Streamwise Vortex Tubes Research Articles

Flow dynamics and heat transfer characteristics of flows past a zigzag cylinder in a bounded domain

A comprehensive numerical and experimental study is conducted to investigate the flow dynamics and heat transfer characteristics of flows past a novel wavy-axis circular cylinder placed symmetrically between two parallel walls. For comparison, the flow past a corresponding straight-axis cylinder within the same bounded domain is also studied. The investigations were primarily conducted at Reynolds numbers of 626 and 680, based on the average velocity and diameter of the cylinder, with a blockage ratio of 0.42, based on the widest area of the channel. At these flow conditions, the straight cylinder expectedly showed a “reverse” von Kármán type wake. However, the special zigzag cylinder showed fundamentally distinct flow patterns at the wake leading to a significant drag reduction and a heat transfer enhancement, compared to the performance of the straight cylinder. The pressure drop of the zigzag cylinder is 14 % and 19.4 % lower than that of the straight cylinder, with a higher convective heat transfer coefficient of 24 % and 9 %, respectively, for Reynolds numbers of 626 and 680. The substantial drag reduction is attributed to the formation of steady flow pattern in the wake indicating the suppression of unsteady vortex shedding. The heat transfer enhancement was mainly caused by the formation of elongated vortical structures principally aligned in the streamwise direction. The creation of these streamwise vortex tubes tends to more efficiently mix the fluid between the near-wall area and the core region of the channel than the near-planar vortex shedding associated to the straight cylinder. It was shown that the 3D shape of the zigzag cylinder generates a spanwise velocity component, which results in the creation of a dominant streamwise vorticity component that eventually develops into sustained vortex tubes.

Wake structures behind an oscillating bubble rising close to a vertical wall

In the present study, the wake structures behind an oscillating (zigzagging in a plane) air bubble, rising in a close vicinity of a vertical wall are experimentally investigated using a high-speed two-phase particle image velocimetry. While varying the distance between the rising bubble and the wall, the spatial and temporal variations in the spanwise and streamwise vorticity components contained in the wake vortices, in addition to the bubble trajectory, are measured in a tank filled with water. In particular, the Lagrangian streamwise vorticity fields in the bubble wake have been reconstructed and investigated in detail with different conditions. Without the wall, it is confirmed that there exist counter-rotating streamwise vortex tubes in the bubble wake, agreeing with the case of a two-dimensional zigzagging bubble, as reported in the literatures. It is also found that the hairpin vortex chain structures, initially attached to the bubble rear, evolve to detached vortex ring structures as the bubble rises in an oscillating path. While the detailed vortex structures show up quite differently from the reference case depending on the distance to the wall (e.g., actual bubble-wall collision), in general the wake behind the bubble as it moves toward and away from the wall can be summarized as: (i) transition to the detached vortex ring structures is accelerated; (ii) streamwise length of vortex tubes is shortened (evolution is interfered); (iii) counter-rotating vortex tubes approaching the wall tend to slightly bounce off and slide away (being dissipated fast) from each other on the wall; and (iv) boundary-layer like secondary flow structures are induced on the wall due to additional viscous effects. These wall-induced wake modification indicates that more fluid energy is wasted due to the wall interference, rather than being used to force the lateral movement of the bubble, which agrees with the reduced amplitude and wavelength of the oscillating bubble path on the wall. Finally, this explanation has been further confirmed by estimating the vortex-induced lateral forces acting on the bubble for each case.

Lateral Spreading Mechanism of a Turbulent Spot and a Turbulent Wedge

We examine the spreading of turbulent spots and wedges into a surrounding laminar Blasius boundary layer. The spreading is not due to the lateral propagation of turbulent eddies but rather to a developing disturbance in the surrounding spanwise vorticity of the laminar boundary layer. We concentrate on the mechanisms for generating streamwise vorticity. In particular, inclined generally streamwise vortex tubes along the spot/wedge boundary tilt mean shear vortex lines either up or down. These lines subsequently tend to either lag back or lead forward. As the leading or lagging vortex lines continue to wrap around and reinforce the causative inclined tube, the lines arch up or down. The outboard portion of the resulting arch must acquire a vertical, ωy, component of vorticity which induces the rollup of a new inclined tube now outboard of the first. Close to the wall the arching mechanism is inhibited by the no through flow boundary condition while far from the wall the process is inhibited by the lack of sufficient mean spanwise vorticity.

Numerical study on evolution of subharmonic varicose low-speed streaks in turbulent channel flow

The evolution of two spanwise-aligned low-speed streaks in a wall turbulent flow, triggered by the instability of the subharmonic varicose (SV) mode, is studied by a direct numerical simulation (DNS) method in a small spatial-periodic channel. The results show that the SV low-speed streaks are self-sustained at the early stage, and then transform into subharmonic sinuous (SS) low-speed streaks. Initially, the streamwise vortex sheets are formed by shearing, and then evolve into zigzag vortex sheets due to the mutual induction. As the intensification of the SV low-speed streaks becomes prominent, the tilted streamwise vortex tubes and the V-like streamwise vortex tubes can be formed simultaneously by increasing \( + \frac{{\partial u}} {{\partial x}}\). When the SV low-speed streaks break down, new zigzag streamwise vortices will be generated, thus giving birth to the next sustaining cycle of the SV low-speed streaks. When the second breakdown happens, new secondary V-like streamwise vortices instead of zigzag streamwise vortices will be generated. Because of the sweep motion of the fluid induced by the secondary V-like streamwise vortices, each decayed low-speed streak can be divided into two parts, and each part combines with the part of another streak, finally leading to the formation of SS low-speed streaks.

Numerical investigations on the wake structures of micro-ramp and micro-vanes

Based on large eddy simulation, combined with the high-order WENO (weighted essentially non-oscillatory schemes) scheme, immersed boundary method and adaptive mesh refinement technique, the supersonic flow past a wall-mounted micro-ramp and two micro-vanes have been simulated. The different wake structures are presented and discussed. Our numerical results showed that wake structures behind the micro-ramp are more complicated, including ring-like vortex train, and streamwise vortex tubes etc. However, the wake structures of the micro-vanes are quite simple; they are mainly the two counter-rotating streamwise vortex tubes. The control of boundary flow of both is achieved through the energy exchange between the main stream and the boundary layer and is presented mainly by the upwash and downwash motion of gases under the entrainment of vortex tubes.

Transient, three-dimensional simulation of particle dispersion in flows around a circular cylinder Re = 140–260)

To understand three-dimensional dispersion of particles in the flow around a bluff body, direct numerical simulations of particle-laden wakes of a circular cylinder with Reynolds number ranging from 140 to 260 were performed. The domain decomposition method and high-order finite-difference schemes were applied to solve the fluid flow. A Lagrangian tracking solver was developed to trace the trajectories of each particle in the non-uniform grid system. It is observed that the predicted coherent structures and vortex dislocation frequency agree well with those of previous experimental studies. Particles at low Stokes numbers follow the vortex motion and can disperse into the core regions of the vortex-street and the recirculating region. Particles at larger Stokes numbers try to maintain their own motion, but take on a non-uniform distribution in the wake due to the strong folding effect of shed vortices. But for particles at intermediate Stokes numbers, higher concentration occurs in the outer boundary regions of the vortices as well as the thin band regions connecting adjacent vortex structures. Besides the spanwise vortex structures, the streamwise vortex tubes also have a remarkable effect on particle dispersion, which results in a ‘mushroom’ shape particle distribution in the wake. Furthermore, non-uniform forcing at inlet has additional effect on particle dispersion and mixing.

On coherent structures in a three-dimensional transitional plane jet

Direct numerical simulation of coherent structures in the three-dimensional transitional jet with a moderate Reynolds number of 5000 was conducted. The finite volume method was used to discretize the governing equations in space and the low-storage, three-order Runge-Kutta scheme was used for time integration. The comparisons between the statistical results of the flow field and the related experimental data were performed to validate the reliability of the present numerical schemes. The emphasis was placed on the study of the spatial evolution of the three-dimensional coherent vortex structures as well as their interactions. It is found that the evolution of the spanwise vortex structures in three-dimensional space is similar to that in two-dimensional jet. The spanwise vortex structures are subject to three-dimensional instability and induce the formation of the streamwise and lateral vortex structures. Going with the breakup and mixing of the spanwise vortex structures, the streamwise and transverse vortex tubes also fall to pieces and the mixing arranged small-scale structures are formed in the flow field. Finally, the arrangement relationship among the spanwise, the streamwise and the lateral vortex structures was analyzed and their interactions were also discussed.

Remote Sensing Observations of Effects of Mountain Blocking on Travelling Gravity-Shear Waves and Associated Clouds

Trapped Kelvin–Helmholtz (K–H) waves and vortices were monitored as they were generated immediately upwind of a mountain and driven into the barrier by a low-level jet. A stratus cloud visually revealed the embedded, propagating, gravity-shear waves. Interactions of the waves with the mountain were deciphered using remote sensing measurements of the structure, motions, and microphysics within the cloud and conceptual models based on existing theories. The observations show that the mountain acted as a dam to the flow that was primed for, but did not spontaneously induce, the waves. In response to the blocking, the waves spatially developed a pattern of formation, amplification, and breakdown between the upstream flow and the barrier, and altered the associated clouds in the process. Notably, radar signatures of velocity variance depicted organized, intertwined ribbons of relatively large vorticity within the wave layer. These provided measured evidence of the vortex sheet and streamwise vortex tubes predicted by advanced K–Hinstability theory, the three-dimensional version of Scorer's `stripe', the layer of rotational fluid between opposed flows that led to the wave generation. A theory of resonant interaction of wave trains, but with blocking imposed, appears to explain the internal structure of the pile-up of the flow and wave amplification approaching the barrier. Evolution of the supporting atmospheric thermal structure and introduction of a boundary-layer flow reversal follow a current model of blocking, although some features may have developed more directly from wave-driven mixing. The remote sensors also measured the influence of the waves on the cloud liquid water, including a cumulative enlargement of droplets as they were carried through a series of waves.

K-1416 超音速における混合層の数値シミュレーション(G05-4 PTV計測と混合層)(G05 流体工学部門一般講演)

In this study, a numerical calculation of supersonic-subsonic mixing layers is performed by solving the three dimensional compressible Navie-Storkes equations in the generalized coordinates. Calculations at convective Mach number of 0.52 suggest the existence of streamwise vortex tubes in the startially developing turbulent mixing layer. Also, a close relation between vorticity and pressure is noticed. The vortices reveal fairly stable behavior in a wide range of x direction.

Instabilities in Three‐dimensional Simulations of Astrophysical Jets Crossing Tilted Interfaces

Three-dimensional numerical simulations of light supersonic hydrodynamic jets have been performed to quantify the crucial roles of the interstellar medium (ISM) and intracluster medium (ICM) in defining the gross morphologies of powerful radio galaxies. Such a jet emerges through a power-law atmosphere (ISM) of its host galaxy and then crosses into a hotter, but less dense, ICM. Our eight medium-resolution simulations are followed to lengths of 45 initial jet radii. Simulations with different jet velocities, jet densities, extensions of the ISM (along the jet's axis), and inclination angles of the ISM/ICM interface are compared. The shear layer between the jet and the shock-processed gas is affected by nonlinear hydrodynamical instabilities. Complex patterns of asymmetric vortex rings and superposed streamwise vortex tubes arise in the cocoon, while internal shocks form in the jet. The low-Mach number jets have higher growth rates of instabilities, in comparison with higher Mach number jets, and the Mach disks or working surfaces at the heads of the jets break down. The growth of Rayleigh-Taylor instabilities along the contact discontinuity between the shocked ambient plasma and the shocked jet's plasma appears to trigger the entrainment of heavier external gas into the jet. Greater tilts of the interface induce more wiggling and ribboning of the jets, but none of these simulations evinces substantial jet bending.

A study of streamwise vortex structure in a stratified shear layer

The existence of an organized streamwise vortical structure, which is superimposed on the well known coherent spanwise vorticity in nominally two-dimensional free shear layers, has been studied extensively. In the presence of stratification, however, buoyancy forces contribute to an additional mechanism for the generation of streamwise vorticity. As the spanwise vorticity layer rolls up and pulls high-density fluid above low-density fluid, a local instability results. The purpose of the current investigation is to force the three-dimensional instability in the stratified shear layer. In this manner, we experimentally observe the effect of buoyancy on the streamwise vortex tube evolution, the evolution of the buoyancy-induced instability, and the interaction between these two vortical structures. A simple numerical model is proposed which captures the relevant physics of the flow evolution. It is found that, depending on the location, streamwise vortices resulting from vortex stretching may be weakened or enhanced by the stratification. Buoyancy-induced vortex structures are shown to form where the unstable part of the interface is tilted by the streamwise vortex tubes. These vortices strengthen initially, then weaken downstream, the timescale for this process depending upon the degree of stratification. For initial Richardson numbers larger than about 0.03, the baroclinically weakened vortex tubes eventually disappear as the flow evolves downstream and the baroclinically generated vortices dominate the three-dimensional flow structure.

Baroclinic generation of streamwise vorticity in a stratified shear layer

The existence of an organized streamwise vortical structure, which is superimposed on the well known coherent spanwise vorticity in nominally two-dimensional free shear layers, has been studied extensively. In the presence of stratification, however, buoyancy forces contribute to an additional mechanism for the generation of streamwise vorticity. The purpose of the current investigation is to force the three-dimensional instability in the stratified shear layer. In this manner, we experimentally observe the effect of buoyancy on the streamwise vortex tube evolution, the evolution of the buoyancy-induced instability, and the interaction between these two vortical structures. It is found that streamwise vortices resulting from vortex stretching are weakened in regions of locally stable stratification. Buoyancy-induced vortex structures are shown to form where the unstable part of the interface is tilted by the streamwise vortex tubes. These vortices strengthen initially, then weaken downstream, the time scale for this process depending upon the degree of stratification. For initial Richardson numbers larger than about 0.03, the baroclinically weakened vortex tubes eventually disappear as the flow evolves downstream and the baroclinically generated vortices dominate the three-dimensional flow structure.

Three-dimensional vorticity modes in the wake of a flat plate

The three-dimensional development of the wake behind a flat plate separating two laminar streams of equal velocity, subjected to perturbations in its initial conditions, is studied experimentally and numerically at moderate Reynolds numbers. The effect of single waves as well as subharmonic streamwise forcing is discussed. For the case of a single wave, streamwise forcing combined with a sinusoidal spanwise perturbation, the two distinct three-dimensional vorticity modes found in an early study [J. Fluid Mech. 190, 1 (1988)], are further studied and their symmetry properties analyzed. Depending on the orientation of the spanwise perturbation, the counter-rotating pairs of streamwise vortex tubes forming in the braids are shown to induce undulations in the cores of the Karman-like vortices, resulting in either an in-phase or a varicose configuration. Furthermore, when the wake is subjected to subharmonic streamwise forcing, additional modes of the topology of the vorticity field are shown to exist. The evolution of these subharmonic three-dimensional modes is analyzed as a function of the initial conditions.

Topology of the vorticity field in three-dimensional shear layers and wakes

An experimental and numerical study of the three-dimensional transition of plane wakes and shear layers behind a flat plate is presented. Flow visualization techniques are used to monitor the response of laminar flows at moderate Reynolds numbers (≈100) to perturbations periodically distributed along the span. In this way, the formation and evolution of streamwise vortex tubes and their interaction with the spanwise vortices are analyzed. The flow was studied numerically by means of three-dimensional inviscid vortex dynamics. Assuming periodicity in the spanwise and the streamwise direction, we discretize the vorticity field into two layers of vortex filaments with finite core diameter. Comparison between experiment and visualization indicates that important features of the three-dimensional evolution can be reproduced by inviscid vortex dynamics. Vortex stretching in the strain field of the spanwise rollers appears to be the primary mechanism for the three-dimensional transition in this type of flows.

Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices

The three-dimensional development of a plane free shear layer subjected to small sinusoidal perturbations periodically placed along the span is experimentally studied. Both laser induced fluorescence and direct interface visualization are used to monitor the interface between the two fluids. The development of the different flow stabilities is obtained through analysis of the temporal and spatial evolution of the interface separating the two streams. It is shown that the characteristic time of growth of the two-dimensional shear instability is much shorter than that of the three-dimensional instability. The primary Kelvin-Helmholtz instability develops first, leading to the formation of an almost two-dimensional array of spanwise vortex tubes. Under the effect of the strain field created by the evolving spanwise vortices, the perturbed vorticity existing on the braids undergoes axial stretching, resulting in the formation of vortex tubes whose axes are aligned with the principal direction of the positive strain field. During the formation of these streamwise vortex tubes, the spanwise vortices maintain, to a great extent, their two-dimensionality, suggesting an almost uncoupled development of both instabilities. The vortex tubes formed through the three-dimensional instability of the braids further undergo nonlinear interactions with the spanwise vortices inducing on their cores a wavy undulation of the same wavelength, but 180° phase shifted with respect to the perturbation. In addition, it is shown that owing to the nature of the three-dimensional instability, the effect of vertical and axial perturbations are coupled. Finally, the influence of the amplitude and wavelength of the perturbation on the development of the two- and three-dimensional instabilities is described.