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Two major problems in viscoelastic turbulence, the effects of polymers on the laminar-turbulent transition dynamics and the origin of the maximum drag reduction asymptote, can be both better understood in the regime near the margin of turbulence. In the first part of this thesis, direct numerical simulation trajectories initiated from the edge state are used to follow its unstable manifold into the turbulent basin. In Newtonian flow, the growth of turbulence starts with the intensification of velocity streaks and a sharp rise in the Reynolds shear stress. It is followed by a quick breakdown into high-intensity small-scale fluctuations before entering the core of turbulence. Adding drag-reducing polymers does not affect the initial growth of turbulence but stabilizes the primary streak-vortex structure, which help the flow circumvent the breakdown stage. Throughout the process, polymers act in reaction to the growing turbulence and do not drive the instability. This part not only reveals the transition dynamics into turbulence but also presents a comprehensive view of the bursting stage observed in the near-wall self-sustaining cycle, which starts as the flow leaves hibernating turbulence and is redirected towards the turbulent basin by the unstable manifold of the edge state. On the other hand, this thesis also discusses the effects of polymer addition on the laminar-turbulent transition in extended domains. Localized turbulent spot can be clearly observed in the large box, and this turbulent region will spread as well as tend to “split” but finally fill up the whole domain before it is separated. Polymers do not affect the flow dynamics until the burst. Similarly, vortex structures rapidly break down into small scales after the first bursting of Reynolds shear stress, but polymer additives depress this process. The thesis offers a clear and comprehensive overview of the transition into turbulence in the presence of drag-reducing polymers. Future work remains in two major directions. The first is to pinpoint the flow states responsible for the quantitative origin of the universal upper limit of drag reduction observed in experiments. The second is to determine the role, if any, of elasticity-driven instabilities in the transition. / Thesis / Master of Applied Science (MASc) / Turbulence exists everywhere and can be observed in most fluid flows occurring in nature. To reduce the energy consumption, frictional resistance in the turbulence must be considered in fluid transportation. It has been known since the 1940s that a small amount of long-chain polymer additives can dramatically reduce such drag. The mechanism of drag reduction has attracted extensive attention. Two problems of particular interest are the upper limit of drag reduction (termed maximum drag reduction) and the polymer effects on the laminar-turbulent transition. In this thesis, full transient trajectories from marginal turbulent states towards sustained turbulence in both Newtonian and polymeric flows are monitored by direct numerical simulations. It is observed that polymer additives do not affect the initial growth of turbulence but prevent flows from breaking into strong but small-scale fluctuations afterwards. In a more extended domain, turbulence starts as localized spots which spread across the channel. Adding polymers changes the dynamics of turbulence propagation as well. In addition to the aforementioned problems, this study also sheds lights on the so-called bursting events intermittent surges in turbulent activities observed in experiments.

Yes / In this paper, an analytical model that represents the streamwise velocity distribution for open channel flow with submerged flexible vegetation is studied. In the present vegetated flow modelling, the whole flow field has been separated into two layers vertically: a vegetated layer and a non-vegetated free-water layer. Within the vegetated layer, an analysis of the mechanisms affecting water flow through flexible vegetation has been conducted. In the non-vegetated layer, a modified log-law equation that represents the velocity profile varying with vegetation height has been investigated. Based on the studied analytical model, a sensitivity analysis has been conducted to assess the influences of the drag and friction coefficients on the flow velocity. The investigated ranges of drag and friction coefficients have also been compared to published values. The findings suggest that the drag and friction coefficient values are non-constant at different depths and vegetation densities, unlike the constant values commonly suggested in literature. This phenomenon is particularly clear for flows with flexible vegetation, which is characterised by large deflection.

In transonic flow, the aerodynamic interference that occurs on a strut-braced wing airplane, pylons, and other applications is significant. The purpose of this work is to provide relationships to estimate the interference drag of wing-strut, wing-pylon, and wing-body arrangements. Those equations are obtained by fitting a curve to the results obtained from numerous Computational Fluid Dynamics (CFD) calculations using state-of-the-art codes that employ the Spalart-Allmaras turbulence model. In order to estimate the effect of the strut thickness, the Reynolds number of the flow, and the angle made by the strut with an adjacent surface, inviscid and viscous calculations are performed on a symmetrical strut at an angle between parallel walls. The computations are conducted at a Mach number of 0.85 and Reynolds numbers of 5.3 and 10.6 million based on the strut chord. The interference drag is calculated as the drag increment of the arrangement compared to an equivalent two-dimensional strut of the same cross-section. The results show a rapid increase of the interference drag as the angle of the strut deviates from a position perpendicular to the wall. Separation regions appear for low intersection angles, but the viscosity generally provides a positive effect in alleviating the strength of the shock near the junction and thus the drag penalty. When the thickness-to-chord ratio of the strut is reduced, the flowfield is disturbed only locally at the intersection of the strut with the wall. This study provides an equation to estimate the interference drag of simple intersections in transonic flow. In the course of performing the calculations associated with this work, an unstructured flow solver was utilized. Accurate drag prediction requires a very fine grid and this leads to problems associated with the grid generator. Several challenges facing the unstructured grid methodology are discussed: slivers, grid refinement near the leading edge and at the trailing edge, grid convergence studies, volume grid generation, and other practical matters concerning such calculations. / Ph. D.

The accuracy of the calculated drag force in OpenRocket was examined in this investigation for a rocket traveling at subsonic, transonic and supersonic speeds. The idea was to compare the computed drag coefficients in OpenRocket to the drag coefficients obtained by running multiple computational fluid dynamics (CFD) simulations in Ansys Fluent. Specifically, the freestream Mach number and altitude parameters were varied for a geometric model of the Mjöllnir rocket. The results obtained converged several orders of magnitude and were exceptionally stable. Both the physical accuracy and numerical independence of the results was verified through examining the solutions' contour plots and conducting multiple sensitivity analyses. The conclusion was that OpenRocket overpredicts the Mjöllnir rocket's drag coefficients by 12 % to 73 % for all examined freestream Mach numbers and altitudes. Additionally, an empirical relationship was found for how the Mjöllnir rocket's drag coefficient changes with altitude and the freestream Mach number. In particular, it is a multivariate function that can be considered valid for an altitude of h ≤ 10 km and a freestream Mach number of 0.2 ≤ M ≤ 3.0. The empirical relationship fitted exceedingly well with simulation data and merits further investigation.

Studiens syfte är att undersöka möjligheter till att implementera kommunikativa dragen i utvecklandet av matematikundervisningen genom lärares perspektiv och erfarenheter. Denna studie besvarar tre forskningsfrågor som rör utmaningar, framgångsfaktorer, de kommunikativa dragens effekter och användningen av dessa strategier i undervisningen. I denna fallstudie användes en metodkombination av observation och intervju. Resultaten visade att implementeringen av de kommunikativa dragen stötte på flera utmaningar, såsom tidsbegränsningar och elevers varierande förutsättningar. Det identifierades också framgångsfaktorer, såsom tillgängligheten till dragen, möjligheten att anpassa dragen och en trygg miljö. Att beskriva och resonera var de mest använda kommunikativa dragen av lärarna, medan andra användes i mindre utsträckning. Studien visar att det är möjligt för lärare att med relativt lite stöd introducera kommunikativa drag i undervisningen och att de ser det som ett användbart verktyg för att stödja elevernas kommunikation och matematiska utveckling.

No / Vegetation remains to be an important factor that can hinder the river flow. It needs innovative management scheme, in order to adapt these changes and ensure sustainability of their multiple usages. Vegetation plays an important role in floods and droughts adaptation within river system to alleviate any flood that may propagates from river to its surrounding. Vegetation within river can also retard its flow to cause building-up of deposition, and further adding to uncertainty of water use under extreme droughts. Due to these, it is important to study and understand vegetation drag behaviour toward flow in order to prevent flood risk and water security with hydrological drought in the basin and any other negative impact caused by it. In this study, an analytical approach for river flooding has been studied by improved representation of drag coefficient CD in flow velocity distribution modelling. The analysis of flow parameters, i.e. Reynolds number, on the drag coefficient CD has been conducted. The presented model has been used and analysed in open channel flows with flexible vegetation. In modelling, the flexible vegetated channel layers were divided into vegetation, top of vegetation and water layer zones in the model. The balance of forces for each layer has been established by validation using different reported measured data. The modelling results showed reasonably corresponding prediction of velocity profile in flows with flexible vegetation.