The objective of this study is to characterize the mechanism of drag reduction by comparing the dynamical eigenfunctions of a turbulent pipe flow against those of two known cases of drag reduced flows. The first is forced drag reduction by spanwise wall oscillation, and the second is natural drag reduction found in relaminarizing flow. The dynamics are examined through a Karhunen-Lo`eve (KL) expansion of the direct numerical simulation flow field results. The direct numerical simulation (DNS) is performed using NEK5000, a spectral element Navier-Stokes solver, the first exponentially convergent investigation of DNS of turbulence in a pipe. The base flow is performed at a Reynolds number of Re = 150, resulting in a KL dimension of D_KL = 2130. As in turbulent channel flow, propagating modes are found, characterized with constant phase speed, and contribute of 80.58% of the total fluctuating energy. Based upon wavenumber characteristics and coherent vorticity visualization, four subclasses of propagating modes and two subclasses of non-propagating modes are discovered, qualitatively similar to the horseshoe (hairpin) vortex structure reported in literature. The drag reduced case is performed at the same Reynolds number with a spanwise velocity A+ = 20, a period of T+ = 50, and is driven by a constant pressure gradient. This results in a increase of flow rate by 27 %, and the KL dimension is reduced to D_KL = 102, a 96% reduction. The propagating modes, in particular the wall modes, are pushed away from the wall, resulting in a 34% increase in their advection speed, and a shift away from the wall of the root-mean-square and Reynolds stress peaks. The relaminarizing case observes the chugging motion of the mean flow rate when the Reynolds number is barely turbulent, at Re = 95. This chugging motion is the relaminarization of the flow, resulting in an increased flow rate, and then before complete relaminarization, the flow regains its turbulent state. This occurs because the lift modes, which are responsible for the majority of the energy in the inertial range of the energy spectra, decrease by two or three orders of magnitude. The chugging ends when the wall modes restart the turbulent cascade, and the lift modes are repopulated with energy. A model for the energy path is developed, with energy going from the pressure gradient to the shear modes, then to the roll modes, then to the wall modes, and then finally to the lift modes. It is concluded that drag reduction in a flow can be achieved by disrupting any leg of this model, thus disrupting the self-sustaining mechanism of turbulence. The spanwise wall oscillation shortened the life span of the wall modes, thus limiting their ability to pass energy to the lift modes. Likewise, the low Reynolds number did not provide enough energy to sustain the lift modes, and so relaminarization began. The contribution of this work is twofold. Firstly, the structure of turbulent pipe flow is examined and visualized for the first time using the Karhunen-Lo`eve method. The second, and perhaps greatest contribution of this work, is that the mechanism of drag reduction has been characterized as the link between the wall modes and the lift modes. This will allow future work on developing real methods of drag reduction, and eventually porting it to high Reynolds number flows, like that of an oil pipeline at Re= 40, 000. To achieve this, certain questions remain to be answered, such as what is the most efficient method of disrupting the wall-lift mechanism? Is there a single structure that can be identified and manipulated that gives a similar eect? Once answered, this will allow for a new generation of pipelines to be developed, and considering the implications in petroleum industry alone, will result in a significant contribution to the economy of the world. / Ph. D.

Large-eddy simulations are carried out to study the combined effects of roughness and favourable pressure gradient in boundary layer flows, where the high acceleration (on smooth walls) may cause flow reversion to the quasi-laminar state. A sand-grain roughness model is used, with the no-slip boundary condition modeled by an immersed boundary method. The properties and accuracies of the scheme are studied, the roughness model is validated, and the spatial-resolution requirements are determined. The roughness model is applied to boundary layers subject to mild or strong acceleration, with simulations carried out underlining the effects of three parameters: the acceleration parameter, the roughness height, and the inlet Reynolds number. The roughness effects are limited to the roughness sublayer; the outer layer is affected indirectly only, through the changes that roughness causes in the relaminarization and retransition processes. The roughness significantly affects the inner-layer quantities like the friction velocity and the friction coefficient, while the local Reynolds number, the outer-layer mean velocity, as well as the Reynolds stresses beyond the roughness sublayer, are not sensitive to the roughness. The acceleration decreases the Reynolds stresses in the overlap region and promotes a laminar-like velocity profile. The acceleration leads to stabilization of near-wall structures and causes one-dimensional turbulence. The roughness generates small-scale structures at the bottom wall, which disturb the larger structures originally stabilized by the pressure gradient, leading to a decrease in the Reynolds-stress anisotropy. Roughness increases the Reynolds stresses in the roughness sublayer and tends to restore the fully turbulence flow early. The inlet Reynolds number affects the flow stability by determining the viscous length scale compared to the roughness length scales, and by determining how far the roughness effect extents into the boundary layer. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2011-10-17 11:19:08.063

Turbulent boundary layers approximating those found on the NASA Orion Multi-Purpose Crew Vehicle (MPCV) thermal protection system during atmospheric reentry from the International Space Station have been studied by direct numerical simulation, with the ultimate goal of reducing aerothermodynamic heating prediction uncertainty. Simulations were performed using a new, well-verified, openly available Fourier/B-spline pseudospectral code called Suzerain equipped with a ``slow growth'' spatiotemporal homogenization approximation recently developed by Topalian et al. A first study aimed to reduce turbulence-driven heating prediction uncertainty by providing high-quality data suitable for calibrating Reynolds-averaged Navier--Stokes turbulence models to address the atypical boundary layer characteristics found in such reentry problems. The two data sets generated were Ma[approximate symbol] 0.9 and 1.15 homogenized boundary layers possessing Re[subscript theta, approximate symbol] 382 and 531, respectively. Edge-to-wall temperature ratios, T[subscript e]/T[subscript w], were close to 4.15 and wall blowing velocities, v[subscript w, superscript plus symbol]= v[subscript w]/u[subscript tau], were about 8 x 10-3 . The favorable pressure gradients had Pohlhausen parameters between 25 and 42. Skin frictions coefficients around 6 x10-3 and Nusselt numbers under 22 were observed. Near-wall vorticity fluctuations show qualitatively different profiles than observed by Spalart (J. Fluid Mech. 187 (1988)) or Guarini et al. (J. Fluid Mech. 414 (2000)). Small or negative displacement effects are evident. Uncertainty estimates and Favre-averaged equation budgets are provided. A second study aimed to reduce transition-driven uncertainty by determining where on the thermal protection system surface the boundary layer could sustain turbulence. Local boundary layer conditions were extracted from a laminar flow solution over the MPCV which included the bow shock, aerothermochemistry, heat shield surface curvature, and ablation. That information, as a function of leeward distance from the stagnation point, was approximated by Re[subscript theta], Ma[subscript e], [mathematical equation], v[subscript w, superscript plus sign], and T[subscript e]/T[subscript w] along with perfect gas assumptions. Homogenized turbulent boundary layers were initialized at those local conditions and evolved until either stationarity, implying the conditions could sustain turbulence, or relaminarization, implying the conditions could not. Fully turbulent fields relaminarized subject to conditions 4.134 m and 3.199 m leeward of the stagnation point. However, different initial conditions produced long-lived fluctuations at leeward position 2.299 m. Locations more than 1.389 m leeward of the stagnation point are predicted to sustain turbulence in this scenario. / text