Momentum evolution of ejected and entrained fluid during laminar vortex ring formation (original) (raw)

Measurement of ambient fluid entrainment during laminar vortex ring formation

Planar laser induced fluorescence (PLIF) and digital particle image velocimetry (DPIV) combined with Lagrangian coherent structure (LCS) techniques are utilized to measure ambient fluid entrainment during laminar vortex ring formation and relate it to the total entrained volume after formation is complete. Vortex rings are generated mechanically with a piston-cylinder mechanism for a jet Reynolds number of 1,000, stroke ratios of 0.5, 1.0 and 2.0, and three velocity programs (Trapezoidal, triangular negative and positive sloping velocity programs). The quantitative observations of PLIF agree with both the total ring volume and entrainment rate measurements obtained from the DPIV/LCS hybrid method for the jet Reynolds number of 1,000, trapezoidal velocity program and stroke ratio of 2.0 case. In addition to increased entrainment at smaller stroke ratios observed by others, the PLIF results also show that a velocity program utilizing rapid jet initiation and termination enhances ambient fluid entrainment. The observed trends in entrainment rate and final entrained fluid fraction are explained in terms of the vortex roll-up process during vortex ring formation.

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.

Fluid entrainment by isolated vortex rings

Journal of Fluid Mechanics, 2004

Of particular importance to the development of models for isolated vortex ring dynamics in a real fluid is knowledge of ambient fluid entrainment by the ring. This time-dependent process dictates changes in the volume of fluid that must share impulse delivered by the vortex ring generator. Therefore fluid entrainment is also of immediate significance to the unsteady forces that arise due to the presence of vortex rings in starting flows. Applications ranging from industrial and transportation, to animal locomotion and cardiac flows, are currently being investigated to understand the dynamical role of the observed vortex ring structures. Despite this growing interest, fully empirical measurements of fluid entrainment by isolated vortex rings have remained elusive. The primary difficulties arise in defining the unsteady boundary of the ring, as well as an inability to maintain the vortex ring in the test section sufficiently long to facilitate measurements. We present a new technique for entrainment measurement that utilizes a coaxial counter-flow to retard translation of vortex rings generated from a piston-cylinder apparatus, so that their growth due to fluid entrainment can be observed. Instantaneous streamlines of the flow are used to determine the unsteady vortex ring boundary and compute ambient fluid entrainment. Measurements indicate that the entrainment process does not promote self-similar vortex ring growth, but instead consists of a rapid convection-based entrainment phase during ring formation, followed by a slower diffusive mechanism that entrains ambient fluid into the isolated vortex ring. Entrained fluid typically constitutes 30% to 40% of the total volume of fluid carried with the vortex ring. Various counter-flow protocols were used to substantially manipulate the diffusive entrainment process, producing rings with entrained fluid fractions up to 65%. Measurements of vortex ring growth rate and vorticity distribution during diffusive entrainment are used to explain those observed effects, and a model is developed to relate the governing parameters of isolated vortex ring evolution. Measurement results are compared with previous studies of the process, and implications for the dynamics of starting flows are suggested.

A METHOD TO CAPTURE VORTEX RINGS IN STARTING PARTICLE-LADEN JETS

Euler-Lagrangian four-way coupling Large Eddy Simulation is performed to study the characteristics of the leading vortex ring of a starting particle-laden jet. The vertical distributions of vorticity, tracer concentration and concentration are obtained by horizontally integrating over the same height at the center plane. The edge of the "vortex ring" is distinguished by the first minimum of circulation after the peak value; the "tracer ring" is identified by the minimum slope of its vertical distribution; and the "particle ring" is determined by the first maximum after the minimum particle concentration. Among these, the "particle ring" is the biggest, and the "tracer ring" is the smallest. The tracer ring is found to be the most coherent and conserved, making it most suitable for future formation number analysis.

Experiments on the trajectory and circulation of the starting vortex

Various reasons have been given as to why the trajectories and circulations of vortices generated at sharp edges do not follow classical similarity-theory predictions for at least an initial short time. Amongst these are the effect of the particular flow geometry (e.g. duct with wedge, nozzle) distant from the salient edge (for rectilinear vortices); axisymmetry (for ring vortices) ; end effects (for rectilinear vortices) ; viscous diffusion; finite thickness of the detaching shear layer, as well as secondary vorticity caused by the interaction of the primary vortex with the edge at which it was generated. A further process that may be active is that of viscous entrainment. Experiments, in which essentially straight-line vortices were generated, indicate that of the seven possibilities mentioned, the first five do not play a significant part. All models consist of a basic flow onto which the modelled vortex is superposed. Thus either the basic flow or the vortex model are at fault. The basic flow onto which the vortex is superposed may well not be a pure edge flow, but one that is already taking on the character of an entraining jet flow. On the other hand, the vortex model fails to incorporate secondary vorticity which, particularly when rolled up, might be expected to be dynamically important.

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.

Circulation and formation number of laminar vortex rings

Journal of Fluid Mechanics, 1998

The formation time scale of axisymmetric vortex rings is studied numerically for relatively long discharge times. Experimental findings on the existence and universality of a formation time scale, referred to as the ‘formation number’, are confirmed. The formation number is indicative of the time at which a vortex ring acquires its maximal circulation. For vortex rings generated by impulsive motion of a piston, the formation number was found to be approximately four, in very good agreement with experimental results. Numerical extensions of the experimental study to other cases, including cases with thick shear layers, show that the scaled circulation of the pinched-off vortex is relatively insensitive to the details of the formation process, such as the velocity programme, velocity profile, vortex generator geometry and the Reynolds number. This finding might also indicate that the properly scaled circulation of steady vortex rings varies very little. The formation number does depen...

Measurement of Entrainment Rate in the Initial Region of Swirling Jets

2012

The entrainment rate in the initial region of axisymmetric turbulent swirling air jets has been measured by Particle Image Velocimetry (PIV) for a number of swirl strengths from S = 0 up to S = 1.5 and two Reynolds numbers. From the complete PIV maps of the jet and its surroundings, entrainment has been evaluated by using two methods: a) integration of the radial profiles of time-mean axial velocity of the jet; b) direct measurements of the radial velocity component of ambient air entrained into the jet. The entrainment rate increases with increasing axial distance from the nozzle in a non linear way and shows a rapid enhancement with the swirl number, particularly after inception of vortex breakdown and when the processing vortex core (PVC) is observed. The results allow to better understand the entrainment process in swirling jets and related effects on mixture formation and flame structure in industrial burners. Introduction Entrainment is an essential feature of shear flows and ...

On the structure of vortex rings from inclined nozzles

Journal of Fluid Mechanics, 2011

We carry out numerical simulations to investigate the vortex dynamics of laminar, impulsively driven flows through inclined nozzles in a piston-cylinder apparatus. Our simulations are motivated by the need to provide a complete description of the intricate vortical structures and governing mechanisms emerging in such flows as documented in the experiments of Webster & Longmire (Phys. We show that the flow is dominated by the interaction of two main vortical structures: the primary inclined vortex ring at the nozzle exit and the secondary stopping ring that arises due to the entrainment of the flow into the cylinder when the piston stops moving. These two structures are connected together with pairs of vortex tubes, which evolve from the continuous vortex sheet initially connecting the primary vortex ring with the interior cylinder wall. In the exterior of the nozzle the key mechanism responsible for the breakup of the vortical structure is the interaction of the stronger inclined primary ring with the weaker stopping ring near the longest lip of the nozzle. In the interior of the nozzle the dynamics is governed by the axial stretching of the secondary ring and the ultimate impingement of this ring on the cylinder wall. Our simulations also clarify the kinematics of the azimuthal flow along the core of the primary vortex ring documented in the experiments by Lim (Phys. Fluids, vol. 10, 1998, pp. 1666-1671. We show that the azimuthal flow is characterized by a pair of two spiral saddle foci at the long and short lips of the nozzle through which ambient flow enters and exits the primary vortex core.

The formation number of vortex rings formed in uniform background co-flow

Journal of Fluid Mechanics, 2006

The formation of vortex rings generated by an impulsively started jet in the presence of uniform background co-flow is studied experimentally to extend previous results. A piston-cylinder mechanism is used to generate the vortex rings and the co-flow is supplied through a transparent shroud surrounding the cylinder. Digital particle image velocimetry (DPIV) is used to measure the development of the ring vorticity and its eventual pinch off from the generating jet for ratios of the co-flow to jet velocity (R v) in the range 0-0.85. The formation time scale for the ring to obtain maximal circulation and pinch off from the generating jet, called the formation number (F), is determined as a function of R v using DPIV measurements of circulation and a generalized definition of dimensionless discharge time or 'formation time'. Both simultaneous initiation and delayed initiation of co-flow are considered. In all cases, a sharp drop in F (taking place over a range of 0.1 in R v) is centred around a critical velocity ratio (R crit). As the initiation of co-flow was delayed, the magnitude of the drop in F and the value of R crit decreased. A kinematic model based on the relative velocities of the forming ring and jet shear layer is formulated and correctly predicts vortex ring pinch off for R v > R crit. The results of the model indicate the reduction in F at large R v is directly related to the increased convective velocity provided to the ring by the co-flow.