Helium jets discharging normally into a swirling air flow

The characteristics of helium jets injected normally to a swirling air flow are investigated experimentally using laser Doppler and hot-wire anemometers. Two jets with jet-to-crossflow momentum flux ratios of 0.28 and 12.6 are examined. The jets follow a spiral path similar to that found in the swirling air flow alone. Swirl acts to decrease jet penetration, but this is being counteracted by the lighter jet fluid density which is being pressed towards the tube center by the inward pressure gradient. Consequently, in spite of the large variation in momentum flux ratio, jet penetration into the main flow for the two jets investigated is about the same. The presence of the jet is felt only along the spiral path and none at all outside this region. Upstream of the jet, the oncoming swirling flow is essentially unaffected. These characteristics are quite different from jets discharging into a uniform crossflow at about the same momentum flux ratios, and can be attributed to the combined effects of swirl and density difference between the jet fluid and the air stream. Finally, the jets lose their identity in about fifteen jet diameters.List of symbols C mean volume concentration of helium - C _j mean volume concentration of helium at jet exit - c fluctuating volume concentration of helium - instantaneous volume concentration of helium - c RMS volume concentration of helium - D _j jet nozzle diameter - D _T diameter of tube - F flatness factor of c - J = _j U _j ² / _a U _a ^{gn 2} jet-to-crossflow momentum flux ratio - P(c) probability density function of c - r radial coordinate measured from tube centerline - R = D _T /2 radius of tube - Re _j = D _j U _j / _j jet Reynolds number - S = = tan swirl number - Sk skewness of c - instantaneous axial velocity - u RMS axial velocity - U mean axial velocity - local average mean axial velocity across tube - U _j jet exit velocity - U _a overall average mean axial velocity across tube - instantaneous circumferential velocity - w RMS circumferential velocity - W mean circumferential velocity - x axial coordinate measured from exit plane of swirler - x ₁ axial coordinate measured from centerplane of normal jet - y normal distance measured from tube wall - _j jet fluid kinematic viscosity - _a air density - _j jet fluid density - vane angle (constant)     

Behaviour of carbon dioxide jets in a confined swirling flow

An investigation of jet mixing in confined swirling flow, using carbon dioxide as the jet fluid, was carried out. In order to compare the present results with previous measurements by So et al¹ on homogeneous and helium jet mixing, the experiments were carried out in the same facility and under the same test conditions. Contrary to the flow characteristics found in helium jet mixing in confined swirling flow, density difference and swirl combined to give rise to an accelerated decay of the jet and increased mixing between jet and swirling air. Consequently, the second reversed flow region observed in the swirling flow was only slightly displaced downstream. This contrasted with a radial displacement of the second reversed flow region by the helium jets and a complete destruction of the reversed flow regions by the air jets.     

Shock wave configurations and flow structures in non-axisymmetric underexpanded sonic jets

An experimental and numerical study of underexpanded free sonic jet flows issuing from rectangular, elliptical and slot nozzles has been undertaken. Aspect ratios (AR) of 1, 2, and 4 are described at pressure ratios (exit plane pressure to ambient pressure), of 2 and 3. There is good qualitative agreement between the experimental observations and the numerical predictions. In the case of rectangular jets, a complex system of shock waves forming the incident shock system is identified. This shock wave system originates at the corners of the nozzle exits, and proceeds downstream. Mach reflections are found to occur on the incident shock wave surface as well as the presence of a Mach disk terminating the first jet cell. This Mach disk has the shape of a square, a hexagon, or an octagon depending on the nozzle shape. For slot and elliptical jets, the formation of the incident shock wave was not observed along the minor axis plane of the nozzle for AR > 2. The incident shock wave was observed to originate downstream of the nozzle exit in the major axis plane. This wave system undergoes a transition to Mach reflection as it propagates downstream of the nozzle exit. In all cases tested, the shape of the jet boundary is significantly distorted. In rectangular jets, the narrowing of the jet boundary along the diagonal axis of the nozzle exit is observed, and in the case of the elliptical and slot jets axis switching is noted.     

Solution to the problem of a swirling jet from an annular orifice

The problem of the propagation of a laminar immersed fan jet with swirling was considered in [1–3]. In [1], the jet source scheme was used to find a self-similar solution for a weakly swirling jet. An attempt to solve by an integral method the analogous problem for a jet emanating from a slit of finite size was made in [2]. In [3], the equations of motion for a jet with arbitrary swirling were reduced under a number of assumptions to the equations that describe the flow of a flat immersed jet. This paper gives the numerical solution to the problem of the propagation of a radial jet emanating with arbitrary swirling from a slit of finite size and an analytic solution for the main section of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 49–54, March–April, 1991.     

On the shapes of swirling annular jets of a liquid

Annular jets of an incompressible liquid moving in a gas at rest are of interest for applications. A critical analysis of the investigations into jets from centrifugal nozzles is contained in [1]. These investigations elucidated the experimentally observed tulip and bubble jet shapes, and also predict the existence of annular jets of periodic shape. However, simplifications of the flow details are made to obtain the results. For example, in the equations describing the equilibrium of the forces acting on the film, no allowance is made for forces that arise on account of the curving of its shape in the meridional sections nor for the variability of the tangential velocity component in the field of the centrifugal forces. In the present paper, the method of [2] is used to derive equations that describe the flow of swirling annular jets of liquid with uniform profile of the longitudinal velocities in an undisturbed ideal medium with allowance for surface tension and gravity forces and also the pressure difference outside and within the jet. The results of calculations are given that illustrate the dependence of the jet shapes on the relative contributions of the capillary and inertial forces and also the pressure difference, the intensity of the initial swirling, the angle at which the liquid leaves the nozzle, and the gravity force.Translated from Izyestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 144–148, September–October, 1979.I am grateful to V. Ya. Shkadov for interest in the work.     

The nonlinear evolution of swirling jets

We investigate the mechanisms of vorticity concentration, reorientation and stretching in a swirling jet, whose dynamics is dominated by the competition of a Kelvin-Helmholtz-type vortex sheet instability and a centrifugal Rayleigh instability. To this end, we employ an inviscid Lagrangian vortex filament technique. It is found that the axial jet velocity profile breaks the symmetry of the pure swirling flow. Conversely, the swirl is seen to modify the case dominated by a Kelvin-Helmholtz instability in that it results in the formation of counterrotating vortex rings. A pinch-off mechanism is observed which leads to a dramatic decrease in the local jet diameter. Furthermore, the vortex ring circulation is seen to be time dependent.

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Sommario In questo lavoro si analizza la dinamica della vorticità in un setto rotante in cui siano presenti, ed in competizione reciproca, fenomeni di instabilità di Kelvin-Helmholtz e di Rayleigh. A tale scopo si adotta una metodologia di soluzione non viscosa, Lagrangiana a filamenti vorticosi. Viene mostrato come il profilo di velocità assiale del getto altera la simmetria del moto di pura rotazione. Viceversa, la presenza della rotazione modifica il flusso dominato dall'instabilità di Kelvin-Helmholtz attraverso la formazione di anelli vorticosi controrotanti. L'interazione di questi due campi di velocità porta sia ad una considerevole riduzione del diametro locale del getto, sia ad una variazione temporale della circolazione degli anelli vorticosi.

     

Investigation of a submerged air jet during high-intensity swirling

The characteristics have been determined experimentally for the jet flow originating in the vicinity of the shear section of a centrifugal atomizer (up to the sections corresponding to the termination of the reverse flow zone). The distribution has been obtained for the mean velocity, the additive concentration, and the intensities of the turbulent velocity pulsations for different initial swirling.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 6, pp. 148–154, November–December, 1971.The author wishes to thank G. B. Krayushkin for interpretation of the measurements and O. V. Yakovlevskii for taking part in discussion of results.     

Von Kármán's swirling flow problem

Sans résumé     

Direct numerical simulation of confined swirling jets

This study investigates the Lagrangian acceleration and velocity of fluid particles in swirling flows via direct numerical simulation. The intermittency characteristics of acceleration and velocity of fluid particles are investigated at different swirl numbers and Reynolds numbers. The flatness factor and trajectory curvature are used to analyse the effect of Lagrangian intermittency. The joint probability density function of Lagrangian acceleration and turbulence intensity is shown to explain the augmentation effect of Lagrangian intermittency by the strongly swirling levels under the relatively low intensity of turbulence. In addition, the correlation between the Lagrangian acceleration and the turbulence intensity is enhanced as the swirl level increases. It shows the important effect of swirl on the motion behaviour of fluid particles in the strongly swirling flows.     

The stability of viscous liquid jets in a swirling gas

Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet injected into a gas with swirl. Here, the dimensionless parameterJ _e is again introduced, in the meantime, another dimensionless parameterE called as circulation is also introduced to represent the relative swirling intensity. With respect to the spatial growing disturbance mode, the numerical results obtained from solving the dispersion equation reveal the following facts. First, at the same value ofE, in pace with the changing ofJ _e , the variation of disturbance and the critical disturbance mode still keep the same characters. Second, the present results are the same as that of S.P. Lin whenJ _e >1; but in the range ofJ _e <1, it's no more the case, the swirl decreases the axisymmetric disturbance, yet increases the asymmetric disturbance, furthermore the swirl may make the character of the most unstable disturbance mode changed (axisymmetric or asymmetric); the above action of the swirl becomes much stronger whenJ _e ≪1. The project supported by the National Natural Science Foundation of China     

Experiments on the formation of a recirculation zone in swirling coaxial jets

 The near flow field of coaxial air jets, with swirl in the outer one, was studied using flow visualization and hot-wire anemometry. The flow is sensitive to both the swirl number and the mass flow ratio between the outer and inner jets. A necessary condition for the formation of an internal recirculation zone (IRZ) is that the swirl number must exceed a minimum value which depends on the mass flow ratio. Spectral analysis of the velocity fluctuations indicates that the formation of an IRZ in the present flow does not appear to be related to the growth of convective flow instabilities. Analysis of the flow visualization and X-wire data indicates that the vorticity dynamics model for vortex breakdown proposed by Brown and Lopez [J Fluid Mech (1990) 222: 553] provides a plausible mechanism for the formation of an IRZ in this flow. Received: 14 June 1999/Accepted: 7 December 1999     

Spatial instability of a swirling flow

The instability of a swirling flow of an inviscidand incompressible fluid is studied on the assumption that the wavenumber k=k_r + ik_i of the disturbance is complex while its frequency ω is real. This implies that the disturbance grows with distance along the axis of the swirling flow, but it does not grow with time. The occurrence of such disturbance is called spatial instability, in contrast to the temporal instability, in which k is a real number and ω=ω_r + iω_i is a complex one. The results show that spatial instability analysis is a useful tool for the comprehensive understanding of the instability behaviours of a swirling flow.     

Dynamics of heavy particles in two swirling jets

We report flow visualisations and laser Doppler anemometry (LDA) velocity measurements in the near field of two swirling jets. The Reynolds number based on jet diameter and bulk velocity at the nozzle exit is 1.4 × 10⁵. In the first jet, a small recirculation region is formed around the jet axis, while, in the second, the streamwise velocity remains positive and overshoots near the jet centre. In both cases, flow visualisations show that the vortex core of the jets is depleted of seeding particles. By using time-averaged distributions of the streamwise and tangential velocities measured at the nozzle outlet, the dynamics of the particles is simulated, by integrating their simplified equations of motion. The particles trajectory thus computed agrees well with that observed in the flow visualisations. Although the turbulence intensity is substantially different in the core of the two jets, its effect on the seeding concentration is localised near the edge of the core.     

The method of dynamic mode decomposition in shallow water and a swirling flow problem

In this paper, a new vector‐filtering criterion for dynamic modes selection is proposed that is able to extract dynamically relevant flow features from dynamic mode decomposition of time‐resolved experimental or numerical data. We employ a novel modes selection criterion in parallel with the classic selection based on modes amplitudes, in order to analyze which of these procedures better highlight the coherent structures of the flow dynamics. Numerical tests are performed on two distinct problems. The efficiency of the proposed criterion is proved in retaining the most influential modes and reducing the size of the dynamic mode decomposition model. By applying the proposed filtering mode technique, the flow reconstruction error is shown to be significantly reduced. Copyright © 2016 John Wiley & Sons, Ltd.     

Finite-amplitude instability of axisymmetric submerged jets

The effects associated with the finite-amplitude instability of submerged jets are numerically modeled. The investigation is carried out within the framework of the Euler inviscid model using the Bubnov-Galerkin method. The stability of an axisymmetric air jet submerged in an infinite fluid volume is considered with allowance for surface tension forces. The nonlinear evolution of a large-scale sinusoidal disturbance, stable according to the linear theory, is traced. The effect of an intense small-scale surface ripple on the development of the large-scale disturbance is studied, together with the reaction of the latter on the amplitude of the small-scale ripple.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 100–107, January–February, 1990.     

Some polynomial solutions for the non-axisymmetric Boussinesq problem

Solutions to the Boussinesq problem for the circular punch without axial symmetry can be obtained from corresponding axisymmetric solutions by parametric differentiation. The method is applied to the problem of the tilted flat punch, originally solved by Green, and to the indentation of a cylindrical surface by a flat circular punch.     

High-speed observation of ultrahigh-speed submerged water jets

Some peculiar phenomena occur around ultrahigh-speed submerged water jets accompanied by very severe cavitation erosion. Using the flow visualization technique with a xenon flash, the water jets were carefully observed, and the spatial distributions of highly erosive impulsive pressures around the jets were measured by means of a pressure-sensitive film technique. The effects of the injection pressure and the nozzle configuration are systematically clarified. Thus, the characteristics and structures of ultrahigh-speed submerged water jets are clearly shown.     

Supersonic swirling flow past a blunt body

The problem of supersonic swirling flow past a blunt body is studied numerically on the basis of the complete Navier-Stokes equations.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 158–160, November–December, 1994.