Reynolds Number Turbulent Boundary Layer Research Articles

On the Formation Mechanisms of Artificially Generated High Reynolds Number Turbulent Boundary Layers

We investigate the evolution of an artificially thick turbulent boundary layer generated by two families of small obstacles (divided into uniform and non-uniform wall normal distributions of blockage). One- and two-point velocity measurements using constant temperature anemometry show that the canonical behaviour of a boundary layer is recovered after an adaptation region downstream of the trips presenting $$150~\%$$ higher momentum thickness (or equivalently, Reynolds number) than the natural case for the same downstream distance ( $$x\approx 3\,$$ m). The effect of the degree of immersion of the trips for $$h/\delta \gtrsim 1$$ is shown to play a secondary role. The one-point diagnostic quantities used to assess the degree of recovery of the canonical properties are the friction coefficient (representative of the inner motions), the shape factor and wake parameter (representative of the wake regions); they provide a severe test to be applied to artificially generated boundary layers. Simultaneous two-point velocity measurements of both spanwise and wall-normal correlations and the modulation of inner velocity by the outer structures show that there are two different formation mechanisms for the boundary layer. The trips with high aspect ratio and uniform distributed blockage leave the inner motions of the boundary layer relatively undisturbed, which subsequently drive the mixing of the obstacles’ wake with the wall-bounded flow (wall-driven). In contrast, the low aspect-ratio trips with non-uniform blockage destroy the inner structures, which are then re-formed further downstream under the influence of the wake of the trips (wake-driven).

大型風洞による高レイノルズ数乱流境界層実験の試み

High Reynolds number turbulent boundary layer measurement is performed in the RTRI's Large-scale low-noise wind tunnel in Maibara Japan. The momentum thickness Reynolds number is up to approximately 7×104 . The mean velocity profile shows a clear log-law region with Kármán constant 0.38. The turbulent intensity profile also shows the log-law scaling predicted by attached eddy model. These data will be used as the fundamental data base made in Japan which is also applicable to industrial application including railway technology.

Enhancing the accuracy of measurement techniques in high Reynolds number turbulent boundary layers for more representative comparison to their canonical representations

Existing differences between experimental, computational and theoretical representations of a particular flow do not allow one-to-one comparisons, prevent us from identifying the absolute contributions of the various sources of uncertainty in each approach, and highlight the importance of developing suitable corrections for experimental techniques. In this study we utilize the latest Pitot tube correction schemes to develop a technique which improves on the outcome of hot-wire measurements of mean velocity profiles in ZPG turbulent boundary layers over the range 11500<Reθ<21500. Measurements by Bailey et al. (2013), carried out with probes of diameters ranging from 0.2 to 1.89 mm, supplemented by other data with larger diameters up to 12.82 mm, are used first to develop a somewhat improved Pitot tube correction which is based on viscous, shear and near-wall schemes (which contribute with around 85% of the effect), together with a turbulence scheme which accounts for 15% of the whole correction. The correction proposed here leads to similar agreement with available high-quality datasets in the same Reynolds number range as the one proposed by Bailey et al. (2013), but this is the first time that the contribution of the turbulence scheme is quantified. In addition, four available algorithms to correct wall position in hot-wire measurements are tested, using as benchmark the corrected Pitot tube profiles with artificially simulated probe shifts and blockage effects. We find that the κB-Musker correction developed in this study produces the lowest deviations with respect to the introduced shifts. Unlike other schemes, which are based on a prescribed near-wall region profile description, the κB-Musker is focused on minimizing the deviation with respect to the κ̃B̃ relation, characteristic of wall-bounded turbulent flows. This general approach is able to locate the wall position in probe measurements of the wall-layer profiles with around one half the error of the other available methods. The difficulties encountered during the development of adequate corrections for high-Re boundary layer measurements highlight the existing gap between the conditions that can be reproduced and measured in the laboratory and the so-called canonical flows.

Drag Reduction Via Spanwise Transversal Surface Waves at High Reynolds Numbers

The impact of transversal spanwise traveling surface waves on the wall-shear stress distribution of high Reynolds number turbulent boundary layer flows is analyzed using high-resolution large-eddy simulations. The Reynolds numbers based on the friction velocity are Ret = 540, 906, 1908, and 2250. The surface wave motion defined by the amplitude, the wavelength, and the phase speed in inner coordinates is constant for the investigated Ret range. When the Reynolds number is increased, the drag reduction decreases from 11 % to 1 %. That is, in contrast to the result in the literature for actuated channel flow, which shows the drag reduction (DR) as a function of the Reynolds number based on the friction velocity to be proportional to \(Re_{\tau }^{-0.2}\) for Ret = 1000, the current analysis for evolving turbulent boundary layers over actuated surfaces leads to DR\(\sim Re_{\tau }^{-1}\). The detailed analysis of the velocity profiles in the viscous sublayer clearly shows that the major difference in the velocity gradient occurs above the trough where the velocity gradient is reduced by increasing Reynolds number. At low Reynolds numbers, the peak value of the wall-normal vorticity distribution above the moving wave crest and above the moving wave trough is much smaller than that of the non-actuated wall resulting in a pronounced drag reduction. At increasing Reynolds number, the difference in the wall-normal vorticity distribution in the near-wall region for the actuated and the non-actuated wall becomes smaller leading to a lower drag reduction. The analysis of the anisotropy map shows that the wall actuation excites the two-component turbulence in the viscous sublayer above the crest and the trough. That is, unlike passively controlled flow, the drag reducing mechanism is related not to the one-component but to the two-component state in the anisotropy map.

High spatial range velocity measurements in a high Reynolds number turbulent boundary layer

Here, we detail and analyse a multi-resolution particle image velocity measurement that resolves the wide range of scales prevalent in a zero pressure gradient turbulent boundary layer at high Reynolds numbers (up to Reτ ≈ 20 000). A unique configuration is utilised, where an array of eight high resolution cameras at two magnification levels are used simultaneously to obtain a large field of view, while still resolving the smaller scales prevalent in the flow. Additionally, a highly magnified field of view targeted at the near wall region is employed to capture the viscous sublayer and logarithmic region, with a spatial resolution of a few viscous length scales. Flow statistics from these measurements show good agreement with prior, well resolved hot-wire anemometry measurements. Analysis shows that the instantaneous wall shear stress can be reliably computed, which is historically known to be challenging in boundary layers. A statistical assessment of the wall shear stress shows good agreement with existing correlations, prior experimental and direct numerical simulation data, extending this view to much higher Reynolds numbers. Furthermore, conditional analysis using multiple magnification levels is detailed, to study near-wall events associated with high skin friction fluctuations and their associated overlaying structures in the log region. Results definitively show that the passage of very large-scale positive (or negative) velocity fluctuations are associated with increased (or reduced) small-scale variance in wall shear stress fluctuations.

Multiscale Geometry and Scaling of the Turbulent-Nonturbulent Interface in High Reynolds Number Boundary Layers

The scaling and surface area properties of the wrinkled surface separating turbulent from nonturbulent regions in open shear flows are important to our understanding of entrainment mechanisms at the boundaries of turbulent flows. Particle image velocimetry data from high Reynolds number turbulent boundary layers covering three decades in scale are used to resolve the turbulent-nonturbulent interface experimentally and, for the first time, determine unambiguously whether such surfaces exhibit fractal scaling. Box counting of the interface intersection with the measurement plane exhibits power-law scaling, with an exponent between -1.3 and -1.4. A complementary analysis based on spatial filtering of the velocity fields also shows power-law behavior of the coarse-grained interface length as a function of filter width, with an exponent between -0.3 and -0.4. These results establish that the interface is fractal-like with a multiscale geometry and fractal dimension of Df≈2.3-2.4.

Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes

AbstractThis article reports on one component of a larger study on measurement of the zero-pressure-gradient turbulent flat plate boundary layer, in which a detailed investigation was conducted of the suite of corrections required for mean velocity measurements performed using Pitot tubes. In particular, the corrections for velocity shear across the tube and for blockage effects which occur when the tube is in close proximity to the wall were investigated using measurements from Pitot tubes of five different diameters, in two different facilities, and at five different Reynolds numbers ranging from ${\mathit{Re}}_{\theta } = 11\hspace{0.167em} 100$ to 67 000. Only small differences were found amongst commonly used corrections for velocity shear, but improvements were found for existing near-wall proximity corrections. Corrections for the nonlinear averaging of the velocity fluctuations were also investigated, and the results compared to hot-wire data taken as part of the same measurement campaign. The streamwise turbulence-intensity correction was found to be of comparable magnitude to that of the shear correction, and found to bring the hot-wire and Pitot results into closer agreement when applied to the data, along with the other corrections discussed and refined here.

0510 高レイノルズ数乱流境界層の対数領域における確率密度関数の自己相似性(OS5-3 壁乱流:統計,構造,動力学の理解,OS5 壁乱流:統計,構造,動力学の理解)

Recently, a relation between the mean velocity profile (MVP) and the turbulence intensity distribution have been reported as these have logarithmic portion in the almost same range of distance from the wall. We focus on the relation between MVP and probability density function (PDF) of measured velocity. We found the two characteristic regions in the Kullback-Leibler divergence distribution in the high Reynolds number turbulent boundary layer at Re_τ =7100. These regions have self-similarity of PDF, but each similarity is not equal. So, these regions have different statistic characteristics each other. We found that these regions are connected to two characteristic regions of quasi logarithmic region and classical logarithmic region in MVP.

0309 一様吹出しを伴う高レイノルズ数乱流境界層のデタッチドエディシミュレーション(OS3-2 流れの抵抗低減,OS3 流れの抵抗低減)

0309 一様吹出しを伴う高レイノルズ数乱流境界層のデタッチドエディシミュレーション(OS3-2 流れの抵抗低減,OS3 流れの抵抗低減)

A constraint for the subgrid-scale stresses in the logarithmic region of high Reynolds number turbulent boundary layers: A solution to the log-layer mismatch problem

This paper addresses one of the most persisting problems in wall-modeled large eddy simulation (LES): the overshoot of the mean velocity gradient near the wall, often referred to as the “log-layer mismatch” problem. An analysis of the relationship between turbulent kinetic energy budgets and mean velocity gradient is elaborated for both direct numerical simulations and LES of fully developed channel flow at high Reynolds number. Based on the analysis, a self-adaptive Smagorinsky model for LES of high-Reynolds-number boundary layer flows is proposed, in which the Smagorinsky coefficient is dynamically adjusted so that a logarithmic mean velocity distribution is captured. The model is then implemented in a second-order finite-volume code, and applied to a high-Reynolds-number channel flow with rough walls. We find that the desired logarithmic mean velocity distribution is well predicted for different resolutions and grid aspect ratios.

About turbulence statistics in the outer part of a boundary layer developing over two-dimensional surface roughness

The influence of surface roughness on a high Reynolds number turbulent boundary layer is investigated in the light of Townsend's wall similarity hypothesis. There is conflicting information in the literature about the effect of surface roughness on the flow structure in the outer layer. Flows over roughness consisting of spanwise rods appear to show unusually strong interaction between the wall and the wake region. It has been suggested that flows which show strong modifications in the outer layer suffer from lack of scale separation between the roughness scale and the largest scale given by the boundary layer thickness. One of the flows which have documented significant roughness effects across the entire layer is the boundary layer developing over roughness made up of spanwise aligned square bars. Here we compare one such flow taken at relatively low Reynolds number with measurements for a boundary layer which develops at much higher Reynolds number. The high Reynolds number (Reθ = 32 600) assures that the range of scale is wide, while at the same time the size of the roughness elements is sufficiently large for the flow to be fully rough. Both sets of data are compared to a smooth wall reference boundary layer and from probability distributions, the quadrant contributions to the shear stress and triple correlation profiles, we show that the outer layer changes are significantly reduced when increasing the Reynolds number and thereby the range of scales. In this case the wall perturbation of the flow is shown to be much smaller than reported in other experiments using the same geometry. Here we find that the modifications in the turbulent structure are limited to about five times the roughness scale. This is in accordance with the wall similarity hypothesis.

Flow organization near shear layers in turbulent wall-bounded flows

Coherent vortex clusters are extracted from a boundary layer direct numerical simulation database by means of conditional averages associated with the local occurrence of strong shear layers, extending the work of Klewicki and Hirschi (J. C. Klewicki and C. R. Hirschi, Flow field properties local to near-wall shear layers in a low Reynolds number turbulent boundary layer, Phys. Fluids 16 (2004), p. 4163). The results support strong association between shear layers and vortex tubes, and suggest that latter are primarily produced upon roll-up of vortex sheets. Four configurations, which are characterized in terms of the vorticity field geometry and their contribution to the turbulent shear stress and skin friction, are recovered. The vortex modes associated with streamwise and wall-normal aligned shear layers resemble symmetric and one-legged hairpin vortices, and suggest that inner–outer layers interactions may be important in stimulating the eruption of near-wall shear layers. The modes associated with quasi-longitudinal shear layers closely recall the staggered vortices arrangement proposed in models of wall turbulence self-sustainment (J. Jeong, F. Hussain, W. Schoppa, and J. Kim, Coherent structures near the wall in a turbulent channel flow, J. Fluid Mech. 332 (1997), p. 185), and also highlight a mechanism of generation of secondary vorticity through a rubbing effect (P. Orlandi, Vortex dipole rebound from a wall, Phys. Fluids A 2 (1990), p. 1429).

The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Reθ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.

Full 3D correlation tensor computed from double field stereoscopic PIV in a high Reynolds number turbulent boundary layer

The turbulence structure near a wall is a very active subject of research and a key to the understanding and modeling of this flow. Many researchers have worked on this subject since the fifties Hama et al. (J Appl Phys 28:388–394, 1957). One way to study this organization consists of computing the spatial two-point correlations. Stanislas et al. (C R Acad Sci Paris 327(2b):55–61, 1999) and Kahler (Exp Fluids 36:114–130, 2004) showed that double spatial correlations can be computed from stereoscopic particle image velocimetry (SPIV) fields and can lead to a better understanding of the turbulent flow organization. The limitation is that the correlation is only computed in the PIV plane. The idea of the present paper is to propose a new method based on a specific stereoscopic PIV experiment that allows the computation of the full 3D spatial correlation tensor. The results obtained are validated by comparison with 2D computation from SPIV. They are in very good agreement with the results of Ganapthisubramani et al. (J Fluid Mech 524:57–80, 2005a).

High Reynolds number effects in wall turbulence

A review of recent advances in the study of high Reynolds number turbulent boundary layers is given. The emergent regime of very large-scale structures in the logarithmic region and their subsequent influence on the near-wall cycle challenges many of the previously held assumptions regarding scaling of turbulent boundary layers at high Reynolds numbers. Experimental results are presented to illustrate the superimposition of large-scale energy onto the near-wall cycle, together with an interaction well described by an amplitude modulation effect. Both phenomena are shown to increase in magnitude (as compared to viscous-scaled events) as Reynolds number increases. These observations lead to a possible model for a statistically representative near-wall velocity signal (giving accurate energy spectra) based on a given filtered velocity signal from the log region of a high Reynolds number turbulent flow.

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.

Particle Image Velocimetry Study of Rough-Wall Turbulent Flows in Favorable Pressure Gradient

This paper reports an experimental investigation of the effects of wall roughness and favorable pressure gradient on low Reynolds number turbulent flow in a two-dimensional asymmetric converging channel. Flow convergence was produced by means of ramps (of angles 2 deg and 3 deg) installed on the bottom wall of a plane channel. The experiments were conducted over a smooth surface and over transitionally rough and fully rough surfaces produced from sand grains and gravel of nominal mean diameters 1.55 mm and 4.22 mm, respectively. The dimensionless acceleration parameter was varied from 0.38×10−6 to 3.93×10−6 while the Reynolds number based on the boundary layer momentum thickness was varied from 290 to 2250. The velocity measurements were made using a particle image velocimetry technique. From these measurements, the distributions of the mean velocity and Reynolds stresses were obtained to document the salient features of transitionally and fully rough low Reynolds number turbulent boundary layers subjected to favorable pressure gradient.

Development of a Hot-Wire Probe with Two Parallel Wires Placed Closely Together

We manufactured a new hot-wire probe with two parallel wires placed closely together for measuring a transitional boundary-layer flow. The main feature of this new probe is that it is much smaller than a conventional multi-sensor probe, such as an X-type probe. Thus, the new probe can be regarded as a sensor similar in configuration to a single normal probe and is expected to provide high spatial resolution for fluctuating velocities in a transitional boundary layer. The measurement principle is very simple, as the streamwise and the normalwise velocity components are simultaneously obtained from the sums and the differences of the linearized outputs of two hot-wire circuits with the aid of the look-up-matrix method. It was found that the complicated relations between the hot-wire-circuit outputs and the flow angle can be simplified by limiting the flow angle to within θ = ±30 deg. The new hot-wire probe was used to measure the velocity profiles in a low Reynolds number turbulent boundary layer. The results revealed that the probe is a useful tool for measuring velocities in a transitional boundary layer having a thickness of only several mm.

Measurements of skin friction in water using surface stress sensitive films

The measurement of skin friction on hydrodynamic surfaces is of significant value for the design of advanced naval technology, particularly at high Reynolds numbers. Here we report on the development of a new sensor for measurement of skin friction and pressure that operates in both air and water. This sensor is based on an elastic polymer film that deforms under the action of applied normal and tangential loads. Skin friction and pressure gradients are determined by monitoring these deformations and then solving an inverse problem using a finite element model of the elastic film. This technique is known as surface stress sensitive films. In this paper, we describe the development of a sensor package specifically designed for two-dimensional skin friction measurements at a single point. The package has been developed with the goal of making two-dimensional measurements of skin friction in water. Quantitative measurements of skin friction are performed on a high Reynolds number turbulent boundary layer in the 12 inch water tunnel at Penn State University. These skin friction measurements are verified by comparing them to measurements obtained with a drag plate as well as by performing two-dimensional velocity measurements above the sensor using a laser Doppler velocimetry system. The results indicate that the sensor skin friction measurements are accurate to better than 5% and repeatable to better than 2%. The directional sensitivity of the sensor is demonstrated by positioning the sensor at several orientations to the flow. A final interesting feature of this sensor is that it is sensitive to pressure gradients, not to static pressure changes. This feature should prove useful for monitoring the skin friction on a seafaring vessel as the operating depth is changed.

Measurements of the wall pressure spectra on a full-scale experimental towed array

Turbulent wall pressure data acquired during tests of a full-scale experimental towed array over a range of tow speeds in straight tows and turns is presented. The experimental towed array contained a linear array of sensors mounted at the fluid–solid interface to measure the spectra of the wall pressure fluctuations due to the cylindrical turbulent boundary layer. The physics are dominated by the growth of a thick, high Reynolds number turbulent boundary layer at arc length Reynolds numbers as high as 9×10 8. The measured wavenumber-frequency spectra, autospectra, cross-spectral decay and convection velocities are presented. A well-defined convective ridge exists in the wavenumber-frequency spectra obtained during straight tows and turns. Turns give rise to a complicated fluid–structure interaction problem, but do not lead to the separation of the turbulent boundary layer. As the array moves through a turn, flow-induced vibrations of the array are shown to dominate the spectra at low frequencies, with more rapid decay in the measured coherence occurring at higher frequencies. The use of tow speed as a velocity scale is shown to collapse autospectra and convection velocities.