Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re _θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy ⁺=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re _θ =23,200 and previously reported data for a much thinner boundary layer at Re _θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re _θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations. Received: 9 June 2000/Accepted: 26 January 2001     

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.     

Influence of Reynolds number on characteristics of turbulent wall boundary layers

Hot-wire anemometer measurements, using two types of probes, are reported for wall boundary layer flows with particular attention being given to the near-wall region and to measurements at high Reynolds numbers up to R 15,000. To obtain accurate near-wall measurements, the influence of wall proximity on hot-wire readings was eliminated by using a highly insulating wall material. Measurements were carried out with a single hot-wire boundary layer probe to obtain the longitudinal velocity informatemperature-wake sensor for the cross flow tion and a hot-wire, information.The results provided in the paper include measurements of averaged properties like mean velocity, rms-quantities of velocity fluctuations, probability density distributions etc. Conditional averages are also provided in order to yield information related to coherent flow structures present in boundary layer flows. It is shown that these structure remain present up to the highest Reynolds number investigated in the present study. The conditionally averaged data provide quantitative information on the mechanisms that are involved in the production of turbulence in boundary-layer flows.     

Low Reynolds number axisymmetric turbulent boundary layer on a cylinder

In the present study, an axisymmetric turbulent boundary layer growing on a cylinder is investigated experimentally using hot wire anemometry. The combined effects of transverse curvature as well as low Reynolds number on the mean and turbulent flow quantities are studied. The measurements include the mean velocity, turbulence intensity, skewness and flatness factors in addition to wall shear stress. The results are presented separately for the near wall region and the outer region using dimensionless parameters suitable for each case. They are also compared with the results available in the open literature.The present investigation revealed that the mean velocity in near wall region is similar to other simple turbulent flows (flat plate boundary layer, pipe and channel flows); but it differs in the logarithmic and outer regions. Further, for dimensionless moments of higher orders, such as skewness and flatness factors, the main effects of the low Reynolds number and the transverse curvature are present in the near wall region as well as the outer region.     

Vortex reynolds number in turbulent boundary layers

The effects of vortex Reynolds number on the statistics of turbulence in a turbulent boundary layer have been investigated. Vortex Reynolds number is defined as the ratio of circulation around the vortex structure to the fluid viscosity. The vortex structure of the outer region was modeled and a full numerical simulation was then conducted using a high-order spectral method. A unit domain of the outer region of a turbulent boundary layer was assumed to be composed of essentially three elements: a wall, a Blasius mean shear, and an elliptic vortex inclined at 45° to the flow direction. The laminar base-flow Reynolds number is roughly in the same range as that of a turbulent boundary layer based on eddy viscosity, and the vortex-core diameter based on the boundary-layer thickness is nearly the same as the maximum mixing length in a turbulent boundary layer. The computational box size, namely, 500, 150, and 250 wall units in the streamwise, surface-normal, and spanwise directions, respectively, is approximately the same as the measured quasi-periodic spacings of the near-wall turbulence-producing events in a turbulent boundary layer. The effects of vortex Reynolds number and the signs of the circulation on the moments of turbulence were examined. The signs mimic the ejection and sweep types of organized motions of a turbulent boundary layer. A vortex Reynolds number of 200 describes the turbulence moments in the outer layer reasonably well.     

LDA measurements in low Reynolds number turbulent boundary layer

LDA measurements of the mean velocity in a low Reynolds number turbulent boundary layer allow a direct estimate of the friction velocity U from the value of /y at the wall. The trend of the Reynolds number dependence of / is similar to the direct numerical simulations of Spalart (1988).     

High Reynolds number thick axisymmetric turbulent boundary layer measurements

Experimental measurements of the wall shear stress and momentum thickness for thick axisymmetric turbulent boundary layers are presented. The use of a full-scale towing tank allowed zero pressure gradient turbulent boundary layers to be developed on cylinders with diameters of 0.61, 0.89, and 2.5 mm and lengths ranging from 30 m to 150 m. Moderate to high Reynolds numbers (10⁴<Re <10⁵, 10⁸<Re _L<10⁹) are considered. The relationship between the mean wall shear stress, cylinder diameter, cylinder length, and speed was investigated, and the spatial growth of the momentum thickness was determined. The wall shear stress is significantly higher, and the spatial growth of the boundary layers is shown to be lower than for a comparable flat-plate case. The mean wall shear stress exhibits variations with length that are not seen in zero pressure gradient flat plate turbulent boundary layers. The ratio of outer to inner boundary layer length scales is found to vary linearly with Re , which is qualitatively similar to a flat plate turbulent boundary layer. The quantitative effect of a riblet cylindrical cross-sectional geometry scaled for drag reduction based on flat plate criteria was also measured. The flat plate criteria do not lead to drag reduction for this class of boundary layer shear flows.List of symbols a cylinder radius, mm - A _s total cylindrical surface area, m² - C _d tangential drag coefficient - D drag force, Newtons - boundary layer thickness, mm - * displacement thickness, mm - h riblet height, mm - L cylinder length, m - kinematic viscosity, m²/s - momentum thickness, mm - fluid density, kg/m³ - r radial coordinate, mm - Re _L Reynolds number based on length= - Re Reynolds number based on momentum thickness= - s riblet spacing, mm - _w mean wall shear stress, N/m² - u(r) mean streamwise velocity, m/s - u friction velocity= - U _o tow speed, m/s - x streamwise coordinate, m     

Surface roughness effects in turbulent boundary layers

The effects of surface roughness on a turbulent boundary layer are investigated by comparing measurements over two rough walls with measurements from a smooth wall boundary layer. The two rough surfaces have very different surface geometries although designed to produce the same roughness function, i.e. to have nominally the same effect on the mean velocity profile. Different turbulent transport characteristics are observed for the rough surfaces. Substantial effects on the stresses occur throughout the layer showing that the roughness effects are not confined to the wall region. The turbulent energy production and the turbulent diffusion are significantly different between the two rough surfaces, the diffusion having opposite sign in the region γ/δ < 0.5. Although velocity spectra exhibit differences between the three surfaces, the mean energy dissipation rate does not appear to be significantly affected by the roughness. Received: 19 August 1998/Accepted: 16 February 1999     

Enhancement of finite Reynolds number effects: Inner-outer sublayer interaction in the turbulent boundary layer

Residual Reynolds number effects in the established data for the velocity profile in turbulent boundary layers (and in pipe or channel flows) are found to be remarkably large. We combine two eddy-viscosity models (with overlapping validity in the inertial sublayer) and show (both analytically and numerically) that this enhancement (which involves a viscous correlation length) arises from inner-outer sublayer interaction.     

Reynolds number effects on a turbulent boundary layer with separation,reattachment, and recovery

The present paper addresses experimental studies of Reynolds number effects on a turbulent boundary layer with separation, reattachment, and recovery. A momentum thickness Reynolds number varies from 1,100 to 20,100 with a wind tunnel enclosed in a pressure vessel by varying the air density and wind tunnel speed. A custom-built, high-resolution laser Doppler anemometer provides fully resolved turbulence measurements over the full Reynolds number range. The experiments show that the mean flow is at most a very weak function of Reynolds number while turbulence quantities strongly depend on Reynolds number. Roller vortices are generated in the separated shear layer caused by the Kelvin–Helmholtz instability. Empirical Reynolds number scalings for the mean velocity and Reynolds stresses are proposed for the upstream boundary layer, the separated region, and the recovery region. The inflectional instability plays a critical role in the scaling in the separated region. The near-wall flow recovers quickly downstream of reattachment even if the outer layer is far from an equilibrium state. As a result, a stress equilibrium layer where a flat-plate boundary layer scaling is valid develops in the recovery region and grows outward moving downstream.     

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.     

Shock-induced turbulent boundary layers

Experimental data for an incompressible turbulent moving surface boundary layer are reviewed and a theoretical extension of their predictions is suggested for the case of finite free stream velocities. It is argued that such a boundary layer provides an incompressible analogue for shock-induced turbulent boundary layers. Coles's transformation is used to predict the behaviour of the shock-induced case from the incompressible analogue. These predictions are used to attempt to correlate the available experimental shock-induced turbulent boundary layer data. It is felt that the correlations are reasonably successful for some of the data. It is suggested that the remaining data have been affected by the premature arrival of the contact region and reflected rarefaction wave.     

Thermal boundary condition effects on heat transfer in turbulent rough-wall boundary layers

Measurements and predictions are presented which investigate the effects of thermal boundary condition on heat transfer in the turbulent rough-wall boundary layer. Stanton number measurements are reported for the turbulent flow of air over rough plates with a variety of thermal boundary conditions on two separate rough surfaces. The cases considered are constant wall temperature, constant wall heat flux, step wall temperature, and piecewise linear wall temperature distributions. These measurements and data from other sources are compared with predictions using finite difference solutions of the discrete element roughness model and with superposition solutions. The predictions and the measurements are in good to excellent agreement.In dieser Arbeit werden Messungen und Berechnungen gezeigt, die den Einfluß der thermischen Randbedingungen auf die Wärmeübertragung in turbulenten Grenzschichten an rauhen Wänden untersuchen. Es werden Messungen der Stanton Zahl für turbulente Luftströmung über rauhe Platten an zwei separaten Oberflächen unter einer Reihe von thermischen Randbedingungen dargestellt. Die betrachteten Fälle sind konstante Wandtemperatur, konstanter Wärmestrom durch die Wand, abgestufte Wandtemperatur und stückweise konstante Wandtemperatur. Diese Messungen, sowie Daten anderer Untersuchungen, werden mit Berechnungen durch Finite-Differenzen Lösungen des Diskrete-Elemente-Rauhheits-Modells und Superpositionslösungen verglichen. Berechnungen und Messungen liegen in guter bis ausgezeichneter Übereinstimmung.     

Reynolds number effects on the mixing behavior of axisymmetric turbulent jets

Measurements of time-averaged jet fluid mass fraction and unmixedness are reported along the centerlines of axisymmetric jets having Reynolds numbers (Re) covering a range of 3,950–11,880. Jet gases investigated are propane, carbon tetrafluoride, and sulfur hexafluoride. The slopes for the fall off of inverse centerline mass fraction with distance are found to be independent of Re for moderate downstream distances, but virtual origins for the data are shown to move downstream with increasing Re. Unmixedness measurements show that flows with higher Re require longer flow distances to achieve asymptotic behavior. Results of other investigations reported in the literature are discussed which support the conclusions of this work. The relationship between the centerline mixing and entrainment behaviors of these flows is explored.     

Bursting frequency in turbulent boundary layers

Employing laser Doppler anemometry and VITA techniques, the bursting frequency in turbulent boundary layers has been measured over the Reynolds-number range 320 to 1470. The result indicates that the mean and non-dimensional bursting frequency scaled with the variables appropriate for the wall region was constant and independent of Reynoids number. When the same data are plotted using the outer variables of boundary layer to normalize the bursting frequency, the non-dimensional frequency increases as the Reynolds number increases. This is in agreement with the results of Blackwelder et al. (1983) who used hot wire anemometry and VITA technique. The project is supported by the National Natural Science Foundation of China     

Some equilibrium turbulent boundary layers

Using the Coles additive law of the wall and law of the wake for the mean velocity profile of a two-dimensional turbulent boundary layer, a differential equation for the friction and wake parameters is derived from the momentum integral equation with a view to finding out the conditions under which the boundary layer can exhibit equilibrium. It is predicted that equilibrium is possible for boundary layers in favorable pressure gradient over smooth as well as k-type rough walls. When the roughness height is allowed to increase linearly with the streamwise distance, equilibrium exists also in zero pressure gradient. For a d-type rough wall, equilibrium is possible for a certain range of pressure gradients, from favorable to adverse. Most of the predictions are verified by evaluating the friction and wake parameters from the available experimental data on mean velocity measurements.     

Interactive boundary layers in turbulent flow

An asymptotic analysis of the structure of the flow at high Reynolds number around a streamlined body is presented. The boundary layer is turbulent. This question is studied with the successive complementary expansion method, SCEM. The starting point is to look for a uniformly valid approximation (UVA) of the velocity field, including the boundary layer and the external flow. Thanks to the use of generalized expansions, SCEM leads to the theory of interactive boundary layer, IBL. For many years, IBL model has been used successfully to calculate aerodynamic flows. Here, the IBL model is fully justified with rational mathematical arguments. The construction of a UVA of the velocity profile in the boundary layer is also studied. To cite this article: J. Cousteix, J. Mauss, C. R. Mecanique 335 (2007).