Smooth and rough turbulent boundary layers at high Reynolds number

A 2-D turbulent boundary layer experiment with zero pressure gradient (ZPG) has been carried out over a rough and a smooth surface using two cross hot-wire probes. Wind tunnel speeds of 10 m/s and 20 m/s were set up in order to investigate the effects of the upstream conditions and the Reynolds number on the downstream flow. For a given set of upstream conditions, such as the wind tunnel speed, trip wire size and location, the three components of the velocity field were measured from about 14 m from the inlet of the wind tunnel to 30 m downstream. This experiment is unique because it achieves Reynolds numbers as high as R120,000, for which measurements of the mean velocity are reported. It is shown that by fixing the upstream conditions, the mean deficit profiles collapse with the freestream velocity, , but to different curves depending on the upstream conditions and surface roughness. Moreover, the effects of the upstream conditions, the Reynolds number, and roughness are completely removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits scaling, . Consequently, the true asymptotic profile in the turbulent boundary layer is found in ZPG flow regardless of the range of Reynolds number, surface conditions and initial conditions.     

Vortical structures in a turbulent far-wake: effect of Reynolds number

The effect of the Reynolds number on vortical structures in a turbulent far-wake has been investigated for Re_d (based on the free stream velocity and the cylinder diameter) =2800 and 9750. Velocity data were obtained using two orthogonal arrays of 16 X-wires, eight in the (x,y)-plane and eight in the (x,z)-plane. Structures were detected in both planes using a technique based on vorticity concentration and circulation. Conditional streamlines and contours of vorticity based on spanwise structures, i.e. detections in the (x,y)-plane, reveal that the streamwise size of spanwise structures increases as Re_d increases. The interrelationship is investigated between detections simultaneously identified in the two planes. Transverse structures, i.e. detections in the (x,z)-plane, correspond, with a relatively high probability, to spanwise structures, in conformity with a distortion in the (y,z)-plane of spanwise structures. Those that correspond, with relatively high probability, to the saddle between consecutive spanwise structures are interpreted in terms of ribs, whose signatures are detectable in instantaneous data. The probability is also high for transverse structures to occur between the focus of a spanwise structure and its associated saddle when Re_d=9750, but not when Re_d=2800. This is consistent with an increased vortex pairing frequency at the higher Re_d, as observed in instantaneous sectional streamlines.     

Investigation of the three-dimensional intermediate wake topology for a square cylinder at high Reynolds number

Simultaneous multi-point hotwire measurements are used to investigate the three-dimensional wake topology of a square cylinder at high Reynolds numbers. Wavelet techniques are applied to detect the flow structures and to inquire on the validity or extension of previously proposed low Reynolds number topological models to turbulent wakes. Our results suggest that a flow topological model similar to the horizontal perturbation model proposed by Meiburg and Lasheras (J Fluid Mech 190:1–37, 1988) but with alternate rib cuts in the horizontal plane is plausible for the intermediate wake topology.

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Surface‐sampled simulations of turbulent flow at high Reynolds number

A new approach to turbulence simulation, based on a combination of large eddy simulation (LES) for the whole flow and an array of non–space‐filling quasi‐direct numerical simulations (QDNS), which sample the response of near‐wall turbulence to large‐scale forcing, is proposed and evaluated. The technique overcomes some of the cost limitations of turbulence simulation, since the main flow is treated with a coarse‐grid LES, with the equivalent of wall functions supplied by the near‐wall sampled QDNS. Two cases are tested, at friction Reynolds number Re_τ=4200 and 20000. The total grid point count for the first case is less than half a million and less than 2 million for the second case, with the calculations only requiring a desktop computer. A good agreement with published direct numerical simulation (DNS) is found at Re_τ=4200, both in the mean velocity profile and the streamwise velocity fluctuation statistics, which correctly show a substantial increase in near‐wall turbulence levels due to a modulation of near‐wall streaks by large‐scale structures. The trend continues at Re_τ=20000, in agreement with experiment, which represents one of the major achievements of the new approach. A number of detailed aspects of the model, including numerical resolution, LES‐QDNS coupling strategy and subgrid model are explored. A low level of grid sensitivity is demonstrated for both the QDNS and LES aspects. Since the method does not assume a law of the wall, it can in principle be applied to flows that are out of equilibrium.     

Coherent and turbulent process analysis in the flow past a circular cylinder at high Reynolds number

This article presents an experimental study of the turbulent flow past a circular cylinder at high Reynolds number by means of advanced optical measurements techniques. Following previous studies using standard PIV and stereoscopic PIV (3C PIV), TRPIV and 3C-TRPIV have been employed in low subsonic wind tunnel environment. The database consisting of statistical and time-dependent fields aims at providing a physical analysis of the coherent and turbulent part, as well as a proper basis for validation and improvement of recent turbulence modelling approaches for strongly detached flow at high Reynolds number. As the nonlinear interaction between the coherent and turbulent dynamics have to be taken into account in a model, particular attention is paid to a decomposition of the flow into a coherent and a turbulent part, and to the analysis of their dynamics. This is achieved both using phase averaging and Proper Orthogonal Decomposition. For phase averaging, the two first POD coefficients are used for the evaluation of the vortex shedding phase angle. Furthermore, selected results of a Detached Eddy Simulation which had been validated by means of the experiment, are also presented to contribute to the physical analysis. The present study's experimental data resolved in space and time allow the confirmation of the conditional averaging for the turbulent stresses evaluation, by alleviating their overestimation due to phase jitter that occurs between the trigger signal and the velocity, when the phase angle is determined from a wall pressure signal. A more accurate physical analysis of the flow is achieved, particularly regarding the occurrence of irregular vortex shedding.     

Large-scale dynamics in high Reynolds number jets and jet flames

The far-field large-scale dynamics of a momentum-driven Re = 2 × 10⁸ non-reacting jet and a Re = 3 × 10⁷ jet diffusion flame are presented and compared. The results are derived from computer graphic volume rendering of a set of sequential images of each flow. When compared to conventional display techniques, volume rendering, by allowing many frames of a movie sequence to be presented simultaneously, more clearly shows the detailed flow evolution. For the non-reacting jet we see the passage and growth of large-scale organized structures up through the jet column, the axial velocity decay of the structures, the fluid entrainment patterns, and occasional pairing events. A rendering of a non-sequential set of images shows no discernible organized component. Volume rendering of the reacting jet shows a similar pattern of burning large-scale organized structures which convert over considerable axial distances but without the corresponding velocity decay, similar to observations of laboratory flames. The images presented here are believed to be some of the most direct visual evidence to date for large-scale organized motions in the far-field of high Reynolds number, fully developed jets and jet flames. Since conditional sampling techniques are not used, we believe that the volume renderings seen here are likely to be representative of the natural development of jet flows.     

Calculation of Reynolds stresses in turbulent supersonic flows

The baseline numerical procedure of interest in this study combines flux vector splitting, flux difference splitting and an explicit treatment of the diffusion terms of the flow equations. The viscous terms are treated explicitly to preserve the wave propagation properties of the Euler fluxes and permit splitting. The experience with this scheme has been limited to laminar or, at best, ‘eddy viscosity’ flows. In this paper the applicability of the scheme is extended to include the calculation of turbulent Reynolds stresses in supersonic flows. The schemes and our implementation are discussed. Both laminar and turbulence subsets of the Reynolds/Favre-averaged equations are tested, with a discussion of relative performance. The test problem for turbulence consists of a zero-pressure-gradient supersonic boundary layer as well as a supersonic boundary layer experiencing the combined effects of adverse pressure gradient, bulk compression and a concave streamline curvature. Excellent agreement with experimental measurements is observed for most of the quantities compared, which suggests that the numerical procedures presented in this paper are potentially very useful.     

Double large field stereoscopic PIV in a high Reynolds number turbulent boundary layer

An experiment on a flat plate turbulent boundary layer at high Reynolds number has been carried out in the Laboratoire de Mecanique de Lille (LML, UMR CNRS 8107) wind tunnel. This experiment was performed jointly with LEA (UMR CNRS 6609) in Poitiers (France) and Chalmers University of Technology (Sweden), in the frame of the WALLTURB European project. The simultaneous recording of 143 hot wires in one transverse plane and of two perpendicular stereoscopic PIV fields was performed successfully. The first SPIV plane is 1?cm upstream of the hot wire rake and the second is both orthogonal to the first one and to the wall. The first PIV results show a blockage effect which based on both statistical results (i.e. mean, RMS and spatial correlation) and a potential model does not seem to affect the turbulence organization.     

TR-PIV measurement of the wake behind a grooved cylinder at low Reynolds number

A comparative study of the wakes behind cylinders with grooved and smooth surfaces was performed with a view to understand the wake characteristics associated with the adult Saguaro cacti. A low-speed recirculation water channel was established for the experiment; the Reynolds number, based on the free-stream velocity and cylinder diameter (D), was kept at Re_D=1500. State-of-the-art time-resolved particle image velocimetry (TR-PIV) was employed to measure a total of 20 480 realizations of the wake field at a frame rate of 250 Hz, enabling a comprehensive view of the time- and phase-averaged wake pattern. In comparison to the wake behind the smooth cylinder, the length of the recirculation zone behind the grooved cylinder was extended by nearly 18.2%, yet the longitudinal velocity fluctuation intensity was considerably weakened. A global view of the peaked spectrum of the longitudinal velocity component revealed that the intermediate region for the grooved cylinder, which approximately corresponds to the transition region where the shear layer vortices interact, merge and shed before the formation of the Karman-like vortex street, was much wider than that for the smooth one. The unsteady events near St=0.3-0.4 were detected in the intermediate region behind the grooved cylinder, but no such events were found in the smooth cylinder system. Although the formation of the Karman-like vortex street was delayed by about 0.6D downstream for the grooved cylinder, no prominent difference in the vortex street region was found in the far wake for both cylinders. The Proper Orthogonal Decomposition (POD) method was used extensively to decompose the vector and swirling strength fields, which gave a close-up view of the vortices in the near wake. The first two POD modes of the swirling strength clarified the spatio-temporal characteristics of the shear layer vortices behind the grooved cylinder. The small-scale vortices superimposed on the shear layers behind the grooved cylinder were found to be generated and convected downstream in the same phase, which would significantly reduce the fluctuating force on the cylinder surface.     

Turbulence properties in the cylinder wake at high Reynolds numbers

The present contribution analyses the turbulence properties in unsteady flows around bluff body wakes and provides a database for improvement and validation of turbulence models, concerning the present class of nonequilibrium flows. The flow around a circular cylinder with a low aspect ratio and a high blockage coefficient is investigated. This confined environment is used in order to allow direct comparisons with realisable 3-D Navier–Stokes computations avoiding ‘infinite’ conditions. The flow is investigated in the beginning of the critical regime at Reynolds number 140 000. The analysis is carried out by means of 2-D PIV, of 3-C PIV and of high-frequency 2-D PIV. The experimental analysis contributes to confirm the validity of advanced statistical turbulence modelling for unsteady flows around bodies.     

Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD

The flow past a circular cylinder at high Reynolds number is studied by means of PIV, 3C-PIV and Time-Resolved PIV techniques. One of the goals of this study was to allow comparisons with numerical simulations on a domain identical to that of the experiment. For this reason, the cylinder was placed in a confined environment, with a high blockage and a low aspect ratio, thereby allowing computations on a mesh of reasonable size, and avoiding “infinite conditions”. This paper deals with the decomposition of the flow in a coherent and random parts. To this aim, phase averaged quantities were first obtained using the wall pressure signal on the cylinder as a trigger signal. This was achieved using both conditional sampling and LSE with similar results. This decomposition is then analysed using the Time Resolved PIV measurements, as well as by comparison of the contributions of the organised and turbulent fluctuations to the time-independent Reynolds stress tensor with those estimated from velocity spectra by interpolation and integration of the continuous part. In agreement with other studies, it is found that the contribution of the turbulent motion is overestimated as a result of the occurence of phase jitter between the trigger and velocity signal. A POD analysis was then performed to extract the coherent motion and to compare this decomposition with that obtained by phase averaging. Similarly to the phase averaging, the POD allows the decomposition of the time-independent stress tensor as the sum of two contributions corresponding to the first N modes, and the rest of the modes. This decomposition is then analysed by comparing these contributions to those obtained from the velocity spectra, according to the value N chosen. It is found that these contributions are strongly dependent on N, and the contribution of the first modes greatly overestimate the coherent motion if N is too large. In order to obtain a good decomposition of the flow in coherent and random parts, the difficulty in this case lies in the choice of the modes. Finally, the POD coefficients of the first two modes are used instead of the pressure signal to determine the phase of the vortex shedding, and the phase averaging is reconsidered. It is found that the phase averaged vortices are less smeared by the averaging process, the turbulent stresses better follow the evolution of the vortices, and the contributions of both coherent and turbulent fluctuations are found to agree well with those evaluated from the velocity spectra. This enhancement is obtained because the phase angle is determined directly from the velocity fields to be averaged, thereby reducing the phase-jitter effect. A comparison with a detached eddy simulation is also briefly shown and demonstrates the high level of agreement obtainable between simulation and experiment, as well as confirming the enhancement of the phase averaging using this procedure.     

Direct numerical simulation of supersonic pipe flow at moderate Reynolds number

We study compressible turbulent flow in a circular pipe at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies. Regarding velocity statistics, we find that Huang’s transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson (2016) yields better representation of the effects of strong variation of density and viscosity occurring in the buffer layer on the mean velocity distribution. A clear logarithmic layer is recovered in terms of transformed velocity and wall distance coordinates at the higher Reynolds number under scrutiny (Re_τ ≈ 1000), whereas the core part of the flow is found to be characterized by a universal parabolic velocity profile. Based on formal similarity between the streamwise velocity and the passive scalar transport equations, we further propose an extension of the above compressibility transformations to also achieve universality of passive scalar statistics. Analysis of the velocity/temperature relationship provides evidence for quadratic dependence which is very well approximated by the thermal analogy proposed by Zhang et al. (2014). The azimuthal velocity and scalar spectra show an organization very similar to canonical incompressible flow, with a bump-shaped distribution across the flow scales, whose peak increases with the wall distance. We find that the size growth effect is well accounted for through an effective length scale accounting for the local friction velocity and for the local mean shear.     

Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number

Two- and three-dimensional numerical simulations of the flow around two circular cylinders in tandem arrangements are performed. The upstream cylinder is fixed and the downstream cylinder is free to oscillate in the transverse direction, in response to the fluid loads. The Reynolds number is kept constant at 150 for the two-dimensional simulations and at 300 for the three-dimensional simulations, and the reduced velocity is varied by changing the structural stiffness. The in-line centre-to-centre distance is varied from 1.5 to 8.0 diameters, and the results are compared to that of a single isolated flexible cylinder with the same structural characteristics, m^?=2.0 and ζ=0.007. The calculations show that significant changes occur in the dynamic behaviour of the cylinders, when comparing the flow around the tandem arrangements to that around an isolated cylinder: for the tandem arrangements, the lock-in boundaries are wider, the maximum displacement amplitudes are greater and the amplitudes of vibration for high reduced velocities, outside the lock-in, are very significant. The main responsible for these changes appears to be the oscillatory flow in the gap between the cylinders.     

Stability of a supersonic flat-plate wake (Comparison of numerical and experimental results)

The stability of the wake downstream of a plat plate with a blunt trailing edge is numerically investigated at a supersonic freestream velocity. The calculated stability characteristics are compared with the experimental data.     

Calibration and use of inclined hot wires in a supersonic turbulent wake

The calibration of inclined hot wires used with constant temperature anemometers is performed for Mach numbers 2 and 3. The determination of the three relevant sensitivity coefficients is made for overheat ratios from 0.3 to 0.8. A strong unexpected influence of the overheat is observed independent of the apparatus used. Some particular behaviour of the angular sensitivity coefficient is observed for small-size wires; the origin of the two kinds of behaviour observed is not explained but is thought to be due to geometrical characteristics. Careful calibrations should be performed for each wire prior to any measurements. The study of turbulent stresses in a symmetrical wake at Mach 3.3 is then performed. It allows a check on the validity of the method using characteristic properties of such a flow.     

Investigation of the three-dimensional turbulent near-wake structure past a flat plate by tomographic PIV at high Reynolds number

This paper reports an experimental investigation of the high-Reynolds number turbulent flow past a thin flat plate with sharp untapered edges, by means of tomographic PIV. The experiments, carried out in the S4 wind tunnel of IMFT, have quantified the three-dimensional coherent vortex structures, by means of 3-D Proper Orthogonal Decomposition and reconstruction. The interaction of the most energetic coherent structures with the random turbulence is discussed. Furthermore, Proper Orthogonal Decomposition (POD), analysis allowed evaluation of three-dimensional phase-averaged dynamics that quantified the vortex shedding mechanism as well as the influence of higher modes associated with the finer-scale turbulence.     

Large eddy simulation of a developing turbulent boundary layer at a low Reynolds number

A spectral code has been used to simulate a developing turbulent boundary layer at low Reynolds number Re_θ (based on free stream velocity and momentum thickness) between 353 and 576. The starting field was generated by allowing a step change of temperature to diffuse outwards from one wall in a fully developed channel flow. The thermal boundary layer so created was conditionally sampled to convert it into a momentum boundary layer with an irrotational free stream region, a process which is justified by appeal to experiments. This initial field was allowed to develop until the momentum boundary layer thickness δ₉₉₅ had grown to about 1·5 times its original thickness. The results of the simulation have been compared with a wide range of experimental data. The outcome of this comparison is generally very satisfactory; the main trends of the experiments are well reproduced and our simulation supplements and extends the existing sets of experimental data. The simulation also gives pressure statistics which cannot be obtained experimentally. In particular, it gives the contribution of pressure diffusion to the balance equations for the Reynolds stress and indicates the error produced by omitting this term.     

The effect of Reynolds number on a turbulent far-wake

The turbulent far-waked generated by a circular cylinder is investigated for two values (1350 and 4600) of the Reynolds number Re _θ (based on the free stream velocity and the momentum thickness). Two arrays of sixteen X-wires, eight in the (x,?y)-plane and eight in the (x,?z)-plane, are used to capture the main features of the large-scale motion in two orthogonal planes. Both the magnitude of the measured Reynolds stresses and the size of the two-point velocity and vorticity correlation contours increase with Reynolds number. The probability density function and spectra of the velocity signals also exhibit differences with Re _θ. A comparison of centerline turbulence intensities with those in the literature suggests that the Reynolds number dependence may disappear for Re _θ?5000.     

Numerical study of turbulent plane Couette flow at low Reynolds number

A direct numerical simulation of fully developed turbulent plane Couette flow has been performed. Unsteady large-scale structures, which contributed to the instantaneous energy level, were observed. These evolving and drifting vortical structures vanished after time-averaging, and the resulting mean velocity and streamwise turbulence intensity compared favourably with recent laboratory data.