Incoming Boundary Layer Research Articles

Corner Separation Dynamics in a Linear Compressor Cascade

This paper considers the inherent unsteady behavior of the three-dimensional (3D) separation in the corner region of a subsonic linear compressor cascade equipped of 13 NACA 65-009 profile blades. Detailed experimental measurements were carried out at different sections in spanwise direction achieving, simultaneously, unsteady wall pressure signals on the surface of the blade and velocity fields by time-resolved particle image velocimetry (PIV) measurements. Two configurations of the cascade were investigated with an incidence of 4 deg and 7 deg, both at Re=3.8×105 and Ma = 0.12 at the inlet of the facility. The intermittent switch between two statistical preferred sizes of separation, large, and almost suppressed, is called bimodal behavior. The present PIV measurements provide, for the first time, time-resolved flow visualizations of the separation switch with an extended field of view covering the entire blade section. Random large structures of the incoming boundary layer are found to destabilize the separation boundary. The recirculation region, therefore, enlarges when these high vorticity perturbations blend with larger eddies situated in the aft part of the blade. Such a massive detached region persists until its main constituting vortex suddenly breaks down and the separation almost completely vanishes. The increase of the blockage during the separation growth phase appears to be responsible for this mechanism. Consequently, the proper orthogonal decomposition (POD) analysis is carried out to decompose the flow modes and to contribute to clarify the underlying cause-effect relations, which predominate the dynamics of the present flow scenario.

Cost-effective hybrid RANS-LES type method for jet turbulence and noise prediction

Jets at higher Reynolds numbers have a high concentration of energy in small scales in the nozzle vicinity. This is challenging for large-eddy simulation, potentially placing severe demands on grid density. To circumvent this, we propose a novel procedure based on well-known Reynolds number (Re) independent of jets. We reduce the jet Re while rescaling the boundary layer properties to maintain incoming boundary layer thickness consistent with high Re jet. The simulations are carried out using hybrid large-eddy simulation type of approach which is incorporated by using near-wall turbulence model with modified properties. No subgrid scale model is used in these simulations. Hence, they effectively become numerical large-eddy simulation with Reynolds-averaged Navier–Stokes covering the full boundary layer region. The noise post-processing is carried out using the Ffowcs-Williams-Hawking approach. The simulations are made for Mach numbers (M) of 0.75 and 0.875 (cold and hot). The results for the overall sound pressure level are observed to be within 2–3% of the measurements, and directivity of sound is also captured accurately for both the cases. Hence, the low Re simulations can be more beneficial in saving time and cost while providing reasonably accurate results.

Transient Characterization of the Reattachment of a Massively Separated Turbulent Boundary Layer Under Flow Control

The transient dynamics of a high Reynolds number separated flow over a two-dimensional ramp submitted to pulsed fluidic control is investigated. A spanwise array of 22 round jets, located upstream of the flap leading edge, is used as actuator to generate co-rotating vortical structures. Simultaneous measurements of wall friction using hot-film anemometry and phase-averaged velocity using 2D2C PIV are conducted. The PIV plane encompasses the incoming boundary layer upstream the flap leading edge, the separation bubble and the natural reattachment region. The dynamics of the separated flow is studied for successive sequences of pulsed actuation. Pockets of turbulence are periodically generated by the separation process and pushed downstream. After the transition period, the controlled flow shows large amplitude oscillations around a steady mean, particularly for the separation area. The transient dynamics of the flow at the actuation activation is also studied. The separated flow is strongly modified by the actuation from the first pulse. Characteristic times of the transient dynamics can be determined by fitting a first-order model with delay on the data. For the reattachment, the dimensionless characteristic rising times defined as \(\tau _{r}^{+} = \tau _{r} ~ U_{0} ~/~ L_{sep}\) of 11.7 for the friction gain, 4.8 for the separation length and 4.1 for the first mode of a Conditional Proper Orthogonal Decomposition analysis of the phase-averaged velocity fields were found. These values are in good agreement with previous studies and are of particular interest for modeling the transients and for further closed-loop control applications.

Shock wave–boundary layer interaction in supersonic flow over a forward-facing step

We study in the present work a Mach 2.5 flow over a forward-facing step. The focus of the work is the flow ahead of the step, in particular, the unsteady interactions between the shock, the boundary layer and the separation bubble. The primary geometrical parameter in the problem is the ratio of the step height to the incoming boundary layer thickness,$h/\unicode[STIX]{x1D6FF}$, which is kept fixed at 2. Results are presented from detailed particle image velocimetry (PIV) measurements in two orthogonal planes to obtain a reasonable picture of the whole flow field. The mean velocity field in the central cross-stream or wall-normal ($x$–$y$) plane shows that the incoming boundary layer separates upstream of the step forming a large separation bubble ahead of the step, which can be relatively well resolved in PIV measurements compared to the compression ramp cases. Wall pressure fluctuation spectra close to the separation location show a dominant frequency ($f$) that is two orders of magnitude smaller than the characteristic frequency of the incoming boundary layer ($U_{\infty }/\unicode[STIX]{x1D6FF}$), consistent with low-frequency motions of the shock that have received a lot of recent attention ($U_{\infty }$ $=$ free-stream velocity,$\unicode[STIX]{x1D6FF}$ $=$ boundary layer thickness). PIV measurements in the wall-normal plane show large variations in shock position with time. The shock position measured from velocity data outside the boundary layer is found to be well correlated with the reverse flow area ahead of the step, and weakly correlated to structures in the incoming boundary layer. In contrast, the shock foot, determined from velocity data within the boundary layer, is found to be well correlated to the low- and high-speed streaks in the incoming boundary layer, in addition to the reverse flow area ahead of the step. Instantaneous velocity fields in the spanwise ($x$–$z$) plane parallel to the lower wall show that the shock is broadly two-dimensional with small spanwise ripples, while the recirculation region has very large spanwise variations. The spanwise-averaged shock location is found to be well correlated to the most upstream location of the recirculation region over a spanwise length ($x_{r,min}^{sp}$). Instantaneous velocity fields show that when some part of the recirculation region is far upstream, the corresponding nearly two-dimensional shock is also far upstream. On the other hand, when$x_{r,min}^{sp}$is relatively downstream, the resulting shock is also found to be downstream. Hence, the present results suggest that for the forward-facing step configuration, the large-scale streamwise motions of the shock are mainly correlated to the most upstream point of the recirculation region, which has large spanwise variations.

Zonal large-eddy simulation of a tip leakage flow

The flow induced by the clearance between the tip of an isolated airfoil and an end-plate is investigated numerically, using a zonal approach with large-eddy simulation in the region of interest. The results are analyzed in comparison with available experimental data, presented in a companion paper. The incoming boundary layer and the pressure distribution around the blade are evaluated. The description of the inflow-jet deviation, with an averaged approach, enables to represent the proper loading on the airfoil. Also, particular attention is paid to the powerful tip-leakage vortex. The vortex characteristics are investigated using specific functions to locate its center and quantify its width. Overall, good results are obtained for the flow statistics and spectra. Furthermore, a very good description of the far-field pressure is achieved using the acoustic analogy, and the results confirm that the tip-flow essentially radiates in the central frequency range (0.7 kHz, 7 kHz).

An experimental study on the aeromechanics and wake characteristics of a novel twin-rotor wind turbine in a turbulent boundary layer flow

The aeromechanic performance and wake characteristics of a novel twin-rotor wind turbine (TRWT) design, which has an extra set of smaller, auxiliary rotor blades appended in front of the main rotor, was evaluated experimentally, in comparison with those of a conventional single-rotor wind turbine (SRWT) design. The comparative study was performed in a large-scale wind tunnel with scaled TRWT and SRWT models mounted in the same incoming turbulent boundary layer flow. In addition to quantifying power outputs and the dynamic wind loadings acting on the model turbines, the wake characteristics behind the model turbines were also measured by using a particle image velocimetry system and a Cobra anemometry probe. The measurement results reveal that, while the TRWT design is capable of harnessing more wind energy from the same incoming airflow by reducing the roots losses incurred in the region near the roots of the main rotor blades, it also cause much greater dynamic wind loadings acting on the TRWT model and higher velocity deficits in the near wake behind the TRWT model, in comparison with those of the SRWT case. Due to the existence of the auxiliary rotor, more complex vortex structures were found to be generated in the wake behind the TRWT model, which greatly enhanced the turbulent mixing in the turbine wake, and caused a much faster recovery of the velocity deficits in the turbine far wake. As a result, the TRWT design was also found to enable the same downstream turbine to generate more power when sited in the wake behind the TRWT model than that in the SRWT wake, i.e., by mitigating wake losses in typical wind farm settings.

Unsteady Shock Motion in a Transonic Flow over a Wall-Mounted Hemisphere

Particle image velocimetry measurements have been conducted for a Mach 0.8 flow over a wall-mounted hemisphere with a strongly separated wake. The shock foot was found to typically sit just forward of the apex of the hemisphere and move within a range of about . Conditional averages based upon the shock foot location show that the separation shock is positioned upstream along the hemisphere surface when reverse velocities in the recirculation region are strong and is located downstream when they are weaker. The recirculation region appears smaller when the shock is located farther downstream. No correlation was detected of the incoming boundary layer with the shock position nor with the wake recirculation velocities. These observations are consistent with recent studies concluding that, for large, strong separation regions, the dominant mechanism is the instability of the separated flow rather than a direct influence of the incoming boundary layer.

A Linearized $$k-\epsilon $$ k - ϵ Model of Forest Canopies and Clearings

A linearized analysis of the Reynolds-averaged Navier–Stokes (RANS) equations is proposed where the $$k-\epsilon $$ turbulence model is used. The flow near the forest is obtained as the superposition of the undisturbed incoming boundary layer plus a velocity perturbation due to the forest presence, similar to the approach proposed by Belcher et al. (J Fluid Mech 488:369–398, 2003). The linearized model has been compared against several non-linear RANS simulations with many leaf-area index values and large-eddy simulations using two different values of leaf-area index. All the simulations have been performed for a homogeneous forest and for four different clearing configurations. Despite the model approximations, the mean velocity and the Reynolds stress $$\overline{u'w'}$$ have been reasonably reproduced by the first-order model, providing insight about how the clearing perturbs the boundary layer over forested areas. However, significant departures from the linear predictions are observed in the turbulent kinetic energy and velocity variances. A second-order correction, which partly accounts for some non-linearities, is therefore proposed to improve the estimate of the turbulent kinetic energy and velocity variances. The results suggest that only a region close to the canopy top is significantly affected by the forest drag and dominated by the non-linearities, while above three canopy heights from the ground only small effects are visible and both the linearized model and the simulations have the same trends there.

The Influence of Incoming Boundary Layer on the Flow around the Surface Excrescence

This paper is concerned with the accurate prediction of parasitic drag due to excrescences introduced by structural repairs to aircraft wings and fuselage. Numerical computations are carried out to quantify the effect of isolated surface excrescences in a turbulent boundary layer on a flat plate. Both step excrescence in 2-D domain and wall-mounted hexahedron in 3-D domain are considered in the investigation. Various approaches for calculating drag coefficient increments for wing repair plates are presented. Menter's Shear Stress Transport (SST k-ω) turbulence model is employed here for its accurate prediction of aeronautics flows at typical repair locations with strong adverse pressure gradients and separation. Solutions are obtained via a high-order numerical scheme and an implicit time-marching approach on a multi-block structured mesh. A grid resolution study was carried out to confirm the accuracy of the computations. From the results curves are drawn showing the variation of parasitic drag components for a range of controlled speed (Mach 0.1 to 0.8), local Reynolds number (104 to 107) and the height of excrescence (y+=102 to 104).

Unsteadiness in a large turbulent separation bubble

The unsteady behaviour of a massively separated, pressure-induced turbulent separation bubble (TSB) is investigated experimentally using high-speed particle image velocimetry (PIV) and piezo-resistive pressure sensors. The TSB is generated on a flat test surface by a combination of adverse and favourable pressure gradients. The Reynolds number based on the momentum thickness of the incoming boundary layer is 5000 and the free stream velocity is$25~\text{m}~\text{s}^{-1}$. The proper orthogonal decomposition (POD) is used to separate the different unsteady modes in the flow. The first POD mode contains approximately 30 % of the total kinetic energy and is shown to describe a low-frequency contraction and expansion, called ‘breathing’, of the TSB. This breathing is responsible for a variation in TSB size of approximately 90 % of its average length. It also generates low-frequency wall-pressure fluctuations that are mainly felt upstream of the mean detachment and downstream of the mean reattachment. A medium-frequency unsteadiness, which is linked to the convection of large-scale vortices in the shear layer bounding the recirculation zone and their shedding downstream of the TSB, is also observed. When scaled with the vorticity thickness of the shear layer and the convection velocity of the structures, this medium frequency is very close to the characteristic frequency of vortices convected in turbulent mixing layers. The streamwise position of maximum vertical turbulence intensity generated by the convected structures is located downstream of the mean reattachment line and corresponds to the position of maximum wall-pressure fluctuations.

Reattachment heating upstream of short compression ramps in hypersonic flow

Hypersonic shock-wave/boundary-layer interactions with separation induce unsteady thermal loads of particularly high intensity in flow reattachment regions. Building on earlier semi-empirical correlations, the maximum heat transfer rates upstream of short compression ramp obstacles of angles $$15^{\circ }\leqslant \theta \leqslant 135^{\circ }$$ are here discretised based on time-dependent experimental measurements to develop insight into their transient nature ( $$M_{e}$$ = 8.2–12.3, $$Re_h= 0.17\times 10^{5}$$ – $$0.47\times 10^{5}$$ ). Interactions with an incoming laminar boundary layer experience transition at separation, with heat transfer oscillating between laminar and turbulent levels exceeding slightly those in fully turbulent interactions. Peak heat transfer rates are strongly influenced by the stagnation of the flow upon reattachment close ahead of obstacles and increase with ramp angle all the way up to $$\theta =135^{\circ }$$ , whereby rates well over two orders of magnitude above the undisturbed laminar levels are intermittently measured ( $$q'_\mathrm{max}>10^2q_{u,L}$$ ). Bearing in mind the varying degrees of strength in the competing effect between the inviscid and viscous terms—namely the square of the hypersonic similarity parameter $$(M\theta )^2$$ for strong interactions and the viscous interaction parameter $$\bar{\chi }$$ (primarily a function of Re and M)—the two physical factors that appear to most globally encompass the effects of peak heating for blunt ramps ( $$\theta \geqslant 45^{\circ }$$ ) are deflection angle and stagnation heat transfer, so that this may be fundamentally expressed as $$q'_\mathrm{max}\propto {q_{o,2D}}$$ $$\theta ^2$$ with further parameters in turn influencing the interaction to a lesser extent. The dominant effect of deflection angle is restricted to short obstacle heights, where the rapid expansion at the top edge of the obstacle influences the relaxation region just downstream of reattachment and leads to an upstream displacement of the separation front. The extreme heating rates result from the strengthening of the reattaching shear layer with the increase in separation length for higher deflection angle.

Study of a Supercritical Roughness Element in a Hypersonic Laminar Boundary Layer

In this study, the mean flow organization ahead and behind a supercritical cylindrical roughness element immersed in an incoming laminar boundary layer at edge Mach number 6.48 is investigated by means of schlieren visualization, infrared thermography, and planar particle image velocimetry. The schlieren images provide a general overview of the shock-wave system developing around the roughness element. The surface heat transfer map obtained with infrared thermography provides an overall description of the near-wall flow organization in the streamwise and spanwise directions. The off-surface flow topology is inspected with particle image velocimetry in the symmetry plane of the recirculation region upstream of the roughness element. The flow approaching the roughness element separates, forming a main recirculation region adjacent to the stagnation line at the cylinder leading edge. The reattachment vortex is responsible for a heat flux local peak in front of the protuberance. Secondary, more complex local foci and stagnation points are observed upstream of the roughness element, which also correspond to the local maximum of turbulent kinetic energy and surface heat transfer.

Experimental characterization of turbulent subsonic transitional–open cavity flow

Turbulent subsonic “transitional–open” cavity flow was investigated by wind-tunnel tests. The investigated cavity configuration had a length-to-depth ratio of 6.25 and a width-to-depth ratio of 2. The cavity was exposed to a free-stream Mach number of 0.40 and a Reynolds number (based on cavity depth) of $$1.6\times 10^6$$ , with a turbulent incoming boundary layer. Measurements of velocity and wall pressures were taken simultaneously, which enabled the analysis of velocity–pressure cross-correlations. Special attention is paid to the shear layer that develops over the cavity and an emphasis is placed on the analysis of its characteristics and its stability. Application of linear hydrodynamic stability theory, together with examining velocity–pressure cross correlations, revealed that the behavior of the cavity shear layer is analogous to a free shear layer, approximately up to mid-length of the cavity, where further downstream nonlinear interactions occur.

Large Eddy Simulations of flow around a circular cylinder close to a flat seabed

Large Eddy Simulations (LES) with Smagorinsky subgrid scale model are used to study the turbulent flow and wake dynamics behind a circular cylinder close to a horizontal, plane wall at subcritical Reynolds number. The focus is on investigating the details of the flow around the cylinder placed at different distances from the wall and immersed in boundary layers of various thicknesses.The Reynolds number is Re = 13,100. The simulations with gap to diameter ratios (G/D) of 0.2, 0.6 and 1 are carried out in order to investigate the changes of the flow field and the vortex shedding due to the presence of the plane wall. The influence of the incoming boundary layer profile is investigated through simulations with logarithmic boundary layer inlet profile of thickness 0.48D and 1.6D, and compared with a uniform inlet flow profile. 2D and 3D simulations are performed for Re ranging from 100 to 13,100, to explore the importance of the flow three-dimensionality. The flow field in the cylinder wake, as well as the mean flow values, the spectral analysis and the pressure distribution on the cylinder surface are computed to study the flow physics due to the influences of the wall.

Flow regimes in a trapped vortex cell

This paper presents results of an experimental investigation on the flow in a trapped vortex cell, embedded into a flat plate, and interacting with a zero-pressure-gradient boundary layer. The objective of the work is to describe the flow features and elucidate some of the governing physical mechanisms, in the light of recent investigations on flow separation control using vortex cells. Hot-wire velocity measurements of the shear layer bounding the cell and of the boundary layers upstream and downstream are reported, together with spectral and correlation analyses of wall-pressure fluctuation measurements. Smoke flow visualisations provide qualitative insight into some relevant features of the internal flow, namely a large-scale flow unsteadiness and possible mechanisms driving the rotation of the vortex core. Results are presented for two very different regimes: a low-Reynolds-number case where the incoming boundary layer is laminar and its momentum thickness is small compared to the cell opening, and a moderately high-Reynolds-number case, where the incoming boundary layer is turbulent and the ratio between the momentum thickness and the opening length is significantly larger than in the first case. Implications of the present findings to flow control applications of trapped vortex cells are also discussed.

Instabilities in oblique shock wave/laminar boundary-layer interactions

The interaction of an oblique shock wave and a laminar boundary layer developing over a flat plate is investigated by means of numerical simulation and global linear-stability analysis. Under the selected flow conditions (free-stream Mach numbers, Reynolds numbers and shock-wave angles), the incoming boundary layer undergoes separation due to the adverse pressure gradient. For a wide range of flow parameters, the oblique shock wave/boundary-layer interaction (OSWBLI) is seen to be globally stable. We show that the onset of two-dimensional large-scale structures is generated by selective noise amplification that is described for each frequency, in a linear framework, by wave-packet trains composed of several global modes. A detailed analysis of both the eigenspectrum and eigenfunctions gives some insight into the relationship between spatial scales (shape and localization) and frequencies. In particular, OSWBLI exhibits a universal behaviour. The lowest frequencies correspond to structures mainly located near the separated shock that emit radiation in the form of Mach waves and are scaled by the interaction length. The medium frequencies are associated with structures mainly localized in the shear layer and are scaled by the displacement thickness at the impact. The linear process by which OSWBLI selects frequencies is analysed by means of the global resolvent. It shows that unsteadiness are mainly associated with instabilities arising from the shear layer. For the lower frequency range, there is no particular selectivity in a linear framework. Two-dimensional numerical simulations show that the linear behaviour is modified for moderate forcing amplitudes by nonlinear mechanisms leading to a significant amplification of low frequencies. Finally, based on the present results, we draw some hypotheses concerning the onset of unsteadiness observed in shock wave/turbulent boundary-layer interactions.

主流乱れがキャビティ音および音源に及ぼす影響

Flow and acoustic fields for cavity flows were directly simulated for various intensities of freestream turbulence to clarify what effects freestream turbulence had on cavity tones. The depth-to-length ratio of the cavity, D/L, was 0.5 and 2.5. The incoming boundary layer was laminar. Acoustic resonance in the direction of the cavity depth occurred in the flow over the cavity with D/L = 2.5. The results for the intensity of freestream turbulence 2.3% revealed that the reduced level of cavity tone in a cavity flow with acoustic resonance was greater than that in a flow without acoustic resonance. The contributions of the intensity and spanwise coherence of the sound source to reducing the cavity tone were investigated. The effects of spanwise coherence of the sound source ware dominant in the cavity flow with acoustic resonance. However, these factors were almost the same as those without acoustic resonance.

Effects of Freestream Turbulence on Cavity Tone and Sound Source

To clarify the effects of freestream turbulence on cavity tones, flow and acoustic fields were directly predicted for cavity flows with various intensities of freestream turbulence. The freestream Mach number was 0.09 and the Reynolds number based on the cavity length was 4.0 × 104. The depth-to-length ratio of the cavity,D/L, was 0.5 and 2.5, where the acoustic resonance of a depth-mode occurs forD/L= 2.5. The incoming boundary layer was laminar. The results for the intensity of freestream turbulence of Tu = 2.3% revealed that the reduced level of cavity tones in a cavity flow with acoustic resonance(D/L=2.5)was greater than that without acoustic resonance(D/L=0.5). To clarify the reason for this, the sound source based on Lighthill’s acoustic analogy was computed, and the contributions of the intensity and spanwise coherence of the sound source to the reduction of the cavity tone were estimated. As a result, the effects of the reduction of spanwise coherence on the cavity tone were greater in the cavity flow with acoustic resonance than in that without resonance, while the effects of the intensity were comparable for both flows.

Fluctuating pressure measurements in a turbulent separation bubble

Fluctuating pressure measurements are performed on the test surface above a pressure-induced, turbulent separation bubble. The Reynolds number of the incoming turbulent boundary layer is Re θ ≃ 5000 . The results confirm the presence of a low-frequency breathing mode, caused by the contraction and expansion of the bubble, and a medium-frequency shedding mode, caused by the roll-up and shedding of spanwise vortices in the shear layer bordering the recirculating region. The signatures of both modes are shown to be consistent throughout the span of the test section. In addition, another fluctuating mode is observed and related to the presence of slowly rotating vortices close to the test-section sidewalls. Des mesures de pression instationnaire sont effectuées dans une zone de décollement turbulente générée sur une surface plane par une combinaison de gradients de pression adverse et favorable. Le nombre de Reynolds de la couche limite amont est de Re θ ≃ 5000 . Les résultats confirment la présence d'un mode de « respiration » basse fréquence causé par la contraction et l'expansion de la zone décollée, ainsi que d'un mode convectif causé par l'enroulement et le lâcher de structures tourbillonaires au sein de la couche de mélange. La signature des deux modes est observée sur toute l'envergure de la surface d'essai. De plus, un troisième mode fluctuant est observé à proximité des parois latérales, relié à la présence de tourbillons trombes.

Numerical Investigation of Contrasting Flow Physics in Different Zones of a High-Lift Low-Pressure Turbine Blade

Using a range of high-fidelity large eddy simulations (LES), the contrasting flow physics on the suction surface, pressure surface, and endwalls of a low-pressure turbine (LPT) blade (T106A) was studied. The current paper attempts to provide an improved understanding of the flow physics over these three zones under the influence of different inflow boundary conditions. These include: (a) the effect of wakes at low and high turbulence intensity on the flow at midspan and (b) the impact of the state of the incoming boundary layer on endwall flow features. On the suction surface, the pressure fluctuations on the aft portion significantly reduced at high freestream turbulence (FST). The instantaneous flow features revealed that this reduction at high FST (HF) is due to the dominance of “streak-based” transition over the “Kelvin–Helmholtz” (KH) based transition. Also, the transition mechanisms observed over the turbine blade were largely similar to those on a flat plate subjected to pressure gradients. On pressure surface, elongated vortices were observed at low FST (LF). The possibility of the coexistence of both the Görtler instability and the severe straining of the wakes in the formation of these elongated vortices was suggested. While this was true for the cases under low turbulence levels, the elongated vortices vanished at higher levels of background turbulence. At endwalls, the effect of the state of the incoming boundary layer on flow features has been demonstrated. The loss cores corresponding to the passage vortex and trailing shed vortex were moved farther from the endwall with a turbulent boundary layer (TBL) when compared to an incoming laminar boundary layer (LBL). Multiple horse-shoe vortices, which constantly moved toward the leading edge due to a low-frequency unstable mechanism, were captured.