The pressure fluctuations under a high Reynolds Number, rough-wall, turbulent, boundary layer have been studied in the Virginia Tech Stability Wind Tunnel. Rough surfaces of varying element height (1-mm, 3-mm), shape (hemispheres, cylinders) and spacing (5.5-mm, 10.4-mm, 16.5-mm) were investigated in order to ascertain how the turbulent pressure fluctuations change with changes in roughness geometry. Rough surfaces which contain two types of elements are investigated and relationships between the combination surface and the individual surfaces have been uncovered. Measurements of the wall pressure fluctuations were made using pinhole microphones and hotwire measurements were made to obtain the velocity and turbulence field. Among the principal findings is the development of two scaling laws for the low frequency pressure fluctuations. Both of these are based on the idea that the defect between the edge velocity and some local boundary layer velocity sustains the pressure fluctuations in the outer regions of the flow. The first scaling uses the broadband convection velocity as the local velocity of the large scale pressure fluctuations. The second scaling uses the mean boundary layer velocity. Both these scalings appear more robust than the previously proposed scalings for the low frequency region and are able to scale the pressure spectra of all the data to within 3.5-dB. In addition, it was proven that the high frequency shear friction velocity scaling of Meyers et al. (2015) is universal to rough surfaces of different element shape and density. Physical insights into the shear friction velocity, on which this scaling is based, have been revealed. This includes an empirical formula which estimates the element pressure drag coefficient from the roughness density and the Reynolds number. The slopes in the mid-frequency region were found to vary with element density and microphone location such that a useful scaling could not be determined for this region. The possibility of an overlap region is explored and the expectation of a -1 slope is disproved. It is hypothesised that an evanescent decay of the mid-frequency pressure fluctuations occurs between their actual location and the wall where they are measured. A method for accounting for this decay is presented in order to scale the pressure fluctuations in this region. Lastly, a piecewise interpolation function for the pressure spectrum of rough wall turbulent boundary layers was proposed. This analytical function is based on the low frequency scaling on mean velocity and the high frequency scaling of Meyers et al. (2015) The mid-frequency is estimated by a spline interpolation between these two regions. / Ph. D.

Couette, pipe, channel, and zero-pressure gradient (ZPG) turbulent boundary layer (TBL) flows have classically been considered as canonical wall-bounded turbulent flows since their near-wall behavior is generally considered to be universal, i.e. invariant of the flow case and the Reynolds number. Nevertheless, the idea that large-scale motions, being dominant in regions further away from the wall, might interact with and influence small-scale fluctuations close to the wall has not been disregarded. This view was mainly motivated due to the observed failure of collapse of the Reynolds normal stresses in viscous scaling. While this top-down influence has been studied extensively over the last decade, the idea of a bottom-up influence (backward energy transfer) is less examined. One exception was the recent experimental work on a Couette flow by Kawata, T. & Alfredsson, P. H. (Phys. Rev. Lett. 120, 244501, 2018). In the present work, a spectral representation of the Reynolds Stress transport equation is used to perform a scale-by-scale analysis of the terms in the equation. Two flow cases were studied: first, a Direct Numerical Simulation (DNS) of a Couette flow at a similar Reynolds number as Kawata and Alfredsson. The Reynolds number was ReT = 120, viscosity v. Second, a Large Eddy Simulation (LES) of a ZPG TBL at ReT = 730, 1270, and 2400. For both cases the classic interscale transport or turbulent kinetic energy was observed. However, also an inverse interscale transport of Reynolds shear stress was observed for both cases.

Many flow cases in fluid dynamics face undesirable flow separation due to ad-verse pressure gradients on wall boundaries. This occurs, for example, due togeometrical reasons as in a highly curved turbine-inlet duct or on flow-controlsurfaces such as wing trailing-edge flaps within a certain angle-of-attack range.Here, flow-control devices are often used in order to enhance the flow and delayor even totally eliminate flow separation. Flow control can e.g. be achieved byusing passive or active vortex generators (VGs) for momentum mixing in theboundary layer of such flows. This thesis focusses on such passive and activeVGs and their modelling for computational fluid dynamics investigations. First, a statistical VG model approach for passive vane vortex genera-tors (VVGs), developed at the Royal Institute of Technology Stockholm andthe Swedish Defence Research Agency, was evaluated and further improvedby means of experimental data and three-dimensional fully-resolved computa-tions. This statistical VVG model approach models those statistical vortexstresses that are generated at the VG by the detaching streamwise vortices.This is established by means of the Lamb-Oseen vortex model and the Prandtllifting-line theory for the determination of the vortex strength. Moreover, thisansatz adds the additional vortex stresses to the turbulence of a Reynolds-stresstransport model. Therefore, it removes the need to build fully-resolved three-dimensional geometries of VVGs in a computational fluid dynamics mesh. Usu-ally, the generation of these fully-resolved geometries is rather costly in termsof preprocessing and computations. By applying VVG models, the costs arereduced to that of computations without VVGs. The original and an improvedcalibrated passive VVG model show sensitivity for parameter variations suchas the modelled VVG geometry and the VVG model location on a flat plate inzero- and adverse-pressure-gradient flows, in a diffuser, and on an airfoil withits high-lift system extracted. It could be shown that the passive VG modelqualitatively and partly quantitatively describes correct trends and tendenciesfor these different applications. In a second step, active vortex-generator jets (VGJs) are considered. They were experimentally investigated in a zero-pressure-gradient flat-plate flow atTechnische Universitä̈t Braunschweig, Germany, and have been re-evaluated for our purposes and a parameterization of the generated vortices was conducted. Dependencies of the generated vortices and their characteristics on the VGJsetup parameters could be identified and quantified. These dependencies wereused as a basis for the development of a new statistical VGJ model. This modeluses the ansatz of the passive VVG model in terms of the vortex model, theadditional vortex-stress tensor, and its summation to the Reynolds stress ten-sor. Yet, it does not use the Prandtl lifting-line theory for the determinationof the circulation but an ansatz for the balance of the momentum impact thatthe VGJ has on the mean flow. This model is currently under developmentand first results have been evaluated against experimental and fully-resolvedcomputational results of a flat plate without pressure gradient. / <p>QC 20120511</p>

This thesis explores the effects of favourable pressure gradient on the structure of turbulent boundary layers (TBL). In this context, the structure of three types of boundary layers namely a zero-pressure-gradient boundary layer, equilibrium boundary layers under favourable pressure gradient and relaminarising boundary layers is investigated mostly from the point of view of large-scale dynamics. This covers a whole range of flows on the so-called Reynolds number - pressure gradient diagram - from turbulent zero pressure gradient flows to relaminarising flows at relatively low Reynolds numbers. The study of turbulent and relaminarising boundary layers is carried out primarily using direct numerical analyses and some limited experiments in this thesis. The direct numerical simulations (DNS) of a zero-pressure-gradient turbulent boundary layer (ZPG TBL) is validated against the experimental and DNS data available in the literature. Furthermore, the important question of time-averaged signature of a large scale vortex structure and its relation with the two-point correlations in the context of ZPG TBL is addressed. In this context, a synthetic flow consisting of hairpin vortex structures is generated. The two-point correlations in the synthetic TBL and a real TBL are found to be qualitatively similar. This shows that the vortex structure leaves a time-averaged footprint in the form of correlations of velocity and vorticity. A study of two-point correlations in a real TBL shows that the structure angle deduced from two-point correlations varies with wall-normal location. The structure angle is small near the wall and increases away from the wall in agreement with the previous studies. The small angle close to the wall signifies the presence of streamwise structure. Away from the wall, this streamwise coherence is lost and the correlation contours become more isotropic. The presence of the wall and the mean shear affects smaller scales making them anisotropic close to the wall. Towards the edge of the boundary layer, smaller scales tend to become isotropic leading to -5/3 law in the energy spectrum. Further, a relation between a passive scalar in a flow and vorticity is explored. It is found that the scalar product of vorticity and scalar gradient is conserved in a non-diffusive situation. This assertion is demonstrated under various flow conditions. Despite the differences in Schmidt numbers, the structures observed in the outer layer are similar in both numerical and experimental flow visualisations. Further, the equilibrium turbulent boundary layers under favourable pressure gradient are studied. The numerical simulations of equilibrium sink flow TBL are validated against the experimental results of Dixit (2010). A study of two-point correlations reveals that the near-wall structure angle decreases with a favourable pressure gradient in sink flow TBLs. In the outer region, the loss of streamwise coherence occurs at a wall-normal location closer to the wall than in an ZPG TBL. Edge intermittency study reveals that the flow is non-turbulent beyond y/δ = 0.8 inside the mean boundary layer edge. The variation of the ratio of pressure gradient to Reynolds shear stress gradient shows that this ratio is very large (> 50) beyond y/δ = 0.8. The dominance of pressure gradient makes this part of sink flow TBL to behave like a Euler-region. Small scales in sink flow TBL tend to be isotropic near the edge of the boundary layer and spectra shows -5/3 law akin to ZPG TBL, albeit at lower Reynolds numbers. The concept of equilibrium is extended to flows with wall transpiration. The sink flow TBL is a special case of more generalised equilibrium TBLs with wall transpiration. Conditions required for the flow with wall transpiration are derived. It is observed that there is a systematic variation of various statistical properties with wall velocity. Further, it is observed that the motion in these equilibrium flows is purely active like in sink flow TBL. In equilibrium TBL, the Reynolds shear stress is directly related to mean velocity. So we have at our disposal an exact relation between the Reynolds shear stress and the mean velocity gradient without the need to do any ad-hoc modelling for the sink flow. This is an interesting observation from the point of view of modelling TBLs using eddy-viscosity. Eddy-viscosity model derived from sink flow TBL data is found to predict the mean velocity profiles in flows with wall transpiration with a sufficient accuracy. Similarly, it is plausible that any general non-equilibrium flow may be treated as a departure from equilibrium. With suitable modifications, eddy viscosity obtained from equilibrium TBL may be used to model them without invoking ad-hoc assumptions. Finally, the effect of initial Reynolds number on the process of relaminarisation is studied numerically and experimentally. ZPG TBLs with two different initial Reynolds number are subjected to different degrees of acceleration. However, the pressure gradient history is same in both the cases. It is observed that the flow with a higher initial Reynolds number relaminarises at a lower pressure gradient value than the flow with a lower initial Reynolds number. Assessment of different parameter criteria reveals that the criterion proposed by Narasimha & Sreenivasan (1973) is appropriate for the prediction of the onset of relaminarisation. Further, the structures in relaminarising flows are studied. The near-wall structure angle is found to decrease with the increasing FPG and the streamwise length of the structure also increases. The low and high speed streaks in the near-wall region are found to become longer and less undulating with an increase in the spanwise spacing. A stabilisation mechanism of near-wall streaks is also presented which suggests that the kinematic effect of mean vertical velocity directed towards the wall is responsible for the stabilisation of streaks.