When an electrically conducting fluid moves through a magnetic field, fluid mechanics and electromagnetism are coupled. This interaction is the object of magnetohydrodynamics, a discipline which covers a wide range of applications, from electromagnetic processing to plasma- and astro-physics. In this dissertation, the attention is restricted to turbulent liquid metal flows, typically encountered in steel and aluminium industries. Velocity measurements in such flows are extremely challenging because liquid metals are opaque, hot and often corrosive. Therefore, non-intrusive measurement devices are essential. One of them is the Lorentz force flowmeter. Its working principle is based on the generation of a force acting on a charge, which moves in a magnetic field. Recent studies have demonstrated that this technique can measure efficiently the mean velocity of a liquid metal. In the existing devices, however, the measurement depends on the electrical conductivity of the fluid. In this work, a novel version of this technique is developed in order to obtain measurements that are independent of the electrical conductivity. This is particularly appealing for metallurgical applications, where the conductivity often fluctuates in time and space. The study is entirely numerical and uses a flexible computational method, suitable for industrial flows. In this framework, the cost of numerical simulations increases drastically with the level of turbulence and the geometry complexity. Therefore, the simulations are commonly unresolved. Large eddy simulations are then very promising, since they introduce a subgrid model to mimic the dynamics of the unresolved turbulent eddies. The first part of this dissertation focuses on the quality and reliability of unresolved numerical simulations. The attention is drawn on the ambiguity that may arise when interpretating the results. Owing to coarse resolutions, numerical errors affect the performances of the discrete model, which in turn looses its physical meaning. In this work, a novel implementation of the turbulent strain rate appearing in the models is proposed. As opposed to its usual discretisation, the present strain rate is in accordance with the discrete equations of motion. Two types of flow are considered: decaying turbulence located far from boundaries, and turbulent flows between two parallel and infinite walls. Particular attention is given to the balance of resolved kinetic energy, in order to assess the role of the model. The second part of this dissertation deals with a novel version of Lorentz force flowmeters, consisting in one or two coils placed around a circular pipe. The forces acting on each coil are recorded in time as the liquid metal flows through the pipe. It is highlighted that the auto- or cross-correlation of these forces can be used to determine the flowrate. The reliability of the flowmeter is first investigated with a synthetic velocity profile associated to a single vortex ring, which is convected at a constant speed. This configuration is similar to the movement of a solid rod and enables a simple analysis of the flowmeter. Then, the flowmeter is applied to a realistic three-dimensional turbulent flow. In both cases, the influence of the geometrical parameters of the coils is systematically assessed.

A new large eddy simulation (LES) code is developed and used to investigate non-local features of turbulent planetary boundary layers (PBLs). The LES code is based on filtered Navier-Stokes equations, which describe motions of incompressible, Boussinesq fluid at high Reynolds numbers. The code computes directly large-scale, non-universal turbulence in the PBL whereas small-scale, universal turbulence is parameterized by a dynamic mixed subgrid closure. The LES code is thoroughly tested against high quality laboratory and field data. This study addresses non-local properties of turbulence which emphasis on the stable stratification. Its basic results are as follows. The flow stability in PBLs is generally caused by two mechanisms: the negative buoyancy force (in the stable density stratification) and the Coriolis force (in the rotating system). The latter stabilizes the flow if the earth’s vorticity and the turbulent vorticity are anti-parallel. The Coriolis force stability suppresses large-scale turbulence and makes large eddies asymmetric. The density stratification suppresses vertical scales of turbulence. Joint actions of the Coriolis and the buoyancy forces result in a more complex behavior of turbulence. Particularly, the layers of vigorous turbulence may appear in the course of development of low-level jets in baroclinic atmosphere. Non-local effects determine integral measures of PBLs, first of all the PBL depth. This study clearly demonstrates its pronounced dependences on the Coriolis parameter, the Kazanski-Monin internal stability parameter, and newly introduced imposed-stability and baroclinicity parameters. An LES database is created and used to validate an advanced PBL-depth formulation. LES support the idea that PBLs interact with the stably stratified free flow through the radiation of gravity waves, excited by large turbulent eddies at the interface.

Turbocharging the internal combustion (IC) engine is a common technique to increase the power density. If turbocharging is used with the downsizing technique, the fuel consumption and pollution of green house gases can be decreased. In the turbocharger, the energy of the engine exhaust gas is extracted by expanding it through the turbine which drives the compressor by a shaft. If a turbocharged IC engine is compared with a natural aspirated engine, the turbocharged engine will be smaller, lighter and will also have a better efficiency, due to less pump losses, lower inertia of the system and less friction losses. To be able to further increase the efficiency of the IC engine, the understanding of the highly unsteady flow in turbochargers must be improved, which then can be used to increase the efficiency of the turbine and the compressor. The main objective with this thesis has been to enhance the understanding of the unsteady flow in turbocharger and to assess the sensitivity of inflow conditions on the turbocharger performance. The performance and the flow field in a radial turbocharger turbine working under both non-pulsatile and pulsatile flow conditions has been assessed by using Large Eddy Simulation (LES). To assess the effects of different operation conditions on the turbine performance, different cases have been considered with different perturbations and unsteadiness of the inflow conditions. Also different rotational speeds of the turbine wheel were considered. The results show that the turbine cannot be treated as being quasi-stationary; for example,the shaft power varies for different frequencies of the pulses for the same amplitude of mass flow. The results also show that perturbations and unsteadiness that are created in the geometry upstream of the turbine have substantial effects on the performance of the turbocharger. All this can be summarized as that perturbations and unsteadiness in the inflow conditions to the turbine affect the performance. The unsteady flow field in ported shroud compressor has also been assessed by using LES for two different operational points. For an operational point near surge, the flow field in the entire compressor stage is unsteady, where the driving mechanism is an unsteadiness created in the volute. For an operational point far away from surge, the flow field in the compressor is relatively much more steady as compared with the former case. Although the stable operational point exhibits back-flow from the ported shroud channels, which implies that the flow into the compressor wheel is disturbed due to the structures that are created in the shear layer between the bulk flow and the back-flow from the ported shroud channels. / QC20100622

Buoyant flows are characterized with unsteady large-scale structures and thus time-dependent large eddy simulation (LES) is generally favored. In this dissertation, to further explore LES for buoyant flow, an LES code based on a collocated grid system is first developed. A multigrid solver using a control strategy is developed for the pressure Poisson equations. The control strategy significantly accelerated the convergence rate. A temperature solver using a fourth-order Runge-Kutta approach is also developed. The LES code is extensively tested before it is applied. Although the collocated grid system will introduce conservation errors, in tests of a steady lid-driven cavity flow and transient start-up flow, the effect of the non-conservation of the collocated grid system was not significant. <p>In LES, the effect of SGS scales is represented by SGS models. A novel dynamic nonlinear model (DNM) for SGS stress is tested using isothermal channel flow at Reynolds number 395. The kinetic energy dissipation and geometrical characteristics of the resolved scale and SGS scale with respect to the DNM are investigated. In general, the DNM is reliable and has relatively realistic geometrical properties in comparison with the conventional dynamic model in the present study. In contrast to a pure advecting velocity field, a scalar (temperature) field displays very different characteristics. The modelling of SGS heat flux has not been as extensively studied as that of SGS stress partly due to the complexity of the scalar transport. In this dissertation, LES for a turbulent combined forced and natural convection is studied. The DNM model and a nonlinear dynamic tensor diffusivity model (DTDM-HF) are applied for the SGS stress and heat flux, respectively. The combined effect of the nonlinear models is compared to that of linear models. Notable differences between the nonlinear and linear SGS models are observed at the subgrid-scale level. At the resolved scale, the difference is smaller but relatively more distinguishable in terms of quantities related to the temperature field. <p>Finally, the geometrical properties of the resolved velocity and temperature fields of the thermal flow are investigated based on the LES prediction. Some universal geometrical patterns have been reproduced, e.g. the positively skewed resolved enstrophy generation and the alignment between the vorticity and vortex stretching vectors. The present research demonstrates that LES is an effective tool for the study of the geometrical properties of a turbulent flow at the resolved-scales. The wall imposed anisotropy on the flow structures and orientation of the SGS heat flux vector are also specifically examined. In contrast to the dynamic eddy diffusivity model, the DTDM-HF successfully predicts the near-wall physics and demonstrates a non-alignment pattern between the SGS heat flux and temperature gradient vector.

Large-eddy simulation (LES) is emerging as a promising computational tool for reacting flows. High-order schemes for LES are desirable to achieve improved solution accuracy with reduced computational cost. In this study, a parallel, block-based, three-dimensional high-order central essentially non-oscillatory (CENO) finite-volume scheme for LES of premixed turbulent combustion is developed for Cartesian mesh. This LES formulation makes use of the flame surface density (FSD) for subfilter-scale reaction rate modelling. An algebraic model is used to approximate the FSD. A detailed explanation of the governing equations for LES and the mathematical framework for CENO schemes are presented. The CENO reconstruction is validated and is also applied to three-dimensional Euler equations prior to its application to the equations governing LES of reacting flows.

Large-eddy simulation (LES) is emerging as a promising computational tool for reacting flows. High-order schemes for LES are desirable to achieve improved solution accuracy with reduced computational cost. In this study, a parallel, block-based, three-dimensional high-order central essentially non-oscillatory (CENO) finite-volume scheme for LES of premixed turbulent combustion is developed for Cartesian mesh. This LES formulation makes use of the flame surface density (FSD) for subfilter-scale reaction rate modelling. An algebraic model is used to approximate the FSD. A detailed explanation of the governing equations for LES and the mathematical framework for CENO schemes are presented. The CENO reconstruction is validated and is also applied to three-dimensional Euler equations prior to its application to the equations governing LES of reacting flows.

Hydrogen (H2) enrichment of hydrocarbon fuels in lean premixed systems is desirable since it can lead to a progressive reduction in greenhouse-gas emissions, while paving the way towards pure hydrogen combustion. In recent decades, large-eddy simulation (LES) has emerged as a promising tool to computationally describe and represent turbulent combustion processes. However, a considerable complication of LES for turbulent premixed combustion is that chemical reactions occur in a thin reacting layer at small scales which cannot be entirely resolved on computational grids and need to be modelled. In this thesis, subfilter-scale (SFS) modelling for LES of lean H2-enriched methane-air turbulent premixed combustion was investigated. Two- and three-dimensional fully-compressible LES solvers for a thermally perfect reactive mixture of gases were developed and systematically validated. Two modelling strategies for the chemistry-turbulence interaction were pursued: the artificially thickened flame model with a power-law SFS wrinkling approach and the presumed conditional moment (PCM) coupled with the flame prolongation of intrinsic low-dimensional manifold (FPI) chemistry tabulation technique. Freely propagating and Bunsen-type flames corresponding to stoichiometric and lean premixed mixtures were considered. Validation of the LES solvers was carried out by comparing predicted solutions with experimental data and other published numerical results. Head-to-head comparisons of different SFS approaches, including a transported flame surface density (FSD) model, allowed to identify weaknesses and strengths of the various models. Based on the predictive capabilities of the models examined, the PCM-FPI model was selected for the study of hydrogen-enrichment of methane. A new progress of reaction variable was proposed to account for NO. The importance of transporting species with different diffusion coefficients was demonstrated, in particular for H2. The proposed approach was applied to a Bunsen-type configuration, reproducing key features observed in the experiments: the enriched flame was shorter, which is attributed to a faster consumption of the blended fuel; and the enriched flame displayed a broader two-dimensional curvature probability density function. Furthermore, reduced levels of carbon dioxide (CO2), increased levels of nitrogen monoxide (NO), and a slight increase in the carbon monoxide (CO) levels in areas of fully burned gas were predicted for the enriched flame.

This dissertation consists of two parts, i.e. dynamic approaches for subgrid-scale (SGS) stress modelling for large eddy simulation and advanced assessment of the resolved scale motions related to turbulence geometrical statistics and topologies. The numerical simulations are based on turbulent Couette flow. The first part of the dissertation presents four contributions to the development of dynamic SGS models. The conventional integral type dynamic localization SGS model is in the form of a Fredholm integral equation of the second kind. This model is mathematically consistent, but demanding in computational cost. An efficient solution scheme has been developed to solve the integral system for turbulence with homogeneous dimensions. Current approaches to the dynamic two-parameter mixed model (DMM2) are mathematically inconsistent. As a second contribution, the DMM2 has been optimized and a modelling system of two integral equations has been rigorously obtained. The third contribution relates to the development of a novel dynamic localization procedure for the Smagorinsky model using the functional variational method. A sufficient and necessary condition for localization is obtained and a Picard's integral equation for the model coefficient is deduced. Finally, a new dynamic nonlinear SGS stress model (DNM) based on Speziale's quadratic constitutive relation [J. Fluid Mech., 178, p.459, 1987] is proposed. The DNM allows for a nonlinear anisotropic representation of the SGS stress, and exhibits a significant local stability and flexibility in self-calibration. In the second part, the invariant properties of the resolved velocity gradient tensor are studied using recently developed methodologies, i.e. turbulence geometrical statistics and topology. The study is a posteriori based on the proposed DNM, which is different than most of the current a priori approaches based on experimental or DNS databases. The performance of the DNM is further validated in terms of its capability of simulating advanced geometrical and topological features of resolved scale motions. Phenomenological results include, e.g. the positively skewed resolved enstrophy generation, the alignment between the vorticity and vortex stretching vectors, and the pear-shape joint probability function contour in the tensorial invariant phase plane. The wall anisotropic effect on these results is also examined.

A 3d parallel CFD code is written to investigate the characteristics of and differences between Large Eddy Simulation (LES) models in the context of simulating a thermal buoyant plume. An efficient multigrid scheme is incorporated to solve the Poisson equation, resulting from the fractional step, projection method used to solve the Low Mach Number (LMN) Navier-Stokes equations. A wide range of LES models are implemented, including a variety of eddy models, structure models, mixed models and dynamic models, for both the momentum stresses and the temperature fluxes. Generalised gradient flux models are adapted from their RANS counterparts, and also tested. A number of characteristics are observed in the LES models relating to the thermal plume simulation in particular and turbulence in general. Effects on transition, dissipation, backscatter, equation balances, intermittency and energy spectra are all considered, as are the impact of the governing equations, the discretisation scheme, and the effect of grid coarsening. Also characteristics to particular models are considered, including the subgrid kinetic energy for the one-equation models, and constant histories for dynamic models. The argument that choice of LES model is unimportant is shown to be incorrect as a general statement, and a recommendation for when the models are best used is given.

Hydrogen (H2) enrichment of hydrocarbon fuels in lean premixed systems is desirable since it can lead to a progressive reduction in greenhouse-gas emissions, while paving the way towards pure hydrogen combustion. In recent decades, large-eddy simulation (LES) has emerged as a promising tool to computationally describe and represent turbulent combustion processes. However, a considerable complication of LES for turbulent premixed combustion is that chemical reactions occur in a thin reacting layer at small scales which cannot be entirely resolved on computational grids and need to be modelled. In this thesis, subfilter-scale (SFS) modelling for LES of lean H2-enriched methane-air turbulent premixed combustion was investigated. Two- and three-dimensional fully-compressible LES solvers for a thermally perfect reactive mixture of gases were developed and systematically validated. Two modelling strategies for the chemistry-turbulence interaction were pursued: the artificially thickened flame model with a power-law SFS wrinkling approach and the presumed conditional moment (PCM) coupled with the flame prolongation of intrinsic low-dimensional manifold (FPI) chemistry tabulation technique. Freely propagating and Bunsen-type flames corresponding to stoichiometric and lean premixed mixtures were considered. Validation of the LES solvers was carried out by comparing predicted solutions with experimental data and other published numerical results. Head-to-head comparisons of different SFS approaches, including a transported flame surface density (FSD) model, allowed to identify weaknesses and strengths of the various models. Based on the predictive capabilities of the models examined, the PCM-FPI model was selected for the study of hydrogen-enrichment of methane. A new progress of reaction variable was proposed to account for NO. The importance of transporting species with different diffusion coefficients was demonstrated, in particular for H2. The proposed approach was applied to a Bunsen-type configuration, reproducing key features observed in the experiments: the enriched flame was shorter, which is attributed to a faster consumption of the blended fuel; and the enriched flame displayed a broader two-dimensional curvature probability density function. Furthermore, reduced levels of carbon dioxide (CO2), increased levels of nitrogen monoxide (NO), and a slight increase in the carbon monoxide (CO) levels in areas of fully burned gas were predicted for the enriched flame.