Large Eddy Simulation of Compressible Subsonic Turbulent Jet Starting From a Smooth Contraction Nozzle

Compressible subsonic turbulent starting jet with a relatively large Reynolds number of significant practical importance is investigated using large eddy simulation (LES), starting from a smooth contraction nozzle. The computational domain of truncated conical shape is determined through the comparison of the time-averaged numerical solution with the particle imaging velocimetry measurements for the steady jet. It is shown that the starting jet consists of a leading vortex ring followed by a quasi-steady jet, and the instantaneous velocity field exhibits contraction and expansion zones, corresponding to the high pressure (HP) and low pressure (LP) regions formed by the convecting vortex rings, and are related to the Kelvin-Helmholtz instability. The thin boundary layer inside the smooth contraction nozzle evolves into a shear layer at the nozzle exit and develops with the downstream penetration of the jet. Using λ ₂ criterion, the formation and evolution of the vortical structures are temporally visualized, illustrating distortion of vortex rings into lobed shapes prior to break-down. Rib-shape streamwise vortex filaments exist in the braid region between a pair of consecutive vortex rings due to secondary instabilities. Finally, formation and dynamics of hairpin vortices in the shear layer is identified.     

On the Effect of Pipe Boundary Layer Growth on the Formation of a Laminar Vortex Ring Generated by a Piston/Cylinder Arrangement

The growth of a boundary layer at the nozzle wall during laminar vortex ring formation by a nozzle flow generator (piston/cylinder arrangement) is analysed theoretically and numerically and used for modelling the formation of real vortex rings. The predictions of the model are in good agreement with previous experimental and numerical results. Received 19 January 2000 and accepted 17 August 2001     

Penetration length and diameter development of vortex rings generated by impacting water drops

The formation of water drops underneath nozzles was studied numerically to provide the basis for repeatable experimental drop formation. The drops detached from the nozzle and impacted on a free water surface forming vortex rings. Experimental results obtained through kinematographic studies of the penetration and growth of these vortex rings are presented. Variations of the penetration depth were measured, depending on the nozzle height above the water surface where the drops were formed. The experiments revealed that it is the state of oscillation at impact that defines the penetration length. Interesting variations of the vortex ring diameter with time were recorded. A good overall understanding of the behavior of the diameter variation was obtained when it was plotted as a function of the penetration depth.     

Acoustic Sounding of Vortex Rings in a Continuously Stratified Fluid

The experimental simulation of solitary vortex rings in a stratified fluid performed using high-frequency echo-sounding and optical visualization methods shows that on the range from turbulent to laminar regimes the vortex is a volume inhomogeneity with a sound scattering cross-section m _vU ⁵, where U is the translational velocity. The absolute value of m _v is determined by the microscale component of the vortex microstructure, which is commensurable with the sounding sonic wave length.     

The decay of confined vortex rings

Vortex rings are produced during the ejection of fluid through a nozzle or orifice, which occurs in a wide range of biological conditions such as blood flow through the valves of the heart or through arterial constrictions. Confined vortex ring dynamics, such as these, have not been previously studied despite their occurrence within the biological flow conditions mentioned. In this work, we investigate laminar vortex rings using particle image velocimetry and develop a new semi-empirical model for the evolution of vortex ring circulation subject to confinement. Here we introduce a decay parameter ?? which exponentially grows with increasing vortex ring confinement ratio, the ratio of the vortex ring diameter (D _VR) to the confinement diameter (D), with the relationship $\beta=4.38 \exp(9.5D_{\rm VR}/D),$ resulting in a corresponding increase in the rate of vortex ring circulation decay. This work enables the prediction of circulation decay rate based on confinement, which is important to understanding naturally occurring confined vortex ring dynamics.     

A note on the cause of rebound in the head-on collision of a vortex ring with a wall

It is well documented that a trailing vortex pair approaching the ground, and a vortex ring colliding head-on with a rigid plane, experience a reversal in axial velocity which is commonly referred to as rebound. One explanation of this phenomenon suggests that it is essentially an inviscid process due to the effect of the finite core-size, whereas another and more widely accepted explanation attributes it to the influence of a secondary vortex which is generated at the surface by viscous effects. The aim of this paper is to assess experimentally the validity of these competing explanations. To achieve this, flow visualization studies of the collision of a vortex ring with a wall are compared with those of the head-on collision of two identical rings. The head-on collision is designed to mimic the inviscid, free-slip case of a ring/wall interaction. This paper describes the experimental findings.A version of this paper was presented at the 10th Australasian Fluid Mechanics Conference, University of Melbourne, Australia, 11–15 December 1989     

Vortex formation process in gravity-driven starting jets

Experiments were conducted to investigate the vortex formation process in gravity-driven starting jets at three Reynolds numbers ( 3,528 and 4,716, where D is the nozzle diameter, the average discharging velocity and ν the kinematic viscosity). Planar laser induced fluorescence (PLIF) was used to visualize the flow while particle image velocimetry (PIV) was used to quantify the 2D velocity and vorticity fields. Vortex leapfrogging was found to appear at Re = 2,358, while pinch-off for the leading vortex was observed in the other two cases. Conditions for the vortex pinch-off appeared to be different from those found in the piston-driven starting jets. Although the leading vortex attained the maximum circulation and energy level very quickly after the jet was initiated, its detachment from the main stem may not be achieved necessarily. Attempt had been made to elaborate the different flow characteristics for respective cases from the related distribution of circulation and energy level via the measured velocity field by PIV.     

Formation and evolution of vortex rings induced by interactions between shock waves and a low-density bubble

The deformation and instability of a low-density spherical bubble induced by an incident and its reflected shock waves are studied by using the large eddy simulation method. The computational model is firstly validated by experimental results from the literature and is further used to examine the effect of incident shock wave strength on the formations and three-dimensional evolutions of the vortex rings. For the weak shock wave case (Ma?=?1.24), the baroclinic effect induced by the reflected shock wave is the key mechanism for the formation of new vortex rings. The vortex rings not only move due to the self-induced effect and the flow field velocity, but also generate azimuthal instability due to the pressure disturbance. For the strong shock wave case (Ma?=?2.2), a boundary layer is formed adjacent to the end wall owing to the approach of vortex ring, and unsteady separation of the boundary layer near the wall results in the ejection and formation of new vortex rings. These vortex rings interact in the vicinity of the end wall and finally collapse to a complicated vortex structure via azimuthal instability. For both shock wave strength cases, the evolutions of vortex rings due to the instability lead to the formation of the complicated structure dominated by the small-scale streamwise vortices.     

Sound radiation by a system of vortices

The radiation of sound in a slightly compressible medium by elementary vortex formations is considered-two vortex filaments with identical intensities which radiate cylindrical waves, and two vortex rings with identical intensities which radiate spherical waves. It is shown that in the first case the sound intensity is proportional to M⁴, where T_ij=₀u_iu_j is the Mach number (N is the vortex intensity, 2h is the distance between vortices, and c is the speed of sound). In the second case, in a coordinate system fixed with the vortex rings, the sound intensity is proportional to M⁵, which is in agreement with the results of Lighthill [1, 2].In conclusion I wish to thank A. M. Obukhov for posing the problem and his discussion of the results.     

Identification of zones in a free evolving vortex ring

A direct numerical simulation of a three-dimensional free evolving vortex ring has been performed to understand some features of the dynamics of vortex rings. In previous experiments, a persistent wake has been observed and the direct simulation has clarified the causes of this wake formation. A kinematic alignment analysis of the vorticity vector with the eigenvectors of the strain-rate tensor, together with vorticity visualisations, have been employed to explain the growth of the Widnall instabilities. The analysis has shown the presence of two different zones, the first characterised by intense vorticity and low strain rate and the second with opposite features. In the former, there is a ring core which maintains its coherence even in the long term, in the latter there are elongated structures contributing to the deformation of the ring.     

Interaction of the vortex structures formed in parallel pulsed jets

The experimental investigation of the lateral interaction of the heads of pulsed jets and primary shock waves at various nozzle spacings and pressure ratio numbers is described. The various stages of formation of a composite pulsed jet issuing from a multinozzle block are classified and the flow development mechanisms are explored. It is shown for both a block and a single nozzle the shock wave travels with almost the same velocity, whereas the jet front formed at the exit from a single nozzle moves much more slowly than the jet front formed beyond a nozzle block. Long-lived lateral bursts of gas, whose dimensions are an order greater than those of the jet bursts, are detected. Their long period of existence considerably increases the stabilization time of the steady-state structure and parameters as compared with a single pulsed jet with the same flow rate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 153–159, November–December, 1987.     

A flow field study of an elliptic jet in cross flow using DPIV technique

The digital particle image velocimetry (DPIV) technique has been used to investigate the flow fields of an elliptic jet in cross flow (EJICF). Two different jet orientations are considered; one with the major axis of the ellipse aligned with the cross flow (henceforth referred to as a low aspect ratio (AR) jet), and the other with the major axis normal to the cross flow (henceforth referred to as a high aspect ratio jet). Results show that the vortex-pairing phenomenon is prevalent in the low aspect ratio jet when the velocity ratio (VR)3, and is absent in the high aspect ratio jet regardless of the velocity ratio. The presence of vortex pairing leads to a substantial increase in the leading-edge peak vorticity compared to the lee-side vorticity, which suggests that vortex pairing may play an important role in the entrainment of ambient fluid into the jet body, at least in the near-field region. In the absence of vortex pairing, both the leading-edge and the lee-side peak vorticity increase monotonically with velocity ratio regardless of the aspect ratio. Moreover, time-averaged velocity fields for both AR=0.5 and AR=2 jets reveal the existence of an unstable focus (UF) downstream of the jet, at least for VR2. The strength and the location of this focus is a function of both the velocity ratio and aspect ratio. In addition, time-averaged vorticity fields show a consistently higher peak-averaged vorticity in the low aspect ratio jet than in the high aspect ratio jet. This behavior could be due to a higher curvature of the vortex filament facing the cross flow in the low aspect ratio jet, which through mutual interaction may lead to higher vortex stretching, and therefore higher peak-averaged vorticity.Nomenclature A nozzle or jet cross-sectional area - AR aspect ratio, defined as the ratio of the nozzle cross-stream dimension to its streamwise dimension, =H/L - D characteristic jet diameter (for circular jet only) - D_h hydraulic diameter, =4A/P - D_major major axis of an elliptic nozzle - D_minor minor axis of an elliptic nozzle - H cross-stream dimension of the nozzle - L streamwise dimension of the nozzle - P perimeter of the nozzle - Re_j jet Reynolds number, =V_jD/ - VR velocity ratio, =V_j/V - V_j mean jet velocity - V mean cross-flow velocity - x downstream distance from jet center - X cross-plane vorticity - kinematic viscosity     

Effect of an Exit-Wedge Angle on Pinch-off and Mass Entrainment of Vortex Rings in Air

The effects of exit-wedge angle on evolution, formation, pinch-off, propagation and diffusive mass entrainment of vortex rings in air were studied using digital particle image velocimetry. Vortex rings were generated by passing a solenoid-valve-controlled air jet through a cylindrical nozzle. Experiments were performed over a wide range of exit-wedge angles (10° ≤ α ≤ 90°) of the cylindrical nozzle, initial Reynolds numbers (450 ≤ Re ≤ 4,580) and length-to-diameter ratios (0.9 ≤ L/D ≤ 11) of the air jet. For sharp edges (α ≤ 10°), a secondary ring may emerge at high Reynolds numbers, which tended to distort the vortex ring if ingested into it. For blunt edges (α ≥ 45°), by contrast, stable vortex rings were produced. The formation phase of a vortex ring was found to be closely related to its evolution pattern. An exit-wedge angle of 45° was found to be optimal for rapid pinch-off and faster propagation and better stability of a vortex ring. Diffusive mass entrainment was found to be between 35% and 40% in the early stages of a vortex ring propagation and it gradually increased throughout the course of vortex ring propagation. Entrainment fraction was found to be sensitive to the L/D ratio of the initial jet and decreases when the L/D ratio is increased.     

Computational analysis of exit conditions on the sound field of turbulent hot jets

A hybrid computational fluid dynamics (CFD) and computational aeroacoustics (CAA) method is used to compute the acoustic field of turbulent hot jets at a Reynolds number $Re=316,000$ and a Mach number $M=0.12$. The flow field computations are performed by highly resolved large-eddy simulations (LES), from which sound source terms are extracted to compute the acoustic field by solving the acoustic perturbation equations (APE). Two jets are considered to analyze the impact of exit conditions on the resulting jet sound field. First, a jet emanating from a fully resolved non-generic nozzle is simulated by solving the discrete conservation equations. This computation of the jet flow is denoted free-exit-flow (FEF) formulation. For the second computation, the nozzle geometry is not included in the computational domain. Time averaged exit conditions, i.e. velocity and density profiles of the first formulation, plus a jet forcing in form of vortex rings are imposed at the inlet of the second jet configuration. This formulation is denoted imposed-exit-flow (IEF) formulation. The free-exit-flow case shows up to 50% higher turbulent kinetic energy than the imposed-exit-flow case in the jet near field, which drastically impacts noise generation. The FEF and IEF configurations reveal quite a different qualitative behavior of the sound spectra, especially in the sideline direction where the entropy source term dominates sound generation. This difference occurs since the noise sources generated by density and pressure fluctuations are not perfectly modeled by the vortex ring forcing method in the IEF solution. However, the total overall sound pressure level shows the same qualitative behavior for the FEF and IEF formulations. Towards the downstream direction, the sound spectra of the FEF and IEF solutions converge.     

A visual study of vortex-induced subcritical instability on a flat plate laminar boundary layer

This paper reports results of our experimental investigation on flow instability on a flat plate laminar boundary layer caused by a captive vortex migrating far outside the boundary layer. Results show that the sign of the circulation associated with the vortex is the main determinant for the severity of the boundary layer instability. A captive vortex with an opposite sign to that of the unperturbed shear layer vorticity causes a breakdown ahead of it, while the one with the same sign as the unperturbed shear layer vorticity gives rise to weaker excitation trailing it. Additional parameters that influence the flow instability are the strength and distance of the vortical disturbance from the boundary layer, as well as the translational speed of the vortex. These experimental results compliment the corresponding theoretical analysis of Sengupta et al. (J Fluid Mech 493:277–286, 2003).     

Active control of an axisymmetric jet with distributed electromagnetic flap actuators

Miniature electromagnetic flap actuators are developed and mounted on the periphery of the nozzle exit of an axisymmetric jet to induce various flow modes and enhance mixing processes. It is demonstrated that the flap actuators can significantly modify the large-scale vortical structures. In particular, when the flaps are driven in anti-phase on either side of the jet, alternately inclined and bent vortex rings are generated, and the jet bifurcates into two branches. Since the vortex rings are formed at the very vicinity of the nozzle exit, the bifurcation is accomplished as close as x/D=3.     

Investigation of flow beyond a supersonic nozzle by an electron-beam technique

The results of an experimental study of a flow of rarefied gas of density 10^–5 g/cm³ beyond the cutoff of a hypersonic nozzle (M11) by means of an electron beam with energy up to 43 keV are presented. The density and velocity fields at different distances from the nozzle and various receiver pressures were measured using this method and the static and total pressure fields were also measured with the help of a Pitot tube. The flow parameters beyond the nozzle were calculated for two limiting cases: with equilibrium condensation and without condensation. This calculation is compared with the experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–117, January–February, 1976.The authors thank S. N. Romanenko for help with the electron-beam experiments.     

Two-dimensional transonic vortex flows of an ideal gas

Equations are obtained for two-dimensional transonic adiabatic (nonisoenergetic and nonisoentropic) vortex flows of an ideal gas, using the natural coordinates (=const is the family of streamlines, and =const is the family of lines orthogonal to them). It is not required that the transonic gas flow be close to a uniform sonic flow (the derivation is given without estimates). Solutions are found for equations describing vortex flows inside a Laval nozzle and near the sonic boundary of a free stream.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 105–109, September–October, 1973.     

Inviscid vortex structures in the shock layers of conical flows around V wings

The applicability of the criteria of existence of inviscid vortex structures (vortex Ferri singularities) is studied in the case in which a contact discontinuity of the corresponding intensity proceeds from the branching point of the λ shock wave configuration accompanying turbulent boundary layer separation under the action of an inner shock incident on the leeward wing panel. The calculated and experimental data are analyzed, in particular, those obtained using the special shadow technique developed for visualizing supersonic conical streams in nonsymmetric, Mach number 3 flow around a wing with zero sweep of the leading edges and the vee angle of 2π /3. The applicability of the criteria of existence of inviscid vortex structures is established for contact discontinuities generated by the λ shock wave configuration accompanying turbulent boundary layer separation realized under the action of a shock wave incident on the leeward wing panel. Thus, it is established that the formation of the vortex Ferri singularities in a shock layer is independent of the reason for the existence of the contact discontinuity and depends only on its intensity.     

不定原点喷嘴射流中流体物理的实验研究

为了能够更好地了解不定源喷嘴（indeterminate origin nozzle）射流中的物理过程，本文应用平面激光诱导荧光技术对一个大尺度的水射流进行了实验研究。流场显示的实验结果表明不定源喷嘴在射流的剪切层引入了蘑菇形反向旋转的涡对。这些涡的矢量方向与射流方向相同或相反，被称为流向涡（streamwise vortex）。由于射流中存在开尔文一亥姆霍兹不稳定，每当一个横向涡（spanwisevortex，即涡的矢量方向与射流方向垂直）从喷嘴脱流时会产生瞬时的低压，该瞬时低压促使向内发展的流向涡对在喷嘴的凹槽处生成。这些涡对在向下游流动的过程中会重组并在喷嘴的尖峰面生成向外发展的涡对。这些流向涡极大地影响了射流的发展。流向涡与横向涡的相互作用促使射流更早地发展成为湍流。由于流向涡同时也在射流中引入了径向的剪切流动，因此导致了更多的湍流生成从而增强了射流与周围流体的混合。