Rough-wall Boundary Layers Research Articles

1108 せん断乱流中の速度及び圧力スペクトルとその普遍性(2)(OS11-2 広範囲レイノルズ数におけるせん断流,OS11広範囲レイノルズ数におけるせん断流)

The local isotropy hypothesis presented by Kolmogorov seems to work well as a good approximation depending on the nature of large-scale anisotropy. We discuss how the large-scale anisotropy penetrates the small scales by investigating the anisotropic spectrum measured in the rough wall boundary layers and also the pressure spectra.

Turbulence Over Urban-type Roughness: Deductions from Wind-tunnel Measurements

Turbulence data from experiments conducted over a staggered cube array, modelling a neutrally stable atmospheric boundary layer in an urban environment, are presented. The results support the contention that organised eddy structures in the near-wall region differ significantly from those in regular smooth-wall flows or in rough-wall boundary layers with much smaller h/δ ratios (where δ and h are the boundary-layer thickness and the height of the roughness elements, respectively). Attention is concentrated on spatial correlations, spectra (and thus the dominant length and time scales), maps of anisotropy invariants and quadrant analyses of the stress tensor. Results are obtained within both the roughness sublayer (i.e. the region above the roughness but within which the flow is spatially inhomogeneous) and the canopy region (i.e. below the height of the roughness elements) and discussion includes consideration of the turbulence kinetic energy balance at various heights.

Self-preservation of a Turbulent Boundary Layer over d-type Roughness

Using a direct drag balance measurement for the local wall shear stress, self-preserving development of a turbulent boundary layer was achieved experimentally over a d-type rough surface without pressure gradients. The wall shear stress and mean velocity measurements confirmed the requirements for exact self-similarity and highly similar Reynolds stress profiles within the Reynolds number range for a constant skin friction coefficient. Under the condition that the boundary layer flow is completely independent of Reynolds number, the effect of wall roughness was investigated with respect to the similarity laws for the wall layer as well as the outer layer. Experimental observation reveals the wall similarity y u y U κ τ = ∂ ∂ to be applicable to the present rough wall boundary layer remaining the accepted value of Karman constant to be κ = 0.41. Otherwise, investigation of the wake strength in the mean velocity and Reynolds stress profiles reveals that the wall roughness does affect the outer layer structure. Reynolds stress measurements indicate that the primary effect of wall roughness on turbulence properties is in the component normal to the wall.

Outer layer similarity in fully rough turbulent boundary layers

Turbulent boundary layer measurements were made on a flat plate covered with uniform spheres and also on the same surface with the addition of a finer-scale grit roughness. The measurements were carried out in a closed return water tunnel, over a momentum thickness Reynolds number (Re θ ) range of 3,000–15,000, using a two-component, laser Doppler velocimeter (LDV). The results show that the mean profiles for all the surfaces collapse well in velocity defect form. Using the maximum peak to trough height (Rt) as the roughness length scale (k), the roughness functions (ΔU+) for both surfaces collapse, indicating that roughness texture has no effect on ΔU+. The Reynolds stresses for the two rough surfaces also show good agreement throughout the entire boundary layer and collapse with smooth wall results outside of the roughness sublayer. Quadrant analysis and the velocity triple products show changes in the rough wall boundary layers that are confined to y<8ks, where ks is the equivalent sand roughness height. The present results provide support for Townsend’s wall similarity hypothesis for uniform three-dimensional roughness. However, departures from wall similarity may be observed for rough surfaces where 5ks is large compared to the thickness of the inner layer.

Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls

The Reynolds number similarity hypothesis of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, UK, 1976)] states that the turbulence beyond a few roughness heights from the wall is independent of the surface condition. The underlying assumption is that the boundary layer thickness δ is large compared to the roughness height k. This hypothesis was tested experimentally on two types of three-dimensional rough surfaces. Boundary layer measurements were made on flat plates covered with sand grain and woven mesh roughness in a closed return water tunnel at a momentum thickness Reynolds number Reθ of ∼14000. The boundary layers on the rough walls were in the fully rough flow regime (ks+⩾100) with the ratio of the boundary layer thickness to the equivalent sand roughness height δ∕ks greater than 40. The results show that the mean velocity profiles for rough and smooth walls collapse well in velocity defect form in the overlap and outer regions of the boundary layer. The Reynolds stresses for the two rough surfaces agree well throughout most of the boundary layer and collapse with smooth wall results outside of 3ks. Higher moment turbulence statistics and quadrant analysis also indicate the differences in the rough wall boundary layers are confined to y&amp;lt;5ks. The present results provide support for Townsend’s Reynolds number similarity hypothesis for uniform three-dimensional roughness in flows where δ∕ks⩾40.

404 粗面乱流境界層の対数速度分布と変動速度確率密度関数型について(G05-8 乱流,G05 流体工学)

The logarithmic velocity region is studied in zero-pressura-gradient turbulent boundary layers on the rough wall. We have already proposed the definition of log-law region in the case of smooth wall with using the probability density of velocity fluctuation. In this report this idea is expanded into the rough wall boundary layers, and extracted log-law region is discussed from the point of PDF profiles, and also its Reynolds number dependence is studied based on the experimental data.

Mechanism of Momentum Exchange in the Vicinity of a Roughness Element for the Boundary Layer Developing over the Rough Wall Arranged with Two-Dimensional Square Ribs (Flow Visualization of Eddy Formed in a Cavity)

Flow visualization has been performed in the vicinity of a roughness element for the rough wall boundary layers developing over the roughness with pitch ratio p of 2 and 4 at a low Reynolds-number. The momentum thickness Reynolds numbers at streamwise distance x=865mm for p=2 and 4 were 300 and 500, respectively. For p=2, typical flow patterns are classified into 4 patterns which are consistent with those of Townes et al., otherwise 3 patterns were recognized for p=4. The frequency fm, the sum of the frequency of each flow pattern, which is closely associated with the momentum exchange normalized with the cavity width b and the friction velocity uτ for p=4 takes larger value compared with that of p=2. This quantitative result can be related that the pressure drag acting on a roughness element for p=4 s larger than that of p=2.

Similarity of instantaneous and filtered velocity fields in the near wall region of zero-pressure gradient boundary layer

Instantaneous velocity distributions in the viscous and roughness sublayers and in the lower parts of the logarithmic-law region of flat-plate boundary layers over smooth and rough surfaces are measured using a hot-wire rake consisting of two X-wire and nine single-sensor probes in order to investigate the turbulence structure and similarity of the instantaneous and filtered velocity profiles near the wall. The results can provide useful information as to the treatment of flow in this region in a large-eddy type simulation of high Reynolds-number flows over smooth and rough walls. The instantaneous velocity profiles feature large-scale structures but random fluctuations of considerable amplitude are superimposed and no similarity that is applicable to instantaneous unconditioned profiles can be derived. Conditionally averaged profiles based on the magnitudes of the wall shear and normal velocity in the buffer layer, however, show trends related to the sweep-ejection type events. The filtered profiles normalized by the filtered instantaneous friction velocity show similarity that progressively extends its region from the immediate neighborhood of the wall to the log layer as the filter size is increased. The minimum streamwise length of the filter size required to show logarithmic similarity is found to be as large as 1800 wall units. Similar results are obtained for rough-wall boundary layers if the instantaneous friction velocity is replaced by the equivalent velocity scale implied by the velocity just outside the roughness-influenced sublayer at about 10 viscous units from the wall, or about 1.5 times the height of the roughness bars from the wall. The sub-grid stress components have are obtained from the data and implication for modeling is discussed.

The Effect of Vegetation Density on Canopy Sub-Layer Turbulence

The canonical form of atmospheric flows near theland surface, in the absence of a canopy, resembles a rough-wallboundary layer. However, in the presence of an extensive and densecanopy, the flow within and just above the foliage behaves as aperturbed mixing layer. To date, no analogous formulation existsfor intermediate canopy densities. Using detailed laser Dopplervelocity measurements conducted in an open channel over a widerange of canopy densities, a phenomenological model that describesthe structure of turbulence within the canopy sublayer (CSL) isdeveloped. The model decomposes the space within the CSL intothree distinct zones: the deep zone in which the flow field isshown to be dominated by vortices connected with vonKarman vortex streets, butperiodically interrupted by strong sweep events whose features areinfluenced by canopy density. The second zone, which is near thecanopy top, is a superposition of attached eddies andKelvin–Helmholtz waves produced by inflectional instability in themean longitudinal velocity profile. Here, the relative importanceof the mixing layer and attached eddies are shown to vary withcanopy density through a coefficient α. We show that therelative enhancement of turbulent diffusivity over its surface-layer value near the canopy top depends on the magnitude ofα. In the uppermost zone, the flow follows the classicalsurface-layer similarity theory. Finally, we demonstrate that thecombination of this newly proposed length scale and first-orderclosure models can accurately reproduce measured mean velocity andReynolds stresses for a wide range of roughness densities. Withrecent advancement in remote sensing of canopy morphology, thismodel offers a promising physically based approach to connect theland surface and the atmosphere without resorting to empiricalmomentum roughness lengths.

Effect of Roughness on Wall-Bounded Turbulence

Direct numerical simulation of turbulent incompressible plane-channel flow between a smooth wall and one covered with regular three-dimensional roughness elements is performed. While the impact of roughness on the mean-velocity profile of turbulent wall layers is well understood, at least qualitatively, the manner in which other features are affected, especially in the outer layer, has been more controversial. We compare results from the smooth- and rough-wall sides of the channel for three different roughness heights of h + = 5.4, 10.8, and 21.6 for Reτ of 400, to isolate the effects of the roughness on turbulent statistics and the instantaneous turbulence structure at large and small scales. We focus on the interaction between the near-wall and outer-layer regions, in particular the extent to which the near-wall behavior influences the flow further away from the surface. Roughness tends to increase the intensity of the velocity and vorticity fluctuations in the inner layer. In the outer layer, although the roughness alters the velocity fluctuations, the vorticity fluctuations are relatively unaffected. The higher-order moments and the energy budgets demonstrate significant differences between the smooth-wall and rough-wall sides in the processes associated with the wall-normal fluxes of the Reynolds shear stresses and turbulence kinetic energy. The length scales and flow dynamics in the roughness sublayer, the spatially inhomogeneous layer within which the flow is directly influenced by the individual roughness elements, are also examined. Alternative mechanisms involved in producing and maintaining near-wall turbulence in rough-wall boundary layers are also considered. We find that the strength of the inner/outer-layer interactions are greatly affected by the size of the roughness elements.

Large-scale anisotropy effect on small-scale statistics over rough wall turbulent boundary layers

According to the local isotropy hypothesis presented by Kolmogorov, small-scale velocity fluctuations should be universal in any kind of turbulent flow when the Reynolds number is sufficiently large. This is one of the key assumptions in turbulence phenomena. At this stage, the question is not whether this assumption is correct or not, but rather how the local isotropy works as a good approximation depending on the nature of the large-scale anisotropy. In this paper, we report on how the large-scale anisotropy penetrates the small scales. Based on the experiments performed in the strong mean shear flow on the rough-wall boundary layer, we consider how the local isotropy is restored. The anisotropic parameter S* is defined as a ratio of the time scale caused by the mean velocity gradient and the Kolmogorov time scale. It is found that the local isotropy is achieved in the dissipation range even in S*≃0.1. On the other hand, there is no clear evidence of isotropy in the inertial range. Due to the strong mean shear, the second-order structure functions do not satisfy the exact power-law relation but they indicate the convex shape plotted in the logarithmic coordinate. Computing the local slope and the curvature of structure functions, we found they are a strong function of anisotropic parameter.

Probability density function of turbulent velocity fluctuations in a rough-wall boundary layer.

The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and independent, the Fourier coefficients tend to Gaussian and independent of each other. Velocity fluctuations accordingly tend to Gaussian. However, if energy-containing motions are intermittent or contaminated with bounded-amplitude motions such as wavy wakes, the Fourier coefficients tend to non-Gaussian and dependent of each other. Velocity fluctuations accordingly tend to non-Gaussian. These situations are found in our experiment of a rough-wall boundary layer.

Short-range vertical dispersion from a ground level source in a turbulent boundary layer

The short-range vertical dispersion of a passive containment in a neutrally stratified turbulent boundary layer can be usefully characterised by a number of approaches, such as a vertical diffusivity, K z , a vertical Gaussian dispersion parameter, σ z , and an entrainment velocity, w e . σ z and w e are approximately related by w e ∝d σ z /d t . While the Gaussian model is widely used in most air quality applications, the entrainment velocity is widely used in wind tunnel studies and models for the dispersion of hazardous gases. This paper summarises experiments in three simulated rough-wall atmospheric boundary layers (two in the US and one in the UK), which lead to the conclusion that for passive releases the entrainment coefficient α in the formula w e =αu ∗ is α =0.65±0.05. This value is consistent with a recent analysis of the Prairie Grass data (out to x =100 m, where vertical profiles were obtained) that gave α =0.63±0.05. Somewhat surprisingly we were not able to locate a theoretical analysis that could reproduce these results without recourse to some empirical input.

Stability characteristics of the virtual boundary method in three-dimensional applications

The refined stability analysis of the virtual boundary method proposed by Goldstein et al. (1994) and modified by Saiki and Biringen (1996) is carried out for applications to three-dimensional turbulent flows in complex geometry. The precise stability boundaries in the forcing parameter space for various time-advancing schemes are provided under the assumption that the virtual boundary points are densely distributed. From these and the relevant investigation of frequency of the forced system, the optimum gains of the feedback forcing are suggested. Stability regimes of the Runge–Kutta schemes of various order are much wider than those of the Adams–Bashforth schemes. Specially, the third-order Runge–Kutta scheme allows the use of an order-one CFL number in the integration of the feedback forcing, rendering the method applicable to turbulent flows with complex boundaries. The three-dimensional turbulent flow caused by a surface-mounted box was simulated using a spectral method for evaluation, confirming the stability limit proposed by theoretical estimate. The method was then applied to simulations of the flow around an impulsively starting cylinder and of the rough-wall turbulent boundary layer flow.

Rough Wall Boundary Layer on Plates in Open Channels

Experiments were performed to measure the characteristics of a turbulent boundary layer developing on a rough surface placed in an open channel flow at close proximity to the free surface. Streamwise velocity measurements were made with a one-component laser Doppler velocimeter system at the top of the spherical roughness elements. Measurements at three stations downstream of the plate leading edge show the growth of the boundary layer on the rough wall and its interaction with the exterior open-channel flow and the free surface. Resorting to the turbulence profile provides an alternative definition of the boundary layer thickness. The near-wall flow follows the well-known logarithmic law with a shift due to roughness. In the outer layer, there are two opposing effects: the free surface tends to decrease the wake component while the roughness tends to increase it. The streamwise turbulence intensity is affected by the shear and turbulence in the exterior flow, the effect of the free surface being greater than that of wall roughness.

The Effects of Surface Roughness on the Mean Velocity Profile in a Turbulent Boundary Layer

Experimental measurements of the mean velocity profile in a canonical turbulent boundary layer are obtained for four different surface roughness conditions, as well as a smooth wall, at moderate Reynolds numbers in a wind tunnel. The mean streamwise velocity component is fitted to a correlation which allows both the strength of the wake, Π, and friction velocity, Uτ, to vary. The results show that the type of surface roughness affects the mean defect profile in the outer region of the turbulent boundary layer, as well as determining the value of the skin friction. The defect profiles normalized by the friction velocity were approximately independent of Reynolds number, while those normalized using the free stream velocity were not. The fact that the outer flow is significantly affected by the specific roughness characteristics at the wall implies that rough wall boundary layers are more complex than the wall similarity hypothesis would allow.

Large eddy simulation of the flow around a low-rise building immersed in a rough-wall turbulent boundary layer

The objective of this paper is to validate the large eddy simulation (LES) technique for predicting a flow around an obstacle under the condition that a turbulent flow is approaching the obstacle. The turbulent inflow data were generated for both a smooth surface and rough surfaces by the method we had proposed. A half-height cube was immersed in the turbulent boundary layers with several types of vertical velocity profile. With regard to the pressure distributions on the surface of the half-height cube, the computed time-averaged and rms values are in good agreement with previous experimental ones. However, the peak pressure coefficients are underestimated, especially compared to full-scale data.

The effects of wall roughness on the separated flow over a smoothly contoured ramp

Experimental measurements address the effects on a turbulent boundary layer of wall roughness on a flat plate and a ramp that produces a separation bubble over the ramp trailing edge. A fully rough flow condition is achieved on the upstream flat plate. The main effect of the wall roughness on the outer layer turbulence on a flat plate is to change the friction velocity. The separation region is substantially larger for the rough-wall case. The rough-wall boundary layer turbulence is less sensitive to the onset of an adverse pressure gradient over the ramp, producing substantially smaller Reynolds stress peaks in upstream flat-plate, wall-unit coordinates.

Temporal turbulent flow structure for supersonic rough-wall boundary layers

Temporal turbulent flow structure for supersonic rough-wall boundary layers

The critical Reynolds number for rough-wall boundary layers

Rough-wall boundary layers become aerodynamically smooth if the ‘roughness Reynolds number’ Re ∗=u ∗z 0/ν becomes sufficiently small. Conventional wisdom is that Re ∗ should exceed at least two and perhaps be as much as five before viscous effects are insignificant. This criterion is assessed for the types of rough wall commonly used in laboratory simulations of atmospheric boundary layers—arrays of sharp-edged obstacles with significant separation between each obstacle. It is demonstrated that for such surfaces the roughness length z 0 remains constant for falling roughness Reynolds numbers down to at least Re ∗=1 . Viscous effects are shown to change the near-wall Reynolds stresses only for Re ∗ below similar values, so that z 0-scaling (rather than scaling based on ν/u ∗ ) remains appropriate down to at least Re ∗=1 . One of the practical implications of this result is that wind-tunnel simulations of atmospheric boundary layers can be successful at lower wind speeds (or with smaller roughness elements) than previously supposed.