Karen A. Flack

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 Reyn...

Review of Hydraulic Roughness Scales in the Fully Rough Regime

A review of predictive methods used to determine the frictional drag on a rough surface is presented. These methods utilize a wide range of roughness scales, including roughness height, pitch, density, and shape parameters. Most of these scales were developed for regular roughness, limiting their applicability to predict the drag for many engineering flows. A new correlation is proposed to estimate the frictional drag for a surface covered with three-dimensional, irregular roughness in the fully rough regime. The correlation relies solely on a measurement of the surface roughness profile and builds on previous work utilizing moments of the surface statistics. A relationship is given for the equivalent sandgrain roughness height as a function of the root-mean-square roughness height and the skewness of the roughness probability density function. Boundary layer similarity scaling then allows the overall frictional drag coefficient to be determined as a function of the ratio of the equivalent sandgrain roughness height to length of the surface. DOI: 10.1115/1.4001492

Examination of a critical roughness height for outer layer similarity

The existence of a critical roughness height for outer layer similarity between smooth and rough wall turbulent boundary layers is investigated. Results are presented for boundary layer measurements on flat plates covered with sandgrain and woven mesh with the ratio of the boundary layer thickness to roughness height (δ∕k) varying from 16 to 110 at Reθ=7.3×103–13×103. In all cases tested, the layer directly modified by the roughness (the roughness sublayer) is confined to a region <5k or <3ks from the wall (where ks is the equivalent sandgrain roughness height). In the larger roughness cases, this region of turbulence modification extends into the outer flow. However, beyond 5k or 3ks from the wall, similarity in the turbulence quantities is observed between the smooth and rough wall boundary layers. These results indicate that a critical roughness height, where the roughness begins to affect most or all of the boundary layer, does not exist. Instead, the outer flow is only gradually modified with increas...

Turbulence structure in rough- and smooth-wall boundary layers

Turbulence measurements for rough-wall boundary layers are presented and compared to those for a smooth wall. The rough-wall experiments were made on a woven mesh surface at Reynolds numbers approximately equal to those for the smooth wall. Fully rough conditions were achieved. The present work focuses on turbulence structure, as documented through spectra of the fluctuating velocity components, swirl strength, and two-point autoand cross-correlations of the fluctuating velocity and swirl. The present results are in good agreement, both qualitatively and quantitatively, with the turbulence structure for smooth-wall boundary layers documented in the literature. The boundary layer is characterized by packets of hairpin vortices which induce lowspeed regions with regular spanwise spacing. The same types of structure are observed for the roughand smooth-wall flows. When the measured quantities are normalized using outer variables, some differences are observed, but quantitative similarity, in large part, holds. The present results support and help to explain the previously documented outer-region similarity in turbulence statistics between smoothand rough-wall boundary layers.

Turbulent Boundary Layers on a Systematically Varied Rough Wall

Results of an experimental investigation of the flow over a model roughness are presented. The series of roughness consists of close-packed pyramids in which both the height and the slope were systematically varied. The aim of this work was to document the mean flow and subsequently gain insight into the physical roughness scales which contribute to drag. The mean velocity profiles for all nine rough surfaces collapse with smooth-wall results when presented in velocity-defect form, supporting the use of similarity methods. The results for the six steepest surfaces indicate that the roughness function ΔU+ scales almost entirely on the roughness height with little dependence on the slope of the pyramids. However, ΔU+ for the three surfaces with the smallest slope does not scale satisfactorily on the roughness height, indicating that these surfaces might not be thought of as surface “roughness” in a traditional sense but instead surface “waviness.”

Turbulent Boundary Layers Over Surfaces Smoothed by Sanding

Abstract : Flat-plate turbulent boundary layer measurements have been made on painted surfaces, smoothed by sanding. The measurements were conducted in a closed return water tunnel, over a momentum thickness Reynolds number (Re(theta)) range of 3000 to 16,000, using a two-component laser Doppler velocimeter (LDV). The mean velocity and Reynolds stress profiles are compared with those for smooth and sandgrain rough walls. The results indicate an increase in the boundary layer thickness (d) and the integral length scales for the unsanded, painted surface compared to a smooth wall. More significant increases in these parameters, as well as the skin-friction coefficient (C(f)) were observed for the sandgrain surfaces. The sanded surfaces behave similarly to the smooth wall for these boundary layer parameters. The roughness functions (DeltaU(+)) for the sanded surfaces measured in this study agree within their uncertainty with previous results obtained using towing tank tests and similarity law analysis. The present results indicate that the mean profiles for all of the surfaces collapse well in velocity defect form. The Reynolds stresses also show good collapse in the overlap and outer regions of the boundary layer when normalized with the wall shear stress.

Turbulence structure in a boundary layer with two-dimensional roughness

+ and −uv � + , increase, although the mean flow is not as significantly affected. Large-scale turbulent motions originating at the wall lead to increased spatial scales in the outer flow. The dominant feature of the outer flow, however, remains hairpin vortex packets which have similar inclination angles for all wall conditions. The differences between boundary layers over two- dimensional and three-dimensional roughness are attributable to the scales of the motion induced by each type of roughness. This study has shown three-dimensional roughness produces turbulence scales of the order of the roughness height k while the motions generated by two-dimensional roughness may be much larger due to the width of the roughness elements. It is also noted that there are fundamental differences in the response of internal and external flows to strong wall perturbations, with internal flows being less sensitive to roughness effects.

Reynolds-number scaling of turbulent channel flow

Results of an experimental study of smooth-wall, fully developed, turbulent channel flow are presented. The Reynolds number (Rem) based on the channel height and the bulk mean velocity ranged from 10 000 to 300 000. The present results indicate that the skin-friction coefficient (Cf) closely follows a power law for Rem < 62 000. At higher Reynolds numbers, Cf is best described by a log law. Detailed two-component velocity measurements taken at friction Reynolds numbers of Reτ = 1000–6000 indicate that the mean flow and Reynolds shear stress display little or no Reynolds-number dependence. The streamwise Reynolds normal stress (u′2¯+), on the other hand, varies significantly with Reynolds number. The inner peak in u′2¯+ is observed to grow with Reynolds number. Growth in u′2¯+ farther from the wall is documented over the entire range of Reynolds number giving rise to a plateau in the streamwise Reynolds normal stress in the overlap region of the profile for Reτ = 6000. The wall-normal Reynolds normal stres...

Turbulence structure in boundary layers over periodic two- and three-dimensional roughness

Measurements are presented from turbulent boundary layers over periodic two- and three-dimensional roughness. Cases with transverse rows of staggered cubes and cases with solid square transverse bars of two sizes were considered. Previous results by Volino, Schultz & Flack (J. Fluid Mech. vol. 635, 2009, p. 75) showed outer-layer similarity between cases with three-dimensional roughness and smooth walls, and deviations from similarity in cases with large two-dimensional transverse bars. The present results show that differences also occur with small two-dimensional bars and to a lesser extent when the bars are replaced with rows of staggered cubes. Differences are most apparent in correlations of turbulence quantities, which are of larger spatial extent for the rough-wall cases. The results with the staggered cubes indicate that part of the periodic roughness effect is caused by the repeated disturbance and recovery of the boundary layer as it encounters a row of roughness followed by a smooth surface. A larger effect, however, is due to the blockage caused by the two-dimensional transverse bars, which extend across the entire width of the boundary layer. The small two-dimensional bars have a larger effect than the staggered cubes, in spite of the bar height being only 11 viscous units and 1/7 of the cube height. The effect of the small bars extends well into the outer flow, indicating that effects observed previously with larger bars were not due only to a thickening of the roughness sublayer. The observed differences between the rough- and smooth-wall results are believed to be caused by large-scale attached eddies which extend from the roughness elements to the edge of the boundary layer.

Secondary Flow Measurements in a Turbine Passage With Endwall Flow Modification

A flow modification technique is introduced in an attempt to allow increased turbine inlet temperatures. A large-scale two half-blade cascade simulator is used to model the secondary flow between two adjacent turbine blades. Various flow visualization techniques and measurements are used to verify that the test section replicates the flow of an actual turbine engine. Two techniques are employed to modify the endwall secondary flow, specifically the path of the passage vortex. Six endwall jets are installed at a location downstream of the saddle point near the leading edge of the pressure side blade. These wall jets are found to be ineffective in diverting the path of the passage vortex. The second technique utilizes a row of 12 endwall jets whose positions along the centerline of the passage are based on results from an optimized boundary layer fence. The row of jets successfully diverts the path of the passage vortex and decreases its effect on the suction side blade. This can be expected to increase the effectiveness of film cooling in that area. The row of jets increases the aerodynamic losses in the passage, however. Secondary flow measurements are presented showing the development of the endwall flow, both with and without modification.