Vortex induction and mass entrainment in a small-aspect-ratio elliptic jet (original) (raw)
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Characteristics of Small Vortices in a Turbulent Axisymmetric Jet
Journal of Fluids Engineering-transactions of The Asme, 2005
Characteristics of Small Vortices in a Turbulent Axisymmetric Jet Characteristics of small vortices were studied in axisymmetric jets wherein the Kolmogorov scale was approached by progressively decreasing the Reynolds number while still maintaining turbulent flow. A periodic forcing introduced far upstream of the jet nozzle ensured that the jet was turbulent. A vortex eduction tool was developed and applied to the high-pass filtered 2D velocity field in the axial plane of a turbulent jet while varying Re between 140 and 2600. Vortex population, energy, vorticity, and rms (root-meansquare velocity fluctuations) of the high-pass filtered field were measured to elucidate vortex characteristics. The observed population of vortices decreases dramatically at the Kolmogorov scale. The observed increase in vortex population with decreasing vortex size appears to be in accord with the space-filling argument, in that the vortex population in a two-dimensional domain should grow as R −2. The energy density curve obtained from vortex statistics reproduces the −5/3 slope for the inertial subrange, and the highpass filtered field accounts for approximately two-thirds of the total rms.
Vortex dynamics and entrainment mechanisms in lobed jets
2007
Two isothermal turbulent air jets from lobed nozzles with inclined and respectively non inclined lobes and a circular reference jet with the same initial Reynolds number were experimentally studied. Quantitative image processing of time resolved visualizations as well as hot-wire measurements of the velocity spectra allowed an objective understanding of the vortex roll-up mechanisms. Unlike the circular jet, where the primary rings are continuous, the Kelvin-Helmholtz vortices in the lobed jet flows are discontinuous at the locations where the exit plane curvature turns to infinite. Primary structures detach at different frequencies whether they are shed in the lobe troughs or at the lobe sides. The ``cutting'' of the Kelvin-Helmholtz vortices enables the development of permanent secondary streamwise structures. Their momentum flux transport role is thus rendered more efficient and seems to be amplified by the double inclination of the injection boundary. The quantification of the entrained flow rates by means of LDA measurements perfectly agrees with these observations.
Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis
Physics of Fluids, 2014
The instability dynamics of inviscid liquid jets issuing from elliptical orifices is studied, and effects of the surrounding gas and the liquid surface tension on the stability behavior are investigated. A dispersion relation for the zeroth azimuthal (axisymmetric) instability mode is derived. Consistency of the analysis is confirmed by demonstrating that these equations reduce to the well-known dispersion equations for the limiting cases of round and planar jets. It is shown that the effect of the ellipticity is to increase the growth rate over a large range of wavenumbers in comparison to those of a circular jet. For higher Weber numbers, at which capillary forces have a stabilizing effect, the growth rate decreases with increasing ellipticity. Similar to circular and planar jets, increasing the density ratio between gas and liquid increases the growth of disturbances significantly. These theoretical investigations are complemented by experiments to validate the local linear stability results. Comparisons of predicted growth rates with measurements over a range of jet ellipticities confirm that the theoretical model provides a quantitatively accurate description of the instability dynamics in the Rayleigh and first wind-induced regimes.
Vortex dynamics and entrainment mechanisms in low Reynolds orifice jets
Journal of Visualization, 2008
Classical planar 2D-PIV measurements and time-resolved visualizations enriched by low-level processing are used for the reconstruction of the Kelvin-Helmholtz vortex passing in the near field of a circular and a 6-lobed orifice jet flow. In the circular jet, the entrainment is produced in the braid region, being interrupted in the presence of the Kelvin-Helmholtz ring. The latter compresses the streamwise vortices and alters their self-induction role. Conversely, the 6-lobed orifice geometry allows the cutting of the Kelvin-Helmholtz structures into discontinuous ring segments. Consequently, into these discontinuity regions streamwise large scale structures are developing. These streamwise structures are permanent thus controlling and enhancing the jet entrainment which is not altered by the Kelvin-Helmholtz structures passing.
The significance of vortex ring formation to the impulse and thrust of a starting jet
Physics of Fluids, 2003
The recent work of Gharib, Rambod, and Shariff ͓J. Fluid Mech. 360, 121 ͑1998͔͒ studied vortex rings formed by starting jets generated using a piston-cylinder mechanism. Their results showed that vortex rings generated from starting jets stop forming and pinch off from the generating jet for sufficiently large values of the piston stroke to diameter ratio (L/D), suggesting a maximization principle may exist for propulsion utilizing starting jets. The importance of vortex ring formation and pinch off to propulsion, however, rests on the relative contribution of the leading vortex ring and the trailing jet ͑which appears after pinch off͒ to the impulse supplied to the flow. To resolve the relative importance of the vortex ring and trailing jet for propulsion, a piston-cylinder mechanism attached to a force balance is used to investigate the impulse and thrust generated by starting jets for L/D ratios in the range 2-8. Two different velocity programs are used, providing two different L/D values beyond which pinch off is observed, in order to determine the effect of vortex ring pinch off. Measurements of the impulse associated with vortex ring formation show it to be much larger than that expected from the jet velocity alone and proportionally larger than that associated with a trailing jet for L/D large enough to observe pinch off. The latter result leads to a local maximum in the average thrust during a pulse near L/D values associated with vortex rings whose circulation has been maximized. These results are shown to be related to the nozzle exit over-pressure generated during vortex ring formation. The over-pressure is in turn shown to be associated with the acceleration of ambient fluid by vortex ring formation in the form of added and entrained mass.
Effects of controlled vortex generation and interactions in transverse jets
Physical Review Fluids
This experimental study examined the effects of controlled vortex generation and interactions created by axisymmetric excitation of a transverse jet, with a focus on the structural and mixing characteristics of the flow. The excitation consisted of a double-pulse forcing waveform applied to the jet, where two distinct temporal square-wave pulses were prescribed during a single forcing period. The two distinct pulses produced vortex rings of different strength and celerity, the strategic selection of which promoted vortex ring interactions or collisions in the near field to varying degrees. Jet flow conditions corresponding to a transitionally convectively and absolutely unstable upstream shear layer (USL) in the absence of forcing, at a jet-to-cross-flow momentum flux ratio of J = 10, and to an absolutely unstable USL at J = 7, were explored for a jet Reynolds number of 1800. Acetone planar laser-induced fluorescence imaging was utilized to quantify the influence of different prescribed temporal waveforms. All forcing conditions enhanced the spread, penetration, and molecular mixing of the jet as compared to the unforced jet, though to differing degrees. Interestingly, when the jet was convectively unstable, forcing which promoted vortex collisions provided the greatest enhancement in molecular mixing, whereas the absolutely unstable jet produced the greatest enhancement in mixing when the vortex rings did not interact, with important implications for optimized jet control.
Numerical Study of Elliptic and Coaxial Jets with Variable Density
Mechanika, 2012
Nomenclature D-nozzle diameter, mm; D a-co-flowing diameter, mm; D eq = D e-equivalent diameter of elliptic nozzle, mm; F c-mass fraction; L p-potential core length from density field; L a-co-flowing length, mm; M-outer to inner specific momentum flux ratio; R v-outer to inner bulk velocity ratio; S-outer to inner density ratio; U-jet exit mean velocity, m/s; U a-co-flowing velocity, m/s; X-distance to nozzle, m; ρ-density: ρ * normalized density = (ρ−ρ e)/(ρ i −ρ e) or (ρ−ρ He)/(ρ i −ρ He); (-) i-relative to inner jet; (-) e-relative to external jet; (-) a-relative to ambient fluid.
Momentum evolution of ejected and entrained fluid during laminar vortex ring formation
The evolution of total circulation and entrainment of ambient fluid during laminar vortex ring formation has been addressed in a number of previous investigations. Motivated by applications involving propulsion and fluid transport, the present interest is in the momentum evolution of entrained and ejected fluid and momentum exchange among the ejected, entrained fluid and added mass during vortex ring formation. To this end, vortex rings are generated numerically by transient jet ejection for fluid slug length-to-diameter (L/D) ratios of 0.5–3.0 using three different velocity programs [trapezoidal, triangular negative slope (NS), and positive slope (PS)] at a jet Reynolds number of 1,000. Lagrangian coherent structures (LCS) were utilized to identify ejected and entrained fluid boundaries, and a Runge-Kutta fourth order scheme was used for advecting these boundaries with the numerical velocity data. By monitoring the center of mass of these fluid boundaries, momentum of each component was calculated and related to the total impulse provided by the vortex ring generator. The results demonstrate that ejected fluid exchanges its momentum mostly with added mass during jet ejection and that the momentum of the entrained fluid at jet termination was < 11% of the total ring impulse in all cases except for the triangular NS case. Following jet termination, momentum exchange was observed between ejected and entrained fluid yielding significant increase in entrained fluid's momentum. A performance metric was defined relating the impulse from over-pressure developed at the nozzle exit plane during jet ejection to the flow evolution, which increased preferentially with L/D over the range considered. An additional benefit of this study was the identification of the initial (i.e., before jet initiation) location of the fluid to be entrained into the vortex ring.
Analysis of Entrainment at the Turbulent/Non-Turbulent Interface of a Square Jet
Volume 7A: Fluids Engineering Systems and Technologies, 2013
Particle image velocimetry measurements are carried out to study the entrainment at the interface between the non-turbulent and turbulent regions in a square jet. Jet Reynolds number based on the hydraulic diameter of the jet is 50,000. Measurements cover up to 25 diameters downstream of the nozzle exit using five horizontal field-of-views in the central plane of the jet. The turbulent/non-turbulent interface is identified using a velocity criterion and a suitable thresholding method. Using vorticity and swirling strength it is shown that the turbulent/non-turbulent interface separates the rotational and irrotational regions of the flow. Instantaneous velocity vector field superimposed with the turbulent/non-turbulent interface are presented. The relation between the vortex cores in the vicinity of the turbulent/non-turbulent interface and the contractions and expansions noticed in the jet velocity field are explained. Entrainment into the jet is evaluated at each axial distance by identifying the points falling inside the turbulent region of the jet. Compared to a round jet, the square jet entrains more ambient fluid. In addition, normal volume fluxes going through the turbulent/non-turbulent interface of the square jet are found to be larger compared to that of a round jet.
Experiments in Fluids, 2008
Particle image velocimetry measurements and time-resolved visualization are used for the reconstruction of the Kelvin–Helmholtz vortex passing in the near field of a round jet and of a lobed jet. For the round jet, the entrainment is produced in the braid region, where streamwise structures develop. In the Kelvin–Helmholtz ring, entrainment is dramatically affected by the attenuation of the streamwise structures. As for the lobed jet, the special geometry introduces a transverse shear leading to a breakdown of the Kelvin–Helmholtz structures into “ring segments.” Streamwise structures continuously develop at the resulting discontinuity regions and control the lobed jet self-induction. In this case, the entrainment rate is less affected by the primary structures dynamics.