Turbulent flow in a ribbed channel: Flow structures in the vicinity of a rib

PIV measurements are performed in a channel with periodic ribs on one wall. The emphasis of this study is to investigate the flow structures in the vicinity of a rib in terms of mean velocities, Reynolds stresses, probability density functions (PDF), and two-point correlations. The PDF distribution of u′ is bimodal in the separated shear layer downstream of the rib. The maximum Reynolds shear stresses occur at the leading edge of the rib. Based on quadrant analysis, it is found that ejection motions make a dominant contribution to the Reynolds shear stress in this region. Moreover, topology-based visualization is applied to the separation bubble upstream of the rib. Salient critical points and limit cycles are extracted, which gives clues to the physical processes occurring in the flow.     

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.     

Parametric study of separation and transition characteristics over an airfoil at low Reynolds numbers

Time-resolved surface pressure measurements are used to experimentally investigate characteristics of separation and transition over a NACA 0018 airfoil for the relatively wide range of chord Reynolds numbers from 50,000 to 250,000 and angles of attack from 0° to 21°. The results provide a comprehensive data set of characteristic parameters for separated shear layer development and reveal important dependencies of these quantities on flow conditions. Mean surface pressure measurements are used to explore the variation in separation bubble position, edge velocity in the separated shear layer, and lift coefficients with angle of attack and Reynolds number. Consistent with previous studies, the separation bubble is found to move upstream and decrease in length as the Reynolds number and angle of attack increase. Above a certain angle of attack, the proximity of the separation bubble to the location of the suction peak results in a reduced lift slope compared to that observed at lower angles. Simultaneous measurements of the time-varying component of surface pressure at various spatial locations on the model are used to estimate the frequency of shear layer instability, maximum root-mean-square (RMS) surface pressure, spatial amplification rates of RMS surface pressure, and convection speeds of the pressure fluctuations in the separation bubble. A power-law correlation between the shear layer instability frequency and Reynolds number is shown to provide an order of magnitude estimate of the central frequency of disturbance amplification for various airfoil geometries at low Reynolds numbers. Maximum RMS surface pressures are found to agree with values measured in separation bubbles over geometries other than airfoils, when normalized by the dynamic pressure based on edge velocity. Spatial amplification rates in the separation bubble increase with both Reynolds number and angle of attack, causing the accompanying decrease in separation bubble length. Values of the convection speed of pressure fluctuations in the separated shear layer are measured to be between 35 and 50% of the edge velocity, consistent with predictions of linear stability theory for separated shear layers.     

Eigenmode decomposition of the turbulent shear layer above a square rib

1D, 2D and fully 3D structural information is extracted from a large-eddy simulation of turbulent flow over a square rib, using Proper Orthogonal Decomposition. In this paper, we focus on the shear layer separating at the leading edge and developing above and behind the top face of the flow obstacle. The two-point correlation tensor, required for the solution of the related eigenvalue problem, is provided from a large-eddy simulation for a Reynolds number of about 50 000 (based on obstacle height and incoming bulk velocity). The results indicate that the eigenmode decomposition is a very useful tool to extract organized structures even from very complex turbulent velocity fields at high Reynolds numbers. A significant amount of turbulent energy can still be captured by a relatively small number of modes.     

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.     

Turbulent separated reattached flow in a two-dimensional curved-wall diffuser

A turbulent separation-reattachment flow in a two-dimensional asymmetrical curved-wall diffuser is studied by a two-dimensional laser doppler velocimeter. The turbulent boundary layer separates on the lower curved wall under strong pressure gradient and then reattaches on a parallel channel. At the inlet of the diffuser, Reynolds number based on the diffuser height is 1.2×10⁵ and the velocity is 25.2m/s. The results of experiments are presented and analyzed in new defined streamline-aligned coordinates. The experiment shows that after Transitory Detachment Reynolds shear stress is negative in the near-wall backflow region. Their characteristics are approximately the same as in simple turbulent shear layers near the maximum Reynolds shear stress. A scale is formed using the maximum Reynolds shear stresses. It is found that a Reynolds shear stress similarity exists from separation to reattachment and the Schofield-Perry velocity law exists in the forward shear flow. Both profiles are used in the experimental work that leads to the design of a new eddy-viscosity model. The length scale is taken from that developed by Schofield and Perry. The composite velocity scale is formed by the maximum Reynolds shear stress and the Schofield-Perry velocity scale as well as the edge velocity of the boundary layer. The results of these experiments are presented in this paper.     

Development of a Two-velocities Hybrid RANS-LES Model and its Application to a Trailing Edge Flow

The flow around a trailing edge is computed with a new hybrid method designed to more clearly separate the effects of total and sub-grid turbulent stress-modelling on the time-averaged and instantaneous velocity fields, and in turn, mean momentum and kinetic energy balances. These two velocity fields independently define Reynolds averaged and sub-grid-scale viscosities, and distinct stresses, at the same location. In particular, resolved eddies can emerge, or sweep in and out of the Reynolds averaged near wall layer, without being dampened by higher levels of the viscosity in this RANS dominated layer. The two-field hybrid model, first tested on channel flows, gives accurate predictions of mean velocities and stresses for different Reynolds numbers and coarse meshes. For the trailing edge flow the results of the hybrid model are close to the reference fine LES for mean velocity and turbulent content, whereas the DES-SST on the same coarse mesh gives too early separation.     

Experimental Study on the Behaviour of Local Laminar Separation Bubble at a Rectangular Wing Section

This paper identifies laminar separation bubbles at the root or span-wise midsection of a rectangular wing using direct surface pressure measurements in the wind tunnel and analyses their behavior at different Reynolds numbers and angles of attack. The separation, transition, and reattachment locations are determined as functions of the angles of attack and the Reynolds number. The transition structure and turbulence characteristics in the separated shear layer are studied using laser Doppler velocimetry. Surface pressure data and simultaneously acquired velocity signals are correlated to show the pattern of growing disturbances in the shear layer. Surface oil flow visualizations clarified the wingtip and separation bubble’s interactions near the leading edge of the wing at the higher angles of attack. Turbulence statistics are also calculated from the streamwise velocity distributions, and an apparent deviation is observed for the skewness and flatness values from the normal distributions in the near-wall region. The separation bubble effect on aerodynamic coefficients of a 3D rectangular wing root section is studied and reported.

     

Unsteady separated and reattaching turbulent flow over a two-dimensional square rib

The spatio-temporal characteristics of the separated and reattaching turbulent flow over a two-dimensional square rib were studied experimentally. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. Profiles of time-averaged streamwise velocity and wall-pressure fluctuations showed that the shear layer separated from the leading edge of the rib sweeps past the rib and directly reattaches on the bottom wall (x/H=9.75) downstream of the rib. A thin region of reverse flow was formed above the rib. The shedding large-scale vortical structures (fH/U₀=0.03) and the flapping separation bubble (fH/U₀=0.0075) could be discerned in the wall-pressure spectra. A multi-resolution analysis based on the maximum overlap discrete wavelet transform (MODWT) was performed to extract the intermittent events associated with the shedding large-scale vortical structures and the flapping separation bubble. The convective dynamics of the large-scale vortical structures were analyzed in terms of the autocorrelation of the continuous wavelet-transformed wall pressure, cross-correlation of the wall-pressure fluctuations, and the cross-correlation between the wall pressure at the time-averaged reattachment point and the streamwise velocity field. The convection speeds of the large-scale vortical structures before and after the reattachment point were U_c=0.35U₀ and 0.45U₀, respectively. The flapping motion of the separation bubble was analyzed in terms of the conditionally averaged reverse-flow intermittency near the wall region. The instantaneous reattachment point in response to the flapping motion was obtained; these findings established that the reattachment zone was a 1.2H-long region centered at x/H=9.75. The reverse-flow intermittency in one period of the flapping motion demonstrated that the thin reverse flow above the rib is influenced by the flapping motion of the separation bubble behind the rib.     

CHARACTERISTICS OF LOW-FREQUENCY VARIATIONS EMBEDDED IN VORTEX-SHEDDING PROCESS

Experiments were made to study the flow characteristics in the near-wake region of a two-dimensional bluff body, namely a trapezoidal cylinder (prism) or a circular cylinder. The instantaneous velocity signals obtained at the inner edge of the separated shear layer and in the neighbourhood of the rear end of the vortex formation region show the presence of low-frequency variations at Reynolds numbers of 10⁴. The low-frequency variations noted in the velocity signals and the base pressure measured at the bluff body appear to be well correlated. These experimental observations suggest a physical picture that the variations of vortex formation length and base pressure are closely related in a real-time manner.     

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.     

Synthetic Turbulence Generators for RANS-LES Interfaces in Zonal Simulations of Aerodynamic and Aeroacoustic Problems

The paper presents the detailed formulation and validation results of simple and robust procedures for the generation of synthetic turbulence aimed at providing artificial turbulent content at the RANS-to-LES interface within a zonal Wall Modelled LES of attached and mildly separated wall-bounded flows. There are two versions of the procedure. The aerodynamic version amounts to a minor modification of a synthetic turbulence generator developed by the authors previously, but the acoustically adapted version is new and includes an internal damping layer, where the pressure field is computed by “weighting” of the instantaneous pressure fields from LES and RANS. This is motivated by the need to avoid creating spurious noise as part of the turbulence generation. In terms of pure aerodynamics, the validation includes canonical shear flows (developed channel flow, zero pressure gradient boundary layer, and plane mixing layer), as well as a more complex flow over the wall-mounted hump with non-fixed separation and reattachment, with emphasis on a rapid conversion from modeled to resolved Reynolds stresses. The aeroacoustic applications include the flow past a trailing edge and over a two-element airfoil configuration. In all cases the methodology ensures a very acceptable accuracy for the mean flow, turbulent statistics and, also, the near- and far-field noise.     

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.     

Expansion ratio effects on the separated shear layer and reattachment downstream of a backward-facing step

Experiments were carried out to study the behavior of the incompressible turbulent separated shear layer and subsequent reattachment, downstream of a backward-facing step in a channel. The main objective of the study was to determine the effect of the expansion ratio on the development of the mean velocity and turbulence intensity in the shear layer and on the evolution of wall static pressure downstream of the step. The step height-to-upstream channel height ratio was varied between 0.5 and 2.13 while all inlet conditions were kept constant. Both hot-wire anemometry and frequency shifted laser Doppler anemometry were used for the velocity measurements. The Reynolds number based on free stream velocity and channel height upstream of the step was 16,600. The expansion ratio was found to have a particularly strong influence in the development of the turbulent, separated shear layer. Larger step height-to-inlet channel height ratios lead to higher turbulence intensities and faster growth of the unstable shear layer. As a result of this, shorter normalized reattachment lengths occurred with lager expansion ratios. For all the expansion ratios studied, the mean reattachment lenght was uniform along the spanwise direction except very near the side walls.     

Some Features of a Turbulent Separated Flow and Heat Transfer Behind a Step and a Rib. 2. Heat Transfer in a Separated Flow

Results of an experimental study of heat transfer in a separated flow behind a step and a rib are presented. The influence of the obstacle height (H = 6–30 mm) on heat and mass transfer and the structure of the thermal boundary layer is studied. The features of heat transfer in recirculation and relaxation zones of the separated flow are analyzed, and the effect of separation on intensification and suppression of turbulent heat transfer is determined.     

PIV investigation of the shear layer vortices in the near wake of a circular cylinder

Particle image velocimetry measurements are performed in the near wake of a circular cylinder at a Reynolds number of 12,500. Attention is focused on the shear layer that develops just downstream of the separation point from the cylinder surface to investigate the possible existence of a preferred spatio-temporal organization in this flow region and the possible occurrence of the vortex pairing phenomenon. Eddy structures are identified in instantaneous velocity maps in order to investigate their spatial relationships. For that purpose a vortex extraction procedure is designed, based on the wavelet transform of instantaneous maps of the swirling strength. This algorithm allows not only the detection of the vortical structures from the instantaneous velocity fields, giving access to their instantaneous location, but also the estimation of their main characteristics such as their radius, intensity and convection velocity. The vortex population detected in the shear layer is found to be of small diameter compared to that of the von Kármán vortex and of rather high intensity, in agreement with the existence of a thin shear layer. The strong flapping motion of the shear layer and its complex spatial development is also confirmed. By employing conditional analysis of the computed data and their proper scaling, the surrounding of the detected vortex cores is investigated. A preferred spatial vortex separation is detected and is shown to vary with the longitudinal distance from the origin of the shear layer, in agreement with the qualitative behavior of a turbulent plane mixing layer. Evidence of the occurrence of the vortex pairing or amalgamation mechanisms in the shear layer is also demonstrated.     

Flow structure on a three-dimensional wing subjected to small amplitude perturbations

Small amplitude angular perturbations, of the order of one-half degree, can substantially modify the flow structure along a three-dimensional wing configuration, which is quantitatively characterized using a technique of high-image-density particle image velocimetry. Excitation at either the fundamental or the first subharmonic of the spanwise-averaged instability frequency of the separating shear layer from the stationary wing nearly eliminates the large-scale separation zone along the wing at high angle of attack. The physics of the flow is interpreted in terms of time-mean streamlines, vorticity and Reynolds stress, in conjunction with phase-averaged patterns of instantaneous vorticity. Distinctive vorticity patterns occur along the leading edge when the time-averaged separation zone is minimized.     

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.     

Adverse pressure gradient turbulent flows over rough walls

An experimental study of a fully developed turbulent channel flow and an adverse pressure gradient (APG) turbulent channel flow over smooth and rough walls has been performed using a particle image velocimetry (PIV) technique. The rough walls comprised two-dimensional square ribs of nominal height, k = 3 mm and pitch, p = 2k, 4k and 8k. It was observed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. Similarly, rib roughness significantly increased the level of turbulence production, Reynolds stresses and wall-normal transport of turbulence kinetic energy and Reynolds shear stress well beyond the roughness sublayer. On the contrary, the distributions of the eddy viscosity, mixing length and streamwise transport of turbulence kinetic energy and Reynolds shear stress were reduced by wall roughness, especially in the outer layer. Adverse pressure gradient produced a further reduction in the mean velocity (in comparison to the results obtained in the parallel section) but increased the wall-normal extent across which the mean flow above the ribs is spatially inhomogeneous in the streamwise direction. APG also reinforced wall roughness in augmenting the equivalent sand grain roughness height. The combination of wall roughness and APG significantly increased turbulence production and Reynolds stresses except in the immediate vicinity of the rough walls. The transport velocities of the turbulence kinetic energy and Reynolds shear stress were also augmented by APG across most part of the rough-wall boundary layer. Further, APG enhanced the distributions of the eddy viscosity across most of the boundary layer but reduced the mixing length outside the roughness sublayer.     

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.