Comparison between rough- and smooth-wall turbulent boundary layers

Measurement of the local skin friction coefficient and re-examination of the Reynolds-number-effect on the mean flow quantities were made in a zero-pressure gradient, smooth wall, turbulent boundary layer. In order to do this fairly, the two-dimensionality of the flow field was carefully adjusted. And, the wall shear stress τω was determined by direct measurement using a floating element device. The Reynolds number based on the momentum thickness Rθ=U1θ / ν ranges from 840 to 6 220. The present experimental results of cf propose a new empirical formula which well represents the present experimental data and confirms that the Karman constant χ=0.41, which implies a slope of the logarithmic linear layer, is independent of Rθ down to Rθ=860, whereas the additive constant varies with Rθ. The magnitude of the wake parameter takes an asymptotic value of 0.62 if the Reynolds number is sufficiently high. The effect of Rθ on all the turbulent intensities is evident even within the viscous sublayer. The constant stress layer does exist in the Reynolds shear stress profiles despite that the constant value varies with Rθ.

Fully rough submerged plane wall-jets

In this paper, we present the results of a turbulent boundary layer developing over a rod-roughened wall with a spacing of \(\lambda /k = 8\) (\(\lambda\) is the spacing between two adjacent roughness elements, and \(k\) is the rod diameter). Static pressure measurements are taken around a single roughness element to accurately determine the friction velocity, \(U_\tau\) and the error in the origin, \(d_0\), which are the two prominent issues that surround rough-wall boundary layers. In addition, velocity measurements are taken at several streamwise locations using hot-wire anemometry to obtain \(C_\mathrm{f}\) from the momentum integral equation. Results showed that both methods give consistent values for \(U_\tau\), indicating that the contribution of the viscous drag over this rough wall is negligible. This supports the results of Perry et al. (J Fluid Mech 177:437–466, 1969) and Antonia and Luxton (J Fluid Mech 48(04):721–761, 1971) in a boundary layer and of Leonardi et al. (2003) in a channel flow but does not agree with those of Furuya et al. (J Fluids Eng 98(4):635–643, 1976). The results show that both \(U_{\tau }\) and \(d_0\) can be unambiguously measured on this particular rough wall. This paves the way for a proper comparison between the boundary layer developing over this wall and the smooth-wall turbulent boundary layer.

Three-dimensional velocity distributions and corresponding wall stresses are measured concurrently in the inner part of a turbulent boundary layer over a smooth wall using digital holographic microscopy. The measurements are performed in a square duct channel flow atReδ= 50000 andReτ= 1470. A spatial resolution of 3–8 wall units (δυ= μm) in streamwise and spanwise directions and 1 wall unit in the wall-normal direction are sufficient for resolving buffer layer structures and for measuring the instantaneous wall shear stresses from velocity gradients in the viscous sublayer. Mean velocity and Reynolds stress profiles agree well with previous publications. Rudimentary observations classify the buffer layer three-dimensional flow into (i) a pair of counter-rotating inclined vortices, (ii) multiple streamwise vortices, some of them powerful, and (iii) no apparent buffer layer structures. Each appears in about one third of the realizations. Conditional sampling based on local wall shear stress maxima and minima reveals two types of three-dimensional buffer layer structures that generate extreme stress events. The first structure develops as spanwise vorticity lifts from the wall abruptly and within a short distance of about 10 wall units, creating initially a vertical arch. Its only precursors are a slight velocity deficit that does not involve an inflection point and low levels of vertical vorticity. This arch is subsequently stretched vertically and in the streamwise direction, culminating in formation of a pair of inclined, counter-rotating vortices with similar strength and inclination angle exceeding 45°. A wall stress minimum exists under the point of initial lifting. A pair of stress maxima develops 35δυdownstream, on the outer (downflow) sides of the vortex pair and is displaced laterally by 35–40δυfrom the minimum. This flow structure exists not only in the conditionally averaged field but in the instantaneous measurement as well and appears in 16.4% of the realizations. Most of the streamwise velocity deficit generated by this phenomenon develops during this initial lifting, but it persists between the pair of vortices. Distribution of velocity fluctuations shows that spanwise transport of streamwise momentum plays a dominant role and that vertical transport is small under the vortices. In other regions, e.g. during initial lifting, and between the vortices, vertical transport dominates. The characteristics of this structure are compared to early experimental findings, highlighting similarities and differences. Abundance of pairs of streamwise vortices with similar strength is inconsistent with conclusions of several studies based on analysis of direct numerical simulation (DNS) data. The second buffer layer structure generating high wall stresses is a single, predominantly streamwise vortex, with characteristic diameter of 20–40δυand inclination angle of 12°. It generates an elongated, strong stress maximum on one side and a weak minimum on the other and has been observed in 20.4% of the realizations. Except for a limited region of sweep above the high-stress region, this low-lying vortex mostly induces spanwise momentum transport. This structure appears to be similar to those observed in several numerical studies.

Measurements in both smooth and rough wall boundary layers show that the rms of the Reynolds shear stress fluctuation is approximately twice the wall shear stress value in the region close to the wall and equal to about three times the local shear stress throughout most of the smooth wall layer.

The wind tunnel models and instrumentation used as well as data reduction and error analysis techniques employed are described for an experimental study conducted to measure directly skin friction and obtain profiles of mean velocity, axial and normal turbulence intensity, and Reynolds stress in the untripped boundary on a large diameter axisymmetric body. Results are given for such a body with a (1) smooth, solid surface; (2) a sandpaper roughened, solid surface; (3) a sintered metal, porous surface; (4) a "smooth'' performated titanium surface; (5) a rough, solid surface made of fine diffusion bonded screening; and (6) a rough, porous surface made of the same screening. The roughness values were in low range (k+ 5 to 7) just above what is normally considered "hydraulically smooth''. Measurements were taken at several axial locations and tow or normal stream freestream velocities, 45.1 m/sec and 53.5 m/sec.

The objective of this paper is to study the combined effects of rib roughness and adverse pressure gradient produced in an asymmetric diffuser on turbulent flows. The two-dimensional asymmetric diffuser was comprised of a straight flat floor and a curved roof. The diffuser section was preceded and followed by straight parallel walls. The complete test conditions were comprised of a reference smooth floor and repeated arrays of transverse square ribs glued onto the floor to produce three pitch-to-height ratios, p∕k=3, 6, and 8. The curved roof was kept smooth in all the experiments. For each of the four test conditions, a particle image velocimetry was used to conduct detailed velocity measurements within the diverging section and also at locations upstream and downstream of the diverging section. From these measurements, the mean streamlines, mean velocities, turbulent intensities, Reynolds shear stress, and production terms in the transport equations for the turbulent kinetic energy and Reynolds stresses were obtained. The results obtained in the diverging section showed that the boundary layers that developed on the ribs thickened considerably at the expense of those adjacent to the roof opposite to the ribs. The streamlines and mean velocity profiles over the ribs showed that adverse pressure gradient increased the roughness sublayer substantially. Adverse pressure gradient and rib roughness also increased the drag and levels of the turbulent intensities, Reynolds shear stress and production terms compared to smooth-wall zero pressure gradient turbulent boundary layer. It appears, however, that adverse pressure gradient enhanced turbulence more effectively than it increased drag.

This paper presents experimental investigation of upstream roughness and Reynolds number effects on the recirculation region over a smooth forward facing step. The upstream rough wall was produced from 1.5 mm sand grains and the Reynolds number based on step height, Reh, was varied from 2040 to 9130 for both the upstream smooth and rough walls. For the smooth wall, the reattachment length increased monotonically with Reh to an asymptotic value of 2.2 step heights for Reh ≥ 6380. Upstream roughness reduced the reattachment length by 44% because of larger momentum deficit and higher turbulence level in the rough wall boundary layer. The mean velocities and Reynolds stresses were also reduced by roughness. The Reynolds shear stress and production of turbulent kinetic energy showed high negative values at the leading edge of the step indicating counter-gradient diffusion. The implications of these results for standard eddy viscosity models are discussed.

A numerical study of drag reduction by mini-belts in a smooth wall turbulent boundary layer is carried using a second-moment closure turbulence model. The main objective of this exploratory work is to investigate the possibility of using mini-belts, driven by frictional drag only, to reduce the drag of a smooth wall. The results clearly show that such technique can be an effective and cheap means for achieving drag reduction. Furthermore, it is observed that, in contrast to riblets, the use of mini-belts does not suffer from geometrical or size constraints in the context of drag reduction. Also mini-belts will always reduce the skin friction regardless of the flow regime (laminar, transitional and turbulent). These advantages may quite well balance the major difficulty related to their mounting in practical situations

Two-component LDA measurements in smooth wall and d-type rough wall boundary layers indicate that there are important differences in the turbulence intensities over a significant distance above the two surfaces. All the Reynolds stresses—especially the shear stress—are larger over the d-type rough wall, reflecting the relatively strong momentum exchange which occurs over the roughness cavities. Flow visualisations indicate that this exchange is associated with strong ejections of cavity fluid into the outer flow.

An impressive number of experimental and numerical studies of turbulent flows over rough walls has appeared over the last 20 years. Much useful information has been obtained in terms of the turbulence structure both near the roughness canopy and in the outer flow region. However, the issue of whether or not the outer region of the boundary layer is affected by the nature of the wall has yet to be resolved satisfactorily. While the available data, mostly at sufficiently large values of the Reynolds numbers and δ∕k (δ and k are the boundary layer thickness and characteristic roughness height, respectively), seem to suggest that 3D and transverse 2D rough surfaces may affect the outer layer differently, this suggestion can only be tested rigorously once the measurement of the wall-normal velocity fluctuation over the transverse 2D roughness is improved. With the benefit of the channel flow DNS data, it is argued that, for this latter surface type, the wall shear stress, as inferred from the form drag or drag balance, has actually been measured reasonably accurately in the past.

The wall pressure fluctuations for a zero pressure gradient high Reynolds number turbulent boundary layer were studied for both smooth and rough surfaces. The deterministic rough wall was composed of 3-mm hemispheres spaced in a 16.5-mm square array. Boundary layer flow variables were determined through use of a flat-head pitot, single and three-component hotwire anemometer systems. Boundary layer thicknesses up to 0.246-m with Reθ as large as 73000 were reached over smooth surfaces, with δ up to 0.228-m and Reθ as large as 80200 being reached over rough surfaces. The surface pressure fluctuations were measured using B&K 1/8 th inch microphones fitted with 1⁄2-mm pinhole caps and arranged with both spanwise and streamwise separations to provide surface pressure autospectra, phase, coherence and space-time correlation data. The results clearly show an overlap region in the rough-wall boundary layer spectrum with a slope of -1.33, substantially higher than the -0.8 normally seen in smooth wall boundary layers. Comparison with other data sets shows a measure of collapse in the wall pressure spectrum when Blake’s (1970) inner variable scaling is used. Additionally, it was found that roughness noise predictions using the smooth wall surface pressure spectrum would underestimate the scattered noise amplitude at low to mid frequencies, and would overestimate the peak frequency and high frequency amplitudes.

The effects of surface roughness on a spatially developing turbulent boundary layer (TBL) are investigated by performing direct numerical simulations of TBLs over rough and smooth walls. The Reynolds number based on the momentum thickness was varied in the range Reθ = 300 ∼ 1400. The roughness elements were periodically arranged two-dimensional spanwise rods, and the roughness height was k = 1.5θin, where θin is the momentum thickness at the inlet, which corresponds to k/δ = 0.045 ∼ 0.125, δ being the boundary layer thickness. To avoid generating a rough-wall inflow, which is prohibitively difficult, a step change from smooth to rough was placed 80θin downstream from the inlet. The spatially developing characteristics of the rough-wall TBL were examined. Along the streamwise direction, the friction velocity approached a constant value, and self-preserving forms of the turbulent Reynolds stress tensors were obtained. Introduction of the roughness elements affected the turbulent stress not only in the roughness sublayer but also in the outer layer. Despite the roughness-induced increase of the turbulent Reynolds stress tensors in the outer layer, the roughness had only a relatively small effect on the anisotropic Reynolds stress tensor in the outer layer. Inspection of the triple products of the velocity fluctuations revealed that introducing the roughness elements onto the smooth wall had a marked effect on vertical turbulent transport across the whole TBL. By contrast, good surface similarity in the outer layer was obtained for the third-order moments of the velocity fluctuations.

It has been recognized for some years that the bursting phenomenon is a common feature of turbulent boundary layers irrespective of wall roughness condition. In confirmation of Theodorsen’s original conjecture, there is now a convincing body of evidence, particularly deriving from recent direct numerical simulation studies, that the dynamics of this bursting process over smooth walls, is directly linked to the presence of powerful vortical structures with a general horseshoe-type configuration, embedded in the wall flow field. The present paper describes the results of physical experiments which demonstrate that these vortex structures are also present in turbulent boundary layers over rough walls and that they are similarly linked to the bursting events. Novel velocity measurement techniques were used in the investigation which, for the first time in physical fluid mechanics research, allowed quasi-instantaneous vortex lines to be traced through a three-dimensional block of flow space to reveal the vortical structures. The preliminary results from a second investigation are also presented which demonstrate that, just as in the smooth wall case, the spanwise flow structure adjacent to a rough boundary exhibits a well defined cross-flow wavelength. The measurements indicate that this wavelength, which reflects the spanwise scale of the near-wall vortex structures, is directly proportional to the size of the boundary roughness elements under fully rough conditions. Consistent with Townsend’s ‘attached-eddy’ hypothesis, the vortical structures are observed to increase in scale with increasing wall distance while remaining attached back to the vorticity generation zone at the boundary. The paper commences with a review of the status of current knowledge relating to coherent vortical structures in turbulent boundary layers and its interpretation in the context of large scale geophysical flows.

The oblique shock impinging on the supersonic turbulent boundary layer leads to a mixing layer and the emergence of large-scale coherent structures within the interaction zone which leave significant velocity defect and turbulence amplification downstream. In the present study, we investigate the turbulence recovery in the post-shock region by exploiting direct numerical simulation data of the oblique-shock/turbulent boundary layer interaction flow at the incoming Mach number of $2.28$ and the shock angle of $33.2^\circ$ , with special attention paid to the contribution of the mixing layer and large-scale structures to flow dynamics. For that purpose, we propose to split the mean velocity, Reynolds stresses and spanwise spectra into a canonical portion that is constructed according to the statistics of canonical turbulent boundary layers, and a mixing-layer-induced portion. We found that the hidden mixing layer grows with the boundary layer thickness and that the induced mean shear and Reynolds stresses decay at different rates. The mean velocity recovers to the canonical profiles at a distance of 13 boundary layer thicknesses downstream where the mixing-layer-induced mean shear ceases to have strong impacts. The recovery of Reynolds stresses requires 10 boundary layer thicknesses in the near-wall region but a much longer streamwise extent in the outer region due to the slow decay of large-scale motions. These large-scale motions superpose on the near-wall turbulence, intensifying the turbulent fluctuations, yet having a trivial impact on the skin friction, for the contribution of the mixing-layer-induced mean shear and Reynolds shear stress are balanced by the advection term. We further establish a simple physical model capable of approximately predicting the streamwise evolution of mixing-layer-induced mean shear and turbulent kinetic energy. This model suggests that the complete recovery of turbulence in the outer region requires a streamwise extent of approximately 50 boundary layer thicknesses.