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A computational investigation was undertaken to examine techniques for predicting supersonic dynamic flows, involving unsteadiness over fixed and moving surfaces. The fixed geometries examined were cylinder-flares and compression ramps, and the moving body geometries a pitching aerofoil and a rapidly deployed flap. Investigation into the characteristics of incipient separation of a supersonic cylinder-flare flow revealed that the separated length varied with a power of the flare angle and that the variation in height of the separated region varies in a bi-modal manner with flare angle. For small-scale separations (flare angles less than those which would traditionally have been expected to induce separation) the height of the separated region was seen to vary slowly with flare angle. For larger flare angles, the separation bubble was found to grow rapidly in height and length with increasing flare angle and produce significant deflection of the external flow. Computations of a Mach 5, compression ramp induced unsteady shock boundary layer interaction exhibited self-sustained oscillations at frequencies and amplitudes consistent with experimental data. Large dynamic structures (up to 1.7 boundary layer thicknesses in extent) were observed, and their production, propagation and deformation illustrated. By modifying the turbulent viscosities produced by a non-dimensional implementation of the Baldwin-Lomax turbulence model (using under- relaxation) a turbulence model was produced which accurately predicted separation lengths for a series of Mach 6.85 compression ramp flows encompassing laminar, transitional and turbulent flow regimes (dependent on ramp angle). A technique was developed to enable efficient computation of dynamically moving and/or deforming body flows. This technique was based on hierarchical, adaptive mesh refinement coupled with automatic generation of body surfaces, in which mesh adaption was used to capture the body geometry to within a specified accuracy. This, in conjunction with automatic cell creation and destruction, enabled the derivation of steady and unsteady, time accurate, conservative boundary conditions. This algorithm was used to compute a quasi-steady laminar supersonic pitching aerofoil flow, and an unsteady turbulent supersonic flap deployment. In both cases agreement with experiment was found to be good.

A new formulation of Delayed Detached-Eddy Simulation (DDES) based upon elliptic relaxation is derived and implemented within a finite-volume framework. This new formulation is based upon the φ − f RANS model which has previously demonstrated both improved modelling of the near-wall physics and numerical robustness for industrial applications. The φ − f DDES model is calibrated and validated using Decaying Isotropic Turbulence (DIT) to establish the validity of the derivation and to calibrate the model constants. In light of the numeri- cal scheme requirements for DDES, a hybrid numerical scheme is proposed and implemented, which is shown to perform in the intended manner.Initially, three DDES formulations (SA-DDES, SST-DDES and φ − f DDES) are compared on the 2D periodic hills test case at Re = 10590 and Re = 37000. This test case primarily serves as a validation case to evaluate whether the im- plementation and calibration were correct. The flow over a NACA0021 airfoil post-stall at 60o incidence is then evaluated; a test case that DDES was origi- nally devised for (i.e massive separation from an airfoil). The three formulations are then evaluated on a 2D wall-mounted hump which exhibits largely geometry induced separation, but is still sensitive to the modelling of the initial separated shear layer and upstream turbulence levels. The final case is the Ahmed car body which combines both geometry and pressure-induced separation from a 3D surface. This complex flow is challenging for any turbulence modelling approach and is sensitive to the underlying RANS model.A general sensitivity to the underlying RANS model is demonstrated for the majority of the test cases investigated. The φ − f DDES model is shown to have encouraging performance on these wide range of test cases compared to the established SST-DDES and SA-DDES models. Whilst the φ − f DDES model is not a fix for the shortcomings of DDES, it is shown to be a practical and robust alternative to the established SST-DDES and SA-DDES variants that have become the de facto choice for many DDES users.

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In this thesis, the flow and heat transfer in dimpled channels have been investigated using the Reynolds-averaged Navier-Stokes (RANS) approach. The primary objective of this investigation is to identify the capabilities of RANS models to reproduce the characteristics of the flow and heat transfer in dimples. The flow in dimpled channels has been chosen as the test case due to their relevance to gas turbine cooling applications, as well as the fairly complex flow features over dimples, which poses a challenge to turbulence modelling. Five turbulence models have been tested in the present work. These include: the Launder and Sharma k-epsilon model, both the Craft et al. (1996) and (2000) cubic k-epsilon models, the Hanjalic and Jakirlic Reynolds stress model (RSM), as well as the Craft (1998) two-component limit (TCL) RSM. The models have been chosen such that all three classes of RANS closure were tested. The tested models have been applied to two dimpled channel configurations with increasing complexity. In the first, the flow over a single dimple in a channel has been considered, while in the second, the case of a staggered array of dimples has been examined. Moreover, across these two configurations, the effect of the dimple depth, the channel height and the Reynolds number have also been investigated. The results show that all models produce a physically viable solution for the problem of the flow in dimpled channels. Nevertheless, the Craft et al. (1996) and (2000) cubic k-ε models, as well as the Craft (1998) TCL RSM, predicted dimple flow structures that deviate from the expected state. In general, the main flow characteristics are reproduced by the RANS models, and the predicted mean velocity profiles are in good agreement with the data. All models report an overall enhancement in heat transfer levels when using dimples in comparison to those of a plane channel.

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The thesis introduces a new version of an elliptic-blending low-Reynolds-number eddy-viscosity Reynolds-averaged Navier Stokes model. It is a model intended to be implemented in an industrial solver. It will be argued that there is still room for such a simple model, though eddy-viscosity models must rely on developments specificallymade for higher order formulations. It is the aim of the v2-f model to integrate elements of Reynolds-stress modelling developments into a simpler formulation, but the former paradoxically suffers from numerical stiffness, which kept it out of reachof industry researchers everyday simulations. The v2-f formulation endeavours to reproduce the near-wall asymptotic behaviour of the turbulent quantities, as sounder alternative to empirical damping functions, and the required near-wall balance of small terms represents a numerical challenge. The present work first provides a comprehensive review of v2-f developments proposed over the past twenty years, and the different remedies for the numericalstiffness linked to the original formulation. The review focuses on ten v2-f variants, proposed between 1991 and 2006, whose behaviour is compared in some fundamental flows: the channel flow for five different Reynolds numbers, the asymptotic case of the logarithmic layer at infinite Reynolds number and the case of a flow with homogeneous sheared turbulence. Based on the conclusions of the review, the thesis proposes new developments. Firstly, the derivation of a new model, namely the φ - α model, is introduced. It relies on the resolution of two non-dimensional variables: φ represents the wall-normal anisotropy and α is a wall-proximity sensor. It is argued that only this formulation can address the numerical problems already mentioned without altering the predictions. Secondly, additional upgrades of the φ - α model are proposed to correct the dissipation rate equation. The aim is to improve the model behaviour in some specific regions of a boundary layer, by isolating some viscous terms and by improving the representation of turbulent transport at the edge of a boundary layer. Final developments are combined in a new model, the BL-v2/k model. The φ - α and BL-v2/k models are then validated for a set of two pressure induced separated flows and two buoyant flows, and beneficial effects of the proposed developments on the predictions are demonstrated. The numerical properties of the convergency of the BL-v2/k model are also reported at the end of this work.

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Catalytic converters are widely used in the automotive industry to comply with increasingly stringent emissions regulations. The flow distribution across the catalyst substrate significantly aects its conversion eciency. Measuring the flow in a catalyst system is challenging; computational fluid dynamics (CFD) provides an alternative approach for the assessment of different design concepts and is therefore commonly employed to model flow behaviour. This thesis studies the application of CFD to modelling ow in a two-dimensional system consisting of a catalyst monolith downstream of a wide-angled planar diuser, with total included angle 60°. Computational models are developed using the commercial CFD software STAR-CCM+. Flow predictions are compared to experimental data collected by Mat Yamin, (2012) and also as part of this study. Measurements were obtained on a two-dimensional isothermal flow rig using particle image velocimetry (PIV) and hot-wire anemometry (HWA). Steady flow studies compare different methods of modelling the monolith. Models include the common approach of modelling the monolith as a porous medium and the computationally expensive individual channels model. A hybrid model is developed that combines the two approaches, benefiting from the respective merits of each method. Two monolith lengths are considered, with flow at varying Reynolds numbers. The porous model predicts the downstream velocity prole well for the shorter monolith but overpredicts flow maldistribution for the longer monolith. The inclusion of an entrance effect to account for the pressure losses associated with oblique entry into the monolith channels is studied. Best agreement in downstream velocity is observed when the pressure losses are limited using a critical angle approach. The individual channels model is found to be the most consistently accurate across monolith lengths, attributable to the accurate capture of flow behaviour upon entry into the monolith channels. A novel hybrid model is proposed, which combines the computational efficiency of the porous model with the geometrical accuracy of individual channels. The model is evaluated and is found to provide results similar to the individual channels model, with improved predictions of velocity maxima and minima. Pulsating flow studies present three transient flow regimes with similar inlet pulse shapes and varying Reynolds number and frequency. Predicted velocities in the diuser are in good agreement with PIV flow fields, however CFD predicts higher magnitudes at the shear layer. The model predicts large residual vortices present at the end of the cycle where experimental data shows none; it is concluded that CFD underpredicts turbulence diffusion. Evidence of cyclic variation in experimental data highlights the limitation of URANS turbulence models.

This dissertation presents a study of hyperbolic turbulence modelling for the Gaussian ten-moment equations. In gaskinetic theory, moment closures offer the possibility of deriving a series of gas-dynamic governing equations from the Boltzmann equation. One typical example, the Gaussian ten-moment model, which takes the form of hyperbolic-relaxation equations, is considered as a competitive model for viscous gas flow when heat transfer effects are negligible. The hyperbolic nature of this model gives it several numerical advantages, compared to the Navier-Stokes equations. However, until this study, the application of the ten-moment equations has been limited to laminar flows, due to the lack of appropriate turbulence models. In this work, the ten-moment equations are, for the first time, Reynolds-averaged. The resulting equations inherit the hyperbolic balance-law form from the original equations with new unknowns, which require approximation by turbulence models. Most of the traditional turbulence models for the Reynolds-averaged Navier-Stokes equations are not perfectly well-suited for the Reynolds-averaged ten-moment equations, because the second-order derivatives presented in these models can break the pure hyperbolic nature of the original model. The relaxation methods are therefore proposed in this project to reform the existing turbulence models. Two relaxation methods, the Chen-Levermore-Liu p-system and Cattaneo-Vernotte models, are used to hyperbolize the Prandtl’s one-equation model, standard k-ε model and Wilcox k-ω model. The hyperbolic versions of these turbulence models are first shown to be equivalent to their original forms. They are then coupled to the Reynolds-averaged ten-moment equations to build the overall hyperbolic governing equations for turbulence flows. An axisymmetric version of Reynolds-averaged ten-moment equations is also derived. A dispersion analysis is conducted for the resulting governing equations, which shows the corresponding dispersive behaviour and stability. The effect of the relaxation parameters is investigated through several numerical tests. All derived turbulence models are applied to solve canonical validation test problems, including two-dimensional planar mixing-layer, free-jet and circular free-jet. The numerical evaluations are analysed and compared against existing experimental measurements.