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.     

Near Field Round Jet Flow Downstream from an Abrupt Contraction Nozzle with Tube Extension

Round air jet development downstream from an abrupt contraction coupled to a uniform circular tube extension with length to diameter ratio L/D?=?1.2 and L/D?=?53.2 is studied experimentally. Smoke visualisation and systematic hot film velocity measurements are performed for low to moderate Reynolds numbers 1130?<?Re _b ?<?11320. Mean and turbulent velocity profiles are quantified at the tube exit and along the centerline from the tube exit down to 20 times the diameter D. Flow development is seen to be determined by the underlying jet structure at the tube exit which depends on Reynolds number, initial velocity statistics at the tube exit and the presence/absence of coherent structures. It is shown that the tube extension ratio L/D as well as the sharp edged abrupt contraction influence the initial jet structure at the tube exit. For both L/D ratios, the presence of the abrupt contraction results in transitional jet flow in the range 2000?<?Re _b ?<?4000 and in flow features associated with forced jets and high Reynolds numbers Re _b ?>?10⁴. The tube extension ratio L/D downstream from the abrupt contraction determines the shear layer roll up so that for L/D?=?1.2 flow visualisation suggests the occurrence of toroidal vortices for Re _b ?<?4000 whereas helical vortices are associated with the transitional regime for L/D?=?53.2. Found flow features are compared to features reported in literature for smooth contraction nozzles and long pipe flow.     

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.     

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).     

Analysis and reconstruction of a pulsed jet in crossflow by multi-plane snapshot POD

In this work, snapshot proper orthogonal decomposition (POD) is used to study a pulsed jet in crossflow where the velocity fields are extracted from stereoscopic particle image velocimetry (SPIV) results. The studied pulsed jet is characterized by a frequency f = 1 Hz, a Reynolds number Re _j  = 500 (based on the mean jet velocity ${\overline{U}_{j}}$  = 1.67 cm/s and a mean velocity ratio of R = 1). Pulsed jet and continuous jet are compared via mean velocity field trajectory and Q criterion. POD results of instantaneous, phase-averaged and fluctuating velocity fields are presented and compared in this paper. Snapshot POD applied on one plane allows us to distinguish an organization of the first spatial eigenmodes. A distinction between “natural modes” and “pulsed modes” is achieved with the results obtained by the pulsed and unforced jet. Secondly, the correlation tensor is established with four parallel planes (multi-plane snapshot POD) for the evaluation of volume spatial modes. These resulting modes are interpolated and the volume velocity field is reconstructed with a minimal number of modes for all the times of the pulsation period. These reconstructions are compared to orthogonal measurements to the transverse jet in order to validate the obtained three-dimensional velocity fields. Finally, this POD approach for the 3D flow field reconstruction from experimental data issued from planes parallel to the flow seems capable to extract relevant information from a complex three-dimensional flow and can be an alternative to tomo-PIV for large volume of measurement.     

A flow field study of an elliptic jet in cross flow using DPIV technique

The digital particle image velocimetry (DPIV) technique has been used to investigate the flow fields of an elliptic jet in cross flow (EJICF). Two different jet orientations are considered; one with the major axis of the ellipse aligned with the cross flow (henceforth referred to as a low aspect ratio (AR) jet), and the other with the major axis normal to the cross flow (henceforth referred to as a high aspect ratio jet). Results show that the vortex-pairing phenomenon is prevalent in the low aspect ratio jet when the velocity ratio (VR)3, and is absent in the high aspect ratio jet regardless of the velocity ratio. The presence of vortex pairing leads to a substantial increase in the leading-edge peak vorticity compared to the lee-side vorticity, which suggests that vortex pairing may play an important role in the entrainment of ambient fluid into the jet body, at least in the near-field region. In the absence of vortex pairing, both the leading-edge and the lee-side peak vorticity increase monotonically with velocity ratio regardless of the aspect ratio. Moreover, time-averaged velocity fields for both AR=0.5 and AR=2 jets reveal the existence of an unstable focus (UF) downstream of the jet, at least for VR2. The strength and the location of this focus is a function of both the velocity ratio and aspect ratio. In addition, time-averaged vorticity fields show a consistently higher peak-averaged vorticity in the low aspect ratio jet than in the high aspect ratio jet. This behavior could be due to a higher curvature of the vortex filament facing the cross flow in the low aspect ratio jet, which through mutual interaction may lead to higher vortex stretching, and therefore higher peak-averaged vorticity.Nomenclature A nozzle or jet cross-sectional area - AR aspect ratio, defined as the ratio of the nozzle cross-stream dimension to its streamwise dimension, =H/L - D characteristic jet diameter (for circular jet only) - D_h hydraulic diameter, =4A/P - D_major major axis of an elliptic nozzle - D_minor minor axis of an elliptic nozzle - H cross-stream dimension of the nozzle - L streamwise dimension of the nozzle - P perimeter of the nozzle - Re_j jet Reynolds number, =V_jD/ - VR velocity ratio, =V_j/V - V_j mean jet velocity - V mean cross-flow velocity - x downstream distance from jet center - X cross-plane vorticity - kinematic viscosity     

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.     

On vortex shedding from low aspect ratio dual step cylinders

A dual-step cylinder is comprised of two cylinders of different diameters. A large diameter cylinder (D) with low aspect ratio (L/D) is attached to the mid-span of a small diameter cylinder (d). The present study investigates the effect of Reynolds number (Re_D) and L/D on dual step cylinder wake development for D/d=2, 0.2≤L/D≤3, and two Reynolds numbers, Re_D=1050 and 2100. Experiments have been performed in a water flume facility utilizing flow visualization, Laser Doppler Velocimetry (LDV), and Particle Image Velocimetry (PIV). The results show that vortex shedding occurs from both the large and small diameter cylinders for 1≤L/D≤3 at Re_D=2100 and 2≤L/D≤3 at Re_D=1050. At these conditions, large cylinder vortices predominantly form vortex loops in the wake and small cylinder vortices form half-loop vortex connections. At lower aspect ratios, vortex shedding from the large cylinder ceases, with the dominant frequency in the large cylinder wake attributed to the passage of vortex filaments connecting small cylinder vortices. At these lower aspect ratios, the presence of the large cylinder induces periodic vortex dislocations. Increasing L/D increases the frequency of occurrence of vortex dislocations and decreases the dominant frequency in the large cylinder wake. The identified changes in wake topology are related to substantial variations in the location of boundary layer separation on the large cylinder, and, consequently, changes in the size of the vortex formation region. The results also show that the Reynolds number has a substantial effect on wake vortex shedding frequency, which is more profound than that expected for a uniform cylinder.     

Analytical and experimental investigations of the pulsed air–water jet

This paper describes a new way of generating pulsed air–water jet by entraining and mixing air into the cavity of a pulsed water jet nozzle. Based on the theory of hydro-acoustics and fluid dynamics, a theoretical model which describes the frequency characteristic of the pulsed air–water jet is outlined aimed at gaining a better understanding of this nozzle for generating pulses. The calculated result indicates that as the air hold-up increases, the jet oscillation frequency has an abrupt decrease firstly, and then reaches a minimum gradually at α (air hold-up)=0.5, finally it gets increased slightly. Furthermore, a vibration test was conducted to validate the present theoretical result. By this way, the jet oscillation frequency can be obtained by analyzing the vibration acceleration of the equal strength beam affected by the jet impinging. Thereby, it is found that the experimental result shows similar trend with the prediction of the present model. Also, the relationship between vibration acceleration and cavity length for the pulsed water jet follows a similar tendency in accord with the pulsed air–water jet, i.e. there exists a maximum for each curve and the maximum occurs at the ratio of L/d₁ (the ratio of cavity length and upstream nozzle diameter) =2.5 and 2.2, respectively. In addition, experimental results on specimens impinged by the pulsed water jet and pulsed air–water jet show that the erosion depth increases slightly with air addition within a certain range of cavity length. Further, this behavior is very close to the vibration test results. As for erosion volume, the air entrained into the cavity significantly affects the material removal rate.     

Flow structure and heat transfer of impingement jet

This paper presents the characteristics of flow behavior and thermal fields of both free and impingement jets issued from circular orifice nozzle at Re = 9,700. The flow behavior of a single round jet and impingement jet were observed by smoke flow visualization recorded by a high speed video camera with 5,000 frames per second. Heat transfer coefficient on the impingement surface was calculated varying the Reynolds number and the separation distance between nozzle exit and plate. Time-series analysis was applied to the visualization image to get the information of time variation of flow behavior. Probability distribution of vortex scale induced by the jet at discrete positions was investigated. Experimental results show that the potential core is not a continuous phenomenon with time and the frequency of vortex ring formation have similar features regardless of whether the impingement plate was set on or not, furthermore the time-series analysis with flow visualization images makes clear the detailed flow behavior.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.     

Visualization and structure of confined, milliscale, unsteady impinging slot jets and associated vortices

Flow characteristics of confined, laminar milliscale slot jets are investigated from visualizations, as they impinge upon a flat target plate, with a fully developed velocity profile at the nozzle exit. The effects of Reynolds number Re and normalized nozzle-to-plate distance H/B are considered for a nozzle width B of 1.0 mm. Transition from a stable symmetric jet to an unsteady oscillating jet is observed as the Reynolds number increases (with H/B constant), where the Reynolds number associated with this transition decreases as the normalized nozzle-to-plate distance H/B increases. Instantaneous visualizations show unsteady lateral distortions of jet columns at experimental conditions corresponding to the presence of continuous sinusoidal oscillations, intermittent oscillating motion of the jet column, and jet flow fluctuation/flapping motion. Also apparent in flow visualization sequences are smoke signatures associated with instantaneous vortex structures, which form as secondary flows develop in fluid which, initially, is just adjacent to and within the jet column. Associated jet and vortex structural changes are described as different modes of unsteadiness are present, including characterization of jet column unsteadiness using jet column oscillation frequency, and lateral and streamwise extents of jet distortion.     

Study on the radial jet velocity distribution of two closely spaced opposed jets

The experimental and theoretical researches on the radial jet of two opposed jets have been carried out in this paper. The radial velocities of opposed jets with various exit velocities, nozzle diameters and nozzle separations were measured experimentally by a hot-wire anemometer (HWA). The results show that, the normalized radial velocities are self-similar across various radial sections at r ? 1.5D and the radial velocity profiles can be described by a Gaussian distribution function. The half-width increases linearly with increasing radial distance at r ? 1.5D, and spreading rates of radial jet are about 0.121. The normalized radial velocity at impingement plane increases firstly, and then decreases with the increasing normalized radial distance. The normalized radial velocity is independent on nozzle diameter, nozzle separation and exit velocity. The maximum radial velocity at impingement plane is proportional to the exit velocity, and it is inversely proportional to the 0.551th power of the normalized nozzle separation. The position of the maximum radial velocity increases with the nozzle separation at L/D < 1, and keeps invariant at L/D ? 1.     

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.     

Near-wake flow characteristics of a circular cylinder close to a wall

Flow characteristics in the near wake of a circular cylinder located close to a fully developed turbulent boundary layer are investigated experimentally using particle image velocimetry (PIV). The Reynolds number based on the cylinder diameter (D) is 1.2×10⁴ and the incident boundary layer thickness (δ) is 0.4D. Detailed velocity and vorticity fields in the wake region (0<x/D<6) are given for various gap heights (S) between the cylinder and the wall, with S/D ranging from 0.1 to 1.0. Both the ensemble-averaged (including the mean velocity vectors and Reynolds stress) and the instantaneous flow fields are strongly dependent on S/D. Results reveal that for S/D⩾0.3, the flow is characterized by the periodic, Kármán-like vortex shedding from the upper and lower sides of the cylinder. The shed vortices and their evolution are revealed by analyzing the instantaneous flow fields using various vortex identification methods, including Galilean decomposition of velocity vectors, calculation of vorticity and swirling strength. For small and intermediate gap ratios (S/D⩽0.6), the wake flow develops a distinct asymmetry about the cylinder centreline; however, some flow quantities, such as the Strouhal number and the convection velocity of the shed vortex, keep roughly constant and virtually independent of S/D.     

Three-dimensional numerical simulations of cross-flow around four cylinders in an in-line square configuration

This paper presents a numerical study of three-dimensional (3-D) laminar flow around four circular cylinders in an in-line square configuration. The investigation focuses on effects of spacing ratio (L/D) and aspect ratio (H/D) on 3-D flow characteristics, and the force and pressure coefficients of the cylinders. Extensive 3-D numerical simulations were performed at Reynolds number of 200 for L/D from 1.6 to 5.0 at H/D=16 and H/D from 6 to 20 at L/D=3.5. The results show that the 3-D numerical simulations have remedied the inadequacy of 2-D simulations and the results are in excellent agreement with the experimental results. The relation between 3-D flow patterns and pressure characteristics around the four cylinders is examined and discussed. The critical spacing ratio for flow pattern transformation was found to be L/D=3.5 for H/D=16, while a bistable wake pattern was observed at L/D=1.6 for the same aspect ratio. Moreover, a transformation of flow pattern from a stable shielding flow pattern to a vortex shedding flow pattern near the middle spanwise positions of the cylinders was observed and was found to be dependent on the aspect ratio, spacing ratio, and end wall conditions. Due to the highly 3-D nature of the flows, different flow patterns coexist over different spanwise positions of the cylinders even for the same aspect ratio. It is concluded that spacing ratio, aspect ratio, and the no-slip end wall condition have important combined effects on free shear layer development of the cylinders and hence have significant effects on the pressure field and force characteristics of the four cylinders with different spacing ratios and aspect ratios.     

Thermal study of an array of inline horizontal cylinders below a nearly adiabatic ceiling

Steady state two-dimensional free convection heat transfer from a horizontal, isothermal cylinder in a horizontal array of cylinders consists of three isothermal cylinders, located underneath a nearly adiabatic ceiling is studied experimentally. A Mach–Zehnder interferometer is used to determine thermal field and smoke test is made to visualize flow field. Effects of the cylinders spacing to its diameter (S/D), and cylinder distance from ceiling to its diameter (L/D) on heat transfer from the centered cylinder are investigated for Rayleigh numbers from 1500 to 6000. Experiments are performed for an inline array configuration of horizontal cylinders of diameters D = 13 mm. Results indicate that due to the nearly adiabatic ceiling and neighboring cylinders, thermal plume resulted from the centered cylinder separates from cylinder surface even for high L/D values and forming recirculation regions. By decreasing the space ratio S/D, the recirculation flow strength increases. Also, by decreasing S/D, boundary layers of neighboring cylinders combine and form a developing flow between cylinders. The strength of developing flow depends on the cylinders Rayleigh number and S/D ratio. Due to the developing flow between cylinders, the vortex flow on the top of the centered cylinder appears for all L/D ratios and this vortex influences the value of local Nusselt number distribution around the cylinder.Variation of average Nusselt number of the centered cylinder depends highly on L/D and the trend with S/D depends on the value of Rayleigh number.     

On the analysis of an impinging jet on ground effects

Laser Doppler measurements and flow visualization are presented for a turbulent circular jet emerging into a low-velocity cross-stream and, then, impinging on a flat surface perpendicular to the jet-nozzle axis. The experiments were performed for a Reynolds number based on the jet-exit conditions of 6 × 10⁴, a jet-to-crossflow velocity ratio of 30 and for an impingement height of 5 jet diameters and include mean and turbulent velocity characteristics along the two normal directions contained in planes parallel to the nozzle axis. The results, which have relevance to flows found beneath VSTOL aircraft in ground effect, show the presence of a complex 3-D scarf vortex formed around the impinging jet. In zones where measurement data are not available, the flow details are numerically-visualized using a solution of the finite difference form of the fully threedimensional Reynolds-averaged Navier-Stokes equations, incorporating the turbulence viscosity concept. The turbulent structure of the flow is affected by flow distortion at the impinging zone, which results in an unconventional behaviour of the dimensionless structure parameters that determine the empirical constants in engineering models of turbulence. The relative magnitude of the terms involved in the transport equations for the turbulent stresses is quantified from the experimental data in order to assess the importance of these effects and show the extent to which the turbulent structure of the impingement zone is affected by extra rates of strain.     

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.     

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.