Gerrit E. Elsinga

Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in a supersonic (Mach 2) turbulent boundary layer in the region between y/? = 0.15 and 0.89. The Reynolds number based on momentum thickness Re? = 34000. The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low-speed fluid, consistent with Tomkins & Adrian (J. Fluid Mech., vol. 490, 2003, p. 37). The observed hairpin structure is also a statistically relevant structure as is shown by the conditional average flow field associated to spanwise swirling motion. Spatial low-pass filtering of the velocity field reveals streamwise vortices and signatures of large-scale hairpins (height > 0.5?), which are weaker than the smaller scale hairpins in the unfiltered velocity field. The large-scale hairpin structures in the instantaneous velocity fields are observed to be aligned in the streamwise direction and spanwise organized along diagonal lines. Additionally the autocorrelation function of the wall-normal swirling motion representing the large-scale hairpin structure returns positive correlation peaks in the streamwise direction (at 1.5? distance from the DC peak) and along the 45° diagonals, which also suggest a periodic arrangement in those directions. This is evidence for the existence of a spanwise–streamwise organization of the coherent structures in a fully turbulent boundary layer.

Three-dimensional instantaneous structure of a shock wave/turbulent boundary layer interaction

An experimental study is carried out to investigate the three-dimensional instantaneous structure of an incident shock wave/turbulent boundary layer interaction at Mach 2.1 using tomographic particle image velocimetry. Large-scale coherent motions within the incoming boundary layer are observed, in the form of three-dimensional streamwise-elongated regions of relatively low- and high-speed fluid, similar to what has been reported in other supersonic boundary layers. Three-dimensional vortical structures are found to be associated with the low-speed regions, in a way that can be explained by the hairpin packet model. The instantaneous reflected shock wave pattern is observed to conform to the low- and high-speed regions as they enter the interaction, and its organization may be qualitatively decomposed into streamwise translation and spanwise rippling patterns, in agreement with what has been observed in direct numerical simulations. The results are used to construct a conceptual model of the three-dimensional unsteady flow organization of the interaction.

Universal aspects of small-scale motions in turbulence

Two aspects of small-scale turbulence are currently regarded universal, as they have been reported for a wide variety of turbulent flows. Firstly, the vorticity vector has been found to display a preferential alignment with the eigenvector corresponding to the intermediate eigenvalue of the strain rate tensor; and secondly, the joint probability density function (p.d.f.) of the second and third invariant of the velocity gradient tensor, Q and R , has a characteristic teardrop shape. This paper provides an explanation for these universal aspects in terms of a spatial organization of coherent structures, which is based on an evaluation of the average flow pattern in the local coordinate system defined by the eigenvectors of the strain rate tensor. The approach contrasts with previous investigations, which have relied on assumed model flows. The present average flow patterns have been calculated for existing experimental (particle image velocimetry) or numerical (direct numerical simulation) datasets of a turbulent boundary layer (TBL), a turbulent channel flow and for homogeneous isotropic turbulence. All results show a shear-layer structure consisting of aligned vortical motions, separating two larger-scale regions of relatively uniform flow. Because the directions of maximum and minimum strain in a shear layer are in the plane normal to the vorticity vector, this vector aligns with the remaining strain direction, i.e. the intermediate eigenvector of the strain rate tensor. Further, the QR joint p.d.f. for these average flow patterns reveals a shape reminiscent of the teardrop, as seen in many turbulent flows. The above-mentioned organization of the small-scale motions is not only found in the average patterns, but is also frequently observed in the instantaneous velocity fields of the different turbulent flows. It may, therefore, be considered relevant and universal.

Evolution and lifetimes of flow topology in a turbulent boundary layer

The average rates of change in the invariants of the velocity gradient tensor (Q and R) have been determined experimentally in the outer layer of a turbulent boundary layer as a function of the invariants themselves. Subsequent integration yields trajectories in the QR plane describing the average evolution of the local flow topology following a fluid particle. The trajectories reveal inward spiraling orbits around and converging to the origin. The orbit’s period is nearly constant at 14.3δ/Ue corresponding to 470ν/uτ2, which may be regarded as the characteristic lifetime of the energy containing eddies in this part of the boundary layer. Furthermore, an empirical model for the average Q and R evolution is presented that reproduces the main features of the orbits in the vicinity of the origin. The deviation of the QR trajectories of individual fluid particles from the average trajectory is discussed in relation to the significant scatter observed in the rates of change in the invariants around their average.

Tomographic 3D-PIV and Applications

Tomographic particle image velocimetry is a 3D PIV technique based on the illumination, recording, reconstruction and analysis of tracer-particle motion within a three-dimensional measurement volume. The recently developed technique makes use of several simultaneous views of the illuminated particles, typically 4, and their three-dimensional reconstruction as a light-intensity distribution by means of optical tomography. The reconstruction is performed with the MART algorithm (multiplicative algebraic reconstruction technique), yielding a 3D distribution of light intensity discretized over an array of voxels. The reconstructed tomogram pair is then analyzed by means of 3D crosscorrelation with an iterative multigrid volume-deformation technique, returning the three-component velocity vector distribution over the measurement volume. The implementation of the tomographic technique in time-resolved mode by means of high repetition rate PIV hardware has the capability to yield 4D velocity information. The first part of the chapter describes the operation principles and gives a detailed assessment of the tomographic reconstruction algorithm performance based upon a computer-simulated experiment. The second part of the chapter proposes four applications on two flow cases: 1. the transitional wake behind a circular cylinder; 2. the turbulent boundary layer developing over a flat plate. For the first case, experiments in air at ReD = 2700 are described together with the experimental assessment of the tomographic reconstruction accuracy. In this experiment a direct comparison is made between the results obtained by tomographic PIV and stereo-PIV. Experiments conducted in a water facility on the cylinder wake shows the extension of the technique to time-resolved measurements in water at ReD = 540 by means of a low repetition rate PIV system. A high data yield is obtained using high-resolution cameras (2k × 2k pixels) returning 650k vectors per volume. Measurements of the turbulent boundary layer in air at Reθ = 1900 provide a clear visualization of streamwise-aligned low-speed regions as well as hairpin vortices grouped into packets. Finally, in similar flow conditions the boundary layer is measured using a high repetition rate PIV system at 5kHz, where the spatiotemporal evolution of the flow structures is visualized revealing a mechanism for the rapid growth of a Q2 event, possibly associated to the generation of hairpin-like structures.

Interfaces and internal layers in a turbulent boundary layer

New experimental research is presented on the characteristics of interfaces and internal shear layers that are present in a turbulent boundary layer (TBL). The turbulent/non-turbulent (T/NT) interface at the outer boundary of the TBL shows the presence of a finite jump in streamwise velocity and is characterised by a thin shear layer. It appears that similar layers of high shear occur also within the TBL which separate regions of almost uniform momentum. It turns out that they exhibit similar characteristics as the external T/NT interface. Furthermore, the spatial growth rate of the TBL, that is derived from theoretical analysis, can be correctly predicted from a momentum balance near the external T/NT interface. Similarly, the entrainment velocities for the average internal layers have been determined. Results indicate that internal layers move slower in the vicinity of the wall, whereas they move faster than the large scale boundary layer growth rate in the outer region of the TBL. It is believed that shear layers bound large scale flow regions of approximately uniform momentum. Hence, the entrainment velocities of these internal layers may be interpreted as growth rates of the large scale motions in a TBL.

Feather roughness reduces flow separation during low Reynolds number glides of swifts.

ABSTRACT Swifts are aerodynamically sophisticated birds with a small arm and large hand wing that provides them with exquisite control over their glide performance. However, their hand wings have a seemingly unsophisticated surface roughness that is poised to disturb flow. This roughness of about 2% chord length is formed by the valleys and ridges of overlapping primary feathers with thick protruding rachides, which make the wing stiffer. An earlier flow study of laminar–turbulent boundary layer transition over prepared swift wings suggested that swifts can attain laminar flow at a low angle of attack. In contrast, aerodynamic design theory suggests that airfoils must be extremely smooth to attain such laminar flow. In hummingbirds, which have similarly rough wings, flow measurements on a 3D printed model suggest that the flow separates at the leading edge and becomes turbulent well above the rachis bumps in a detached shear layer. The aerodynamic function of wing roughness in small birds is, therefore, not fully understood. Here, we performed particle image velocimetry and force measurements to compare smooth versus rough 3D-printed models of the swift hand wing. The high-resolution boundary layer measurements show that the flow over rough wings is indeed laminar at a low angle of attack and a low Reynolds number, but becomes turbulent at higher values. In contrast, the boundary layer over the smooth wing forms open laminar separation bubbles that extend beyond the trailing edge. The boundary layer dynamics of the smooth surface varies non-linearly as a function of angle of attack and Reynolds number, whereas the rough surface boasts more consistent turbulent boundary layer dynamics. Comparison of the corresponding drag values, lift values and glide ratios suggests, however, that glide performance is equivalent. The increased structural performance, boundary layer robustness and equivalent aerodynamic performance of rough wings might have provided small (proto) birds with an evolutionary window to high glide performance. Summary: Swift feather roughness enhances boundary layer mixing, which reduces flow separation during low Reynolds number glides, enabling swifts to attain high glide performance with rough wings.

Comparison of Tomo-PIV and 3D-PTV for microfluidic flows

Two 3D-3C velocimetry techniques for micro-scale measurements are compared: tomographic particle image velocimetry (Tomo-PIV) and 3D particle-tracking velocimetry (3D-PTV). Both methods are applied to experimental data from a confined shear-driven liquid droplet over a moving surface. The droplet has 200 ?m height and 2?mm diameter. Micro 3D-PTV and Tomo-PIV are used to obtain the tracer particle distribution and the flow velocity field for the same set of images. It is shown that the reconstructed particle distributions are distinctly different, where Tomo-PIV returns a nearly uniform distribution over the height of the volume, as expected, and PTV reveals a clear peak in the particle distribution near the plane of focus. In Tomo-PIV, however, the reconstructed particle peak intensity decreases in proportion to the distance from the plane of focus. Due to the differences in particle distributions, the measured flow velocities are also different. In particular, we observe Tomo-PIV to be in closer agreement with mass conservation. Furthermore, the random noise level is found to increase with distance to the plane of focus at a higher rate for 3D-PTV as compared to Tomo-PIV. Thus, for a given noise threshold value, the latter method can measure reliably over a thicker volume.

The effect of particle image blur on the correlation map and velocity measurement in PIV

In PIV particle image blur is usually observed near fluid optical interfaces, i.e. shock waves, and thin flow structure with large density variations, e.g. shear layers and boundary layers. In such an environment the particle image is not only subject to blur, but is also displaced from its actual position due to refraction, which is denoted as optical displacement. In this study particle image blur near a shock wave is investigated in relation to the auto- and cross-correlation map, measurement accuracy and confidence level. The results from a numerical study are supported by PIV measurements of a shock wave in a supersonic wind tunnel. It is demonstrated that particle images are blurred in the direction of lower refractive index (directional blurring). The particle images are also skewed. Therefore particle image blur not only causes correlation peak broadening due to the fact that the particle images increase in size, but more importantly can introduce an asymmetry in the correlation peak and in turn introduce a small bias error in the measured velocity. However, experimental results indicate that particle image blur itself is not the main cause for the increase in measurement uncertainty near shock waves, but that the reduced accuracy can be attributed to the optical displacement. The observation of particle image blur can be used as a detection criterion for a qualitative assessment of the optical displacement. Certain combinations of experimental parameters (viewing angle, f/# and interrogation window size) yield significant errors in the measured velocity. Under certain circumstances optical distortion can become so strong to introduce an unphysical acceleration within the shock wave, visualized as an inflection point with positive slope in the velocity profile across the shock. The study provides some practical suggestions to limit the effect of aero-optical distortion on the velocity measurement.

Universality and scaling phenomenology of small-scale turbulence in wall-bounded flows

The Reynolds number scaling of flow topology in the eigenframe of the strain-rate tensor is investigated for wall-bounded flows, which is motivated by earlier works showing that such topologies appear to be qualitatively universal across turbulent flows. The databases used in the current study are from direct numerical simulations (DNS) of fully developed turbulent channel flow (TCF) up to friction Reynolds number Re ? ? 1500, and a spatially developing, zero-pressure-gradient turbulent boundary layer (TBL) up to Re ? ? 4300 (Re ? ? 1400). It is found that for TCF and TBL at different Reynolds numbers, the averaged flow patterns in the local strain-rate eigenframe appear the same consisting of a pair of co-rotating vortices embedded in a finite-size shear layer. It is found that the core of the shear layer associated with the intense vorticity region scales on the Kolmogorov length scale, while the overall height of the shear layer and the distance between the vortices scale well with the Taylor micro scale. Moreover, the Taylor micro scale collapses the height of the shear layer in the direction of the vorticity stretching. The outer region of the averaged flow patterns approximately scales with the macro scale, which indicates that the flow patterns outside of the shear layer mainly are determined by large scales. The strength of the shear layer in terms of the peak tangential velocity appears to scale with a mixture of the Kolmogorov velocity and root-mean-square of the streamwise velocity scaling. A quantitative universality in the reported shear layers is observed across both wall-bounded flows for locations above the buffer region.