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.     

Experimental investigation of vortex rings impinging on inclined surfaces

Vortex–ring interactions with oblique boundaries were studied experimentally to determine the effects of plate angle on the generation of secondary vorticity, the evolution of the primary vorticity and secondary vorticity as they interact near the boundary, and the associated energy dissipation. Vortex rings were generated using a mechanical piston-cylinder vortex ring generator at jet Reynolds numbers 2,000–4,000 and stroke length to piston diameter ratios (L/D) in the range 0.75–2.0. The plate angle relative to the initial axis of the vortex ring ranged from 3 to 60°. Flow analysis was performed using planar laser-induced fluorescence (PLIF), digital particle image velocimetry (DPIV), and defocusing digital particle tracking velocimetry (DDPTV). Results showed the generation of secondary vorticity at the plate and its subsequent ejection into the fluid. The trajectories of the centers of circulation showed a maximum ejection angle of the secondary vorticity occurring for an angle of incidence of 10°. At lower incidence angles (<20°), the lower portion of the ring, which interacted with the plate first, played an important role in generation of the secondary vorticity and is a key reason for the maximum ejection angle for the secondary vorticity occurring at an incidence angle of 10°. Higher Reynolds number vortex rings resulted in more rapid destabilization of the flow. The three-dimensional DDPTV results showed an arc of secondary vorticity and secondary flow along the sides of the primary vortex ring as it collided with the boundary. Computation of the moments and products of kinetic energy and vorticity magnitude about the centroid of each vortex ring showed increasing asymmetry in the flow as the vortex interaction with the boundary evolved and more rapid dissipation of kinetic energy for higher incidence angles.     

Dynamics of prolate jellyfish with a jet-based locomotion

Swimming jellyfish deliver momentum to the surrounding fluid in the form of vortices. A three-dimensional computational model was adopted to investigate the characteristic flow patterns produced by jellyfish with a jet-based locomotion and the process of vortex generation. The interaction between jellyfish and the surrounding fluid may be simulated using the immersed boundary method. The vortex structures generated in the wake were elucidated in detail. The vortices were formed due to the contraction and expansion of the elastic bell. A dimensionless temporal parameter was employed to analyze the vortex formation process. During the early stage of contraction, the vortices were dominantly generated by the stroke. The ejected fluid from the inside of the bell was then entrained into the vortices, thereby decreasing the vorticity at the core and increasing the total circulation within the vortex ring. The Froude propulsion efficiency increased as the vortex formation number increased, implying that the propulsion in the way of growing the vortex structures was favorable in terms of the efficiency.     

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.     

Particle removal from a surface by a bounded vortex flow

A bounded vortex flow consists of an axisymmetric vortex that is confined top and bottom between two plates (the “confinement plate” and “impingement plate”, respectively) and surrounded laterally by a swirling annular slot jet. The bottom of the vortex terminates on the boundary layer along the impingement plate and the top of the vortex is drawn into a suction port positioned at the center of the confinement plate. The circumferential flow within the annular jet is important for supplying circulation to the central wall-normal vortex. This flow field is proposed as a method for mitigation of dust build-up on a surface, where the vortex–jet combination supplements the more traditional vacuum port by enhancing the surface shear stress and related particle transport rate. The paper reports on a computational study of the velocity field and particle transport by a bounded vortex flow. Fluid flow computations are performed using a finite-volume approach for an incompressible fluid and particle transport is simulated using a discrete-element method. Computations are performed for different values of two dimensionless parameters – the ratio of the plate separation distance and the average radial location of the jet inlet (the dimensionless confinement height) and the ratio of flow rate withdrawn at the suction outlet and that injected by the jet (the flow rate ratio). For small values of the flow rate ratio, the impinging jet streamlines pass down to the boundary layer along the bottom surface and then travel up the vortex core. By contrast, for large values of flow rate ratio, the annular jet is quickly entrained into the suction outlet and no wall-normal vortex is formed. Particles are observed to roll along the impingement surface in a direction determined by the fluid shear stress lines. Particles roll outward when they lie beyond a separatrix curve of the surface shear stress lines, where particles within this separatrix curve roll inward, piling up at the center of the flow field. A toroidal vortex ring forms for the small confinement height case with flow rate ratio equal to unity, which yields double separatrix curves in the shear stress lines. The inward rolling particles intermittently lift up due to collision forces and burst away from the impingement surface, eventually to become entrained into the flow out the suction port or resettling back onto the impingement surface.     

Characteristics of counter-rotating vortex rings formed ahead of a compressible vortex ring

Characteristics of high Mach number compressible vortex ring generated at the open end of a short driver section shock tube is studied experimentally using high-speed laser sheet-based flow visualization. The formation mechanism and the evolution of counter rotating vortex ring (CRVR) formed ahead of the primary vortex ring are studied in details for shock Mach number (M) 1.7, with different driver section lengths. It has been observed that the strength of the embedded shock, which appears at high M, increases with time due to the flow expansion in the generating jet. Strength of the embedded shock also varies with radius; it is strong at smaller radii and weak at larger radii; hence, it creates a velocity gradient ahead of the embedded shock. At critical Mach number (M _c ≥ 1.6), this shear layer rolls up and forms a counter rotating vortex ring due to Biot-Savart induction of the vortex sheet. For larger driver section lengths, the embedded shock and the resultant shear layer persists for a longer time, resulting in the formation of multiple CRVRs due to Kelvin–Helmholtz type instability of the vortex sheet. CRVRs roll over the periphery of the primary vortex ring; they move upstream due to their self-induced velocity and induced velocity imparted by primary ring, and interact with the trailing jet. Formation of these vortices depends strongly upon the embedded shock strength and the length of the generating jet. Primary ring diameter increases rapidly during the formation and the evolution of CRVR due to induced velocity imparted on the primary ring by CRVR. Induced velocity of CRVR also affects the translational velocity of the primary ring considerably.     

Combustion and stabilization characteristics of a branched flame under Helmholtz-type excitations

 The combustion and pollution characteristics of the newly rediscovered “branched flame” are experimentally investigated using a Helmholtz-type excitation. Under specific excitation conditions, high-amplitude Helmholtz excitation induces side jet ejection, which leads to a branched flame. Intense combustion and enhanced heat transfer due to strong oscillation of the flame and hot gases of the branched flame increase the heating effectiveness and fuel saving. Strong velocity oscillation results in accumulation of jet fluid ahead of the ring structure for generation of the side jet. In the side-jet evolution, the strong entrainment of the ring vortex in the initial stages followed by the early growth of the streamwise vortical structures greatly shortens the route to mixing transition of fuel and air in the upstream region of the flame. This enhanced premixing process of the side jet leading to high F probability, which is defined as the probability of the presence of a premixture of fuel and air with concentration within the flammability limits, and low strain rate has significant implications for the stabilization of the branched flame. NOx emission indices for the branched flames can be 30% higher and CO emission indices 50% lower than the unexcited case. Received: 5 June 2000 / Accepted: 21 March 2001     

Computational study of buoyancy effects in a laminar starting jet

Vortical structures formed in evolving jets are important in applications such as fuel injection in diesel engines and fuel leaks. When the jet fluid is different from the ambient fluid, the buoyancy can play an important role in determining the jet flow structure, and hence, the entrainment and fluid mixing processes. In the present study, a jet of helium injected in air is investigated, with emphasis placed on delineating the buoyancy effects on vector–scalar fields during the starting phase. We utilize a computational model, previously validated to predict the flow field of low-density gas jets. The model incorporates finite volume approach to solve the transport equation of helium mass fraction coupled with conservation equations of mixture mass and momentum. Computations were performed for a laminar jet to characterize the advancing jet front, and to capture the formation and propagation of vortex rings and the related pinch-off process. Results show significant effects of buoyancy on jet advancement, as well as on vorticity and helium concentration in the core of the vortex rings.     

Vortex ring velocity and minimum separation in an infinite train of vortex rings generated by a fully pulsed jet

A pulsed jet with a period of no flow between pulses (i.e., a fully pulsed jet) produces a multiplicity of vortex rings whose characteristics are determined by the jet pulsing parameters. The present study analyzes the case of impulsively initiated and terminated jet pulses in the limit of equal pulse duration and period to determine the minimum possible vortex ring separation obtainable from a fully pulsed jet. The downstream character of the flow is modeled as an infinite train of thin, coaxial vortex rings. Assuming inviscid flow and matching the circulation, impulse, kinetic energy, and frequency of the jet and vortex ring train allow the properties of the vortex ring train to be determined in terms of the ratio of jet slug length-to-diameter ratio (L/D) used for each pulse. The results show the minimum ring separation may be made arbitrarily small as L/D is decreased and the corresponding total ring velocity remains close to half the jet velocity for L/D < 4, but the thin-ring assumption is violated for L/D > 1.5. The results are discussed in the context of models of pulsed-jet propulsion.     

Mass and momentum transport in the near field of swirling turbulent jets. Effect of swirl rate

Local transport of the flow momentum and scalar admixture in the near-field of turbulent swirling jets (Re = 5,000) has been investigated by using a combination of the particle image velocimetry and planar laser-induced fluorescence methods. Advection and turbulent and molecular diffusions are evaluated based on the measured distributions of the mean velocity and concentration and the Reynolds stresses and fluxes. As has been quantified from the data, the flow swirl intensifies the entrainment of the surrounding fluid and promotes mass and momentum exchange in the outer mixing layer. A superimposed swirl results in the appearance of a wake/recirculation region at the jet axis and, consequently, the formation of an inner shear layer. In contrast to the scalar admixture, the momentum exchange in the inner shear layer is found to be strongly intensified by the swirl. For the jet with the highest considered swirl rate, a substantial portion of the surrounding fluid is found to enter the unsteady central recirculation zone, where it mixes with the jet that is issued from the nozzle. The contribution of the coherent velocity fluctuations, which are induced by large-scale vortex structures, to the turbulent transport has been evaluated based on triple decomposition, which was based on proper orthogonal decomposition analysis of the velocity data sets. For the considered domain of the jet with the highest swirl rate and vortex breakdown, the contributions of detected helical vortex structures, inducing pressing vortex core, to the radial fluxes of the flow momentum and the scalar admixture are found to locally exceed 65% and 80%, respectively.     

Structure and evolution of the airflow generated by a slender body entry near a tube

When a slender body moving forward in open air enters into a confined region, two important unsteady aerodynamic phenomena are generated. An exiting flow is created with a direction opposite to the body movement and inside the confined region, a compression wave is formed. Generation mechanism of compression wave have been extensively studied but so far, no detailed investigation of the exiting flow has ever been reported. The experimental study presented in this paper was undertaken to gain insight into the structure and the evolution of the exit-flow. Experiments were conducted with an axisymmetric apparatus and the explored range of the moving body speed was 5–50 m/s. The study focused on the influence of the body speed and the body nose geometry on the flow. It was shown that the air ejected from the tube entrance generates an annulus jet accompanied by a vortex ring. The vortex development was clarified using laser sheet visualizations associated with unsteady pressure and velocity measurements at the tube entrance. It is constituted by four phases, the pre-vortex phase, the vortex development phase, the vortex convection phase and the vortex breakdown phase. The duration of each of these steps was found to be independent of both the studied parameters in a non-dimensional time scale. Furthermore, neither the body speed nor the nose geometry induced significant changes on the vortex ring evolution, except for extreme conditions (low body speed, V_M.B.<15 m/s, and/or very long nose geometry, L_nose/D_M.B.>6). The evolution of the vortex ring was compared to that of ‘classical’ vortex ring generated at a tube exit by a piston motion with large non-dimensional stroke length. Main similarities and differences were discussed in the paper. In particular, the formation number of vortex ring observed in our experiments was found to be significantly smaller.     

Stereo-PIV study of flow around a maneuvering fish

Stereoscopic PIV was used to measure the three-component velocity distribution around a live fish. At the same time, shadow images of the fish were captured by additional cameras in order to reconstruct the three-dimensional shape of the fish. The side jet shed against the swept tail during turning was evident in the results. The height of the jet was approximately equal to the height of the tail fin, and a vortex ring was observed around the side jet. Based on the circulation and diameter of the vortex ring, the impulse and time-averaged force in terms of the side jet were estimated.     

An experimental investigation of jet flows through a row of forward expanded holes into a mainstream over a concave surface

This study performed detailed measurements of jet flows through a row of forward expanded holes into a mainstream over a concave surface using digital particle image velocimetry. Each of ejected holes had a streamwise inclined angle of 35° bounded on a concave surface with constant radius of 382 mm. The spacing of adjacent holes is 1.5D. The density and the momentum flux ratio of the mainstream to the jet flow were 1.0. Results show detailed 2D mean velocity maps on several horizontal and vertical planes and a 3D streamline pattern of jet mean velocity. The streamlines of 3D mean velocity clearly display different flow characteristics of the ejected jet flow along the transverse direction. In addition, the particle trajectory of a ring enclosing an ejected jet above the injection hole was also presented to show movement of jet.     

Vortex dynamics and mass entrainment in turbulent lobed jets with and without lobe deflection angles

Passive control of jet flows in order to enhance mixing and entrainment is of wide applicative interest. Our purpose is to develop new air diffusers for HVAC systems, by using lobed geometry nozzles, in order to ameliorate users the thermal comfort. Two turbulent 6-lobed air jets with and without lobe deflection angles were studied experimentally and compared with a reference circular jet having the same initial Reynolds number. The main objective was to analyze the modifications occurring in the vortex dynamics of the flow, firstly by replacing a circular tube with a straight lobed tube, and secondly by a lobed tube having a double inclination of the lobes. Rapid visualizations of the flows and hot-wire measurements of the streamwise velocity spectra allow understanding the vortex roll-up mechanisms. Unlike the circular jet, where the primary rings are continuous, the Kelvin–Helmholtz vortices in the lobed jet flows were found to be discontinuous. The resulting “ring segments” detach at different frequencies whether they are shed in the lobe troughs or at the lobe sides. One explanation relies on the strong variation of the exit plane curvature. Additionally, a speculative scenario of the vortical dynamics is advanced by the authors. The discontinuous nature of the K–H vortices enables the development of secondary streamwise structures, non-influenced by the passage of the primary structures as in the case of the circular jet. Thus, the momentum flux transport role played by the streamwise structures is rendered more efficient and leads to a spectacular increase in the entrainment rate in the initial region. The amount of fluid being entrained in the lobed jet by the streamwise structures is drastically amplified by the double inclination of the nozzle exit boundary.     

Vortices,Complex Flows and Inertial Particles

The properties of vortical structures at high Reynolds number in uniform flows and near rigid boundaries are reviewed. New properties are derived by analysing the dynamics of the main flow features and the related integral constraints, including the relations between mean swirl and bulk speed, the relative level of internal fluctuations to bulk properties, and connections between the steadiness and topology of the structures. A crucial property that determines energy dissipation and the transport of inertial particles (with finite fall speed) is the variation across the structure of the ratio of the mean strain rate (Σ) to the mean vorticity (Ω). It is shown how, once such particles are entrained into the vortical regions of a coherent structure, they can be transported over significant distances even as the vortices grow and their internal structure is distorted by internal turbulence, swirling motions and the presence of rigid boundaries. However if the vortex is strongly distorted by a straining motion so that Σ is greater than Ω, the entrained particles are ejected quite rapidly. These mechanisms are consistent with previous studies of entrained and sedimenting particles in disperse two phase flows over flat surfaces, and over bluff obstacles and dunes. They are also tested in more detail here through laboratory observations and measurements of 50–200-μm particles entrained into circular and non-circular vortices moving first into still air and then onto rigid surfaces placed parallel and perpendicular to the direction of motion of the vortices.     

The effect of density ratio on the near field of a naturally occurring oscillating jet

The triangular oscillating jet nozzle generates a triangular jet partially confined within an axi-symmetric chamber to produce a large scale flow oscillation that has application in thermal processes. Particle image velocimetry and oscillation frequency measurements were conducted to investigate the influence of the jet fluid to ambient fluid density ratio on the resulting oscillating flow. The investigation was conducted with a jet momentum flux of 0.06 kg m s⁻² (Re = 7.3−47.2 × 10³) and density ratios ranging from 0.2 to 5.0. The initial spread and decay of the emerging jet was found to depend upon the density ratio but in a more complex way than does an unconfined jet. Both the spread and decay are strongly influenced by the instantaneous angle of jet deflection, with greater deflection leading to increased spreading and decay of the jet. Decreasing the density ratio below unity results in a rapid decrease in the deflection angle, while increasing the density ratio above unity results in an increase in the deflection angle, albeit with less sensitivity. The frequency of oscillation was also shown to depend on the density ratio with an increase in the density ratio causing a decrease in the dominant oscillation frequency.     

The formation of vortex rings in a strongly forced round jet

The periodic formation of vortex rings in the developing region of a round jet subjected to high-amplitude acoustic forcing is investigated with High-Speed Particle Image Velocimetry. Harmonic velocity oscillations ranging from 20 to 120% of the mean exit velocity of the jet was achieved at several forcing frequencies determined by the acoustic response of the system. The time-resolved history of the formation process and circulation of the vortex rings are evaluated as a function of the forcing conditions. Overall, high-amplitude forcing causes the shear layers of the jet to breakup into a train of large-scale vortex rings, which share many of the features of starting jets. Features of the jet breakup such as the roll-up location and vortex size were found to be both amplitude and frequency dependent. A limiting time-scale of t/T ≈ 0.33 based on the normalized forcing period was found to restrict the growth of a vortex ring in terms of its circulation for any given arrangement of jet forcing conditions. In sinusoidally forced jets, this time-scale corresponds to a kinematic constraint where the translational velocity of the vortex ring exceeds the shear layer velocity that imposes pinch-off. This kinematic constraint results from the change in sign in the jet acceleration between t = 0 and t = 0.33T. However, some vortex rings were observed to pinch-off before t = 0.33T suggesting that they had acquired their maximum circulation. By invoking the slug model approximations and defining the slug parameters based on the experimentally obtained time- and length-scales, an analytical model based on the slug and ring energies revealed that the formation number for a sinusoidally forced jet is L/D ≈ 4 in agreement with the results of Gharib et al. (J Fluid Mech 360:121–140, 1998).     

Impulse generated during unsteady maneuvering of swimming fish

The relationship between the maneuvering kinematics of a Giant Danio (Danio aequipinnatus) and the resulting vortical wake is investigated for a rapid, ‘C’-start maneuver using fully time-resolved (500 Hz) particle image velocimetry (PIV). PIV illuminates the two distinct vortices formed during the turn. The fish body rotation is facilitated by the initial, or “maneuvering” vortex formation, and the final fish velocity is augmented by the strength of the second, “propulsive” vortex. Results confirm that the axisymmetric vortex ring model is reasonable to use in calculating the hydrodynamic impulse acting on the fish. The total linear momentum change of the fish from its initial swimming trajectory to its final swimming trajectory is balanced by the vector sum of the impulses of both vortex rings. The timing of vortex formation is uniquely synchronized with the fish motion, and the choreography of the maneuver is addressed in the context of the resulting hydrodynamic forces.     

Characteristics of Sonic Jets with Tabs

The results of an experimental investigation on the effect of a vortex generator in the form of a mechanical tab placed at the nozzle exit on the evolution of jet and its decay are reported in this paper. Jets from a sonic nozzle with and without tabs operated at nozzle pressure ratios from 2 to 7 were studied. Tabs with two combinations of length-to-width ratio were investigated by keeping the blockage area constant. The tabs offered a blockage of 10.18% of the nozzle exit area. The centerline pitot pressure decay shows that for the tabbed jet a maximum core reduction of about 75% can be achieved at a nozzle pressure ratio (NPR) 7 compared to an uncontrolled jet. The shadowgraph pictures show that the tabs drastically weaken the shock structure in the jet core and disperse the supersonic zone of the flow making them occupy a greater zone of the flow field compared to the plain nozzle. This causes the waves to become weaker and the jet to spread faster. The tabs are found to shed counter-rotating vortices all along the edges, resulting in enhanced mixing. Isobaric contours reveal that the streamwise vortices cause an inward indentation of the entrained mass into the jet core and an outward ejection of core flow. To understand the distortion introduced by tabs on the jet cross-section and its growth leading to bifurcation of the jet, a surface coating visualization method was developed and employed.     

Momentum transfer in a vertical down flow liquid jet ejector: case of self gas aspiration and emulsion flow

Momentum transfer in a vertical liquid jet contactor consisting of an ejector supported in a vertical column has been studied, using three different liquids as motive fluids, and air as the entrained gas.On the basis of macroscopic momentum and energy balance, an overall loss factor is derived. Moreover, an empirical correlation is proposed to predict the mass flow rate of entrainment by the liquid jet system. Finally, an expression to predict the volumetric flow rate of the carried fluid available at a pressure higher than atmospheric, is given.