Effect of compressibility on the discharge coefficient of orifices and. The discharge coefficient is a dimensionless number used to characterise the flow and pressure loss behaviour of nozzles and orifices in fluid systems. Additionally, the discharge coefficient of this orifice was determined to be 0. The accurate prediction of the compressible nozzle flows is still challenging for the. Nozzle geometry variations on the discharge coefficient.
I am trying to determine the discharge coefficient of a restrictor geometry. As the flow approaches the critical regime local sonic condition, measurements diverge from the theoretical result due to the nononedimensionality of the flow. Among their major conclusions were that discharge coefficients for the flared holes is higher than that for cylindrical holes, and external cross flow up to a mach number of 0. Pdf discharge coefficients for compressible flow through small. The discharge coefficient for knifeedge orifices correlates very well with a dimensionless pressure drop for the entire range of diameters, gases, pressures and temperatures studied. Analysis of compressible and incompressible flows through see. Q is the flow rate through the meter and through the pipe, in cfs for u. Flow coefficient gpm p sg specific gravity qa actual flow gpm p actual pressure drop p 1p 2 psi where. The bigger the cv, the more flow a valve can pass with a given pressure drop. An investigation of steady compressible flow through.
To find the coefficient of discharge for orifice meter. To find the coefficient of discharge for venturi meter. The discharge coefficient cd relates the actual mass flow rate to the theoretical. Orifice sizing principles chemical engineering now. An orifice plate is a thin plate with a hole in it, which is usually placed in a pipe.
Discharge coefficients for incompressible noncavitating flow through long orifices a. These approximations are then compared to obtain the most probable representation of asme flow nozzle data according to a mathematical method developed in the paper. These pressures normally refer to values in perhaps notional plenums at the entrance and exit of a duct or a system fitting such as a valve. Pdf a novel method to determine the discharge coefficient of. The discharge coefficients were correlated with a velocity head parameter which consisted of the ratio of the velocity head of the flow through the orifice to the velocity head of the flow approaching the orifice axis for various approach mach numbers.
They compared results of axial velocity and pressure gradient results for three interpolation schemes firstorder. The data have been reduced for correlation purposes to a discharge coefficient defined as the fraction of the isentropic, adiabatic mass flow rate attained by real. The properties of the flow at each point in the venturi throat are now known for operation of the venturi at critical flow conditions. Ugarte mechanical, industrial and manufacturing engineering department, northeastern university, boston, ma 02115, usa diffusionshaped. Devices with a lower coefficient of discharge may not necessarily have a lower permanent loss for the same flow. All of the other parameters are the same as defined above. What is the relationship between the flow coefficient c v and the discharge coefficient c d by jeff sines, senior product engineer, engineered software, inc. From numerous experimental and theoretical studies, the slip ratio, s, has been determined to range from s 1. In 1940, medaugh and johnson 3 return to judd and kings experiment and mea. The value of the ratio of pressure at which maximum flow is obtained varies somewhat depending on the actual fluid. Flow coefficients cv values the valve flow coefficient cv is a number which represents a valves ability to pass flow.
In order to examine the effect of flow parameter such as mach number at nozzle exit on the discharge coefficient, the computed profiles of sonic lines for cylindrical, conical convergent nozzles and divergent orifices are illustrated in figure 7a, b and c, respectively. When a fluid whether liquid or gaseous passes through the orifice, its pressure builds up slightly upstream of the orifice. Venturi meter and orifice meter are the commonly used flow meters for measuring massvolumetric flow rate or velocity of the flowing fluid. Relationship between flow coefficient and discharge coefficient. Determining the coefficient of discharge for a draining container. Discharge coefficients for compressible flow through small. Modeling compressible air flow in a charging or discharging vessel and assessment of polytropic exponent abstract in this work, the classic problem of chargi ng and discharging of a pressurized tank is studied. The certifications are based on isentropic ideal nozzle flow equations for incompressible flow of water and compressible flow of air and steam. The work was motivated by inaccurate estimation of egr flow and volumetric efficiency during the turbocharger lag period, based on constant discharge coefficient c d assumption at high reynolds numbers re d. Brahma i 2019 measurement and prediction of discharge coefficients in highly compressible pulsating flows to improve egr flow estimation and modeling of engine flows. Markland journal of mechanical engineering science 1965 7.
A venturi contour designed specifically for use at critical flow conditions is described, and a theoretical method is presented for determining the discharge coefficient of this venturi. Orifices and nozzles are typically used to deliberately reduce pressure, restrict flow or to measure flow rate. Pdf this paper presents a study of the compressibleflow behavior of light gases through small orifices and convergent nozzles with. Most probable discharge coefficients for asme flow nozzles. Discharge coefficients for compressible flow 1699 vi fig. In a nozzle or other constriction, the discharge coefficient also known as coefficient of discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge, i. Methods exist for determining the coefficient of discharge as a function of the reynolds number. Certified prv discharge coefficient values are reported in the pressure relief device certifications, nb18 1 from the national board of boiler and pressure vessel inspectors. The discharge coefficient does not correlate with the throat reynolds number for compressible flow. Previous studies of orifice discharge coefficients with the approachingflow perpen dicular to the orifice axis.
Discharge coefficients for compressible flow 1703 rf. In a nozzle or other constriction, the discharge coefficient is the ratio of the actual discharge to the theoretical discharge, i. An experimental investigation was conducted to determine. The discharge coefficient differs from unity due to the nonuniformity of flow parameters such as mach number at the nozzle exit and presence of boundary layer viscous effect. Discharge coefficients for incompressible noncavitating. Discharge coefficients for compressible flow through smalldiameter. Discharge coefficients for thick plate orifices with approach flow. Predictionof discharge coefficient of venturimeter at low. The widely used flow meters in the industries are orifice meter, venturimeter and pitot tube.
This occurs when the flow becomes sonic and the flow. The computed discharge coefficients for cylindrical, conical convergent nozzles and conical divergent orifices are plotted against the radius of curvatures r, convergent angles. Venturimeter and orifice meter are more convenient and. On the flow of a compressible fluid through orifices. Discharge coefficient measurements for flow through compound. The discharge coefficient of the tooth in a single cavity labyrinth seal was equivalent to that in a multiple tooth labyrinth seal indicating that flow downstream had negligible effect on the discharge coefficient. Could the reason possibly be, that cfx assumes a constant cp. The discharge coefficient does not correlate with the throat reynolds number for compressible flow through knifeedge orifices. Throughout the subsequent analysis of compressible flows the effect of friction will be neglected, it being recognized that the. Proper use of conventional prv discharge coefficients. Modeling compressible flow through an orifice 5 june 23, 2010 applied flow technology 2955 professional place, colorado springs, co 80904 usa 719 686 fax 719 6861001. Their experiment, while not exactly the same as judd and king, showed that the discharge coefficient is a function of the flows exit velocity through the orifice, especially for reynolds numbers between 1 and 10,000.
Pdf discharge coefficients for compressible flow through. Moreover, an analogous behavior of the discharge coefficient for larger. The discharge coefficient for compressible and incompressible flows depended only on the reynolds number based on clearance. In the range of reynolds numbers between 10 4 and 10 5 the dimensionless mass flow, g mt 0 12 d 2 p o, and the coefficient of discharge, c d, are independent of the reynolds number. Good communication between various groups involved with fluid piping systems is critical for the proper design, operation, and determination of cost for many systems in residential, commercial, and industrial applications. Fm 308 flow measurement by venturi and orifice meter.
This paper presents the cfd analysis that was carried out to verify the flow through venturi meter and the discharge coefficient determined by the experiment using dry gas. Fm 308 flow measurement by venturi and orifice meter objectives. A new theory for the compressible flow through an orifice is presented which provides a significant advance over the approach currently employed. Compressible flow through a twodimensional slit pdf free.
An investigation of the coefficient of discharge of liquids through small round orifices by w. Compressible flow on completion of this tutorial you should be able to define entropy derive expressions for entropy changes in fluids derive bernoullis equation for gas derive equations for compressible isentropic flow derive equations for compressible isothermal flow solve problems involving compressible flow. Nozzle geometry variations on the discharge coefficient core. A cv of 1 means a valve will pass 1 gallon per minute gpm of 60of water with a pressure drop. Discharge coefficients of squareedged orifices for measuring. Particularly annular seals are one of the most widely used in. Engsoft that an orifice does not exhibit a maximum flow at a critical pressure ratio is reflected in other sources as well. How can i set the cp of air to a polynomial in cfx. Seals are basic mechanical devices used in machinery to avoid undesired flow losses of working fluids. This experiment allows students to ga in a deeper understanding of polytropic processes and compressible flows.
Introduction throughout industry and research critical orifices are used to regulate gas flow rates by setting an upper limit to the volumetric flow rate. Measurement and prediction of discharge coefficients in. The discharge coefficient, c, will be less than one, because the actual pipemeter flow rate will be less than the. The venturi discharge coefficient is then simply the product of 0. In 1962, hal implemented a power series solution to the axisymmetric compressible po tential flow equation to determine an analytical expression. Modeling compressible air flow in a charging or discharging. Twophase critical flow using moody equilibrium flow model refs. It has been known for some time that when a gas flows through an orifice the coefficient of discharge increases as the ratio of the downstream pressure to the. Discharge coefficients of squareedged orifices for. Iftheflowofairis not perfectly steady,thecapacity between the orifice and theflow nozzle on theend of the line introducesatime lag, sothat, though the.
I ran the calculation in cfx, and got the mass flow rate equivalent to a cd of 1. The experiment is divided into three distinct parts. The wide variation of discharge coefficients for a squareedged orifice in highly compressible pulsating flow was investigated and characterized by dimensionless groups. Discharge coefficient for nozzles and orifices neutrium. On the compressible flow through an orifice journal of. The discharge coefficient for knifeedge orifices correlates very well with a.
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