Orifice Coefficient Research Articles

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.

Dual-objective optimization strategy of self-adaptive transient pressure controller in water delivery engineering

ABSTRACT Controlling pressure impact of water hammer is an important guarantee for safe and stable running of pipeline systems. Previously, we proposed a spring self-adaptive auxiliary control (SAC) system to improve the pressure control ability of a surge tank. However, the working efficiency of the SAC system is affected by various parameters. A reasonable designing strategy becomes an urgent need to properly determine the parameters of the SAC controller. In this study, based on our calibrated numerical model, various transient responses of a SAC system with different parameters were further investigated. The latency response threshold and the spring orifice coefficient were identified to be the two most sensitive parameters that determine the controller working efficiency. Based on the objectives of reducing the in-pipe extreme pressure and in-tank water level fluctuation, an analytical dual-objective optimizing Method was proposed for application. The results demonstrated that the pressure control capability of SAC controller can be optimized by the proposed method.

Thermal Elastohydronamic Lubrication Characteristics of Inclined Double-roller Enveloping Hourglass Worm Drive

To grasp thermal elastohydrodynamic lubrication (TEHL) characteristics of the conjugating tooth-pairs of inclined double-roller enveloping hourglass worm drive in transmission process. The numerical solutions of line contact thermal EHL were obtained based on meshing theory of this worm drive and the theory of EHL. The TEHL line contact numerical solution of this worm drive is solved by using the multigrid method, and the TEHL film pressure and thickness are got at the same time. The effects of roller radius, offset distance, orifice coefficient and inclined angler on the TEHL characteristics and temperature rise are analysed and compared. The results show that with the increase of roller radius, offset distance and inclined angler, the secondary pressure peak decreases and moves to the outlet region, and the oil film thickness decreases accordingly, with increase in orifice coefficient the second pressure peak rises and move toward the inlet, the film thickness increases. The maximum temperature rises of film, worm and worm gear contact surface reduce as the roller radius, orifice coefficient and inclined angler increase, rose as the offset distance increases. It can reduce temperature rise and improve the oil film thickness thought the optimization calculation in the design.

Effects of Different Nozzle Orifice Shapes on Water Droplet Characteristics for Sprinkler Irrigation

In common irrigation systems, sprinklers are mounted with circular nozzles, but innovative noncircular nozzles can save water and energy by improving fragmentation in a low–intermediate pressure irrigation system. In order to investigate the effects of nozzle orifice shapes (circular, square, and equilateral triangular) on droplet characteristics, experiments using high-speed photography and water droplet spectrum measurement were performed. Using ImageJ to observe with the overlapped droplets and using the self-compiled programs of MATLAB to observe the morphology of droplets, we extracted the outlines of droplets. In addition, several empirical formulas for the prediction of droplets were obtained by way of a regression analysis of the experimental data. In particular, the shape coefficient of the nozzle orifice and the operating pressure of the nozzle were added to these formulas as variable factors to make them applicable to a variety of nozzles and working conditions. The results show that with the increase in shape coefficient, the jet atomization intensifies, and the droplets breaking from the jet will be dense and uniform. The velocity distribution of the droplets conforms to exponential functions (R2 > 0.7). The prediction formulas of diameter and kinetic energy were established with coefficients of determination exceeding 0.95. In low pressure conditions, the specific power multiplies at the end of spraying, and the maximum is proportional to the nozzle orifice coefficient. The impact-driven arm compensates for the disadvantage of the noncircular nozzles with the high irrigation-specific power, by producing a wider diameter gradient of droplets. Therefore, innovative sprinklers based on noncircular nozzles can be applied in a low–intermediate pressure system to increase water use efficiency, reduce energy consumption, and reduce costs.

Continuum simulation of non-local effects in a granular silo discharge flow using a regularized μ(I) rheology model

The effect of non-local momentum transport on a silo discharge process is numerically investigated using a continuum simulation with the μ(I) rheology model in which the gradient expansion model is adopted to account for the non-local effects due to the non-uniform field of inertial number I [Bouzid et al., Phys. Rev. Lett. 111, 238301 (2013)]. The singularity for I = 0 is handled with a regularization scheme [Lin and Yang, J. Comput. Phys. 420, 109708 (2020)]. Compared to the discharge dynamics predicted with the local μ(I) rheology model, the non-local effect enhances the velocity field to increase the volume discharge flow rate Q, especially when the silo orifice L is narrower. Both the local and non-local flow simulations conform to the Beverloo relation Q=Cρg(L−kd)3/2, where d is the intrinsic grain diameter but the non-local effects appear to lessen the orifice reduction effect coefficient k. The difference between the local and the non-local flow rates ΔQ¯, made dimensionless by ρgd3/2, grew monotonically with decreasing L/d with a slight enhancement if the silo height-to-width aspect ratio deviates from unity. Finally, we evaluated the ratio of the shear strain rate to the instantaneous maximum value to define a high-shear zone when the ratio is above a threshold and studied its evolution from the onset to the end of the discharge process. Interestingly, non-local momentum transport helped to reduce the size of the high-shear zone to give a more uniformly fluidized central zone above the orifice.

Experimental and Numerical Study of Orifice Coefficient of Cargo Tank Design of LNG Vessels

Liquid cargo storage tanks of liquefied natural gas (LNG) carriers are designed by strict standards to maintain the cryogenic state (−163 °C). For most LNG cargo storage tanks, it is mandatory to install a system that can safely store leaked fluid for 15 days in the case of leakage of liquid cargo due to crack of the insulation system. To ensure safety, it is necessary to predict the amount of LNG spilling from the cracks in the insulation panels. Although international regulations are provided, they rely on a conservative and consistent coefficient. In this study, experimental and numerical methods were applied to examine the design factor used to predict the flow rate in the tank design process. To check the amount of leakage that occurs under pressure conditions of LNG tanks, an experiment was conducted using crack specimens and pressure containers filled with water. In order to simulate the leakage of LNG, the amount of leakage was predicted using the Computational Fluid Dynamics (CFD) method. The distribution of leakage quantity was investigated according to the shape of the crack through the pressure vessel experiment and the analysis. Through CFD analysis, the leakage rate of LNG was calculated for each operating pressure condition through the crack. Finally, the results of this study examined the need to identify and reconsider the coefficients due to international guidelines and other factors in calculating orifice coefficients applied to the design of LNG tanks.

Experimental study and modeling of weeping rate in rectangular large‐scale valve trays

AbstractWeeping is an important hydraulic parameter that needs to be considered for valve trays and for calculations in the distillation field. Therefore, the accurate prediction of weep rate is crucial for the optimal design of valve trays. First, the effects of gas and liquid loads and weir height on weep rate, tray pressure drop, and actual bubbling area were studied in a 1.5 m × 0.61 m cold simulator. Second, the weep modes on the valve tray were analyzed in detail. A theoretical model was then derived to calculate weeping. The model showed a clear relationship between the weep rate and the fractional bubbling area. The experimental data showed that the weir height substantially affected the orifice coefficient of the liquid passing through the valve. Finally, the relation between weir height and orifice coefficient was obtained by fitting the experimental data. The agreements were good, and the maximum deviations were approximately 25%.

Three-dimensional numerical analysis of near-wall single-orifice ventilated bubble dynamics

Bubbling from near-wall orifices is widely used in ocean engineering, such as ship drag reduction, sewage treatment, underwater vehicle control technology and so on. But at present, most studies on ventilated bubble do not take into account the influence of the wall on the development of the bubble. Based on the potential flow theory, combined with mesh smoothing technique and mesh subdivision technique, the boundary element method is adopted to study the 3D ventilated bubble growth in this paper. The bubble is generated by ventilation during the vertical upward movement of the rotary body with a single horizontal orifice on the wall. And the convergence of the model is studied by modifying the mesh size. Meanwhile, the numerical simulation results agree well with the experimental results. Finally, with the existence of the inflow, the effects of different inflow velocities, ventilation rates, the diameters of the orifice and surface tension coefficients on the development process and flow characteristics of the bubble were studied. The results show that the inflow velocity is the main influencing factor of the bubble development process. The ventilation rate and the diameter of the orifice have some influence on the development process of the bubble. And the surface tension coefficient has little effect on the development process of the bubble.

Surface to sewer flow exchange through circular inlets during urban flood conditions

Abstract Accurately quantifying the capacity of sewer inlets (such as manhole lids and gullies) to transfer water is important for many hydraulic flood modelling tools. The large range of inlet types and grate designs used in practice makes the representation of flow through and around such inlets challenging. This study uses a physical scale model to quantify flow conditions through a circular inlet during shallow steady state surface flow conditions. Ten different inlet grate designs have been tested over a range of surface flow depths. The resulting datasets have been used (i) to quantify weir and orifice discharge coefficients for commonly used flood modelling surface–sewer linking equations and (ii) to validate a 2D finite difference model in terms of simulated water depths around the inlet. Calibrated weir and orifice coefficients were observed to be in the range 0.115–0.372 and 0.349–2.038, respectively, and a relationship with grate geometrical parameters was observed. The results show an agreement between experimentally observed and numerically modelled flow depths but with larger discrepancies at higher flow exchange rates. Despite some discrepancies, the results provide improved confidence regarding the reliability of the numerical method to model surface to sewer flow under steady state hydraulic conditions.

Theoretical Research of Roller Enveloping the Side-worm Gear Pairs Drive

Roller enveloping the side-worm gear pairs drive is proposed basing on roller enveloping hourglass worm drive. Roller enveloping the side-worm gear pairs drive means to assembling the roller on the end surface of the worm wheel equally. The hourglass worm tooth surface equation can be deduced by applying spatial meshing theory and differential geometry theory. The hourglass worm numerical models can be concluded by applying Matalb software to finish numerical simulation. At the same time ,this theory also focus on analyzing the roller radius R, orifice coefficient K1 , circumferential angle of worm gear for the meshing performance of this drive. According to the analysis, it can be concluded as that the roller radius is 5~20mm.

Serially Actuated Locomotion for Soft Robots in Tube-Like Environments

Soft robots are able to complete tasks that traditional robots cannot, thus providing new opportunities for robots to navigate confined spaces. These tasks include pipe inspection and endoluminal surgical applications. The research objective of this letter is to present a design methodology for soft robots capable of traversing a cannula or pipe using only passive elements, a single pressure source, and while avoiding blockage, that is, avoiding full occlusion of the cannula to still allow fluid flow. The robot consists of three segments, each with actuators and valves, and is driven by hydraulics (water). The actuators were built using the FREE method and optimized for the specific task of traversing a cannula with a diameter of 19 mm. An experimental approach was used to create a pressure-volume relationship from the kinematic fiber-reinforced elastomer enclosure (FREE) model. The passive valves were built as flow restrictors and modeled with the nonlinear orifice equation. A simulation and grid search was performed over a range of valve coefficients. An objective function was then maximized to produce orifice coefficients that augmented extension of the robot per input pressure cycle. The physical robot was then constructed and tested in a cannula. This resulted in a robot that was serially actuated, never fully occluded the cannula, and was able to successfully locomote a cannula at a rate of 27 ± 4 mm per two-second cycle. This experimental result was close to the simulated result of 28 mm per cycle.

The influence of strainer types on the flow and droplet velocity characteristicsof ceramic flat-fan nozzles

This study focused on determining the effect of various strainer types and their usage without strainer on the flow and droplet velocity characteristics of ceramic flat-fan nozzles. The nozzle types discussed are the standard (APE), low pressure drift reduction (ADI), and wide pressure range (AXI). The results of this study show that the orifice coefficient (k) of the ADI nozzle with a preorifice was lower than those of the API and AXI nozzles. The ball check strainers had a limiting effect on the nozzle's flow rate. The pressure exponent coefficients (n) were 0.57 for the API nozzle and 0.62 for the ADI and AXI nozzles used with ball check strainers. The n coefficient ranged from 0.47 to 0.49 for the API and AXI nozzles and from 0.50 to 0.53 for the ADI nozzle, used with typical strainers and without a strainer. The flow rate deviations of APE, ADI, and AXI nozzles used with a ball check strainer were determined as -12.0%, -11.4%, and -14.5%, respectively. The lowest Cd means were found in all nozzle types with ball check strainers, and the means were determined as 0.45, 0.58, and 0.71 for the ADI, AXI, and API nozzles, respectively. The Cd means of the nozzles with typical strainers, which is the same as usage without a strainer, were between 0.58 and 0.60 for the ADI nozzle, 0.82 and 0.85 for the AXI nozzle, and 0.91 and 0.94 for the API nozzle. Knowledge of the discharge coefficient of the nozzles used with various strainer types provided a reasonable estimation of the maximum droplet velocity at the nozzle orifice exit. The maximum droplet velocity at the nozzle orifice exit increased as droplet size increased. The droplets produced by the nozzles with ball check strainers had features that restricted the nozzle's flow. These were higher maximum velocity, kinetic energy, and stopping distance.

The Effects of Strainer Types on Flow Characteristics of Anti-Drift

This study investigated the effects of four different strainer types on flow characteristics (orifice coefficient (k), exponent coefficient (n), individual flow rate deviation (φ) and discharge coefficient (Cd)) of different nozzle types. The volumetric flow rates of anti-drift (AD) and multi-range (LU) flat-fan nozzles of three different orifice sizes were determined at different operational pressures (1.5, 3.0, 4.0, 6.0 and 8.0 bars). In each treatment, the nozzles were used together with cup screen strainer of 50-mesh, slotted strainer, cylindrical strainers of 40-, 50-, and 80-meshes, and ball-check strainers of 50- and 80-meshes. The flow rate measurements were also obtained without strainers. The relation between the flow rate (Q) and spray pressure (P) for each nozzle combination (nozzle type, strainer type, and orifice size) was presented using the power regression model . The “k” coefficient, which is the slope of the line referring to the relation between the nozzle flow rate and spray pressure, was evaluated as a comparison parameter between the nozzle combinations. The “k” mean values of the nozzle types using with ball-check strainers were lower than those of the without strainer, cup screen, slotted and cylindrical strainers. This result showed that the volumetric flow rate decreased with respect to the other nozzle combinations operated at the same operational pressure. Thus, the deviation rate from the nominal flow rate of the nozzles used with the ball-check strainers exceeded the acceptable deviation limit of ±10%. As the “n” coefficients of the LU and AD nozzles used with cup screen, slotted, cylindrical strainers and without strainers were close to 0.50, the ball-check strainers resulted in increasing the “n” coefficient of the nozzles. The “n” coefficient of the nozzles used with the ball-check strainers of 50- and 80- meshes was determined as 0.586 and 0.608 for the AD nozzle, respectively and, 0.576 and 0.584 for the LU nozzle, respectively. The ball-check strainers dramatically decreased the discharge coefficient (Cd) of the nozzles compared to the other strainers and the usage without strainer. For the cup screen, slotted, cylindrical strainers and the usage without strainer, the Cd means ranged from 0.67 to 0.77 for the AD nozzle, and 0.91 to 0.94 for the LU nozzle. The Cd means of the nozzles used with the ball-check strainers of 50- and 80- meshes were determined as 0.39 and 0.34 for the AD nozzle, respectively, and 0.56 and 0.53 for the LU nozzle, respectively.

Numerical investigation on effects of nozzle’s geometric parameters on the flow and the cavitation characteristics within injector’s nozzle for a high-pressure common-rail DI diesel engine

In the present paper, the influences of nozzle’s geometric parameters on the flow and the cavitation characteristics within injector’s nozzle have been numerically investigated on basis of a high-pressure common-rail DI diesel engine. For obtaining more beneficial information, five essential parameters (the pressure difference on the nozzle, circular bead of nozzle’s inlet, orifice coefficient, the ratio of nozzle’s length to orifice’s diameter, and the roughness of orifice’s inner wall) have been investigated. The variation regulations of the flow and the cavitation characteristics induced by the mentioned parameters have been observed and analysed in terms of the distributions of essential physical fields (including statistic pressure field, velocity magnitude field, turbulent kinetic energy field, mass transfer coefficient field, and vapour’s volume fraction field) and the variation regulations of crucial physical parameters (including mass flow rate, flow coefficient, average vapour’s volume fraction, average flow velocity at orifice’s outlet, and average turbulent kinetic energy at orifice’s outlet). The main results obtained in the present investigation have illustrated how the cavitation occurs, develops and extinguishes within nozzle; meanwhile, how each geometric parameter affects the flow and the cavitation characteristics within nozzle have been explored.

Stability Analysis of BWR-HD: An Optimized Boiling Water Reactor with High Power Density

A boiling water reactor (BWR) with high power density (BWR-HD) was designed through an optimization search that was constrained to a square lattice fuel array. It has a power level of 5000 MW(thermal), equivalent to a 26% uprated Advanced BWR (ABWR), the latest version of operating BWR. This results in economic benefits, estimated to be ~20% capital and operations and maintenance costs and similar total fuel cycle cost per unit electricity. The stability of the ABWR and BWR-HD were assessed for the three modes of density wave oscillations: single-channel thermal hydraulics, coupled neutronic regional core oscillations, and coupled neutronic global core oscillations. The sensitivity to design parameters such as inlet subcooling, presence of water rods, and inlet orifice coefficient as well as to changes in reactor power, flow rate, and void coefficient were examined using the STAB frequency domain code. The BWR-HD’s stability performance and sensitivity were concluded to be similar to those of the ABWR. The results of the frequency domain analysis indicate that the shorter core and smaller void coefficient lowered the oscillation decay ratio, while the cooler inlet temperature and higher void fraction increased the decay ratio. Also the S3K code was utilized to perform three-dimensional coupled stability analysis and to formulate an operation exclusion zone region for the BWR-HD design. It was found that a reduction in the allowable operational zone of the BWR-HD design is warranted, due to its decay ratio being higher than that of the ABWR for whole-core oscillations. However, the inlet orificing (pressure loss coefficient) of the assemblies can be increased to obtain the same stability performance as the ABWR. This strategy is deemed plausible since the pumping power needed for the BWR-HD, even with the increase in pressure losses at the inlet of assemblies, will still be less than that of the ABWR and will have negligible effects on the safety performance.

A study on the direct leakage of rotary air preheater with multiple seals

The direct leakage of rotary air preheater was studied both experimentally and numerically. We have tested different seal structures from single to triple seals cases, which are used in real air preheater equipments to control the direct leakage. To describe the effect of the gap width and inlet pressure on the orifice coefficient and in terms of the air leakage engineering modifying factor, some improved relationships were obtained, which are superior over the traditional ones because of their better accuracy. The main factors that affect the air leakage are the air flow expansion, inlet velocity at the seal gap entrance, and the flow boundary conditions on the seal plate surface. The first upstream seal accounts for most of the total pressure drop on the entire multiple-seal system. The simulation results on the multiple-seal system show that the system of triple seals is better in controlling the leakage than that of the double seals when the seal gap is small; however, when the seal gap increases up to a critical value, the difference between the double- and triple-seal becomes negligible.

Comparison of the results of theoretical and experimental studies of the compression rate of fluid flow in flat slit-shaped channel

The paper presents the results of experimental studies of hydraulic drive with throttle control. The fluid flow is considered in a flat slit-like throttle channel accompanied by the appearance of cavitation phenomena. The comparison of the results of the calculation of flow compression rate, performed on the basis of the jets theory in accordance with the procedure proposed by Professor S.S. Rudnev, is presented in the paper together with the values ​​of the rate obtained by experimental methods. The study of the orifice coefficient for a flow with forming a closed cavity is conducted using an equivalent circuit.

Analysis of flow through an orifice meter: CFD simulation

Orifice meters are the most common instruments used for fluid flow measurement because of its ruggedness, simple mechanical construction and other known advantages. Orifice coefficients are empirical because of difficulty in accurately predicting the effects of geometrical complicacy and flow separation from the wall on the flow. In the present paper, Computational Fluid Dynamics (CFD) simulation has been used to predict the orifice flow with better accuracy. CFD simulations have been performed using OpenFOAM-1.6 solver and validated with the published experimental data of Nail (1991) and Morrison et al. (1993). CFD simulations have been validated with pressure drop and energy balance of our experimental data of water as fluid. The outcomes of the CFD simulations in terms of profiles of velocity, pressure, etc. are discussed in detail. A new scheme has been proposed to track vena-contracta with the help of CFD and with a suitable provision in the hardware of orifice meter. The new scheme maintains the existing advantages of orifice meters and provides better accuracy and sensitivity.

Numerical Analysis and Optimization of Oxygen Separation from Air via Pressure Swing Adsorption

A pressure swing adsorption air separation process in a commercial aircraft using 13X zeolite with a more complex cycle than the classic Skarstrom was simulated via a predictive dynamic model to evaluate and optimize oxygen generation system. The coupled mass, energy, and momentum differential equations were discretized using the implicit central finite-difference technique and the obtained equations were solved by Newton-Raphson method. The validated model in conjunction with an optimization procedure (Successive Quadratic Programming) was utilized to investigate the oxygen separation efficiency as a function of β (ratio between the bed time constant and the particle diffusion time constant), Cfp (purge orifice coefficient), θcycle (cycle time), Cff (feed valve), Cfe (exhaust valve) and pH* (high pressure operation). A set of optimum values (β=150, Cfp=0.7, θcycle=1.5, Cff=31, Cfe=52 and pH*=3.8) was obtained and recommended to achieve maximum recovery (0.26) at 98% purity.

SCWR single channel stability analysis using a response matrix method

A system response matrix method, which directly solves the linearized differential equations in the matrix form without Laplace transformation, is introduced for the supercritical fluids flow instability analysis. The model is developed and applied to the single channel or parallel channel type instability analyses of a typical proposed Supercritical Water Reactor (SCWR) design. A uniform axial heat flux is assumed, and the dynamics of the fuel rods and water rods are not considered in this paper. The sensitivity of the decay ratio (DR) to the axial mesh size is analyzed and found that the DR is not sensitive to mesh size once sufficient number of axial nodes is applied. The sensitivity of the stability to inlet orifice coefficient is conducted for the hot channel and found that a higher inlet orifice coefficient will make the system more stable. The susceptibility of stability to operating parameters such as mass flow rate, power and system pressure is also performed. It is found that the SCWR stability sensitivity feature can be improved by carefully choosing the inlet orifice coefficients and operating parameters. The stability feature of the average channel is also analyzed with an equivalent inlet orifice coefficient. Finally, the manufacturing feasibility of the inlet orifices for both the hot channel and average channel is studied and found to be favorable.