A Theory of Sharp-Edged Orifices

1937 ◽  
Vol 4 (2) ◽  
pp. A53-A54
Author(s):  
W. E. Howland

Abstract The author presents a figure in which the coefficient of discharge Cd, velocity Cv, and contraction Cc determined by several investigators are plotted logarithmically as points against Reynolds’ numbers. Curves for the coefficients drawn by the author, based on theoretical considerations, show good agreement with the experimental data, thus throwing some light upon the basic phenomena of the discharge of sharp-edged orifices. The variation of the coefficient of discharge of a circular orifice as a function of the Reynolds number is explained as a purely viscous phenomenon for low Reynolds numbers, and by means of a momentum analysis for higher speeds. The analysis presented by the author leads to the development of several formulas for the discharge coefficient, which formulas are in fair agreement with experimental results.

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Noriyuki Furuichi ◽  
Kar-Hooi Cheong ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
...  

The throat tap nozzle of the American Society of Mechanical Engineers performance test code (ASME PTC) 6 is widely used in engineering fields, and its discharge coefficient is normally estimated by an extrapolation in Reynolds number range higher than the order of 107. The purpose of this paper is to propose a new relation between the discharge coefficient of the throat tap nozzle and Reynolds number by a detailed analysis of the experimental data and the theoretical models, which can be applied to Reynolds numbers up to 1.5 × 107. The discharge coefficients are measured for several tap diameters in Reynolds numbers ranging from 2.4 × 105 to 1.4 × 107 using the high Reynolds number calibration rig of the National Metrology Institute of Japan (NMIJ). Experimental results show that the discharge coefficients depend on the tap diameter and the deviation between the experimental results and the reference curve of PTC 6 is 0.75% at maximum. New equations to estimate the discharge coefficient are developed based on the experimental results and the theoretical equations including the tap effects. The developed equations estimate the discharge coefficient of the present experimental data within 0.21%, and they are expected to estimate more accurately the discharge coefficient of the throat tap nozzle of PTC 6 than the reference curve of PTC 6.


1980 ◽  
Vol 101 (2) ◽  
pp. 257-279 ◽  
Author(s):  
S. C. R. Dennis ◽  
S. N. Singh ◽  
D. B. Ingham

The problem of determining the steady axially symmetrical motion induced by a sphere rotating with constant angular velocity about a diameter in an incompressible viscous fluid which is at rest at large distances from it is considered. The basic independent variables are the polar co-ordinates (r, θ) in a plane through the axis of rotation and with origin at the centre of the sphere. The equations of motion are reduced to three sets of nonlinear second-order ordinary differential equations in the radial variable by expanding the flow variables as series of orthogonal Gegenbauer functions with argument μ = cosθ. Numerical solutions of the finite set of equations obtained by truncating the series after a given number of terms are obtained. The calculations are carried out for Reynolds numbers in the range R = 1 to R = 100, and the results are compared with various other theoretical results and with experimental observations.The torque exerted by the fluid on the sphere is found to be in good agreement with theory at low Reynolds numbers and appears to tend towards the results of steady boundary-layer theory for increasing Reynolds number. There is excellent agreement with experimental results over the range considered. A region of inflow to the sphere near the poles is balanced by a region of outflow near the equator and as the Reynolds number increases the inflow region increases and the region of outflow becomes narrower. The radial velocity increases with Reynolds number at the equator, indicating the formation of a radial jet over the narrowing region of outflow. There is no evidence of any separation of the flow from the surface of the sphere near the equator over the range of Reynolds numbers considered.


2010 ◽  
Vol 646 ◽  
pp. 415-439 ◽  
Author(s):  
HARISH N DIXIT ◽  
RAMA GOVINDARAJAN

A vortex placed at a density interface winds it into an ever-tighter spiral. We show that this results in a combination of a centrifugal Rayleigh–Taylor (CRT) instability and a spiral Kelvin–Helmholtz (SKH) type of instability. The SKH instability arises because the density interface is not exactly circular, and dominates at large times. Our analytical study of an inviscid idealized problem illustrates the origin and nature of the instabilities. In particular, the SKH is shown to grow slightly faster than exponentially. The predicted form lends itself for checking by a large computation. From a viscous stability analysis using a finite-cored vortex, it is found that the dominant azimuthal wavenumber is smaller for lower Reynolds number. At higher Reynolds numbers, disturbances subject to the combined CRT and SKH instabilities grow rapidly, on the inertial time scale, while the flow stabilizes at low Reynolds numbers. Our direct numerical simulations are in good agreement with these studies in the initial stages, after which nonlinearities take over. At Atwood numbers of 0.1 or more, and a Reynolds number of 6000 or greater, both stability analysis and simulations show a rapid destabilization. The result is an erosion of the core, and breakdown into a turbulence-like state. In studies at low Atwood numbers, the effect of density on the inertial terms is often ignored, and the density field behaves like a passive scalar in the absence of gravity. The present study shows that such treatment is unjustified in the vicinity of a vortex, even for small changes in density when the density stratification is across a thin layer. The study would have relevance to any high-Péclet-number flow where a vortex is in the vicinity of a density-stratified interface.


1960 ◽  
Vol 82 (3) ◽  
pp. 729-733 ◽  
Author(s):  
M. Bogema ◽  
P. L. Monkmeyer

Tests have been conducted to determine the usefulness of the quadrant edge orifice as a fluid-metering device for low Reynolds number flow. As a result of numerous laboratory tests to determine the behavior of the discharge coefficient with changing Reynolds number, the following are discussed: The range of constant discharge coefficient, reproducibility of orifice plates, diameter ratio effects, upstream roughness effects, reinstallation effects, and effects of pressure tap location.


1965 ◽  
Vol 180 (1) ◽  
pp. 331-356 ◽  
Author(s):  
L. J. Kastner ◽  
J. C. McVeigh

In view of the importance of accurate measurement of flow rate at low Reynolds numbers, there have been numerous attempts to develop metering devices having constant discharge coefficients in the range of pipe Reynolds numbers between about 3000 and 200 and even below this latter value, and some of these attempts have achieved a reasonable degrees of success. Nevertheless, some confusion exists regarding the dimensions and range of utility of certain designs which have been recommended and further information is necessary in order that the situation may be clarified. The aims of the present investigation, which is believed to be wider in scope than any published in this field in recent years, were to review and correlate existing knowledge and to make an experimental study of the properties of various types of orifice in the low range of Reynolds numbers. Arising from this it was hoped that a design might be evolved which not only had a satisfactorily constant discharge coefficient throughout the range but was also simple to manufacture and reproduce, even for small orifice diameters of the order of 0.5 in or less, and it is believed that some success in attaining this aim was achieved. The first section of the paper contains a review of previous investigations classified into three main groups. In the second part of the paper, experiments with various types of orifice plate are described and it is shown that a properly proportioned single-bevelled orifice has as good a performance in the low Reynolds number range as that of any of the more complicated shapes.


1962 ◽  
Vol 84 (4) ◽  
pp. 415-418 ◽  
Author(s):  
Marvin Bogema ◽  
Bradford Spring ◽  
M. V. Ramamoorthy

Quadrant edge orifices offer constant discharge coefficients to much lower Reynolds numbers than do sharp edge orifices, nozzles, or venturi meters. Published results show different values for the lower limit of constancy. This paper presents experimental results which indicate that at flows below pipe Reynolds number of 4000 the discharge coefficient variation is related to the degree of velocity profile development in the upstream meter run.


Author(s):  
Noriyuki Furuichi ◽  
KarHooi Cheong ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
...  

The high accurate throat tap flow nozzle with four different diameter taps is developed and its discharge coefficients are measured in the Reynolds number range from 1.5×106 to 1.4×107 using the high Reynolds calibration facility of AIST,NMIJ. The discharge coefficient of a throat tap nozzle extrapolated according to ASME PTC 6 are confirmed to deviate 0.37% at Red=1.4×107 from the experimental results. The high accurate flow nozzle developed can reduce this extrapolation error of the discharge coefficient to high Reynolds numbers by using the equations of discharge coefficients, which is determined as a function of Reynolds number and tap diameter based on the experimental results of four different diameter taps. The error of extrapolated discharge coefficient using the derived equations is estimated to be less than 0.1% at Red=1.4×107. The present results show that the throat tap flow nozzle developed is expected to work as a high accurate flowmeter even under the extrapolation of the discharge coefficient toward high Reynolds numbers.


Author(s):  
Tim Burdett ◽  
Jason Gregg ◽  
Kenneth Van Treuren

The standard of living throughout the world has increased dramatically over the last 30 years and is projected to continue to rise. This growth leads to an increased demand on conventional energy sources, such as fossil fuels. However, these are finite resources. Thus, there is an increasing demand for alternative energy sources, such as wind energy. Much of current wind turbine research focuses on large-scale (>1 MW), technologically-complex wind turbines installed in areas of high average wind speed (>20 mph). An alternative approach is to focus on small-scale (1–10kW), technologically-simple wind turbines built to produce power in low wind regions. While these turbines may not be as efficient as the large-scale systems, they require less industrial support and a less complicated electrical grid since the power can be generated at the consumer’s location. To pursue this approach, a design methodology for small-scale wind turbines must be developed and validated. This paper addresses one element of this methodology, airfoil performance prediction. In the traditional design process, an airfoil is selected and published lift and drag curves are used to optimize the blade twist and predict performance. These published curves are typically generated using either experimental testing or a numeric code, such as PROFIL (the Eppler Airfoil Design and Analysis Code) or XFOIL. However, the published curves often represent performance over a different range of Reynolds numbers than the actual design conditions. Wind turbines are typically designed from 2-D airfoil data, so having accurate airfoil data for the design conditions is critical. This is particularly crucial for small-scale, fixed-pitched wind turbines, which typically operate at low Reynolds numbers (<500,000) where airfoil performance can change significantly with Reynolds number. From a simple 2-D approach, the ideal operating condition for an airfoil to produce torque is the angle of attack at which lift is maximized and drag is minimized, so prediction of this angle will be compared using experimental and simulated data. Theoretical simulations in XFOIL of the E387 airfoil, designed for low Reynolds numbers, suggest that this optimum angle for design is Reynolds number dependent, predicting a difference of 2.25° over a Reynolds number range of 460,000 to 60,000. Published experimental data for the E387 airfoil demonstrate a difference of 2.0° over this same Reynolds number range. Data taken in the Baylor University Subsonic Wind Tunnel for the S823 airfoil shows a similar trend. This paper examines data for the E387 and S823 airfoils at low Reynolds numbers (75,000, 150,000, and 200,000 for the S823) and compares the experimental data with XFOIL predictions and published PROFIL predictions.


2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.


Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 216
Author(s):  
Emanuel A. R. Camacho ◽  
Fernando M. S. P. Neves ◽  
André R. R. Silva ◽  
Jorge M. M. Barata

Natural flight has consistently been the wellspring of many creative minds, yet recreating the propulsive systems of natural flyers is quite hard and challenging. Regarding propulsive systems design, biomimetics offers a wide variety of solutions that can be applied at low Reynolds numbers, achieving high performance and maneuverability systems. The main goal of the current work is to computationally investigate the thrust-power intricacies while operating at different Reynolds numbers, reduced frequencies, nondimensional amplitudes, and mean angles of attack of the oscillatory motion of a NACA0012 airfoil. Simulations are performed utilizing a RANS (Reynolds Averaged Navier-Stokes) approach for a Reynolds number between 8.5×103 and 3.4×104, reduced frequencies within 1 and 5, and Strouhal numbers from 0.1 to 0.4. The influence of the mean angle-of-attack is also studied in the range of 0∘ to 10∘. The outcomes show ideal operational conditions for the diverse Reynolds numbers, and results regarding thrust-power correlations and the influence of the mean angle-of-attack on the aerodynamic coefficients and the propulsive efficiency are widely explored.


Sign in / Sign up

Export Citation Format

Share Document