Velocity statistics and flow structures observed in bypass transition using stereo PTV

It is known from smoke visualizations that in a transitional boundary layer subjected to free-stream turbulence, streaks appear and eventually break down to turbulence after wavy motions. In order to observe the streaky structures directly, a stereo particle-tracking velocimetry system using hydrogen bubbles in a water channel has been developed and validated against laser Doppler velocimetry. Mean flow statistics show good agreement with previous results. With the developed measurement system, the instantaneous spanwise distribution of the streamwise and wall-normal velocities can be measured fast enough to resolve the time development of the streaky structures. Measurements of instantaneous spanwise distributions of the streamwise and wall-normal velocity disturbances show strong negative correlation between the wall-normal and streamwise velocities in the streaks. Published online: 19 November 2002     

Bypass transition receptivity modes

The prediction of bypass transition remains an important problem in many engineering applications. This is largely because there is no suitable theoretical model for bypass transition and predictions are made using empirical models. This paper presents numerical results for the receptivity of a zero pressure gradient boundary layer subjected to simple freestream waveforms which are the constituent parts of a turbulent flow field. Significant receptivities are only obtained for a minority of freestream waveforms and these lead to two types of flow structure in the boundary layer. The first type of flow structure is essentially two dimensional in nature and consists of two rows of counter-rotating spanwise vortices and is induced by freestream waves of large normal and spanwise wavelength and streamwise wavelengths approximately equal to the boundary layer thickness. The second type of flow structure are the streamwise streaks frequently observed in flow visualisation experiments. These streaks are induced by freestream waves of long streamwise and normal wavelength and spanwise wavelengths in the range of 14.5-46 θ (1.7-5.4δ). The freestream waves can be formed of velocity components in any direction, however the boundary layer is most receptive to fluctuations that lie in a plane perpendicular to the streamwise direction. The overall receptivity to a full spectrum of waves typical of freestream turbulence is considered and is shown to have similar characteristics to those from experiments.     

On the etiology of shear layer vortices

In an effort to isolate the mechanism by which streamwise structures form in turbulent wall layers, evolution equations were derived for the streamwise velocity and vorticity perturbations about a mean turbulent fully developed channel flow. The stability of these equations, which take their most concise form when derived from the Generalized Lagrangian mean equations of Andrews and McIntyre, are studied assuming normal modes and infinitesimal disturbances. The resulting stability diagram yields, inter alia, the spanwise periodicity of the resulting structures, which we term shear layer vortices. If streaks are thought of as the footprints of these vortices, we then have a formal way of determining the spacing of streaks. The first three modes of instability are determined; at the first not just two vortices form per period, but four. It is also evident that an intense local shear layer forms about the plane in which the convection velocity equals the mean Eulerian velocity.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This work was supported in part by the U.S. Office of Naval Research under SRO IV Grant No. N00014-85-K-0172 and in part by the National Science Foundation Grant CTS-9008477.     

Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.     

Characterization of Turbulent Structures in a Transonic Backward-Facing Step Flow

A transonic backward-facing step flow, at a free stream Mach number of 0.8 and a Reynolds number of 1.86 × 10⁵ with respect to the step height, was investigated experimentally by means of planar and stereo Particle Image Velocimetry (PIV) measurements for multiple fields of view. The primary aim of this analysis is to examine whether the large temporal variations of the reattachment location is associated with the presence of large scale coherent flow structures. The mean flow reattaches ≈6.1±0.2 times the step height downstream of the step. This value fluctuates temporally as much as ±3 step heights. Measurements of the wake flow in horizontal planes show that the strong variations of the reattachment length are associated with spanwise variations of the streamwise velocity. Two-point correlations revealed large–scale coherent regions with a length of up to 7 step heights and a dominant spanwise wave-length of 1.5…2.5 step heights. Furthermore, close to the step large structures are found, which span more than 5 step heights in spanwise direction. The Reynolds stress distribution of the separated region strongly suggests that the initial streamwise momentum is transferred to the vertical component as well as to the spanwise component in comparable portions by the deformation of the initial Kelvin-Helmholtz vortices and the generation of secondary ones. As a result, the separated shear layer is characterized by eddies of various sizes and orientations. The mean flow field only shows the primary separation bubble and a secondary recirculation region. No stationary streamwise vortices could be found for the tested Reynolds number.     

Manipulation of the reverse-flow region downstream of a fence by spanwise vortices

The experimental investigation of a turbulent separated flow over a fence is presented. By introducing a periodic disturbance upstream of the separation region in front of the fence, the time averaged length of the separation region downstream of the fence was reduced by as much as 40%. Two types of flow manipulation were applied: an oscillating cross-flow with zero net mass-flux through a spanwise slot in the floor of the test section and a spanwise oriented, oscillating spoiler. The cross-flow was generated by a loudspeaker system connected to a chamber underneath the spanwise slot. Both types of flow manipulation generate spanwise vortices at the fence that convect into the region downstream of the fence where they enhance the mixing in the shear layer and reduce the time mean length of the reverse-flow region downstream of the fence. Velocity profiles phase averaged with respect to the forcing frequency and phase triggered flow visualisations show that the spanwise vortices cause the long reverse-flow region of the unmanipulated flow to break up into separate smaller regions. While the time mean length of the reverse-flow region is reduced in the manipulated case, the length of the region where instantaneous reverse-flow occurs is not changed. The data presented include wall pulsed-wire measurements of the wall shear-stress and its turbulent fluctuations, and LDA measurements of the streamwise and the wall-normal velocity components and turbulent stresses.     

Maintenance of Oscillations in Three-Dimensional Traveling Waves in Plane Poiseuille Flows

Two solutions of three-dimensional Navier–Stokes equations are studied numerically. These solutions describe the fluid motion in a plane channel, are of the traveling-wave form, and are periodic in the streamwise and spanwise directions. It is shown that, in each solution, the oscillations arise as a result of linear instability in the streamwise averaged velocity field. This instability is due to the existence of streamwise streaks known as the regions where the velocity is higher or lower than the mean velocity. A mechanism for the maintenance of streamwise vortices causing the formation of streaks is revealed. The obtained results confirm and extend the existing knowledge about the mechanism for the formation of near-wall turbulent structures.     

PIV measurements of the near-wake behind a sinusoidal cylinder

The three-dimensional near-wake structures behind a sinusoidal cylinder have been investigated using a particle image velocimetry (PIV) measurement technique at Re=3,000. The mean velocity fields and spatial distributions of ensemble-averaged turbulence statistics for flows around the sinusoidal and corresponding smooth cylinders were compared. The near-wake behind the sinusoidal cylinder exhibited pronounced spanwise periodic variations in the flow structure. Well-organized streamwise vortices with alternating positive and negative vorticity were observed along the span of the sinusoidal cylinder. They suppress the formation of the large-scale spanwise vortices and decrease the overall turbulent kinetic energy in the near-wake of the sinusoidal cylinder. The sinusoidal surface geometry significantly modifies the near-wake structure and strongly controls the three-dimensional vortices formed in the near-wake.     

Turbulence in a skewed three‐dimensional wall‐bounded shear flow: effect of mean vorticity on structure modification

Mean‐flow three‐dimensionalities affect both the turbulence level and the coherent flow structures in wall‐bounded shear flows. A tailor‐made flow configuration was designed to enable a thorough investigation of moderately and severely skewed channel flows. A unidirectional shear‐driven plane Couette flow was skewed by means of an imposed spanwise pressure gradient. Three different cases with 8°, 34°and 52°skewing were simulated numerically and the results compared with data from a purely two‐dimensional plane Couette flow. The resulting three‐dimensional flow field became statistically stationary and homogeneous in the streamwise and spanwise directions while the mean velocity vector V and the mean vorticity vector Ω remained parallel with the walls. Mean flow profiles were presented together with all components of the Reynolds stress tensor. The mean shear rate in the core region gradually increased with increasing skewing whereas the velocity fluctuations were enhanced in the spanwise direction and reduced in the streamwise direction. The Reynolds shear stress is known to be closely related to the coherent flow structures in the near‐wall region. The instantaneous and ensemble‐averaged flow structures were turned by the skewed mean flow. We demonstrated for the medium‐skewed case that the coherent structures should be examined in a coordinate system aligned with V to enable a sound interpretation of 3D effects. The conventional symmetry between Case 1 and Case 2 vortices was broken and Case 1 vortices turned out to be stronger than Case 2. This observation is in conflict with the common understanding on the basis of the spanwise (secondary) mean shear rate. A refined model was proposed to interpret the structure modifications in three‐dimensional wall‐flows. What matters is the orientation of the mean vorticity vector Ω relative to the vortex vorticity vector ω _v, that is, the sign of Ω · ω _v. In the present situation, Ω · ω _v > 0 for the Case 1 vortices causing a strengthening relative to the Case 2 vortices. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Large Eddy Simulation of boundary layer transition over an isolated ramp-type micro roughness element

Boundary layer transition over an isolated surface roughness element is investigated by means of numerical simulation. Large Eddy Simulation (LES) flow-modeling approach is employed to study flow characteristics and transition phenomenon past a roughness element immersed within an incoming developing boundary layer, at a height-based Reynolds number of 1170. LES numerical results are compared to experimental data from literature showing the time-averaged velocity distribution, the velocity fluctuation statistics and the instantaneous flow topology.Despite slight difference in the intensity of streamwise velocity fluctuations, the present LES results and experimental data show very good agreement. The mean flow visualization shows streamwise counter-rotating vortices pairs formation downstream of the obstacle. The primary pair induces an upwash motion and a momentum deficit that creates a Kelvin-Helmholtz type flow instability. The instantaneous flow topology reveals the formation of coherent K-H vortices downstream that produce turbulent fluctuations in the wake of the roughness element. These vortices are streched and lifted up when moving downstream. The velocity fluctuations results show that the onset of the turbulence is dominated by the energy transfer of large-scale vortices.     

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.     

Numerical study on evolution of subharmonic varicose low-speed streaks in turbulent channel flow

The evolution of two spanwise-aligned low-speed streaks in a wall turbulent flow, triggered by the instability of the subharmonic varicose (SV) mode, is studied by a direct numerical simulation (DNS) method in a small spatial-periodic channel. The results show that the SV low-speed streaks are self-sustained at the early stage, and then transform into subharmonic sinuous (SS) low-speed streaks. Initially, the streamwise vortex sheets are formed by shearing, and then evolve into zigzag vortex sheets due to the mutual induction. As the intensification of the SV low-speed streaks becomes prominent, the tilted streamwise vortex tubes and the V-like streamwise vortex tubes can be formed simultaneously by increasing \( + \frac{{\partial u}}{{\partial x}}\). When the SV low-speed streaks break down, new zigzag streamwise vortices will be generated, thus giving birth to the next sustaining cycle of the SV low-speed streaks. When the second breakdown happens, new secondary V-like streamwise vortices instead of zigzag streamwise vortices will be generated. Because of the sweep motion of the fluid induced by the secondary V-like streamwise vortices, each decayed low-speed streak can be divided into two parts, and each part combines with the part of another streak, finally leading to the formation of SS low-speed streaks.     

PIV investigation of flow behind surface mounted permeable ribs

The flow behind surface mounted permeable rib geometries, i.e. solid, slit, split-slit and inclined split-slit ribs have been studied using flow visualization and PIV (2-C and 3-C) technique in streamwise and cross-stream measurement planes. The objective behind this study is to understand the flow structures responsible for heat transfer/mixing enhancement with simultaneous pressure penalty reduction by permeable rib geometries. The Reynolds number based on the rib height has been set equal to 5,538 and the open area ratio of permeable ribs is equal to 20%. The permeable rib geometries have shorter reattachment length in comparison to the solid rib. The maximum 41% reduction in reattachment length is observed for the inclined split-slit rib. The splitter mounted inside the slit leads to two corner vortices behind it. The corner vortices drag the flow from the primary recirculation bubble region towards the rib resulting in drop of the reattachment length. Two horseshoe vortices are present in the flow through the slit at both sides of the splitter due to the upstream flow separation. The slit inclination moves these horseshoe vortices closer to the bottom wall. A film like flow through the slit is present near the downstream corner of the inclined split-slit rib. The spanwise velocity gradient due to the splitter leads to vorticity and turbulence enhancement by vortex stretching. The inclination of the slit and the use of a splitter inside the slit are two important design parameters responsible in generation of near-wall longitudinal vortices. The flow field behind permeable ribs is dominated by vortical structures with definable critical flow patterns, i.e. node, saddle and foci. These predominant swirling flow motions contribute to the mixing enhancement behind permeable rib geometries. On leave from Mechanical Engineering Department, IIT Kanpur, U.P. 208016, India     

Large Eddy Simulation of Separated Flow over a Two-dimensional Hump with and without Control by Means of a Synthetic Slot-jet

Large Eddy Simulations for two flows separating from a two-dimensional hump in a duct are reported and discussed. The flows differ through the presence or absence of a synthetic slot-jet injected in a sinusoidal manner, i.e. at zero net mass-flow rate, close to the location of separation and intended to reduce (“control”) the extent of the separated region. Results reported include instantaneous visualisations, pre-multiplied spectra, wall-pressure distributions, streamfunction fields and profiles of velocity and second moments. For both flows, agreement between the simulations and the experimental results is generally good, especially in respect of the overall control effectiveness of the synthetic jet, despite the use of an approximate wall treatment bridging the viscous sublayer. Proper Orthogonal Decomposition of the velocity field is used to study structural features, and this shows that the most energetic mode in the base flow is representative of large streamwise vortices in the separated region, while in the controlled flow, most of the energetically dominant modes are associated with large spanwise vortices.     

Near-wall structure of three-dimensional turbulent boundary layers

 Modifications to near-wall turbulent boundary layer structure with increased three-dimensionality have been investigated through the use of hydrogen bubble wire flow visualization. Results indicate that three-dimensionality does not influence the strength or sign of near-wall streamwise vortices. Increased three-dimensionality does stabilize the near-wall structure resulting in less ejection type activity. The spanwise spacing between low-speed streaks also decreased slightly with increased cross-flow. Received: 15 October 1996/Accepted: 2 April 1997     

The Effect of Pressure Gradient on Boundary Layer Receptivity

This paper presents numerical results for the receptivity of three laminar boundary layers with zero (ZPG), adverse (APG) and favourable (FPG) pressure gradients. Each boundary layer is subjected to a series of simple freestream waveforms which can be considered as constituent parts of either an isotropic or a non-isotropic turbulent freestream. Each freestream waveform has a single frequency in each spatial direction and is divided into two mutually perpendicular components. The first component has a zero spanwise velocity and hence lies in the streamwise normal plane whereas the second component lies in a plane which is perpendicular both to this plane and the spatial frequency vector. High boundary layer receptivities are only obtained for a minority of these waveforms and so only the resulting flow structures for these waveforms are considered in detail. The dominant flow structures are identified as either Tollmien Schlichting (T-S) waves or streaky structures. The streaky structures can be induced by both freestream components, but the response to the second component, which results in streamwise vortices in the freestream, is considerably stronger and occurs over a much larger streamwise frequency range. The boundary layer is only receptive to a relatively narrow band of spanwise wavelengths ranging from approximately one to four times the local boundary layer thickness. The APG leads to receptivities which are more than double those for the FPG case. The ratio of the freestream fluctuation streamwise wavelength to the distance from the plate leading edge is identified as an important influential parameter for receptivity leading to streaks. Significant T-S activity is only observed for APG, but is also detected for ZPG.     

Flow field analysis of a turbulent boundary layer over a riblet surface

The near-wall flow structures of a turbulent boundary layer over a riblet surface with semi-circular grooves were investigated experimentally for the cases of drag decreasing (s ⁺=25.2) and drag increasing (s ⁺=40.6). One thousand instantaneous velocity fields over riblets were measured using the velocity field measurement technique and compared with those above a smooth flat plate. The field of view was 6.75 × 6.75 mm² in physical dimension, containing two grooves. Those instantaneous velocity fields were ensemble averaged to get turbulent statistics including turbulent intensities and turbulent kinetic energy. To see the global flow structure qualitatively, flow visualization was also carried out using the synchronized smoke-wire technique under the same experimental conditions. For the case of drag decreasing (s ⁺=25.2), most of the streamwise vortices stay above the riblets, interacting with the riblet tips frequently. The riblet tips impede the spanwise movement of the streamwise vortices and induce secondary vortices. The normalized rms velocity fluctuations and turbulent kinetic energy are small near the riblet surface, compared with those over a smooth flat plate. Inside the riblet valleys, these are sufficiently small that the increased wetted surface area of the riblets can be compensated. In addition, in the outer region (y ⁺ > 30), these values are almost equal to or slightly smaller than those for the smooth plate. For the case of drag increasing (s ⁺=40.6), however, most of the streamwise vortices stay inside the riblet valleys and contact directly with the riblet surface. The high-speed down-wash flow penetrating into the riblet valley interacts actively with the wetted riblet surface and increases the skin friction. The rms velocity fluctuations and turbulent kinetic energy have larger values compared with those over a smooth flat plate. Received: 24 March 1999/Accepted: 10 March 2000     

The effect of boundary conditions by the side of the nozzle of a low Reynolds number jet

The near flow field of an axially symmetric water jet at Reynolds numbers from about 1,000 to 10,000 is investigated using laser-induced fluorescence (LIF), laser Doppler anemometry and particle tracking velocimetry. Spanwise and streamwise vortices are detected on the longitudinal plane and on cross-sections. Attention is focused onto the effects of rigid or free boundaries sideways to the nozzle outlet (no-slip or free-slip conditions), and particularly on the start up, growth and interaction of large vortical structures. On average, for the free-slip jet these structures develop more gradually and closer to the nozzle than for the no-slip jet; the local mixedness (derived from LIF measurements) is also higher for the free-slip case. Moreover, the measured velocity field decreases more slowly, with a longer potential core and a higher shear layer (momentum) thickness for the free-slip rather than for the no-slip conditions. The relation between spanwise and streamwise large-scale vortices is clarified by the observation that the ejection of fluid in cross-sections through streamwise vortices is coupled to the pairing of spanwise vortices on the longitudinal section.     

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.