The recent growth of the size of wind farms highlights the need for a deeper understanding of the mesoscale phenomena in a stably stratified atmosphere, such as atmospheric gravity waves, as the effect on the power generation can be significant. This thesis is a numerical study of the effect of wind farm layout on atmospheric gravity wave excitation and the resulting feedback on wind farm performance. Wind farms in this study have varying power density, streamwise or spanwise turbine spacing, aspect ratio, hub height, rotor diameter, shape, or orientation with respect to the freestream, and are situated in a conventionally neutral boundary layer in offshore conditions. Moreover, the wind farms can be horizontally or vertically staggered. To investigate the atmospheric gravity wave excitation, the effect of wind farm layout on the Froude number and inversion Froude number governing the internal and interfacial waves respectively is studied using several high-fidelity Large Eddy Simulations. Then, AGW wavelength and wind farm efficiency are parametrically studied using a fast reduced-order model. Specifically, the non-local efficiency is considered, which is a measure of the global blockage effect induced by the atmospheric gravity waves. It is found that the length scale used in the Froude number must be adjusted to the wind farm, and is dependent on the turbine spacing and farm shape. The inversion Froude number is based on the phase speed of the interfacial waves. It is suggested that the phase speed must be based on shallow-water theory and deep-water theory for small and large turbine spacings respectively. In other words, for small turbine spacings the wind farm acts as an entity, while for large turbine spacings, the farm acts as a collection of individual turbines. Finally, the streamwise and spanwise turbine spacing (and consequently the power density), and the aspect ratio primarily govern the non-local efficiency.

The flow of air over a swept wing initially starts in a smooth laminar state (referred to as base flow) and entrains disturbances which subsequently grow and transition the flow to a chaotic, turbulent state. Active efforts have been made to study and control these disturbances, which manifest as stationary crossflow modes. Excrescences in the form of a forward-facing step (FFS) impose a base flow deformation in the form of a rapid near-wall pressure change, flow separation, and strong upwash. This modifies the behaviour of stationary crossflow instability and subsequently leads to an upstream or downstream shift of transition location depending on FFS height. The mechanisms responsible for the above behavioural modification are unknown, motivating the current thesis. The evolution of primary stationary crossflow instability, in its linear growth phase, is studied through a spanwise invariant, synthetic, and idealized rapid base flow deformation imposed by changing the near-wall pressure distribution of a clean swept flat plate (possessing a favourable pressure gradient) via Gaussian-like pressure variations. An energy balance framework is developed that identifies the production term's behaviour as the differentiator between regions of perturbation growth and decay. The behaviour of the production term is described by two competing mechanisms, the first controlled by wall-tangential base flow shear and the second controlled by wall-tangential base flow acceleration or deceleration. The balance of these mechanisms shows that perturbations grow faster than the clean case in regions of wall-tangential base flow deceleration and slower than the clean case in regions of wall-tangential base flow acceleration. Perturbations are even found to attenuate in some cases when a region of wall-tangential base flow acceleration follows a region of wall-tangential base flow deceleration. The modification of energy transfer mechanisms brings into question whether the initial modal stationary crossflow mode deviates from modal character on interacting with the base flow deformation. The Orr mechanism is shown to identify differences in perturbation behaviour from local modal character. However, criteria from the literature hint towards an absence of any non-modal effects. Finally, the extent to which a synthetic idealized base flow deformation mimics the effects of an FFS on deforming the base flow and changing trends of stationary crossflow instability evolution is tested to show the applicability of methods developed in the thesis to instances of natural base flow deformation. The progress in understanding mechanisms by which a deformed base flow affects the linear phase of primary stationary crossflow instability growth leads to suggestions on devices that can be tested to delay this phase of instability growth. These devices could potentially also delay subsequent stages of instability growth and hopefully lead to the development of novel transition delay techniques.

 Distributed surface roughness elements characterise Thermal Protection Systems (TPS) typical of supersonic and hypersonic flows. The presence of these distributed roughness elements cause an increase in drag and heat transfer.  As opposed to incompressible flow over roughness elements, there are very few experimental and numerical studies on supersonic flow over roughness. The most fundamental computational technique wherein, all scales of turbulence is resolved is Direct Numerical Simulation (DNS). The cost of performing DNS of fully resolved roughness is even higher than canonical DNS because of the refined mesh needed to solve the roughness elements.  To overcome this limitation, the current thesis aims at exploring low cost alternatives to DNS of fully resolved roughness for studying the effect of drag and heat transfer in supersonic flow over rough walls. DNS results from fully resolved full channel cube roughness for Mach 2 and Mach 4 at friction Reynolds number Re_τ = 500,1000  are analyzed. The results from the low cost models are compared against the fully resolved roughness simulated using full channels. Three lower-cost alternative, namely DNS of minimal channel flow of fully resolved roughness, DNS of modelled roughness and resolved RANS are considered. As for the DNS of minimal channel flow, it is found that the velocity shift ΔU⁺ is predicted accurately and therefore the added drag. However, it cannot be used to predict the temperature field because of lack of outer layer similarity for the thermodynamic statistics. As for the modeled roughness, an extension of the model by Busse and Sandham originally developed for incompressible flows is considered. In this case the roughness geometry is substituted by the additional drag and heat transfer that it induces on the flow, which take the form of source terms in the momentum and energy equations. We perform 17 DNS simulations with modeled roughness and compare the results to the fully resolved simulation. We find that the parametric forcing method is able to predict the velocity shift with good accuracy, although recovering the equivalent roughness height from the model parameters can only be done a posteriori. The model is able to qualitatively reproduce the temperature field, but thermodynamic statistics are inaccurate when compared to DNS of the fully resolved geometry. The final computational technique is RANS. In real case applications, RANS require the use of wall functions, and in the case of rough walls knowledge of the equivalent roughness height k_s⁺ is necessary. We attempt to see if RANS of fully resolved roughness can be used to estimate the velocity shift ΔU⁺ and therefore  k_s⁺ by limiting ourself to the  linear Spalart-Allmaras (SA) model. It is found to be inaccurate in computing the mean velocity profile at  k_s⁺≈ 40 with improvements in accuracy observed for k_s⁺≈ 80 when compared with the results from DNS for cube roughness element. However, the accuracy is still low to be used for estimating k_s⁺. 

Large Eddy Simulations (LES) of a novel type of wing/body junction called the anti-fairing are performed in the current thesis to study the complex turbulent flow physics involved in the junction area and also to obtain a clear understanding of the drag reduction capabilities of the anti-fairing. In regards to that, two separate LES are performed: one for the baseline case with a Rood wing/flat plate combination and another with the Rood wing/anti-fairing combination. A detailed comparative study is performed between the two cases to observe important differences in junction flow characteristics. Both the simulations are performed on a 25 million immersed boundary Cartesian mesh by solving the incompressible Navier-Stokes equations using the in-house finite volume LES solver called INCA. Results from the LES study confirms the existence of the propulsive pressure mechanism of drag reduction for the anti-fairing case, previously proposed by Belligoli et al. However, the results also show that there exists a secondary drag reduction mechanism caused by a combination of increase in approach boundary layer momentum thickness and dampening of the turbulence associated with the horseshoe vortex (HSV) upstream of the wing. This secondary mechanism has been found to be caused by the convex dent present at the start of the anti-fairing geometry. The total drag reduction for the anti-fairing case comes out to be 1.8%. A new parameter called junction drag is defined which accounts for the drag only due to the presence of a junction. The reduction in junction drag obtained for the anti-fairing case is about 6.8%. Apart from the LES analysis, a RANS analysis has also been performed to further investigate the drag reduction capabilities of anti-fairing for different approach boundary layer thicknesses and anti-fairing depths. All the RANS analysis have been performed on a 5 million body-fitted mesh by solving the incompressible Navier-Stokes using the open source finite-volume solver OpenFOAM. Results from the RANS analysis indicate that there exists an optimum depth for the anti-fairing which corresponds to the least drag. Furthermore, it is found that the effect of approach boundary layer thickness is mostly on changing the base drag of the case where no anti-fairing is present, rather than actually affecting the performance of the anti-fairing at different depths.

Being able to solve numerically partial differential equations is fundamental for engineers to evaluate, optimize and improve industrial equipments. The framework of mimetic finite element methods allows engineers to find solutions characterized by strong conservation properties: this may result in a pointwise divergence free-flow field. However, sometimes, the computation of the solution of partial differential equations is time consuming, as a results, to reduce the computational time, engineers and mathematicians have developed hybrid methods.
The objective of this thesis is the development of a hybrid mixed finite element formulation of the vector Laplace equation without spurious modes. Discontinuous elements permit an higher degree of parallelism, and, at the end, a lower computational time. Lagrange multipliers are used to impose continuity between discontinuous elements. These turn out to be not only mathematical features but they are connected to the physical variables of the problem. Furthermore, it has been found that the usage of a new Lagrange multiplier, on the intersection of 4 or more elements, removes the spurious modes. Therefore, the associated system of equation is non-singular. The usage of the hybrid finite element methods reduces the computational time while maintaining the pointwise divergence constraint and the optimal convergence rate of all variables.
At the end, the mixed hybrid formulation is modified to solve the Stokes equations. Lagrange multipliers are used as boundary conditions. Solution of the lid-driven Stokes flow is shown.

In 2011 a relatively new type of numerical scheme has been introduced: Active Flux schemes. In this type of scheme an extra degree of freedom is added to the cell interfaces of a regular finite volume grid. This enables the use of non-conservative update methods for these additional variables, as conservation is automatically adhered to by the cell integral values. This increases the order of accuracy of the scheme, while allowing a broader range of update methods. This thesis proposes a new update method based on minimizing the truncation error of a Taylor series expansion. This way, a linear update scheme can be created for each unique stencil. An adaptive mesh refinement algorithm is implemented to conform the mesh to local high-frequency phenomena such as shock waves. A high-resolution simulation shows that the adaptive method reaches error levels of a uniform mesh while using ~9.6 times less computational cells.

The project concerns uncertainty reduction of parameters of a thermodynamic equation of state for a dense gas, using Bayesian inference. The dense gas considered is D6 siloxane and the equation of state used is the polytropic van der Waals equation. The shock tube data comes from the flexible asymmetric shock tube (FAST) experiment. This is modeled using the quasi-one-dimensional Euler equations with a source term that depends on time. A surrogate model based on sparse grids and a sensitivity analysis using Sobol' indices are both applied. The Markov chain Monte Carlo technique is applied to sample from the posterior probability distribution on the chosen parameters of the computer model. The results indicated that some of the thermodynamic parameters were identified, but that their mean values showed a disagreement with the true values in the literature.

Feadship yachts are designed for the leisure and cruising across the oceans. These luxury yachts are mostly powered by diesel engines or in some cases, a diesel-hybrid system. To prevent the inconvenience and the discomfort arising from the diesel exhaust gases for passengers, Feadship yachts are equipped with an underwater exhaust outlet. These underwater exhaust outlets are located on the side of the hull close to the dynamic waterline. It consists of an external appendage called "scoop" which creates a low pressure region for the exhaust outlet. During recent sea trials of the Feadship yachts, undesirable variations in the exhaust back-pressure were observed at the underwater outlet. These undesirable variations led to a situation with either too high back-pressure or too low back-pressure. An excessive back-pressure will increase the fuel consumption and will damage the diesel engine. Contrary, an extremely low back-pressure will give a visible exhaust flow above water thereby discolouring the hull and contaminating the deck with exhaust gases and steam.

An ideal scoop design would substantially reduce the above described problems. To investigate the optimal design for a scoop, a numerical method will be used. The method applicable in this study will be the Mutiphase Flow models from the commercial Computational Fluid Dynamics (CFD) software called Star CCM+. A multiphase fluid interaction between the exhaust gases and sea water will be examined to find the physical phenomenon affecting the back-pressure at the underwater outlet. In return, this phenomenon will be useful for a thorough analysis of the different scoop designs and how this design could impact the back-pressure. Furthermore, the validation of the numerical method will be carried out against the data procured from sea trials of the yachts with current scoop design.

To conclude, design recommendations for an optimal scoop geometry will be provided such that it can reduce the excessive back pressure, have a low resistance and prevent the discolouring of the hull.

A robust and flexible numerical framework was developed for modelling of dielectric-barrier discharge applicable to plasma actuated flow control. In OpenFOAM, a solver was built which solves convection-diffusion equations for ionized species coupled to Gauss’ law for electrostatics and includes a chemical model to account for the various chemical reactions taking place in non-equilibrium cold plasma. The framework relies on a predictor-corrector method and was verified and qualitatively validated in 1D using a volumetric cathode-fall glow discharge case. Quantitative validation in 1D and extension to 2D was recommended for future work as steps towards increased capability of the solver.