Study of vortex breakdown by particle tracking velocimetry (PTV)

The spiral-type breakdown of a slender vortex was quantitatively investigated with PTV. Multiexposed pictures of the illuminated meridional midplane were processed to obtain the instantaneous 2-D velocity field and vorticity distribution. The periodic change of flow patterns with respect to time is clearly shown in a time-series of pictures. The 2-D velocity fields contained a stagnation point in the midplane located outside of the centerline. Additionally it was observed, that this point rotates around the centerline in the same way as the outer flow. A comparison with measurements of a bubble-type breakdown indicates a strong similarity to the spiral-type breakdown. The results reveal that the slope, winding and diameter of the spiral vortex-core determine the different observable forms. The first part of the deflected vortex-core near the breakdown point causes an asymmetric backflow due to induction, the strength of which depends on the slope of the deflected vortexcore. This is responsible for the radial distance between stagnation point and centerline. In case of the observed bubble-type breakdown the spiral is compressed which results in a stable stagnation point at the centerline.     

Vortex breakdown: Transition between bubble- and spiral-type breakdown

Depending on volume flux, flow visualizations in a water tunnel showed bubble-, spiral-type breakdown, and periodic transition between both. The initiation and development of bubble-type breakdown can be explained by a nonlinear feedback model. A growing asymmetry of the circumferential vorticity distribution leads to the transition to spiral-type. These conjectures are supported by experiments in which an artificially generated vortex ring induced initiation of bubble- and transition to spiral-type breakdown. To simulate vortex breakdown Navier-Stokes equations for three-dimensional, unsteady, and incompressible flows were solved. A comparison between experimental and numerical flow visualizations showed a good agreement.

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Sommario La visualizzazione del flusso in una galleria idrodinamica mostra, a seconda della portata volumetrica, una rottura delle linee vorticose di tipo a bolle, a spirale oppure una transizione periodica tra queste due. L'inizio ed il successivo sviluppo del fenomeno di rottura a bolla può venire spiegato attraverso un modello non lineare. Successivamente, all'aumentare dell'asimmetria nel profilo della vorticità circonferenziale, si ha la transizione alla rottura a spirale. Queste ipotesi vengono confermate dagli esperimenti in cui l'insorgere di ciascun tipo di rottura viene indotto attraverso un anello vorticoso generato artificalmente. Per analizzare il fenomeno della rottura delle linee vorticose sono state risolte le equazioni di Navier-Stokes per un flusso incomprimibile, tridimensionale, non stazionario. I risultati numerici ottenuti si sono mostrati in buon accordo con le visualizzazioni sperimentali.

     

Numerical calculations of three-dimensional turbulent vortex breakdown

Numerical solutions to the three-dimensional, unsteady, incompressible Reynolds-averaged Navier-Stokes equations have been obtained for bubble-type vortex breakdown. Two different turbulence models were employed: (1) standard K-ε and (2) an explicit, regularized algebraic Reynolds stress model. Results are computed at a Reynolds number of 10,000. The algebraic Reynolds stress model produced a breakdown bubble with a larger length-to-diameter ratio than did the K-ε model. Breakdown also occurred at lower levels of adverse pressure gradient for the algebraic stress model than for the K-ε model. In each case single-cell breakdown structures resulted. This is contrasted with numerical calculations for laminar breakdown which reveal the existence of complex multicell bubble breakdown structures.     

三角翼前缘涡的某些破裂形式及特性研究

基于流动显示和PIV技术测量的实验结果，对三角翼前缘涡破裂的一些形式和破裂特性进行了分析和讨论。通过PIV测量所得到的涡量分布证实了在螺旋破裂的情况下，涡核的螺旋方向与前缘涡的旋转方向相反，及双螺旋破裂形式的存在等。进而对螺旋波的形成机理提出了与有关文献不同的看法。     

Interchangeability of vortex-breakdown types

In order to investigate the connection between the bubble and the spiral form of vortex breakdown, experiments were conducted: an external disturbance in the form of an azimuthally spinning waveform was imposed in a pipe. The azimuthal wave number was varied by adjusting the phase difference among four oscillating pistons mounted circumferentially on the pipe. By imposing a disturbance of zero azimuthal wave number, a spiral was transformed into a bubble, and this occurred only for selective piston frequencies; the vortex breakdown which altered from the spiral to the bubble moved upstream, where it remained as a bubble as long as the external disturbance remained. Once the disturbance was removed, the bubble returned to a spiral. By imposing a disturbance of azimuthal wave number +1 (the first circumferential mode rotating in the same direction as the mean swirl), a bubble was transformed into a spiral for selective piston frequencies, and the spiral moved downstream. These preferred frequencies were found to be the same as the unexcited frequencies observed in the spiral in its natural state. As long as the external disturbance was imposed, the breakdown altered from the bubble to the spiral remained as a spiral; once the disturbance was removed, the spiral reverted to a bubble. By imposing a disturbance with azimuthal wave number -1 (the first circumferential mode rotating in the opposite direction to the mean swirl), no change was detected in either a bubble or a spiral. By imposing a disturbance with azimuthal wave number 2 (the second circumferential mode), for selective piston frequencies a bubble was transformed into what appears to be the so-called two-tailed type. Thus, it appears that hydrodynamic instability plays a role in interchanging vortex breakdown types, and a comparison with available stability theories is discussed.     

Interaction of heat release and vortex breakdown during flame flashback driven by combustion induced vortex breakdown

The interaction of heat release by chemical reaction and the flow dominates flame transition in swirling flows caused by combustion induced vortex breakdown (CIVB). The simultaneous application of 1 kHz high-speed particle imaging velocimetry (PIV) for the analysis of the flow field and OH planar laser-induced fluorescence for the detection of the flame front is particularly useful for the improvement of the understanding of the observed fast CIVB driven flame propagation. For the first time, the combination of both techniques was successfully applied to confined swirling flows. In the study, the flow field characteristics of an aerodynamically stabilized burner system with CIVB are analyzed in great depth. The influence of geometric parameters of the swirl generator was investigated and conclusions concerning the proper burner design of vortex breakdown premix burners are drawn from the experimental results. In particular, the effect of the vortex core with respect to the stability of the swirl stabilized burner is analyzed. The contribution of combustion to vortex breakdown is shown comparing isothermal and reacting flows. The presented data reveals that at the onset of CIVB driven flame transition, the azimuthal vorticity leads to the formation of a closed recirculation bubble at the tip of the internal recirculation zone. Once this bubble propagates upstream, the flame is able to follow and propagate relative to the bulk flow velocity with a velocity far beyond the turbulent flame speed. The interaction of reaction and flow was observed for different volumetric heat releases. The experiments confirm the CIVB theory of the authors, which was initially developed on the basis of a CFD study alone. Both the volume expansion and the baroclinic torque have an effect on whether fast flame propagation occurs. Whereas the volume expansion caused by the heat release stabilizes the flow field and the reaction, the baroclinic torque stimulates flame transition. For upstream propagation the flame tip has to have a position downstream of the stagnation point of the bubble. Else, the required transition inducing force is insufficient and the flame remains stable. In case the flame reaches positions too close or even upstream of the stagnation point, the fast propagation is interrupted or even prohibited. The key finding that the relative position of flame and stagnation bubble governs CIVB is discussed on the basis of high-speed LIF/PIV data as well as chemiluminescence. Since essentially the same behavior has been observed before in tests of a totally different swirler design and flow field, the conclusion can be made that the root cause for CIVB independent of the special geometry has been found.     

Some Observations of Vortex Breakdown in a Confined Flow with Solid Body Rotation

The occurrence of breakdown in slender vortex flows as a ``bubble'' or ``spiral'' pattern depends on the degree of radial deflection of the vortex core from its original axis as shown in [1]. A smooth transition from a bubble to a spiral-type ``mode'' can be forced by inducing a small asymmetric disturbance which led to the conclusion, that the patterns do not represent different fundamental modes of breakdown. The subject presented herein addresses the following question: how does breakdown evolve in a swirling flow in which the vortex core is forced on a straight axis? In addition, what is the effect of turbulent inflow conditions? This type of vortex conditions is achieved in a spinning tube flow. The swirl is introduced at the entrance of the rotating tube with a honeycomb package and maintained by the viscous action in the boundary layer of the spinning tube. A diffuser at the end induces an adverse pressure gradient to force the breakdown. Flow visualization experiments are carried out to characterize the nature of breakdown over a range of different flow conditions. For some selected characteristic stages, detailed velocity fields were obtained using the method of Digital Particle-Image-Velocimetry (DPIV). The results show, that for the range of parameters investigated, breakdown is initiated at Rossby-numbers below a critical value of Ro ≈ 0.6 similar to those observed in other experiments. The bursted part of the vortex has a near axi-symmetric slender conical shape containing approximately stagnant flow. Its downstream end is characterized by a jump-like contraction where the flow evolves into a jet with enhanced swirl on the axis. It is only in this region downstream of the jump-like contraction that asymmetric instabilities and wavy flow patterns could be observed. Perturbations caused by them travel upstream but do not change the near-axisymmetric shape of the bursted part of the vortex.     

Vortex dynamics of turbulence–coherent structure interaction

We study the interaction between a coherent structure (CS) and imposed external turbulence by employing direct numerical simulations (DNS) designed for unbounded flows with compact vorticity distribution. Flow evolution comprises (i) the reorganization of turbulence into finer-scale spiral filaments, (ii) the growth of wave-like perturbations within the vortex core, and (iii) the eventual arrest of production, leading to the decay of ambient turbulence. The filaments, preferentially aligned in the azimuthal direction, undergo two types of interactions: parallel filaments pair to form higher-circulation “threads”, and anti-parallel threads form dipoles that self-advect radially outwards. The consequent radial transport of angular momentum manifests as an overshoot of the mean circulation profile—a theoretically known consequence of faster-than-viscous vortex decay. It is found that while the resulting centrifugal instability can enhance turbulence production, vortex decay is arrested by the dampening of the instability due to the “turbulent mixing” caused by instability-generated threads. Ensemble-averaged turbulence statistics show strong fluctuations within the core; these are triggered by the external turbulence, and grow even as the turbulence decays. This surprising growth on a normal-mode-stable vortex results from algebraic amplification through “linear transient growth”. Transient growth is examined by initializing DNS with the “optimal” modes obtained from linear analysis. The simulations show that the growth of transient modes reproduces the prominent dynamics of CS-turbulence interaction: formation of thread-dipoles, growth of core fluctuations, and appearance of bending waves on the column’s core. At the larger Reynolds numbers prevailing in practical flows, transient growth may enable accelerated vortex decay through vortex column breakdown.     

脉冲激光等离子体与正激波相互作用的PIV实验研究

脉冲激光等离子体与超声速流场相互作用在飞行器减阻隔热、点火助燃等方面具有重要的应用价值.纹影实验方法只能定性或半定量地反映流动状态.为定量研究速度分布和旋涡结构,针对激光等离子体及其与正激波相互作用过程开展粒子图像测速PIV实验研究.在激波管实验平台上建立了纳秒脉冲激光能量沉积系统和PIV测量系统,通过定量测量,探明了激光等离子体引致的激光空气泡以及热核的流动特性,揭示了激光等离子体在正激波冲击下的流动特性与演化规律,并给出了激光能量大小和位置对相互作用过程的影响.结果表明:激光空气泡内的速度分布在激光入射方向上并不关于击穿点对称,而是在靠近激光入射方向一侧的流速略大于远离激光入射方向一侧;斜压导致热核在演化初期产生涡环,后期则由剪切主导;正激波与激光空气泡界面、热核界面相互作用时,产生斜压涡量,当激光能量为87.8 mJ、正激波马赫数1.4时,热核在正激波作用下产生的涡量比在静止空气中演化时大1个数量级;激光与正激波相互作用的关键过程是热核在正激波冲击下演化成涡环,在激波波前注入激光能量能够获得更加显著的涡环.     

Transition process from one celled vortex to two celled vortex

Changes in the flow structure, the vorticity distribution and the stream function during the transition process from the one celled vortex to the two celled vortex following a rapid change in the radial Reynolds number have been examined. Starting from a thin filament-like structure corresponding to the one celled vortex. a thick vortex core first grew up from the outlet region and turned into a cylindrical structure corresponding to the two celled vortex. The vorticity distribution also changed from a single-summit type to a ring-summit type.     

Three-dimensional flow structures and associated turbulence in the tip region of a waterjet pump rotor blade

Stereo particle image velocimetry measurements focus on the flow structure and turbulence within the tip leakage vortex (TLV) of an axial waterjet pump rotor. Unobstructed optical access to the sample area is achieved by matching the optical refractive index of the transparent pump with that of the fluid. Data obtained in closely spaced planes enable us to reconstruct the 3D TLV structure, including all components of the mean vorticity and strain-rate tensor along with the Reynolds stresses and associated turbulence production rates. The flow in the tip region is highly three-dimensional, and the characteristics of the TLV and leakage flow vary significantly along the blade tip chordwise direction. The TLV starts to roll up along the suction side tip corner of the blade, and it propagates within the passage toward the pressure side of the neighboring blade. A shear layer with increasing length connects the TLV to the blade tip and initially feeds vorticity into it. During initial rollup, the TLV involves entrainment of a few vortex filaments with predominantly circumferential vorticity from the blade tip. Being shed from the blade, these filaments also have high circumferential velocity and appear as swirling jets. The circumferential velocity in the TLV core is also substantially higher than that in the surrounding passage flow, but the velocity peak does not coincide with the point of maximum vorticity. When entrainment of filaments stops in the aft part of the passage, newly forming filaments wrap around the core in helical trajectories. In ensemble-averaged data, these filaments generate a vortical region that surrounds the TLV with vorticity that is perpendicular to that in the vortex core. Turbulence within the TLV is highly anisotropic and spatially non-uniform. Trends can be traced to high turbulent kinetic energy and turbulent shear stresses, e.g., in the shear layer containing the vortex filaments and the contraction region situated along the line where the leakage backflow meets the throughflow, causing separation of the boundary layer at the pump casing. Upon exposure to adverse pressure gradients in the aft part of the passage, at 0.65–0.7 chord fraction in the present conditions, the TLV bursts into a broad turbulent array of widely distributed vortex filaments.     

Physics of forced unsteady flow for a NACA 0015 airfoil undergoing constant-rate pitch-up motion*

The unsteady Navier-Stokes (NS) analysis of Osswald, Ghia and Ghia in velocity-vorticity variables is modified to study the dynamic stall phenomenon for a NACA 0015 airfoil undergoing constant Ω₀ pitch-up maneuvers at Reynolds number Re =10 000 and 45000. The use of third-order accurate biased upwind differencing for the nonlinear convective terms in the vorticity transport equation removes the spurious oscillations observed in the earlier studies by the authors for these values of Re. The fully implicit and vectorized ADI-BGE method of the authors is used to solve the unsteady NS equations. Instantaneous inertial surface vorticity, which is an invariant of the choice of reference frame selected, is employed to determine the location of separation of the boundary-layer flow on the suction surface; also a separation bubble embedded within the boundary layer is observed for both cases somewhere between the leading edge and the quarter-chord point. Primary, secondary, tertiary and quarternary vortices have been observed before the dynamic-stall vortex evolves and gathers its maximum strength.     

Experimental investigation of the unsteady structure of a transitional plane wall jet

 A laminar wall jet undergoing transition is investigated using the particle image velocimetry (PIV) technique. The plane wall jet is issued from a rectangular channel, with the jet-exit velocity profile being parabolic. The Reynolds number, based on the exit mean velocity and the channel width, is 1450. To aid the understanding of the global flow features, laser-sheet/smoke flow visualizations are performed along streamwise, spanwise, and cross-stream directions. Surface pressure measurements are made to correlate the instantaneous vorticity distribution with the surface pressure fluctuations. The instantaneous velocity and vorticity field measurements provide the basis for understanding the formation of the inner-region vortex and the subsequent interactions between the outer-region (free-shear-layer region) and inner-region (boundary-layer region) vortical structures. Results show that under the influence of the free-shear-layer vortex, the local boundary layer becomes detached from the surface and inviscidly unstable, and a vortex is formed in the inner region. Once this vortex has formed, the free-shear-layer vortex and the inner-region vortex form a vortex couple and convect downstream. The mutual interactions between these inner- and outer-region vortical structures dominate the transition process. Farther downstream, the emergence of the three-dimensional structure in the free shear layer initiates complete breakdown of the flow. Received: 8 November 1995/Accepted: 6 November 1996     

Study of vortex breakdown by particle tracking velocimetry (PTV)

Using a quasi three-dimensional instantaneous measurement technique, which combines particle tracking velocimetry (PTV) with volume scanning, first quantitative experimental results of the unsteady and asymmetric interior region of vortex breakdown were obtained. The study was carried out in a low speed flow through a cylindrical tube. A vortex was generated by a set of guidevanes and subjected to an adverse pressure gradient causing its breakdown. By scanning a pulsed illuminated planar laser light sheet, a set of meridional and azimuthal cuts of the flow was obtained. With PTV the recorded particle paths in the cuts were processed in order to obtain the instantaneous two-dimensional velocity field, mean streamlines and vorticity distribution. Moreover, the three-dimensional shape of the appearing breakdown, visualized with fluorescent dye, was reconstructed from the cuts. The results revealed that the shape of the bubble nearly equals the streamsurface of the stagnation point. According to the conditions in the water tunnel a single tilted vortex ring at the open rear part of the bubble dominates the interior flow structure of the bubble as first noted by Sarpkaya (1971). The vortical flow is bulged over the bubble, restored and intensified at the lower end. The gathered data lead to the conclusion that the vortex axis remains parallel to the centerline.     

Impact of buoyancy on vortex ring development in the near field

The development of a buoyant vortex ring in the near field was examined experimentally, and the findings were compared with those of a non-buoyant ring with a similar Reynolds number. The experiments were performed in a water tank, and the vortices were produced by a cylindrical tube of aspect ratio 2. Laser sheet flow visualization and PIV measurements were carried out. In the near field, the initial column of the buoyant fluid breaks down due to the presence of Rayleigh–Taylor instability at the buoyant fluid interface. Subsequently, a large diameter vortex ring with a large spreading rate, compared with the non-buoyant ring, emerges. The celerity of buoyant vortex continued to decrease throughout the range examined, in contrast to the constant celerity of the non-buoyant ring. The vorticity in the core of buoyant and non-buoyant vortex rings is symmetric and has a Gaussian distribution. However, the buoyant vortex ring evolves into a thin core ring, whereas the non-buoyant ring becomes a thick core ring shortly after the ring formation. This difference is brought on by the rapid entrainment and the significant growth of the buoyant ring following the breakup of the initial formation.     

Two- and three-dimensional numerical simulations of the clap–fling–sweep of hovering insects

The importance of three-dimensional effects for flapping wings is addressed by means of numerical simulation. In particular, the clap–fling–sweep mechanism is examined. The flow at the beginning of the downstroke is shown to be in reasonable agreement with the two-dimensional approximation. After the wings move farther than one chord length apart, three-dimensional effects become essential. Two values of the Reynolds number are considered. At Re=128, the spanwise flow from the wing roots to the wing tips is driven by the centrifugal forces acting on the mass of the fluid trapped in the recirculation bubble behind the wings. It removes the excess of vorticity and delays the periodic vortex shedding. At Re=1400, vortex breakdown occurs past the outer portion of the wings, and multiple vortex filaments are shed into the wake.     

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.     

Evolution of an initially columnar vortex terminating normal to a no-slip wall

The early evolution of an initially columnar vortex normal to a solid wall was examined. The vortex was generated by a pair of flaps in a water tank. Detrimental effects from the wall during the vortex generation were avoided by producing the vortex normal to a free surface and subsequently bringing a horizontal plate into contact with the surface. Digital particle image velocimetry (DPIV) measurements of the velocity and vorticity, together with laser induced fluorescence (LIF) visualizations, in a meridional plane revealed a toroidal structure with the appearance of an axisymmetric vortex breakdown bubble. Agreement was found between the measurements and numerical simulations of the axisymmetric Navier–Stokes equations. The results show that the flow in the effusive corner region is dominated by a Bödewadt-type spatially oscillatory boundary layer within the core region and a potential-like vortex boundary layer at large radii. The toroidal structure results from the interaction between these two boundary layers, leading to the roll up of a dominant shear layer within the Bödewadt structure, and does not develop from the columnar vortex itself.     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.     

A visual study on complex flow structures and flow breakdown in a boundary layer transition

A visualization study is conducted on the excited laminar-turbulent transition within a flat plate boundary layer flow in a water tunnel. The hydrogen bubble technique is employed to investigate the complex characteristics of the flow structure and its breakdown in the later stages of the transition. A new flow structure is observed, which involves two secondary hairpin vortices outboard of both legs of a primary hairpin vortex. This complex structure is argued to be a precursor of a turbulent spot in this K-type transition. Also reported in the paper is the evolution of the flow structure and its subsequent breakdown, manifested by the emergence of dark spots, low-speed fluid bumps, and near-wall hairpin vortex groups. The results indicate that the near-wall flow breakdown is the result of instability of a local three-dimensional high-shear layer between the low-speed fluid bump and the outer higher-speed region.