Discharge Coefficients For Flow Research Articles

Evaluation of discharge coefficients for bottom rack flow under constant and variable specific energy

ABSTRACT Bottom racks are widely used in mountainous regions as intake structures for diverting water from the mainstream for different purposes. Most of the studies on bottom rack flow consider the concept of invariant specific energy. The present study experimentally investigates the specific energy loss in horizontal transverse bottom rack flow for Froude number varying from 0.1 to 1.5, discharge from 0.010 m3/s to 0.076 m3/s, spacing between bars varying from 0.004 m to 0.028 m and parameter (a/L) varying from 0.041 to 0.102. Experimental investigations suggest that the specific energy loss cannot be neglected in the bottom rack flow. Variation of specific energy loss with Froude number indicates its dependence on flow and rack geometry parameters. Based on the regression analysis of experimental data, the expressions developed for the discharge coefficient ‘C1ʹ for the constant specific energy approach are evaluated. The study also developed expressions for the discharge coefficient ‘C2ʹ, for variable specific energy. Significant agreement between observed and computed discharge based on developed ‘C2ʹ establishes the efficacy of developed expressions.

Numerical modelling of trapezoidal weir flow with RANS, LES and DES models

The characteristics of the trapezoidal weir flow are measured using a one-dimensional laser Doppler anemometer for two different flow conditions. The governing equations of the flow are solved using Standard k–e, Realizable k–e, Modified k–ω and Reynolds Stress Model based on the Reynolds-Averaged Navier–Stokes Equations and by Large Eddy and Detached Eddy Simulations. ANSYS-Fluent package program is used for the numerical analysis of flow with the same experimental conditions. The free surface of the trapezoidal weir flow is computed by the volume of fluid method. The effect of the selected grid structure on the numerical results is examined by Grid Convergence Index. Moreover, two-dimensional (2D) and three-dimensional (3D) analyses of the trapezoidal weir flow are included to estimate the effects of side walls. Experimental results of the velocity field and free surface profiles are compared to the numerical results of 2D and 3D simulations for the validation purposes. From the comparisons it is concluded that the Reynolds Stress Model estimates the flow field more accurately compared with those of the other models used in the present study. Furthermore, the flow characteristics such as turbulence kinetic energy, energy spectrum and pressure distributions for different flow rates are presented. Lastly, the discharge coefficients for different flow–weir configurations are compared experimentally and numerically.

Numerical Study on Performance Characteristics of Multihole Orifice Plate

The multi-hole orifice plate is one of the effective devices for measuring flow rate accurately. In this study, an experimental and numerical investigation of the flow characteristics behavior caused by a water flow through a multi-hole orifice configuration is reported. A circular centered single hole orifice and a multi-hole orifices are used for the test. Orifices of interest for present study have an area ratio of 0.36, the equivalent diameter ratio of 0.6 and number holes 9, 16 and 25. Discharge coefficients for flow through multi-hole orifices are evaluated. Parameters investigated were the number of holes, orifice pressure drop and Reynolds number. In the present work, k-ε turbulence model has been used to predict velocity fields, pressure loss and discharge coefficient around this device. Advantages gained by using multiple holes in an orifice plate instead of a single hole are discussed. It is shown that number of holes, orifice diameter and aspect ratio influences the discharge coefficients. Tests were conducted under laboratory conditions. The experimental results were compared with numerical modeling and appropriate conclusions are discussed.

G508 シェルアンドチューブ型熱交換器における管・バッフル漏れ流れ(GS5-2 内部流,一般セッション)

An experimental study has been made of the baffle-tube leakage in shell-and-heat exchangers. The discharge coefficients for flow through the multiple annular orifices are same as pressure coefficient for flow through a single annular orifice at Z=29 (Z: orifice shape factor). In the case of Z=67, the discharge coefficients are unsuitable.

Discharge Coefficient for a Water Flow through a Bottom Orifice of a Conical Hopper

Discharge coefficients for water flow through a vertical, circular orifice at the bottom of a conical hopper were experimentally studied in the present paper. The conical hopper consists of a cylindrical hopper of inside diameter of 48 cm and a bottom cone of side slope of 45°. Experiments were carried out under different orifice diameters and water heads. The dependence of the discharge coefficient on the orifice diameter and water head was analyzed, and then an empirical relation was developed by using a dimensional analysis and a regression analysis. The results show that the larger orifice diameter or higher water head have a smaller discharge coefficient and the orifice diameter plays more significant influence on the discharge coefficient than the water head does. The discharge coefficient of water flow through a bottom orifice is larger than that through a sidewall orifice under the similar conditions of the water head, orifice diameter, and hopper size.

Discharge coefficients for flow through holes normal to a rotating shaft

A possible design for a more compact gas turbine engine uses contra-rotating high pressure (HP) and intermediate pressure (IP) turbine discs. Cooling air for the IP turbine stages is taken from the compressor and transferred to the turbine stage via holes in the drive shaft. The aim of this work was to investigate the discharge coefficient characteristics of the holes in this rotating shaft, and, in particular, to ascertain whether the sense of rotation of the shaft with respect to the discs affected these significantly. This paper reports mostly on experimental measurements of the discharge coefficients. Some CFD modelling of this flow was carried out and this has helped to explain the experimental work. The experimental results show the effects on the discharge coefficient of rotational speed, flow rate, and co- and contra-rotations of the shaft relative to the discs. The measured values of the discharge coefficient are compared with established experimental data for non-rotating holes in the presence of a cross-flow. For stationary shaft and discs, co-rotation of the shaft and discs and differential rotation with the disc speed less than the shaft (in the same rotational direction), the discharge coefficients are in reasonable agreement with these data. For differential rotation (including contra-rotation) with the disc speed greater than the shaft, there is a significant decrease in discharge coefficient.

Characteristics of flow through small sharp-edged cylindrical orifices

The discharge coefficients for flow through small sharp-edged cylindrical orifices of diameters between 0.3 and 2 mm and aspect ratios between 1 and 50 are evaluated. The characteristics of flow in the separated, attached and cavitated flow regions are determined. It is shown that while the discharge coefficient scales with the Reynolds number and aspect ratio in the attached flow regions, the diameter influences the discharge coefficient in the separated flow region. The onset of cavitation in the orifice is also seen to be dependent on the diameter and aspect ratio. The hysteresis in the flow and the violent disintegration of the jet observed for an aspect ratio of about 5 are discussed.

Discharge coefficients for compressible flow through small-diameter orifices and convergent nozzles

This paper presents a study of the compressible-flow behavior of light gases through small orifices and convergent nozzles with diameters ranging from 0.9 to 1.9 mm. The subsonic and critical-flow regions for 16 orifice and nozzle flow elements with the following geometries have been tested experimentally: sharp or knife-edge orifices, straight-bore orifices, rounded-entry nozzles, and elliptical-entry nozzles. Air flow was primarily studied, but data for carbon dioxide, argon, helium, and two distinct argon-helium mixtures were also collected. In addition, the upstream temperature was varied from 295 to 700 K. 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 fluids in an actual orifice or nozzle. An error analysis shows that the reported discharge coefficients are accurate to ± 1.2% for air flow and ± 1.6% for the other gases studied. The discharge coefficient for knife-edge orifices correlates very well with a dimensionless pressure drop for the entire range of diameters, gases, pressures and temperatures studied. The discharge coefficient does not correlate with the throat Reynolds number for compressible flow through knife-edge orifices. Moreover, an analogous behavior of the discharge coefficient for larger diameters than those tested is expected for knife-edge and thin-plate orifices. Straight-bore orifices, with length-to-diameter ratios close to or slightly greater than unity, yield discharge coefficients which are approximately independent of flow rate, upstream temperature, and gas properties. These discharge coefficients are, however, highly sensitive to the length-to-diameter ratio of the straight bore. Finally, the discharge coefficients for both rounded- and elliptical-entry nozzles correlate well with a throat Reynolds number. The correlation shows that as the Reynolds number is decreased the discharge coefficient drops precipitously for Re < 20,000. For Re > 20,000 the discharge coefficient increases slowly with increasing Reynolds number. This behavior is consistent with both previous data and fluid dynamics theory for rounded- and elliptical-entry nozzles.

Experimental determination of the discharge coefficients for critical flow through an axisymmetric nozzle

Experimental determination of the discharge coefficients for critical flow through an axisymmetric nozzle

Experimental Determination of the Discharge Coefficients for Critical Flow through an Axisymmetric Nozzle

Discharge coefficients for critical flow nozzles were determined experimentally for hydrogen, helsum, nitrogen, and argon over a Reynolds number range from 10 to 10. Above values of about 200, the measured coefficients are in excellent agreement with those predicted by a straightforward application of boundary-layer theory. The results suggest that in many cases experimental calibration of metering nozzles might be avoided.

Paper 8: Measurement of Pulsating Air Flow by Means of a Bi-Directional Orifice Meter

This paper discusses experiments carried out to investigate the errors involved when applying the steady flow methods of air measurement to air flows which are pulsating at frequencies between 30 and 130 cycles per second (Hz). The mass flow measurements for steady and pulsating flow conditions are obtained by using four different sizes of bi-directional square-edged orifice plates with D and D/2 pressure tappings and a comparison of discharge coefficients for the subsonic flow of air in a 1-in diameter pipe, and the measurements cover a range of mass flows up to 0·03 lb/s. Attempts are made to determine suitable correction factors and thus establish a commercially satisfactory means of air flow measurement from the delivery side of a two-lobed, Roots-type positive displacement blower. The following effects are discussed: (1) the significance of the non-dimensional parameters involved, and (2) the effect of pulse shape.

Discharge Coefficients for Incompressible Non-Cavitating Flow through Long Orifices

The results of a number of previous investigations of the discharge characteristics of parallel-bore orifices with length/diameter ratios up to 10 and Reynolds numbers up to about 105are collected and discussed, together with new data which extend to Reynolds number as low as unity.Simple empirical expressions, which fit the data well, are suggested for design purposes.