of the grate inlets by iteration. This study can provide important references for the design and selection of grate inlets for urban drainage systems and also provide support for accurate simulation of urban floods.

Study on Film Cooling Performance of Round Hole Embedded in Different Shaped Craters and Trenches

Film cooling effectiveness can be improved significantly by embedding a round hole in trenches or craters. In this study, film cooling performances of a transverse trench, W-shaped trench and elliptic trench were compared and analyzed in detail. The CFD models for trench film cooling were established and validated via the experimental results. Inside the transverse trench, a pair of recirculating vortices is formed, which promotes the coolant spreading in a lateral direction. The decrease of trench width and increase of trench depth both improve the film cooling effectiveness of the transverse trench. For the W-shaped trench, the guide effect of the corner angle further improves the lateral spreading capability of coolant and generates higher cooling effectiveness than a transverse trench with the same depth and width. The flow characteristics of the elliptic trench are similar to that of the round hole, and the kidney vortex pair takes a dominant role in the flow fields downstream of the coolant exit. Accordingly, the elliptic trench generates the worst cooling performance in these shaped trenches. The increase of trench depth and decrease of trench width both result in an increase of the discharge coefficient for trench film cooling. For the W-shaped trench, the increase of the corner angle causes a decrease of the discharge coefficient. For the elliptic trench, the discharge coefficient increases with the decrease of the elliptic aspect ratio (major axis/minor axis).

Comprehensive optimization design of aerodynamic and electromagnetic scattering characteristics of serpentine nozzle

Comprehensive optimization design of serpentine nozzle with trapezoidal outlet was studied to improve its aerodynamic and electromagnetic scattering performance. Serpentine nozzles with different center offsets and different ratios of the bases of the trapezoidal outlet were generated based on curvature control regulation. Computational Fluid Dynamics (CFD) simulations have been conducted to obtain the flow field in the nozzle, and Forward-Backward Iterative Physical Optics (FBIPO) method was applied to study the electromagnetic scattering characteristics of the nozzle. Guarantee Convergence Particle Swarm Optimization (GCPSO) algorithm based on Radial Basis Function (RBF) neural network was used to optimize the geometry of the nozzle in consideration of its aerodynamic and electromagnetic scattering characteristics. The results show that the GCPSO method based on RBF can be used to optimize the aerodynamic characteristics of the internal flow and the scattering characteristics of the cavity of the serpentine nozzle with irregular outlet. The optimized model has a higher center offset and a lower ratio of the bases of the trapezoidal outlet after optimization compared to the original model. The optimized model leads to a slight change in aerodynamic performance, with a total pressure recovery coefficient increase of 0.31% and a discharge coefficient increase of 0.41%. In addition, the Radar Cross Section (RCS) decreases also by around 83.33% and the overall performance is significantly improved, with a decrease of the optimized objective function by around 38.74%.

Experimental Study of Composite Inclined Weir – Gate Hydraulic Structure

Composite hydraulic structure is widely used in irrigation system which consists of two parts. The first part is responsible for overflow regime and is represented by a weir, whereas the second part is responsible for underflow regime and is represented by a gate. Both elements play significant role to control, measured, and divert the flow. So it dominates the hydraulic regimes of open channel or river with high responsibility and accuracy. The target of this study is to investigate the effect of the composite hydraulic structure installation at various inclination angles (from 45-135 degree) with the flume bed, which is horizontal, and adopt the normal position of composite device ( angle equal to 90 degree) as guide in discussion with various angles. Several experimental works were carried out in hydraulic laboratory flume at the Basrah Engineering Technical College under free flow condition with various geometrical dimensions of combined rectangular weir and rectangular gate in order to investigate the effect of inclination angle on major flow factors such as actual discharge, discharge coefficient, depth of water in downstream zone of flume, cross sectional area of flow that cross or pass the weir and gate respectively. Also, this study mentions the percentage of increase in discharge coefficient and variation in actual discharge, discharge coefficient and Reynolds Number with cross sectional area of flow that cross the gate.

Discharge coefficient for rectangular notch using a dimensional analysis technique

The rectangular weir (notch) is a common device used to regulate and measure discharge in irrigation projects. The current research was based mainly on laboratory experiments studying the hydraulic characteristics of rectangular notches. Four rectangular notches were used in this research in different models. Notches for all models were designed with the same shape, arrangement, and width (4 cm), but differed in height, with examples at 6, 8, 10, and 12 cm. The main objective of this research was to study the influence of rectangular notch dimensions and upstream water depth on discharge coefficients.The results obtained from this research indicate that the relationship between the discharge coefficient and the upstream water depth is a power function. The values of the discharge coefficient increase with increases in the values of the upstream water depth. The relationship between the discharge coefficient and the Reynolds number is also a power function, and an increase in the Reynolds number leads to a decreased discharge coefficient. In addition, when the value of the Reynolds number is high (turbulent flow), the values of the discharge coefficient converge to an approximately constant value. The flow in all runs was subcritical and the relationship between discharge coefficient and Froude number was also found to be a power function. An increase in Froude number thus leads to a decrease in discharge coefficient. The slope of the discharge coefficient-Froude number curve values gradually decreases until the value the discharge coefficient reaches an approximately constant value. A dimensional analysis technique was used to estimate the values of the discharge coefficient for various rectangular notch dimensions, and an empirical equation for discharge coefficient estimating was derived using regression procedure. This equation has a coefficient of determination R2 of 0.955.

Flow characteristics of a pintle injector element

The flow characteristics of a pintle injector element were studied by theory and experiments. A spray angle model was firstly proposed based on our previous work, and then a model on the discharge coefficient of the orifice was also derived. Then, experiments were conducted by a pintle injector element which was simplified from pintle injectors with discrete radial orifices. Snapshots of the sprays were captured by using backlit photography technique. Results show that the pintle injector forms an arched cloak-like spray. The spray pattern and breakup are heavily related to the local momentum ratio and Reynolds numbers of jet and film. The spray angles obtained from the snapshots coincide with theory well. Meanwhile, a semi-empirical model of discharge coefficient of the orifice was proposed based on the experiments. It is found that the spray angle and discharge coefficient are dominated by the local momentum ratio. The spray angle and discharge coefficient increase along with local momentum ratio and tend to be stable for large local momentum ratios. Besides, discharge coefficient of the orifice is also found to be slightly affected by the ratio of jet diameter to film thickness.

Spray characteristics of aluminized-gel fuels sprayed using pressure-swirl atomizer

A slurry fuel is a non-Newtonian shear-thinning fluid with high viscosity. The fuel has a high energy density and has advantages in feed control. When the slurry fuel is injected using a swirl atomizer, the spray characteristics change because the rheological characteristics are different from those of the conventional liquid fuel. In particular, the metallic fuel contained in the slurry is an important parameter that dominates the rheological properties, breakup mechanism, and performance of the slurry swirl spray. In this study, an experimental analysis was performed to investigate the effect of aluminum particles on the spray characteristics of the slurry fuel. The rheological properties (shear-viscosity traces), mass flow rate, and discharge coefficient of the slurry composition were measured, and the influences of the particle content and mean diameter on the spray characteristics of the slurry fuel were explained. The content and mean diameter of the particles were found to be proportional to the viscosity of the slurry, and the flow behavior changes with respect to the particles. As the viscosity increases because of the particles, the mass flow rate and discharge coefficient increase because of the increase in the liquid-film thickness. The kerosene gel and slurry swirl spray undergo a breakup process via an aerodynamic mechanism, forming web-like ligaments, which do not appear in the kerosene because of increase in viscosity. As the injection pressure is increased, the frequency of the pulsation generated in the liquid film increases, and the web-like ligaments tend to be dense. When the particle content decreases, the same phenomenon occurs. As the particle content increases, the breakup length tends to increase with the increase in the thickness of the liquid film. However, the breakup mechanism changes depending on the thickness of the liquid film when the mean diameter of the particles changes. The spray angle is inversely related to the viscosity change due to the particles.

Study of the hydraulic properties of the cylindrical crested weirs

Since the cylindrical and circular crested weirs are economical and easily made compared to some other weirs, they can be used to measure the flow velocity, the water discharge and flow surface control structures in the canals and reservoirs. In this paper, the hydraulic properties of the cylindrical and circular crested weirs, such as the discharge coefficient, the depth on the crest of the weir and the energy loss in 18 laboratory models categorized in 5 categories have been investigated. The results of the experiments indicated that in both the cylindrical and circular crested weirs by increasing the total partial head, the discharge coefficient increases and any changes in the upstream wall slope has no effect on the discharge coefficient. Also, the partial energy loss more occurs in the cylindrical weirs than the half shaped cylindrical weirs and by increasing the downstream inclination angle, the partial energy loss increases subsequently. The partial flow depth on the crest of both the cylindrical and half shaped cylindrical weirs is equal to 0.7 and by increasing of the upstream inclination angle, the partial flow depth on the crest in the values greater than 0.6, increases slightly and the downstream inclination angle changes of the partial flow depth has no effect on the crest.

Overflow Characteristic of Cylindrical Shape Crest Weirs over Horizontal Bed

The most common types of weirs are the broad-crested weir, the sharp-crested weir, the circular crested weir and the ogee crested weir. Advantages of the cylindrical weir shape include the stable overflow pattern, the ease to pass floating debris, the simplicity of design compared to ogee crest design and the associated lower costs. In present study, it was investigated the overflow characteristics of circular weirs in laboratory for various cylinder radii of three sizes (11.4, 9.0, 6.3 cm), and the models fixed on the channel bed vertically to the direction of flow. The result shows that the increase in the ratio of head to weir radius ratio (Hw/R) value causes an increase in discharge coefficient (Cd) value for the same height of weir. It was observed that the cylinder size (i.e. radius of cylindrical weir (R)) has an effect on the (Cd). The flow magnification factor (qw/qs) increases with an increase in (Hw/R) value and values of (qw/qs) were always higher than one for all values of (Hw/R), this means that weirs of cylindrical shape performed better than those of sharp crest for any value of weir radius tested in this study

Flow of power-law fluids in simplex atomizers

This paper presents a computational analysis of flow of time-independent, purely-viscous, power-law fluids in simplex atomizers using the volume-of-fluid (VOF) method. Flow of shear-thinning (0.4 < n < 1), Newtonian ( n = 1) and shear thickening fluids (1 < n < 1.2) has been considered. The effect of power-law index and atomizer geometry on the flow and atomizer performance has been investigated. Three geometry parameters have been considered, viz., the atomizer constant which is the ratio of inlet area to the product of swirl chamber diameter and the exit diameter, the ratio of swirl chamber diameter to exit orifice diameter, and the length-to-diameter ratio of the exit orifice. The dimensionless film thickness at exit, spray cone angle, and the discharge coefficient for different values power-law index as well as those with varying atomizer geometry are reported. The pressure drop across the atomizer has been kept constant in all simulations. A change in the power-law index significantly alters the flow field in the in the swirl chamber of the atomizer. The velocity magnitudes and liquid film thickness at the orifice exit change with the power-law index. With fixed atomizer geometry, the pseudoplastic fluids tend to produce thinner liquid sheet, larger spray cone angle, and have lower discharge coefficient compared to dilatant fluids. Changes in the atomizer geometry have a significant impact on the flow for all values of power-law index. The spray cone angle decreases and the discharge coefficient and the film thickness increase with increasing atomizer constant. With increasing D s/ d o, the dimensionless film thickness at exit increases whereas the dimensional film thickness decreases monotonically. The discharge coefficient increases and the spray cone angle decreases with increasing D s/ d o. The discharge coefficient, the spray cone angle, and the film thickness decrease with increasing l o/ d o. A significant finding is that the variations of film thickness, spray cone angle, and discharge coefficient with a change in atomizer geometry are similar for different values of fluid power-law index, although the numerical values depend on the power-law index. This has important implications for atomizer design and industrial applications as most atomizers are designed for, and characterized with, Newtonian fluids.

A study of the critical nozzle for flow rate measurement of high-pressure hydrogen gas

The mass flow rate measurement using a critical nozzle shows the validity of the inviscid theory, indicating that the discharge coefficient increases and approaches unity as the Reynolds number increases under the ideal gas law. However, when the critical nozzle measures the mass flow rate of a real gas such as hydrogen at a pressure of hundreds bar, the discharge coefficient exceeds unity, and the real gas effects should be taken into account. The present study aims at investigating the flow features of the critical nozzle using high-pressured hydrogen gas. The axisymmetric, compressible Navier-Stokes computation is employed to simulate the critical nozzle flow, and a fully implicit finite volume method is used to discretize the governing equation system. The real gas effects are simulated to consider the intermolecular forces, which account for the possibility of liquefying hydrogen gas. The computational results are compared with past experimental data. It has been found that the coefficient of discharge for real gas can be corrected properly below unity adopting the real gas assumption.

A Study on the Effects of Porosity on Discharge Coefficient in Cross-Ventilated Buildings Based on Wind Tunnel Experiments

A study was performed on the effects of porosity on discharge coefficient and airflow characteristics under the condition where uniform approaching flow directly faces to and enters the opening by using wind tunnel experiment and CFD analysis. The evaluation was performed on porosities in the range 0.4% - 64%. The results of wind tunnel experiments suggest that the discharge coefficient increases when the porosity is higher. The results of CFD analysis reveal that the contraction of airflow when it passes through the opening is correlated with discharge coefficient, and that the discharge coefficient increases when flow contraction does not occur. When porosity increases, the retardment of the streamtube ceases to occur in the region upstream of the opening, and this leads to the elimination of flow contraction, hence the increase of discharge coefficient. When we evaluated the limitation of application of the local dynamic similarity model on porosity, the effectiveness of the model was confirmed well when the porosity was 16% or lower regardless of wind direction. The validity of the model was also confirmed under the condition where airflow goes along the wall surface before reaching the opening even when the porosity was 36% or more.

Experimental study of endwall and tip clearance flows in a two - dimensional turbine rotor blade cascade - effect of incidence angle

Experimental investigations were carried out on a two-dimensional cascade fitted with a 120° deflection rotor blades to study the effect of incidence angle on the endwall flow in the presence of tip clearance. A total of five incidence angles, namely: -10°, -5°, 0°, 5°, 10° were chosen and for each incidence angle, the experiments were conducted for five tip clearance values at a constant space -chord ratio of 0.79. The results are presented in the form of contours of static pressure coefficient on the endwall and the blade tip surface. In addition, the variation of static pressure coefficient ahead of the blade leading edge and from the pressure surface to the suction surface at various axial stations, and discharge coefficient at different axial stations are presented. The results indicate that the adverse pressure gradient upstream of the leading edge is reduced as tip clearance is increased. The contours of static pressure coefficient on the endwall indicate a deep low-pressure trough near the suction surface in comparison to the normal trough for zero clearance. Loading also increases as incidence changes from the negative to positive values. Due to area contraction caused by the tip separation vortex, the fluid moving towards the tip gap from the pressure side is accelerated. Downstream of the tip separation vortex, the endwall pressure increases due to flow mixing. The maximum value of discharge coefficient increases and the point at which maximum value occurs shifts towards leading edge when incidence is changed from -10° to 10°.

Discharge coefficient with flow from under radial gates on a weir of practical profile

The results of experiments showed that with an increase of the relative head from 0.75 to 1.0 with the remaining quantities constant, there is an increase of the discharge coefficient (Fig. 2), The maximum increase of the discharge coefficient reached 4.6%. An increase of the relative head from 1.0 to 1.4 leads either to some reduction of the discharge coefficient (to 2%) or it remains practically constant. The discharge coefficient increases with an increase of the relative height of the gate axis.

Problems in Measuring Steam Flow at 1250 Psia and 950 F With Nozzles and Orifices

Abstract Measurement of steam flow at 1250 psia and 950 F with nozzles and orifices is discussed (a) during their calibration and (b) during performance tests on a turbine. All primary elements were constructed to ASME specifications, the nozzles being of long-radius, low-ratio design with throat taps, the orifices employing radius taps. The calibrations for the flow nozzles indicated that reliable repeatable results could be obtained although one nozzle exhibited an abrupt increase in discharge coefficient of about 0.5 per cent at about 2 per cent pressure differential. The measured coefficients of discharge were within Power Test Code “probable tolerances” of ±1.25 per cent. The calibrations of the orifices were of little value because of permanent distortion of the orifice plates as a result of difference in expansion between the plates and their holding flanges. For measuring steam flows to the turbine, additional orifices were made up of different material, reducing distortion of the plates to the point of being negligible. The results of the turbine test with orifices and nozzles in series indicated excellent agreement between the flows based on orifice data using calculated coefficients and those determined from nozzle data using coefficients obtained from the calibration. Some trouble was experienced from deposits found around the nozzle throat taps. While this paper presents data indicating excellent agreement of the two methods of flow measurement during the turbine-performance tests, it also points out the need for more experimentation and knowledge of steam-flow measurement at elevated temperatures and pressures.