There have been very few studies investigating the rough wall pressure spectra under fully rough flows, which are relevant to many common engineering applications operating within this regime. This investigation uses the Virginia Tech Stability Wind Tunnel to perform experiments on a series of high Reynolds number zero pressure gradient turbulent boundary layers formed over rough walls in an effort to better understand and characterize the behavior of the rough wall pressure spectrum. The boundary layers were fully rough, and the boundary layer height remained sufficiently larger than the height of the roughness elements. Two rough surfaces were tested. One consisted of an array of 1-mm ordered hemispherical elements spaced 5.5-mm apart, and the other contained 3-mm hemispherical elements randomly spaced, but with the same element density as 1/3 of the 1-mm ordered roughness. The wall pressure spectrum and its scaling were then studied in detail, and it was found that the rough wall turbulent pressure spectrum at vehicle relevant conditions is defined by three scaling regions. One of which is a newly discovered high frequency scaling defined by viscosity, but controlled by the friction velocity adjusted to exclude the pressure drag on the roughness elements. Based on these three scaling regions an empirical model describing the wall pressure spectra for hydraulically smooth, traditionally rough, and fully rough flows was explored. Two point wall pressure fluctuations were also analyzed for each surface condition, and it was found that the roughness inhibits the convective velocities within the inner portions of the boundary layer. / Master of Science

The present understanding of the structure and dynamics of turbulent boundary layers on aerodynamically smooth walls has been clarified over the last decade or so. However, the dynamics of turbulent boundary layers over rough surfaces is much less well known. Nevertheless, there are many industrial and environmental flow applications that require understanding of the mean velocity and turbulence in the immediate vicinity of the roughness elements.</p> <p>This thesis reports the effects of surface roughness on the flow characteristics in a turbulent boundary layer. Both experimental and numerical investigations are used in the present study. For the experimental study, comprehensive data sets are obtained for two-dimensional zero pressure-gradient turbulent boundary layers on a smooth surface and ten different rough surfaces created from sand paper, perforated sheet, and woven wire mesh. The physical size and geometry of the roughness elements and freestream velocity were chosen to encompass both transitionally rough and fully rough flow regimes. Three different probes, namely, Pitot probe, single hot-wire, and cross hot-film, were used to measure the velocity fields in the turbulent boundary layer. A Pitot probe was used to measure the streamwise mean velocity, while the single hot-wire and cross hot-film probes were used to measure the fluctuating velocity components across the boundary layer. The flow Reynolds number based on momentum thickness, , ranged from 3730 to 13,550. The data reported include mean velocity, streamwise and wall-normal turbulence intensities, Reynolds shear stress, triple correlations, as well as skewness and flatness factors. Different scaling parameters were used to interpret and assess both the smooth- and rough-wall data at different Reynolds numbers, for approximately the same freestream velocity. The appropriateness of the logarithmic law and power law proposed by George and Castillo (1997) to describe the mean velocity in the overlap region was also investigated. The present results were interpreted within the context of the Townsends wall similarity hypothesis. </p> <p>Based on the mean velocity data, a novel correlation that relates the skin friction to the ratio of the displacement and boundary layer thicknesses, which is valid for both smooth- and rough-wall flows, was proposed. In addition, it was also found that the application of a mixed outer scale caused the velocity profile in the outer region to collapse onto the same curve, irrespective of Reynolds numbers and roughness conditions. The present results showed that there is a common region within the overlap region of the mean velocity profile where both the log law and power law are indistinguishable, irrespective of the surface conditions. For the power law formulation, functional relationships between the roughness shift, and the power law coefficient and exponent were developed for the transitionally rough flows. The present results also suggested that the effect of surface roughness on the turbulence field depends to some degree on the specific characteristics of the roughness elements and also the component of the Reynolds stress tensor being considered. </p> <p>In the case of the numerical study, a new wall function formulation based on a power law was proposed for smooth and fully rough wall turbulent pipe flow. The new formulation correctly predicted the friction factors for smooth and fully rough wall turbulent pipe flow. The existing two-layer model realistically predicted the velocity shift on a log-law plot for the fully rough turbulent boundary layer. The two-layer model results also showed the effect of roughness is to enhance the level of turbulence kinetic energy and Reynolds shear stress compared to that on a smooth wall. This enhanced level extends into the outer region of the flow, which appears to be consistent with present and recent experimental results for the boundary layer.

The present understanding of the structure and dynamics of turbulent boundary layers on aerodynamically smooth walls has been clarified over the last decade or so. However, the dynamics of turbulent boundary layers over rough surfaces is much less well known. Nevertheless, there are many industrial and environmental flow applications that require understanding of the mean velocity and turbulence in the immediate vicinity of the roughness elements.</p> <p>This thesis reports the effects of surface roughness on the flow characteristics in a turbulent boundary layer. Both experimental and numerical investigations are used in the present study. For the experimental study, comprehensive data sets are obtained for two-dimensional zero pressure-gradient turbulent boundary layers on a smooth surface and ten different rough surfaces created from sand paper, perforated sheet, and woven wire mesh. The physical size and geometry of the roughness elements and freestream velocity were chosen to encompass both transitionally rough and fully rough flow regimes. Three different probes, namely, Pitot probe, single hot-wire, and cross hot-film, were used to measure the velocity fields in the turbulent boundary layer. A Pitot probe was used to measure the streamwise mean velocity, while the single hot-wire and cross hot-film probes were used to measure the fluctuating velocity components across the boundary layer. The flow Reynolds number based on momentum thickness, , ranged from 3730 to 13,550. The data reported include mean velocity, streamwise and wall-normal turbulence intensities, Reynolds shear stress, triple correlations, as well as skewness and flatness factors. Different scaling parameters were used to interpret and assess both the smooth- and rough-wall data at different Reynolds numbers, for approximately the same freestream velocity. The appropriateness of the logarithmic law and power law proposed by George and Castillo (1997) to describe the mean velocity in the overlap region was also investigated. The present results were interpreted within the context of the Townsends wall similarity hypothesis. </p> <p>Based on the mean velocity data, a novel correlation that relates the skin friction to the ratio of the displacement and boundary layer thicknesses, which is valid for both smooth- and rough-wall flows, was proposed. In addition, it was also found that the application of a mixed outer scale caused the velocity profile in the outer region to collapse onto the same curve, irrespective of Reynolds numbers and roughness conditions. The present results showed that there is a common region within the overlap region of the mean velocity profile where both the log law and power law are indistinguishable, irrespective of the surface conditions. For the power law formulation, functional relationships between the roughness shift, and the power law coefficient and exponent were developed for the transitionally rough flows. The present results also suggested that the effect of surface roughness on the turbulence field depends to some degree on the specific characteristics of the roughness elements and also the component of the Reynolds stress tensor being considered. </p> <p>In the case of the numerical study, a new wall function formulation based on a power law was proposed for smooth and fully rough wall turbulent pipe flow. The new formulation correctly predicted the friction factors for smooth and fully rough wall turbulent pipe flow. The existing two-layer model realistically predicted the velocity shift on a log-law plot for the fully rough turbulent boundary layer. The two-layer model results also showed the effect of roughness is to enhance the level of turbulence kinetic energy and Reynolds shear stress compared to that on a smooth wall. This enhanced level extends into the outer region of the flow, which appears to be consistent with present and recent experimental results for the boundary layer.

Le biofilm épilithique (anciennement périphyton), agrégat phototrophe d’organismes se développant sur le fond des cours d’eau, joue un rôle essentiel dans le fonctionnement des hydroécosystèmes fluviaux comme la Garonne. Pour améliorer la modélisation à l’échelle du tronçon de rivière de ces systèmes, il est nécessaire de prendre en compte les caractéristiques locales de l’écoulement notamment pour la prédiction de l’évolution de la biomasse. Les méthodes expérimentales actuelles ne permettent pas d’accéder aux grandeurs hydrodynamiques locales proches du fond rugueux, dans la zone dite de ’canopée’. Le travail présenté ici vise donc à compléter ces résultats par des simulations numériques directes, avec une méthode de frontières immergées, d’écoulements turbulents de couche limite hydrauliquement rugueuse formée d’hémisphères. L’objectif est double : il s’agit d’une part de mettre en relation les motifs de colonisation et la croissance du biofilm observés expérimentalement aux caractéristiques locales de l’écoulement, et d’autre part, de quantifier les flux d’espèces chimiques entre la canopée et la pleine eau et ce, en fonction du type d’arrangement des obstacles formant le fond, du confinement et du nombre de Reynolds rugueux. Après avoir validé la méthode numérique sur des cas proches de ceux rencontrés dans les expériences, et vérifié que les grandeurs hydrodynamiques moyennes et turbulentes dans la pleine eau sont en bon accord avec les résultats expérimentaux, plusieurs campagnes de simulations ont été réalisées pour deux types d’arrangements du fond (aligné et décalé), plusieurs confinements et une gamme de nombre de Reynolds rugueux représentatifs des écoulements en rivière. Ce travail a pu mettre en évidence que le biofilm colonise préférentiellement les zones de faible cisaillement local et un critère de colonisation a été déterminé. Des simulations avec transfert d’espèce chimique ont été réalisées pour différentes valeurs du nombre de Schmidt et ont permis de quantifier les flux d’échange en fonction de ce paramètre. / The epilithic biofilm, aggregate set of phototrophic organisms growing on the bed of rivers, plays an essential role in the functioning of hydro-ecosystems such as the Garonne river. To improve the modeling of these systems it is necessary to take into account the local conditions in the region close to the rough bottom, named ’canopy’. Direct numerical simulations with a immersed boundary method are used to simulate turbulent boundary layer flows with a rough wall composed of hemipheres. The aim of these simulations is twofold : (1) investigate the influence of local flow conditions on the biofilm colonization and growth processes and (2) quantify the transfers of chemical species between the canopy region and the main water column, for various hemispheres arrangement, confinement and turbulent Reynolds number encountered in natural rivers. This work allowed to show that biofilm colonization first occurs in low-to-moderate local shear stress at the hemisphere surface. Simulations with the transport of a passive scalar were performed for various Schmidt number, and gave an estimation of the mass fluxes as a function of this parameter.