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.     

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.     

Flow field investigation in rotating rib-roughened channel by means of particle image velocimetry

The turbulent velocity field over the rib-roughened wall of an orthogonally rotating channel is investigated by means of two-dimensional particle image velocimetry (PIV). The flow direction is outward, with a bulk Reynolds number of 1.5 × 10⁴ and a rotation number ranging from 0.3 to 0.38. The measurements are obtained along the wall-normal/streamwise plane at mid-span. The PIV system rotates with the channel, allowing to measure directly the relative flow velocity with high spatial resolution. Coriolis forces affect the stability of the boundary layer and free shear layer. Due to the different levels of shear layer entrainment, the reattachment point is moved downstream (upstream) under stabilizing (destabilizing) rotation, with respect to the stationary case. Further increase in rotation number pushes further the reattachment point in stabilizing rotation, but does not change the recirculation length in destabilizing rotation. Turbulent activity is inhibited along the leading wall, both in the boundary layer and in the separated shear layer; the opposite is true along the trailing wall. Coriolis forces affect indirectly the production of turbulent kinetic energy via the Reynolds shear stresses and the mean shear. Two-point correlation is used to characterize the coherent motion of the separated shear layer. Destabilizing rotation is found to promote large-scale coherent motions and accordingly leads to larger integral length scales; on the other hand, the spanwise vortices created in the separating shear layer downstream of the rib are less organized and tend to be disrupted by the three-dimensional turbulence promoted by the rotation. The latter observation is consistent with the distributions of span-wise vortices detected in instantaneous flow realizations.     

Spatio-temporal analysis of the turbulent flow in a ribbed channel

The turbulent flow in a channel with transverse ribs over one wall is studied experimentally. The height of the obstacles is about one tenth of the channel height, and the spacing is 10 times their height. The Reynolds number based on the channel hydraulic diameter and bulk flow velocity is 15,000. Velocity fields are obtained with high spatial and temporal resolution along the streamwise/wall-normal plane by means of time-resolved particle image velocimetry. Beside mean velocity and Reynolds stresses, the flow is investigated through two-point correlations, distributions of spanwise-swirling events, space–time velocity diagrams and power spectral density. Although the separated flow reattaches before the following obstacle is approached, a strong rib-to-rib interaction occurs. Spanwise vortices, 0.2 rib heights in size, are generated in the free shear layer, travel across the whole pitch, and may impact on the next rib. The large scale motions triggered by the separation grow in size until they reach the following obstacle. Flapping of the separated shear layer is observed at frequencies consistent with previous studies, causing the instantaneous reattachment point to fluctuate. The flapping initiates at the downstream edge of the obstacle tip, rather than at the upstream edge where the instantaneous separation occurs.     

The effect of aspect ratio on the flow over a rearward-facing step

In this study, we investigate the effect of the spanwise width on the mixing layer behind a rearward-facing step. Results for aspect ratios (tunnel width/step height) of 10 and 4 and Reynolds numbers of 11,000 and 5,000 are presented. A frequency shifted, single component LDV system was used to obtain mean streamwise velocity profiles, turbulence intensity profiles, and normal velocity spectra at four streamwise and three spanwise positions for each test case. The mean velocity and turbulence intensity profiles are constant across the width of the test section for either of the Reynolds numbers considered, but there are significant differences among the cases studied. At a distance greater than three step heights down-stream of the step, the peak turbulence intensity is greater for higher aspect ratio and is relatively insensitive to Reynolds number. The peak frequency is lower and the spectrum is narrower for a higher aspect ratio in the region near the step.     

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.     

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.     

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.     

Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

Direct numerical simulation of turbulent flow in a spanwise rotating square duct at high rotation numbers

In this paper, direct numerical simulations have been performed to study the effects of Coriolis force on the turbulent flow field confined within a square duct subjected to spanwise system rotations at high rotation numbers. In response to the system rotation, secondary flows appear as large streamwise counter-rotating vortices, which interact intensely with the four boundary layers and have a significant impact on flow statistics, velocity spectra and coherent structures. It is observed that at sufficiently high rotation numbers, a Taylor–Proudman region appears and complete laminarization is almost reached near the top and side walls. The influence of large organized secondary flows on the production rate and re-distribution of turbulent kinetic energy has been investigated through a spectral analysis. It is observed that the Coriolis force dominates the transport of Reynolds stresses and turbulent kinetic energy, and forces the spectra of streamwise and vertical velocities to synchronize within a wide range of scales.     

Velocity measurements of streamwise roll cells in rotating plane Couette flow

For the first time, quantitative velocity measurements in rotating plane Couette flow are demonstrated. Particle image velocimetry is used at a low Reynolds number with anti-cyclonic, i.e. destabilising rotation, where the instability is expected to give rise to steady streamwise-oriented roll cells. The streamwise and spanwise velocities of the roll cells were measured on the centreplane of the flow and at two planes on either side. The streamwise velocity is spanwise periodic with an amplitude variation approximately ±42 % of half the velocity difference between the moving walls. The wall-normal velocity was estimated by assuming steady, laminar and streamwise-independent flow. Despite the large amplitude of the disturbance, both the spanwise wave length and amplitude ratio between the streamwise and wall-normal components were close to what is obtained from linear theory. A splitting event of a roll cell was also captured by the velocity measurements and its development followed in time.     

Control of a three-dimensional turbulent shear layer by means of oblique vortices

The effect of local forcing on the separated, three-dimensional shear layer downstream of a backward-facing step is investigated by means of large-eddy simulation for a Reynolds number based on the step height of 10,700. The step edge is either oriented normal to the approaching turbulent boundary layer or swept at an angle of \(40^\circ \). Oblique vortices with different orientation and spacing are generated by wavelike suction and blowing of fluid through an edge parallel slot. The vortices exhibit a complex three-dimensional structure, but they can be characterized by a wavevector in a horizontal section plane. In order to determine the step-normal component of the wavevector, a method is developed based on phase averages. The dependence of the wavevector on the forcing parameters can be described in terms of a dispersion relation, the structure of which indicates that the disturbances are mainly convected through the fluid. The introduced vortices reduce the size of the recirculation region by up to 38%. In both the planar and the swept case, the most efficient of the studied forcings consists of vortices which propagate in a direction that deviates by more than \(50^\circ \) from the step normal. These vortices exhibit a spacing in the order of 2.5 step heights. The upstream shift of the reattachment line can be explained by increased mixing and momentum transport inside the shear layer which is reflected in high levels of the Reynolds shear stress \(-\rho \overline{u'v'}\). The position of the maximum of the coherent shear stress is found to depend linearly on the wavelength, similar to two-dimensional free shear layers.     

Experimental Investigation of Three-Dimensional Vortex Structures Downstream of Vortex Generators Over a Backward-Facing Step

An experimental investigation of vortex generators has been carried out in turbulent backward-facing step (BFS) flow. The Reynolds number, based on a freestream velocity U₀ = 10 m/s and a step height h = 30 mm, was Re_h = 2.0 × 10⁴. Low-profile wedge-type vortex generators (VGs) were implemented on the horizontal surface upstream of the step. High-resolution planar particle image velocimetry (2D-2C PIV) was used to measure the separated shear layer, recirculation region and reattachment area downstream of the BFS in a single field of view. Besides, time-resolved tomographic particle image velocimetry (TR-Tomo-PIV) was also employed to measure the flow flied of the turbulent shear layer downstream of the BFS within a three-dimensional volume of 50 × 50 × 10 mm³ at a sampling frequency of 1 kHz. The flow control result shows that time-averaged reattachment length downstream of the BFS is reduced by 29.1 % due to the application of the VGs. Meanwhile, the Reynolds shear stress downstream of the VGs is considerably increased. Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) have been applied to the 3D velocity vector fields to analyze the complex vortex structures in the spatial and temporal approaches, respectively. A coherent bandwidth of Strouhal number 0.3 < St_h < 0.6 is found in the VG-induced vortices, and moreover, Λ-shaped three-dimensional vortex structures at St_h = 0.37 are revealed in the energy and dynamic approaches complementarily.     

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     

Experimental Investigation of Separated Shear Flow under Subharmonic Perturbations over a Backward-Facing Step

Subharmonic-perturbed shear flow downstream of a two-dimensional backward-facing step was experimentally investigated. The Reynolds number was Re_h = 2.0 ×10⁴, based on free-stream velocity and step height. Planar 2D-2C particle image velocimetry was employed to measure the separating and reattaching flow in the horizontal-vertical plane in the center position. The subharmonic perturbations were generated by an oscillating flap which was implemented over the step edge and driven by periodic Ampere force. The subharmonic frequency was 55 Hz as the half of the fundamental frequency of the turbulent shear layer. As a result of the subharmonic perturbations, the size of recirculation region behind the backward-facing step is reduced and the time-averaged reattachment length is 31.0% shorter than that of the natural flow. The evolution of vortices, including vortex roll-up, growth and breakdown process, is analyzed by using phase-averaging, cross-correlation function and proper orthogonal decomposition. It is found that Reynolds shear stress is considerably increased in which the vortices roll up and then break down further downstream. In particular, rapid growth of vortices based on the “step mode” occurs at approximate half of the recirculation region, caused by in interaction between the shear layer and the recirculation region. Furthermore, the coherent structures, which are represented by a phase-correlated POD mode pair, are reconstructed in phases in order to show regular patterns of the subharmonic-perturbed coherent structures.     

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).     

Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow

Using a three-dimensional (3-D) particle-tracking velocimeter, detailed turbulent flow measurements were made in a plane channel with a one-sided 50% abrupt expansion, which acted as a backward-facing step. The turbulent channel flow reached a fully developed state well upstream of the step. The Reynolds number based on the upstream centerline velocity and the step height H was 5540. With the mean reattachment point located at 6.51H downstream of the step, the measurement region ranged from −2H upstream to 12H downstream of the step. Various turbulent statistics and the energy budget were calculated from numerous instantaneous vector distributions. As in previous experimental investigations, the Reynolds normal and shear stresses had maximum values upstream of the reattachment. The stress anisotropy tensor revealed a peculiar phenomenon near the reattachment wall, wherein the spanwise normal stress was the largest among the three normal stresses. The triple velocity correlations indicated large values in the separating shear layer, and hence the turbulent diffusion was a major term in the energy budget. Comparison was made between the present results and those of the direct numerical simulation (DNS) of Le et al. (1993), and it was found that the mean and fluctuating velocities, the Reynolds shear stress, and the turbulent energy budget were in excellent agreement, although there was a considerable difference in the inflow conditions.     

Coherent structures and riblets

This work deals with the effect of the riblets on the coherent structures near the wall. The emphasis is put on the genesis of the quasi-streamwise vortices in the presence of the riblets. The quasi-streamwise vortices regenerate by the tilting of wall normal vorticity induced by prevailing structures. This requires a mechanism which leads to a temporal streamwise dependence near the elongated flow structures and to a subsequent formation of new wall normal vorticity. It is suggested here that the action of existing quasi-streamwise vortices on the sidewalls of wall normal vorticity may create a local, streamwise dependent spanwise velocity and therefore, a secondary wall normal vorticity field. A preliminary analysis of the set-up and the time and space development of this secondary three-dimensional flow associated with the regeneration mechanism, is given. An attempt is made, in order to explain the drag reduction performed by the riblets through an intermittent model, based on the protrusion height. Logical estimates of the amount of drag reduction are obtained. The differences between the mechanism suggested here and those based on forced control experiments are also discussed.     

Streamwise evolution of an inclined cylinder wake

The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity components using an eight-hotwire vorticity probe in a wind tunnel at a Reynolds number Re_d of 7,200 based on free stream velocity (U _∞) and cylinder diameter (d). The measurements were conducted at four different inclination angles (α), namely 0°, 15°, 30°, and 45° and at three downstream locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of α on the three coherent vorticity components are negligibly small for α ≤ 15°. When α increases further to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing α. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger α. This is because the streamwise spacing between the spanwise vortices is bigger for a larger α, resulting in a weak interaction between the vortices and hence slower decaying rate in the streamwise direction. For all tested α, the coherent contribution to [`(v<sup>2</sup>)] \overline{{v^{2}}} is remarkable at x/d = 10 and 20 and significantly larger than that to [`(u²)] \overline{{u^{2}}} and [`(w<sup>2</sup>)]. \overline{{w^{2}}}. This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to [`(u²)] \overline{{u^{2}}} and [`(v²)] \overline{{v^{2}}} decays slower as moving downstream for a larger α, consistent with the slow decay of the coherent spanwise vorticity for a larger α.     

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.