Numerical investigation of three-dimensionally evolving jets subject to axisymmetric and azimuthal perturbations

1991 ◽  
Vol 230 ◽  
pp. 271-318 ◽  
Author(s):  
J. E. Martin ◽  
E. Meiburg
Keyword(s):  
Shear Layer ◽  
Vortex Ring ◽  
Three Dimensional ◽  
Vortex Rings ◽  
Streamwise Vorticity ◽  
Plane Shear ◽  
Axisymmetric Jet ◽  
Spatially Periodic ◽  
Extensional Strain ◽  
Global And Local

We study the inviscid mechanisms governing the three-dimensional evolution of an axisymmetric jet by means of vortex filament simulations. The spatially periodic calculations provide a detailed picture of the processes leading to the concentration, reorientation, and stretching of the vorticity. In the purely axisymmetric case, a wavy perturbation in the streamwise direction leads to the formation of vortex rings connected by braid regions, which become depleted of vorticity. The curvature of the jet shear layer leads to a loss of symmetry as compared to a plane shear layer, and the position of the free stagnation point forming in the braid region is shifted towards the jet axis. As a result, the upstream neighbourhood of a vortex ring is depleted of vorticity at a faster rate than the downstream side. When the jet is also subjected to a sinusoidal perturbation in the azimuthal direction, it develops regions of counter-rotating streamwise vorticity, whose sign is determined by a competition between global and local induction effects. In a way very similar to plane shear layers, the streamwise braid vorticity collapses into counter-rotating round vortex tubes under the influence of the extensional strain. In addition, the cores of the vortex rings develop a wavy dislocation. As expected, the vortex ring evolution depends on the ratio R/θ of the jet radius and the jet shear-layer thickness. When forced with a certain azimuthal wavenumber, a jet corresponding to R/θ = 22.6 develops vortex rings that slowly rotate around their unperturbed centreline, thus preventing a vortex ring instability from growing. For R/θ = 11.3, on the other hand, we observe an exponentially growing ring waviness, indicating a vortex ring instability. Comparison with stability theory yields poor agreement for the wavenumber, but better agreement for the growth rate. The growth of the momentum thickness is much more dramatic in the second case. Furthermore, it is found that the rate at which streamwise vorticity develops is strongly affected by the ratio of the streamwise and azimuthal perturbation amplitudes.

Large- and small-scale vortical motions in a shear layer perturbed by tabs

1999 ◽  
Vol 382 ◽  
pp. 307-329 ◽  
Author(s):  
JUDITH K. FOSS ◽  
K. B. M. Q. ZAMAN
Keyword(s):  
Shear Layer ◽  
Pitch Angle ◽  
Large Scale ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Small Scale ◽  
Streamwise Vortices ◽  
Streamwise Vorticity ◽  
Cross Sectional ◽  
Scale Population

The large- and small-scale vortical motions produced by ‘delta tabs’ in a two-stream shear layer have been studied experimentally. An increase in mixing was observed when the base of the triangular shaped tab was affixed to the trailing edge of the splitter plate and the apex was pitched at some angle with respect to the flow axis. Such an arrangement produced a pair of counter-rotating streamwise vortices. Hot-wire measurements detailed the velocity, time-averaged vorticity (Ωx) and small-scale turbulence features in the three-dimensional space downstream of the tabs. The small-scale structures, whose scale corresponds to that of the peak in the dissipation spectrum, were identified and counted using the peak-valley-counting technique. The optimal pitch angle, θ, for a single tab and the optimal spanwise spacing, S, for a multiple tab array were identified. Since the goal was to increase mixing, the optimal tab configuration was determined from two properties of the flow field: (i) the large-scale motions with the maximum Ωx, and (ii) the largest number of small-scale motions in a given time period. The peak streamwise vorticity magnitude [mid ]Ωx−max[mid ] was found to have a unique relationship with the tab pitch angle. Furthermore, for all cases examined, the overall small-scale population was found to correlate directly with [mid ]Ωx−max[mid ]. Both quantities peaked at θ≈±45°. It is interesting to note that the peak magnitude of the corresponding circulation in the cross-sectional plane occurred for θ≈±90°. For an array of tabs, the two quantities also depended on the tab spacing. An array of contiguous tabs acted as a solid deflector producing the weakest streamwise vortices and the least small-scale population. For the measurement range covered, the optimal spacing was found to be S≈1.5 tab widths.

Simulation of particle dispersion in an axisymmetric jet

1988 ◽  
Vol 186 ◽  
pp. 199-222 ◽  
Author(s):  
J. N. Chung ◽  
T. R. Troutt
Keyword(s):  
Mixing Layer ◽  
Jet Flow ◽  
Particle Dispersion ◽  
Vortex Rings ◽  
Local Flow ◽  
Discrete Vortex ◽  
Turbulent Mixing Layer ◽  
Axisymmetric Jet ◽  
Free Jet ◽  
Global And Local

Particle dispersion in an axisymmetric jet is analysed numerically by following particle trajectories in a jet flow simulated by discrete vortex rings. Important global and local flow quantities reported in experimental measurements are successfully simulated by this method.The particle dispersion results demonstrate that the extent of particle dispersion depends strongly on γτ, the ratio of particle aerodynamic response time to the characteristic time of the jet flow. Particles with relatively small γτ values are dispersed at approximately the fluid dispersion rate. Particles with large γτ values are dispersed less than the fluid. Particles at intermediate values of γτ may be dispersed faster than the fluid and actually be flung outside the fluid mixing region of the jet. This result is in agreement with some previous experimental observations. As a consequence of this analysis, it is suggested that there exists a specific range of intermediate γτ at which optimal dispersion of particles in the turbulent mixing layer of a free jet may be achieved.

Formation of a Counter-Rotating Vortex Pair in a Plume in a Cross-Flow

2010 ◽  
Author(s):  
Masahiko Shinohara
Keyword(s):  
Vortex Ring ◽  
Three Dimensional ◽  
Cross Flow ◽  
Vortex Pair ◽  
Boussinesq Approximation ◽  
Streamwise Vorticity ◽  
Three Dimensional Flow ◽  
Flow Feature ◽  
Heated Area ◽  
Counter Rotating Vortex Pair

Numerical simulations are performed to study the formation of a counter-rotating vortex pair (CVP), a dominant flow feature in plumes inclined in a cross-flow. The unsteady three-dimensional flow fields are calculated by a finite difference method using the Boussinesq approximation. A plume rises from an isothermally heated square surface facing upward in air. Calculations show that the CVP originates not from horizontal spanwise vorticity in the velocity boundary layer on the bottom wall around the heated area, but from horizontal streamwise vorticity just above each side of the heated area. When the cross-flow begins after a plume forms a vortex ring in the cap above the heated area in a still environment, the vortex ring does not form a CVP. However, as the cap and the stem of the plume move downwind, a rotation about the streamwise axis appears just above each side edge of the heated area and grows into the CVP. We discuss the effect of entrainment into the stem and cap on the formation of the streamwise rotation that causes the CVP.

scholarly journals Three-dimensional visualization of the interaction of a vortex ring with a stratified interface

2017 ◽  
Vol 820 ◽  
pp. 549-579 ◽  
Author(s):  
Jason Olsthoorn ◽  
Stuart B. Dalziel
Keyword(s):  
Vortex Ring ◽  
Time Scale ◽  
Richardson Number ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Vortex Rings ◽  
Mixing Efficiency ◽  
Two Dimensional ◽  
Displacement Mode ◽  
Dimensional Instability

The study of vortex-ring-induced stratified mixing has long played a key role in understanding externally forced stratified turbulent mixing. While several studies have investigated the dynamical evolution of such a system, this study presents an experimental investigation of the mechanical evolution of these vortex rings, including the stratification-modified three-dimensional instability. The aim of this paper is to understand how vortex rings induce mixing of the density field. We begin with a discussion of the Reynolds and Richardson number dependence of the vortex-ring interaction using two-dimensional particle image velocimetry measurements. Then, through the use of modern imaging techniques, we reconstruct from an experiment the full three-dimensional time-resolved velocity field of a vortex ring interacting with a stratified interface. This work agrees with many of the previous two-dimensional experimental studies, while providing insight into the three-dimensional instabilities of the system. Observations indicate that the three-dimensional instability has a similar wavenumber to that found for the unstratified vortex-ring instability at later times. We determine that the time scale associated with this instability growth has an inverse Richardson number dependence. Thus, the time scale associated with the instability is different from the time scale of interface recovery, possibly explaining the significant drop in mixing efficiency at low Richardson numbers. The structure of the underlying instability is a simple displacement mode of the vorticity field.

A study of streamwise vortex structure in a stratified shear layer

1994 ◽  
Vol 281 ◽  
pp. 247-291 ◽  
Author(s):  
David G. Schowalter ◽  
Charles W. Van Van Atta ◽  
Juan C. Lasheras
Keyword(s):  
Shear Layer ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Streamwise Vorticity ◽  
Vortical Structures ◽  
Flow Evolution ◽  
Spanwise Vorticity ◽  
Unstable Part ◽  
Dimensional Instability ◽  
Vortex Tubes

The existence of an organized streamwise vortical structure, which is superimposed on the well known coherent spanwise vorticity in nominally two-dimensional free shear layers, has been studied extensively. In the presence of stratification, however, buoyancy forces contribute to an additional mechanism for the generation of streamwise vorticity. As the spanwise vorticity layer rolls up and pulls high-density fluid above low-density fluid, a local instability results. The purpose of the current investigation is to force the three-dimensional instability in the stratified shear layer. In this manner, we experimentally observe the effect of buoyancy on the streamwise vortex tube evolution, the evolution of the buoyancy-induced instability, and the interaction between these two vortical structures. A simple numerical model is proposed which captures the relevant physics of the flow evolution. It is found that, depending on the location, streamwise vortices resulting from vortex stretching may be weakened or enhanced by the stratification. Buoyancy-induced vortex structures are shown to form where the unstable part of the interface is tilted by the streamwise vortex tubes. These vortices strengthen initially, then weaken downstream, the timescale for this process depending upon the degree of stratification. For initial Richardson numbers larger than about 0.03, the baroclinically weakened vortex tubes eventually disappear as the flow evolves downstream and the baroclinically generated vortices dominate the three-dimensional flow structure.

Dynamics of a vortex ring in a rotating fluid

1996 ◽  
Vol 317 ◽  
pp. 215-239 ◽  
Author(s):  
R. Verzicco ◽  
P. Orlandi ◽  
A. H. M. Eisenga ◽  
G. J. F. Van Heijst ◽  
G. F. Carnevale
Keyword(s):  
Vortex Ring ◽  
Stokes Equations ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Swirl Flow ◽  
Degree Of Polarization ◽  
Navier Stokes ◽  
Vortex Rings ◽  
Rotating Fluid ◽  
Translation Velocity

The formation and the evolution of axisymmetric vortex rings in a uniformly rotating fluid, with the rotation axis orthogonal to the ring vorticity, have been investigated by numerical and laboratory experiments. The flow dynamics turned out to be strongly affected by the presence of the rotation. In particular, as the background rotation increases, the translation velocity of the ring decreases, a structure with opposite circulation forms ahead of the ring and an intense axial vortex is generated on the axis of symmetry in the tail of the ring. The occurrence of these structures has been explained by the presence of a self-induced swirl flow and by inspection of the extra terms in the Navier–Stokes equations due to rotation. Although in the present case the swirl was generated by the vortex ring itself, these results are in agreement with those of Virk et al. (1994) for polarized vortex rings, in which the swirl flow was initially assigned as a ‘degree of polarization’.If the rotation rate is further increased beyond a certain value, the flow starts to be dominated by Coriolis forces. In this flow regime, the impulse imparted to the fluid no longer generates a vortex ring, but rather it excites inertial waves allowing the flow to radiate energy. Evidence of this phenomenon is shown.Finally, some three-dimensional numerical results are discussed in order to justify some asymmetries observed in flow visualizations.

scholarly journals Head-on collisions of vortex rings upon round cylinders

2017 ◽  
Vol 833 ◽  
pp. 648-676 ◽  
Author(s):  
T. H. New ◽  
B. Zang
Keyword(s):  
Vortex Ring ◽  
Three Dimensional ◽  
Diameter Ratio ◽  
Vortex Rings ◽  
Strong Interactions ◽  
Small Scale ◽  
Secondary Vortex ◽  
Time Resolved ◽  
Flow Models ◽  
Flat Surfaces

Vortical structures and behaviour associated with vortex-ring collisions upon round cylinders with different cylinder-to-vortex-ring diameter ratios were studied using laser-induced fluorescence and time-resolved particle-image velocimetry techniques. Circular vortex rings of Reynolds number 4000 and three diameter ratios of $D/d=1$, 2 and 4 were considered in the present investigation. Results reveal that the collision behaviour is very different from that associated with flat surfaces, in which vortex disconnection and reconnection processes caused by the strong interactions between primary and secondary vortex rings produce small-scale vortex ringlets that eject away from the cylinders. For the cylinder with the largest diameter ratio used here, these vortex ringlets move towards each other along the collision axis, where they eventually collide to produce a vortex dipole that propagates upstream. However, as the diameter ratio decreases, these vortex ringlets are produced further away from the collision axis, which results in them ejecting away from the cylinder at increasingly larger angles relative to the collision axis. Trajectories of key vortex cores were extracted from the experimental results to demonstrate quantitatively the strong sensitivity of these vortical motions upon the diameter ratio. Furthermore, significant differences in the primary vortex-ring circulation along convex surfaces and straight edges after the collisions are observed. In particular, vortex flow models are presented here to better illustrate the highly three-dimensional flow dynamics of the collision behaviour, as well as highlighting the strong dependency of the secondary vortex-ring formation, vortex disconnection/reconnection processes, and ejection of the resulting vortex ringlets upon the diameter ratio. As such, these results are expected to shed more light on the more general scenario of vortex-ring collisions upon arbitrarily contoured solid boundaries.

Three-dimensional tertiary motions in a plane shear layer

1983 ◽  
Vol 135 (-1) ◽  
pp. 1 ◽  
Author(s):  
M. Nagata ◽  
F. H. Busse
Keyword(s):  
Shear Layer ◽  
Three Dimensional ◽  
Plane Shear

Three-dimensional vortex dynamics in a rectangular sudden expansion

1995 ◽  
Vol 289 ◽  
pp. 1-27 ◽  
Author(s):  
J. R. Hertzberg ◽  
C. M. Ho
Keyword(s):  
Shear Layer ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Sudden Expansion ◽  
Vortex Rings ◽  
Velocity Measurements ◽  
Inlet Channel ◽  
System Flow ◽  
Component Velocity ◽  
System Geometry

A detailed experimental study of flow in a rectangular sudden expansion using both active and passive forcing techniques has been made. The configuration consists of a 2:1-aspect-ratio rectangular channel which undergoes a sudden expansion such that the backward-facing step height (h) is uniform, and equal to the minor side of the inlet channel. Passive forcing was provided by the system geometry; the rectangular vortex rings formed in the shear layer of the expanding jet undergo self-induction, deforming the jet cross-section and introducing transverse velocities not found in plane or axisymmetric configurations. Active forcing was induced by periodic fluctuations in the system flow rate at the jet natural frequency. This served to enhance the unusual three-dimensional effects and phase-lock the flow for ensemble analysis. The results presented here include a description of the evolution of an isolated vortex in this configuration obtained from flow visualization of a suddenly started jet, as well as forced steady-state three-component velocity measurements which are used to characterize the flow field. The evolution of a rectangular vortex ring in the jet shear layer is traced, and both fluctuating and time-constant transverse velocities are related to the passage of the vortex structures.

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