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.     

Regimes of spray formation in gas-centered swirl coaxial atomizers

Spray formation in ambient atmosphere from gas-centered swirl coaxial atomizers is described by carrying out experiments in a spray test facility. The atomizer discharges a circular air jet and an axisymmetric swirling water sheet from its coaxially arranged inner and outer orifices. A high-speed digital imaging system along with a backlight illumination arrangement is employed to record the details of liquid sheet breakup and spray development. Spray regimes exhibiting different sheet breakup mechanisms are identified and their characteristic features presented. The identified spray regimes are wave-assisted sheet breakup, perforated sheet breakup, segmented sheet breakup, and pulsation spray regime. In the regime of wave-assisted sheet breakup, the sheet breakup shows features similar to the breakup of two-dimensional planar air-blasted liquid sheets. At high air-to-liquid momentum ratios, the interaction process between the axisymmetric swirling liquid sheet and the circular air jet develops spray processes which are more specific to the atomizer studied here. The spray exhibits a periodic ejection of liquid masses whose features are dominantly controlled by the central air jet.     

Liquid flow in a simplex swirl nozzle

Pressure-swirl nozzles are widely used in applications such as combustion, painting, air-conditioning, and fire suppression. Understanding the effects of nozzle geometry and inlet flow conditions on liquid film thickness, discharge coefficient and spray angle is very important in nozzle design. The nozzle-internal flow is two-phase with a secondary flow which makes its detailed analysis rather complex. In the current work, the flow field inside a pressure-swirl nozzle is studied theoretically. Using the integral momentum method, the growth of the boundary layer from the nozzle entry to the orifice exit is investigated and the velocity through the boundary layer and the main body of the swirling liquid is calculated. A numerical modeling and a series of experiments have also been performed to validate the theoretical results. The effect of various geometrical parameters is studied and results are compared for viscous and inviscid cases. In addition, the condition in which the centrifugal force of the swirling flow overcomes the viscous force and induces an air core is predicted. The theoretical analysis discussed in this paper provides better criteria for the design and the performance analysis of nozzles.     

Theoretical and experimental investigations of gear-rattling

Rattling vibrations in gear boxes are a noise problem of modern cars following the requirement to be as quiet as possible. The paper presents an uniform approach to model such vibrations based on classical impact theory and applying modern methods of topological dynamics. Some comparisons of theory and measurements utilizing a test set-up of a rattling machine are presented. They demonstrate the practical relevancy of the presented theory.     

Atomization of glycerin with a twin-fluid swirl nozzle

Atomization of liquids with high viscosity is always a challenge, especially when small diameter droplets and high liquid flow rates are simultaneously required. In the present research, the performance of a Venturi–vortex twin-fluid swirl nozzle is examined, attending to its capabilities to generate droplets with diameters below 20 µm when atomizing pure glycerin at room temperature. In this nozzle, air is injected tangentially in a central convergent section, and discharges suctioning the liquid fed to a coaxial chamber, here using a gear pump. The resulting spray is visualized and analyzed. Droplet size distributions are measured with a laser diffractometer. As expected, droplet diameter increases with liquid flow rate, and quickly diminishes when air flow rate is increased. Sauter mean diameters (SMD) below 15 µm can be obtained even when atomizing pure glycerin. However, these values are obtained for relatively low glycerin flow rates (∼5 l/h), and with rather wide distributions. For 10 l/h and an air-to-liquid mass flow rate ratio (ALR) of 13.7 more than 26% of the glycerin volume is atomized in droplets smaller than 20 µm. Liquid ligaments are observed near the nozzle exit, but they tend to break up while moving downstream.     

Study on the characteristic of the spray angle in pressure swirl spray atomisation

Based on the suggested atomisation theory for the swirl spray conical film, the formula for the spray angle characteristic of pressure swirl spray atomisation θ=tg^-12·(1-φ) is derived from the relation of acting forces in swirl spray.The spray angle characteristics of swirl spray are worked out with various formulas and compared with actual test data. The results show that the derived formulas for spray angle in this article agree comparatively well with the results from experiments, and that the expressions are simple. They are of definite value in practice.     

Theoretical and experimental studies on air gap membrane distillation

Air gap membrane distillation (AGMD) is an innovative membrane separation technique for pure water extraction from aqueous solutions. In this study, both theoretical and experimental investigations are carried out on AGMD of different aqueous solutions, namely, tap water, salted water, dyed solutions, acid solutions, and alkali solutions. A simple mechanistic model of heat and mass transfer associated with AGMD is developed. Simple relationships of permeate flux, total heating or cooling load and thermal efficiency of AGMD with respect to the membrane distillation temperature difference are obtained. Effects of solution concentration and the width of the air gap in AGMD are analyzed. In the experimental study, the experiments were conducted using 1m PTFE membrane with a membrane distillation temperature difference up to 55^∘C. The AGMD system yields a permeate flux of pure water of up to 28kg/m²h. Direct comparison of the experimental results with the proposed modeling predictions shows a fairly good match. Received on 19 May 1998     

Apparatus for investigating the liquid-nitrogen distribution in the spray cone of a jet flowing out of a nozzle into an air flow

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 93–97, September–October, 1991.     

Theoretical and experimental investigations of low Mach number turbulent cavity flows

Theoretical and experimental investigations are conducted for rectangular cavities of varying sizes in low Mach number turbulent flows. Emphasis is put on the characterization of the generation of self-sustained oscillations in order to develop methods of active control applied to the aeroacoustics of cavity flows. A linearized stability analysis for low Mach number flows is proposed in which the interface of the cavity is modeled by a vorticity layer. Subsequently, the cavity flow is investigated experimentally in a subsonic wind tunnel, using pressure measurements and a phase-locked particle image velocimetry system. Experimental results indicate that the oscillation process is governed by convective waves, with no definite influence of convected vortical structures. The good agreement between the experimental data and the predictions given by the model allows the identification of the oscillations of the cavity interface via the parameters issued from the theoretical analysis.List of symbols c speed of sound, m/s - f frequency, Hz - G Greens function - h displacement of the vorticity layer, m - K_R Rayleigh conductivity of the aperture, m - k₀ acoustic wavenumber, rad/m - k,n, Rossiter formula parameters - M Mach number of the freestream - pressure, Pa - Q volume flux, m³/s - Re_L Reynolds number Re_L=UL/ - Re_x1 Reynolds number Re_x1=Ux₁/ - Re Reynolds number Re=U/ - S frequency based Strouhal number - T period, s - t time, s - U,U,U^± freestream velocity, m/s - v velocity, m/s - W,L,D model cavity dimensions, m - w,l,d analytical cavity dimensions, m - x,y Cartesian coordinates, m - boundary-layer thickness, m - vorticity thickness, m - * boundary-layer displacement thickness, m - ,^± velocity potential, m²/s - acoustic wavelength, m - kinematic viscosity, m²/s - boundary-layer momentum thickness, m - ₀ density, kg/m³ - pulsation based Strouhal number - angular frequency, rad/s - vorticity, s ^–1 - , non-dimensional coordinates x₁,y₁ - non-dimensional displacement h     

In-cylinder swirl formation process in a four-valve diesel engine

An experimental study is presented on the steady flow in a four-valve diesel engine rig by using hot-wire anemometry. Through the analysis of the in-cylinder three-dimensional flow field of a four-valve diesel engine, the in-cylinder swirl formation process at various valve lift was investigated. A new criterion is proposed for predicting the emergence of a stable-swirl formation interface, based on swirl angular momentum flux. A stable-swirl formation interface exists when the main swirl angular momentum flux is nearly equal to the in-cylinder air total angular momentum flux. Received: 13 March 2000/Accepted: 7 February 2001     

Numerical and experimental investigations of pseudo-shock systems in a planar nozzle: impact of bypass mass flow due to narrow gaps

During previous investigations on pseudo-shock systems, we have observed reproducible differences between measurement and simulations for the pressure distribution as well as for size and shape of the pseudo-shock system. A systematic analysis of the deviations leads to the conclusion that small gaps of $\Delta z=O(10^{-4})$  m between quartz glass side walls and metal contour of the test section are responsible for this mismatch. This paper describes a targeted experimental and numerical study of the bypass mass flow within these gaps and its interaction with the main flow. In detail, we analyze how the pressure distribution within the channel as well as the size, shape and oscillation of the pseudo-shock system are affected by the gap size. Numerical simulations are performed to display the flow inside the gaps and to reproduce and explain the experimental results. Numerical and experimental schlieren images of the pseudo-shock system are in good agreement and show that especially the structure of the primary shock is significantly altered by the presence of small gaps. Extensive unsteady flow simulations of the geometry with gaps reveal that the shear layer between subsonic gap flow and supersonic core flow is subject to a Kelvin–Helmholtz instability resulting in small pressure fluctuations. This leads to a shock oscillation with a frequency of $f= O(10^5) \hbox {s}^{-1}$ . The corresponding time scale $\tau $  (s) is 16 times higher than the characteristic time scale $\tau _\delta =\delta /U_\infty $ of the boundary layer given by the ratio of the boundary layer thickness $\delta $ directly ahead of the shock and the undisturbed free stream velocity $U_\infty $ . To assess the reliability of our numerical investigations, the paper includes a grid study as well as an extensive comparison of several RANS turbulence models and their impact on the predicted shape of pseudo-shock systems.     

Theoretical analysis of heat and mass transfer in swirl atomizers

In this study, theoretical analyses have been performed to investigate the effects of atomizer construction and controlled pressure difference of swirl atomizers. The analysis of fluid field in the swirl chamber is governed by mass/energy conservation rules; in the region outside the nozzle, the analysis of oscillation of liquid sheet is based on Squire’s expression for the amplitude growth rate. With some physical assumptions of control volume, initial values and model correlation, analytical results make it possible to predict film thickness, velocity distribution, spray cone angle and droplet size directly. The distribution of velocity profile and boundary layer thickness in the swirl chamber have been established with the aid of MATLAB. Based on the results we obtained, we here propose the change of individual design parameter and its corresponding flow number to optimize the performance of swirl atomizers.     

Theoretical and experimental investigation of the frequency characteristics of the negative corona discharge in a hot turbulent air jet

The negative corona discharge in a hot turbulent air jet is investigated experimentally and theoretically, within the framework of a discrete dischargemodel making it possible to determine its frequency characteristics. When using the discrete dischargemodel, in contrast to describing the discharge as a continuous electric charge motion, it is assumed that, like in the experiment, the charge is transferred within the discharge space by separate portions. This was noted in an old monograph [1]. Some results on this subject were presented in [2]. In [3], a discrete model of the corona discharge was developed and realized numerically for a system of spherical electrodes in the presence of a hydrodynamic source at the center of the system. In the present study, certain results earlier obtained are generalized. An approximate, using similarity and dimensional methods, model is proposed for the negative corona discharge in a hot turbulent air jet and the frequency discharge characteristics under these conditions are investigated experimentally.     

Effect of ideal-gas flow swirl on the optimum supersonic contour of an axisymmetric nozzle with break

The effect of swirling the flow at the nozzle inlet on the shape of the optimum supersonic section with a break at the point of intersection of the limiting characteristic and the contour is investigated within the framework of the ideal (inviscid and non-heat-conducting) gas model. A direct method based on reduction to a problem of nonlinear programming is used for the numerical solution of the corresponding variational problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 155–160, May–June, 1989.In conclusion, the authors wish to thank N. I. Tillyaeva and A. N. Kraiko for participating in the discussions and A. A. Glazunov for assisting with the work.     

Numerical and experimental investigations on the cavitating flow in a cascade of hydrofoils

The cavitating flow in a cascade of three hydrofoils was investigated by experimental means and numerical simulation. Experiments on the 2D-hydrofoils cascade were carried out at Darmstadt University of Technology in a rectangular test section of a cavitation tunnel. A numerical model developed at LEGI (Grenoble) to describe the unsteady behaviour of cavitation, including the shedding of vapour structures, was applied to the hydrofoils cascade geometry. Results of both experimental and numerical studies show a strong interaction between the cavities of each flow channel besides the typical self-oscillation of cloud cavitation. A detailed comparison of the results allows an interpretation of the interaction mechanisms to be proposed.     

Theoretical and experimental investigations of the flow of a viscous fluid near the line of intersection of a cylindrical surface and a flat surface

Flow along a corner was investigated at large Reynolds numbers in, for example, [1–3]. The present author [4] considered flow in the neighborhood of a corner formed by the intersection of a plane and a concave cylindrical surface, the main attention being devoted to the formation of the three-dimensional boundary layer on the plane near the corner. It was shown that the curvature of one of the intersecting surfaces changes the flow pattern qualitatively. In the present paper, we report an investigation of the formation of the flow on a concave cylindrical surface near such a corner and consider how the flow is rearranged in the neighborhood of a corner in, for example, a channel of rectangular cross section that has an initial straight section and then a bend with a discontinuity of the curvature of the line of intersection of the concave and flat sides of the channel. The results are given of some experimental investigations of flow near the line of intersection of a flat wall and a curved (concave and convex) wall at a bend in a rectangular channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 64–68, January–February, 1983.I thank G. M. Bam-Zelikovich for constant interest in the work and A. I. Ruban for a number of extremely helpful comments.     

An experimental investigation of hypervelocity flow in a conical nozzle

The flow in a conical nozzle is examined experimentally for a range of hypervelocity conditions in a free-piston shock tunnel. The pitot pressure levels compare reasonably well with an inviscid numerical prediction which includes a correction for the growth of the nozzle wall boundary layer. The size of the nozzle wall boundary layer seems to be well predicted by semi-empirical expressions developed for perfect gas flows, as do data from other free-piston shock tunnels.