Loss Coefficients for Fluid Meters

1977 ◽  
Vol 99 (1) ◽  
pp. 245-248 ◽  
Author(s):  
R. P. Benedict
Keyword(s):  
Discharge Coefficient ◽  
Generalized Equation ◽  
Differential Pressure ◽  
Loss Coefficient ◽  
Contraction Coefficient ◽  
Loss Parameter ◽  
Loss Coefficients

A generalized equation is derived which describes the loss coefficient for any differential pressure type fluid meter. This loss coefficient is given in terms of dimensionless factors including: meter geometry, discharge coefficient, contraction coefficient, and diffuser efficiency. The equation applies equally well for venturis, nozzles, and orifices, installed in pipes or with plenum inlets. Another equation is derived which relates the previously published ASME loss parameter for fluid meters to this new generalized loss coefficient.

Axial Flow Compressor and Turbine Loss Coefficients: A Comparison of Several Parameters

1972 ◽  
Vol 94 (3) ◽  
pp. 193-201 ◽  
Author(s):  
L. E. Brown
Keyword(s):  
Mach Number ◽  
Test Data ◽  
Axial Flow ◽  
Loss Coefficient ◽  
Low Mach Number ◽  
Loss Parameter ◽  
Loss Coefficients ◽  
Flow Compressor ◽  
Stage Efficiency ◽  
Better Than

Many loss parameters are used in the turbomachinery field for correlating the effects on losses of numerous geometric and aerodynamic variables associated with blade rows. The parameter most common to these correlations is the ratio of a loss parameter to a velocity parameter, here called the loss coefficient. Such loss coefficients of different forms used for compressors by Howell and the NACA and those used for turbines by Ainley and Soderberg, plus an additional one, are compared explicitly for possible use in both compressors and turbines. Over a range of Mach numbers, loss coefficient values are compared with loss levels fixed and for representative blading cascade test data, and pressure recoveries and stage efficiencies are compared with loss coefficient values fixed. It is shown that for a low Mach number the different parameters are equal and interchangeable; however, as the Mach number increases, differences appear and grow larger, so that a given combination of loss coefficient value and Mach number implies different entropy-rise values depending upon which parameter is being used. The criteria used here for comparing the different parameters are that one loss coefficient is better than another a– if its loss coefficient values corresponding to test data vary less over a significant range of Mach number, and b– if the stage efficiency implied by a fixed loss coefficient value varies in a more realistic way over a range of Mach number. The Soderberg parameter was found to be better for both compressors and turbines than the other loss coefficients investigated.

Flow Losses in Abrupt Enlargements and Contractions

1966 ◽  
Vol 88 (1) ◽  
pp. 73-81 ◽  
Author(s):  
R. P. Benedict ◽  
N. A. Carlucci ◽  
S. D. Swetz
Keyword(s):  
Compressible Flow ◽  
Pressure Loss ◽  
Total Pressure ◽  
Loss Coefficient ◽  
Total Pressure Loss ◽  
Constant Density ◽  
Flow Losses ◽  
Loss Parameter ◽  
Loss Coefficients

In this paper, we examine losses associated with compressible and constant-density fluids flowing across abrupt area changes in flow passages. The bases of the conventional constant-density loss coefficients for abrupt enlargements and contractions are first reviewed. A loss parameter based directly on the drop in total pressure is next introduced. Various compressible-flow solutions are then considered. Results are given of new experiments run with air and water flowing across abrupt area changes. The total-pressure-loss parameter is shown to have greater utility and validity than the usual loss coefficient for both compressible and constant-density flows.

A Generalized Discharge Coefficient for Differential Pressure Type Fluid Meters

1974 ◽  
Vol 96 (4) ◽  
pp. 440-448 ◽  
Author(s):  
R. P. Benedict ◽  
J. S. Wyler
Keyword(s):  
Discharge Coefficient ◽  
Pipe Wall ◽  
Reynolds Numbers ◽  
Generalized Equation ◽  
Differential Pressure ◽  
Rational Basis ◽  
Flow Meters ◽  
Type Flow ◽  
New Formulation ◽  
Calibration Laboratories

A generalized rational equation is derived for the discharge coefficient of differential pressure-type fluid meters. Its factors are particularized for throat tap meters, pipe wall tap nozzles, and for orifice-type flow meters. Comparisons are made with available theories and with current Fluid Meter practices, and these support the new formulation. Because of its rational basis, the generalized equation may be useful for extrapolations to Reynolds numbers which lie beyond the capabilities of calibration laboratories.

Impact of Orifice Length/Diameter Ratio on 90 deg Sharp-Edge Orifice Flow With Manifold Passage Cross Flow

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
W. H. Nurick ◽  
T. Ohanian ◽  
D. G. Talley ◽  
P. A. Strakey
Keyword(s):  
Turbulent Flow ◽  
Discharge Coefficient ◽  
Cross Flow ◽  
Head Loss ◽  
Area Ratio ◽  
Loss Coefficient ◽  
Operating Conditions ◽  
Sharp Edge ◽  
Test Facility ◽  
Contraction Coefficient

The available information describing the various stages of flow conditions that occur as the flow transitions from noncavitation to cavitation (turbulent flow), supercavitation, and finally separation in sharp-edge 90 deg orifices is extensive. However, although sharp-edge orifices in cross flow represent a significant number of injection schemes inherent in many applications, data for this configuration are sparse or nonexistent. This study is intended to increase the database and understanding of the driving variables affecting the flow in all of these conditions. Tests were carried out in a unique test facility capable of achieving large variations in back pressure, flowrate, and operating upstream pressure. The configuration and test ranges of this study includes orifice length/diameter ratios from 2 to 10, upstream pressures from 7.03 kg/cm2 to 105.1 kg/cm2, orifice/manifold area ratio of 0.028 to 0.082, and manifold cross flow velocity of from 410 cm/s to 1830 cm/s. The results for these small area ratio configurations support two different first order models, one for cavitation and the other noncavitation both in turbulent flow. Under cavitation conditions the discharge coefficient is related to the contraction coefficient and the cavitation parameter to the 1/2 power. In the noncavitation flow regime the head loss is related to the loss coefficient and the dynamic pressure at the orifice exit. Both the head loss and contraction coefficient were found to be a strong function of the ratio of manifold/orifice exit velocity. Equations are provided defining the relationships that allow determination of the contraction coefficient, discharge coefficient, and head loss between the contraction coefficient, as well as the loss coefficient and operating conditions. Cavitation parameter values for cavitation inception, cavitation, and supercavitation are also provided. The potential flow theory was shown to predict the contraction coefficient when upstream (manifold to vena-contracta) losses are minimal.

Approximation of the discharge coefficient of differential pressure flowmeters using different soft computing strategies

2021 ◽  
Vol 79 ◽  
pp. 101913
Author(s):  
Zhanat Dayev ◽  
Aiat Kairakbaev ◽  
Kaan Yetilmezsoy ◽  
Majid Bahramian ◽  
Parveen Sihag ◽  
...  
Keyword(s):  
Soft Computing ◽  
Discharge Coefficient ◽  
Differential Pressure

Dynamics of matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions and gain or loss effect

2022 ◽  
Author(s):  
Yajie Yang ◽  
Ying Dong
Keyword(s):  
Similarity Transformation ◽  
Soliton Solutions ◽  
Gain Coefficient ◽  
Loss Coefficient ◽  
Matter Wave ◽  
Pitaevskii Equation ◽  
Loss Parameter ◽  
Dynamical Properties ◽  
Bose Einstein ◽  
Loss Effect

Abstract The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross-Pitaevskii equation describing the three-component Bose-Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.

Simulations to Determine Laminar Loss Coefficients for Flow in Circular Ducts With Arbitrary Planar Bifurcation Geometries

2008 ◽  
Author(s):  
Tim A. Handy ◽  
Evan C. Lemley ◽  
Dimitrios V. Papavassiliou ◽  
Henry J. Neeman
Keyword(s):  
Pressure Loss ◽  
Three Dimensional ◽  
Computer Code ◽  
Two Dimensions ◽  
Stagnation Pressure ◽  
Loss Coefficient ◽  
Pressure Losses ◽  
Common Plane ◽  
Loss Coefficients ◽  
Inlet Duct

The goal of this study was to determine laminar stagnation pressure loss coefficients for circular ducts in which flow encounters a planar bifurcation. Flow conditions and pressure losses in these laminar bifurcations are of interest in microfluidic devices, in porous media, and in other networks of small ducts or pores. Until recently, bifurcation geometries had been studied almost exclusively for turbulent flow, which is often found in fluid supply and drain systems. Recently, pressure loss coefficients from simulations of a few arbitrary bifurcation geometries in two-dimensions have been published — the present study describes the extension of these two-dimensional simulations to three-dimensional circular ducts. The pressure loss coefficients determined in this study are intended to allow realistic simulation of existing laminar flow networks or the design of these networks. This study focused on a single inlet duct with two outlet ducts, which were allowed to vary in diameter, flow fraction, and angle — all relative to the inlet duct. All ducts considered in this study were circular with their axes in a common plane. Laminar stagnation pressure loss coefficients were determined by simulating incompressible flow through 475 different geometries and flow condition combinations. In all cases, the flow was laminar in the inlet and outlet ducts with a Reynolds number of 15 in the inlet duct. Simulations of the dividing flow geometries were done using FLUENT and a custom written computer code, which automated the process of creating the three-dimensional flow geometries. The outputs, pressure and velocity distributions at the inlet and outlets, were averaged over the circular ducts and then used to calculate pressure loss coefficients for each of the geometries and flow fraction scenarios simulated. The results for loss coefficient for the geometries considered ranged from 2.0 to 70. The loss coefficient for any geometry increased significantly as the outlet flow fraction increased. A consistent increase in loss coefficient was also observed as a function of decreasing outlet duct diameter. Less significant variation of the loss coefficient was observed as a function of the angles of the outlet ducts.

Computational Fluid Dynamics Analysis of Cooling Tower Inlets

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
H. C. R. Reuter ◽  
D. G. Kröger
Keyword(s):  
Cooling Tower ◽  
Flow Patterns ◽  
Full Scale ◽  
Loss Coefficient ◽  
Cooling Towers ◽  
Cfd Model ◽  
Shell Wall ◽  
Natural Draft ◽  
Flow Losses ◽  
Loss Coefficients

Cooling tower inlet losses are the flow losses or viscous dissipation of mechanical energy affected directly by the cooling tower inlet design, which according to the counterflow natural draft wet-cooling tower performance analysis example given in Kröger (Kröger, 2004, Air-Cooled Heat Exchangers and Cooling Towers: Thermal-Flow Performance Evaluation, Pennwell Corp., Tulsa, OK), can be more than 20% of the total cooling tower flow losses. Flow separation at the lower edge of the shell results in a vena contracta with a distorted inlet velocity distribution that causes a reduction in effective fill or heat exchanger flow area. In this paper, a two-dimensional (axi-symmetric) computational fluid dynamic (CFD) model is developed using the commercial CFD code ANSYS FLUENT, to simulate the flow patterns, loss coefficients and effective flow diameter of circular natural draft cooling tower inlets under windless conditions. The CFD results are compared with axial velocity profile data, tower inlet loss coefficients and effective diameters determined experimentally by Terblanche (Terblanche, 1993, “Inlaatverliese by Koeltorings,” M. Sc. Eng. thesis, Stellenbosch University, Stellenbosch, South Africa) on a cylindrical scale sector model as well as applicable empirical relations found in Kröger, determined using the same experimental apparatus as Terblanche. The validated CFD model is used to investigate the effects of Reynolds number, shell-wall thickness, shell wall inclination angle, fill loss coefficient, fill type, inlet diameter to inlet height ratio and inlet geometry on the flow patterns, inlet loss coefficient and effective diameter of full-scale cooling towers. Ultimately, simple correlations are proposed for determining the cooling tower inlet loss coefficient and inlet effective flow diameter ratio of full-scale cooling towers excluding the effect of rain zones and the structural supports around the cooling tower entrance.

Generalization of Experimental Data for Compressor Cascades at Low Speeds

1970 ◽  
Author(s):  
V. S. Beknev
Keyword(s):  
Experimental Data ◽  
Pressure Distribution ◽  
Loss Coefficient ◽  
Two Dimensional ◽  
Minimum Loss ◽  
Maximum Value ◽  
Isentropic Exponent ◽  
Loss Coefficients ◽  
Low Speeds ◽  
Drag Ratio

The author compares three different approaches for generalization of experimental data for two-dimensional compressor cascades at low speeds: generalization for maximum value of lift-drag ratio, generalization for maximum cascade quality, and generalization for minimum loss coefficient. Some results given, of comparison for incidence and deviation angles, solidities, and loss coefficients, show the largest difference to be for incidence angles and loss coefficients. Influence of isentropic exponent on the airfoil pressure distribution and cascade losses is considered.

Contraction/Expansion Effects in 90° Miter Bends in Rectangular Xurographic Microchannels

2011 ◽  
Author(s):  
Lam Nguyen ◽  
John Elsnab ◽  
Tim Ameel
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Area Ratio ◽  
Loss Coefficient ◽  
Sidewall Roughness ◽  
Cross Sectional ◽  
Loss Coefficients ◽  
Minor Losses ◽  
High Reynolds ◽  
Reported Data

Xurography is an inexpensive rapid prototyping technology for the development of microfluidic systems. Imprecision in the xurographic tape cutting process can result in undesired changes in channel dimensions near features that require a change in cutting direction, such as 90° miter bends. An experimental study of water flow in rectangular xurographic microchannels incorporating 90° miter bends with different channel widths in each leg is reported. A set of twelve microchannels, with channel depth approximately 105 micrometers and aspect ratio ranging from 0.071 to 0.435, were fabricated from double-sided adhesive Kapton® polyimide tape and two rectangular glass plates. The channels were reinforced with a mechanical clamping system, enabling high Reynolds number, Re, flows (up to Re = 3200) where Re was based upon hydraulic diameter and average velocity. Reported data include friction factor and critical Reynolds number for straight microchannels and loss coefficients for flow through 90° miter bends that contain either a contraction or expansion with cross-sectional area ratios of 0.5, 0.333 and 0.2. The critical Reynolds number, Recr, ranged from 1750 to 2300 and was found to be dependent on channel defects such as sidewall roughness, adhesive droplets, and corner imperfections. Loss coefficients through 90° miter bends with expansion decrease rapidly for Re < Recr. At the transition, the loss coefficient suddenly drops and approaches an asymptotic value for Re > Recr. For 90° miter bends with contractions, loss coefficients gradually decrease with increasing Re for 150 < Re < 1400. In addition, the loss coefficient decreases with decreasing area ratio through the contraction or expansion. The minor loss coefficient data were found to be dependent on Reynolds numbers and area ratio of contraction/expansion at the bend. The results suggest that the effect of the contraction/expansion was the dominant mechanism for minor losses in the 90° miter bend.

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