Quasi-streamwise Vortices Research Articles

Distinct Organizational States of Fully Developed Turbulent Pipe Flow

Organizational states of turbulence are identified through novel analysis of large scale pipe flow experiments at a Reynolds number of 35 000. The distinct states are revealed by an azimuthal decomposition of the two-point spatial correlation of the streamwise velocity fluctuation. States with dominant azimuthal wave numbers corresponding to k_{θ}=2,3,4,5,6 are discovered and their structure revealed as a series of alternately rotating quasistreamwise vortices. Such organizational states are highly reminiscent of the nonlinear traveling wave solutions previously identified at Reynolds numbers an order of magnitude lower.

Effects of System Rotation on Vortical Structure in Wall Turbulence

Direct numerical simulations (DNSs) of rotating turbulent Poiseuille flows are performed to study the effects of both cyclonic and anticyclonic system rotation on the kinematics of the quasi-streamwise vortices. By using the second invariant of the deformation tensor, a number of streamwise vortices are detected and averaged in the wall vicinity where the intense sweep motion, i.e., the inrush motion of high-speed fluid toward the wall, is related to the quasi-streamwise vortices. The effects of the system rotation on the angle of vortex axis are clearly observed as studied in longitudinal vortices of the homogeneous shear flow. Moreover, by calculating the probability of the emergence of the counterclockwise vortices (CCVs) around a clockwise vortex (CV), we find that with increase in the anticyclonic system rotation, the probability increases and decreases in the ejection and sweep sides of a CV, respectively. In contrast, cyclonic system rotation attenuates CCVs in both sides of a CV, though it increases at the top of the CV. This distribution of CCVs is found to affect sweep motion related to the quasi-streamwise vortices.

Modification of quasi-streamwise vortical structure in a drag-reduced turbulent channel flow with spanwise wall oscillation

The conditional averaging technique is applied to quasi-streamwise vortices in order to clarify the impact of their structural modification on the resultant drag reduction effect in a turbulent channel flow subjected to spanwise harmonic wall oscillation. The quantitative contributions of quadrant Reynolds shear stresses induced by the quasi-streamwise vortices are calculated on the basis of the Fukagata-Iwamoto-Kasagi identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73 (2002)]. It is found that the Q2 event characterized by upwelling of low-speed fluid away from the wall governs the skin friction drag reduction at relatively small oscillation periods, whereas the Q4 event characterized by downwelling of high speed fluid toward the wall slightly contributes to drag reduction at small oscillation periods, and then to drag increase significantly with increasing the oscillation period. Detailed investigation of the conditionally averaged velocity field around the detected vortices reveals that the suppression of Q2 occurs at a certain phase when the wall motion is applied so as to oppose the rotation of near-wall streamwise vortices, whereas the enhancement of Q4 at a large oscillation period is caused by spanwise tilting of coherent structures due to the alternating spanwise shear induced by spanwise wall oscillation. Based on these findings, we develop a new predictive correlation for drag reduction effect applicable to a wide range of oscillation periods and amplitudes.

Quasi-streamwise counter-rotating vortices generated by convergent riblets in flat plate boundary layer

Flow structures initiated by multiple convergent riblets, arranged in tandem, in the developing laminar boundary layer on a flat plate were qualitatively studied for a flow velocity of 1.5 m/s by means of smoke wire flow visualization. Two different configurations with varying pitch, 3 and 1.5 mm, and a constant height 3 mm, had been considered. Results depict the development of mushroom-like counter-rotating vortices accompanied by symmetrically distributed small-scale co-rotating vortices and subsequent breakdown of the structures. Though the variation of pitch indicates similar flow structures, the point of breakdown of the structures was found to vary significantly. The probable reasons for the breakdown of the structures have also been discussed.

Relative periodic orbits in plane Poiseuille flow

A branch of relative periodic orbits is found in plane Poiseuille flow in a periodic domain at Reynolds numbers ranging from Re=3000 to Re=5000. These solutions consist in sinuous quasi-streamwise streaks periodically forced by quasi-streamwise vortices in a self-sustained process. The streaks and the vortices are located in the bulk of the flow. Only the amplitude, but not the shape, of the averaged velocity components does change as the Reynolds number is increased from 3000 to 5000. We conjecture that these solutions could therefore be related to large- and very large-scale structures observed in the bulk of fully developed turbulent channel flows.

On the near-wall vortical structures at moderate Reynolds numbers

A recent database from direct numerical simulation (DNS) of a turbulent boundary layer up to Reθ=4300 (Schlatter and Örlü, 2010) is analysed to extract the dominant flow structures in the near-wall region. In particular, the question of whether hairpin vortices are significant features of near-wall turbulence is addressed. A number of different methods based on the λ2 criterion (Jeong and Hussain, 1995) is used to extract turbulent coherent structures: three-dimensional flow visualisation with quantitative estimates of hairpin population, conditional averaging and planar hairpin vortex signatures (HVS). First, visualisations show that during the initial phase of laminar–turbulent transition induced via tripping, hairpin vortices evolving from transitional Λ vortices are numerous and can be considered as the dominant structure of the immediate post-transition stage of the boundary layer. This is in agreement with previous experiments and low-Reynolds-number simulations such as Wu & Moin (2009). When the Reynolds number is increased, the fraction of hairpin vortices decreases to less than 2% for Reθ>4000. Second, conditional ensemble averages (Jeong et al., 1997) find hairpins close to the wall at low Reynolds number, while at a sufficient distance downstream from transition, the flow close to the wall is dominated by single quasi-streamwise vortices; even quantitatively, no major differences between boundary layer and channel can be detected. Moreover, three-dimensional visualisations of the neighbourhood of regions of strong swirling motion in planar cuts through the layer (the HVS) do not reveal hairpin vortices, thereby impairing statistical evidences based on HVS. The present results thus clearly confirm that transitional hairpin vortices do not persist in fully developed turbulent boundary layers, and that their dominant appearance as instantaneous flow structures in the outer boundary-layer region is very unlikely.

Velocity–vorticity correlation structure in turbulent channel flow

AbstractA new statistical coherent structure (CS), the velocity–vorticity correlation structure (VVCS), using the two-point cross-correlation coefficient $R_{ij}$ of velocity and vorticity components, $u_i$ and $\omega _j~ (i, j = 1, 2, 3)$, is proposed as a useful descriptor of CS. For turbulent channel flow with the wall-normal direction $y$, a VVCS study consists of using $u_i$ at a fixed reference location $y_r$, and using $|R_{ij} (y_r; x, y, z)|\geqslant R_0$ to define a topologically invariant high-correlation region, called $\mathit{VVCS}_{ij}$. The method is applied to direct numerical simulation (DNS) data, and it is shown that the $\mathit{VVCS}_{ij}$ qualitatively and quantitatively captures all known geometrical features of near-wall CS, including spanwise spacing, streamwise length and inclination angle of the quasi-streamwise vortices and streaks. A distinct feature of the VVCS is that its geometry continuously varies with $y_r$. A topological change of $\mathit{VVCS}_{11}$ from quadrupole (for smaller $y_r$) to dipole (for larger $y_r$) occurs at $y^{+}_r=110$, giving a geometrical interpretation of the multilayer nature of wall-bounded turbulent shear flows. In conclusion, the VVCS provides a new robust method to quantify CS in wall-bounded flows, and is particularly suitable for extracting statistical geometrical measures using two-point simultaneous data from hotwire, particle image velocimetry/laser Doppler anemometry measurements or DNS/large eddy simulation data.

Turbulent structure of high-amplitude pressure peaks within the turbulent boundary layer

AbstractThe positive and negative high-amplitude pressure peaks (HAPP) are investigated in a turbulent boundary layer at $R{e}_{\theta } = $ 1900 in order to identify their turbulent structure. The three-dimensional velocity field is measured within the inner layer of the turbulent boundary layer using tomographic particle image velocimetry (tomo-PIV). The measurements are performed at an acquisition frequency of 10 000 Hz and over a volume of $418\times 149\times 621$ wall units in the streamwise, wall-normal and spanwise directions, respectively. The time-resolved velocity fields are applied to obtain the material derivative using the Lagrangian method followed by integration of the Poisson pressure equation to obtain the three-dimensional unsteady pressure field. The simultaneous volumetric velocity, acceleration, and pressure data are conditionally sampled based on local maxima and minima of wall pressure to analyse the three-dimensional turbulent structure of the HAPPs. Analysis has associated the positive HAPPs to the shear layer structures formed by an upstream sweep of high-speed flow opposing a downstream ejection event. The sweep event is initiated in the outer layer while the ejection of near-wall fluid is formed by the hairpin category of vortices. The shear layers were observed to be asymmetric in the instantaneous visualizations of the velocity and acceleration fields. The asymmetric pattern originates from the spanwise component of temporal acceleration of the ejection event downstream of the shear layer. The analysis also demonstrated a significant contribution of the pressure transport term to the budget of the turbulent kinetic energy in the shear layers. Investigation of the conditional averages and the orientation of the vortices showed that the negative HAPPs are linked to both the spanwise and quasi-streamwise vortices of the turbulent boundary layer. The quasi-streamwise vortices can be associated with the hairpin category of vortices or the isolated quasi-streamwise vortices of the inner layer. A bi-directional analysis of the link between the HAPPs and the hairpin paradigm is also conducted by conditionally averaging the pressure field based on the detection of hairpin vortices using strong ejection events. The results demonstrated positive pressure in the shear layer region of the hairpin model and negative pressure overlapping with the vortex core.

Direct numerical simulation of drag reduction in a turbulent channel flow using spanwise traveling wave-like wall deformation

Drag reduction effects by a spanwise traveling wave of wall deformation in a turbulent channel flow are investigated by means of direct numerical simulation. The flow rate is kept constant at the bulk Reynolds number of Reb = 5600. A parametric study is performed by varying three parameters of the wave (i.e., the amplitude, the wavenumber, and the phase speed). Within the range of parameters investigated, the maximum drag reduction rate and the maximum net energy saving rate are found to be 13.4% and 12.2%, respectively. The drag reduction rate is found to be reasonably scaled by a product of the magnitude of the induced velocity and the thickness of the Stokes layer. An analysis using the FIK identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73 (2002)] with a three-component decomposition reveals that the drag reduction is mainly attributed to a decrease in the random component of the Reynolds shear stress. The turbulence statistics are investigated in detail and the drag reduction mechanism is explained by the induced spanwise flow due to the traveling wave rather than the riblet-like geometric structure. Although the amount of drag reduction rate is comparable to that of the conventional riblets, the quasi-streamwise vortices are found to be suppressed even when the spanwise wavelength is larger than the typical diameter of quasi-streamwise vortices.

Heat transfer enhancement through control of added perturbation velocity in flow field

The characteristics of heat transfer and flow, through an added perturbation velocity, in a rectangle channel, are investigated by Large Eddy Simulation (LES). The downstream, vertical, and upstream control strategy, which can suppress the lift of low speed streaks in the process of improving the performance of heat transfer, are adopted in numerical investigation. Taking both heat transfer and flow properties into consideration, the synthesis performance of heat transfer and flow of three control strategies are evaluated. The numerical results show that the flow structure in boundary layer has been varied obviously for the effect of perturbation velocity and induced quasi-streamwise vortices emerging around the controlled zone. The results indicate that the vertical control strategy has the best synthesis performance of the three control strategies, which also has the least skin frication coefficient. The upstream and downstream strategies can improve the heat transfer performance, but the skin frication coefficient is higher than that with vertical control strategy.

DNS on turbulent heat transfer of viscoelastic fluid flow in a plane channel with transverse rectangular orifices

Heat-transfer characteristics of a viscoelastic turbulence past rectangular orifices were investigated in the context of the reduction effects of fluid elasticity on drag and heat transfer. To simulate the fully-developed channel flow through transverse orifices located periodically at intervals of 6.4 times channel height, we imposed periodic conditions at the upstream and downstream boundaries. To discuss the dissimilarity between the velocity and thermal fields, the molecular Prandtl number was set to be 1.0 and any temperature dependence of the fluid and rheological properties was not considered. In the present condition, the ratio of the reduction rates in drag and heat transfer was found to be 2.8:1.0, revealing that the present flow configuration is better than a smooth channel for avoiding the heat-transfer reduction. This phenomenon was attributed to the sustainment of the quasi-streamwise vortex downstream of the reattachment point despite the absence of strong spanwise vortices emanating from the orifice edge in the viscoelastic fluid. The longitudinal vortices behind the reattachment point caused a high turbulent heat flux and increased the local Nusselt number.

Three-dimensional velocity measurements in a roughness sublayer using microscopic digital in-line holography and optical index matching

Microscopic in-line digital holography and particle tracking are used for measuring the 3D flow field in the inner part of a turbulent boundary layer over a rough surface. This paper focuses on procedures, uncertainty and data quality. Experiments are performed for a rectangular channel flow, at Reτ = 3520, with the top and bottom surfaces containing uniformly distributed pyramidal elements. Optical accessibility through the acrylic rough walls is attained by matching the optical refractive index of the fluid with that of acrylic using a NaI solution in water. Localized particle injection ensures that the seeding is sufficient for detecting 5000–10 000 particle pairs in each hologram pair within the 3.1×2.1×1.8 mm3 sample volume, which covers the entire roughness sublayer. The data quality is assessed by evaluating how well the data satisfy the continuity equation for varying resolutions and procedures. Mean velocity and Reynolds stress profiles are compared to 2D particle image velocimetry data, showing excellent agreement above one roughness height away from the wall, and discrepancies, some of which can be attributed to spatial resolution and bias, closer to the rough wall. Sample instantaneous flow realizations contain low-lying vortices, some with spanwise orientation, and others aligned parallel to the roughness grooves, flooding the lower part of the sublayer. Quasi-streamwise vortices with vertical inclinations of 50°–60° also appear, with a small fraction of them spanning the entire sublayer.

Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow

AbstractThis paper focuses on turbulence structure in a fully developed rough-wall channel flow and its role in subgrid-scale (SGS) energy transfer. Our previous work has shown that eddies of scale comparable to the roughness elements are generated near the wall, and are lifted up rapidly by large-scale coherent structures to flood the flow field well above the roughness sublayer. Utilizing high-resolution and time-resolved particle-image-velocimetry datasets obtained in an optically index-matched facility, we decompose the turbulence into large (${\gt }\lambda $), intermediate ($3\text{{\ndash}} 6k$), roughness ($1\text{{\ndash}} 3k$) and small (${\lt }k$) scales, where $k$ and $\lambda (\lambda / k= 6. 8)$ are roughness height and wavelength, respectively. With decreasing distance from the wall, there is a marked increase in the ‘non-local’ SGS energy flux directly from large to small scales and in the fraction of turbulence dissipated by roughness-scale eddies. Conditional averaging is used to show that a small fraction of the flow volume (e.g. 5 %), which contains the most intense SGS energy transfer events, is responsible for a substantial fraction (50 %) of the energy flux from resolved to subgrid scales. In streamwise wall-normal ($x\text{{\ndash}} y$) planes, the averaged flow structure conditioned on high SGS energy flux exhibits a large inclined shear layer containing negative vorticity, bounded by an ejection below and a sweep above. Near the wall the sweep is dominant, while in the outer layer the ejection is stronger. The peaks of SGS flux and kinetic energy within the inclined layer are spatially displaced from the region of high resolved turbulent kinetic energy. Accordingly, some of the highest correlations occur between spatially displaced resolved velocity gradients and SGS stresses. In wall-parallel $x\text{{\ndash}} z$ planes, the conditional flow field exhibits two pairs of counter-rotating vortices that induce a contracting flow at the peak of SGS flux. Instantaneous realizations in the roughness sublayer show the presence of the counter-rotating vortex pairs at the intersection of two vortex trains, each containing multiple $\lambda $-spaced vortices of the same sign. In the outer layer, the SGS flux peaks within isolated vortex trains that retain the roughness signature, and the distinct pattern of two counter-rotating vortex pairs disappears. To explain the planar signatures, we propose a flow consisting of U-shaped quasi-streamwise vortices that develop as spanwise vorticity is stretched in regions of high streamwise velocity between roughness elements. Flow induced by adjacent legs of the U-shaped structures causes powerful ejections, which lift these vortices away from the wall. As a sweep is transported downstream, its interaction with the roughness generates a series of such events, leading to the formation of inclined vortex trains.

Dynamics of complete turbulence suppression in turbidity currents driven by monodisperse suspensions of sediment

AbstractTurbidity currents derive their motion from the excess density imposed by suspended sediments. The settling tendency of sediments is countered by flow turbulence, which expends energy to keep them in suspension. This interaction leads to downward increasing concentration of suspended sediments (stable stratification) in the flow. Thus in a turbidity current sediments play the dual role of sustaining turbulence by driving the flow and damping turbulence due to stable stratification. By means of direct numerical simulations, it has been shown previously that stratification above a threshold can substantially reduce turbulence and possibly extinguish it. This study expands the simplified model by Cantero et al. (J. Geophys. Res., vol. 114, 2009a, C03008), and puts forth a proposition that explains the mechanism of complete turbulence suppression due to suspended sediments. In our simulations it is observed that suspensions of larger sediments lead to stronger stratification and, above a threshold size, induce an abrupt transition in the flow to complete turbulence suppression. It has been widely accepted that hairpin and quasi-streamwise vortices are key to sustaining turbulence in wall-bounded flows, and that only vortices of sufficiently strong intensity can spawn the next generation of vortices. This auto-generation mechanism keeps the flow populated with hairpin and quasi-streamwise vortical structures and thus sustains turbulence. From statistical analysis of Reynolds stress events and visualization of flow structures, it is observed that settling sediments damp the Reynolds stress events (Q2 events), which means a reduction in both the strength and spatial distribution of vortical structures. Beyond the threshold sediment size, the existing vortical structures in the flow are damped to an extent where they lose their ability to regenerate the subsequent generation of turbulent vortical structures, which ultimately leads to complete turbulence suppression.

Coherent structures in the inner part of a rough-wall channel flow resolved using holographic PIV

AbstractMicroscopic holographic PIV performed in an optically index-matched facility resolves the three-dimensional flow in the inner part of a turbulent channel flow over a rough wall at Reynolds number ${\mathit{Re}}_{\tau } = 3520$. The roughness consists of uniformly distributed pyramids with normalized height of ${ k}_{s}^{+ } = 1. 5{k}^{+ } = 97$. Distributions of mean flow and Reynolds stresses agree with two-dimensional PIV data except very close to the wall (${\lt }0. 7k$) owing to the higher resolution of holography. Instantaneous realizations reveal that the roughness sublayer is flooded by low-lying spanwise and groove-parallel vortical structures, as well as quasi-streamwise vortices, some quite powerful, that rise at sharp angles. Conditional sampling and linear stochastic estimation (LSE) reveal that the prevalent flow phenomenon in the roughness sublayer consists of interacting U-shaped vortices, conjectured in Hong et al. (J. Fluid Mech., 2012, doi:10.1017/jfm.2012.403). Their low-lying base with primarily spanwise vorticity is located above the pyramid ridgeline, and their inclined quasi-streamwise legs extend between ridgelines. These structures form as spanwise vorticity rolls up in a low-speed region above the pyramid’s forward face, and is stretched axially by the higher-speed flow between ridgelines. Ejection induced by interactions among legs of vortices generated by neighbouring pyramids appears to be the mechanism that lifts the quasi-streamwise vortex legs and aligns them preferentially at angles of $54\textdegree \text{{\ndash}} 63\textdegree $ to the streamwise direction.

Influence of active control on STG-based generation of streamwise vortices in near-wall turbulence

AbstractNear-wall streamwise vortices are closely related to the generation of high skin friction in wall-bounded turbulent flows. A common feature of controlled, friction-reduced turbulent flows is weakened near-wall streamwise vortices. In the present study, the streak transient growth (STG) mechanism for generating near-wall streamwise vortices by Schoppa & Hussain (J. Fluid Mech., vol. 453, 2002, pp. 57–108) is employed, and the opposition control proposed by Choi, Moin & Kim (J. Fluid Mech., vol. 262, 1994, pp. 75–110) is imposed during the transient growth process of perturbations to determine how active control affects the generation of quasi-streamwise vortices. In the transient growth stage, when the detection plane is located near the wall (${ y}_{d}^{+ } = 15$), the control can suppress the production of streamwise vorticity by weakening the near-wall vertical velocity; when the detection plane moves away from the wall (${ y}_{d}^{+ } = 28$), the control has the opposite effect. In the vortex generation stage, the control cannot change the dominance of the stretching effect. Controls imposed at different stages reveal the importance of the STG stage in vortex generation. Strengthened out-of-phase control and lessened in-phase control are proposed as an extension of the original opposition-control scheme. Application in a fully developed turbulent channel flow shows that strengthened ${ y}_{d}^{+ } = 10$ control can yield an even higher drag reduction rate than the original ${ y}_{d}^{+ } = 15$ control. Moreover, lessened ${ y}_{d}^{+ } = 28$ control can also achieve drag reduction and turbulence suppression.

난류 채널 유동 내부의 레이놀즈 전단 응력 분포

벽면 난류의 항력과 밀접한 관련이 있는 유동구조를 조사하기 위해 Reτ = 180, 395, 590 의 난류채널유동에 대한 직접수치모사를 수행하였다. 확률밀도함수를 조사하여 레이놀즈 전단응력에 가장 큰 기여를 하는 Q2 이벤트를 파악하였으며 Q2 이벤트의 각도의 변화가 y+ < 50 에서는 벽 단위로 스케일링되며, y/h > 0.5 에서는 채널의 높이로 스케일링 됨을 확인하였다. Q2 이벤트를 조건으로 하는 조건부 평균 유동장을 조사하여 레이놀즈 전단응력의 발생과 관련이 있는 유동구조는 주 유동방향의 보텍스 및 헤어핀 형상의 보텍스임을 보였다. 또한, 순간 유동장을 관찰하여 높은 레이놀즈 전단 응력의 분포가 이러한 보텍스 구조와 관련이 있으며 1.5 ~ 3h 의 크기를 갖는 대형유동구조를 구성함을 확인하였다.

Laminar-turbulent separatrix in a boundary layer flow

The transitional boundary layer flow over a flat plate is investigated. The boundary layer flow is known to develop unstable Tollmien-Schlichting waves above a critical value of the Reynolds number. However, it is also known that this transition can be observed for sub-critical Reynolds numbers. In that case, the basin of attraction of the laminar state coexists with the sustained turbulence. In this article, the trajectory on the separatrix between these two states is simulated. The state on the separatrix is independent from the initial condition and is dynamically connected to both the laminar flow and the turbulence. Such an edge state provides information regarding the basic features of the transitional flow. The solution takes the form of a low speed streak, flanked by two quasi-streamwise sinuous vortices. The shape of the streaks is close to that simulated with the linear optimal perturbation method. This solution is compared to existing results concerning streak breakdown. The simulations are realized in a temporal framework for a local boundary layer, with periodic boundary conditions in the streamwise direction. A dedicated model, based on a scale separation, is presented. The mean flow is a solution of the Prandtl boundary layer equations while the superposed small-scale fluctuations are a solution of the periodic Navier-Stokes equations. The model is validated with turbulent flow simulations and satisfactorily reproduces the physical characteristics of a boundary layer flow, especially in the outer region, where external fluid is entrained toward the boundary layer.

Visualization of Continuous Stream of Grid Turbulence Past the Langston Turbine Cascade

This paper describes a direct numerical simulation visualization study on the migration and distortion of a continuous stream of grid turbulence passing through a representative turbine cascade with and without being segregated by the blade leading edge. For the nonimpinging case, as the turbulent stream starts to enter the turbine cascade, there is a coarsening and reorientation of the small-scale and random grid-turbulence structures into short vortex tubes; inside the cascade, these short vortex tubes are further stretched into relatively long quasi-streamwise vortices. For the impinging case, very long streamwise vortices on the pressure surface are observed that correspond nicely to the “colored-fingers” phenomenon reported in previous turbine heat transfer experiments. The spanwise locations of the observed vortices vary with time. The origin of such turbine pressure-side streamwise vortices is revealedusing a relatively complete sequence of images documenting their life cycle. For the impinging case, the short vortex tubes formed at the stagnation are gradually distorted into the shape of a hockey stick. The long stick is nearly parallel to the blade pressure surface, whereas the short end is bent toward the freestream. This process can be well explained by invoking results from previous fundamental studies on simple stagnation flows and on the stretching and rotation of material lines by the mean strain-rate field under the assumption of rapid distortion. Taken together with earlier investigations on turbine distortion ofmigrating planarwake andmigrating isolated turbulent block, it is quite likely that Taylor–Goertler centrifugal instabilitymay not be an important player in the formation of pressureside elongated streamwise vortices in turbomachinery applications.

Counter-hairpin vortices in the turbulent wake of a sharp trailing edge

AbstractThe unsteady organization and evolution of coherent structures within the turbulent boundary layer and subsequent wake of the sharp symmetric trailing edge of a NACA0012 aerofoil are investigated. The experiments are conducted in an open test-section wind tunnel at ${\mathit{Re}}_{c} = \text{386\hspace{0.167em}000} $ based on the aerofoil chord and ${\mathit{Re}}_{\theta } = 1300$ based on the boundary layer momentum thickness. An initial characterization of the flow field using two-component particle image velocimetry (PIV) is followed by the investigation of the unsteady organization and evolution of coherent structures by time-resolved three-dimensional PIV based on a tomographic approach (Tomo-PIV). The inspection of the turbulent boundary layer prior to the trailing edge in the region between 0.15 and $0. 8\hspace{0.167em} {\delta }_{99} $ demonstrated streaks of low- and high-speed flow, while the low-speed streaks are observed to be more coherent along with strong interaction with hairpin-type vortical structures similar to a turbulent boundary layer at zero pressure gradient. The wake region demonstrated gradual deterioration of both the low- and the high-speed streaks with downstream progress. However, the low-speed streaks are observed to lose their coherence at a faster rate relative to the high-speed streaks as the turbulent flow develops towards the far wake. The weakening of the low-speed streaks is due to the disappearance of the viscous sublayer after the trailing edge and gradual mixing through the transport of the remaining low-speed flow towards the free stream. This transport of low-speed flow is performed by the ejection events induced by the hairpin vortices as they also persist into the developing wake. The higher persistence of the high-speed streaks is associated with counter-hairpin vortical activities as they oppose the deterioration of the high-speed streaks by frequently sweeping the high-speed flow towards the wake centreline. These vortical structures are regarded as counter-hairpin vortices as they exhibit opposite characteristics relative to the hairpin vortices of a turbulent boundary layer. They are topologically similar to the hairpins as they appear to be U-shaped but with inverted orientation, as the spanwise portion is in the vicinity of the wake centreline and the legs are inclined at an approximately $6{0}^{\ensuremath{\circ} } $ to the wake axis in the downstream direction demonstrating a strain-dominated topology. The counter-hairpin vortices are partially wrapped around the high-speed streaks and contribute to the wake development by transporting high-speed flow towards the wake centreline. Similar to the hairpin vortices of a turbulent boundary layer, the occurrence of a complete counter-hairpin vortex is occasional while its derivatives (portions of spanwise or quasi-streamwise vortices) are more frequently observed. Therefore, a pattern recognition algorithm is applied to establish characterization based on an ensemble-averaged counter-hairpin vortex. The formation of the counter-hairpin vortices is due to an additional degree of interaction between the low- and high-speed streaks after the trailing edge across the wake centreline. The shear layer produced along the wake centreline by neighbouring low- and high-speed streaks promotes the formation of spanwise vortices that form the counter-hairpin vortices by connection to quasi-streamwise vortices. Finally, a conceptual model is proposed to depict the three-dimensional unsteady organization and evolution of coherent structures in the wake region based on the hairpin and counter-hairpin vortex signatures.