Meccanica 29:403-410, 1994. © 1994 KluwerAcademic Publishers. Printed in the Netherlands,

On Streamwise Vortical Structures in the Near-Field of Axisymmetric Shear Layers

R. SUPRAYAN and H.E. F I E D L E R Technische Universitiit Berlin, Hermann FOttinger Institut, Strasse des 17 Juni, 135, D-10623 Berlin, Germany

(Received: February 1994; accepted in revised form: April 1994)

Abstract. Pairs of counter-rotating streamwise vortical structures have been observed using the LIF (Laser Induced Fluorescence) flow visualization technique by means of regular, video and high-speed photography in the near-field of an axisymmetric water jet. The temporal evolution of these structures at fixed z /d = 1.0, 2.0, 4.0, and 6.0 in planes perpendicular to the flow direction for Reynolds numbers Re = cd/v = 6000 has been the focus of attention in this investigation (d = nozzle diameter, c = mean exit velocity). These streamwise vortical structures also appear when the formation of Taylor-GONer vortices in the nozzle is suppressed. So far basic questions pertaining to the generation and development of these secondary structures remain unanswered. Understanding of instability and interaction mechanisms can be gained by the analysis of these structures. These also contribute to entrainment and mixing due to their dynamics and large interfacial area.

Sommario. Coppie di strutture tubolari controrotanti sono state osservate usando la tecnica di visualizzazione del flusso LIF (Laser Induced Fluorescence), per mezzo di una telecamera ad alta e bassa velocitL nel campo vicino ad un getto d'acqua assialsimmetrico. Lo studio dell'evoluzione temporale di queste strutture, fissato ~c/d = 1.0, 2.0, 4.0 e 6.0 in piani perpendicolari alia direzione del flusso ed in sezioni longitudinali per x /d = 0 -- 6.0, per numeri di Reynolds Re = cd/v = 6000, ~ stato il punto principale della presente indagine. Queste strutture vorticose appaiono persino quando la formazione dei vortici di Taylor-G0rtler ~ soppressa attivamente e passivamente. Si osserva che rimangono senza risposta questioni basilari concernenti la generazione e lo sviluppo di queste strutture secondarie. Attraverso l'analisi di queste strutture b possibile far progressi nella conoscenza dell'instabilit5 e dei meccanismi d'interazione. Inoltre, tali strutture contribuiscono all'intrappolamento ed al mescolamento dovuti alia loro dinamica ed alia larga area interfacciale.

Key words: Axisymmetric jet, Streamwise vortical structures, Braid instability, Vortex dynamics.

1. I n t r o d u c t i o n

Though the existence of secondary vortical structures alongside large-scale rings in the near

field of a jet has been known for some t ime ([1]), they did not receive much attention until counter-rotating s t reamwise structures in a plane mixing layer were observed and gained

importance thereafter [2]. A short review of the proposed mechanisms describing the deve lopment of s t reamwise

vortical structures in a plane shear layer is presented to show that similar arguments are

consistently used to explain the generation of s treamwise structures in ax isymmetr ic jets. Currently it is not certain as to what extent results f rom the plane mixing- layer could be applied to the ax isymmetr ic jet.

1.1. MODELS FOR THEPLANE SHEAR LAYER

J imenez et al. [3] proposed that the field of a plane shear layer is dominated by a lateral undulat ion (i.e. the spanwise vortex core deforms) and persists downst ream to form long longitudinal structures. These concentrations of s t reamwise counter-rotating pairs in the braid- region between the pr imary spanwise vortices and above and below the vortex cores was also

404 R. Suprayan and H. E. Fiedler

believed to be caused by three-dimensional instability of the spanwise structures either before or after the first pairing interaction.

Lasheras et al. ([4]) observed that the concentrated streamwise vorticity was always seen to form first on the braids between consecutive spanwise vortices and then to propagate into the cores of the latter. However, they conclude that these structures are formed due to the effect of localized three-dimensional disturbances upstream. The streamwise vorticity generated through this effect was then supposed to spread laterally by strong self-induction under the effect of the strain field created by the spanwise vortices.

Theoretical work and numerical simulations ([5]) showed that streamwise vorticity intro- duced in the mixing layer would be stretched in the braids between the spanwise vortices under the positive strain existing in that region.

1.2. MODELS FOR THE AXISYMMETRIC SHEAR LAYER

An hypothesis that the longitudinal structures develop from the so called Widnall or crown instability still persists ([6]). The observed waviness of a slender vortex ring is supposed to break off to form the longitudinal vortex pairs.

The concept of secondary instability originating in upstream disturbances leading to the formation of these secondary structures (similar to [4]) is widely held. The cause or influence of initial disturbances fall into this category.

The extension of the braid instability due to the strain field between the ring vortices comparable to the [5] model is another mechanism often cited. This incorporates disturbances already introduced in this region which amplify owing to the large strain in the braid region.

Numerical investigations ([7], [8]) and experiments ([9]) incorporate the above explanations in terms of braid instability or Widnall instability or a combination of both. On the basis of competition between local and global induction, Martin and Meiburg [7], in their numerical simulations, suggest ring waviness phenomena to dominate for their simulation of r io = 11.3 but braid instability mechanism as the cause of streamwise vortical structures for r io = 22.6.

Local G6rtler instability might also occur caused by the concave curvature of streamlines in the vicinity of ring vortices.

Vortex interaction and induction mechanisms giving rise to new structures have also been reported. Brancher et al. ([10]) mention that instability of the primary vortex tings and that of the braid are deeply intertwined and propose vortex induction mechanisms to account for the arrangement of the vortical structures. Monkewitz and Pfizenmaier ([11]) raise doubts about the possibility of any useful stability theoretical approach to explain the ejection of fluid radially out of the jet centreline and tend towards vortex induction arguments to complete the azimuthal instability mode.

Contradictions exist as to whether the shedding of longitudinal structures appear upstream ([12]) or downstream ([13]) of the vortex core undergoing deformation.

Thus, the real mechanism for the generation of streamwise vortical structures in a round jet is still unknown and the origin and evolution of the corresponding vorticity has not yet been conclusively determined by experiment.

Streamwise Vortical Structures 405

mirror

×/d ~ 2 3 /-, 5 6 P

Argon-ion camera laser

Fig. 1. LIF technique using disodium fluorescein and argon-ion laser to obtain radial cross-sections in an axisym- metric water jet at fixed z/d positions 1.0-6.0.

2. Experimental Set-up

The experiments were conducted in a water jet facility with a 2.54 cm diameter nozzle exit. The jet fluid was dyed with disodium fluorescein and radial and longitudinal sections of the flow were illuminated by a light sheet from an argon ion laser (Figure 1). The mean top- hat velocity was 24.0 cm/s corresponding to a Reynolds number of 6000 based on nozzle diameter and mean velocity, rio was 33.0 in these investigations. Regular photographs, video images and high-speed images at 200 and 500 fps were obtained under appropriate lighting conditions and chemical concentrations. The experimental facility was redesigned and improved to incorporate as far as possible the removal of initial condition disturbances (e.g. air-bubbles in the settling chamber, vibrations due to the pump). The formation of Taylor- GOrtler vortices in the jet nozzle was suppressed. The active control consisted of keeping the internal nozzle boundary layer as thin as possible with suction. Passive prevention was realized by a continuously convex nozzle. The flow was not artificially excited.

3. Observat ions of Radial Cross-Sections from Photographs [Re = 6000 x/d=l .0 , 2.0, 4.0 and 6.0]

Radial cross-sections depicting the structural configurations at z / d = 1.0, 2.0, 4.0 and 6.0 in the near region of the water jet were obtained for a velocity c = 24 cm/s (Figures 2-5). These photographs were taken with an increased concentration of the fluorescent dye of 0.01 M (as compared to 0.0025 M for the video and high-speed experiments) with an 3200 ASA film.

Fig. 2. LIF radial cross-sections at z/d = 1 depicting protuberances and a roll-up.

406 R. Suprayan and H. E. Fiedler

Fig. 3. LIF cross-sections at x/d = 2 with vortex rings and streamwise structures.

Fig. 4. LIF cross-sections at z/d = 4 with remnants in the ring and braid region.

They also confirm the structures observed by Liepmann and Gharib ([9]) at video rates for a 2.54 cm diameter nozzle. Though the structural configurations vary for different phases, the photographs depict the structures that occur regularly. The structures observed here are not necessarily symmetric; though such cases do exist.

At x /d = 1.0, we observe outgrowths around the jet perimeter including an initial roll-up. The potential core is filled with dyed fluid, the ambient undyed fluid appearing dark.

The fixed station, x /d =2.0, offers a large variety of structural composition in the ring and braid region, the dominant zeroth mode tings being prevalent with roll-ups. Counter-rotating vortex pairs are present inside and on the outside of the vortex rings, the outer vortex pairs being larger. Through the passage of the vortex rings, radially 'pulsating' vortex pairs are

Fig. 5. LIF radial cross-sections at z/d = 6 showing disintegrated structures.

Streamwise Vortical Structures 407

observed. This is caused by the movement of jet fluid radially outwards and the entrainment of ambient fluid towards the jet centre-line.

By x/d =4.0, the vortex ring and counter rotating vortical structures, having grown larger, still persist. At a fixed x/d position we observe either the passage of vortex rings or the strained braid region accompanied by the potential core fluid varying in diameter. The interaction between the vortex ring, streamwise vortical structures and ambient fluid bring forth a variety of structural configurations at the beginning of the transitional zone. At x/d = 6.0, beyond the potential core region, the structures disintegrate and are not visible except for the extended arms.

The above photographic observations alone being insufficient to explain the development of the streamwise vortical structures, images at video and high speed rates at a fixed station were captured showing temporally the evolving structures in greater detail.

Figures 2-5 depict radial cross-sections of structures at x/d = 1, 2, 4 and 6.

4. Observations of Radial Cross-Sections from High-Speed Photography at 200 fps [ n e : 6 0 0 0 = 2]

(a) (b) Fig, 6. LIF radial cross-section depicting (a) undulations of the outer layer and (b) hair-pin like lines leading to ' counter-rotating vortical structures.

The higher temporal resolution at 200 fps allows a more detailed structural analysis of the images than those obtained at regular photography or at video sampling rates. At x/d=2.0 and Re=6000, we observed wavy undulations on the outer sheath as in Figure 6(a) at a certain phase of development. Thin dyed lines spreading laterally leading to the mushroom like streamwise vortices are depicted in Figure 6(b) similar to the visual studies of Lasheras et al. ([4]). The developing vortical structures move radially outwards with the undulations

408 R. Suprayan and H. E. Fiedler

on their periphery; the latter being split off as remnant pieces of fluid. Thus the presence of wavy undulations does not necessarily indicate their development into streamwise vortical structures.

Fig. 7. L1F longitudinal cross-section showing ring vortices and sheaths.

Fig. 8. LIF longitudinal cross-section with details of multiple vortex induction and the shedding of longitudinal vortical sheaths.

5. Observations of Longitudinal Cross-Sections from High-Speed Photography at 500 fps [Re= 6000]

Investigations at 500 fps reveal early vortex pairing and symmetry after initial roll-ups (Figure 7). Induction between a slower vortex and a smaller, faster one upstream results in the entrainment of ambient fluid. The upstream vortex ring core is flattened followed by stretching (Figure 8) shedding out sheaths of fluid. These appear to remain stationary in the flow direction except when induced downstream or less frequently slightly upstream. Radial movement of the sheaths with the passage of vortex rings is quite frequent. This process of longitudinal shedding of fluid is observed to occur generally after previous pairing upstream being an active process of vortex induction and interaction and entrainment.

6. Discussion and Conclusion

This investigation has raised many questions. The evolution of the streamwise structures does not seem to be totally consistent with any single explanation. High-speed flow visualization at 500 fps of longitudinal sections shows that generally, during pairing or amalgamation, longitudinal sheaths are shed. This is due to the induction and interaction mechanism with the active stretching of the primary structures. They appear often as symmetrical sheaths at both

Streamwise Vortical Structures 409

extremities and are shed into the braid region. Various observations that the instabilities grow in the braid region may be attributed to this observation.

Our observations also confirm the numerical results by Brancher et al. ([10]) and experi- ments by Monkewitz and Pfitzenmeier ([11]) who propose vortex induction mechanism as a viable cause for the radial ejection of fluid in a jet.

Widnall 's analysis of azimuthal instability [6], is only for a slender vortex ring. Its appli- cability in a jet causing streamwise vorticity is valid only with very strong limitations due to core thickness, curvature and the existence of a succession of vortex rings. As such a stability analysis of a row of thick core vortex rings is needed.

Though our observations support the interpretation that the longitudinal sheaths are formed due to vortex induction and interaction mechanisms, on the other hand, we do have photographs that show dyed thin lines leading to the mushroom like counter-rotating structures, and others depicting wavy undulations of the outer sheath. Correspondence between longitudinal and radial cross-sections has still not been established.

The interpretations offered until now probably may not be totally incompatible. Vortex inductions and interactions, braid or ring instabilities may be working together in a more complex way that escapes simple explanation, suggesting further detailed investigations.

Experiments on spatially evolving structures, e.g. by utilizing a high scanning rate to view a quasi-frozen jet flow to help better understand the structural composition, are under way. Simultaneous longitudinal and radial cross-sections could elucidate the structural development at a fixed position clearly. Field measurements and comparisons with numerical experiments could give further insight into the structural dynamics involved.

Acknowledgement

The authors gratefully acknowledge financial support by the German Science Foundation (DFG).

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