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.     

Turbulent flow over a rough backward-facing step

This work characterizes the impacts of the realistic roughness due to deposition of foreign materials on the turbulent flows at surface transition from elevated rough-wall to smooth-wall. High resolution PIV measurements were performed in the streamwise-wall-normal (x–y) planes at two different spanwise positions in both smooth and rough backward-facing step flows. The experiment conditions were set at a Reynolds number of 3450 based on the free stream velocity U_∞ and the mean step height h, expansion ratio of 1.01, and the ratio of incoming boundary layer thickness to the step height, δ/h, of 8. The mean flow structures are observed to be modified by the roughness and they illustrate three-dimensional features in rough backward-facing step flows. The mean reattachment length X_r is significantly reduced by the roughness at one PIV measurement position while is slightly increased by the different roughness topography at the other measurement position. The mean velocity profiles at the reattachment point indicate that the studied roughness weakens the perturbation of the step to the incoming turbulent flow. Comparisons of Reynolds normal and shear stresses, productions of normal stresses, quadrant analysis of the instantaneous shear-stress contributing events, and mean spanwise vorticity reveal that the turbulence in the separated shear layer is reduced by the studied roughness. The results also indicate an earlier separation of the turbulent boundary layer over the current rough step, probably due to the adverse pressure gradient produced by the roughness topography even before the step.     

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.     

An experimental investigation of a large-scale structure of a two-dimensional backward-facing step by using advanced multi-point LDV

Measurements of spatio–temporal velocity fields at the separated shear layer and reattachment region of a two-dimensional backward-facing step flow are carried out simultaneously using a multi-point LDV. The objective of this paper is to clarify experimentally the structure of a large-scale structure of this flow field using a space and time correlation and conditional average. From the results of the correlation of the velocity fluctuation, the moving path of the vortex shedding from the separated shear layer to the reattachment region exhibits two patterns which it moves to near the wall region or the middle of the step height at the reattachment region. Especially, it moves to near the wall region when it grows larger in the separated shear layer. Moreover, the turbulence concerned with reattachment phenomenon transports from the reattachment region to a separated shear layer by recirculation flow. According to these transports of turbulence, a model for large-scale fluctuation is proposed as a self-excitation motion.     

Planar velocity measurements of a two-dimensional compressible wake

The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M_X=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.     

Reynolds number effects on a turbulent boundary layer with separation,reattachment, and recovery

The present paper addresses experimental studies of Reynolds number effects on a turbulent boundary layer with separation, reattachment, and recovery. A momentum thickness Reynolds number varies from 1,100 to 20,100 with a wind tunnel enclosed in a pressure vessel by varying the air density and wind tunnel speed. A custom-built, high-resolution laser Doppler anemometer provides fully resolved turbulence measurements over the full Reynolds number range. The experiments show that the mean flow is at most a very weak function of Reynolds number while turbulence quantities strongly depend on Reynolds number. Roller vortices are generated in the separated shear layer caused by the Kelvin–Helmholtz instability. Empirical Reynolds number scalings for the mean velocity and Reynolds stresses are proposed for the upstream boundary layer, the separated region, and the recovery region. The inflectional instability plays a critical role in the scaling in the separated region. The near-wall flow recovers quickly downstream of reattachment even if the outer layer is far from an equilibrium state. As a result, a stress equilibrium layer where a flat-plate boundary layer scaling is valid develops in the recovery region and grows outward moving downstream.     

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.     

An inclined wall jet: Mean flow characteristics and effects of acoustic excitation

 The mean velocity field of a 30° inclined wall jet has been investigated using both hot-wire and laser Doppler anemometry (LDA). Provided that the nozzle aspect ratio is greater than 30 and the inclined wall angle (β) is less than 50°, LDA measurements for various β show that the reattachment length is independent of the nozzle aspect ratio and the nozzle exit Reynolds number (in the range 6670–13,340). There is general agreement between the reattachment lengths determined by LDA and those determined using wall surface oil film visualisation technique. The role of coherent structures arising from initial instabilities of a 30° wall jet has been explored by hot-wire spectra measurements. Results indicate that the fundamental vortex roll-up frequency in both the inner and outer shear layer corresponds to a Strouhal number (based on nozzle exit momentum thickness and velocity) of 0.012. The spatial development of instabilities in the jet has been studied by introducing acoustic excitation at a frequency corresponding to the shear layer mode. The formation of the fundamental and its first subharmonic has been identified in the outer shear layer. However, the development of the first subharmonic in the inner shear layer has been severely suppressed. Distributions of mean velocities, turbulence intensities and Reynolds shear stress indicate that controlled acoustic excitation enhances the development of instabilities and promotes jet reattachment to the wall, resulting in a substantially reduced recirculation flow region. Received: 24 November 1998/Accepted: 24 August 1999     

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.     

Flow and heat transfer in the wake of a surface-mounted rib with a slit

An experimental study of flow and heat transfer downstream of a surface-mounted rib with a slit is reported. The open area ratios of the slit rib considered are 10, 20, 30, 40 and 50% with respect to the total projected rib area. Experiments were conducted in a wind tunnel, mostly at a hydraulic diameter based Reynolds number of 32,100. The surface Nusselt number distribution was determined by liquid crystal thermography. Results show that the slit inside the rib enhances heat transfer and reduces pressure penalty, with an optimum performance seen at an open area ratio of 20%. To explain this result, a qualitative picture of the flow field behind the rib was obtained by smoke visualization. Time averages and turbulent statistics of the velocity and temperature fluctuations were measured in detail, using hotwire anemometry and cold wire anemometry respectively. For open area ratios less than 30%, measurements show that the flow through the slit modifies the reattaching shear layer from the top of the rib. The resulting reattachment length is smaller, the peak in Nusselt number is higher, and the average heat transfer from the heated surface is enhanced. For the rib with an open area ratio greater than 40%, the lower portion behaves as an independent small rib with its own reattachment region. Simultaneously, the flow downstream of the upper rectangular part shows characteristics of vortex shedding. Thus, the size of the slit is seen to be an additional parameter that can be used to control heat transfer from the solid surface, in comparison to the solid rib.     

THE STRUCTURE OF TURBULENT SHEAR FLOW AROUND A TWO-DIMENSIONAL POROUS FENCE HAVING A BOTTOM GAP

The flow field behind porous fences of geometric porosity ε=38·5% with various bottom gaps (G) has been investigated using a hybrid PTV velocity field measurement technique. Four gap ratiosG /H=0·0, 0·1, 0·2 and 0·3 were tested in this study. One thousand instantaneous velocity vector fields in the x–y plane were consecutively measured for each gap ratio. The free-stream velocity was fixed at 10cm/s and the corresponding Reynolds number based on the fence height (H) was Re=2985. The results show that the gap ratio G/H=0·1 gives the best shelter effect among the four gap ratios tested in this study, having a small shelter parameter ψ in a large area behind the fence. As the gap ratio increases, the region of mean velocity reduction decreases and the lower shear layer developed from the bottom gap expands upward. From the spatial distributions of turbulence statistics including turbulence intensities, Reynolds shear stress and turbulent kinetic energy, the wake characteristics can be divided into two categories depending on the gap ratio. When the gap ratio is aboveG /H=0·2, the turbulence statistics have large values in the lower shear layer. For the gap ratio G/H≤0·1, however, the lower shear layer displays small turbulence-statistics values and approach those of the no-gap case (G/H=0) with increasing distance downstream. In the upper shear layer separated from the fence top, the turbulence statistics are nearly independent of the gap ratio.     

Flow visualization of supersonic laminar flow over a backward-facing step via NPLS

An experimental study on a supersonic laminar flow over a backward-facing step of 5 mm height was undertaken in a low-noise indraft wind tunnel. To investigate the fine structures of Ma = 3.0 and 3.8 laminar flow over a backward-facing step, nanotracer planar laser scattering was adopted for flow visualization. Flow structures, including supersonic laminar boundary layer, separation, reattachment, redeveloping turbulent boundary layer, expansion wave fan and reattachment shock, were revealed in the transient flow fields. In the Ma = 3.0 BFS (backward-facing step) flow, by measuring four typical regions, it could be found that the emergence of weak shock waves was related to the K–H (Kelvin–Helmholtz) vortex which appeared in the free shear layer and that the convergence of these waves into a reattachment shock was distinct. Based on large numbers of measurements, the structure of time-averaging flow field could be gained. Reattachment occurred at the location downstream from the step, about 7–7.5 h distance. After reattachment, the recovery boundary layer developed into turbulence quickly and its thickness increased at an angle of 4.6°. At the location of X = 14h, the redeveloping boundary layer was about ten times thicker than its original thickness, but it still had not changed into fully developed turbulence. However, in the Ma = 3.8 flow, the emergence of weak shock waves could be seen seldom, due to the decrease of expansion. The reattachment point was thought to be near X = 15h according to the averaging result. The reattachment shock was not legible, which meant the expansion and compression effects were not intensive.     

Low Reynolds number axisymmetric turbulent boundary layer on a cylinder

In the present study, an axisymmetric turbulent boundary layer growing on a cylinder is investigated experimentally using hot wire anemometry. The combined effects of transverse curvature as well as low Reynolds number on the mean and turbulent flow quantities are studied. The measurements include the mean velocity, turbulence intensity, skewness and flatness factors in addition to wall shear stress. The results are presented separately for the near wall region and the outer region using dimensionless parameters suitable for each case. They are also compared with the results available in the open literature.The present investigation revealed that the mean velocity in near wall region is similar to other simple turbulent flows (flat plate boundary layer, pipe and channel flows); but it differs in the logarithmic and outer regions. Further, for dimensionless moments of higher orders, such as skewness and flatness factors, the main effects of the low Reynolds number and the transverse curvature are present in the near wall region as well as the outer region.     

Turbulent mixed convection flow over a backward-facing step––the effect of the step heights

Effect of the backward-facing step heights on turbulent mixed convection flow along a vertical flat plate is examined experimentally. The step geometry consists of an adiabatic backward-facing step, an upstream wall and a downstream wall. Both the upstream and downstream walls are heated to a uniform and constant temperature. Laser–Doppler velocimeter and cold wire anemometer were used, respectively, to measure simultaneously the time-mean velocity and temperature distributions and their turbulent fluctuations. The experiment was carried out for step heights of 0, 11, and 22 mm, at a free stream air velocity, u_∞, of 0.41 m/s, and a temperature difference, ΔT, of 30 °C between the heated walls and the free stream air. The present results reveal that the turbulence intensity of the streamwise and transverse velocity fluctuations and the intensity of temperature fluctuations downstream of the step increase as the step height increases. Also, it was found that both the reattachment length and the heat transfer rate from the downstream heated wall increase with increasing step height.     

Free-stream turbulence effects on the instantaneous pressure and forces on cylinders of rectangular cross section

Simultaneous measurements of instantaneous pressure distributions on rectangular cylinders of length to height ratio(B/D) of 1.0, 2.5 and 3.0 in smooth nonturbulent and homogeneous turbulent flows were made and the data were analyzed by phase averaging and spectral analysis in addition to more conventional methods. The turbulence in the inflow stream is nearly homogeneous and isotropic with the intensity and the scale of 5% and 1.2-1.5 times the cylinder height, respectively. The main effects of the turbulence in the inflow free stream of this scale and intensity are to laterally move the separated shear flow off the upstream corners and cause intermittent reattachment on the side surfaces of cylinders of B/D of 2.5 and larger. For the cylinder with smaller B/D, the flow does not reattach with or without turbulence in the free stream, and the instantaneous surface pressure distributions fluctuate quite periodically at a frequency corresponding to the Strouhal frequency of the vortex shedding. The effects of the free-stream turbulence appear in the increased fluctuation on the front surface as buffeting due to the impinging turbulence. When the separated shear layers reattach due to the influence of the free-stream turbulence, the reattachment point moves intermittently, the pressure distributions downstream of the reattachment fluctuate periodically, and a mild peak is formed in the spectra at a frequency much larger than the Strouhal frequency.     

A turbulent plane offset jet with small offset ratio

 Mean velocities and turbulence characteristics of a turbulent plane offset jet with a small offset ratio of 2.125 have been studied using laser Doppler anemometry (LDA). Static pressure measurements highlight the importance of side plates in enhancing two-dimensionality of the jet. The spatial distributions of turbulence intensities and Reynolds shear stress show a high turbulence recirculating flow region close to the nozzle plate between the jet and the offset plate. The LDA results have been used to examine the capability of three different turbulence models (i.e. k–ɛ, RNG and Reynolds stress) in predicting the velocity field of this jet. While all three models are able to predict qualitatively the recirculation, converging and reattachment regions observed experimentally, the standard k–ɛ turbulence model predicts a reattachment length that best agrees with the experimentally determined value. Received: 11 September 1996/Accepted: 30 May 1997     

An experimental study of two flows through an axisymmetric sudden expansion

Two turbulent separated and reattaching flows produced by a sudden expansion in a pipe have been studied. The first was produced by a simple axisymmetric sudden enlargement from a nozzle of diameter 80 mm to a pipe of diameter 150 mm. The second was the flow at the same enlargement with the addition of a centerbody 90 mm downstream of the nozzle exit. Detailed measurements of velocity and skin friction (made primarily using pulsed wires) and of wall static pressure are presented. Without the centerbody the flow structure is similar to that observed in other sudden pipe expansions and over backward-facing steps. A turbulent free shear layer, bearing some similarity to that of a round jet, grows from separation and then reattaches to the pipe wall downstream. Reattachment is a comparatively gradual process, the shear layer approaching the wall at a glancing angle. The introduction of the centerbody causes the shear layer to curve towards the wall and reattach at a much steeper angle. Reattachment is much more rapid; gradients of skin friction and pressure along the wall are many times those without the centerbody. The high curvature of the shear layer strongly influences its turbulent structure, locally suppressing turbulence levels and reducing its growth rate.     

Experimental investigation of flow over a backward-facing step in proximity to a flexible wall

Turbulent flow between a flexible wall and a solid surface containing a backward-facing step (BFS) was investigated using digital particle image velocimetry and high-speed photography. Stationary sheet of paper under tension was positioned above the solid surface in proximity to the BFS. The incoming air flow emerged from a planar nozzle that was located in the solid wall upstream of the BFS. Flows corresponding to two values of the Reynolds number (3,000 and 3,600) based on the step height and the maximum flow velocity at the step location were characterized in terms of patterns of time-averaged velocity, out-of-plane vorticity, streamline topology, and turbulence statistics. In addition, paper sheet oscillation was characterized using high-speed photography. For the control case of a solid upper wall with the geometry that represented the time-averaged paper profile, hydrodynamic frequencies were characterized using unsteady pressure measurements. Frequencies of the natural vibration modes of the paper sheet were well separated from the hydrodynamic frequencies corresponding to the oscillations of the shear layer downstream of the BFS. As the inflow velocity increased, the paper sheet was pulled closer to the solid surface, which resulted in increased confinement of the incoming jet. The flow reattachment length calculated on the basis of time-averaged flow patterns increased with the increasing Reynolds number.     

The Effect of Sweep-Angle Variation on the Turbulence Structure in a Separated,Three-Dimensional Flow

A three-dimensional separated flow behind a swept, backward-facing step is investigated by means of DNS for Re _H = C _∞ H/ν = 3000 with the purpose to identify changes in the statistical turbulence structure due to a variation of the sweep angle α from 0° up to 60°. With increasing sweep angle, the near-wall turbulence structure inside the separation bubble and downstream of reattachment changes due to the presence of an edge-parallel mean flow component W. Turbulence production due to the spanwise shear ∂W/∂y at the wall becomes significant and competes with the processes caused by impingement of the separated shear-layer. Changes due to a sweep angle variation can be interpreted in terms of two competing velocity scales which control the global budget of turbulent kinetic energy: the step-normal component U _∞ = C _∞cosα throughout the separated flow region and the velocity difference C _∞ across the entire shear-layer downstream of reattachment. As a consequence, the significance of history effects for the development into a two-dimensional boundary layer decreases with increasing sweep angle. For α ≥50°, near-wall streaks tend to form inside the separated flow region. Received 7 November 2000 and accepted 9 July 2002 Published online 3 December 2002 RID="*" ID="*" Part of this work was funded by the Deutsche Forschungsgemeinschaft within Sfb 557. Computer time was provided by the Konrad-Zuse Zentrum (ZIB), Berlin. Communicated by R.D. Moser     

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.