Incompressible pulsating flow for low Reynolds numbers in orifice plates

A flow with periodic variations is known as a pulsating flow. A particularly important consequence of these flows occurs in the presence of orifice plates, which are devices related to the determination of discharge in pipes. Based on an experimental methodology, this work presents a study on the effects of pulsation variations and temporal inertia on the discharge coefficient. The work includes situations beyond those contained in the standards, particularly for liquid flows in small diameter pipes with low Reynolds numbers. The experiments were conducted on a flow bench, capable of producing pulsating flows inside pipes. For the experimental study of the transient flow, the propagation of a known flow fluctuation was related to a pressure fluctuation, allowing the dynamic calibration of the measuring system. The value of the dynamic discharge coefficient was determined, and the coefficients of static discharge and quasi-steady were compared. The results showed that the inertial effects significantly affect the value of the discharge coefficient of the orifice plate, reducing the discharge values.     

A novel comprehensive correlation for discharge coefficient of square-edged concentric orifice plate at low Reynolds numbers

Among various differential pressure flow meters, the orifice meter has gained its publicity in applications where cost, space, and ease of maintenance are of high priority. A major problem associated with the use of orifice flow meters at low Reynolds number flows is the significant variation of discharge coefficient (C_d) as a function of orifice geometry and the Reynolds number. In this work, a two-dimensional axisymmetric numerical model was applied to the investigation of viscous, incompressible flow through square-edged concentric orifice plate for the purpose of studying the performance of discharge coefficient consequent to variations of Reynolds number (Re), orifice/pipe diameter ratio (β), and orifice thickness ratio (t*). The analysis of numerical results by means of multiple regression method has yielded a new correlation incorporating the effect of the parameters under study on orifice meter discharge coefficient for orifice bore Reynolds numbers (Re_o) < 250. Results of relevant investigations from the literature are used in the present work as references for the validation of the numerical model as well as the proposed correlation for discharge coefficient.     

Wet gas pressure drop across orifice plate in horizontal pipes in the region of flow pattern transition

As a basis for measuring the mass flow rate of wet gas using differential pressure meters, predicting the pressure drop of a wet gas flowing through orifice plates is important; however, this has not yet been solved satisfactorily, although many studies have reported on that subject. In this study, the pressure drop of wet gas across sharp-edged orifice plates was experimentally investigated in the region of flow pattern transition using air and water as the two phases, and the prediction performance of the available pressure drop models was compared based on the experimental data. The results show that the homogenous flow models overestimate the pressure drop, whereas those models based on the separated flow model often present underestimations. The models reported for wet gas are also incapable of predicting the pressure drop in this region with acceptable accuracy. Through an analysis of the prediction deviations, it is found that the Froude number of the liquid phase has a significant influence on the pressure drop of the wet gas, besides the Froude number of the gas phase. Then, three new correlations that are based on the homogeneous flow, Chisholm model, and Murdock model, respectively, were proposed based on the experimental result.     

The fractal flow conditioner for orifice plate flow meters

The sensitivity of orifice plate flow meters to the quality of the approaching flow continues to be a cause for concern in flow metering. The distortions caused by pipe fittings such as valves, bends, compressors and other devices located upstream of the orifice plate can lead to non-standard velocity profiles and give errors in measurement. The design of orifice plate meters that are independent of the initial flow conditions of the upstream is a major goal in flow metering. Either using a long straight pipe, or a flow conditioner upstream of an orifice plate, usually achieves this goal.The effect of a fractal flow conditioner for both standard and non-standard flow conditions was obtained in experimental work and also using simulations. The measurement of mass flow rate under different conditions and different Reynolds numbers was used to establish a change in discharge coefficient relative to a standard one. The experimental results using the fractal flow conditioner show that the combination of an orifice plate and a fractal flow conditioner is broadly insensitive to upstream disturbances.The simulation results also show that the device can be used as a part of a flow metering package that will considerably reduce installation lengths. Previous work with orifice plates has shown that a combination of flow conditioner and orifice plate was promising. The results of using a combination of the fractal flow conditioner and orifice plate for non-standard flow conditions including swirling flow and asymmetric flow show that this package can preserve the accuracy of metering up to the level required in the Standards.     

Evaluation of multi-holed orifice flowmeters under developing flow conditions – An experimental study

This study focuses on multi-holed orifice plates, which have superior flow measuring characteristics as compared to their conventional counterparts. However, literature is scant on quantitative parametric investigations. In this experimental study, the performance of a multi-holed orifice plate is evaluated for variable number of holes (n), equivalent diameter ratio (EDR), compactness ratio (C), plate thickness ratio (s/d) and upstream developing length (L/D) in developing flow regimes for the Reynolds number range of 24,500–55,500 by using Central Composite Design. A total number of 324 experiments were performed. It was found that EDR has the most significant effect on pressure loss coefficient, followed by ‘n’ and ‘C’. Moreover, it was found out that single orifice (SO) and multi-holed orifice (MO) have almost the same pressure losses for the same value of EDR/β. However, flow develops quickly for MOs. Higher values of coefficient of discharge were observed in the case of MOs as compared to the SOs with little effect of upstream disturbances. The effect of developing length is significant on the accuracy of orifice meter. However, when the multi-holed orifice plates are installed at 2D upstream length, the effect of upstream disturbances are diminished. This result provides the flexibility of installation, which means that multi-holed orifices can be installed at 2D. The experimental data is in good agreement with literature. Finally, an optimum orifice plate (5,0.4,0.7) was selected for flow developing region with minimum pressure loss coefficient based upon the experimental results.     

Experimental study on effect of structural parameters on pressure drop characteristics of multi-orifice plates

Owing to the advantages of rectification, low noise, low pressure loss, and more stable pressure drop signal compared with the characteristics of the conventional single-orifice plate, multi-orifice plates (MOPs) offer a wide range of application prospects in various industrial pipelines. However, owing to its various orifice shapes and orifice layouts, the pressure drop characteristics of MOPs are not fully understood. In this study, the pressure drop characteristics of single-phase flow across a multi-orifice plate, which implies a stable zone (turbulent flow) pressure loss coefficient and the minimum critical Reynolds number of the stable zone, are experimentally investigated in the Reynolds number range of 29,000–146,000 using water as the fluid. Nine MOPs with circular holes evenly arranged in an equilateral triangle are tested. Their structures differ in terms of the equivalent diameter ratio (0.30–0.60), orifice number (64–400), and relative orifice thickness (0.40–1.60). The results show that the minimum critical Reynolds number deceases as the equivalent diameter ratio decreases, the relative orifice thickness increases, and the orifice number increases, which allows an enlarged Reynolds number range for the stable zone. As the equivalent diameter ratio, orifice number, and relative orifice thickness increase, the stable zone pressure loss coefficient of MOPs initially decreases rapidly and gradually approaches a constant. Finally, based on the experimental results of this study, a correlation of the stable zone pressure loss coefficient of MOPs is proposed, which provides a reference for using MOPs in various industrial applications.     

Beta ratio, swirl and Reynolds number dependence of wall pressure in orifice flowmeters

Experimental work has been performed in an effort to gain a better understanding of the flow field inside orifice flowmeters and the pressure field generated on the walls of the pipe and orifice plate. As a part of a larger study, extensive wall pressure measurements have been made on the pipe wall from four pipe diameters upstream of the orifice plate to six pipe diameters downstream, as well as on both the upstream and downstream faces of the orifice plate. These measurements were performed for Reynolds numbers of 54 700; 91 100 and 122 800; for beta ratios of 0.50 and 0.75 with air as the working fluid. An adjustable swirl plate was installed, which was used to impart varying amounts of swirl into the flow upstream of the orifice plate. For each swirl case, Pitot and static pressure probes were used to characterize the upstream flow field while the pipe wall and orifice plate surface pressures were measured.     

Influence of wear on the performance of a multirecess conical hybrid journal bearing compensated with orifice restrictor

In the present work, an analytical study concerning the influence of wear on the performance of a four-pocket hybrid conical journal bearing compensated with an orifice restrictor has been presented. The Reynolds equation governing the flow of lubricant in the clearance space of bearing has been solved using FEM and the Newton Raphson method. The static and dynamic performance characteristics have been presented for the various values of external load, wear depth parameter and for the various values of semi-cone angle. The numerically simulated results suggest that, the performance of the conical bearing is greatly affected by the wear defect.     

An orifice meter for bidirectional air flow measurements: Influence of gas thermo-hygrometric content on static response and bidirectionality

This paper presents the design and calibration of an ISO non-compliant orifice plate flowmeter whose intended use is for respiratory function measurements in the bidirectional air flow range ±9 L/min.The novelty of the proposed sensor consists of a plate beveled in both upstream and downstream sides: a symmetrical geometry is adopted in order to perform bidirectional measurements of flow rate. A mathematical model is introduced to quantify the influence of temperature on the sensor output. Four different positions of the pressure static taps are evaluated in order to maximize bidirectionality. An index is also introduced in order to quantitatively estimate the anti-symmetry of the sensor's response curve.Trials are carried out to evaluate the influence on sensor output of air temperatures (22 °C, 30 °C and 37 °C) at different values of relative humidity (5%, 55% and 85%). Experimental data show a quite good agreement with the theoretical model (R²>0.98 in each condition).The influence of air temperature on the sensor output is minimized by introducing a correction factor based on the theoretical model leading to measurement repeatability better than 2% in overall range of calibration. The mean sensitivity in the calibration range is about 2 kPa L⁻¹·min allowing to obtain a sensor discrimination threshold lower than 0.2 L/min in both directions. The time constant of the whole measurement system, equal to 2.40±0.03 ms, leads to a bandwidth up to 80 Hz making the sensor suitable for respiratory function measurements.     

CFD study of pressure loss characteristics of multi-holed orifice plates using central composite design

The study on the use of multi-holed orifice plate for measuring flow rate is a growing area of research. As compared to standard orifice plate, multi-holed orifice plates (MO) have number of advantages, such as, these plates require minimum straight piping at the upstream without compromising the pressure losses and provide better accuracy in the measurement of flow rates. In this study, a systematic methodology is adopted for investigating the effect of different geometrical parameters on pressure loss coefficient and values of parameters under investigation varied using central composite design. The geometrical parameters chosen for the study are: (a) Number of holes; (b) Multi-hole Diameter ratio and (c) Compactness of holes. Commercial computational fluid dynamics code (ANSYS Fluent) is employed to perform simulations for 15 different settings of these parameters to analyze their effect on pressure loss coefficient and flow development length at downstream of multi-holed orifice plates. It is found that values of pressure loss coefficient is a strong function of multi-hole diameter ratio, whereas, the flow conditioning properties are strongly affected by the number of holes.     

Control of flow around a square cylinder at incidence by using a splitter plate

Passive control of vortex shedding behind a square cylinder at incidence has been conducted experimentally by using a stationary splitter plate for the Reynolds numbers of 3.0×10⁴. The splitter plate was located at the center of the rear face of the square cylinder in tandem. The width of the cylinder and the plate were both chosen to be 30 mm and the incidence angle of the square cylinder was rotated between 0° to 45°. In this study, the combined effects of the splitter plate and angle of incidence on the pressure distributions and vortex-shedding phenomenon were investigated. Vortex shedding frequency was obtained from velocity measurements and aerodynamic force coefficients acted on the cylinder were calculated from pressure distributions. Characteristics of the vortex formation region and location of the flow attachments, reattachments and separation were observed by using the smoke–wire flow visualization technique. For the case with the plate, there is a sudden jump in the Strouhal number in the vicinity of 13° which corresponds to a minimum value of the drag coefficient. At zero angle of incidence, Strouhal number and a drag coefficient of the square cylinder decreased about 20% by means of the splitter plate. Drag reduction was minimum at about 13° and reached its maximum value at about 20°.     

Performance evaluation of an innovative design modification of an orifice meter

This paper evaluates the effect of innovative design modification on the performance of an orifice meter. The orifice meter of 10 mm plate thickness is considered as reference meter and the plate has been modified by changing the surface topology to curvature on both the sides of the orifice plate and the performance has been evaluated using CFD. The performance of the meter is evaluated in terms of coefficient of discharge (C_d) and standard deviation. The study reveals very interesting phenomenon. The newly designed orifice meter has higher discharge coefficient with an improvement of about 22% compared to the reference orifice meter with β-value of 0.6. The performance of the new orifice meter with β-value of 0.6 and radius of curvature of 7.07 mm (2R/d = 0.471) is nearly independent of Reynolds number over the entire range of flow conditions studied (10³ ≤ Re ≤ 10⁶).     

Flow characteristics of back supported V-cone flowmeter (wafer cone) using PIV

The present experimental study has been carried out to evaluate the performance and flow characteristics of the Wafer cone flowmeter using Particle Image Velocimetry (PIV). Two equivalent diameters (β) of 0.62 and 0.72 with combination of two vertex angles (ϕ) namely 30°and 45°are used for the evaluation of the performance of the flowmeter in the range of Reynolds number of 3 × 10³ to 8.19 × 10⁴. The investigation shows that the coefficient of discharge seems to be independent of β-value with the increase in vertex angle. Further, the appropriate location of the downstream pressure tap is also estimated for the cone configuration of β = 0.62 and ϕ = 30°. It is observed that the downstream pressure tap location of 0.8D distance gives a higher value of discharge coefficient compared to 0.0D distance with the error being also lower marginally. PIV data has been analysed for the cone configuration of β = 0.62 and ϕ = 30°at four Reynolds numbers of 3028, 6057, 52755 and 74488 in terms of axial velocity and turbulent intensity. The measurements reveal an interesting phenomenon in terms of the rapid decay of turbulent kinetic energy on the downstream of the cone. This may be due to the interference of the cone wake with the support wake resulting in fast decay. This unique phenomenon leads to the reduction in the requirement of the downstream straight length for the Wafer cone flow meter, unlike other obstruction type flowmeters.     

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.     

节流孔板空化特性分析

管道系统中的各类阀门、文丘里管、孔板等节流件，随系统工作压力和前后压差的增大，会出现气液两相流引起的空化或发生阻塞流，对系统的工作性能和安全造成严重影响。针对以不同规格孔板为代表的节流件，采用理论推导和FLUENT流体力学两相流仿真，结合实验台架所得的空化流动特征，辅以对局部空化气泡的高速微距拍摄结果，提出了斜梯三角形流量曲线以表达节流孔板阻塞流发展变化的全部过程，充分表达了阻塞流发展过程中的局限性特征和阶梯性特征。     

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.     

孔隙高速流动中的气穴观测与噪声特性

为研究阀口高速流动中的旋涡空化机理及其与噪声特性的关系,运用高速摄像、噪声频谱分析等手段对典型阀口孔隙节流处的流场及流动现象进行分析.利用高速摄像机在微距模式下对阀口流场进行观测,最高拍摄速度达120 000幅/s.研究发现空化的产生与流动分离受背压的影响最为明显,进口压力对气穴形态及噪声影响次之;孔口较深时,不同流动参数下气穴初生的位置始终位于节流边与孔壁相交的锐缘区附近,随着阀口开度的变化,初生位置稍有变化.频谱分析同时表明,气穴的形态和尺度是影响噪声的最重要因素之一.     

Analysis of externally pressurized gas-lubricated conical bearings

An analysis is presented of externally pressurized conical gas bearings with discrete point pressure sources in the form of orifices located around the circumference at quarter stations from the end of the bearing. The governing Reynolds equation over the developed bearing area is solved by a direct numerical method to determine the pressure distribution. Numerical results are presented in the form of non-dimensional charts for load capacity, flow rate and stiffness for a conical bearing having L/D_M = 1 and semicone angles from 10° to 40°.     

钟板对液压悬置特性的影响

为揭示钟板数量对液压悬置特性影响,首先,根据液压悬置结构搭建解耦膜、节流盘以及新节流盘液压悬置数学模型,同时分析钟板数量对液压悬置动态特性影响;其次,在高低频状态分析钟板数量对惯性通道、解耦膜通道流量以及上腔压力响应的影响;最后,分析节流盘和新节流盘液压悬置在钟板处的流量和压力响应。计算表明:低频时3种液压悬置的动态特性几乎相同,随着钟板数量增加悬置动态刚度和滞后角略有减小;在节流盘液压悬置的基础上增加钟板不影响解耦膜通道流量和上腔压力响应,但影响悬置的刚度和滞后角。     

Effect of cavosurface angle beveling on the exposure angle of enamel prisms in different cavity sizes

The quality of the micromechanical retention between the enamel prisms exposed through acid etching and adhesive system can be influenced by the relationship between the angle of the exposed enamel prisms and the external surface/restorative material. Therefore, the aim of the present study was to determine the influence of the enamel cavosurface beveling in different cavity sizes on the angle relation between enamel prisms and the restorative material. For this research, 30 human permanent molars were used and divided into three groups according the isthmus aperture of class I cavities (1/4, 1/3, and 1/2 of the intercuspal distance). Cavosurface angle beveling was performed in each tooth buccal or palatal/lingual side, and a resin composite restoration was placed. Each restored tooth was sectioned in buccal/palatal direction followed by analysis in scanning electron microscope. Means of the angles observed between enamel prisms and the restorative material were registered and statistically analyzed by Kruskal‐Wallis test. Results showed higher mean angle values for beveled groups when comparing with the values observed in the unbeveled margins (p < .05) regardless of the isthmus aperture, being 1/4 (beveled = 48.36°; unbeveled = 20.71°), 1/3 (beveled = 39.75°; unbeveled = 29.15°), and 1/2 (beveled = 37.02°; unbeveled = 26.34°). It was also observed that in some unbeveled cavities, there were the presence of laterally exposed enamel prisms (0°), mainly in more conservative cavities. It was concluded that the presence of higher angles values occurred in the samples with beveled margins, without presence of laterally exposed enamel prisms.