Values Of Discharge Coefficient Research Articles

CFD Validation of Incompressible Cross-Flow Discharge Coefficients

Validation against air systems problems is required to enable Computational Fluid Dynamics (CFD) codes to be confidently used in the design of turbine cooling air systems. CFD calculations of orifice cross-flow discharge coefficients (Cd) have been compared with measurements by Rohde et al [1]. Simulations have been carried out for cases with a low main duct Mach number (Md ~ 0.25) using incompressible flow modelling. Comparisons have been made of cross-flow discharge coefficients for a range of pressure-head ratios and Mach numbers. Results at a main duct Mach number of 0.07 were obtained using the standard k-ε.: turbulence model which gave agreement to better than 5% for absolute values of pressure-head ratios and discharge coefficients. The trends in the data for pressure-head ratios and Mach numbers were also reproduced. At a higher main duct Mach number of 0.25, the Mach number in the vicinity of the orifice reached 0.8. As expected this rendered incompressible flow modelling unsuitable, resulting in inaccurate determinations of orifice pressure-drops. Work is already in progress to simulate high Mach number cases using a more suitable compressible flow model. The results obtained so far give confidence that CFD will become a valuable tool for evaluating air system losses in novel configurations.

DISCHAGE COEFFICIENT OF OBLIQUE SIDE WEIRS

An investigation of side-weirs, used as a diversion structures in rivers and canals, is presented. Most commonly, the side-weirs are aligned parallel to the direction of flow in the parent canal, giving an off-take angle, θ of 90 degrees. However, this study investigates performance of oblique side, weirs, that off-takes at an angle less than 90 degrees. Discharge coefficients for oblique weirs are obtained theoretically and experimentally as functions of off-take angle, θ, Fronde number in the parent channel and weir geometry. It is found that a high value of discharge coefficient can be maintained when θ lies between 60and 80 degrees. A side weir with θ equal to 70 degrees is selected for tiuther study with improved frontal apron and approach wall. It is concluded that the value of discharge coefficient can he further increased for a wide range of high Fronde numbers through these improvements.

Direct wind tunnel modelling of natural ventilation for design purposes

The paper describes an investigation into the feasibility of natural ventilation design by means of direct wind tunnel modelling of ventilation rates. The investigation covers the three cases encountered in practice, i.e. wind alone, buoyancy alone and wind and buoyancy combined. The direct determination of ventilation rates from a wind tunnel model is potentially a very powerful tool for natural ventilation design of nondomestic buildings, where the design aim is to specify the size and position of purpose-provided openings. It offers more accuracy in the determination of wind effects than either the indirect use of wind tunnels (where pressure coefficients are measured for use in a mathematical model) or the salt-bath technique. From an analysis of experimental and theoretical results it is concluded that the direct technique is feasible for a wide range of building sizes. Some desirable improvements to the technique have also been identified. Further work is also required to clarify why the observed values of discharge coefficients are larger than might be expected.

Measurements of Discharge Coefficients in Film Cooling

Measurements of discharge coefficients for several film cooling configurations having hole length-to-diameter ratios of 2.3, 4.6, 6.6, and 7.0 are presented. Recently, it was documented that the velocity distributions over the hole exit plane vary significantly with changes in hole length-to-diameter ratio. This paper documents the effects of such variations on coolant discharge coefficients. Due to the short holes, injection in engines is with a substantial amount of coolant departing the upstream portions of the hole exit plane. This results in a higher rate of momentum exchange with the free stream at that location than for longer holes, which permits more uniform exit flows. Discharge coefficient measurements are discussed in terms of this distribution of velocity. This paper also documents the effects of the hole supply plenum geometry on discharge coefficients. When the coolant flow is delivered to the holes with significant momentum either in the direction of the free stream or opposite to that direction, significant changes in discharge coefficient values are observed.

Using an IIST SBLOCA Experiment to Assess RELAP5/MOD3.2

The RELAP5/MOD3.2 code is used at the Institute of Nuclear Energy Research Integral System Test Facility to analyze a 2% cold-leg-break experiment that includes failure of the high-pressure injection system. The assessment code predictions include primary pressure, inventory distribution in the reactor coolant system (RCS), loop flow rate, break flow rate, and core thermal hydraulics. A comparison between the calculated results and the experimental data shows (a) a good match with the predictions of the RCS pressure and hot- and cold-leg fluid temperatures, (b) underprediction of the core and downcomer levels, (c) overprediction of the loop flow rates in single- and two-phase natural circulation, and (d) inadequate prediction of asymmetric coolant holdup in the three steam generators. Also presented are sensitivity studies of choked flow associated with the defaulted values of discharge coefficients in the simulation of the break flow, and of the core bypass area to evaluate the effect of core level depression.

Performance of a tuyère gas distributor

The flow discharge coefficient of tuyere gas distributors with six radial holes was obtained as a function of the tuyere head holes diameter Reynolds number, with the holes to riser flow cross-sectional area ratio as parameter. The fraction of the pressure drop which occurred in the tuyere head holes, a significant parameter for satisfactory operation of a fluidized bed, was also determined. The flow phenomena in the thin-plate standard square-edged orifice meter and in the tuyere discharge holes were studied; the differences in the corresponding discharge coefficient values are discussed in the light of the flow pattern dissimilarities. The possibility of adopting the standard thin-plate square-edged orifice meter or perforated-plate discharge coefficients to calculate the tuyere coefficient was analyzed, as well as the influence of the presence or absence of a solids fluidized bed over the distributor plate.

Numerical and experimental analysis of laminar flow through square-edged orifice with variable thickness

In this work, axisymmetric, viscous, steady, incompressible and laminar flow through square-edged orifices has been studied. A numerical solution of the steady-state vorticity transport equation has been obtained from the two-dimensional Navier-Stokes equations. Finally, streamline patterns, vortex formations and separated flow regions have been predicted. The effects of orifice plate thickness and Reynolds number on the flow characteristics have been investigated numerically and experimentally. The Navier-Stokes equations have also been integrated in order to compute the pressure distributions through the orifice. From these results, the orifice discharge coefficient has been computed and examined as the Reynolds number and the orifice plate thickness were varied. A comparison has been made between the experimental results, the numerical predictions and available experimental results. The predicted flow discharge coefficient values agreed closely with the experimental results.

Flow-Measurement Flumes of Rectangular Compound Cross Section

A series of laboratory experiments were carried out in a flow-measurement flume of a rectangular compound cross section to investigate the effect of the throat width and step height on the values of discharge coefficient, approach-velocity coefficient, and modular limit. For this reason, nine different models made of Plexiglas were tested in a horizontal laboratory flume for a large range of discharges. In each test, the head, h1 , over the crest elevation at depth-measurement section and head, h2 , over the crest elevation in the tailwater channel were measured. The calculated discharge coefficients, modular limits, and approach-velocity coefficients were related to relevant parameters. The consistency between aforementioned quantities and those given in the literature are found to be quite good. Modular limit values as high as 95% are obtained.

Effects of Segmental Obstacles at Inlet Zone on 90.DEG.-Bend Flowmeters.

Discharge coefficients of 90°-bend flometers are affected by factors such as the radius ratio of bend, Reynolds number, secondary flow and bend angle. Effects of segmental obstacles settled in upstream zone of the bend, however, remain to be clarified. This study investigates their effects experimentally, and it may be concluded that when the dimensionless height of the obstacle z/d is in the range of 0.4-0.5, values of discharge coefficients are almost constant, where z is the maximum height of the obstacle, d the inner diameter of the upstream pipe, and the most suitable measuring section is found at a bendangle of θi= 22.5∼33.75°.

Multiphase Flow Metering:An Evaluation of Discharge Coefficients

Abstract The orifice discharge coefficient (CD) is the constant required to correct theoretical flow rate to actual flow rate. It is known that single phase orifice models and methods of prediction of critical flow do not apply to multiphase flow. Thus the questions that must be answered are how do we determine values of discharge coefficient for multiphase flow metering? Can the values of discharge coefficient for critical multiphase flow be used for subcritical flow? Figures, tables and equations of CD are presented with which metered multiphase flow rates can be corrected to obtain actual multiphase flow rates for both critical and subcritical flows. It is shown that CD for multiphase critical flow cannot be the same for multiphase subcritical flow. Introduction Multiphase flow is a complex phenomenon: As a result the majority of published correlations are highly empirical. This affects the general validity of these correlations for all ranges of fluid properties as they are limited to the quality and scope of the data base from which they are developed. Therefore, correlation which performs well within the range of data used to develop it, may fail outside this range. Multiphase flow through restrictions is usually evaluated under critical or subcritical flow conditions. As a standard oilfield practice, wellhead flow performance is evaluated under critical flow while flow performance through subsurface chokes and safety valves is done through subcritical flow. Critical or sonic flow is flow in which downstream pressure and temperature perturbations are not transmitted upstream to affect the flow rate unlike in subcritical flow. Available critical multiphase orifice flow correlations can be categorized as follows(1):Analytical models, applying mathematical analysis based on fundamental principles, to a simplified physical model with the development of equations.Empirical correlations using dimensional analysis to select and group the most important variables.Empirical correlations from field or laboratory data. Examples of category 1 correlations are those of Tangren et al.(2), Ros(3), Poettmann and Beck(4), Ashford(5), a generalized model by Ajienka(6) and Ajienka and Ikoku(7). The simplified form of the generalized model applicable to both continuous liquid phase flow and continuous gas phase flow is given by Equation (1): Equation (1) (Available In Full Paper) where Equation (2) (Available In Full Paper) Equation (3) (Available In Full Paper) Equation (4) (Available In Full Paper) Letting Equation (Available In Full Paper) To be equal to X, then: Equation (5) (Available In Full Paper) Equation (6) (Available In Full Paper) Flow is critical if the pressure ratio (X = Xc) is equal to the critical pressure ratio. Otherwise, flow is subcritical. Ashford's analytical correlation for critical flow is given by: Equation (7) (Available In Full Paper) where Equation (8) (Available In Full Paper) Equation (9) (Available In Full Paper) Equation (10) (Available In Full Paper) While the earlier analytical models assume that critical flow TABLE 1: Empirical coefficients of category 3 correlations. (Available in full paper) Occurs at a constant pressure ratio of 0.554 (for k = 1.04) as with single phase flow, the Ajienka and Ikoku model uses a predicted critical pressure ratio which is realist

An experimental investigation of mass flow characteristics of laval nozzles with transversal injection through an annular slot in the side wall

Measured values of the hydraulic discharge coefficient and the critical mass flowrate are presented. Experiments have been carried out on three Laval nozzles over the following range of flow operating parameters at the inlet of the nozzle: pressure—4 and 8 MPa; water subcooling—from 0 to 50°C; quality of the two-phase mixture—from 0 to 1; and steam superheating—from 0 to 30°C. Transversal injection causes a maximum decrease (30–40%) in the critical mass flowrate at the point corresponding to the discharge of saturated water. Transition from discrete holes to an annular slot in the side wall leads to some increase (up to ∼ 10%) in the critical mass flowrate, while the hydraulic discharge coefficient remains practically constant. The increase in width of the annular slot from 2.57 to 4.59 mm does not cause any systematic change in the transversal injection efficiency. A decrease in length of the cylindrical throat from 156 to 5 mm leads to an increase (∼ 12–20%) in the transversal injection efficiency and to a decrease (∼ 7–12%) in the hydraulic discharge coefficient.

The API/GPA Orifice-Plate Data Base

API and the Gas Processors Assoc. (GPA) have completed a four-year, $1.4 million program to develop a new archival data base for flange tapped orifice coefficients. This paper describes this project and the results to date.

Hydraulics of Perforated Terrace Inlet Risers

ABSTRACT TERRACE inlet risers perforated with circular and slot orifices were tested in the laboratory. The orifice discharge coefficient for a circular orifice in the cylindrical surface of a riser was found to be significantly larger than for a circular orifice in a flat plate. A simple theoretical equation was found to provide good estimates for riser discharge when correct values of discharge coefficient are used. Side orifices should be evenly distributed around the circumference of the riser to reduce vibration.

Results of a comparative in vitro study of Duromedics and Björk-Shiley monostrut mitral heart valve prostheses

Two different mechanical heart valves with annulus diameters 21–29 mm, (five Björk-Shiley monostrut tilting disc valves and five Duromedics bileaflet valves) have been tested in pulsatile flow in the mitral position of a mock circulation. Reflux, pressure, and orifice area have been measured while cardiac output was varied between 2 and 6 1 min −1. Insufficiency, mean orifice area, discharge coefficient, and performance and efficiency indices have been calculated. Mean values of insufficiency for the Björk-Shiley monostrut valves varied between 4.8 and 17.2% while the corresponding values for the Duromedics valves were in the range 6.1–17.3%. Mean values for orifice areas of the Björk-Shiley monostrut valves increased with the larger valve sizes from 101.1 to 210.2 mm 2; for the Duromedics valves the area range was 134.5–262.9 mm 2. Because of the larger orifice areas the values of discharge coefficient and performance index for the Duromedic valves were higher than those for the Björk-Shiley monostrut valves. As the insufficiency of the two mechanical valves was similar, and the orifice area of the bileaflet valves was greater than that of the tilting disc valves, Duromedics valves gave higher values for the efficiency index, which varied between 0.31 and 0.39; for Björk-Shiley monostrut valves the index varied between 0.24 and 0.28 under the same test conditions. This hydrodynamic in vitro comparison of mechanical heart valves showed that the Duromedics bileaflet valves were superior to the Björk-Shiley tilting disc valves.

Measurement of interzonal heat and mass transfer by natural convection

Experiments to measure the interzonal heat and mass transfer were carried out in two full size adjoining rooms under two different conditions. Before starting the tests, one of the rooms was heated to an average temperature of 32°C, while the other room was cooled to an average temperature of 19°C. To start the first type of tests, the auxiliary heating and cooling were turned off and the door blocking the opening opened. For the second test, auxiliary cooling was turned off, while the auxiliary heat was left on in the heated room. Visual observations of the flow phenomenon were made. Velocity and temperature profiles of the air-flow through the opening, and air temperatures in the test rooms were measured. The experimental mass and heat flow rates were computed from the velocity and temperature data and compared with the values predicted by the existing algorithms based on the application of the Bernoulli's equation. The agreement between the measured and predicted values is better for a value of discharge coefficient C = 0.45 than it is for C = 0.611 (the theoretical value of C for a sharp edged orifice quoted in the literature).

Experimental determination of the coefficient of discharge from a channel through perforated walls

Values of discharge coefficient are found for the flow of air from one channel to another through a perforated wall with different dynamic pressures for the flows in both channels.

The effect of disturbed flow conditions on the discharge coefficient of orifice plates

The accurate measurement of flow rate using orifice plates depends upon many factors. One such factor is the condition of the flow in the pipe just upstream of the metering station. The values of discharge coefficient presented in the flow measurement standards are based upon axi-symmetric, fully developed turbulent velocity profiles, with no swirl component. In practice, such ideal flow conditions are very difficult to achieve, because of the effect of various pipe fittings such as bends, tees, and valves upstream of the meter. These fittings distort the velocity profile, and generate secondary flows which are only damped out very slowly by the action of turbulent shear stresses. The aim of this paper is briefly to review the way in which a range of pipe fittings disturb the condition of flow, and then to discuss the ways in which the various classifications of disturbance affect the flow through the orifice plate. From this basic understanding of the physics of the flow field, it is possible to build up a picture of the way in which the discharge coefficient of an orifice plate will be affected in a non-ideal installation, and to appreciate the effect of such variables as the area ratio of the device. The qualitative description given in the paper will be supported and supplemented by reference to an extensive experimental programme being carried out at BHRA Fluid Engineering in conjunction with the National Engineering Laboratory of the Department of Industry, under a Metrology and Standards Requirements Board Contract.

Some Aspects of Quadratic Weirs

The theory of proportional weirs, including the slope discharge continuity theorem, is applied to obtain an excellent solution to the design of a quadratic weir having a compound base. Nine different shaped quadratic weirs were designed and pertinent data for their use are given in enclosed tables. A total of eight weirs with three different shapes were hydraulically tested and results showed consistent discharge coefficient values between 0.607 and 0.610. One particular shape weir was the most sensitive and had the additional advantage of having equal slopes at the junction of the base weir and the upper complimentary weir. The importance of the quadratic weirs as proportional orifices and notch-orifices is stressed and also their usefulness as the most sensitive weirs with the least relative error is underlined.

Slurry flow metering by pressure differential devices

A simple system for measuring slurry concentrations and flow rates by pressure difference devices has been studied. Solids concentrations have been determined by pressure measurements in vertically upwards and downwards sections of the flow, and flow rates measured by a venturi meter located alternately in horizontal, vertically upwards and vertically downwards flows. The venturi performance has been described in terms of a discharge coefficient based on mixture density, and the concentration measurements have been compared to values determined by weigh tank samples. A range of sand slurries with median particle size from 150 to 740μm and an ilmenite slurry with a median particle size of 170μm have been tested. A limited number of tests on a 17μm sand slurry have also been recorded. For fine sand slurries (150μm or below) it was found that the water value of venturi-discharge coefficient applied, so that the accuracy of flow measurements will be limited only by the accuracy of the pressure and specific weight measurements. Experimental values of specific weight from the vertical loop section were on average within 1% of the values from the weigh tank, where the majority of this scatter was caused by the limitations of the weigh tank method. For coarser slurries, the venturi-discharge coefficients depended primarily on solids concentration, with a secondary dependence on Reynolds number, and values were below the water value. An analysis of the flow based on a one-dimensional momentum balance indicated that relative velocity between the phases could account for these low values of discharge coefficient. This was verified by high-speed photography of the flow which suggested a movement of particles towards the centre of the flow at the throat. The overall indications are that the combination of a vertical loop section of flow (for concentration or specific weight measurements) and a venturi meter (for flow rates) provides a simple and accurate means of metering slurry flows. For fine slurries only water calibrations or calibrations from Standards are required.

Steady Compressible Flow through a Single Row of Radial Holes in the Wall of a Pipeline

Measured values of discharge coefficient for air flow through a single row of radial holes in the wall of a pipeline are reported, together with the values of pipe Mach numbers in the immediate vicinity of the holes. A wide range of pressure and area ratios are considered, the flow through the holes being either into or out of the pipe. It is shown that the effects on the measured values of both the pressure level at discharge from the holes and the air temperature are negligible. The agreement between the pressure change in the pipeline due to the holes, obtained experimentally, and that predicted by simple, one-dimensional flow theories is generally unsatisfactory. However, theoretical predictions of the jet efflux angles based on two-dimensional, incompressible, non-viscous flow arguments are in good agreement with those measured, but discrepancies do arise in the prediction of discharge coefficients.