Counter-rotating Vortex Rings Research Articles

A Study of Shock-Induced Transient Jets: The Impact of Exit Conditions on Mach Disk and Vortex Ring

Abstract We investigate the effect of exit pressure history on the flow characteristics of underexpanded transient jets. Using both experiments and numerical simulations, we study the dynamics of shock-cell and vortex structures within these jets. A shock tube with an open-ended configuration allows us to generate transient jets by adjusting the diaphragm pressure ratio and the length of the driver section. Our results indicate that when the shock Mach number exceeds 1.6, a Mach disk forms, indicating a highly underexpanded transient jet at the exit of the shock tube. A distinguishing feature of this jet is the emergence of counter-rotating vortex rings (CRVRs) alongside the initial primary vortex ring. Our findings reveal a substantial influence of both the amplitude and duration of the peak exit pressure on the characteristics of the Mach disk and vortex ring. Notably, the characteristics of the primary vortex ring exhibit significant sensitivity to the formation and evolution of CRVRs. In cases of continuously decreasing exit pressure, the Mach disk follows a consistent self-similar decay pattern, regardless of the peak exit pressure magnitude. Finally, we present an empirical relationship between exit pressure and the characteristics of the Mach disk. In summary, this research provides insight into the complex interaction between the exit pressure history and the flow characteristics in underexpanded transient jets.

On the evolution and circulation dynamics of the counter rotating vortex rings in the starting phases of under-expanded jets

In the starting phases of laminar, axisymmetric, continuously blowing under-expanded jets, the evolution of a counter rotating vortex ring (CRVR) over the periphery of the primary vortex ring (PVR) is numerically investigated. During CRVR evolution, the circulation dynamics of both these vortex rings is also studied. The effect of jet Reynolds number (Rej), jet Mach number (Mj), and pressure ratio (pjpa) on these phenomena is also shown. The CRVR evolution involves the rolling of the CRVR over the PVR periphery followed by the shock–vortex interaction between the CRVR and vortex induced shock (VIS) of the PVR. The PVR and CRVR circulations attain quasi-constancy as the CRVR starts to roll over the PVR periphery. The PVR circulation is shown to attain quasi-constancy even in the absence of its pinch-off (detachment) from the shear layer, which is a manifestation of Kelvin's theorem. The slip-stream strength is found to govern the magnitude of CRVR circulation. New type of discontinuities (induced shocks and vortex sheet) are observed inside the rolling CRVRs, which are generated from medium/high strength slip-streams. Due to the vorticity imparted from such slip-streams, there is self-roll-up of the CRVR leading to the generation of transient spiral stagnation point and vortex sheet which causes the formation of the transient saddle stagnation point. The formation of induced shocks inside CRVRs is due to the combination of two different constraints, i.e., (a) cyclic distribution of fluid properties inside the CRVR and (b) quasi-constancy of the CRVR circulation. The shock–vortex interaction between CRVR and VIS is a weak shock-strong vortex interaction, which occurs due to the constraint of quasi-constancy of net-circulation enclosing both vortex rings (i.e., PVR and CRVR) and causes the weakening of VIS.

Eddy-viscous modeling and the topology of extreme circulation events in three-dimensional turbulence

We discuss the role of particular velocity field configurations – instantons, for short – which are supposed to dominate the flow during the occurrence of extreme turbulent circulation events. Instanton equations, devised for the stochastic hydrodynamic setup of homogeneous and isotropic turbulence, are applied to the interpretation of direct numerical simulation results. We are able in this way to model the time evolution of extreme circulation events for a broad range of scales, through the combined use of eddy viscosity phenomenology and exact creeping instantons. While this approach works well for the core of circulation instantons, it fails to describe their tails. In order to overcome this difficulty, we put forward a numerical treatment of the axisymmetric instanton equations. Circulation instantons are then found to have a surprising topological structure, which consists of a system of paired counter-rotating vortex rings centered around the symmetry axis of a background axisymmetric vortical flow.

On the influence of co-flow on the shocks and vortex rings in the starting phases of under-expanded jets

In the starting phases of continuously blowing under-expanded jets, this numerical study investigates the effect of co-flow (UaUj) (a) on the circulation and evolution of primary vortex ring (PVR) and (b) on the occurrence of Mach reflection, slipstream generation, and subsequent formation of counter rotating vortex rings (CRVRs). With increase in co-flow (UaUj), the PVR circulation gradually decreases. The size of supersonic PVR gradually decreases with increase in co-flow (UaUj), and at high magnitudes of co-flow (UaUj≳0.3), the supersonic PVR attains a circular shape. The strengths of embedded shock (ES) and vortex-induced shock are found to decrease with increase in co-flow (UaUj), and at high magnitudes of co-flow (UaUj≳0.3), these shocks may even cease to form inside the supersonic PVR. An increase in co-flow (UaUj) causes the expansion fan to become more and more narrow. This reduces the acceleration of the supersonic flow inside the inviscid core, thereby weakening the incident oblique shock (IOS), which in turn increases the pressure prevailing downstream of this shock inside the inviscid core. The increase in co-flow (UaUj) also leads to a simultaneous decrease in the pressures prevailing in front of the downstream marching PVR and Mach disk (MD) of the inviscid core due to the reduction in the strength of precursor shock. As the magnitudes of pressures prevailing in the upstream and downstream of Mach disk approach each other, hence, MD also weakens. This shows that with the increase in co-flow (UaUj), there is weakening of the different shocks (i.e., ES, IOS, and MD) involved in Mach reflection. This causes a reduction in the strength of the resulting slipstream, thereby affecting the formation of CRVR patterns.

Spontaneous symmetry breaking for extreme vorticity and strain in the three-dimensional Navier-Stokes equations.

We investigate the spatio-temporal structure of the most likely configurations realizing extremely high vorticity or strain in the stochastically forced three-dimensional incompressible Navier–Stokes equations. Most likely configurations are computed by numerically finding the highest probability velocity field realizing an extreme constraint as solution of a large optimization problem. High-vorticity configurations are identified as pinched vortex filaments with swirl, while high-strain configurations correspond to counter-rotating vortex rings. We additionally observe that the most likely configurations for vorticity and strain spontaneously break their rotational symmetry for extremely high observable values. Instanton calculus and large deviation theory allow us to show that these maximum likelihood realizations determine the tail probabilities of the observed quantities. In particular, we are able to demonstrate that artificially enforcing rotational symmetry for large strain configurations leads to a severe underestimate of their probability, as it is dominated in likelihood by an exponentially more likely symmetry-broken vortex-sheet configuration.This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.

Characteristics of shock tube generated compressible vortex rings at very high shock Mach numbers

Compressible vortex rings are usually formed at the open end of a shock tube. They show exciting flow phenomena during their formation, evolution, and propagation depending on the shock Mach number (Ms) and exit flow conditions. This study considers high shock tube pressure ratio (PR) cases showing hitherto unknown, spectacular flow structures. With hydrogen as a driver section gas at high PR, a supersonic compressible vortex ring having vortex ring Mach number (Mv) >1 is obtained for the first time. The formation of multiple triple points and the corresponding slipstream shear layers and, thus, multiple counter-rotating vortex rings (CRVRs) behind the primary vortex ring at different radial locations, in addition to the usual CRVRs, appears to be a unique characteristic for high Mach number vortex rings. During the formation stage, a vortex layer of reverse circulation than that of the primary vortex ring gets generated from the outer wall of the shock tube. The instability of such a vortex layer creates another series of opposite circulation vortices, which later interfere with the primary vortex core considerably. Also, a near stationary slipstream vortex and multiple fast-moving tiny vortices of opposite circulation to the slipstream vortex are observed near the central zone. Mechanisms for the formation of these complex vortical structures are identified. The implications of these phenomena on the vortex ring's geometric and kinematic characteristics, such as ring diameter, core diameter, circulation, and translational velocity, are discussed in detail, illustrating their differences with low vortex ring Mach number cases considering 0.31 < Mv < 1.08.

Dynamics of two coaxially rising gas bubbles

In this study, the coalescence dynamics of two unequal sized vertically inline bubbles rising in a liquid column have been investigated using the coupled level-set and volume-of-fluid (CLSVOF) method. A wide range of bubble radius ratios of trailing bubble and leading bubble (0.25≤R≤2.0) and separation distances between the bubbles (2.5≤S≤3.5) have been deployed to investigate the evolution of the bubble wakes and bubble shapes. It is discovered that the coalescence time increases with R, the maxima being around 0.75≤R≤1, and then it decreases. With the increase in S, the coalescence time gradually increases. The existence of a pair of counter-rotating vortex rings has been observed between the bubbles, which are seen to accelerate the bubble coalescence process. For the present range of R and S, we show a regime map with four distinct coalescence pathways: coalescence with liquid entrapment, coalescence without liquid entrapment, penetration of the leading bubble, and premature splitting of the trailing bubble.

On the formation and sustenance of the compressible vortex rings in starting axisymmetric jets: A phenomenological approach

The present work numerically investigates the formation and sustenance of a primary vortex ring (PVR) and counter-rotating vortex rings (CRVRs) in laminar, axisymmetric, continuously blowing compressible jets. The effect of jet Reynolds number (Rej), jet Mach number (Mj), and pressure-ratio (pjpa) on these compressible vortex rings and their flow dynamics is explored. The core bow shock is formed in the inviscid core of the transonic/supersonic jets for sustaining the supersonic flow field in the PVR. The embedded shock (ES) and vortex-induced shock (VIS) are also found to sustain the evolving PVR in the supersonic jets. The effect of Mj and pjpa on the circulation and pinch-off of the PVR is also investigated. For over-expanded and perfectly expanded supersonic jets, Kelvin–Helmholtz vortices (KHVs) entrained into the PVR interact with the ES to cause a shock–vortex interaction, which results in the appearance of multiple VISs. It is established that the different events of interaction of KHV with the ES inside the PVR after the pinch-off are a manifestation of two factors: (i) the constraint imposed on the PVR by quasi-time-invariance of circulation around a material curve enclosing the PVR and (ii) the requirement of spatially cyclic property distribution inside the PVR. The shock-shear layer–vortex interaction in under-expanded jets is also investigated using vorticity analysis and oblique shock theory. For under-expanded jets, apart from the Mach-reflection timescale, the CRVR pattern formation is also governed by the initial strength of the slip-stream, which, in turn, is regulated by all three parameters, i.e., Rej, Mj, and pjpa.

Vortex–shock and vortex–vortex interactions in the compressible starting jet from two beveled nozzle configurations

An experiment was conducted to investigate the flow structures in the compressible starting jet from two beveled nozzles (45 $$^{\circ }$$ and 30 $$^{\circ }$$ nozzle angles) of a shock tube using the schlieren technique. In the present study, the pressure ratios between the driver section and the driven section (PR) of 3.5, 7, and 10.5 corresponding to the shock wave Mach numbers ( $$M_\mathrm{s}$$ ) of 1.28, 1.48, and 1.59 were applied to produce three types of compressible vortex rings (CVRs). Owing to the beveled nozzle, the shock wave diffracts twice to produce two coaxial CVRs. For PR = 3.5 with 45 $$^{\circ }$$ beveled nozzle, two shock-free CVRs are formed and merged into one primary CVR, while the two CVRs are separated from each other for the 30 $$^{\circ }$$ beveled nozzle. The main reason is that the strength of the secondary CVR generated from the 30 $$^{\circ }$$ beveled nozzle is much lower than that of the leading CVR. As for PR =7 and 10.5, the embedded shock and counter-rotating vortex rings (CRVRs) appear and constraint the formation of the secondary CVR. As a result, the two CVRs are merged into a primary CVR at a very early stage. In addition, for the two different beveled nozzles, the embedded shock–CVR, CRVR–CVR, and shock cell-trailing vortices interactions are observed and exhibited some differences. Moreover, by identifying the position of the primary CVR, it is found that the propagation velocity of the primary CVR generated from the beveled nozzles is significantly slower than that from a straight nozzle.

On the structures of compressible vortex rings generated by the compressible starting jet from converging and diverging nozzles

Compressible vortex rings (CVRs) are one fundamental supersonic flow structure, which is usually generated by a compressible starting jet from a nozzle. Changes in the nozzle geometry provide efficient passive flow control to modulate the structures of CVRs. In this paper, a shock-tube apparatus with three open-ended nozzle geometries (straight, diverging, and converging nozzles) was designed to generate CVRs. The evolution of CVRs was recorded by using the schlieren technique. Three shock Mach numbers (Ms), including Ms=1.28, 1.48, and 1.59, were designed to generate the three typical CVRs. For Ms=1.28, shock-free CVRs are generated by the three nozzles. The CVR generated by the diverging nozzle has the largest size and was followed by a trailing jet, while the CVR generated by the converging nozzle has the smallest size with a strong turbulent trailing jet. For Ms=1.48, a CVR with embedded shock is generated by the straight nozzle, and the CVR is followed by a counter-rotating vortex ring (CRVR) for Ms=1.59. When the diverging nozzle is applied, multiple shock-cells (including barrel shock, Mach disk, oblique shock) appear in the trailing jet following the CVR, but quickly disappear as the CVR evolves. In contrast, as for the converging nozzle, strong shock-cells form in the trailing jet and interact with primary CVR. In addition, the strongest CRVRs are generated owing to the interaction between trailing shock-cells/vortices and CVRs for Ms=1.59. By identifying the CVR locations, it is found that the CVRs generated by converging nozzle have the largest average propagating velocity. However, as Ms increases, the change in the averaged propagation velocity brought by converging or diverging nozzles becomes slighter.

Formation and dynamics of compressible vortex rings generated by a shock tube

Particle image velocimetry experiments were carried out to investigate the formation and dynamics of compressible vortex rings (CVRs) generated by a shock tube apparatus. Five shock Mach numbers ($$M_\mathrm{s}$$) including $$M_\mathrm{s}=\,1.28$$, 1.39, 1.48, 1.56, and 1.59 are designed to generate the three typical CVRs including shock-free CVRs, CVRs with embedded shock, and CVRs with embedded shock and counter-rotating vortex rings (CRVRs). Experimental results show that after the incident shock leaves the tube exit, CVRs roll up, grow in size, and then pinch off at a certain timescale. By referring to the idea of vortex formation time, CVRs are found to pinch off at the dimensionless formation number within the narrow range of $$F^*=3.5\pm 0.5$$ for the range of $$M_\mathrm{s}=\,1.28$$–1.59. When $$M_\mathrm{s}\ge 1.48$$, the embedded shock appears inside the CVRs and axially stretches the vortex core, therefore significantly affecting the dynamics of CVRs. The maximum axial velocity along the centerline, the non-dimensional mean core radius, and the propagation velocity of CVRs all increase with $$M_\mathrm{s}$$ when $$M_\mathrm{s}\le 1.48$$; however, they no longer increase when $$M_\mathrm{s}>1.48$$ owing to the effects of embedded shock. In addition, the propagation velocity estimated by the formula given by Moore (Proc R Soc Lond A 397:87–97, 1985) shows the better agreement with that obtained by experimental measurement for shock-free CVRs than CVRs with embedded shock and CVRs with CRVRs.

A comparative three-dimensional study of impulsive flow emanating from a shock tube for shock Mach number 1.6

A three-dimensional transient impulsive flow emanating from an open end of a 165-mm driver section shock tube is investigated numerically in the present study for a shock Mach number of 1.6. Here, the main objective was to find out an appropriate model to simulate the early evolution of the high Mach number transient flows by comparing the flow field obtained from two numerical models with both qualitative and quantitative experimental observations. The 3-D numerical simulations were performed by solving RANS equations using the shear stress transport K-ω model and large eddy simulation of the flow with the help of ANSYS CFX software. The experiments were performed with the simultaneous 2-D and 3-D particle image velocimetry systems and high-resolution smoke flow visualizations. The 2-D PIV results were used for comparing the numerical results obtained on a plane, and the 3-D PIV results were used to compare the azimuthal variations across the vortex ring. It is observed that the velocity field of the transient jet, Kelvin–Helmholtz (K–H) vortices at the trailing jet and the interaction of K–H vortices with the primary vortex ring were resolved well in LES quite similar to the experiments. However, the SST K-ω model resolved only the velocity field of the transient jet in the axial region similar to the experiments and dissipated the K–H vortices at the jet boundary. Though both models resolved the shear layer originated from the triple point, they did not predict the rollup and formation of vortices and their interactions observed in a 24 MP camera. This demands the use of a higher spatial resolution. It is also noticed that a substantial adverse pressure gradient experienced by the vortex ring and trailing jet during the early stage of evolution due to the presence of precursor/incident shock was responsible for the pairing up and merging of the shear layer vortices to form a stronger counter-rotating vortex ring. This adverse gradient also plays a dominant role in the azimuthal expansion (rapid increase in diameter) of the vortex ring.

Formation and behavior of counter-rotating vortex rings

Concentric, counter-rotating vortex ring formation by transient jet ejection between concentric cylinders was studied numerically to determine the effects of cylinder gap ratio, \(\frac{\Delta R}{R}\), and jet stroke length-to-gap ratio, \(\frac{L}{\Delta R}\), on the evolution of the vorticity and the trajectories of the resulting axisymmetric vortex pair. The flow was simulated at a jet Reynolds number of 1000 (based on \(\Delta R\) and the jet velocity), \(\frac{L}{\Delta R} \) in the range 1–20, and \(\frac{\Delta R}{R}\) in the range 0.05–0.25. Five characteristic flow evolution patterns were observed and classified based on \(\frac{L}{\Delta R} \) and \(\frac{\Delta R}{R}\). The results showed that the relative position, relative strength, and radii of the vortex rings during and soon after formation played a prominent role in the evolution of the trajectories of their vorticity centroids at the later time. The conditions on relative strength of the vortices necessary for them to travel together as a pair following formation were studied, and factors affecting differences in vortex circulation following formation were investigated. In addition to the characteristics of the primary vortices, the stopping vortices had a strong influence on the initial vortex configuration and effected the long-time flow evolution at low \(\frac{L}{\Delta R}\) and small \(\frac{\Delta R}{R}\). For long \(\frac{L}{\Delta R} \) and small \(\frac{\Delta R}{R}\), shedding of vorticity was sometimes observed and this shedding was related to the Kelvin–Benjamin variational principle of maximal energy for steadily translating vortex rings.

A numerical investigation and design optimization of impingement cooling system with an array of air jets

In the present study, fluid flow, heat transfer and entropy generation in impingement cooling system with an array of air jets for different values of Reynolds number (Re), Velocity Ratio (VR) and Channel Height (H/L) are investigated. The magnitude of overall Nusselt number (Nuov‾) and global total entropy generation (Stot,Ω) is found to increase with increasing Re,VR and decreasing H/L. Further, spectral and proper orthogonal decomposition analyses are performed to analyze spatio-temporal dynamics of vortex structures for unsteady configurations of impingement cooling system. It is observed that, along the interface of jet (both primary and secondary) and ambient fluid, the destabilizing effect of shear forces overcome the stabilizing effect of momentum diffusion. This results in evolution of counter-rotating vortex rings along the interfaces of jet and ambient fluid due to shear layer instability. Finally, Multi-Objective Genetic Algorithm (MOGA) has been implemented to obtain optimum configurations of impingement cooling system where a trade-off between two performance parameters, Nuov‾ and Stot,Ω is obtained.

Holes stabilize freely falling coins

The free fall of heavy bodies in a viscous fluid medium is a problem of interest to many engineering and scientific disciplines, including the study of unpowered flight and seed dispersal. The falling behaviour of coins and thin discs in particular has been categorized into one of four distinct modes; steady, fluttering, chaotic or tumbling, depending on the moment of inertia and Reynolds number. This paper investigates, through a carefully designed experiment, the falling dynamics of thin discs with central holes. The effects of the central hole on the disc’s motion is characterized for a range of Reynolds number, moments of inertia and inner to outer diameter ratio. By increasing this ratio, that is, the hole size, the disc is found to transition from tumbling to chaotic then fluttering at values of the moment of inertia not predicted by the falling modes of whole discs. This transition from tumbling to fluttering with increased hole size is viewed as a stabilization process. Flow visualization of the wake behind annular discs shows the presence of a vortex ring at the disc’s outer edge, as in the case of whole discs, and an additional counter-rotating vortex ring at the disc’s inner edge. The inner vortex ring is responsible for stabilizing the disc’s falling motion. These findings have significant implications on the development of design principles for engineered robotic systems in free flight, and may shed light on the stability of gliding animals.

Investigation of impinging single and twin circular synthetic jets flow field

Synthetic jets are largely used in the electronic cooling field; indeed their heat transfer performances have been widely investigated. The heat transfer performances have been enhanced through the design of innovative synthetic jet devices, as the twin synthetic jets device. Obviously the heat transfer performances of the classic and innovative synthetic jet devices are strictly related to their impinging flow field. Therefore the behavior of impinging single and twin circular synthetic jets in phase opposition is experimentally investigated by using Particle Image Velocimetry (PIV) at Reynolds and Strouhal numbers equal to 5100 and 0.024, respectively. Several nozzle-to-plate distances (H), ranging between 2 and 10 nozzle diameters (D), have been investigated. The time-averaged behavior of the velocity components has been reported and discussed. Their distributions, near the impinging plate, have been described. For the single jet, at short nozzle-to-plate distances (H/D<4) the axial velocity profile near the impinging plate shows a double peak with a minimum on the jet axis. Instead, at high nozzle-to-plate distance (H/D>6), the axial velocity profile is bell-shaped. This is ascribed to the adverse pressure gradient strength and the potential core-like region extension. External oscillations are observed in all the flow field quantities near the impinging plate at 2 diameters from the stagnation point due to a secondary counter rotating vortex ring generation. The presence of such a counter rotating vortex ring decreases as the nozzle-to-plate distance increases. Comparing the two synthetic jet configurations, higher axial velocity and turbulence level but lower axial phase-correlated organized contribution to velocity have been found for the twin case because of the jets interaction. The evolution of the flow field for both configurations has been explained through phase-averaged measurements. High turbulence is observed along the shear layer emanated by the nozzle edge and in the vortex ring core. During the suction phase the saddle point shows a different behavior in the two configurations. In the single case, the saddle point reaches the impinging plate causing injection of air from the plate into the device. Differently the twin configuration generates two saddle points which do not reach the impinging plate because of the presence of the other impinging synthetic jet.

Transient force augmentation due to counter-rotating vortex ring pairs

Of particular significance to biological locomotion is vortex ring interaction. In the wakes of animals, this unsteady process determines the changes in the impulse of counter-rotating vortex ring pairs (VRPs), which consist of two vortex rings with opposite sense of rotation. In this paper, these VRPs are proposed to be of particular importance to unsteady force generation. We carry out numerical computations, simulating the piston–cylinder apparatus, to study the transient changes in the impulse of counter-rotating VRPs composed of a positive and a negative vortex ring. We model the negative vortex ring (NeVR) of a VRP by making reasonable assumptions about their vorticity distributions and spatial locations, which are initially prescribed. The result of modelling is superimposed on the flow, which has a pre-existing positive vortex ring (PoVR), leading to a VRP. The simulation quantitatively demonstrates that the unsteady force resulting from a VRP is significantly larger compared with an isolated PoVR (without an NeVR). The force enhancement is also correlated to vortex configurations. A normalised force coefficient characterising force augmentation over the entire stroke is given. The force augmentation coefficient grows significantly and then reaches a plateau as the momentum input increases. The results are consistent with those in fully unsteady vortex interaction, which involves the generation of an NeVR. It is suggested that counter-rotating VRPs could offer a new perspective to explain unconventional force generation for biological swimming and flying.

Role of slipstream instability in formation of counter-rotating vortex rings ahead of a compressible vortex ring

AbstractCounter-rotating vortex rings (CRVRs) are observed to form ahead of a primary compressible vortex ring that is generated at the open end of a shock tube at sufficiently high Mach numbers. In most of the earlier studies, the embedded shock strength has been asserted as the cause for the formation of CRVRs. In the present study, particle image velocimetry (PIV) measurements and high-order numerical simulations show that CRVRs do not form in the absence of a Mach disk in the sonic under-expanded jet behind the primary vortex ring. Kelvin–Helmholtz-type shear flow instability of the slipstream originating from the triple point of the Mach disk and subsequent eddy pairing, as observed by Rikanati et al. (Phys. Rev. Lett., vol. 96, 2006, art. 174503) in shock-wave Mach reflection, is found to be responsible for CRVR formation. The growth rate of the slipstream in the present problem follows the model proposed by them. The parameters influencing the formation of CRVRs as well as their dynamics is investigated. It is found that the strength of the Mach disk and its duration of persistence results in an exit impulse that determines the number of CRVRs formed.

Phase-resolved and time-averaged puff motions of an excited stack-issued transverse jet

The dynamics of puff motions in an excited stack-issued transverse jet were studied experimentally in a wind tunnel. The temporal and spatial evolution processes of the puffs induced by acoustic excitation were examined using the smoke flow visualization method and high-speed particle image velocimetry. The temporal and spatial evolutions of the puffs were examined using phase-resolved ensemble-averaged velocity fields and the velocity, length scales, and vorticity characteristics of the puffs were studied. The time-averaged velocity fields were calculated to analyze the velocity distributions and vorticity contours. The results show that a puff consists of a pair of counter-rotating vortex rings. An initial vortex ring was formed due to a concentration of vorticity at the lee side of the issuing jet at the instant of the mid-oscillation cycle. A vortex ring rotating in the opposite direction to that of the initial vortex ring was subsequently formed at the upwind side of the issuing jet. These two counter-rotating vortex rings formed a “mushroom” vortex pair, which was deflected by the crossflow and traveled downstream along a time-averaged trajectory of zero vorticity. The trajectory was situated far above the time-averaged streamline evolving from the leading edge of the tube. The velocity magnitudes of the vortex rings at the upwind and the lee side decreased with time evolution as the puffs traveled downstream due to momentum dissipation and entrainment effects. The puffs traveling along the trajectory of zero vorticity caused large velocities to appear above the leading-edge streamline.

A study of the counter rotating vortex rings interacting with the primary vortex ring in shock tube generated flows

The formation and evolution of counter rotating vortex rings (CRVRs) appearing in shock tube-generated flows at high shock Mach numbers (M) have been studied numerically by solving ax symmetric Navier–Stokes equations and compared with experiments. The AUSM + scheme is used for convective terms, and for time stepping a four-stage Runge–Kutta scheme is used. High-speed smoke flow visualizations and optical shadowgraph techniques are employed for verifying the numerical results. It is observed that the strong shear layer formed near the Mach disc in the axial region of the vortex ring plays a dominant role in CRVR formation. A series of CRVRs is formed for longer driver section and higher M as the shear layer persists for longer duration. The interaction of these CRVRs with the primary vortex and trailing jet vortices is studied for (i) different pressure-pulse durations at the open end keeping the amplitude constant, and (ii) varying pulse amplitude when the duration is fixed. Results are also presented comparing a high-amplitude case against a lower-amplitude one with a longer pulse duration. The maximum vorticity inside the first CRVR is found to be higher than the primary vortex ring during its formation.