On swirling jets

An exact solution to the Navier-Stokes equations is found for a jet emanating from the end of a vortex filament into a region filled with a fluid. Depending on the degree of swirling of the jet, a closed or open flow regime is realized. In the case of strong swirling, the solution is not unique. Approximate analytic solutions to problems as well as numerical solutions are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 26–35, January–February, 1979.I am grateful to M. Kh. Pravdin for the numerical calculations.     

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.

     

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.     

Dynamics of swirling jet flows

Experimental investigations of near-field structure of coaxial flows are presented for four different configurations: coaxial jets without rotation (reference case), outer flow rotating only (OFRO), inner-jet rotating only (IJRO) and corotating jets (CRJ). The investigations are performed in a cylindrical water tunnel, with an independent rotation of two coaxial flows. Laser tomography is used to document the flow field, and photographs are shown for different configurations. Time mean velocity profiles obtained by PIV, with and without swirl, are also presented. The dynamics of the swirling jets in the initial region (i.e. near the exit of the jets) is described. The effects of azimuthal velocity and axial velocity ratio variations on flow dynamics are examined. The appearance and growth of the first instabilities are presented and compared with some theoretical results, as is the influence of the rotation (inner or outer) on the dominating structures.     

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     

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.     

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)     

Dynamics of sprinkler jets

The problem of the motion of droplet-air sprinkler jets is examined. On the basis of the equations of a turbulent two-phase boundary layer the trajectories and range of these jets are calculated. A comparison of the calculation results with experiment indicates satisfactory agreement. It is shown that the expression for the range of a body projected at an angle to the horizontal gives exaggerated values for the range, while calculating the range for a single droplet with allowance for the air resistance gives values that are much too low. It has been established that in calculating the motion of sprinkler jets it is necessary to take into account the air resistance to the water droplets reduced as a result of the acceleration of the air in the immediate vicinity of the preceding droplets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 60–67, September–October, 1985.     

Dynamics of premixed confined swirling flames

Considerable effort is currently being extended to examine the fundamental mechanisms of combustion instabilities and develop methods allowing predictions of these phenomena. One central aspect of this problem is the dynamical response of the flame to incoming perturbations. This question is examined in the present article, which specifically considers the response of premixed swirling flames to perturbations imposed on the upstream side of the flame in the feeding manifold. The flame response is characterized by measuring the unsteady heat release induced by imposed velocity perturbations. A flame describing function is defined by taking the ratio of the relative heat release rate fluctuation to the relative velocity fluctuation. This quantity is determined for a range of frequencies and for different levels of incoming velocity perturbations. The flame dynamics is also documented by calculating conditional phase averages of the light emission from the flame and taking the Abel transform of these average images to obtain the flame geometry at various instants during the cycle of oscillation. These data can be useful to the determination of possible regimes of instability. To cite this article: P. Palies et al., C. R. Mecanique 337 (2009).     

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.     

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     

Solution of the problem of flow of a non-axisymmetric swirling submerged jets

This paper considers the problem of a non-axisymmetric swirling jet of an incompressible viscous fluid flowing in a space flooded with the same fluid. The far field of the jet is studied under the assumption that the angular momentum vector corresponding to the swirling of the jet is not collinear to the momentum vector of the jet. It is shown that the main terms of the asymptotic expansion of the full solution for the velocity field are determined by the exact integrals of conservation of momentum, mass, and angular momentum. An analytical solution of the problem describing the axisymmetric swirling jet is obtained.     

Flow and mixing characteristics of swirling double-concentric jets subject to acoustic excitation

Characteristic flow modes, flow evolution processes, jet spread width, turbulence properties, and dispersion characteristics of swirling double-concentric jets were studied experimentally. Jet pulsations were induced by means of acoustic excitation. Streak pictures of smoke flow patterns, illuminated by a laser-light sheet, were recorded by a high-speed digital camera. A hot-wire anemometer was used to digitize instantaneous velocity instabilities in the flow. Jet spread width was obtained through a binary edge identification technique. Tracer-gas concentrations were measured for information on jet dispersions. Two characteristic flow patterns were observed: (1) synchronized vortex rings appeared in the low excitation intensity regime (the excitation intensity less than one) and (2) synchronized puffing turbulent jets appeared in the high excitation intensity regime (the excitation intensity greater than one). In the high excitation intensity regime, the “suction back” phenomenon occurred and therefore induced in-tube mixing. The jet spread width and turbulent fluctuation intensity exhibited particularly large values in the high excitation intensity regime at the excitation Strouhal numbers smaller than 0.85. At the excitation Strouhal numbers >0.85, the high-frequency effect caused significant decay of jet breakup and dispersion—the jet spread width and fluctuation intensity decreased sharply and may, at very high Strouhal numbers, asymptotically approach values almost the same as the values associated with unexcited jets. Exciting the jets at the high excitation intensity regime, the effects of puffing motion and in-tube mixing caused breakup of the jet in the near field and therefore resulted in a small Lagrangian integral time and small length scales of fluctuating eddies. This effect, in turn, caused drastic dispersion of the central jet fluids. It is possible that the excited jets can attain 90 % more improvements than the unexcited jets. We provide a domain regarding excitation intensity and Strouhal number to facilitate identification of characteristic flow modes.     

Dynamics of interaction modes in excited annular jets

Evolution of coherent structures and their interaction dynamics are educed in the near field of an acoustically excited basic annular jet using conditional sampling technique based on a multiple triggering criterion to detect the two dominating modes of structure pattern. Acoustic excitation is applied with an aim to better organize the phase alignment of initial rolling and pairing process in the outer shear layer. Negligible modification of the time-averaged flow field results from the excitation. The educed coherent vorticities show that the two modes of evolution are due to the corresponding two modes of shedding pattern of the wake structures from the centerbody, namely the mode one wake and the mode zero wake. In both modes, the shear-layer mode jet vortex rings in the outer layer are perturbed by the shedding of wake structures in the inner region and interaction involving primary merging of three successive jet vortex rings or their partial circumferential sections is found. This results in the formation of wake-induced structures of the corresponding mode pattern, which possesses concentration of coherent vorticity and fluid circulation over a large spatial extent at 1 < x/D < 2. Secondary interactions, such as vortex tearing, are also observed.     

Numerical study of hysteresis in annular swirling jets with a stepped‐conical nozzle

This study investigates the experimentally observed hysteresis in the mean flow field of an annular swirling jet with a stepped‐conical nozzle. The flow is simulated using the Reynolds‐averaged Navier–Stokes (RANS) approach for incompressible flow with a k–ε and a Reynolds stress transport (RSTM) turbulence model. Four different flow structures are observed depending on the swirl number: ‘closed jet flow’, ‘open jet flow low swirl’, ‘open jet flow high swirl’ and ‘coanda jet flow’. These flow patterns change with varying swirl number and hysteresis at low and intermediate swirl numbers is revealed when increasing and subsequently decreasing the swirl. The influence of the inlet velocity profile on the transitional swirl numbers is investigated. When comparing computational fluid dynamics with experiments, the results show that both turbulence models predict the four different flow structures and the associated hysteresis and multiple solutions at low and intermediate swirl numbers. Therefore, a good agreement exists between experiments and numerics. Copyright © 2006 John Wiley & Sons, Ltd.     

Dynamics of two elliptical particles sedimentation in a vertical channel: chaotic state

The LB-DF/FD method derived from the Lattice Boltzmann Method and direct forcing/fictitious domain method is used to numerically investigate the dynamics and interaction of two elliptical particles settling in an infinitely long channel. One particle (EP0) is initially kept horizontal (major axis perpendicular to sedimentation) for all simulations while the other's (EP1) orientation is varied. It is found that if EP1strays away from horizontality, the particles undergo transitions from a steady state to reach a chaotic state. Furthermore, there are two distinct chaotic states for the particle motion when EP1 orientation is varied, in which a turning point is observed to distinguish the two states.     

Dynamics of single and twin circular jets in cross flow

2D-PIV is used to investigate the near field jet dynamics of a single and a tandem twin jet in cross flow at a blowing ratio of 3. The flow characteristics that were studied included jet trajectory and penetration, windward and leeward jet spread, and the size, location and magnitude of the reverse flow region. The tandem jet setup resulted in configuration where the rear jet was shielded by the front jet that allowed the rear jet to penetrate deeper into the cross stream. The penetration of front jet was found to be comparable to that of the single jet in the near field. Asymmetric jet spread was observed both in the windward and leeward side with higher jet spread in the leeward side for both the single and tandem jet configuration. Furthermore, for the tandem jet condition, the presence of rear jet was found to affect the windward spread of the front jet minimally. The windward and leeward spreads of the rear jet were observed to be decreased by the presence of the front jet. Reverse flow zones confined between the front and rear jets in tandem setup was also observed to be stronger than that of a single jet. A turbulent kinetic energy (TKE) analysis indicates that the behavior of a jet in tandem setup follows the same trend as that of an axisymmetric turbulent jet with low turbulence in the jet core and higher turbulence in the jet shear layer that subsequently transitions to high turbulence production in the jet core as the jet shear layers on windward and leeward side of the jet coalesce.