Multisensor Hot Wire Vorticity Probe Measurements of the Formation Field of Two Corotating Vortices

Experimental evidence is reported, regarding the formation of a pair of co-rotating tip vortices by a split wing configuration, consisting of two half wings at equal and opposite angles of attack. Simultaneous measurements of the three-dimensional vector fields of velocity and vorticity were conducted on a cross plane at a downstream distance corresponding to 0.3 cord lengths (near wake), using an in-house constructed 12-sensor hot wire anemometry vorticity probe. The probe consists of three closely separated orthogonal 4-wire velocity sensor arrays, measuring simultaneously the three-dimensional velocity vector at three closely spaced locations on a cross plane of the flow filed. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. Velocity measurements obtained with an X-wire are also presented for comparison. In this near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an “impermeable” line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. The turbulent flow field is the result of temporal changes in the intensity of the vortex formation and changes in the position of the cores (wandering).     

Tomographic-PIV measurement of the flow around a zigzag boundary layer trip

Tomographic-PIV was used to measure the boundary layer transition forced by a zigzag trip. The resulting instantaneous three-dimensional velocity distributions are used to quantitatively visualize the flow structures. They reveal undulating spanwise vortices directly behind the trip, which break up into individual arches and then develop into the hairpin-like structures typical of wall-bounded turbulence. Compared to the instantaneous flow structure, the structure of the average velocity field is very different showing streamwise vortices. Such streamwise vortices are often associated with the low-speed streaks occurring in bypass transition flows, but in this case clearly are an artifact of the averaging. Rather, the present streaks in the separated flow region directly behind the trip are resulting from the waviness in the spanwise vortices as introduced by the zigzag trip. Furthermore, these streaks and the separated flow region are observed to be related to a large-scale, spanwise uniform unsteadiness in the flow that contributes significantly to the velocity fluctuations over large downstream distances (up to at least the edge of the present measurement domain).     

Population,characteristics and kinematics of vortices in a confined rectangular jet with a co-flow

Vortex behavior and characteristics in a confined rectangular jet with a co-flow were examined using vortex swirling strength as a defining characteristic. On the left side of the jet, the positively (counterclockwise) rotating vortices are dominant, while negatively rotating vortices are dominant on the right side of the jet. The characteristics of vortices, such as population density, average size and strength, and deviation velocity, were calculated and analyzed in both the cross-stream direction and the streamwise direction. In the near-field of the jet, the population density, average size and strength of the dominant direction vortices show high values on both sides of the center stream with a small number of counter-rotating vortices produced in the small wake regions close to jet outlet. As the flow develops, the wake regions disappear, these count-rotating vortices also disappear, and the population of the dominant direction vortices increase and spread in the jet. The mean size and strength of the vortices decrease monotonically with streamwise coordinate. The signs of vortex deviation velocity indicate the vortices transfer low momentum to high-velocity region and high momentum to the low velocity region. The developing trends of these characteristics were also identified by tracing vortices using time-resolved particle image velocimetry data. Both the mean tracked vortex strength and size decrease with increasing downstream distance overall. At the locations of the left peak of turbulent kinetic energy, the two-point spatial cross-correlation of swirling strength with velocity fluctuation and concentration fluctuation were calculated. All the correlation fields contain one positively correlated region and one negatively correlated region although the orientations of the correlation fields varied, due to the flow transitioning from wake, to jet, to channel flow. Finally, linear stochastic estimation was used to calculate conditional structures. The large-scale structures in the velocity field revealed by linear stochastic estimation are spindle-shaped with a titling stream-wise major axis.     

Cross-Stream Vorticity Field Induced by Streamwise Vortices in Unbounded and Wall-Bounded Shear Flows

This computational study examines the unsteady cross-stream vorticity structures that form when one or more streamwise vortices are immersed in homogeneous and boundary-layer shear flows. A quasi-two-dimensional limit is considered in which the velocity and vorticity fields, while still possessing three nonzero components, have vanishing gradient in the streamwise direction. This idealization is suitable to applications such as streamwise vortices that occur along a ship hull or airplane fuselage and it can be used as an idealized representation of the quasi-streamwise vortices in the near-wall region of a turbulent boundary layer. In this quasi-two-dimensional idealization, the streamwise velocity has no effect on the cross-stream velocity associated with the vortex. However, the vortex acts to modify the cross-stream vorticity component, resulting in regions of the flow with strong deviations in streamwise velocity. This paper examines the complex structures that form as the cross-stream vorticity field is wrapped up by the vortex and the effect of these structures on the streamwise velocity field, first for vortices immersed in homogeneous shear flow and then for vortices immersed in a boundary layer along a flat wall. Received 2 January 2002 and accepted 13 August 2002 Published online 3 December 2002 RID="*" ID="*" This project was supported by the Office of Naval Research under Grant Number N00014-01-1-0015. Dr. Thomas Swain is the program manager. Communicated by T.B. Gatski     

The effect of streamwise vortices on the turbulence structure of a separating boundary layer

A high Reynolds number flat plate turbulent boundary layer is investigated in a wind-tunnel experiment. The flow is subjected to an adverse pressure gradient which is strong enough to generate a weak separation bubble. This experimental study attempts to shed some new light on separation control by means of streamwise vortices with emphasize on the change in the boundary layer turbulence structure. In the present case, counter-rotating and initially non-equidistant streamwise vortices become and remain equidistant and confined within the boundary layer, contradictory to the prediction by inviscid theory. The viscous diffusion cause the vortices to grow, the swirling velocity component to decrease and the boundary layer to develop towards a two-dimensional state. At the position of the eliminated separation bubble the following changes in the turbulence structure were observed. The anisotropy state in the near-wall region is unchanged, which indicates that it is determined by the presence of the wall rather than the large scale vortices. However, the turbulence in the outer part of the boundary layer becomes overall more isotropic due to an increased wall-normal mixing and a significantly decreased production of streamwise fluctuations. The turbulent kinetic energy is decreased as a consequence of the latter. Despite the complete change in mean flow, the spatial turbulence structure and the anisotropy state, the process of transfer of turbulent kinetic energy to the spanwise fluctuating component seems to be unchanged. Local regions of anisotropy are strongly connected to maxima in the turbulent production. For example, at spanwise positions in between those of symmetry, the spanwise gradient of the streamwise velocity cause significant production of turbulent fluctuations. Transport of turbulence in the spanwise direction occurs in the same direction as the rotation of the vortices.     

Spanwise characteristics of the separated flow in a suddenly expanding duct

Summary The secondary flow due to the growth of the streamwise vortices near the side walls serves to diminish the spanwise uniformity of the time-mean flow properties. In the region adjacent to the side walls, momentum mixing is enhanced due to the existence of the secondary flow and the separated shear layer spreads faster. There is a corresponding increase in the non-coherent turbulence in this region near the side walls. The increased spreading rates and overall turbulence in the shear layer, in turn, tend to suppress the rolling-up of the separated shear layer into organized structures. This effect is rapidly carried into the core two-dimensional flow region as the streamwise vortex grows under the influence of the adverse pressure gradient. The surface visualizations provide further evidence of the existence of secondary flows near the side walls.     

3-D measurements of separated flow over rigid plates with spanwise periodic cambering at low Reynolds number

Measurements of the flow field around a flat plate and rigid plates with spanwise periodic cambering were performed using volumetric three-component velocimetry (V3V) at a Reynolds numbers of 28,000 at α=12° where the flow is fully separated. The Reynolds normal and shear stresses, and the streamwise, spanwise and normal components of the vorticity vector are investigated for three-dimensionality. Flow features are discussed in context of the periodic cambering and corresponding aerodynamic force measurements. The periodic cambering results in spanwise variation in the reversed-flow region, Reynolds stresses and spanwise vorticity. These spanwise variations are induced by streamwise and normal vortices of opposite directions of rotation. Moreover, measurements were carried out for the cambered plates at α=8°, where a long separation bubble exists, to further understand the behavior of the streamwise and normal vortices. These vortices become more organized and increase in strength and size at the lower angle of attack. It is also speculated that these vortices contribute to the increase in lift at and beyond the onset of stall angle of attack.     

Temporal development of turbulent boundary layers with embedded streamwise vortices

The interaction of streamwise vortices with turbulent boundary layer has been investigated using large-eddy simulation. The initial conditions are a pair of counterrotating Oseen vortices with flow between them directed toward the wall (common-flow-down), superimposed on various instantaneous realizations of a turbulent boundary layer. The time development of the vortices and their interaction with the boundary layer are studied by integrating the filtered Navier-Stokes equations in time. The most important effects of the vortices on the boundary layer are the thinning of the boundary layer between vortices (downwash region) and the thickening of the boundary layer in the upwash region. The vortices first move toward the wall as a result of the self-induced velocity, and then apart from each other because of the image vortices due to the solid wall. The Reynolds stress profiles highlight the highly three-dimensional structure of the turbulent boundary layer modified by the vortices. The presence of significant turbulent activity near the vortex center and in the upwash region suggests that localized instability mechanisms in addition to the convection of turbulent energy by the secondary flow are responsible for this effect. High levels of turbulent kinetic energy and secondary stresses in the vicinity of the vortex center are also observed. The numerical results show good agreement with experimental results.This work was supported by the Office of Naval Research under Grant N00014-89-J-1638. Computer time was supplied by the San Diego Supercomputing Center.     

Streamwise streaks and secondary instability in a two-dimensional bent channel

Streamwise streaks generated from a pair of oblique waves and secondary instability of the streaks are studied in a two-dimensional bent channel. Nonlinear parabolized stability equations (NPSE) are employed to investigate streamwise streaks and vortices. A pair of oblique waves from linear stability analysis is imposed as initial disturbances. Generation of streamwise streaks and vortices and subsequent development are described in detail. The case of plane channel is also studied to provide comparable data. Through comparison, the effect of bent region is clearly highlighted. Results of parametric studies to examine the effect of Reynolds number, radius of curvature, and bent angle are also given and discussed in detail. Secondary instability analysis for the modified mean flow due to the streamwise streaks is carried out by solving a two-dimensional eigenvalue problem. Several unstable modes which can be classified into fundamental and subharmonic mode of secondary instability are identified. Among several unstable modes, two modes are turned out to be dominant modes. Details on these two modes including generation mechanism, typical pattern, and dependency on wave number and streak amplitude are discussed. It is found that the presence of bent channel can lead to early oblique-mode breakdown via strong growth of the streamwise streaks due to the curved section. Such large amplitude of streaks and its secondary instability eventually could trigger transition even for small amplitude oblique waves at subcritical channel Reynolds numbers.     

不定原点喷嘴射流中流体物理的实验研究(英文)

为了能够更好地了解不定源喷嘴(indeterminate origin nozzle)射流中的物理过程,本文应用平面激光诱导荧光技术对一个大尺度的水射流进行了实验研究。流场显示的实验结果表明不定源喷嘴在射流的剪切层引入了蘑菇形反向旋转的涡对。这些涡的矢量方向与射流方向相同或相反,被称为流向涡(streamwise vortex)。由于射流中存在开尔文-亥姆霍兹不稳定,每当一个横向涡(spanwise vortex,即涡的矢量方向与射流方向垂直)从喷嘴脱流时会产生瞬时的低压,该瞬时低压促使向内发展的流向涡对在喷嘴的凹槽处生成。这些涡对在向下游流动的过程中会重组并在喷嘴的尖峰面生成向外发展的涡对。这些流向涡极大地影响了射流的发展。流向涡与横向涡的相互作用促使射流更早地发展成为湍流。由于流向涡同时也在射流中引入了径向的剪切流动,因此导致了更多的湍流生成从而增强了射流与周围流体的混合。     

不定原点喷嘴射流中流体物理的实验研究

为了能够更好地了解不定源喷嘴（indeterminate origin nozzle）射流中的物理过程，本文应用平面激光诱导荧光技术对一个大尺度的水射流进行了实验研究。流场显示的实验结果表明不定源喷嘴在射流的剪切层引入了蘑菇形反向旋转的涡对。这些涡的矢量方向与射流方向相同或相反，被称为流向涡（streamwise vortex）。由于射流中存在开尔文一亥姆霍兹不稳定，每当一个横向涡（spanwisevortex，即涡的矢量方向与射流方向垂直）从喷嘴脱流时会产生瞬时的低压，该瞬时低压促使向内发展的流向涡对在喷嘴的凹槽处生成。这些涡对在向下游流动的过程中会重组并在喷嘴的尖峰面生成向外发展的涡对。这些流向涡极大地影响了射流的发展。流向涡与横向涡的相互作用促使射流更早地发展成为湍流。由于流向涡同时也在射流中引入了径向的剪切流动，因此导致了更多的湍流生成从而增强了射流与周围流体的混合。     

Effect of perforation on flow past a conic cylinder at $${\varvec{Re}}~=~100$$: wavy vortex and sign laws

In order to find the intrinsic physical mechanism of the original Kármán vortex wavily distorted across the span due to the introduction of three-dimensional (3-D) geometric disturbances, a flow past a peak-perforated conic shroud is numerically simulated at a Reynolds number of 100. Based on previous work by Meiburg and Lasheras (1988), the streamwise and vertical interactions with spanwise vortices are introduced and analyzed. Then vortex-shedding patterns in the near wake for different flow regimes are reinspected and illustrated from the view of these two interactions. Generally, in regime I, spanwise vortices are a little distorted due to the weak interaction. Then in regime II, spanwise vortices, even though curved obviously, are still shed synchronously with moderate streamwise and vertical interactions. But in regime III, violently wavy spanwise vortices in some vortex-shedding patterns, typically an \(\Omega \)-type vortex, are mainly attributed to the strong vertical interactions, while other cases, such as multiple vortex-shedding patterns in sub-regime III-D, are resulted from complex streamwise and vertical interactions. A special phenomenon, spacial distribution of streamwise and vertical components of vorticity with specific signs in the near wake, is analyzed based on two models of streamwise and vertical vortices in explaining physical reasons of top and bottom shear layers wavily varied across the span. Then these two models and above two interactions are unified. Finally two sign laws are summarized: the first sign law for streamwise and vertical components of vorticity is positive in the upper shear layer, but negative in the lower shear layer, while the second sign law for three vorticity components is always negative in the wake.     

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES) method at a Reynolds number Re = 8 500. The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric. The proper orthogonal decomposition(POD) analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1% of the turbulent kinetic energy, and hence their impact on the wake dynamics is studied. The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point. The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction. In addition, the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.     

Numerical simulation on evolution of subharmonic low-speed streaks in minimal channel turbulent flow

The evolution of low-speed streaks in the turbulent boundary layer of the minimum channel flow unit at a low Reynolds number is simulated by the direct numer- ical simulation （DNS） based on the standard Fourier-Chebyshev spectral method. The subharmonic sinuous （SS） mode for two spanwise-aligned low-speed streaks is excited by imposing the initial perturbations. The possibilities and the physical realities of the turbulent sustaining in the minimal channel unit are examined. Based on such a flow field environment, the evolution of the low-speed streaks during a cycle of turbulent sus- taining, including lift-up, oscillation, and breakdown, is investigated. The development of streamwise vortices and the dynamics of vortex structures are examined. The results show that the vortices generated from the same streak are staggered along the streamwise direction, while the vortices induced by different streaks tilt toward the normal direction due to the mutual induction effect. It is the spatial variations of the streamwise vortices that cause the lift-up of the streaks. By resolving the transport dynamics of enstrophy, the strength of the vortices is found to continuously grow in the logarithmic layer through the vortex stretching mechanism during the evolution of streaks. The enhancement of the vortices contributes to the spanwise oscillation and the following breakdown of the low-speed streaks.     

Effect of Small Bluntness on Formation of Görtler Vortices in a Supersonic Compression Corner Flow

The influence of small cylindrical bluntness of the leading edge of a flat plate on formation of spatial structures in a nominally two-dimensional supersonic compression corner flow at the Mach number M∞ ≈ 8 and a laminar state of the undisturbed boundary layer is studied by the method of temperature-sensitive paints. Streamwise vortices are found in the region of reattachment of the separated flow in a wide range of Reynolds numbers (0.15 · 10⁶–2.55 · 10⁶) for various angles of flow deflection and plate lengths. It is demonstrated that the existence of these vortices induces spanwise oscillations of the heat transfer coefficient; the amplitude of these oscillations may reach 30%. The maximum deviations of the Stanton number reaching 80% are observed in the case with significant roughness of the leading edge of the flat plate. Both the maximum Stanton numbers in the reattachment region and the amplitude of spanwise oscillations of the Stanton number induced by streamwise vortices are found to decrease significantly in the case of small bluntness of the leading edge. Solutions of three-dimensional Navier–Stokes equations are obtained for some test conditions. The computed results are in good agreement with experimental data, which points to a significant stabilizing effect of small bluntness on the intensity of streamwise vortices.     

Interaction between longitudinal vortices and flat plate boundary layer

The interaction between longitudinal vortices and flat plate boundary layer has been studied numerically for both laminar and turbulent flow situations. The vortices are assumed to be placed in an otherwise two-dimensional boundary layer flow. The flow is assumed to be incompressible and steady. Considering the fact that the velocity, vorticity and temperature gradients in the transverse directions are much larger than the longitudinal (streamwise) gradients for these flows, the original Navier Stokes equations are parabolized in the streamwise direction. A simple model, based on Boussinesq hypothesis, is used for turbulent flow. The discretized equations are then solved step by step in the streamwise direction, using an iterative procedure at each station. Numerical solutions have been obtained for different parameters, such as the Reynolds number, the circulation and the initial position of the vortices. The computed flow patterns and the skin friction coefficient and Stanton number are found to be qualitatively consistent with available experimental results. It is shown that the interaction between the vortices and the boundary layer may severely disturb the boundary layer flow field and thus considerably increase the local skin friction and heat transfer rate on surface of an aircraft.     

The Relaminarization Mechanisms of Turbulent Channel Flow at Low Reynolds Numbers

The mechanisms of laminarization in wall-bounded flows have been investigated by performing direct numerical simulations (DNS) of turbulent channel flows. By decreasing Reynolds numbers systematically, the effects of the low Reynolds number are studied in connection with the near-wall turbulent structure and turbulent statistics. At approximately the critical Reynolds number, the turbulent skin friction is reduced, and the turbulent structure changes qualitatively in the very near-wall region. Instantaneous turbulent structures reveal that streamwise vortices, the cores of which are at y+ 10, disappear, although low speed streaks and Reynolds shear stress are still produced by larger streamwise vortices located in the buffer region y+ > 10. Sweep motions induced by these vortical structures are shifted toward the center of a channel and also significantly deterred, which may heighten the effects of the viscous sublayer over most of the channel section and suppress the regeneration mechanisms of new streamwise vortices in the very near-wall region. To investigate the details of how large-scale coherent vortices affect the viscous sublayer and the relevant small-scale streamwise vortices, a body force is virtually imposed in the wall-normal direction to enhance the large streamwise vortices. As a result, it is found that when they are sufficiently enhanced, the small-scale vortices reappear, and the sweep events are again dominant in the viscous sublayer.     

NUMERICAL RESEARCH ON THE COHERENT STRUCTURES IN A MIXING LAYER WITH CROSS-SHEAR

The evolution of a time-developing mixing layer with cross-shear is simulated numerically using a pseudo-spectral method. The results indicate that stretching by the rollers is responsible for the formation of the streamwise vortices in a mixing layer with cross-shear. When the cross-shear is relatively strong (such as θ=20°), the co-rotating streamwise vortices related to the early spanwise Kelvin–Helmholtz instability are intensified rapidly by stretching and collapse into rib-shaped vortices, which are very similar to the ribs in a plane mixing layer. Atθ =20°, the vortex corresponding to the “quadrupole” in a plane mixing layer is also observed in the core region, and a set of streamwise vortices with signs opposite to those of the vortices containing the ribs lie at the spanwise braid region. The counterparts of the ribs, however, are of flat shape and much weaker. When θ is up to 30°, the ribs are so strong that their counterparts cannot develop. When θ is down to 10°, the symmetry of the streamwise vortices is more obvious, but the ribs do not form. Additionally, it is revealed that the introduction of the strong cross-shear results in enhanced mixing compared to a two-dimensional mixing layer.     

Numerical studies on evolution of secondary streamwise vortices in transitional boundary layers

Formation and evolution of secondary streamwise vortices in the compressible transitional boundary layers over a flat plate are studied using a direct numerical simulation method with high-order accuracy and highly effective non-reflecting characteristic boundary conditions. Generation and development processes of the secondary streamwise vortices in the complicated transitional boundary flow are clearly analyzed based on the of numerical results, and the effects on the formation of the ring-like vortex that is vital to the boundary layer transition are explored. A new mechanism forming the ring-like vortex through the mutual effect of the primary and secondary streamwise vortices is expressed.     

Mechanism of transverse structure formation in supersonic flow past a body

Direct numerical simulation within the framework of the Navier-Stokes equations is applied to study the mechanism of the generation of transverse structures (streamwise vortices) in the problem of supersonic M = 6 flow over a flat plate, when a shock wave is incident on it. The vortices formed at the lateral edges of the plate are shown to be the sources of streamwise streaky structures in the zone of separation of the boundary layer from the plate. Their interaction with the Kelvin-Helmholtz vortices in the region of incidence of the shock on the plate leads to the formation of mushroom-shaped structures (streamwise vortices) similar with the azimuthal Λ-structures in subsonic jets. The plate width effect on the formation and turbulization of the mushroom-shaped structures is considered.