Performance of conical entrance orifice plates at low Reynolds numbers

Results are presented of an experimental investigation into the performance of conical entrance orifice plates manufactured according to BS 1042. Three plates, with diameter ratios of 0.247, 0.360 and 0.448, were tested in the region 100 < Re_D ? 1000 and in both the concentric and the fully eccentric position. The discharge coefficient, C_z, of the orifice was found to agree with that specified in BS 1042 for a diameter ratio of 0.247. For other diameter ratios, the discharge coefficient increased with the diameter ratio, as observed by other workers for the Kent plates. The eccentricity has no appreciable effect on the discharge coefficient, probably due to the effect of viscous action on the flow being more or less the same for the concentric and eccentric position of the orifice at low Reynolds numbers     

Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method

Micro gas flows are often encountered in MEMS devices and classical CFD could not accurately predict the flow and thermal behavior due to the high Knudsen number. Therefore, the gas flow in microgeometries was investigated using the direct simulation Monte Carlo (DSMC) method. New treatments for boundary conditions are verified by simulations of micro-Poiseuille flow, compared with the previous boundary treatments, and slip analytical solutions of the continuum theory. The orifice flow and the corner flow in microchannels are simulated using the modified DSMC codes. The predictions were compared with existing experimental phenomena as well as predictions using continuum theory. The results showed that the channel geometry significantly affects the microgas flow. In the orifice flow, the flow separation occurred at very small Reynolds numbers. In the corner flow, no flow separation occurred even with a high driving pressure. The DSMC results agreed well with existing experimental information.     

The compressible discharge of air through small thick plate orifices

Summary The choking of nozzles at pressure ratios below the critical has long been understood. Knife edge orifices however do not appear to choke. This can be explained and the variation of discharge coefficient with pressure ratio may be calculated. The present paper is an experimental investigation into the discharge through thick plate orifices when the pressure ratio is in the vicinity of its critical value. A comparison is made with the results of other workers and an attempt is made to explain the discharge characteristics of thick plate orifices.Notation C discharge coefficient - D orifice diameter - P absolute static pressure - T thickness of orifice plate Suffixes c critical pressure - d downstream conditions - i incompressible flow conditions - u upstream conditions     

Characteristics of R-123 two-phase flow through micro-scale short tube orifice for design of a small cooling system

We present a new discharge coefficient correction method for the orifice equation for R-123 two-phase flows. In this method, an evaporator is mounted after the orifice as a vapor refrigeration cycle, and the evaporator is used to measure the quality of downstream flow through the orifice. Quality is estimated from the measured temperature and pressure of the evaporator inlet and outlet, respectively, instead of by direct measurement of quality. The condition of upstream flow of the orifice is the liquid state at 3 bar and 60 °C. The liquid flow is changed to two-phase flow after passing through the orifice. Orifice diameters of 300, 350, 400, and 450 μm are used for the experiment, and the results are analyzed. Experiments are conducted for various conditions of flow rate between 20 and 70 ml/min and for cooling loads of 60, 80, and 100 W. The results show that the quality of flow downstream from the orifice can be calculated using the enthalpy difference between the inlet and outlet of the evaporator. An equation to determine the discharge coefficient is formulated as a function of quality. We expect that these results can be used to help design a small cooling system.     

Flow fields and packing states in the discharge flow of noncircular particles—A SIPHPM simulation

Although the discharge flow of spherical materials has been extensively explored, the effect of particle shape on discharge is still poorly understood. The present work explores the two-dimensional discharge flow fields of noncircular particles using the soft-sphere-imbedded pseudo-hard particle model method. Rectangular particles having different aspect ratios (R_a = 1, 1.5, 2–5) and regular polygonal particles having different numbers of sides (N_s = 3–8, 10) are discharged through hopper beds having different orifice widths (D_i = 40, 70.77, 99.13, 125.74, 151.13 mm). The discharge rates of differently shaped particles in different beds are consistent with Beverloo’s relation. Moreover, the flow fields are computed and evaluated to study the effects of R_a, N_s, and D_i on particle discharge. The characteristics of particle–particle connections in the discharge process are evaluated according to the temporal evolution and spatial distribution of the contact points. Additionally, the effect of the initial packing on the discharge profile is investigated. The findings help clarify the discharge of noncircular particles.     

Study of cavitation phenomena based on a technique for visualizing bubbles in a liquid pressurized chamber

In this paper, the influence of nozzle geometry on cavitation and near-nozzle spray behavior under liquid pressurized ambient is studied. For this purpose, eight steel drilled plates, with different diameters and degrees of conicity of their holes, are analyzed. A special near-nozzle field visualization technique, using a test rig pressurized with fuel, is used. Due to the difference in refractive index between liquid and vapor phase, bubbles present at the outlet of the orifice are visualized. The pressure conditions at which bubbles start appearing at the orifice outlet are compared with those at which choked flow appears. The results showed that pressure conditions for inception of cavitation obtained in the visualization tests differs from those seen for choked flow (5–8% in terms of cavitation number). In addition to this, the images taken are analyzed to get the angle of the jet formed by fuel bubbles, showing that it increases significantly for those conditions more prone to cavitate. Furthermore, comparison of bubbles generation when increasing or decreasing backpressure indicates the presence of hysteresis in cavitation inception phenomena.     

Finite Element Solution of Laminar Flow through Square-Edged Orifice with a Variable Thickness

A numerical analysis of laminar flow through square-edged orifice has been studied for Reynolds number in the range 0 < Re₀ < 2000 with β values varying from 0.2 to 0.8 and with l* values varying from 1/16 to 1. It is shown thai the flow discharge coefficient gradually decreases when the orifice thickness/diameter ratio increases for a high porosity.     

Experimental study of wall curvature and bypass flow effects on orifice discharge coefficients

This paper presents the results of an experimental study investigating the impact of wall curvature and bypass flow on the discharge coefficients of circular orifices. To extend the range of currently available discharge coefficients, the ratio of the orifice to the pipe diameter is varied from 0.25 to 0.67. Functional relationships are developed that relate a free-discharge orifice coefficient to the ratio of the orifice diameter to the pipe diameter and the total head (velocity and pressure heads) upstream of the orifice. In addition, the use of the projected area versus surface area of the orifice for determining discharge coefficients is investigated and the results show that both approaches yield similar observations. The results of this experimental study are particularly useful for the case of sparger design.     

Variable viscosity squeeze films and bubble removal in the manufacture of panel material

A mathematical model is developed for the two-dimensional flow of an incompressible Newtonian fluid which is being squeezed between two rigid, impermeable plates. The fluid viscosity varies linearly with temperature. The model is intended to elucidate a problem of air bubble entrapment which arises in the manufacture of panel material, particularly in the manufacture of ‘corner’ profiles. The results show that when the two plates have the same shape, the pressure gradient is such that bubbles are likely to be expelled throughout the contact, except in the central region. When a corner profile is manufactured it is likely that bubbles will be retained, thereby leading to flaws in the final product.     

Confined impinging twin air jets at high Reynolds numbers

An experimental study is carried out to investigate flow characteristics of confined twin jets issuing from the lower surface and impinging normally on the upper surface. Pressure distributions on the impingement and confinement plates were obtained for Reynolds numbers ranging from 30,000 to 50,000, nozzle-to-plate spacing (H/D) in the range of 0.5-4 and jet-to-jet spacing (L/D) in the range of 0.5-2. Smoke-wire technique was used to visualize the flow behavior. The effects of Reynolds number, nozzle-to-plate spacing and jet-to-jet spacing on the flow structure are examined. The subatmospheric regions occur on both impingement and confinement plates at the nozzle-to-plate spacing up to 1 for all studied Reynolds numbers and jet-to-jet spacings in consideration. They lie nearly up to the same radial location at both surfaces and move radially outward from the stagnation points with increasing nozzle-to-plate spacing and jet-to-jet spacing. It is concluded that there exists a relation between the subatmospheric regions and peaks in heat transfer coefficients for low spacings in the impinging jets.     

Viscous and Inviscid Instabilities of Flow Along a Streamwise Corner

Here we consider the stability of flow along a streamwise corner formed by the intersection of two large flat plates held perpendicular to each other. Self-similar solutions for the steady laminar mean flow in the corner region have been obtained by solving the boundary layer equations for zero and nonzero streamwise pressure gradients. The stability of the mean flow is investigated using linear stability analysis. An eigensolver has been developed to solve the resulting linear eigenvalue problem either in a global mode to obtain an approximation to all the dominant eigenmodes or in a local mode to refine a particular eigenmode. The stability results indicate that the entire spectrum of two-dimensional and oblique viscous modes of a two-dimensional Blasius boundary layer is active in the case of a corner layer as well, but away from the cornerline. In a corner region of finite spanwise extent, the continuous spectrum of oblique modes degenerates to a discrete spectrum of modes of increasing spanwise wave number. The effect of the corner on the two-dimensional viscous instability is small and decreases the growth rate. The growth rate of outgoing oblique disturbances is observed to decrease, while the growth rate of incoming oblique disturbances is enhanced by the corner. This asymmetry between the outgoing and incoming viscous modes increases with increasing obliqueness of the disturbance. The instability of a zero pressure gradient corner layer is dominated by the viscous modes; however, an inviscid corner mode is also observed. The critical Reynolds number of the inviscid mode rapidly decreases with even a small adverse streamwise pressure gradient and the inviscid mode becomes the dominant one. Received 17 March 1998 and accepted 28 April 1999     

The numerical simulation of stretch flange forming

Simulations of stretch flange forming operations are undertaken using explicit dynamic finite element calculations utilizing various quadratic and non-quadratic yield criteria. Both circular and square cut-out blanks are investigated with corresponding circular and square punches. Simple stretch flanges are considered, utilizing a single punch to expand the cut-out, as well as z-flanges, which employ a back-up punch to form the second bend needed in the z-flange profile. Results from a model of an automotive inner component incorporating a cut-out with stretch flange corner features are also presented. Predictions utilizing the Barlat-89 criterion are shown to accurately capture the effect of yield anisotropy (R-value). The predicted strains from the corner regions of square cut-out stretch flange laboratory specimens are shown to be similar to those within the automotive inner panel, supporting the use of laboratory-scale stretch flange experiments to simulate the larger panels. Measured limit strains from the stretch flange formability experiments are compared to forming limit diagram (FLD) data from dome specimens. Stretch flange formability is shown to exceed allowable levels predicted using a classical FLD approach, particularly for simple stretch flanges, indicating that the FLD approach is overly conservative.     

A semi-empirical model of two-phase flow of refrigerant-134a through short tube orifices

Measurements were conducted on Refrigerant-134a flowing through short tube orifices with length-to-diameter (L/D) ratios ranging from 5 to 20. Both two-phase and subcooled liquid flow conditions entering the short tube were examined for upstream pressures ranging from 896 to 1448 kPa and for qualities as high as 10% and subcoolings as high as 13.9°C. Data were analyzed as a function of the main operating variables and tube geometry. Semi-empirical models for both single- and two-phase flow at the inlet of the short tubes were developed to predict the mass flow of Refrigerant-134a through short tube orifices.

Choked flow conditions for Refrigerant-134a were typically established when downstream pressures were reduced below the saturation pressure corresponding to the inlet temperature. The flow rate strongly depended on the upstream pressure and upstream subcooling/quality. The mass flow also depended on cross-sectional area and short tube length. The mass flow model utilized a modified orifice equation that formulated the mass flow as a function of normalized operating variables and short tube geometry. For a two-phase flow entering the short tube, the modified orifice equation was corrected using a theoretically derived expression that related the liquid portion of the mass flow under two-phase conditions to a flow that would occur if the flow were a single-phase liquid. It was found that for sharp-edged short tubes with single- and two-phase flow, approximately 95% of the measured data and model's prediction were within ±15% of each other.     

A phase averaged PIV study of circular and non-circular synthetic turbulent jets issuing from sharp edge orifices

An extensive experimental study using Particle Image Velocimetry (PIV) on synthetic jets issuing from different orifice shapes is reported. All data are phase and time averaged to derive mean velocity, half-velocity width and rms velocity profiles in the near field of the jet (0 < X/D < 7), at a Reynolds number around 10,000. Different non-circular orifice shapes as rectangular, square, elliptic and triangular are considered and results are compared to those of the circular orifice in order to investigate the effect of asymmetry on the turbulent flow field in view of mixing enhancement. The measurements are carried out on two orthogonal planes to capture three dimensional features of non-circular jets. Results show highest velocity decay rate for elongated orifices, especially the rectangular one, in comparison to the circular one, both in phase and time-averaged plots. Time averaged results show higher velocity decay rate of synthetic jets in comparison to those of continuous ones. It is also observed that, for X/D > 5, only profiles of circular and square jets become partially self-similar. For synthetic jets, higher turbulence content is measured for all orifice shapes at the centerline and close to the orifice exit in comparison to continuous jets.     

Comparison of heat transfer distributions on a flat plate impinged by under-expanded jets from a convergent nozzle and a circular orifice

Experiments are carried out for a circular orifice and a nozzle for the same contraction ratio to explore the heat transfer characteristics. The pressure ratios covered in this study are 2.36, 3.04, 3.72, 4.4 and 5.08 for jet to plate distances (z/d) of 2, 4, 6 and 8. The presence of vena contracta and absence of the stagnation bubble in the orifice flow are confirmed from the surface pressure distributions. It is found that higher Nusselt number for the orifice than the nozzle are due to different shock structures and shear layer dynamics. Peak Nusselt number is found as high as 84 % than that for the nozzle. In the wall jet region, the heat transfer rates for the orifice and nozzle are almost of the same order, thus producing steeper temperature gradients under similar operating conditions. The average heat transfer rates are almost 25 % higher for the orifice than that of the nozzle. The recovery factors are in general higher in case of orifice than the nozzle. However, this has not resulted in decreasing the heat transfer rates due to shear layer dynamics.     

Critique of Southwell plots with proposals for alternative methods

The theory of the Southwell plot is outlined and its history traced. Examples are given in which the technique fails to give a straight line; these are classified into low-load and higher-load nonlinearities. It is shown that the former may be due to inherent zero errors in the deflection measurement and that this can cause serious errors in the apparent critical loadP _c. A new approach involving “pivot points” is introduced and used to formulate plots which may help to linearize the data; an application to one of Karman's classical column tests is given. For plates, use is made of a general post-critical equation of which Donnell's result for a simply supported square plate is a special case. A new graphical technique is proposed for findingP _c for plates with small imperfections, and applied to example data from published test results. A more general numerical technique is also proposed and applied to results from a test during which the experimental boundary conditions were changing.     

Dynamic fluid flow behaviour of a tank draining through a vertical tube

This paper describes the unsteady draining of a sealed tank partially filled with water. The water discharges via a vertical tube into an open tank at atmospheric conditions. The air inflow, compensating for the volume of the discharged liquid, enters the system in an oscillatory manner, much like the “gulping” seen in an upended beer bottle. A mathematical model, based closly on that derived by Dougall & Kathiresan [Chem. Engng Commun. 8, 289–304 (1981)], has been applied to predict the pressure fluctuations in the closed tank. The rate of water discharge from the tank has been predicted and gives a much closer agreement with experimental results than a prediction based on a steady counter-current flooding limitation approach. A drift flux model has been used to describe the two-phase flow effect in the tube and the Wallis flooding criterion has been modified for use in the slug flow regime to describe the boundary conditions at the bottom of the tube. The pressure fluctuations in the sealed tank have been measured and compared with results obtained from the mathematical prediction for a variety of tube diameters.     

Theoretical and experimental studies on the coefficient of discharge and spray cone angle of a swirl spray pressure nozzle using a power-law non-Newtonian fluid

An extension of earlier work is made in the present paper to determine both theoretically and experimentally the coefficient of discharge and spray cone angle of a swirl nozzle using a time-independent purely viscous power-law non-Newtonian fluid. The theoretical predictions are made through an approximate analytical solution of the hydrodynamics of flow inside the nozzle. Experiments are carried out with aqueous solutions of CMC (carboxymethyl cellulose sodium salt) powder of various concentrations as the working fluids. The rheological properties of the working fluids are established by a capillary tube viscometer. From both the theoretical and experimental analyses, the pertinent independent input parameters are recognised as the generalised Reynolds number at inlet to the nozzle Re_Gi, the flow behaviour index of the fluid n, length-to-diameter ratio of the swirl chamber L₁/D₁, spin chamber angle 2α and the orifice-to-swirl-chamber-diameter ratio D₁/D₁. Although the theory predicts the correct qualitative trend in all cases, it does not agree well with the experimental results. Therefore, on the basis of the theoretical results, emperical relationships between nozzle characteristics and input parameters heve been established. Finally it is recognised that, regarding the injection conditions and fluid properties, the generalised Reynolds number at nozzle inlet Re_Gi and the flow behaviour index n have inverse and direct effects, respectively, on the coefficient of discharge, but have a negligible influence on the spray cone angle. Amongst the nozzle geometries, an increase in the values of D₂/D₁ and 2α or a decrease in the value of L₁/D₁ decrease the coefficient of discharge and increase the spray cone angle.     

Three-dimensional numerical simulations of cross-flow around four cylinders in an in-line square configuration

This paper presents a numerical study of three-dimensional (3-D) laminar flow around four circular cylinders in an in-line square configuration. The investigation focuses on effects of spacing ratio (L/D) and aspect ratio (H/D) on 3-D flow characteristics, and the force and pressure coefficients of the cylinders. Extensive 3-D numerical simulations were performed at Reynolds number of 200 for L/D from 1.6 to 5.0 at H/D=16 and H/D from 6 to 20 at L/D=3.5. The results show that the 3-D numerical simulations have remedied the inadequacy of 2-D simulations and the results are in excellent agreement with the experimental results. The relation between 3-D flow patterns and pressure characteristics around the four cylinders is examined and discussed. The critical spacing ratio for flow pattern transformation was found to be L/D=3.5 for H/D=16, while a bistable wake pattern was observed at L/D=1.6 for the same aspect ratio. Moreover, a transformation of flow pattern from a stable shielding flow pattern to a vortex shedding flow pattern near the middle spanwise positions of the cylinders was observed and was found to be dependent on the aspect ratio, spacing ratio, and end wall conditions. Due to the highly 3-D nature of the flows, different flow patterns coexist over different spanwise positions of the cylinders even for the same aspect ratio. It is concluded that spacing ratio, aspect ratio, and the no-slip end wall condition have important combined effects on free shear layer development of the cylinders and hence have significant effects on the pressure field and force characteristics of the four cylinders with different spacing ratios and aspect ratios.     

Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.