Lower Discharge Coefficient Research Articles

Experimental study of hydraulic losses in linear and nonlinear weirs: A comparative analysis

ABSTRACT With increased length of the crest in a certain width range, the labyrinth weirs increase the discharge capacity. In this study, a laboratory flume was used with a length of 8 m and a width and height of 0.6 m, in which the hydraulic loss of linear/non-linear, labyrinth, triangular, and trapezoidal weirs were investigated. Dimensional analysis using the Buckingham methodology showed that the discharge coefficient (Cd) is a function of parameters such as hydraulic head ratio (Ht/P), weir shape factor (Sf), and hydraulic loss ratio (Hf/P). The results showed that the ATRL weir has a lower discharge coefficient than the ALR by 44% and ATPL a lower discharge coefficient than ALR by 50%. The ATRL weir has a higher hydraulic loss than ALR by 2300% and a higher hydraulic loss than ATPL by 2000%. The TRL weir has a higher hydraulic loss than LR by 4900% and a higher hydraulic loss than TPL by 5700%. The TRL weir has a lower discharge coefficient than LR by 41% and TPL by 43%. The best correlation with the Cubic statistical model was obtained in the TPL weir in terms of discharge coefficient and in the ALR weir in terms of hydraulic loss.

Study on full-coverage film cooling characteristics on turbine vanes under the effect of trailing-edge shock wave

In transonic turbines, the oblique shock wave emanating from the stator's trailing edge impinges on the neighboring suction side, which has a complex effect on boundary layer flow. Numerical studies were performed to investigate the influence of oblique shock wave on suction-side film cooling, and the numerical results were validated by model experiments. The sudden increase of static pressure downstream of shock wave is adverse to coolant outflow, and cooling effectiveness shows a notable drop. Furthermore, injecting coolant into boundary layer can increase kinetic energy, and weaken flow separation caused by shock wave. Detailed influences of geometric and thermodynamic parameters on film cooling performance were analyzed. The increase of pressure ratio causes the downward motion of shock wave, which is beneficial to film cooling. The increase of hole size improves cooling effectiveness before shock wave, but reduces cooling effectiveness after shock wave. Cooling effectiveness decreases as hole inclination angle, hole pitch and spacing increases. Adding hole diameter or reducing hole inclination angle, hole pitch and spacing can increase discharge coefficient. Laminated cooling and film cooling were compared. By introducing jet impingement and pin fins, laminated structures can generate higher cooling effectiveness but lower discharge coefficient.

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.

Performance Against Cavity Index and Discharge Coefficient between Broad and Sharp Crested Weirs

The purpose of this research is examining the performance of rectangular broad and sharp crested weirs in terms of cavity index and discharge coefficient. For this purpose, a computational fluid dynamics CFD code FLUENT is applied. Firstly, the code verified by applies on the experiments work of Hagre et al 1994 the results show excellent agreements between CFD and Hager et al 1994. Secondly the code applied on both broad and sharp crested weirs. The results demonstrate that broad crested weirs have a lower discharge coefficient than sharp crested weirs, implying that broad crested weirs have a lower ability to discharge flow than sharp crested weirs. While the cavity index of a broad crested weir is lower than that of a sharp crested weir, the risk of cavitation is lower for a broad crested weir. Finally, designers should use caution when deciding which type of crest to use in their designs.

A numerical study on the in-nozzle cavitating flow and near-field jet breakup of a spirally grooved hole nozzle using a LES-VOF method

To enhance fuel atomization for diesel engines, a spirally grooved hole (SGH) nozzle, in which several spiral arc grooves are set on the inner wall of tapered holes of a nozzle, forming flower-shaped cross sections, was designed. In this paper, the multi-phase flow inside and outside the SGH nozzle was calculated using a volume-of-fluid, large eddy simulation (VOF-LES) method to clarify the effects of spirally grooved hole on the cavitating flow and primary breakup characteristics for diesel nozzles. The calculation was carried out under injection pressure of 150 MPa and ambient pressure of 0.1 MPa for a SGH nozzle, and a non-grooved tapered hole (NSH) nozzle as a reference. Numerical results showed that the wall-guide effect of the spiral grooves in the hole of the SGH nozzle led to partially spiral flow of the fluid at the outer part of the nozzle hole, which in turn produced considerable centrifugal force on the liquid core, providing additional dynamics for the breakup of liquid jets besides aerodynamic effects. As a result, the deformation of the surface of the liquid column in a shorter distance from the outlet of the SGH nozzle were observed, and more ligaments and droplets were formed in the near-field, i.e., the breakup of the jet emerging from the SGH nozzle was substantially enhanced. The partially spiral flow also resulted in a largely wider near-field spreading angle and finer droplets than those of the NSH nozzle, with a penalty of 11.8% lower discharge coefficient.

Comparison of single-hole and multi-hole orifice energy consumption

Nowadays, with rising energy prices, energy efficiency is playing an important role in all industries. Differential pressure-based measuring instruments are still widely used instruments with orifice flow meters being the most popular ones. Due to its simplicity, reliability, and ease of maintenance, orifice flow meters are very common measuring instruments in many industries. As these instruments are differential pressure-based instruments, they are increasing energy costs due to increased pressure loss. Conventional single-hole orifice (SHO) flow meters have many advantages but also some disadvantages that are affecting energy efficiency. These disadvantages like higher pressure difference, slower pressure recovery, lower discharge coefficient can be overcome by multi-hole orifice (MHO) flow meters. Computational fluid dynamics (CFD) simulations were used to study energy consumption of both SHO and MHO with four different β parameters. Results showed MHO to be more energy efficient compared to SHO with same β parameter. These results are showing one more advantage MHO have compared to SHO, but further research is needed to make them a drop-in replacement.

Experimental research of single-hole and multi-hole orifice gas flow meters

As energy efficiency is becoming more important today due to limited energy resources as well as their rising prices and environment issues, it is crucial to have reliable measurement data of different fluids in production processes. Because of its simplicity, affordability and reliability, orifice flow meters are again becoming subject of numerous researches. Conventional single-hole orifice (SHO) flow meter has many advantages but also some disadvantages like higher pressure drop, slower pressure recovery, lower discharge coefficient etc. Some of these disadvantages can be overcame by multi-hole orifice (MHO) flow meter while still maintaining advantages of conventional SHO meter. Both SHO and MHO flow meters with same β ratios were experimentally tested and compared. Results showed better (lower) singular pressure loss coefficient and lower pressure drop in favour of the MHO flow meter. Experimental data indicates that MHO flow meter is superior to the conventional orifice flow meter, but further research is necessary to make the MHO a drop-in replacement for a SHO flow meter.

Experimental Study on Pressure Losses in Circular Orifices With Inlet Cross Flow

The ability to understand and predict the pressure losses of orifices is important in order to improve the air flow within the secondary air system. This experimental study investigates the behavior of the discharge coefficient for circular orifices with inlet cross flow which is a common flow case in gas turbines. Examples of this are at the inlet of a film cooling hole or the feeding of air to a blade through an orifice in a rotor disk. Measurements were conducted for a total number of 38 orifices, covering a wide range of length-to-diameter ratios, including short and long orifices with varying inlet geometries. Up to five different chamfer-to-diameter and radius-to-diameter ratios were tested per orifice length. Furthermore, the static pressure ratio across the orifice was varied between 1.05 and 1.6 for all examined orifices. The results of this comprehensive investigation demonstrate the beneficial influence of rounded inlet geometries and the ability to decrease pressure losses, which is especially true for higher cross flow ratios where the reduction of the pressure loss in comparison to sharp-edged holes can be as high as 54%. With some exceptions, the chamfered orifices show a similar behavior as the rounded ones but with generally lower discharge coefficients. Nevertheless, a chamfered inlet yields lower pressure losses than a sharp-edged inlet. The obtained experimental data were used to develop two correlations for the discharge coefficient as a function of geometrical as well as flow properties.

Effects of V-type intersecting hole on the internal and near field flow dynamics of pressure atomizer nozzles

The coalescence of a pair of sub-holes forms a V-type intersecting hole for pressure atomizer nozzles. This design makes use of the internal impact effect to promote the breakup of liquid jets, enhancing liquid-gas mixing. To clarify the physical structure of the in- and near nozzle flow field for the V-type intersecting hole atomizer nozzles, high speed photography was employed to visualize the in-orifice and near field flow behaviors of four atomizer nozzles, three of which were V-type intersecting hole nozzles with impact angle varied from 30° to 50°, and the other one was a cylindrical hole nozzle as a reference. In-nozzle flow and jet images in both the intersecting plane and its axial normal plane were captured. The results show that the use of V-type intersecting holes in an atomizer nozzle eliminates the generation of cavitation inside the nozzle orifices even under the conditions of strong hydraulic flip for the reference nozzle, leading to 15%–50% higher discharge coefficients than those of the reference nozzle, and yields fan-shaped jets, which least and most disperse at the intersecting plane and its axial normal plane, respectively. Furthermore, these fan-shaped jets demonstrate superior radial dispersion, in terms of 1–5 times larger normalized cross sectional areas than those of the reference nozzle. Moreover, increasing the impact angle enhances the internal impact effect, resulting in wider spreading angles and larger cross sectional areas of the jets, however, lower discharge coefficients.

Investigation of the effect of nozzle inlet rounding on diesel spray formation and combustion

In this study, the effect of nozzle inlet rounding on diesel spray formation and combustion is investigated. In order to take into account nozzle geometry, two different nozzle geometries (sharp inlet and rounded inlet) were used in the experiments. Diesel spray injected into a constant volume combustion chamber was modeled by using KIVA3V R2 code. One dimensional nozzle flow model was used in numerical simulations. This model calculates nozzle discharge coefficient and updates the initial droplet radius and droplet velocities according to nozzle inlet geometry. Diesel fuel is represented by diesel oil surrogate mechanism which consists of 71 species and 323 reactions. The numerical spray results were validated with macroscopic spray characterization data obtained by constant volume experiments. Results showed that inlet rounding increases discharge coefficient. At high ambient pressure conditions, sharp and rounded nozzles have similar spray internal structure. However, it is observed that sharp inlet nozzle produces smaller droplets that shorten spray tip penetration and autoignition delay period due to low discharge coefficient. Comparing spray combustion of rounded and sharp inlet nozzles, it is showed that rounded inlet nozzle has lower combustion temperature, less NO and soot concentration than sharp inlet nozzle.

Fan Efficiency Improvement via Changing Guide Blade Shape Under Various Operating Conditions

The aim of this study is to examine the influence of sweep and tangential blade lean the guide vanes (GV) on the pressure losses in the blade row, and development of an approach to creating the GV with a rationally-shaped blades to ensure increased efficiency in the partial operating conditions. A numerical simulation method was used for research. As an object to be studied, was used an axial fan comprising an impeller and a GV, which were profiled to have constant circulation of velocity in radius. Verification of numerical simulation was based on the experimental data of fan. It comprised a GV with a straight blade and a circular-arc blade, with an impeller remained stationary in both cases. Among the turbulence models under consideration, preference is given to k-ω, as under operating conditions close to design ones, its result falls within the confidence span of the experimental characteristics, and at much higher and lower discharge coefficients a discrepancy is 4% at most. In addition to the characteristics, the fields of pressure losses in GV have been analyzed. Numerical modeling allowed us to have a well-reproduced structure of losses in the stationary blade row. Analysis of pressure loss fields has shown that in the original GV near the hub, on the blade back, under design conditions a flow breakdown takes off. In view of the research, was designed a new GV with a modified blade geometry. The GV blade axis near the hub was bent in the circumferential direction by 0.1 length of the blade. In the near-hub cross-sections the blade chord was increased by 10%. The results of numerical simulation have shown that, with the flow less than the designed one, a change of just the GV blade tip sections leads to reduced break-down zone near the hub by about 40% under both operating conditions without raising profile losses and to improved fan efficiency, which reduces fan drive power consumption under typical operating conditions in the propulsion system.

Studying Subsidence Coefficient of Mirages and Dynamic Storage Volume of Karstic Springs of Khorram Abad, West of Iran

The studied subject is about subsidence coefficient of mirages and dynamic storage volume of Karstic springs in Khorram Abad in West of Iran. Subsidence coefficient indicates ability of groundwater discharge and hydrologic properties of the environment; meaning effective porosity and transfer coefficient of springs. In general, in developed Karstic zones, each direct line of subsidence curve indicates a discharge regime. Obtained results from the study show that subsidence branch of Golestan, Motahari, Niloofar (changaei), Navekech, Dore Robat mirages have subsidence coefficient with mild slope and low value, which demonstrate passage of water through a seams system at the karst springs. Q and whirlpool stone mirages have two subsidence coefficients, which indicate passage of water through two seam systems in Karstic environment of springs. According to obtained results, process of changes in subsidence branch in these mirages has had at the first a mild slope and low discharge coefficient and in continue, its discharge would be declined with sharper slope and high discharge coefficient. In order to estimate dynamic storage volume of springs, MAILET general equation is applied, which is suitable for subsidence branch of hydrographs of centralized springs discharge. Following, dynamic storage volume of studied springs is analyzed and obtained results are presented in this study respectively.

Numerical simulations for multi-hole orifice flow meter

The measurement of flow rate is important in many industrial applications including rocket propellant stages. The orifice flow meter has the advantages of compact size and weight. However, the conventional single-hole orifice flow meter suffers from higher pressure drop due to lower discharge coefficient (Cd). This can be overcome by the use of multi-hole orifice flow meter. Flow characteristics of multi-hole orifice flow meters are determined both numerically and experimentally over a wide range of Reynolds numbers. Computational fluid dynamics (CFD) is used to simulate the flow in the single- and multi-hole orifice flow meters. Experiments are carried out to validate the CFD predictions. The discharge coefficients for the different orifice configurations are determined from the CFD simulations. It is observed that the pressure loss in the multi-hole orifice flow meter is significantly lower than that of single-hole orifice flow meter of identical flow area due to the early reattachment of flow in the case of the multi-hole orifice meter. The influence of different geometrical and flow parameters on discharge coefficient is also determined.

Hydraulic characterization of Diesel and water emulsions using momentum flux

Diesel and water emulsions have the potential to be used in compression ignition engines to control the emissions of NOx and PM. Very little is known about the influence emulsification will have on the fuel sprays formed during injection. This paper outlines the measurement of the momentum flux of injection sprays of Diesel fuel and Diesel fuel emulsions containing 10% and 20% water, with the goal of hydraulically characterizing the sprays and identifying the influence emulsification may have on them. The momentum flux, mass flow, instantaneous mass flow, discharge coefficient, injection velocity, momentum coefficient and momentum efficiency have been examined. The injections were carried out in a high pressure chamber filled with nitrogen. The measured momentum flux is observed to increase with increasing injection pressure in a linear form. Increasing the ambient density in the chamber resulted in a decrease in the measured momentum flux. The emulsified fuel sprays had a very similar momentum flux as the neat Diesel fuel sprays. The total mass of emulsified fuel injected was less than for neat Diesel at corresponding condition. The instantaneous mass flow rate was determined using a normalized form of the momentum flux measurement and the independently measured total mass injected. The emulsions tended to have a lower discharge coefficient and there is no evidence that the nozzle is cavitating at these conditions. The emulsified fuels have tended to have a higher injection velocity than the neat Diesel fuel sprays. The momentum efficiency is introduced, which uses the instantaneous mass measurement and the theoretical velocity of the spray. The emulsified fuels have a larger momentum efficiency, a result of their high injection velocity compared with the neat Diesel fuel.

Experimental and numerical investigations of mechanisms in fluidic spray control

A fluidic control method in an axisymmetric spray orifice is investigated experimentally and numerically. In this method, a nominally steady secondary flow is introduced through an annular slot placed near the vena contracta along the orifice wall to control the cavitation, and thus the spray, at pressures up to 550kPa driving pressure difference. Images of cavitation, measurements of droplet sizes and discharge coefficients, and CFD modeling are combined to explore the flow physics leading to the production of small droplets. Experimental results suggest that the secondary flow is incapable of confining cavitation to the region upstream of the slot, and generally a larger secondary flow rate results in a lower discharge coefficient, and a larger fraction of small droplets. The homogeneous model-based CFD code of Chen and Heister was employed to model the internal flows, which indicated that a high pressure region upstream of the slot, large pressure fluctuations in the orifice, and long cavitation lengths are the favorable conditions for atomization. The CFD simulations, together with experimental measurements, correlate the orifice geometry and flow structures to droplet sizes. Understanding the relationship between flow structures and droplet sizes helps to design orifices in favor of production of small droplets.

A computational investigation on the influence of the use of elliptical orifices on the inner nozzle flow and cavitation development in diesel injector nozzles

In this paper a computational study was carried out in order to investigate the influence of the use of elliptical orifices on the inner nozzle flow and cavitation development. With this aim, a large number of injection conditions have been simulated and analysed for 5 different nozzles: four nozzles with different elliptical orifices and one standard nozzle with circular orifices. The four elliptical nozzles differ from each other in the orientation of the major axis (vertical or horizontal) and in the eccentricity value, but keeping the same outlet section in all cases. The comparison has been made in terms of mass flow, momentum flux and other important non-dimensional parameters which help to describe the behaviour of the inner nozzle flow: discharge coefficient (Cd), area coefficient (Ca) and velocity coefficient (Cv). The simulations have been done with a code able to simulate the flow under either cavitating or non-cavitating conditions. This code has been previously validated using experimental measurements over the standard nozzle with circular orifices. The main results of the investigation have shown how the different geometries modify the critical cavitation conditions as well as the discharge coefficient and the effective velocity. In particular, elliptical geometries with vertically oriented major axis are less prone to cavitate and have a lower discharge coefficient, whereas elliptical geometries with horizontally oriented major axis are more prone to cavitate and show a higher discharge coefficient.

Behavior of the Discharge Coefficient for the Overflow Characteristics of Oblique Circular Weirs

This paper presents an experimental study and analysis for effect of the geometrical characteristics, of the oblique cylindrical weir on discharge coefficient, wherefrom three sizes used for the weir and two angles for the deviation.From the results, it was found that the coefficient of discharge is affected by geometrical characteristics represented by radius of the weir and the angle of inclination with the wall of the channel. It was noticed that the increase in the radius of the weir lead to a low discharge coefficient of the cylindrical weir. And found that discharge coefficient of the oblique weir is higher than the discharge coefficient of the normal weir. And the value of discharge coefficient is directly proportional with the weir inclination.

Effect of Inlet Slot Number on the Spray Cone Angle and Discharge Coefficient of Swirl Atomizer

Liquid atomization is a process of changing the liquid into small droplets. There are many applications which are related to liquid atomization including fuel injection in combustion systems and also in agricultural sprays. In pressure swirl atomizer, the liquid is injected into the atomizer through tangential port and a swirling motion is formed inside the swirl chamber. At high strength of swirling motion, an air core will be visible inside the atomizer. The liquid is then discharged from the orifice to form a spray which breaks up the liquid into small droplets. The objective of this paper is to report on the effect of inlet slot number (n) on the spray cone angle and discharge coefficient (Cd). The injection pressure was varied in the range of 2 to 8bar and water was used as the working fluid. Experimental data shows that the spray cone angle increases as the injection pressure increased, regardless of inlet slot number. It is also observed that the atomizer with the most number of inlet slots produces widest spray. The effect of injection pressure on spray cone angle is more prominent at a lower range of injection pressure and greater number of inlet slot. The spray cone angle increases by only 5.4% as the inlet slot number increased from 2 to 5 for an injection pressure of 2bar, but increases by 10.7% for an injection pressure of 8bar. Furthermore, it is found that higher injection pressure and lesser number of inlet slot leads to lower discharge coefficient. It also noticed that, greater number of inlet slot has higher discharge coefficient.

Film Cooling Performance of Converging-Slot Holes With Different Exit-Entry Area Ratios

Film cooling performances of two kinds of converging-slot-hole (console) with different exit-entry area ratios have been measured using a new transient liquid crystal measurement technique, which can process the nonuniform initial wall temperature. Four momentum ratios are tested. The film cooling effectiveness distribution features are similar for the two consoles under all the momentum ratios. Consoles with smaller exit-entry area ratio produce higher cooling effectiveness. And the laterally averaged cooling effectiveness results show that the best momentum ratio for both consoles’ film cooling effectiveness distribution is around 2. For both consoles, the heat transfer in the midspan region is stronger than that in the hole centerline region in the upstream but gradually becomes weaker as flowing downstream. With the momentum ratio increasing, the normalized heat transfer coefficient h∕h0 of both consoles increases. In the upstream, the heat transfer coefficient of console with small exit-entry area ratio is higher. But in the downstream, the jets’ turbulence and the couple vortices play notable elevating effect on the heat transfer coefficient for large exit-entry area ratio case, especially under small momentum ratios. Consoles with smaller exit-entry area ratio provide better thermal protection because of higher cooling effectiveness. And the distributions of heat flux ratio are similar with those of cooling effectiveness because the influence of η on q∕q0 is larger. For the consoles, smaller exit-entry area ratios produce lower discharge coefficients when the pressure variation caused by the hole shape is regarded as flow resistance.

Enhancement of entrainment rates in liquid–gas ejectors

Ejectors are widely used as effective distributors in many chemical and bioprocess industries. Gas entrainment rate as a function of liquid flow rate in ejectors is investigated using nozzles of different geometries. The data are analyzed through macro-energy balance for each phase considering air and water inlet line discharge coefficients. Nozzles with smaller discharge coefficients are effective in producing higher vacuum and hence higher entrainment rates. It has been observed that the factor limiting the air entrainment rate is the low discharge coefficient in the air inlet line. Higher air inlet line discharge coefficients can increase the entrainment rate.