The first part of this thesis deals with detonations in gaseous reactive mixtures. Various technological applications have been proposed involving detonations, particularly in the field of propulsion. However, it has been confirmed experimentally that detonations generally exhibit an unstable behaviour, leading to complicated flow structures. A thorough understanding of the evolution of detonation waves is needed before they can be used for propulsion purposes. Herein, we present the first detailed numerical study of three-dimensional structures in gaseous detonations. This study is based on a parallelized, unsplit, shock-capturing algorithm. We show that we can reproduce all types of detonations that have been observed experimentally. The advancements in the field of gaseous compressible reactive flows paved the way for the study of the significantly more complex phenomena that occur in the flow of two-phase, heterogeneous compressible reactive mixtures. In the second part of this thesis, we develop a new shock-capturing algorithm for the study of these flows. We first present a new numerical procedure for solving exactly the Riemann problem of compressible two-phase flow models containing non-conservative products. We then examine the accuracy and robustness of three known methods for the integration of the non-conservative products. The issue of existence and uniqueness of solutions to the Riemann problem is also discussed. Due to the ill-posedness of the Riemann problem of standard two-phase models, we present and analyze, in the third and last part of this work, a conservative approximation to reduced one-pressure one-velocity models for compressible two-phase flows that contain non-conservative products. Herein, we develop an exact Riemann solver for the proposed reduced model. Further, we investigate the structure of the steady two-phase detonation waves admitted by this model. Finally, we report on numerical simulations of the transmission of a purely gaseous detonation to heterogeneous mixtures. The effect of the solid particles on the structure of the resulting two-phase detonation is discussed in detail.

This thesis presents the derivation of the theory leading to the determination of the governing equations of chemically reacting flows under local thermodynamic equilibrium, which rigorously takes into account effects of elemental (de)mixing. As a result, new transport coefficients appear in the equations allowing a quantitative predictions and helping to gain deeper insight into the physics of chemically reacting flows at and near local equilibrium. These transport coefficients have been computed for both air and carbon dioxide mixtures allowing the application of this theory to both Earth and Mars entry problems in the framework of the methodology for the determination of the catalytic activity of Thermal Protections Systems (TPS) materials. Firstly, we analyze the influence of elemental fraction variations on the computation of thermochemical equilibrium flows for both air and carbon dioxide mixtures. To this end, the equilibrium computations are compared with several chemical regimes to better analyze the influence of chemistry on wall heat flux and to observe the elemental fractions behavior along a stagnation line. The results of several computations are presented to highlight the effects of elemental demixing on the stagnation point heat flux and chemical equilibrium composition for air and carbon dioxide mixtures. Moreover, in the chemical nonequilibrium computations, the characteristic time of chemistry is artificially decreased and in the limit the chemical equilibrium regime, with variable elemental fractions, is achieved. Then, we apply the closed form of the equations governing the behavior of local thermodynamic equilibrium flows, accounting for the variation in local elemental concentrations in a rigorous manner, to simulate heat and mass transfer in CO2/N2 mixtures. This allows for the analysis of the boundary layer near the stagnation point of a hypersonic vehicle entering the true Martian atmosphere. The results obtained using this formulation are compared with those obtained using a previous form of the equations where the diffusive fluxes of elements are computed as a linear combination of the species diffusive fluxes. This not only validates the new formulation but also highlights its advantages with respect to the previous one : by using and analyzing the full set of equilibrium transport coefficients we arrive at a deep understanding of the mass and heat transfer for a CO2/N2 mixture. Secondly, we present and analyze detailed numerical simulations of high-pressure inductively coupled air plasma flows both in the torch and in the test chamber using two different mathematical formulations: an extended chemical non-equilibrium formalism including finite rate chemistry and a form of the equations valid in the limit of local thermodynamic equilibrium and accounting for the demixing of chemical elements. Simulations at various operating pressures indicate that significant demixing of oxygen and nitrogen occurs, regardless of the degree of nonequilibrium in the plasma. As the operating pressure is increased, chemistry becomes increasingly fast and the nonequilibrium results correctly approach the results obtained assuming local thermodynamic equilibrium, supporting the validity of the proposed local equilibrium formulation. A similar analysis is conducted for CO2 plasma flows, showing the importance of elemental diffusion on the plasma behavior in the VKI plasmatron torch. Thirdly, the extension of numerical tools developed at the von Karman Institute, required within the methodology for the determination of catalycity properties for thermal protection system materials, has been completed for CO2 flows. Non equilibrium stagnation line computations have been performed for several outer edge conditions in order to analyze the influence of the chemical models for bulk reactions. Moreover, wall surface reactions have been examined, and the importance of several recombination processes has been discussed. This analysis has revealed the limits of the model currently used, leading to the proposal of an alternative approach for the description of the flow-surface interaction. Finally the effects of outer edge elemental fractions on the heat flux map is analyzed, showing the need to add them to the list of parameters of the methodology currently used to determine catalycity properties of thermal protection materials.

No description available.

No description available.

Debris-flows pose serious hazards to communities in mountainous regions of the world and are often responsible for loss of life and damages to infrastructure. Characterised by high flow velocity, large impact forces and long runout, debris-flows have potential discharges several times greater than clear water flood discharges and possess much greater erosive and destructive potential. In combination with poor temporal predictability, they present a significant hazard to settlements, transport routes and other infrastructure located at the drainage points (fan-heads) of watersheds. Thus, it is important that areas vulnerable to debris-flows are identified in order to aid decisions on appropriate land-uses for alluvial fans. This research has developed and tested a new GIS-based procedure for identifying areas prone to debris-flow hazards in the Coromandel/Kaimai region, North Island, New Zealand. The procedure was developed using ESRI Arc View software, utilising the NZ 25 x 25 m DEM as the primary input. When run, it enabled watersheds and their associated morphometric parameters to be derived for selected streams in the study area. Two specific parameters, Melton ratio (R) and watershed length were then correlated against field evidence for debris-flows, debris-floods and fluvial processes at stream watershed locations in the study area. Overall, strong relationships were observed to exist between the evidence observed for these phenomena and the parameters, thus confirming the utility of the GIS procedure for the preliminary identification of hydrogeomorphic hazards such as debris-flow in the Coromandel/Kaimai region study area. In consideration of the results, the procedure could prove a useful tool for regional councils and CDEM groups in regional debris-flow hazard assessment for the identification of existing developments at risk of debris-flow disaster. Furthermore, the procedure could be used to provide justification for subsequent, more intensive local investigations to fully quantify the risk to people and property at stream fan and watershed locations in such areas.

Agricultural intensification on the Canterbury Plains in New Zealand has lead to the degradation of natural streams and rivers through lowering of water quality and significant reduction of surface flows from the use of ground and surface water resources. However, this same agricultural expansion has led to the development of a network of permanently flowing open water races to supply stock water to farms across the Canterbury Plains. Stock water races form an extensive network, with approximately 6,500 km of races. Initially I surveyed 62 water races and compared habitat characteristics, water quality, benthic invertebrate and fish communities with nearby natural streams. Races are characterised physically by straight, narrow and shallow channels, and small, uniform substrate. Water races are more turbid than natural streams, and can have high summer temperatures. The benthic macroinvertebrate communities of water races contained a range of taxa, including some not found in natural streams, but communities were less diverse than communities in natural streams, and tended to be dominated by a limited set of generalist taxa. A longitudinal study of three water races showed gradients in physical characteristics of races, including a downstream decrease in channel width, water depth, current velocity and substrate size. However, few strong longitudinal changes to community structure were found, as the generalist taxa commonly occurring in water races were able to tolerate conditions throughout the race network. To test if macroinvertebrate communities were limited by the homogeneous habitat of water races, I conducted a substrate manipulation experiment, where large cobbles and small boulders were added to reaches in five water races. Despite an increase in substrate and current heterogeneity, there were few significant changes to the macroinvertebrate communities over the four months of the manipulation. This outcome does not eliminate low habitat heterogeneity as a limiting factor for water race communities. Rather, the benthic invertebrate community throughout the water race network is a product of the homogeneous habitat, which limits the availability of colonists of taxa that would benefit from increased habitat diversity. A survey of the fish assemblages of water races found races had a depauperate fish community. Only two species were commonly found in water races, and the average species richness of races was 1.5. By contrast natural streams had a higher diversity of fish species (mean 4 three species), and contained representatives of a greater number of species that are typical of streams and rivers on the Canterbury Plains. My research has shown that stock water races provide an important source of aquatic biodiversity on the plains, both in addition to natural streams and in their own right. However, the biodiversity value of stock water races could be improved with enhancement of in-stream habitat.

I evaluated the spatial and temporal patterns of the avian communities in the Colorado River delta, Mexico, and their relationship with vegetation type and surface water. I also developed plausible conservation and restoration guidelines for riparian areas and native birds in the region. The study included monthly point counts at 30 transects (240 points) from May 2002 to July 2003, breeding counts at 175 sites (3 times per year) during 2002 and 2003, and habitat measurements at the survey points.The most common species were Mourning Doves, Red-winged Blackbirds, and Brown-headed Cowbirds, but another 64 species were commonly found, including Verdins, Song Sparrows, Yellow-breasted Chats and Abert's Towhees. Surface water was the most important habitat feature related to avian richness and density regardless of vegetation type or land cover (P < 0.005). During summer, species richness was explained by variations in water and the cover of cottonwoods (r2 = 0.56, P < 0.001), and the variation in bird densities was explained by variations in water and the cover of willows (r2 = 0.35, P = 0.003).When comparing native versus saltcedar dominated sites, both with the presence (wet) or absence (dry) of surface water, the diversity of birds was more influenced by the presence of water than by vegetation type. Bird abundance was more influenced by vegetation type, but water also had an important effect, as wet sites had higher bird abundance than dry sites with the same vegetation type, and saltcedar wet areas had similar avian abundance to native dry sites. On all cases, the presence of water was an important factor determining the ecological value, in terms of avian richness, abundance, and diversity, of both native riparian and saltcedar areas. Saltcedar areas with surface water had avian characteristics similar to native riparian sites.The dedication of instream flows and pulse floods, the maintenance of vegetation cover and structural diversity, and an increase of older riparian stands will secure the viability of existing bird populations and will increase the probability of recovery of the species that are still extirpated from the floodplain of the Colorado River in Mexico.

We performed large eddy simulation of the flow over a series of two- and three-dimensional dune geometries at laboratory scale using the Lagrangian dynamic eddy-viscosity subgrid-scale model. First, we studied the flow over a standard 2D transverse dune geometry, then bedform three-dimensionality was imposed. Finally, we investigated the turbulent flow over barchan dunes. The results are validated by comparison with simulations and experiments for the 2D dune case, while the results of the 3D dunes are validated qualitatively against experiments. The flow over transverse dunes separates at the dune crest, generating a shear layer that plays a crucial role in the transport of momentum and energy, as well as the generation of coherent structures. Spanwise vortices are generated in the separated shear; as they are advected, they undergo lateral instabilities and develop into horseshoe-like structures and finally reach the surface. The ejection that occurs between the legs of the vortex creates the upwelling and downdrafting events on the free surface known as “boils”. The three-dimensional separation of flow at the crestline alters the distribution of wall pressure, which may cause secondary flow across the stream. The mean flow is characterized by a pair of counter-rotating streamwise vortices, with core radii of the order of the flow depth. Staggering the crestlines alters the secondary motion; two pairs of streamwise vortices appear (a strong one, centred about the lobe, and a weaker one, coming from the previous dune, centred around the saddle). The flow over barchan dunes presents significant differences to that over transverse dunes. The flow near the bed, upstream of the dune, diverges from the centerline plane; the flow close to the centerline plane separates at the crest and reattaches on the bed. Away from the centerline plane and along the horns, flow separation occurs intermittently. The flow in the separation bubble is routed towards the horns and leaves the dune at the tips. Barchan dunes induce two counter-rotating streamwise vortices, along each of the horns, which direct high-momentum fluid toward the symmetry plane and low-momentum fluid near the bed away from the centerline. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2013-05-27 18:58:48.969

The Earth’s magnetic field is generated by fluid motion of liquid iron in the outer core. Flows at the top of the outer core are believed to be responsible for the secular variation (SV) observed at the surface of the Earth. Modelling of this flow is open to considerable ambiguity, though methods adopting different physical assumptions do lead to similar flow velocity regimes. Some aspects of the ambiguities are investigated in this thesis. The last decade has seen a significant improvement in the capability to observe the global field at high spatial resolution. Several satellite missions have been launched, providing a rich new set of scalar and vector magnetic measurements from which to model the global field in detail. These data complement the existing record of groundbased observatories, which have continuous temporal coverage at a single point. I exploit these new data to model the secular variation (SV) globally and attempt to improve the core flow models that have been constructed to date. Using the approach developed by Mandea and Olsen (2006) I create a set of evenly distributed ‘Virtual Observatories’ (VO), at 400km above the Earth’s surface, encompassing satellite measurements from the CHAMP satellite over seven years (2001-2007), inverting the SV calculated at each VO to infer flow along the core-mantle boundary. Direct comparison of the SV generated by the flow model to the SV at individual VO can be made. Thus, the residual differences can be investigated in detail. Comparisons of residuals from flow models generated from a number of VO datasets provide evidence that they are consistent with internal and external field effects in the satellite data. I also show that the binning and processing of the VO data can induce artefacts, including sectorial banding, into the residuals. By employing the core flows from the inversion of SV data it may be possible to forecast the change of the present magnetic field (as measured) forwards in time for a short time period (e.g. less than five years) within an acceptable error budget. Using simple advection of steady or non-steady flows to forecast magnetic field change gives reasonably good fit to field models such as GRIMM, POMME or xCHAOS (< 50nT root mean square difference after five years). The forecast of the magnetic field change can be improved by optimally assimilating measurements of the field into the forecast from flow models at discrete points in time (e.g. annually). To achieve this, an Ensemble Kalman Filter (EnKF) can be used to the capture non-linearity of the model and delineate the error bounds by means of a Monte Carlo representation of the field evolution over time. In the EnKF model, an ensemble of probable state vectors (Gauss coefficients) evolve over time, driven by SV derived from core flows. The SV is randomly perturbed at each step before addition to the state vectors. The mean of the ensemble is chosen as the most likely state (i.e. field model) and the error associated with the estimate can be gauged from the standard deviation from the mean. I show an implementation of the EnKF for steady and non-steady flows generated from ‘Virtual Observatory’ field models, compared to the field models GRIMM and xCHAOS over the period 2002–2008. Using the EnKF, the maximum difference never exceeds 25nT over the period. This promising approach allows measurements to be included into model predictions to improve the forecast.

We say that a~graph admits a~nowhere-zero k-flow if we can assign a~direction and a~positive integer (<k) as a~flow to each edge so that total in-flow into $v$ and total out-flow from $v$ are equal for each vertex $v$. In 1954, Tutte conjectured that every bridgeless graph admits a~nowhere-zero 5-flow and the conjecture is still open. Kochol in his recent papers introduces a~computational method how to prove that a~minimal counterexample cannot contain short circuits (up to length 10). In this Thesis, we provide a~comprehensive view on this method. Moreover, since Kochol does not share his implementation and in order to independently verify the method, we provide our source code that validates Kochol's results and extend them: we prove that any minimal counterexample to the conjecture does not contain any circuit of length less than 12. Powered by TCPDF (www.tcpdf.org)