The vortex ring velocity resulting from an impacting water drop

Experimental observations are reported on the evolution of a vortex ring for the first 70 ms after it is created by the impact of a dyed water drop upon a pool of clear water. The 2.6 mm diameter drops were released from two heights. The drops impacted the pool with Weber numbers of 23.2 and 16.6 and Froude numbers of 25.2 and 18.0. The Reynolds number of the resulting relaminarized vortex rings based on their diameter was in the range of 320 to 390. Precisely controlled multiple exposure photographs were used to measure the position and shape of the vortex ring versus time, and calculate velocity. It is proposed here that the appropriate time scale is the time it takes for the impact crater to reach its maximum depth. Excellent agreement was found when using this scaling to compare both the present data sets and that previously published for a larger drop.This work was supported by the Natural Sciences and Engineering Research Council of Canada Grant No. OGP 00 41747. Mr. B. Faulkner is thanked for help with the strobe-timing     

Large Eddy Simulation of Compressible Subsonic Turbulent Jet Starting From a Smooth Contraction Nozzle

Compressible subsonic turbulent starting jet with a relatively large Reynolds number of significant practical importance is investigated using large eddy simulation (LES), starting from a smooth contraction nozzle. The computational domain of truncated conical shape is determined through the comparison of the time-averaged numerical solution with the particle imaging velocimetry measurements for the steady jet. It is shown that the starting jet consists of a leading vortex ring followed by a quasi-steady jet, and the instantaneous velocity field exhibits contraction and expansion zones, corresponding to the high pressure (HP) and low pressure (LP) regions formed by the convecting vortex rings, and are related to the Kelvin-Helmholtz instability. The thin boundary layer inside the smooth contraction nozzle evolves into a shear layer at the nozzle exit and develops with the downstream penetration of the jet. Using λ ₂ criterion, the formation and evolution of the vortical structures are temporally visualized, illustrating distortion of vortex rings into lobed shapes prior to break-down. Rib-shape streamwise vortex filaments exist in the braid region between a pair of consecutive vortex rings due to secondary instabilities. Finally, formation and dynamics of hairpin vortices in the shear layer is identified.     

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.     

Thermocapillary convection in an annular cylindrical container

The liquid–gas interface of a liquid in an annular container is subjected to a temperature gradient. Since shear stress on the free liquid surface depends on the temperature it shall create a variable shear stress on the surface which in turn yields by viscous traction a thermocapillary convection in the bulk of the liquid. For constant temperature T ₂ > T ₁ on the outer cylindrical wall and T ₁ on the inner wall a steady convection shall emerge. The morphology of the ensuing flow is investigated as a function of the diameter ratio and the liquid height ratio and exhibits the growth of bottom rim vortex rings, which unite to single vortex rings of opposite flow direction to the original single strong vortex ring above it. The results also show how such a system depends on the magnitude of the diameter ratio and the liquid height ratio. The evaluation of the results exhibits the evolution of vortex rings.     

Formation and basic parameters of vortex rings

This paper describes an experimental study of the properties of vortex rings with variation of parameters of the air jet expelled from a round nozzle by a special device. Characteristics of the vortex rings were determined by hotwire anemometer measurements of the velocity field at a certain distance from the nozzle exit where vortex formation is presumably completed. A mathematical model for the formation of a vortex ring based on conservation laws is proposed, and a comparison of theoretical results with experimental data is given.     

Vortex rings in radially confined domains

The dynamics of vortex rings generated within confined domains are relevant to important hydrodynamic processes such as flow past heart valves or severe arterial constrictions. However, despite their importance, these flows have not received much attention to date. This study examines the development and evolution of radially confined vortex rings. Time-resolved digital particle image velocimetry was used to investigate two levels of radial confinement and a range of vortex ring strengths. We found that for severely confined vortex rings, the formation time and peak circulation values were unaffected for L/D ₀?<?4 cases and slightly affected for larger L/D ₀ cases. After pinch-off, circulation decay was observed with an approximately constant normalized circulation decay rate. We found that with increasing circulation strength, the nondimensional time delay between the pinch-off and the onset of circulation decay reduced due to an increased vortex ring diameter within the confinement domain and a reduction in the necessary time for the surface induced and core vorticity regions to interact. This study uncovers the dynamics of radially confined vortex rings and show that the nondimensional rate of circulation decay is dependent on the vortex ring confinement ratio (ratio of the vortex ring orifice diameter to the diameter of the outer cylinder), and the time delay between the vortex pinch-off and the onset of circulation is dependent on the vortex ring circulation strength.     

Active control of an axisymmetric jet with distributed electromagnetic flap actuators

Miniature electromagnetic flap actuators are developed and mounted on the periphery of the nozzle exit of an axisymmetric jet to induce various flow modes and enhance mixing processes. It is demonstrated that the flap actuators can significantly modify the large-scale vortical structures. In particular, when the flaps are driven in anti-phase on either side of the jet, alternately inclined and bent vortex rings are generated, and the jet bifurcates into two branches. Since the vortex rings are formed at the very vicinity of the nozzle exit, the bifurcation is accomplished as close as x/D=3.     

On the Effect of Pipe Boundary Layer Growth on the Formation of a Laminar Vortex Ring Generated by a Piston/Cylinder Arrangement

The growth of a boundary layer at the nozzle wall during laminar vortex ring formation by a nozzle flow generator (piston/cylinder arrangement) is analysed theoretically and numerically and used for modelling the formation of real vortex rings. The predictions of the model are in good agreement with previous experimental and numerical results. Received 19 January 2000 and accepted 17 August 2001     

Evaluation of FFT-based cross-correlation algorithms for PIV in a periodic grooved channel

The design of a pneumatic droplet generator to produce small (~0.2 mm diameter) water droplets on demand is described. It consists of a cylindrical, liquid-filled chamber with a small nozzle set into its bottom surface, connected to a gas cylinder through a solenoid valve. Rapidly opening and closing the valve sends a pressure pulse to the liquid, ejecting a single droplet through the nozzle. Gas in the chamber escapes through a vent hole so that the pressure drops rapidly and more droplets do not emerge. We photographed droplets as they emerged from the nozzle, and recorded pressure fluctuations in the chamber. We determined the duration of the pressure pulse required to generate a single drop; longer pulses produced satellite drops. The length of the water jet when its tip detached and the diameter of the droplet that formed could be predicted using results from linear stability analysis. The peak pressure in the cavity could be increased by raising the supply pressure, increasing the width of the pressure pulse, or by reducing the size of the pressure relief vent.     

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).     

Volumetric velocity measurements of vortex rings from inclined exits

Vortex rings were generated by driving pistons within circular cylinders of inner diameter D = 72.8 mm at a constant velocity U ₀ over a distance L = D. The Reynolds number, U ₀ L/(2ν), was 2500. The flow downstream of circular and inclined exits was examined using volumetric 3-component velocimetry (V3V). The circular exit yields a standard primary vortex ring that propagates downstream at a constant velocity and a lingering trailing ring of opposite sign associated with the stopping of the piston. By contrast, the inclined nozzle yields a much more complicated structure. The data suggest that a tilted primary vortex ring interacts with two trailing rings; one associated with the stopping of the piston, and the other associated with the asymmetry of the cylinder exit. The two trailing ring structures, which initially have circulation of opposite sign, intertwine and are distorted and drawn through the center of the primary ring. This behavior was observed for two inclination angles. Increased inclination was associated with stronger interactions between the primary and trailing vortices as well as earlier breakdown.     

A pneumatic droplet-on-demand generator

The design of a pneumatic droplet generator to produce small (~0.2 mm diameter) water droplets on demand is described. It consists of a cylindrical, liquid-filled chamber with a small nozzle set into its bottom surface, connected to a gas cylinder through a solenoid valve. Rapidly opening and closing the valve sends a pressure pulse to the liquid, ejecting a single droplet through the nozzle. Gas in the chamber escapes through a vent hole so that the pressure drops rapidly and more droplets do not emerge. We photographed droplets as they emerged from the nozzle, and recorded pressure fluctuations in the chamber. We determined the duration of the pressure pulse required to generate a single drop; longer pulses produced satellite drops. The length of the water jet when its tip detached and the diameter of the droplet that formed could be predicted using results from linear stability analysis. The peak pressure in the cavity could be increased by raising the supply pressure, increasing the width of the pressure pulse, or by reducing the size of the pressure relief vent.     

The effects of acceleration in jets: kinematics of the near field vortices

Direct and large-eddy simulations (DNS/LES) of accelerating round jets are used to analyze the effects of acceleration on the kinematics of vortex rings in the near field of the jet (x/D < 12). The acceleration is obtained by increasing the nozzle jet velocity with time, in a previously established (steady) jet, and ends once the inlet jet velocity is equal to twice its initial value. Several acceleration rates (α = 0.02–0.6) and Reynolds numbers (Re _D = 500–20000) were simulated. Acceleration maps were used to make a detailed study of the kinematics of vortex rings in accelerating jets. One of the effects of the acceleration is to cause a number of new primary and secondary vortex merging events that are absent from steady jets. As the acceleration rate α increases, both the number of primary merging events between rings and the axial position where these take place decreases. The statistics for the speed of the starting ring that forms at the start of the acceleration phase for each simulation, agree well with the statistics for the “front” speed observed by Zhang and Johari (Phys Fluids 8:2185–2195, 1996). Acceleration maps and flow visualizations show that during the acceleration phase the near field coherent vortices become smaller and are formed at an higher frequency than in the steady jet, and their (mean) shedding frequency increases linearly with the acceleration rate. Finally, it was observed that the acceleration decreases the spreading rate of the jet, in agreement with previous experimental works.      

聚能装药对混凝土靶板的侵彻研究

系统开展了不同药型罩材料、不同锥角、不同壁厚的聚能装药在不同炸高下侵彻混凝土试验, 研究了罩材料、锥角、壁厚、炸高等结构参数对漏斗坑直径、侵彻孔洞直径、漏斗坑深度以及侵彻深度等参数的影响规律;应用空腔膨胀理论计算了混凝土靶体阻力, 采用改进的伯努利方程和两阶段空腔膨胀理论获得了混凝土靶板在侵彻体作用下的侵彻深度和孔洞直径, 理论结果与试验结果基本吻合;基于AUTODYN 软件平台, 采用与试验一致的聚能装药结构, 开展了57 种工况下侵彻体成形过程的数值模拟研究, 并对其中典型工况的侵彻混凝土过程进行了数值模拟, 计算所得孔洞直径和侵彻深度与试验结果吻合较好, 在此基础上深入探讨了聚能装药作用下混凝土漏斗坑的形成机理, 分析表明, 铝药型罩的开坑机理不同于钢和铜药型罩.      

超高韧性水泥基复合材料—纤维混凝土组合靶体抗两次打击试验研究

超高韧性水泥基复合材料（ultra high toughness cementitious composites, UHTCC）具有超高的韧性、良好的耐久性和优异的耗能效果,这些特性使得UHTCC在防护工程中具有广阔的应用前景。为了更好地研究UHTCC与纤维混凝土组合结构在二次打击条件下的抗侵彻性能,首先测量了UHTCC和聚乙烯醇纤维增强混凝土（polyvinl alcohol fiber reinforced concrete, FRC）的基本力学参数。然后采用25 mm口径的弹道滑膛炮对直径为750 mm、高为600 mm的圆柱形UHTCC靶体、FRC靶体、UHTCC-FRC组合靶体（UHTCC-FRC composite target）进行了弹体速度为550 m/s的二次侵彻试验,得到了弹体和三类靶体的破坏数据,包括弹体的侵彻深度、弹体的磨蚀、靶体迎弹面的开坑直径和面积、弹坑深度、迎弹面的裂纹数量以及裂纹最大宽度。在此基础上分析了骨料、结构形式和两次打击的间距对UHTCC-FRC组合靶体抗侵彻性能的影响。结果表明:相同试验条件下,与普通混凝土和超高性能混凝土相比,UHTCC能够有效的减小迎弹面的开坑直径,但会增加弹体侵彻深度;将50 mm的UHTCC置于组合靶的迎弹面可以有效地减少迎弹面的开坑直径;弹体二次侵彻深度大于弹体一次侵彻深度,靶体在二次冲击下的开坑面积小于靶体初次冲击下的开坑面积。     

Heat transfer augmentation between impinging circular air jet and flat plate using finned surfaces and vortex generators

An experimental investigation is performed to study the effect of the finned surfaces and surfaces with vortex generators on the local heat transfer coefficient between impinging circular air jet and flat plate. Reynolds number is varied between 7000 and 30,000 based on the nozzle exit condition and jet to plate spacing between 0.5 and 6 nozzle diameters. Thermal infrared imaging technique is used for the measurement of local temperature distribution on the flat plate. Fins used are in the form of cubes of 2 mm size spaced at a pitch of 5 mm on the target plate and hexagonal prism of side 2.04 mm and height of 2 mm spaced at a pitch of 7.5 mm. Vortex generators in the form of a equilateral triangle of side 4 mm are used. Effect of number of rows of vortex generators, radius of a row, number of vortex generators in a row and inclination angle (i.e., the angle between the plane of the target plate and the plane of the vortex generators) on Nusselt number is studied. It is observed that the heat transfer coefficient between the impinging jet and the target plate is sensitive to the shape of the fin. The increase in the heat transfer coefficient up to 77% depending on the shape of the fin, nozzle plate spacing and the Reynolds number is observed. The augmentation in the heat transfer for the surfaces vortex generators are higher than that of the finned surfaces. The heat transfer augmentation in case of vortex generator is as high as 110% for a single row of six vortex generators at a radius of 1 nozzle diameter as compared to the smooth surface at a given nozzle plate spacing of 1 nozzle diameter and a Reynolds number of 25,000 at extreme radial location.     

LES and RANS modelling of under-expanded jets with application to gaseous fuel direct injection for advanced propulsion systems

A density-based solver with the classical fourth-order accurate Runge-Kutta temporal discretization scheme was developed and applied to study under-expanded jets issued through millimetre-size nozzles for applications in high-pressure direct-injection (DI) gaseous-fuelled propulsion systems. Both large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) turbulence modelling techniques were used to evaluate the performance of the new code. The computational results were compared both quantitatively and qualitatively against available data from the literature. After initial evaluation of the code, the computational framework was used in conjunction with RANS modelling (k-ω SST) to investigate the effect of nozzle exit geometry on the characteristics of gaseous jets issued from millimetre-size nozzles. Cylindrical nozzles with various length to diameter ratios, namely 5, 10 and 20, in addition to a diverging conical nozzle, were studied. This study is believed to be the first to provide a direct comparison between RANS and LES within the context of nozzle exit profiling for advanced high-pressure injection systems with the formation of under-expanded jets. It was found that reducing the length of the straight section of the nozzle by 50% resulted in a slightly higher level of under-expansion (∼2.6% higher pressure at the nozzle exit) and ∼1% higher mass flow rate. It was also found that a nozzle with 50% shorter length resulted in ∼6% longer jet penetration length. At a constant nozzle pressure ratio (NPR), a lower nozzle length to diameter ratio resulted in a noticeably higher jet penetration. It was found that with a diverging conical nozzle, a fairly higher penetration length could be achieved if an under-expanded jet formed downstream of the nozzle exit compared to a jet issued from a straight nozzle with the same NPR. This was attributed to the radial restriction of the flow and consequently formation of a relatively smaller reflected shock angle. With the conical nozzle used in this study and a 30 bar injection pressure, an under-expanded hydrogen jet exhibited ∼60% higher penetration length compared to an under-expanded nitrogen jet at 100 μs after start of injection. Moreover, the former jet exhibited ∼22% higher penetration compared to a nitrogen jet issued through the conical profile with 150 bar injection pressure.     

The decay of confined vortex rings

Vortex rings are produced during the ejection of fluid through a nozzle or orifice, which occurs in a wide range of biological conditions such as blood flow through the valves of the heart or through arterial constrictions. Confined vortex ring dynamics, such as these, have not been previously studied despite their occurrence within the biological flow conditions mentioned. In this work, we investigate laminar vortex rings using particle image velocimetry and develop a new semi-empirical model for the evolution of vortex ring circulation subject to confinement. Here we introduce a decay parameter ?? which exponentially grows with increasing vortex ring confinement ratio, the ratio of the vortex ring diameter (D _VR) to the confinement diameter (D), with the relationship $\beta=4.38 \exp(9.5D_{\rm VR}/D),$ resulting in a corresponding increase in the rate of vortex ring circulation decay. This work enables the prediction of circulation decay rate based on confinement, which is important to understanding naturally occurring confined vortex ring dynamics.     

Impact of liquid drops on a rough surface comprising microgrooves

Impact of water drops on a stainless steel surface comprising rectangular shaped parallel grooves is studied experimentally. Geometric parameters of the surface groove structure such as groove depth, groove width and solid pillar width separating any two successive grooves were kept at 7.5, 136 and 66 μm, respectively. The study was confined to the impact of drops in inertia dominated flow regime with Weber number in the range 15–257. Experimental results of drop impact process obtained for the grooved surface were compared with those obtained for a smooth surface to elucidate the influence of surface grooves on the impact process. The grooves definitely influence both spreading and receding processes of impacting liquid drops. A more striking observation from this study is that the receding process of impacting liquid drops is dramatically changed by the groove structure for all droplet Weber number.     

Producing droplets smaller than the nozzle diameter by using a pneumatic drop-on-demand droplet generator

A pneumatic droplet generator to produce water/glycerin droplets smaller than the nozzle diameter is described. The generator consists of a T-junction with a nozzle fit into one opening, the second opening connected to a gas cylinder through a solenoid valve and the third connected to a length of steel tubing. The droplet generator is filled with liquid. Opening the valve for a preset time creates a pulse of alternating negative and positive pressure in the gas above the surface of the liquid, ejecting a single droplet through the nozzle. Droplet formation was photographed and the pressure variation in the droplet generator recorded. The effect of various experimental parameters, such as nozzle size, pressure pulse width and liquid properties on droplet formation was investigated. Small droplets could not be generated when liquid viscosity was too low or too high. For pure water, droplet diameters were several times that of the nozzle. Using more viscous glycerin mixtures, droplets with diameters as small as 65% of the nozzle diameter could be produced.