Vortex Wandering Research Articles

Quantifying the Tip Leakage Vortex Wandering in a Low-Speed Axial Flow Fan via URANS Simulation

The tip leakage vortex is a dominant noise and aerodynamic loss source of low-speed axial flow fans. The tip leakage vortex often has an unsteady behavior, like the periodic motion of the vortex core: the so-called vortex wandering. This periodic vortex wandering results in additional noise, aerodynamic loss, and an oscillation in the moment acting on the blading, which causes an unfavorable vibration of the rotor. In the research campaigns focusing on vortex wandering, complicated measurement techniques (PIV) or high-fidelity but computationally costly simulations are commonly used. The present paper aims to introduce a relatively cost-effective unsteady Reynolds-averaged Navier-Stokes simulation-based investigation method of vortex wandering. The capabilities of the proposed technique are presented through a low-speed axial flow fan case study.

Trailing vortex at drifting ship hull: a numerical study on wandering and turbulence

ABSTRACT Trailing vortices are commonly associated with so-called contrails in the sky. These show instability phenomena which manifest in transverse motions and sudden thickness changes. Aircraft aerodynamics considers this so-called far field whereas for naval hydrodynamics the near-field is of dominating interest. For the latter, vortices are intensively investigated at the propeller, but they emerge also at manoeuvring ship hulls or blunt stern shapes. And this is studied within the current paper: the major trailing vortex next to the KVLCC2 hull at large drift incidence. Numerical simulations with the SST-based IDDES model are conducted with OpenFOAM. The target is to reveal details of the vortex centre flow like the evolution of turbulence and the characteristics and consequences of vortex wandering. The results reveal a low-frequency broadband wandering motion next to a broad turbulent inertial subrange and that about two thirds of resolved TKE can be attributed to wandering.

Experimental investigation on the dynamics of buoyancy-induced vortices

Measurements were conducted within the flow field of a buoyancy-induced vortex at laboratory scale with a constant heat flux as input at the ground with swirl vanes set at 30° and 60° to the radial. Time-averaged velocity data were obtained using two-dimensional Particle Image Velocimetry (PIV). The velocity profiles in both cross-sectional and vertical planes were measured at heights of 0.3 m, 0.45 m, and 0.6 m above the ground level, and the time-averaged tangential, radial and vertical velocity components were derived. Two types of the vortex structures are identified based on the core swirl ratio, showing one-cell and two-cell type vortex structures with 30° and 60° swirl vane angles, respectively. Vortex wandering effects have also been investigated, including the centre distributions for different types of flow structures, and its impact on flow strength and vortex core sizes have also been quantified. Detailed turbulence statistics have been measured after removing the wandering effect, which show high level of turbulence intensities within the vortex core.

Tip leakage flow of a vibrating airfoil in a linear compressor cascade

In turbomachinery, understanding the interaction between blade vibrations and the tip flow is of great interest due to current trends, which tend to thinner airfoils with higher loading and higher efficiencies. The present paper experimentally investigates the unsteady tip leakage flow/vortex (TLF/V) of a vibrating airfoil in a compressor cascade with a large tip gap subjected to bend-mode controlled oscillations. Tip wall pressure distribution and secondary tip flow in the blade channel were studied using high-response pressure measurements and stereoscopic particle image velocimetry. The effects of blade vibrations on the TLF field and the TLV wandering characteristics are explored. The experimental results demonstrate that the TLF field is dominated by the TLV, and the TLV synchronously wanders with the displacement of the blade. Besides, the vortex intensity, the vortex wandering intensity, and turbulence fluctuations are phase-shifted by π/2 concerning the displacement of the blade. In contrast, the velocity deficit in the vortex core is not influenced by blade vibrations. This study provides the phase-resolved tip flow field of a vibrating airfoil with tip gaps in a linear compressor cascade, which is a necessary step toward compressor blade vibration prediction.

Experimental investigation of characteristics and influence of tip leakage vortex wandering in an axial compressor cascade

Vortex wandering is one of the most basic unsteady flow characteristics of the tip leakage vortex (TLV) in compressors. In this study, stereo particle image velocimetry (stereo-PIV) has been conducted in compressor cascades with various tip clearances to investigate the characteristics and influence of TLV wandering. The most effective vortex identification method for stereo-PIV data has been clarified. The wandering characteristics of the TLV are statistically analyzed, and the relationship between the vortex wandering and the dominant proper orthogonal decomposition mode is identified. The results reveal that TLV preferentially wanders along the pitchwise direction in the blade channel and gradually loses the dominant wandering direction downstream of the blade. The large displacement of the vortex center around its mean location is characterized by higher probabilities at small tip clearance size (1% chord length C). The spatial distribution characteristics demonstrate similarly concentric isocontour around the mean vortex center location for large tip clearances (3% and 5% chord length C). The effect of TLV wandering on the secondary velocity distribution, the tip flow blockage, and the distribution of Reynolds stress is explored using the vortex wandering corrected technique. The analysis verifies that the elevated turbulence kinetic energy in the core of the time-averaged uncorrected TLV is caused by vortex wandering rather than vortex deformation. The discussions of the current paper will enhance our knowledge of TLV wandering. Regardless of the reference to TLV, the interpretation of other swirling flows can benefit from the discussions presented here.

Experimental Investigation on the Influence of Swirl Ratio on Tornado-like Flow Fields by Varying Updraft Radius and Inflow Angle

The swirl ratio is the most critical parameter for determining the intensity and structure of tornado-like vortex, defined as the ratio of angular momentum to radial momentum. The angle of entry flow and the updraft radius are two key parameters affecting the swirl ratio. Many laboratory simulators have studied the effect of swirl ratio by changing the angle of entry flow, but there is a lack of research on the updraft radius. Therefore, for a deep sight of the impact of the updraft radius on the swirl ratio and tornado-like vortex, a laboratory tornado simulator capable of adjusting the updraft radius was designed, built, and tested. And, the effects of various swirl ratios caused by the updraft radius and the angle of entry flow on the tornado-like vortices were investigated, in terms of the dual-celled vortex transformation and vortex wandering. It was found that the effects of the updraft radius and the angle of turning vanes on the tornado-like vortices are quite different, and the formation of the dual-celled vortex is more sensitive to the updraft radius, because a larger angular momentum and axial pressure gradient can be provided. In addition, increasing the updraft radius has a greater inhibitory effect on the vortex wandering phenomenon compared to the angle of the turning vanes due to the flow fluctuations induced by turbulence.

The effects of stator-rotor interaction on unsteady characteristics of turbine tip leakage flow

The unsteady flow characteristics of tip leakage flow significantly affect the operation stability of the turbine blade. However, there is currently a lack of research on the unsteady flow characteristics of the tip leakage flow under the stator-rotor interaction. Through experiments with a rotating turbine and simulations of the entire stage and full-annulus turbine stage flow using a self-adaptive method, this study investigates both experimentally and theoretically the impacts of rotor-stator interaction on the dynamic behavior of the tip leakage flow in the turbine. The impacts of stator-rotor interaction on pressure oscillations, mixing, and vortex evolution within the tip leakage flow are investigated. Furthermore, the mechanisms underlying the influence of stator-rotor interaction on the dynamic behavior of the tip leakage flow at different rotor speeds and different tip gaps are also analyzed. The results indicate that the passage vortex (PV) of the guide vane aggravates the instability phases experienced by the tip leakage vortex (TLV), namely vortex wandering and breakdown. Besides, the pulsation intensity of the tip leakage flow decreases, while the pulsation frequency increases as the rotational speed increases. Additionally, it is also observed that there is a significant increase in high-frequency and large-amplitude oscillations in the tip leakage flow with increasing tip gap heights.

Experimental characterization of the flowfield and cavitation physics of a tip-loaded hydrofoil

This paper reports an experimental study of tip vortex flowfield and cavitation inception of a tip-loaded hydrofoil. Vortex strength, wandering, and turbulence statistics are characterized using stereo particle image velocimetry (SPIV) in a water tunnel facility, at a chord Reynolds number of 1.3×106. Cavitation physics are characterized using high-speed videography and dual-hydrophone acoustic cavitation measurements. The loading of the rectangular planform hydrofoil has a maximum at 65% span, 56% greater than that at the root, i.e., the hydrofoil loading is representative of non-elliptically loaded open propellers. Acoustic cavitation inception is quantified and is observed to precede visual cavitation onset using unaided and high-speed imaging. Measurements reported here show that vorticity fluctuations are nearly of the same magnitude as the ensemble vorticity. Instantaneous measurements of vorticity at the trailing edge, 12-chord downstream, and one-chord downstream positions are reported. Their peak magnitudes are located adjacent to the ensemble vortex center and are between four and five times the ensemble mean. The fluctuating vorticity measurements, taken in conjunction with high-speed video observations, provide insight into the hydrodynamic conditions responsible for intermittent cavitation events. The reported measurements elucidate instantaneous and mean turbulence physics associated with vortex cavitation and can provide a validation basis for numerical simulations.

Investigation of the fluctuating velocity in a single-cell tornado-like vortex based on coherent structure extraction

Fluctuating velocity plays an essential role in tornadic winds and the induced transient loads, while its characteristics are rarely considered in existing tornado models. Based on the coherent structure extraction technology, this study investigates the characteristics of the fluctuating velocity in a single-cell tornado-like vortex (TLV) and proposes a unified wind spectrum formula accordingly. First, the performance of proper orthogonal decomposition (POD) and dynamic mode decomposition is compared and validated using synthetic vortices. A single-cell TLV is then generated by large eddy simulation. The relationship between the fluctuating velocity and the coherent structures is analyzed. Finally, a wind spectrum formula is obtained from the fluctuating velocity reconstructed by the first two POD modes that are almost unchanged with height. Thus, it is a unified formula suitable for different heights. The results show that at a lower height in the single-cell TLV, more than 90% of the velocity fluctuation is induced by vortex wandering and size variation. The first two POD modes can accurately reconstruct the fluctuating velocity with an error of less than 8%. The power spectral density of the reconstructed fluctuating velocity agrees well with the Kaimal wind spectrum in the low-frequency subrange and the proposed formula in the high-frequency subrange.

Air-entrained vortex in open intake: Time–frequency analysis and the interaction with subsurface vortices

In this paper, the simple coupled level-set and volume of fluid and bifurcation models are used for the accurate prediction of the flow in an open pump intake with a vertical pipe. The continuous wavelet transform, which is suitable for the vortex detection, is applied to the pressure signals near both air-entrained and subsurface vortices. Low-frequency with long duration for air-entrained vortex due to the vortex wandering and broadband with short duration for floor vortices (dominant in subsurface vortices) due to the generation of extreme strong vortex are observed. The vortex motion mechanism is revealed by the analysis of the transport equation of the vertical vorticity's enstrophy. Different from the previous results in which the tilting effect controls the vortex motion, the stretching effect is found to be dominating when it is large enough. When going through the bell mouth, the air-entrained vortex's vorticity changes the sign and strengthens the vortex with the same sign. On the plane near the bell mouth, three vortex patterns, including co-rotating pair, merging, and counter-rotating pair, are observed. The onset criterion of the vortex merging at a/b = 0.29–0.32 is found to be applicable to the present case. The counter-rotating pair is found to be more stable. Air-entrained vortex serves as an amplification of the strong vortices generated from the subsurface.

Hybrid RANS/LES study of tip leakage vortex instability and turbulence characteristics of a transonic turbine cascade

To conduct detailed investigations about vortex instability and turbulence characteristics near a transonic turbine tip region, a highly accuracy hybrid Reynolds averaged Navier Stokes (RANS) / large eddy simulation (LES) method, namely detached eddy simulation (DES)-type method, is adopted at the exit isentropic Mach number of 0.95. Validation results show that this hybrid method can provide an accurate prediction against experiments. In contrast with the RANS method, this method can exhibit superiority in capturing detailed small-scale flow structures and more realistic turbulence distribution. Based on various identification methods, two predominant instability patterns of tip leakage vortex (TLV), namely, vortex wandering and breakdown have been recognized successfully in its downstream progression. Due to the supplement of tip leakage flow (TLF), the TLV maintains a concentrated vortex morphology with a monotonically increasing transverse wandering magnitude inside the blade passage. Subsequently, the TLV breakdown phenomenon, which is mainly due to the high adverse pressure gradient aggravated by shock waves, can be observed downstream the trailing edge. Meanwhile, a “spiral-type” vortex breakdown is distinguished firstly in a transonic turbine environment, which cannot be found in the previous RANS literature. To investigate the nature of the vortex instability, we perform an analysis based on the vorticity transport equation, it's found that the convection term due to the velocity gradient dominated the leakage vorticity damping. Combined the triple decomposition with the proper orthogonal decomposition (POD) method, the mechanisms of vortex wandering have been further revealed, which exhibits non-zero perturbations in transverse modes and a helical mode in the streamwise direction. Furthermore, detailed analysis of the turbulence characteristics has been also conducted, which contains distributions of Reynolds stress terms and the turbulent kinetic energy (k) along the TLV core trajectory. It can be recognized that the high adverse pressure gradient by shock waves can result in a sharp increase of Reynolds normal stresses (τii), which can stretch the TLV in different directions and exerts detrimental effects on the vortex breakdown. As a complementary, the turbulent anisotropy is also evaluated by the Lumley triangle method, which exhibits a variation from the one-component anisotropy to a two-component morphology as the TLV migrating downstream, while a isotropic turbulence field may be formed downstream the trailing edge due to the intense mixing. Predicted turbulence characteristics, vortical instabilities, and their flow mechanism can provide guide towards lower loss design and flow control of the turbine blade.

Control of afterbody vortices from a slanted-base cylinder using sweeping jets

In this paper, a sweeping jet is applied to control the afterbody vortices behind a slanted-base cylinder for the first time at Reynolds numbers from 87 000 to 200 000. The control effects are examined using stereo particle image velocimetry and surface pressure measurements with the jet momentum coefficient (Cμ) varying from 0.056 to 0.893. It is found that the sweeping jet results in increasingly diffused and larger afterbody vortices as Cμ increases. While an increase in Cμ up to 0.167 leads to a reduction in the circulation of the afterbody vortices and their earlier detachment from the slanted base, a further increase in Cμ introduces additional vorticity into the afterbody vortices leading to higher vortex strength, which could be detrimental to the control purpose. The interaction mechanism of sweeping jets lies in that turbulence is injected into the afterbody vortices as the sweeping jet intersects with these vortices and this subsequently causes diffusion of velocity gradient in the vortices, which weakens their strength. As the sweeping jet spreads itself sideways, while it propagates downstream along the endplate, it pushes the afterbody vortices upward and to the side. The impact of the sweeping jet has resulted in the dominant vortex wandering frequency of the afterbody vortex being locked to that of the sweeping jet. This also causes the afterbody vortices detach themselves from the endplate earlier resulting in a shorter low-pressure footprint on the surface.

Evaluation of the spatiotemporal unsteady characteristics of the tip leakage vortex based on a direct numerical simulation database

The spatiotemporal evolution of the tip clearance vortical structures behind a flat hydrofoil immersed in a turbulent boundary layer over a flat plate was investigated by means of direct numerical simulation, with focus on the unsteady behaviors of the tip-leakage vortex (TLV) and their effects on the flow blockage. It is found that the TLV evolutionary processes can be characterized by three typical phases: the formation phase, the vortex wandering phase, and the vortex splitting and breakdown phase. In the second phase, the TLV is subject to the wall-normal low-frequency wandering motion, which is excited by the induced vortex. The abrupt increase in vortex wandering intensity near the trailing edge of the hydrofoil can be attributed to the frequent occurrence of vortex splitting and breakdown events in the third phase. The time-averaged vortex intensity of the TLV increases gradually in the first and second phases. On the other hand, instantaneous vortex intensity shows an initially decreasing and then increasing trend, as a result of the breakdown of the TLV and the formation of the secondary TLV, respectively. In addition, the investigation of flow blockage caused by the TLV indicates that along the streamwise direction, the time-averaged blockage area and blockage coefficient both follow an exponential distribution. The present results provide a qualitative and quantitative characterization for the spatiotemporal evolution of the TLV, which is critical for improving the efficiency loss and mechanical vibration caused by the unsteady behaviors of the TLV.

Time-resolved particle image velocimetry and pressure sensitive paint measurements of afterbody flow dynamics

A pair of counter-rotating vortices is produced in the wake of typical cargo aircraft fuselages due to their ramp shape. With a fast polymer-ceramic pressure sensitive paint (PC-PSP), we measure the global pressure fluctuations at very low velocities (15 to 75 m/s) in a surrogate cylinder with a slanted edge model. Through spectral proper orthogonal decomposition, we observe a family of convective pressure waves with peak energy at frequencies matching the vortex wandering frequencies in this flow.

Effect of vortex dynamics and instability characteristics on the induced drag of trailing vortices

In this paper, trailing vortices generated by three wingtip configurations, namely the M6 wing and the M6 wing with a blended or split winglet, are experimentally investigated using the Stereo Particle Image Velocimetry (SPIV) technology. Then, linear stability analysis is performed to investigate instability characteristics. Three corresponding trailing vortex patterns, including the isolated trailing vortex without wake (pattern v) and with wake (pattern v-w), co-rotating vortex pair (pattern v-v), are observed in experiments. The strength of trailing vortices, characterized by circulation, is reduced after installing winglets as expected, and the strength of pattern v-v can be further suppressed compared with pattern v-w. Moreover, instability characteristics, such as the eigenvalue spectrum and perturbation mode, are distinctive among these three vortex patterns. The distribution of eigenvalue spectrums indicates that pattern v and pattern v-w are temporally “marginally stable”, while pattern v-v is temporally “unstable.” The primary perturbation mode of pattern v and pattern v-w is the m=-1 helical mode, while |m|>1 for the case of pattern v-v. The effect of vortex dynamics and instability characteristics can be concluded in two aspects. Firstly, the value of induced drag is polluted by about 3% from vortex wandering since vortex wandering affects the tangential velocity and streamwise vorticity of trailing vortices. Secondly, the growth rate and penetration depth perturbation mode affect trailing vortex evolution and further affect induced drag. Specifically, the larger the growth rate and penetration depth are, the more turbulence injects inside the vortex core, thus leading to a quicker and more intense attenuation of trailing vortex, as well as a smaller induced drag. This finding can guide us to manipulate the induced drag in flow control.

Scaling Analysis on the Dynamic and Instability Characteristics of Isolated Wingtip Vortex

The isolated wingtip vortex is generated by an M6 wing under different angles of attack and Reynolds numbers , and is measured within 16 chord length downstream regions. Then, the spatiotemporal local linear stability analysis (LSA) is performed at the azimuthal wavenumber of to analyze the instability characteristics. Experimental results show that the radial circulation of wingtip vortex satisfies a scaling formula. Moreover, the LSA results demonstrate that the instability characteristics, including the stability curve, growth rate eigenvalue spectrum, and perturbation mode, are uniformed in time and space, laying the basis for scaling the wingtip vortex by considering them. In this situation, by plotting the circulation-based Reynolds number and dimensionless wandering amplitude in log scale, it is found that they are in the form of , where and . Particularly, along with the streamwise development, the swirl number of wingtip vortex asymptotically closes to the unstable region in the (, ) plane defined by Fabre and Jacquin (Journal of Fluid Mechanics, Vol. 500, Jan. 2004, pp. 239–262). By considering the role of growth rate in the vortex wandering, an alternative scaling formula , where and , is suggested to describe the wandering development.

Near Field of a Vortex Generated by Chevron-Tipped Flat Plates

Flat plates with chevron tips of variable depths () were designed and their effect on the tip vortex was studied at downstream distances of to at a Reynolds number of 67,000. The test plates were mounted at an angle of attack of 5 deg and the tip vortex was measured using a constant temperature anemometer. The chevron plates formed tip vortices with lower peak tangential velocities and larger core radii as compared to the flat plate (with the exception of the , which had a smaller core radius than the flat plate). It was also found that the tip vortices formed over plates with deeper chevrons exhibited turbulent cores, as opposed to the flat plate and shallow chevron plates. Vortex wandering, an inherent meandering of the tip vortex, was found to be present for every test plate. It results in an overprediction of the core radius and underprediction of the peak tangential velocities. To ensure that the lower peak tangential velocities and larger core radii of the tip vortices formed over chevron tip plates were due to the change in geometry and not a consequence of vortex wandering, Devenport’s correction was applied to the shallow chevron plates; and it was found that after correcting for wandering, the tip vortices formed over chevron tips still had lower peak tangential velocities and larger core radii (with the exception of the plate) as compared to the flat plate.

Experimental investigation on the structures and induced drag of wingtip vortices for different wingtip configurations

As an effective method to reduce induced drag and the risk of wake encounter, the winglet has been an essential device and developed into diverse configurations. However, the structures and induced drag, as well as wandering features of the wingtip vortices ( WTVs) generated by these diverse winglet configurations are not well understood. Thus, the WTVs generated by four typical wingtip configurations, namely the rectangular wing with blended/raked/split winglet and without winglet (Model BL/ RA/ SP/NO for short), are investigated in this paper using particle image velocimetry technology. Comparing with an isolated primary wingtip vortex generated by Model NO, multiple vortices are twisted coherently after installing the winglets. In addition, the circulation evolution of WTVs demonstrates that the circulation for Model SP is the largest, while Model RA is the smallest. By tracking the instantaneous vortex center, the vortex wandering behavior is observed. The growth rate of wandering amplitude along with the streamwise location from the quickest to the slowest corresponds to Model SP, Model NO, Model BL, Model RA in sequence, implying that the WTVs generated by model SP exhibit the quickest mitigation. Considering that the induced drag scales as the lift to power 2, the induced drag and lift are estimated based on the wake integration method, and then the form factor λ, defined by [Formula: see text], is calculated to evaluate the aerodynamic performance. Comparing with the result of Model NO, the form factor decreases by 7.99%, 4.80%, and 2.60% for Model RA, Model BL, Model SP, respectively. In sum, Model RA and BL have a smaller induced drag coefficient but decay slower; while Model SP has a larger induced drag coefficient but decays quicker. An important implication of these results is that reducing the strength of WTVs and increasing the growth rate of vortex wandering amplitude can be the mutual requirements for designing new winglets.

Effects of Longitudinal Vortices on Turbulent Junction Flow Heat Transfer

Turbulent junction flow is a vortex system upstream of a blockage embedded in a turbulent boundary layer, which leads to augmented heat transfer near the blockage. Vortex legs wrap around the blockage and travel downstream as longitudinal vortices. In multistage axial turbines or multiple row tube heat exchangers, these longitudinal vortices can collide with junction flow vortices further downstream. Furthermore, these devices often augment mixing and increase heat transfer with high freestream turbulence. A comprehensive study on how longitudinal vortices affect junction flow heat transfer for different Reynolds numbers, freestream turbulence values, and longitudinal vortex configurations was performed. Longitudinal vortices were generated upstream of a symmetric airfoil using delta winglet vortex generators. Spatially resolved endwall heat transfer coefficients upstream and around the junction were measured using infrared thermography. Time-averaged flowfield measurements of the incoming longitudinal vortices were taken using stereo particle image velocimetry. Longitudinal vortices provided limited heat transfer augmentation around the junction and did not disrupt the time-averaged horseshoe vortex. These interactions were identical at high turbulence, but longitudinal vortices were less effective at augmenting heat transfer, likely due to an increase in vortex wandering. Vortex wandering also led to a broadening in lateral heat transfer profiles.

The evolution of wingtip vortex wandering: a stability analysis based on stereo-PIV experiment

Instability, as a potential mechanism for vortex flow control, is manifested typically in the phenomenon of wingtip vortex wandering. In this paper, the evolution of wingtip vortex generated by a NACA0015 rectangular wing within six chord lengths of its wake at Rec= 2.1 × 105–3.5 × 105 and AoA = 4°–10° is investigated by stereo particle image velocimetry experiment. The streamwise evolution of vortex wandering is clearly captured, which demonstrates strong anisotropy. The amplitude of vortex wandering increases under all conditions, which exhibits greater growth rates in the condition of larger AoA. To account for such phenomenon, spatial linear stability analysis is performed on the base flow obtained by SPIV experiment to investigate quantitatively the amplification of small disturbance and disturbance modes at the experiment conditions. It is discovered that the wingtip vortex in the experiment is marginally stable under all conditions. Furthermore, the spatial growth rates of instability by AoA correspond well with that of wandering amplitude, indicating that the quick enlargement of the amplitude of wandering at larger AoA condition is caused by larger spatial growth rate of disturbance. In addition, the least-stable disturbance mode by LSA reveals a non-zero directed velocity perturbation in the vortex core, which rotates periodically. Such perturbation developing in both time and space, which is stirred by vortex instability, leads to the behavior of wingtip vortex wandering.