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The thesis presents a fluid-structure interaction studies on the hemodynamics of blood flow in the left ventricle and through the mitral valve. The virtual model consists of a mathematical model of the left ventricle coupled with a complex and structurally flexible bi-leaflet valve representing the mitral opening. The mitral valve is a bicuspid valve with anterior and posterior leaflets and it regulates unidirectional blood flow from the left atrium to the left ventricle in the diastole phase. The leaflets are made of chordae, annulus and papillary muscles. The goal of this study is to provide biomedical engineers and clinical physicians with a virtual laboratory tool to understand the dynamics of blood flow in a diseased heart and aid in the design of novel artificial heart valves. To this end, the simulation studies present an increasingly complex model of the heart to evaluate the vortex ring formation and evolution of the diastole phase in the left ventricle; and to characterize the septal-anterior motion in a diseased heart with obstructive hypertrophic cardiomyopathy. Finally, in collaboration with an industrial partner, the fluid-structure modeling framework was used to evaluate the performance of a new accelerated artificial valve tester. / Graduate

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Computational fluid dynamics (CFD) plays an important role in many scientific applications, ranging from designing more effective boat engines or aircraft wings to predicting tomorrow's weather, but at the cost of requiring huge amounts of computing time. Also, traditional algorithms suffer from scalability limitations, making them hard to parallelize massively. As a relatively new and promising method for computational fluid dynamics, the Lattice Boltzmann algorithm tries to solve the scalability problems of conventional, but well-tested algorithms in computational fluid dynamics. Through its inherently local structure, it is well suited for parallel processing, and has been implemented on many different kinds of parallel platforms. Adapteva's Epiphany platform is a modern, low-power manycore architecture, which is designed to scale up to thousands of cores, and has even more ambitious plans for the future. Hardware support for floating-point calculations makes it a possible choice in scientific settings. The goal of this thesis is to analyze the performance of the Lattice Boltzmann algorithm on the Epiphany platform. This is done by implementing and testing the lid cavity test case in two and three dimensions. In real applications, high performance on large lattices with millions of nodes is very important. Although the tested Epiphany implementation scales very good, the hardware does not provide adequate amounts of local memory and external memory bandwidth, currently preventing widespread use in computational fluid dynamics.

Significant progress has been made towards developing an effective solution method for predicting low-speed flows through vertical-axis wind turbines. A Godunov-type finite-volume scheme has been developed for the solution of the Euler equations in two-dimensions on a multi-block mesh. The proposed algorithm features a parallel block-based adaptive mesh refinement scheme and a mesh adjustment procedure to enable straightforward meshing of irregular solid boundaries. A low-Mach-Number preconditioner is used in conjunction with a dual timestepping scheme to reduce the computational costs of simulating low-speed unsteady flows. A second-order backwards differencing time-marching scheme is used for the outer physicaltime discretization, and an explicit optimally-smoothing multi-stage time-stepping scheme with multigrid acceleration is used for the inner pseudo-time loop. Results are presented for various low-speed flows that demonstrate the suitability of the algorithms for wind turbine flows. Additional theory and discussion are also presented for extension of the schemes to the full Navier-Stokes equations.

Significant progress has been made towards developing an effective solution method for predicting low-speed flows through vertical-axis wind turbines. A Godunov-type finite-volume scheme has been developed for the solution of the Euler equations in two-dimensions on a multi-block mesh. The proposed algorithm features a parallel block-based adaptive mesh refinement scheme and a mesh adjustment procedure to enable straightforward meshing of irregular solid boundaries. A low-Mach-Number preconditioner is used in conjunction with a dual timestepping scheme to reduce the computational costs of simulating low-speed unsteady flows. A second-order backwards differencing time-marching scheme is used for the outer physicaltime discretization, and an explicit optimally-smoothing multi-stage time-stepping scheme with multigrid acceleration is used for the inner pseudo-time loop. Results are presented for various low-speed flows that demonstrate the suitability of the algorithms for wind turbine flows. Additional theory and discussion are also presented for extension of the schemes to the full Navier-Stokes equations.

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Convergence acceleration techniques for the iterative solution of system of equations arising in the discretisations of compressible flow problems governed by the steady state Euler or Navier-Stokes equations is considered. The system of PDE is discretised using a finite difference or finite volume method yielding a large sparse system of equations. A solution is computed by integrating the corresponding time dependent problem in time until steady state is reached. A convergence acceleration technique based on semicirculant approximations is applied. For scalar model problems, it is proved that the preconditioned coefficient matrix has a bounded spectrum well separated from the origin. A very simple time marching scheme such as the forward Euler method can be used, and the time step is not limited by a CFL-type criterion. Instead, the time step can asymptotically be chosen as a constant, independent of the number of grid points and the Reynolds number. Numerical experiments show that grid and parameter independent convergence is achieved also in more complicated problem settings. A comparison with a multigrid method shows that the semicirculant convergence acceleration technique is more efficient in terms of arithmetic complexity. Another convergence acceleration technique based on fundamental solutions is proposed. An algorithm based on Fourier technique is provided for the fast application. Scalar model problems are considered and a theory, where the preconditioner is represented as an integral operator is derived. Theory and numerical experiments show that for first order partial differential equations, grid independent convergence is achieved.

Doctor of Philosophy (PhD) / In recent times significant public attention has been drawn to the topic of combustion. This has been due to the fact that combustion is the underlying mechanism of several key challenges to modern society: climate change, energy security (finite reserves of fossil fuels) and air pollution. The further development of combustion science is undoubtedly necessary to find improved solutions to manage these combustion science related challenges in the near and long term future. Combustion is essentially an exothermic process, this exothermicity or heat release essentially occurs at small scales, by small scales it meant these scales are small relative to the fluid length scales, for example heat release layer thicknesses in flames are typically much less than the fluid integral length scales. As heat release occurs at small scales this means that in turbulent combustion the small scales of the turbulence (which can be of the order of the heat release layer thickness) can possibly interact and influence the heat release and thus chemistry of the flame reaction zone. Premixed combustion is a combustion mode where the fuel and oxidiser are completely premixed prior to the flame reaction zone, this mode of combustion has been shown to be a promising method to maximise combustion efficiency and minimise pollutant formation. The continued and further application of premixed combustion to practical applications is limited by the current understanding of turbulent premixed combustion, these limitations in understanding are linked to the specific flame phenomena that can significantly influence premixed combustion in a combustion device, examples of such phenomena are: flame flashback, flame extinction and fuel consumption rate – all phenomena that are influenced by the interaction of the small scales of turbulence and chemistry. It is the study and investigation of the interaction of turbulence and chemistry at the small scales (termed finite-rate chemistry) in turbulent premixed flames that is the aim of this thesis which is titled “Finite-rate chemistry effects in turbulent premixed combustion”. Two very closely related experimental burner geometries have been developed in this thesis: the Piloted Premixed Jet Burner (PPJB) and the Premixed Jet Burner (PJB). Both feature an axisymmetric geometry and exhibit a parabolic like flow field. The PPJB and PJB feature a small 4mm diameter central jet from which a high velocity lean-premixed methane-air mixture issues. Surrounding the central jet in the PPJB is a 23.5mm diameter pilot of stoichiometric methane-air products, the major difference between the PPJB and the PJB is that the PJB does not feature a stoichiometric pilot. The pilot in the PPJB provides a rich source of combustion intermediates and enthalpy which promotes initial ignition of the central jet mixture. Surrounding both the central jet and pilot is a large diameter hot coflow of combustion products. It is possible to set the temperature of the hot coflow to the adiabatic flame temperature of the central jet mixture to simulate straining and mixing against and with combustion products without introducing complexities such as quenching and dilution from cold air. By parametrically increasing the central jet velocity in the PPJB it is possible to show that there is a transition from a thin conical flame brush to a flame that exhibits extinction and re-ignition effects. The flames that exhibit extinction and re-ignition effects have a luminous region near the jet exit termed the initial ignition region. This is followed by a region of reduced luminosity further downstream termed the extinction region. Further downstream the flame luminosity increases this region is termed the re-ignition region. For the flames that exhibit extinction and re-ignition it is proposed that intense turbulent mixing and high scalar dissipation rates drives the initial extinction process after the influence of the pilot has ceased (x/D>10). Re-ignition is proposed to occur downstream where turbulent mixing and scalar dissipation rates have decreased allowing robust combustion to continue. As the PJB does not feature a pilot, the flame stabilisation structure is quite different to the PPJB. The flame structure in the PJB is essentially a lifted purely premixed flame, which is an experimental configuration that is also quite unique. A suite of laser diagnostic measurements has been parametrically applied to flames in the PPJB and PJB. Laser Doppler Velocimetry (LDV) has been utilised to measure the mean and fluctuating radial and axial components of velocity at a point, with relevant time and length scale information being extracted from these measurements. One of the most interesting results from the LDV measurements is that in the PPJB the pilot delays the generation of high turbulence intensities, for flames that exhibit extinction the rapid increase of turbulence intensity after the pilot corresponds to the start of the extinction region. Using the LDV derived turbulence characteristics and laminar flame properties and plotting these flames on a traditional turbulent regime diagram indicates that all of the flames examined should fall in the so call distributed reaction regime. Planar imaging experiments have been conducted for flames using the PPJB and PJB to investigate the spatial structure of the temperature and selected minor species fields. Results from two different simultaneous 2D Rayleigh and OH PLIF experiments and a simultaneous 2D Rayleigh, OH PLIF and CH2O PLIF experiment are reported. For all of the flames examined in the PPJB and PJB a general trend of decreasing conditional mean temperature gradient with increasing turbulence intensity is observed. This indicates that a trend of so called flame front thickening with increased turbulence levels occurs for the flames examined. It is proposed that the mechanism for this flame front thickening is due to eddies penetrating and embedding in the instantaneous flame front. In the extinction region it is found that the OH concentration is significantly reduced compared to the initial ignition region. In the re-ignition region it is found that the OH level increases again indicating that an increase in the local reaction rate is occurring. In laminar premixed flames CH2O occurs in a thin layer in the reaction zone, it is found for all of the flames examined that the CH2O layer is significantly thicker than the laminar flame. For the high velocity flames beyond x/D=15, CH2O no longer exist in a distinct layer but rather in a near uniform field for the intermediate temperature regions. Examination of the product of CH2O and OH reveals that the heat release in the initial ignition region is high and rapidly decreases in the extinction region, an increase in the heat release further downstream is observed corresponding to the re-ignition region. This finding corresponds well with the initial hypothesis of an extinction region followed by a re-ignition region that was based on the mean chemiluminescence images. Detailed simultaneous measurement of major and minor species has been conducted using the line Raman-Rayleigh-LIF technique with CO LIF and crossed plane-OH PLIF at Sandia National Laboratories. By measuring all major species it is also possible to define a mixture fraction for all three streams of the PPJB. Using these three mixture fractions it was found that the influence of the pilot in the PPJB decays very rapidly for all but the lowest velocity flames. It was also found that for the high velocity flames exhibiting extinction, a significant proportion of the coflow fluid is entrained into the central jet combustion process at both the extinction region and re-ignition regions. The product of CO and OH conditional on temperature is shown to be proportion to the net production rate of CO2 for certain temperature ranges. By examining the product of CO and OH the hypothesis of an initial ignition region followed by an extinction region then a re-ignition region for certain PPJB flames has been further validated complementing the [CH2O][OH] imaging results. Numerical modelling results using the transported composition probability density function (TPDF) method coupled to a conventional Reynolds averaged Naiver Stokes (RANS) solver are shown in this thesis to successfully predict the occurrence of finite-rate chemistry effects for the PM1 PPJB flame series. To calculate the scalar variance and the degree of finite-rate chemistry effects correctly, it is found that a value of the mixing constant ( ) of approximately 8.0 is required. This value of is much larger than the standard excepted range of 1.5-2.3 for that has been established for non-premixed combustion. By examining the results of the RANS turbulence model in a non-reacting variable density jet, it is shown that the primary limitation of the predictive capability of the TPDF-RANS method is the RANS turbulence model when applied to variable density flows.