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.     

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.     

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.     

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.     

Three-dimensional vortex wake structure of a flapping-wing micro aerial vehicle in forward flight configuration

The unsteady flow field past a backward-facing step in a rectangular duct is investigated by adopting time-resolved particle image velocimetry (PIV) in the Reynolds number range of 2,640–9,880 based on step height and the inlet average velocity. The PIV realizations are subjected to post-processing techniques, namely, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). At low Reynolds numbers, the second spatial POD modes indicate the presence of the shear layer mode, whereas this feature shifts to higher modes at higher Reynolds numbers. The corresponding temporal modes are Fourier-transformed to obtain the dominant frequency, whose Strouhal number corroborates the above observation. Short-time windows in the transverse velocity component along the shear layer are selected to investigate the temporal stability of the flow field by DMD to quantify the growth rate of the shear layer mode. The higher harmonics of this mode are also observed to grow, albeit at lesser rate. By relating to POD analysis, the most energetic structures were found to correspond to the unstable modes. The correlation between these unstable DMD modes and the Fourier-filtered flow fields for the same frequencies indicate better match for the lower operating Reynolds number case as compared to higher ones. The spatial stability analysis demonstrates the growth of the shear layer vortices, which is combined with the temporal stability analysis to evaluate the phase velocity of the identified shear layer structures. The calculated phase velocity magnitude of the shear layer is found to be reasonably below the local velocity as expected.     

Near-wall investigation of backward-facing step flows

The electrodiffusion technique has been used to investigate reattaching and recirculating flows behind a backward-facing step. The instantaneous wall shear rate vectors were determined using the current signals provided by a three-segment electrodiffusion probe. The near-wall extents of two counter-rotating recirculation zones located behind the step were determined under turbulent flow conditions in a water channel. The near-wall flow inside these recirculation zones was found to be very unsteady, with strong low-frequency fluctuations. The streamwise profiles of the wall shear stress were measured at several values of the Reynolds number and a high level of skin friction was obtained in the reverse-flow region. The strong dependence of the peak value of skin friction on the Reynolds number confirms the viscous-dominated character of the reverse flow appearing inside the recirculation zone. Received: 22 May 2000/Accepted: 28 March 2001     

Instability of the separated shear layer in flow past a cylinder: Forced excitation

The receptivity of the separated shear layer for Re = 300 flow past a cylinder is investigated by forced excitation via an unsteady inflow. In order to isolate the shear layer instability, a numerical experiment is set up that suppresses the primary wake instability. Computations are carried out for one half of the cylinder, in two dimensions. The flow past half a cylinder with steady inflow is found to be stable for Re = 300. However, an inlet flow with pulsatile perturbations, of amplitude 1% of the mean, results in the excitation of the shear layer mode. The frequency of the perturbation of the inlet flow determines the frequency associated with the shear layer vortices. For a certain range of forced frequencies the recirculation region undergoes a low‐frequency longitudinal contraction and expansion. An attempt is made to relate this instability to a global mode of the wake determined from a linear stability analysis. Interestingly, this phenomenon disappears when the outflow boundary of the computational domain is shifted sufficiently downstream. This study demonstrates the need of carefully investigating the effect of the location of outflow boundaries if the computational results indicate the presence of low‐frequency fluctuations. The effect of Re and amplitude of unsteadiness at the inlet are also presented. All computations have been carried out using a stabilized finite element formulation of the incompressible flow equations. Copyright © 2007 John Wiley & Sons, Ltd.     

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     

Control of backward-facing step flow using a flapping foil

The effect of oscillating a small foil in plunge on the reattachment of a separated shear layer in a two-dimensional backward-facing step flow has been studied using flow visualization and single component laser Doppler velocimetry (LDV) measurements. It has been shown that a jet instead of a wake is generated by the flapping action of the foil. Results indicate that this action induces strong mixing and entrainment when the foil is located within the recirculation flow region, thereby reducing the reattachment length by as much as 70%. Furthermore, it has been shown that the flapping foil is most effective in reducing the size of the separation zone when placed close to the wall and to the step. It is least effective when placed outside the separated shear layer or downstream of the reattachment zone. Received: 26 August 1999 / Accepted: 29 May 2001     

On the Interaction of Turbulent Shear Layers with Harmonic Perturbations

The problem of coherent perturbations in a turbulent shear layer is considered for the purpose of developing a mathematical model based on a triple decomposition that extracts the coherent components of random fluctuations. The governing equations for the mean and the coherent parts of flow are derived, assuming the eddy-viscosity equivalence for the random part of flow, and solved by iterations to provide a coupled solution of the problem as a whole. Calculations agree well with experimental data in the upstream part of the layer where the mean–coherent flow interaction is the most important. In this region, the interaction changes the mean flow velocity distribution in such a manner that the neutral stability curve is shifted upstream relative to its position in the undisturbed layer and the perturbation intensity decreases further downstream. Experiments show that the coherent waves suppress the turbulent Reynolds stress production downstream of this region, but the model fails to predict the layer spreading correctly probably due to an inadequate turbulence closure of the mean flow. For the case of a turbulent mixing layer, we suggest a new closure relation that takes into account this coherent-random interaction.     

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.     

Computational analysis and flow structure of a transitional separated-reattached flow over a surface mounted obstacle and a forward-facing step

Large-eddy simulation (LES) of transitional separating-reattaching flow on a two-dimensional square surface mounted obstacle and a forward facing step has been performed using a dynamic sub-grid scale model. The Reynolds number based on the uniform inlet velocity and the obstacle/step height is 4.5 × 10³. The mean LES results for both the obstacle and step flow compare reasonably well with the available experimental and DNS data.

The flow structures upstream of the surface-mounted obstacle (referred to hereafter as obstacle) and the forward-facing step (referred to hereafter as FFS) consist of unstable two-dimensional structures and coherent rib-shaped structures. These structures with the aid of 3D streamline visualisation strongly indicate that the upstream separation bubble is a closed one rather than an open one in the sense that there is little evidence to suggest that there is fluid injection from the upstream separation region into the downstream separated region for the two geometries. The spectra and time history for the velocities and pressure fields at locations immediately upstream of the obstacle and FFS (including the recirculation region) were analysed using both the Fourier and wavelet transforms and revealed the unsteady nature of the recirculation region upstream of the obstacle and FFS.

The transition process has been elucidated using both 2D and 3D flow visualisation of the flow. In both geometries (obstacle and FFS), the separated boundary layer downstream of the leading edge shows 2D nature and roll-up shortly downstream of the separation line leading to 2D K-H rolls to be shed from the leading edge. Coherent structures such as the λ-shaped and rib-like vortices commonly associated with a flat plate boundary layer and also found in the separated-reattached flow of a blunt leading edge plate aligned horizontally to a flow are not common in the separated-reattached flow over the obstacle and FFS.     

Large eddy simulation of flows after a bluff body: Coherent structures and mixing properties

This paper performs large eddy simulations (LES) to investigate coherent structures in the flows after the Sydney bluff-body burner, a circular bluff body with an orifice at its center. The simulations are validated by comparison to existing experimental data. The Q function method is used to visualize the instantaneous vortex structures. Three kinds of structures are found, a cylindrical shell structure in the outer shear layer, a ring structure and some hairpin-like structures in the inner shear layer. An eduction scheme is employed to investigate the coherent structures in this flow. Some large streaks constituted by counter-rotating vortices are found in the outer shear layer and some well-organized strong structures are found in the inner shear layer. Finally, the influences of coherent structures on scalar mixing are studied and it is shown that scalar in the recirculation region is transported outward by coherent structures.     

The structure and dynamics of reacting plane mixing layers

The reacting two-dimensional plane mixing layer has been studied in two configurations: a rearward facing step and a two-stream mixing layer. Observations have been made of the steady state behavior, and the unsteady behavior when the flow was forced by a specific acoustic frequency. The steady behavior of the mean properties of the reacting flows is similar to that of non-reacting free shear flows except for the global effects of thermodynamic property changes. The structure of these flows is qualitatively similar to that of non-reacting flows. Vortices form by the two-dimensional Kelvin-Helmholtz instability and grow by subharmonic combination until the mixing layer interacts with the walls. Entrainment is dominated by the two-dimensional vortex motion. Three-dimensional instabilities give rise to secondary vortices which are coherent over several Kelvin-Helmholtz structures and dominate the fine scale mixing process. The mixing transition corresponds to a loss of coherence in the layer. Unsteady behavior occurs when there are resonant interactions with the Kelvin-Helmholtz instability or the instability associated with the recirculation vortex in the rearward facing step flow. Modeling efforts are reported which show promise of simulating the essential features of plane mixing layers.A version of this paper was presented at the ASME Winter Annual Meeting of 1984 and printed in AMD-Vol. 66     

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.     

后台阶流动再附着过程的大涡模拟研究

应用自主开发的大涡模拟程序数值模拟研究了后台阶流动中再附着过程的演变。在流动几何参数不变情况下，给出了再附长度随雷诺数的变化规律，并与实验进行了比较，二者相符得比较好。在此基础上，给出了三种典型雷诺数下，后台阶流动的回流区特征。在湍流情况下，研究了突扩比对再附长度的影响，与实验结果吻合的比较好。详细讨论了湍流情况下大涡拟序结构的瞬时再附着过程。 这些研究结果对具有再附着现象的流动结构的工程应用具有指导意义。     

FLOW PAST TWO CYLINDERS IN TANDEM: INSTANTANEOUS AND AVERAGED FLOW STRUCTURE

A technique of high-image-density particle image velocimetry is employed to characterize the instantaneous and averaged patterns of velocity, vorticity and Reynolds stress due to flow past two cylinders in tandem. These features of the flow patterns are characterized in the gap region as a function of the distance between the cylinders. In turn, they are related to the patterns in the near-wake of the two-cylinder system. Along the gap between the cylinders, small-scale concentrations of vorticity are formed in the separated shear layers. These concentrations buffet the surface boundary layer on the downstream cylinder, and thereby influence the eventual shedding of large-scale vortices. Within the gap, the instantaneous structure of the recirculation zones can exhibit both symmetrical and asymmetrical patterns. In the near-wake of the downstream cylinder, the form of the vortex shedding, as well as the averaged patterns of the flow structure, are substantially altered, relative to the case of a single cylinder. The width of the near-wake, as represented by averaged patterns of vorticity, is substantially narrower and the magnitudes of the peak Reynolds stress are significantly attenuated. On the other hand, if the gap region is sufficiently large such that Kármán-like vortices form between the cylinders, the near-wake of the downstream cylinder shows distinctive patterns, and both the wake width and the magnitude of the Reynolds stresses become larger, relative to those at smaller gap width.     

Time resolved flow-field measurements of a turbulent mixing layer over a rectangular cavity

High Reynolds number, low Mach number, turbulent shear flow past a rectangular, shallow cavity has been experimentally investigated with the use of dual-camera cinematographic particle image velocimetry (CPIV). The CPIV had a 3 kHz sampling rate, which was sufficient to monitor the time evolution of large-scale vortices as they formed, evolved downstream and impinged on the downstream cavity wall. The time-averaged flow properties (velocity and vorticity fields, streamwise velocity profiles and momentum and vorticity thickness) were in agreement with previous cavity flow studies under similar operating conditions. The time-resolved results show that the separated shear layer quickly rolled-up and formed eddies immediately downstream of the separation point. The vortices convect downstream at approximately half the free-stream speed. Vorticity strength intermittency as the structures approach the downstream edge suggests an increase in the three-dimensionality of the flow. Time-resolved correlations reveal that the in-plane coherence of the vortices decays within 2–3 structure diameters, and quasi-periodic flow features are present with a vortex passage frequency of ~1 kHz. The power spectra of the vertical velocity fluctuations within the shear layer revealed a peak at a non-dimensional frequency corresponding to that predicted using linear, inviscid instability theory.     

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.     

Developing and fully developed turbulent flow in ribbed channels

Wall-mounted roughness features, such as ribs, are often placed along the walls of a channel to increase the convective surface area and to augment heat transfer and mixing by increasing turbulence. Depending on the relative roughness size and orientation, the ribs also have varying degrees of increased pressure losses. Designs that use ribs to promote heat transfer encompass the full range of having only a few streamwise ribs, which do not allow fully developed flow conditions, to multiple streamwise ribs, which do allow the flow to become fully developed. The majority of previous studies have focused on perturbing the geometry of the rib with little attention to the spatially and temporally varying flow characteristics and their dependence on the Reynolds number. A staggered rib-roughened channel study was performed using time-resolved digital particle image velocimetry (TRDPIV). Both the developing (entry region) and a fully developed region were interrogated for three Reynolds numbers of 2,500, 10,000, and 20,000. The results indicate that the flow was more sensitive to Reynolds number at the inlet than within the fully developed region. Despite having a similar mean-averaged flowfield structure over the full Reynolds number range investigated, the population and distribution of coherent structures and turbulent dissipation within the fully developed region were also found to be Reynolds number dependent. Exploring the time-accurate flow characteristics revealed that in addition to vortices shed from the rib shear layer, the region of the rib wake was governed by a periodic process of bursting of the wake vortices resulting in the intermittent ejection of the inter-rib recirculation region into the core flow. This periodic process was the driving mechanism resulting in mixing and heat transfer augmentation. A quadrant-splitting burst analysis was also performed to determine the characteristic frequency and duration of inter-rib bursting as well as the wake shedding frequency, both of which were determined to be Reynolds number dependent.