Discharge Coefficient Of Nozzle Research Articles

A NOTE ON THE BUBBLE GROWTH FORCE

A high-flow-rate, 10-stage, low-pressure impactor has been constructed for the in-stack measurement of industrial aerosols. The particle collection characteristics of the stages were determined using solid ammonium fluorescein calibration aerosols in conjunction with greased impaction substrates. Cutpoints of the stages were 10, 5.5, 2.9, 1.7, 0.95, 0.50, 0.32, 0.20, 0.11, and 0.047 (μm aerodynamic diameter. Measurement of the nonideal fluid behavior through the impaction nozzles under compressible flow conditions led to the development of empirical discharge coefficients for sharp entry nozzles. Use of these coefficients allows prediction of stage pressure drops as a function of the nozzle dimensions and the fluid properties at the nozzle inlet. Variations in the low-pressure impactor performance have been predicted as a function of temperature and pressure.

音速ノズル流出係数のレイノルズ数依存性の簡易相対測定法

A novel method to measure the Reynolds number dependence of the discharge coefficient of a critical nozzle relatively against the other critical nozzles is proposed. The method uses three or more series connections of 2 nozzles among the reference and the test nozzles. The two constants, which control the Reynolds number dependence of the discharge coefficient, are derived from comparing the pressure between nozzles in these series connections. The upper condition is kept constant near a reference condition, therefore realization of the facility and performance of the measurement are quite simple. The only instrument the method requires is a pressure gauge which has only a linearity in a narrow range. Its sensitivity is measured utilizing a stable pressure ratio generated by a series connection of two critical nozzles. All of the measured pressure are appeared as ratios in the equations to calculate the two constants, therefore error caused by a zero-shift of the pressure gauge is negligible. An uncertainty analysis and realized measurements on critical nozzles of different designs confirmed its high accuracy in very short measuring time.

Model-based control of mold level in a continuous steel caster under model uncertainties

In tackling the problem of liquid steel level regulation in the mold of a continuous steel caster, the values of some system parameters, such as the clogging degree and the discharge coefficients of nozzles, are seldom precisely known. The discrete control laws developed in this work employ on-line estimated values of these parameters, to produce a stable regulation of mold and tundish levels for an industrial-type two-strand continuous slab caster. The estimation procedure is delayed by one time step (the sampling time) in order to become realizable; when the sampling time is small enough, the discrete control scheme gives stability and convergence properties that are analogous to those of an ideal control scheme with accurate knowledge of the parameter values.

Influence of swirl on the discharge coefficients of sonic nozzles

Flow characteristics of a swirl generator are studied using an open circuit flow loop, and influence of upstream swirl on the discharge coefficients of sonic nozzles is investigated using a high pressure gas flow standard measurement system. The open circuit flow loop consists of swirl generator, testsection, sonic nozzle, suction fan and LDV system. The gas flow measurement system comprises two compressors, storage tank, temperature control loop, sonic nozzle testsection, weighing tank, gyroscopic scale and data acquisition system. Experiments are performed at various nozzle throat diameters, inlet pressures and angles of swirl generator. As the angle of swirl generator becomes larger, axial velocities decrease near the wall and rapidly increase in the pipe core, and swirl velocities increase to form swirl flow. Influence of upstream swirl on discharge coefficients becomes greater as the intensity of swirl increases and as the nozzle throat diameter is enlarged. Variation trend with Reynolds number, however, is very similar each other regardless of swirl intensity.

Discharge coefficients of nozzles and of their combinations in forward and reverse flows

Discharge coefficients of nozzles and of their combinations in forward and reverse flows

Factors influencing on the discharge coefficients of sonic nozzle

Accuracy of gas flow measurements using sonic nozzle and factors which influence on the discharge coefficients of sonic nozzle are investigated with high pressure gas flow standard measurement system. The gas flow measurement system comprises two compressors, storage tank, temperature control loop, sonic nozzle test section, weighing tank, gyroscopic scale and data acquisition system. The experiments are performed at various nozzle throat diameter and inlet pressure. Overall uncertainty of discharge coefficients is estimated to less than .+-.0.2% and most of experimental data fall into this range. Dependence of discharge coefficients on the Reynolds number is good agreement with those suggested in ISO document. The influence of swirl on the discharge coefficients becomes greater as the nozzle throat diameter is enlarged. The discharge coefficient of conical nozzle shows about 4.5% lower discharge coefficients than those of toroidal nozzle, but variation trend with Reynolds number is very similar each other and reproducibility of data is very good.

Mass Flow and Thrust Performance of Nozzles With Mixed and Unmixed Nonuniform Flow

The calculated thrust and mass flow rate of a nozzle depend on the uniformity of the entering flow. The one-dimensional flow equations are extended to arrive at analytic expressions for the predicted performance of a nozzle processing two streams whose properties are determined ahead of the throat. The analysis approach forms the basis for the understanding of flows which have more complex distributions of total pressure and temperature. The uncertainty associated with mixing is examined by the consideration of the two limiting cases: compound flow with no mixing and completely mixed flow. Nozzle discharge and velocity coefficients accounting for non-uniformity are derived. The methodology can be extended to experimentally measured variations of flow properties so that proper geometric design variables may be obtained.

Effects of inlet shapes of critical venturi nozzles on discharge coefficients

The discharge coefficients of critical venturi nozzles were obtained in a high-pressure gas flow standard system, which was a gravitational weighing system. The calibration uncertainty of a critical venturi nozzle of about 8 mm throat diameter was ±0.08% and ±0.14% at upstream stagnation pressures of 4 MPa and 1 MPa, respectively. The discharge coefficients of critical venturi nozzles fabricated according to ISO specifications are in good agreement with ISO correlation. The discharge coefficients for small inlet radius decrease significantly as the inlet length becomes short, owing to separation at the sharp inlet. For nozzles having long inlet radius, the effects of inlet length on the discharge coefficients were relatively small, but the effects become significant at the short inlet length. The effect of separation at the inlet is stronger than that of the boundary layer growth. The experimental results provide excellent support for the shape of critical venturi nozzles suggested by ISO specifications.

Effects of Double-rectangular-slot Design on Impact Sprinkler Nozzle Performance

Some of the main design parameters for double rectangular nozzles are the inside contraction angle, the length-to-width ratio of the rectangular slot, the spacing between two slots, and the angle between the two adjacent slots. The inside contraction angle and slot dimensions and spacing were varied and water application patterns and droplet diameters at the end of the spray stream were evaluated. Pattern radius decreased as slot spacing increased and increased as the length-to-width ratio increased. Sprinkler pattern and droplet diameter were insensitive to the inside contraction angle. The nozzle discharge coefficient was independent of all investigated parameters. Sprinkler rotation speed decreased with slot spacing but increased with the length-to-width ratio.

渦巻噴射弁の流量係数（ＩＩＩ） 高粘性流体の流量係数予測

The discharge coefficient (C) of pressure nozzles can be predicted by the nozzle parameters, which are defined by their nozzle geometries. However, in-spite of using suitable nozzle parameters, the prediction of “C” is still influenced by the diameter of the swirl chamber (“di”) itself.At the case of atomization of low viscosity liquids, “C” decreases with increasing “di”. On the contrary, at the case of atomization of high viscosity liquids, “C”increase with increasing “di”. Also, it is found the transition of these tendencies occurs around the viscosity of 0.06 Pa-s.The influence of the viscosity of liquids and the spraying pressure on the “C” are arranged by the effect of the Reynolds number at the swirl chamber, which is defind by u* (di-do) /2 ρ.It is found that the change of the correlation between “C” and Reynolds number occurs around Re=2000-3000.

渦巻噴射弁の流量係数 （Ｉ） 渦巻噴射弁構造と流量係数

The discharge coefficient (C) of pressure nozzles can be predicted by the nozzle parameters, which are defined by their nozzle geometry. The purpose of this study is to compare the three representative nozzle parameters, “K”, “A'”, and “Δ”. from the viewpoint of practical application.Prediction of “C” by using nozzle Parameter “K” is greatly influenced by the ratio (k=do/ri) of the diameter of swirl insert (do) to the radius of swirl chamber (ri). On the other hand, prediction of “C” by using “A'” or “Δ” does not depend on “k” at the practical range of “k” between 0.2 and 1.0. It was also found that “A'” and “Δ” can be expressed as the function of “K” and “k”, by rearranging their original definitions. Therefore it is considered that “A'” and “Δ” are more widely applicable nozzle parameters.However, inspite of using these suitable nozzle parameters, prediction of “C” is still influhnced by the diameter of the swirl chamber (“di”) itself. It is found that “C” increases with decreasing“di” in the case of atomization of water.

ソニックベンチュリノズルの内径形状と流出係数の高精度測定

ソニックベンチュリノズルの内径形状と流出係数の高精度測定

定積槽方式により測定されたソニックベンチュリノズル流出係数の不確かさ評価

定積槽方式により測定されたソニックベンチュリノズル流出係数の不確かさ評価

Design and Calibration of an In-Stack Low-Pressure Impactor

A high-flow-rate, 10-stage, low-pressure impactor has been constructed for the in-stack measurement of industrial aerosols. The particle collection characteristics of the stages were determined using solid ammonium fluorescein calibration aerosols in conjunction with greased impaction substrates. Cutpoints of the stages were 10, 5.5, 2.9, 1.7, 0.95, 0.50, 0.32, 0.20, 0.11, and 0.047 (μm aerodynamic diameter. Measurement of the nonideal fluid behavior through the impaction nozzles under compressible flow conditions led to the development of empirical discharge coefficients for sharp entry nozzles. Use of these coefficients allows prediction of stage pressure drops as a function of the nozzle dimensions and the fluid properties at the nozzle inlet. Variations in the low-pressure impactor performance have been predicted as a function of temperature and pressure.

Evaluation of Jet-Bit Pressure Losses

Summary An experimental and theoretical study was conducted to resolve discrepancies between observed and calculated pressure losses for fluids flowing through the nozzles of jet bits. The use of a nozzle discharge coefficient of 0.95, which is commonly used for roller-cone bits, results in the calculated pressure drop being up to 30% more than actually occurs, with the average error being 14.7% for 770 data points measured with nine different fluids. A relationship is presented to calculate the discharge coefficient as a function of borehole pressure, nozzle size, and mud density, which reduces the mean absolute error to 3% for these data points. Simply increasing the discharge coefficient to a constant value of 1.02 results in reducing the error to 4.1 % without using the more complicated relationship.

Study on penetration of transient gas jet.

The behavior of single-shot gas jet injected into high pressure gas chamber was investigated with schlieren photography. The configuration of the gas jet was similar to diesel spray and water jet injected into water, and the penetrating distance XS was expressed by the following equation. XS2=a√(α·Pf/Pg)dn·Uo·t/tan θS, where dn=nozzle diameter, Uo=injected gas velocity at nozzle, α=discharge coefficient of nozzle, t=time from infection beginning, θS=average half cone angle of jet, Pf=density of injected gas, Pg=density of surrounding gas and a=empirical constant. The value of a was 2 for the gas jet and the auto-motive diesel spray, and 1 for the high pressure spray (85-180 MPa) of marine diesel.

Swirl Flow in Cylindrical Chamber : 2nd Report. Energy Loss in Chamber and its Effect on Flow Characteristics

The potential theory has been used to analyze the flow characteristics of a swirl spray nozzle, but the theoretical results do not coincide with the experimental ones. One reason for this inconsistency is likely in the energy loss caused by a swirl flow in the vortex chamber. In order to investigate the energy loss, the energy distribution in swirl flow is studied and the flow characteristics of a swirl spray nozzle introducing this effect is analyzed, then the theoretical results are compared with the experimental ones. The results show that the energy loss in the cylindrical chamber is directly proportional to the difference in peripheral velocity head of the fluid, and the energy loss in the vortex chamber must be taken into account to evaluate the discharge coefficient of a swirl spray nozzle.

Inviscid transonic flow field analysis

This paper describes a method for analysing inviscid transonic flow. This method is based on the fact that the angle made by the streamline of the transonic flow and of the corresponding incompressible flow is usually small. By using curvilinear coordinates, the differential equation of the stream function of an inviscid compressible flow is simplified and a general solution of the equation obtained.As examples of the method, transonic solutions are given for flow through twodimensional and axisymmetric Laval nozzles of different throat wall radii together with sonic lines and iso-Mach lines. To determine the discharge coefficients of Laval nozzles, an integral relation is developed. The general behaviour of the transonic flow in the throat region is presented, and the effect of the mass discharge on the Mach number distribution in the nozzle analysed. The effects of the ratio of the specific heats on the characteristics of the flow in the throat region are discussed. For transonic flow around a circular cylinder and a sphere, sonic lines and iso-Mach lines are presented for free-stream Mach number varying from the subcritical to the supercritical, including a free-stream Mach number of one.Part of the results obtained are compared with those available in current literature. For the two-dimensional hyperbolic Laval nozzles, the iso-Mach lines are compared with those given by Cherry (1959) and Serra (1972). For, axisymmetric Laval nozzles, the discharge coefficient and the Mach number at the throatsection for various throat wall radii are compared with those given by Sauer (1944), Hall (1962), Kliegel & Levine (1969), and Klopfer & Holt (1975). The theoretical discharge coefficients are compared with the experimental results by Backet al (1975), Durham (1955), Norton & Shelton (1969) etc. For the transonic flow around a circular cylinder, the iso-Mach lines are compared with Cherry’s exact solution for the quasi-circular cylinder for.M∞ equal to 0.51. The. Mach number distributions on the surface of the circular cylinder are compared with those given by Imai (1941) forM∞ equal to 0.4, by Cherry (1947) forM∞ equal to 0.51, by Dorodnicyn (1956) forM∞ equal to 1, and by Hafez, South & Murman (1979) forM∞ equal to 0.51.The present method has a much wider scope of application, requires simpler computation and gives results with good accuracy. It is being used to analyse supercritical wings and cascades, and we expect to extend its application to the field of transonic unsteady flow.

Effects of Swirling Flow Components on Discharge Coefficients of Constriction Meters

Discharge coefficients of venturi meters and nozzles employed in swirling flows were measured and the change of the coefficients due to swirling components was discussed in relation to the distributions of velocities, pressures and energies measured across sections before and after the constriction meters. Formulae of the discharge coefficients to correct the swirling components were given for the swirling flow range which will be expected to occur in pipe lines in engineering use.

Analytical and Experimental Studies of ASME Flow Nozzles

In this paper, we first present a state of the art review of the published work concerning theoretical nozzle discharge coefficients. Then, we develop a new nozzle discharge coefficient based on an axisymmetric boundary layer solution, which in turn is based on a new axisymmetric potential flow solution. These solutions apply to plenum inlet installations which offer major advantages over conventional ASME pipe inlet installations as to losses, and as to predictability of the discharge coefficient at the higher Reynolds numbers encountered in industry. Next, we present new correlations for static pressure tap errors and apply these to the theoretical (zero tap size) discharge coefficients. Finally, we present new experimental data showing how a laminar boundary layer is preserved and tap error is accordingly minimized for the case of a plenum inlet with ASME nozzle contour.