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This study focuses on the effects of mean (favourable) and large-scale fluctuating pressure gradients on boundary layer turbulence. Two-dimensional (2D) particle image velocimetry (PIV) measurements, some of which are time-resolve...
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This study focuses on the effects of mean (favourable) and large-scale fluctuating pressure gradients on boundary layer turbulence. Two-dimensional (2D) particle image velocimetry (PIV) measurements, some of which are time-resolved, have been performed upstream of and within a sink flow for two inlet Reynolds numbers, Re_θ (x_1) = 3360 and 5285. The corresponding acceleration parameters, K, are 1.3×10~(-6) and 0.6×10~(-6). The time-resolved data at Re_θ (x_1) = 3360 enables us to calculate the instantaneous pressure distributions by integrating the planar projection of the fluid material acceleration. As expected, all the locally normalized Reynolds stresses in the favourable pressure gradient (FPG) boundary layer are lower than those in the zero pressure gradient (ZPG) domain. However, the un-scaled stresses in the FPG region increase close to the wall and decay in the outer layer, indicating slow diffusion of near-wall turbulence into the outer region. Indeed, newly generated vortical structures remain confined to the near-wall region. An approximate analysis shows that this trend is caused by higher values of the streamwise and wall-normal gradients of mean streamwise velocity, combined with a slightly weaker strength of vortices in the FPG region. In both boundary layers, adverse pressure gradient fluctuations are mostly associated with sweeps, as the fluid approaching the wall decelerates. Conversely, FPG fluctuations are more likely to accompany ejections. In the ZPG boundary layer, loss of momentum near the wall during periods of strong large-scale adverse pressure gradient fluctuations and sweeps causes a phenomenon resembling local 3D flow separation. It is followed by a growing region of ejection. The flow deceleration before separation causes elevated near-wall small-scale turbulence, while high wall-normal momentum transfer occurs in the ejection region underneath the sweeps. In the FPG boundary layer, the instantaneous near-wall large-scale pressure gradient rarely becomes positive, as the pressure gradient fluctuations are weaker than the mean FPG. As a result, the separation-like phenomenon is markedly less pronounced and the sweeps do not show elevated small-scale turbulence and momentum transfer underneath them. In both boundary layers, periods of acceleration accompanying large-scale ejections involve near-wall spanwise contraction, and a high wall-normal momentum flux at all elevations. In the ZPG boundary layer, although some of the ejections are preceded, and presumably initiated, by regions of adverse pressure gradients and sweeps upstream, others are not. Conversely, in the FPG boundary layer, there is no evidence of sweeps or adverse pressure gradients immediately upstream of ejections. Apparently, the mechanisms initiating these ejections are either different from those involving large-scale sweeps or occur far upstream of the peak in FPG fluctuations.
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Near-wall turbulence is a subject of prime importance for turbulence modelling. Coherent structures were hypothesized early by Theodorsen in this flow region and have been the subject of intensive research ever since. The overall ...
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Near-wall turbulence is a subject of prime importance for turbulence modelling. Coherent structures were hypothesized early by Theodorsen in this flow region and have been the subject of intensive research ever since. The overall organization of these coherent structures has now been well assessed. Vortical structures appear to play a key role in this organization. Their characteristics and scaling have been studied by many authors as listed in the Introduction. The present contribution to the subject relies on high-resolution stereo particle image velocimetry (PIV) to study these structures. High-quality measurements are performed in a thick turbulent boundary layer at different values of the Reynolds number. The data quality is first assessed by comparing the statistics to those of hot-wire anemometry and direct numerical simulation data. The agreement between the two appears satisfactory. The PIV data are then processed in order to extract the vortex characteristics in a streamwise plane and in a spanwise plane. The statistical characteristics of these vortices are analysed in detail as a function of wall distance. The scaling of the data appears to be universal when the Kolmogorov scales are used. These results are analysed and discussed in terms of their probability density functions. This leads to a question regarding the Kolmogorov cascade in this region of the flow.
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This paper uses matched asymptotic expansions to study the non-localized (which we refer to as global) boundary layer instabilities generated by free-stream acoustic and vortical disturbances at moderate supersonic Mach numbers. T...
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This paper uses matched asymptotic expansions to study the non-localized (which we refer to as global) boundary layer instabilities generated by free-stream acoustic and vortical disturbances at moderate supersonic Mach numbers. The vortical disturbances produce an unsteady boundary layer flow that develops into oblique instability waves with a viscous triple-deck structure in the downstream region. The acoustic disturbances (which for reasons given herein are assumed to have obliqueness angles that are close to a certain critical angle) generate slow boundary layer disturbances which eventually develop into oblique stable disturbances with an inviscid triple-deck structure in a region that lies downstream of the viscous triple-deck region. The paper shows that both the vortically generated instabilities and the acoustically generated oblique disturbances ultimately develop into modified Rayleigh-type instabilities (which can either grow or decay) further downstream.
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This paper is concerned with the high Reynolds number flow over a spanwise-periodic array of roughness elements with interelement spacing of the order of the local boundary-layer thickness. While earlier work by Goldstein et al. (...
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This paper is concerned with the high Reynolds number flow over a spanwise-periodic array of roughness elements with interelement spacing of the order of the local boundary-layer thickness. While earlier work by Goldstein et al. (J. Fluid Mech., vol. 644, 2010, pp. 123-163) and Goldstein et al. (J. Fluid Mech., vol. 668, 2011, pp. 236-266) was mainly concerned with smaller roughness heights that produced relatively weak distortions of the downstream flow, the focus here is on extending the analysis to larger roughness heights and streamwise elongated planform shapes that together produce a qualitatively different, nonlinear behaviour of the downstream wakes. The roughness scale flow now has a novel triple-deck structure that is somewhat different from related studies that have previously appeared in the literature. The resulting flow is formally nonlinear in the intermediate wake region, where the streamwise distance is large compared to the roughness dimensions but small compared to the downstream distance from the leading edge, as well as in the far wake region where the streamwise length scale is of the order of the downstream distance from the leading edge. In contrast, the flow perturbations in both of these wake regions were strictly linear in the earlier work by Goldstein et al. (2010, 2011). This is an important difference because the nonlinear wake flow in the present case provides an appropriate basic state for studying the secondary instability and eventual breakdown into turbulence.
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We examine disturbances leading to optimal energy growth in a spatially developing, zero-pressure-gradient turbulent boundary layer. The slow development of the turbulent mean flow in the streamwise direction is modelled through a...
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We examine disturbances leading to optimal energy growth in a spatially developing, zero-pressure-gradient turbulent boundary layer. The slow development of the turbulent mean flow in the streamwise direction is modelled through a parabolized formulation to enable a spatial marching procedure. In the present framework, conventional spatial optimal disturbances arise naturally as the homogeneous solution to the linearized equations subject to a turbulent forcing at particular wavenumber combinations. A wave-like decomposition for the disturbance is considered to incorporate both conventional stationary modes as well as propagating modes formed by non-zero frequency/streamwise wavenumber and representative of convective structures naturally observed in wall turbulence. The optimal streamwise wavenumber, which varies with the spatial development of the turbulent mean flow, is computed locally via an auxiliary optimization constraint. The present approach can then be considered, in part, as an extension of the resolvent-based analyses for slowly developing flows. Optimization results reveal highly amplified disturbances for both stationary and propagating modes. Stationary modes identify peak amplification of structures residing near the centre of the logarithmic layer of the turbulent mean flow. Inner-scaled disturbances reminiscent of near wall streaks, and amplified over short streamwise distances, are identified in the computed streamwise energy spectra. In all cases, however, propagating modes surpass their stationary counterpart in both energy amplification and relative contribution to total fluctuation energy. We identify two classes of large-scale energetic modes associated with the logarithmic and wake layers of the turbulent mean flow. The outer-scaled wake modes agree well with the large-scale motions that populate the wake layer. For high Reynolds numbers, the log modes increasingly dominate the energy spectra with the predicted streamwise and wall-normal sc
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Experimental measurements of the three-dimensional (3D) velocity field in a moderate Reynolds number zero pressure-gradient boundary layer are presented. The measurements are analysed to produce 3D correlations and conditional ave...
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Experimental measurements of the three-dimensional (3D) velocity field in a moderate Reynolds number zero pressure-gradient boundary layer are presented. The measurements are analysed to produce 3D correlations and conditional averaging techniques are used to further elucidate the underlying structure. The results show clear evidence of vortex-packet-type structures and shed new light on the detailed 3D structure of such packets in a real zero pressure-gradient boundary layer.
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The influence of a single roughness element on the evolution of two-dimensional (2-D) Tollmien-Schlichting (TS) waves is investigated experimentally. Experiments are carried out in a region of zero pressure gradient of an airfoil ...
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The influence of a single roughness element on the evolution of two-dimensional (2-D) Tollmien-Schlichting (TS) waves is investigated experimentally. Experiments are carried out in a region of zero pressure gradient of an airfoil section. Downstream from the disturbance source, TS waves interact with a cylindrical roughness element with a slowly oscillating height. The oscillation frequency of the roughness was approximately 1500 times lower than the wave frequency and approximately 250 times slower than the characteristic time of flow passing the region of transition development. Therefore, the roughness behaved as a quasi-steady disturbance. The set-up enabled us to perform hot-wire measurements phase locked to the waves and to the roughness movement. Experimental results show a scattering of the 2-D waves into oblique ones and a relatively weak distortion of the mean flow for roughness heights as large as 0.2 times the boundary layer displacement thickness (delta*). Transfer functions for TS wave scattering at the roughness are obtained. Results show an unexpected coincidence in shape with acoustic receptivity functions found in Wrz et . (J. Fluid Mech., vol. 478, 2003, pp. 135-163) for the problem of excitation of TS waves by scattering of acoustic waves at surface roughness. In the present work, the ratio between the incoming 2-D wave amplitude to the amplitude of the scattered oblique waves scaled linearly with the roughness height only for very shallow roughness. For roughness elements higher than 0.08 delta* and below 0.2 delta*, the wave scattering exhibited a quadratic variation with respect to the roughness height. In addition, this feature did not vary significantly with respect to TS wave frequency. An analysis of the weakly nonlinear interactions triggered by the roughness element is also carried out, assisted by numerical solution of nonlinear parabolized stability equations, performed for a two-dimensional Blasius boundary layer. A comparison between experiments and simulations reveals that the weakly nonlinear interactions observed are not substantially affected by mean flow distortions that could be produced in the wake of the small and medium sized roughness elements (h < 0.2 delta*). From a practical perspective, results suggest that scattering coefficients might be employed to include the effect of isolated and medium sized roughness elements in transition prediction tools developed for smooth surfaces.
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Utilizing an optically index-matched facility and high-resolution particle image velocimetry measurements, this paper examines flow structure and turbulence in a rough-wall channel flow for Re in the 3520-5360 range. The scales of...
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Utilizing an optically index-matched facility and high-resolution particle image velocimetry measurements, this paper examines flow structure and turbulence in a rough-wall channel flow for Re in the 3520-5360 range. The scales of pyramidal roughness elements satisfy the well-characterized flow conditions, with h/k 50 and k+ = 60 ~ 100, where h is half height of the channel and k is the roughness height. The near-wall turbulence measurements are sensitive to spatial resolution, and vary with Reynolds number. Spatial variations in the mean flow, Reynolds stresses, as well as the turbulent kinetic energy (TKE) production and dissipation rates are confined to y < 2k. All the Reynolds stress components have local maxima at slightly higher elevations, but the streamwise-normal component increases rapidly at y < k, peaking at the top of the pyramids. The TKE production and dissipation rates along with turbulence transport also peak near the wall. The spatial energy and shear spectra show an increasing contribution of large-scale motions and a diminishing role of small motions with increasing distance from the wall. As the spectra steepen at low wavenumbers, they flatten and develop bumps in wavenumbers corresponding to k 3k, which fall in the dissipation range. Instantaneous realizations show that roughness-scale eddies are generated near the wall, and lifted up rapidly by large-scale structures that populate the outer layer. A linear stochastic estimation-based analysis shows that the latter share common features with hairpin packets. This process floods the outer layer with roughness-scale eddies, in addition to those generated by the energy-cascading process. Consequently, although the imprints of roughness diminish in the outer-layer Reynolds stresses, consistent with the wall similarity hypothesis, the small-scale turbulence contains a clear roughness signature across the entire channel.
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The spatial and temporal response characteristics of a laminar separation bubble to impulsive forcing are investigated by means of time-resolved particle image velocimetry and linear stability theory. A two-dimensional impulsive d...
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The spatial and temporal response characteristics of a laminar separation bubble to impulsive forcing are investigated by means of time-resolved particle image velocimetry and linear stability theory. A two-dimensional impulsive disturbance is introduced with an alternating current dielectric barrier discharge plasma actuator, exciting pertinent instability modes and ensuring flow development under environmental disturbances. Phase-averaged velocity measurements are employed to analyse the effect of imposed disturbances at different amplitudes on the laminar separation bubble. The impulsive disturbance develops into a wave packet that causes rapid shrinkage of the bubble in both upstream and downstream directions. This is followed by bubble bursting, during which the bubble elongates significantly, while vortex shedding in the aft part ceases. Duration of recovery of the bubble to its unforced state is independent of the forcing amplitude. Quasi-steady linear stability analysis is performed at each individual phase, demonstrating reduction of growth rate and frequency of the most unstable modes with increasing forcing amplitude. Throughout the recovery, amplification rates are directly proportional to the shape factor. This indicates that bursting and flapping mechanisms are driven by altered stability characteristics due to variations in incoming disturbances. The emerging wave packet is characterised in terms of frequency, convective speed and growth rate, with remarkable agreement between linear stability theory predictions and measurements. The wave packet assumes a frequency close to the natural shedding frequency, while its convective speed remains invariant for all forcing amplitudes. The stability of the flow changes only when disturbances interact with the shear layer breakdown and reattachment processes, supporting the notion of a closed feedback loop. The results of this study shed light on the response of laminar separation bubbles to impulsive forcing,
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Spanwise-periodic roughness designed to excite selected wavelengths of stationary cross-flow modes was investigated in a three-dimensional boundary layer at Mach 3.5. The test model was a sharp-tipped 14° right-circular cone. The...
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Spanwise-periodic roughness designed to excite selected wavelengths of stationary cross-flow modes was investigated in a three-dimensional boundary layer at Mach 3.5. The test model was a sharp-tipped 14° right-circular cone. The model and integrated sensor traversing system were placed in the Mach 3.5 supersonic low disturbance tunnel (SLDT) equipped with an axisymmetric 'quiet design' nozzle at NASA Langley Research Center. The model was oriented at a 4.2° angle of attack to produce a mean cross-flow velocity component in the boundary layer over the cone. The research examined both passive and active surface roughness. The passive roughness consisted of indentations (dimples) that were evenly spaced around the cone at an axial location that was just upstream of the first linear stability neutral growth branch for cross-flow modes. The active roughness consisted of an azimuthal array of micrometre-sized plasma actuators that were designed to produce the effect of passive surface bumps. Two azimuthal mode numbers of the passive and active patterned roughness were examined. One had an azimuthal mode number that was in the band of initially amplified stationary cross-flow modes. This was intended to represent a controlled baseline condition. The other azimuthal mode number was designed to suppress the growth of the initially amplified stationary cross-flow modes and thereby increase the transition Reynolds number. The results showed that the stationary cross-flow modes were receptive to both the passive and active patterned roughness. Only the passive roughness was investigated at a unit Reynolds number where transition would occur on the cone. Transition front measurements using the Preston tube approach indicated that the transition Reynolds number had increased by 35 % with the subcritical wavenumber roughness compared with the baseline smooth tip cone, and by 40 % compared with the critical wavenumber roughness. Based on the similarities in the response of the stationary cross-flow modes with the active roughness, we expect it would produce a similar transition delay.
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