Hairpin Packets Research Articles

S0505-1-5 圧縮性境界層の遷移構造から発生する音波の研究([S0505-1]乱流遷移(1))

Spatial direct numerical simulations are used to study the formation and development of three-dimensional structures in a compressible flat plate boundary layer, where the freestream Mach number is 0.5 and the Reynolds number at the inlet based on the displacement thickness 1000. A pair of stable oblique modes and a two-dimensional unstable T-S wave are superimposed on the laminar profile at the inlet plane of the boundary layer computational box. The magnitudes of the disturbances are chosen to be 1% of the freestream value. Oblique modes with the TS wave produces peak-valley splitting downstream and later hairpin vortices (hairpin packet) on the low speed streak are observed. So-called subharmonic transition appears downstream in the boundary layer. DNS results show that the forming hairpin vortex is responsible for sound waves emission.

Coherent structures in turbulent boundary layers with adverse pressure gradients

The coherent structures in turbulent boundary layers (TBLs) subjected to adverse pressure gradients (APGs) were investigated by analyzing a database of direct numerical simulations. The equilibrium adverse pressure gradient flows were established by using a power law free-stream distribution. The population trends of the spanwise vortices show that the outer regions of the APG TBLs are densely populated with hairpin-like vortices. These vortical structures induce low-momentum regions in the middle of the boundary layers, which result in an outer peak in the Reynolds shear stress. The 3-D features of the hairpin packets were deduced from their spatial characteristics in the spanwise-wall-normal plane. The conditionally averaged velocity fields show that there are counter-rotating v−w swirling motions that represent cross-sectional evidences of the packets. Moreover, two-point correlations and linear stochastic estimations were used to provide statistical information about the hairpin packet motions in the ...

직접수치모사를 이용한 난류경계층 내의 거대난류구조 연구

Direct numerical simulation (DNS) of a turbulent boundary layer with moderate Reynolds number was performed to scrutinize streamwise-coherence of hairpin packet motions. The Reynolds number based on the momentum thickness (θ<SUB>in</SUB>) and free-stream velocity (U<SUB>∞</SUB>) was varied in the range Re<SUB>θ</SUB>=1410~2540 which was higher than the previous numerical simulations in the turbulent boundary layer. In order to include the groups of hairpin packets existing in the outer layer, large computational domain was used (more than 50δo, where δ<SUB>o</SUB> is the boundary layer thickness at the inlet in the streamwise domain). Characteristics of packet motions were investigated by using instantaneous flow fields, two-point correlation and conditional average flow fields in xy-plane. The present results showed that a train of hairpin packet motions was propagating coherently along the downstream and these structures induced the very large-scale motions in the turbulent boundary layer.

Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer

A nominally-zero-pressure-gradient incompressible boundary layer over a smooth flat plate was simulated for a continuous momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 940. Transition which is completed at approximately Reθ = 750 was triggered by intermittent localized disturbances arising from patches of isotropic turbulence introduced periodically from the free stream at Reθ = 80. Streamwise pressure gradient is quantified with several measures and is demonstrated to be weak. Blasius boundary layer is maintained in the early transitional region of 80 &lt; Reθ &lt; 180 within which the maximum deviation of skin friction from the theoretical solution is less than 1%. Mean and second-order turbulence statistics are compared with classic experimental data, and they constitute a rare DNS dataset for the spatially developing zero-pressure-gradient turbulent flat-plate boundary layer. Our calculations indicate that in the present spatially developing low-Reynolds-number turbulent flat-plate boundary layer, total shear stress mildly overshoots the wall shear stress in the near-wall region of 2–20 wall units with vanishing normal gradient at the wall. Overshoots as high as 10% across a wider percentage of the boundary layer thickness exist in the late transitional region. The former is a residual effect of the latter. The instantaneous flow fields are vividly populated by hairpin vortices. This is the first time that direct evidence (in the form of a solution of the Navier–Stokes equations, obeying the statistical measurements, as opposed to synthetic superposition of the structures) shows such dominance of these structures. Hairpin packets arising from upstream fragmented Λ structures are found to be instrumental in the breakdown of the present boundary layer bypass transition.

Three-dimensional instantaneous structure of a shock wave/turbulent boundary layer interaction

An experimental study is carried out to investigate the three-dimensional instantaneous structure of an incident shock wave/turbulent boundary layer interaction at Mach 2.1 using tomographic particle image velocimetry. Large-scale coherent motions within the incoming boundary layer are observed, in the form of three-dimensional streamwise-elongated regions of relatively low- and high-speed fluid, similar to what has been reported in other supersonic boundary layers. Three-dimensional vortical structures are found to be associated with the low-speed regions, in a way that can be explained by the hairpin packet model. The instantaneous reflected shock wave pattern is observed to conform to the low- and high-speed regions as they enter the interaction, and its organization may be qualitatively decomposed into streamwise translation and spanwise rippling patterns, in agreement with what has been observed in direct numerical simulations. The results are used to construct a conceptual model of the three-dimensional unsteady flow organization of the interaction.

Chasing eddies and their wall signature in DNS data of turbulent boundary layers

We present an automated and physically rooted method to identify and temporally track hairpin packets and their wall signatures in direct numerical simulation data of turbulent boundary layers. Statistical tools and pattern-recognition algorithms are combined to identify the coherent structures and their signature on the wall, and object segmentation and feature-tracking algorithms are assessed and enhanced to achieve automatic monitoring of the temporal evolution of individual packets and their wall signatures. The visualization algorithms are validated against the statistical analysis. We demonstrate that the average geometric packet is representative of strong statistical ones. Satisfactory results are presented for the canonical case of an isolated hairpin packet convecting in channel flow, and for fully turbulent boundary layers. The method is also suitable for use in combination with experimental particle image velocimetry (PIV) data.

Characterization of coherent vortical structures in a supersonic turbulent boundary layer

A spatially developing supersonic boundary layer at Mach 2 is analysed by means of direct numerical simulation of the compressible Navier--Stokes equations, with the objective of quantitatively characterizing the coherent vortical structures. The study shows structural similarities with the incompressible case. In particular, the inner layer is mainly populated by quasi-streamwise vortices, while in the outer layer we observe a large variety of structures, including hairpin vortices and hairpin packets. The characteristic properties of the educed structures are found to be nearly uniform throughout the outer layer, and to be weakly affected by the local vortex orientation. In the outer layer, typical core radii vary in the range of 5–6 dissipative length scales, and the associated circulation is approximately constant, and of the order of 180 wall units. The statistical properties of the vortical structures in the outer layer are similar to those of an ensemble of non-interacting closed-loop vortices with a nearly planar head inclined at an angle of approximately 20° with respect to the wall, and with an overall size of approximately 30 dissipative length scales.

Effects of background noise on generating coherent packets of hairpin vortices

We examine the autogeneration process by which new hairpin vortices are created from a sufficiently strong hairpin vortex, leading to the formation of a hairpin packet. Emphasis is placed on the effects of background noise on packet formation. The initial conditions are given by conditionally averaged flow fields associated with the second quadrant (Q2) event in the fully turbulent channel flow direct numerical simulation (DNS) database at Reτ=395. The nonlinear evolution of the initial vortical structure is tracked by performing a spectral simulation. Background noise is introduced by adding small amplitude perturbations to the initial field or by imposing momentum forcing. The background noise gives rise to chaotic development of a hairpin packet. The hairpins become asymmetric, leading to much more complicated packet structures than are observed in the symmetric hairpin vortex train of the flow with a clean background. However, the chaotic packets show the same properties as the clean packet in terms of the rate of growth of vertical and spanwise dimensions and the distance between successive vortices, suggesting that the autogeneration mechanism is robust. The background noise leads to a decrease in the minimum value of the Q2 strength required to trigger autogeneration, indicating that background noise enhances autogeneration, especially in the buffer layer. The autogeneration process is more enhanced by the background noise with wavenumbers kx&amp;lt;kz. Conditionally averaged flow fields around the tall attached vortices in the hairpin packet show that they are associated with elongated low-momentum structures in the streamwise direction. Finally, the autogeneration process was tested in a real turbulent environment taken from an instantaneous field of a turbulent channel flow DNS. The generation of secondary hairpin vortices is clearly observed upstream of the primary hairpin.

Coherent structures in bypass transition induced by a cylinder wake

Flat-plate boundary layer transition induced by the wake vortex of a two-dimensional circular cylinder is experimentally investigated. Combined visualization and velocity measurements show a different transition route from the Klebanoff mode in free-stream turbulence-induced transition. This transition scenario is mainly characterized as: (i) generation of secondary transverse vortical structures near the flat plate surface in response to the von Kármán vortex street of the cylinder; (ii) formation of hairpin vortices due to the secondary instability of secondary vortical structures; (iii) growth of hairpins which is accelerated by wake-vortex induction; (iv) formation of hairpin packets and the associated streaky structures. Detailed investigation shows that during transition the evolution dynamics and self-sustaining mechanisms of hairpins, hairpin packets and streaks are consistent with those in a turbulent boundary layer. The wake vortex mainly plays the role of generating and destabilizing secondary transverse vortices. After that, the internal mechanisms become dominant and lead to the setting up of a self-sustained turbulent boundary layer.

Interactions of a stationary finite-sized particle with wall turbulence

Reliable information on forces on a finite-sized particle in a turbulent boundary layer is lacking, so workers continue to use standard drag and lift correlations developed for a laminar flow to predict drag and lift forces. Here we consider direct numerical simulations of a turbulent channel flow over an isolated particle of finite size. The size of the particle and its location within the turbulent channel are systematically varied. All relevant length and time scales of turbulence, attached boundary layers on the particle, and particle wake are faithfully resolved, and thus we consider fully resolved direct numerical simulations. The results from the direct numerical simulation are compared with corresponding predictions based on the standard drag relation with and without the inclusion of added-mass and shear-induced lift forces. The influence of turbulent structures, such as streaks, quasi-streamwise vortices and hairpin packets, on particle force is explored. The effect of vortex shedding is also observed to be important for larger particles, whoseReexceeds a threshold.

Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3

We demonstrate that data from direct numerical simulation of turbulent boundary layers at Mach 3 exhibit the same large-scale coherent structures that are found in supersonic and subsonic experiments, namely elongated, low-speed features in the logarithmic region and hairpin vortex packets. Contour plots of the streamwise mass flux show very long low-momentum structures in the logarithmic layer. These low-momentum features carry about one-third of the turbulent kinetic energy. Using Taylor's hypothesis, we find that these structures prevail and meander for very long streamwise distances. Structure lengths on the order of 100 boundary layer thicknesses are observed. Length scales obtained from correlations of the streamwise mass flux severely underpredict the extent of these structures, most likely because of their significant meandering in the spanwise direction. A hairpin-packet-finding algorithm is employed to determine the average packet properties, and we find that the Mach 3 packets are similar to those observed at subsonic conditions. A connection between the wall shear stress and hairpin packets is observed. Visualization of the instantaneous turbulence structure shows that groups of hairpin packets are frequently located above the long low-momentum structures. This finding is consistent with the very large-scale motion model of Kim &amp; Adrian (1999).

Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers

This work can be viewed as a reprise of Head &amp; Bandyopadhyay's (J. Fluid Mech. vol. 107, p. 297) original boundary-layer visualization study although in this instance we make use of stereo particle image velocimetry (PIV), techniques to obtain a quantitative view of the turbulent structure. By arranging the laser light-sheet and image plane of a stereo PIV system in inclined spanwise/wall-normal planes (inclined at both plane, instantaneous swirl patterns exhibit a predisposition for counter-rotating vortex pairs (arranged with an ejection at their confluence). Such arrangements are consistent with the hairpin packet model. Correlation and scaling results show outer-scaling to be the correct way to quantify the characteristic spanwise length scale across the log and wake regions of the boundary layers (for the range of Reynolds numbers tested). A closer investigation of two-point velocity correlation contours indicates the occurrence of a distinct two-regime behaviour, in which contours (and hence streamwise velocity fluctuations) either appear to be ‘attached’ to the buffer region, or ‘detaching’ from it. The demarcation between these two regimes is found to scale well with outer variables. The results are consistent with a coherent structure that becomes increasingly uncoupled (or decorrelated) from the wall as it grows beyond the logarithmic region, providing additional support for a wall–awake description of turbulent boundary layers.

Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations

Stereoscopic particle image velocimetry (PIV) measurements are made in streamwise–spanwise and inclined cross-stream planes (inclined at plane, which is consistent with the presence of hairpin packets with a low-speed region lifting away from the wall.

난류경계층의 3차원 헤어핀 다발구조에 대한 실험적 연구

Experimental study on the three-dimensional topology of hairpin packet structures In turbulent boundary layers were earned out Two different Reynolds number based on momentum thickness, Re=514 and 934 were generated in a blowing type wind tunnel under the condition of zero pressure gradient. Simultaneous measurements of velocity fields at a wall-Dormal plane and wall-parallel plane by a plane PlY and a Stereo-PIV systems The two Nd Yag laser systems and three CCD cameras were synchronized to obtain Instantaneous Veiocity fields at the same time To avoid optical noise at the crossing line by the two laser light sheets, a new optical arrangement using polarization was applied. The obtained velocity fields show the existence of hairpin packet structure vividly and the Idealized hairpin vortex signature is confirmed by experiment Two counter-rotating vortex pair which reflects the cutting plane of hairpin legs are found both side of a strong streaky structure when the wall-normal plane cuts the hairpin head<br/>

Packet Structure of Surface Eddies in the Atmospheric Boundary Layer

A smoke visualization experiment has beenperformed in the first 3,m ofneutral and unstable atmospheric boundary layersat very large Reynolds number(ReΘ > 106). Under neutral atmosphericconditions mean wind profiles agreewell with those in the canonical flatplate zero-pressure-gradient turbulentboundary layer. The experiment was designedto minimize the temperaturedifference between the passive marker (smoke)and the air to ensure that anyobserved structures were due to vortical, ratherthan buoyant, motions. Imagesacquired in the streamwise–wall-normal planeusing a planar laser light-sheetare strikingly similar to those observed inlaboratory experiments at low to moderate Reynolds numbers. They reveal large-scaleramp-like structures withdownstream inclination of 3°–35°.This inclination isinterpreted as the hairpin packet growthangle following the hairpin vortexpacket model ofAdrian, Meinhart, and Tomkins.The distribution of this characteristicangle agrees with the results of experiments at far lower Reynolds numbers,suggesting a similarity in structures among low, moderate, and high Reynoldsnumber boundary layers at vastly different scales. These results indicate thatthe hairpin vortex packet model extends over a large range of scales. Theeffect of vertical heat transport in an unstable atmosphere on wall structuresis investigated in terms of the hairpin vortex packet model.

Observation of vortex packets in direct numerical simulation of fully turbulent channel flow

A number of experimental studies have inferred the existence of packets of inclined, hairpin-like vortices in wall turbulence on the basis of observations made in two-dimensional x-y planes using visualization and particle image velocimetry (PIV). However, there are very few observations of hairpins in existing three-dimensional studies made using direct numerical simulation (DNS), and no such study claims to have revealed packets. We demonstrate, for the first time, the existence of hairpin vortex packets in DNS of turbulent flow. The vortex packet structure found in the present study at low Reynolds number, Re_b = 300, is consistent with and substantiates the observations and the results from two-dimensional PIV measurements at higher Reynolds numbers in channel, pipe and boundary layer flows. Thus, the evidence supports the view that vortex packets are a universal feature of wall turbulence, independent of effects due to boundary layer trips or critical conditions in the aforementioned numerical studies. Visualization of the DNS velocity field and vortices also shows the close association of hairpin packets with long low-momentum streaks and the regions of high Reynolds shear stress.

Vortex organization in the outer region of the turbulent boundary layer

The structure of energy-containing turbulence in the outer region of a zero-pressure- gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 &lt; Reθ &lt; 6845 show that the boundary layer is densely populated by velocity fields associated with hairpin vortices. (The term ‘hairpin’ is here taken to represent cane, hairpin, horseshoe, or omega-shaped vortices and deformed versions thereof, recognizing these structures are variations of a common basic flow structure at different stages of evolution and with varying size, age, aspect ratio, and symmetry.) The signature pattern of the hairpin consists of a spanwise vortex core located above a region of strong second-quadrant fluctuations (u &lt; 0 and v &gt; 0) that occur on a locus inclined at 30–60° to the wall.In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian &amp; Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12°, and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart &amp; Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent ‘bursts’, and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.