Scalar (heat or mass) transfer plays an important role in many industrial and engineering applications. Difficulties in experimental measurements means that there is limited detailed information available, especially in the near-wall region. Prediction in simple flows is well documented and the basis for development of many Computational Fluid Dynamics (CFD) models. This is, however, not the case for scalar transfer, especially when the Prandtl (Pr) or Schmidt number (Sc) is much greater than unity. In complex flows that involve separation and reattachment, the scalar transfer coefficient is significantly different to that of fully developed turbulent flow. The purpose of this Thesis is to investigate high Prandtl number (Pr ≥ 10) scalar transfer in fully developed (pipe) and disturbed (sudden pipe expansion) turbulent flow using CFD. Direct Numerical Simulation (DNS) is the most straight-forward approach to the solution of turbulent flows with scalar transfer. However, this technique is computationally intensive because all turbulent scales need to be resolved by the simulation. Large eddy simulation (LES) is a compromise compared to DNS. Instead of resolving all spatial scales, LES resolves only the large-scales with the small-scales being accounted for by a subgrid-scale model. Chapter 2 details the mathematical, numerical and computational details of LES with scalar transfer. From this, an optimized and highly scalable parallel LES solver was developed based on state-of-the-art LES subgrid-scale models and numerical techniques. Chapter 3 provides a verification of the LES solver for fully developed turbulent pipe flow. Reynolds numbers between Re = 180 and 1050 were simulated with a single Prandtl number of Pr = 0.71. Detailed turbulent statistics are provided for Re = 180, 395 and 590 with varying grid resolution for each Reynolds number. The results from these simulations were compared to established experimental and numerical databases of fully developed turbulent pipe and channel flows. The LES solver was shown to be in good agreement with the prior work with most discrepancies being accounted for by only reporting the resolved (large-scale) component directly reported from the LES results. For a Prandtl number close to unity, the mechanisms of turbulent transport and scalar transfer are similar. The near-wall region was shown to be dominated by large-scale sweeping structures that bring high momentum and scalar concentrations to the near-wall region. These are convected parallel to the wall as diffusion mechanisms act to transfer this to the wall where dissipation takes effect. An ejection structure then acts to transport the resultant low momentum, scalar depleted fluid back to the bulk to be replenished and continue the cycle. As the Prandtl number increases, molecular diffusivity decreases relative to viscosity, and the mechanisms of scalar transfer differ to those at Pr = 0.71. This is investigated in Chapter 4 using simulations at Re = 180, 395 and 590, with detailed statistics at Re = 395 for Pr = 0.71, 5, 10, 100 and 200. Where possible the results are compared to other numerical work and the LES solver was shown to accurately resolve the higher Prandtl number flows. There are marked variations in the scalar transfer with increasing Prandtl number as the turbulent scalar transfer becomes concentrated closer to the wall and dominated by large-scale turbulent structures. Sweeping structures are still responsible for bringing the high scalar concentrations towards the wall, however, high Prandtl number scalars are unable to completely diffuse to the wall in the time that the structure is convected parallel to the wall adjacent to the diffusive sublayer. Therefore, most of the high Prandtl number scalar is returned to the bulk via the ejection structure rather than being dissipated at the wall. Chapter 5 uses the sudden pipe expansion (SPE) to investigate disturbed turbulent flow for an inlet Reynolds numbers of Reb = 15600 and a diameter ratio of E = 1.6. These simulation parameters were chosen to match the experimental LDA measurements of Stieglmeier et al. (1989). The LES results for a range of grid resolutions were shown to be in very good agreement with the experimental work. From the LES results it was determined that the fluctuations in the wall shear stress are important in the near-wall turbulent transport. These are the result of eddies originating from the free shear layer down-washing and impinging upon the wall. This is a more effective sweeping mechanism than that observed for the fully developed turbulent pipe flow. Despite the down-wash structures impinging upon the wall, a viscous sublayer still exists in the reattachment region, albeit much thinner than the fully developed turbulent pipe flow further downstream. Using the same Reynolds number and diameter ratio, scalar transfer simulations were also undertaken in the SPE with Prandtl numbers of Pr = 0.71, 5, 10, 100 and 200. An applied scalar flux was used to heat the expanded pipe wall. The LES results are in agreement with experimental Nusselt numbers from Baughn et al. (1984) for Pr = 0.71. The disturbed turbulent flow enhances the scalar transfer and this is the result of down wash events transporting low (cold) scalar from the inlet pipe to the near-wall of the expanded pipe. This cools the heated wall and enhances localized scalar transfer downstream of the expansion. A diffusive sublayer still exists in the reattachment region within the viscous sublayer for Prandtl numbers greater than unity. As the Prandtl number increases the diffusivity decreases relative to viscosity and near-wall scalar transfer enhancement decreases as the diffusion time-scales increase.

Immersed boundary (IB) methods are attractive due to their ability to simulate flow over complex geometries on a simple Cartesian mesh. Unlike conformal grid formulation, the mesh does not need to conform to the shape and orientation of the boundary. This eliminates the need for complex mesh and/or re-meshing in simulations with moving/morphing boundaries, which can be cumbersome and computationally expensive. However, the imposition of boundary conditions in IB methods is not straightforward and numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In a nutshell, IB methods in the literature often suffer from numerical oscillations, implementation complexity, time-step restriction, burred interface, and lack of generality. This limits their ability to mimic conformal grid results and enforce Neumann boundary conditions. In addition, there is no generic IB capable of solving flow with multiple potentials, closely/loosely packed structures as well as IBs of infinitesimal thickness. This dissertation describes a novel 2$ ^{\text{nd}} $ order direct forcing immersed boundary method designed for simulation of two- and three-dimensional incompressible flow problems with complex immersed boundaries. In this formulation, each cell cut by the IB is reshaped to conform to the shape of the IB. IBs are modeled as a series of 2D planes in 3D space that connect seamlessly at the edges of the cut cells, in a way that mimics conformal grid. IBs are represented in a continuous and consistent fashion from one cell to another, thus eliminating spatial pressure oscillations originating from inconsistent description of the IB as well as the traditional stair-step problem, leading to a more accurate resolution of the boundary layer. Boundary conditions are enforced at the exact location of the IB devoid of interpolation, which guarantees sound simulations even on grids with high aspect ratio, and enables simulations of flow packed with multiple IBs in close proximity. Boundary conditions for each phase across the IB are enforced independently, yielding a unique capability to solve flows with zero-thickness IBs. Simulations of a large number of 2D and 3D test cases confirm the prowess of the devised immersed boundary method in solving flows over multiple loosely/closely-packed IBs; stationary, moving and highly morphing IBs; as well as IBs with zero-thickness. Extension of the proposed scheme to solve flow with multiple potentials is demonstrated by simulating transfer and transport of a passive scalar from an array of side-by-side and tandem cylinders in cross-flow. Aquatic vegetation represented by a colony of circular cylinders with low to high solid fraction is simulated to showcase the prowess of the current numerical technique in solving flow with closely packed structures. Aquatic vegetation studies are extended to a colony of flat plates with different orientations to show the capability of the developed method in modeling zero-thickness structures.

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.