Numerical simulation of the upward propagation of a flame in a vertical tube filled with a very lean mixture.

Upwardpropagation of a premixed flame in averticaltubefilled with a very leanmixture is simulated numerically using a single irreversible Arrhenius reaction model with infinitely high activation energy. In the absence of heat losses and preferential diffusion effects, a curved flame with stationary shape and velocity close to those of an open bubble ascending in the same tube is found for values of the fuel mass fraction above a certain minimum that increases with the radius of the tube, while the numerical computations cease to converge to a stationary solution below this minimum mass fraction. The vortical flow of the gas behind the flame and in its transport region is described for tubes of different radii. It is argued that this flow may become unstable when the fuel mass fraction is decreased, and that this instability, together with the flame stretch due to the strong curvature of the flame tip in narrow tubes, may be responsible for the minimum fuel mass fraction. Radiation losses and a Lewis number of the fuel slightly above unity decrease the final combustion temperature at the flame tip and increase the minimum fuel mass fraction, while a Lewis number slightly below unity has the opposite effect.

Modelling of landslides propagation with SPH : effects of rheology and pore water pressure

El estudio desarrollado en este trabajo de tesis se centra en la modelización numérica de la fase de propagación de los deslizamientos rápidos de ladera a través del método sin malla Smoothed Particle Hydrodynamics (SPH). Este método tiene la gran ventaja de permitir el análisis de problemas de grandes deformaciones evitando operaciones costosas de remallado como en el caso de métodos numéricos con mallas tal como el método de los Elementos Finitos. En esta tesis, particular atención viene dada al rol que la reología y la presión de poros desempeñan durante estos eventos. El modelo matemático utilizado se basa en la formulación de Biot-Zienkiewicz v - pw, que representa el comportamiento, expresado en términos de velocidad del esqueleto sólido y presiones de poros, de la mezcla de partículas sólidas en un medio saturado. Las ecuaciones que gobiernan el problema son: • la ecuación de balance de masa de la fase del fluido intersticial, • la ecuación de balance de momento de la fase del fluido intersticial y de la mezcla, • la ecuación constitutiva y • una ecuación cinemática. Debido a sus propiedades geométricas, los deslizamientos de ladera se caracterizan por tener una profundidad muy pequeña frente a su longitud y a su anchura, y, consecuentemente, el modelo matemático mencionado anteriormente se puede simplificar integrando en profundidad las ecuaciones, pasando de un modelo 3D a 2D, el cual presenta una combinación excelente de precisión, sencillez y costes computacionales. El modelo propuesto en este trabajo se diferencia de los modelos integrados en profundidad existentes por incorporar un ulterior modelo capaz de proveer información sobre la presión del fluido intersticial a cada paso computacional de la propagación del deslizamiento. En una manera muy eficaz, la evolución de los perfiles de la presión de poros está numéricamente resuelta a través de un esquema explicito de Diferencias Finitas a cada nodo SPH. Este nuevo enfoque es capaz de tener en cuenta la variación de presión de poros debida a cambios de altura, de consolidación vertical o de cambios en las tensiones totales. Con respecto al comportamiento constitutivo, uno de los problemas principales al modelizar numéricamente deslizamientos rápidos de ladera está en la dificultad de simular con la misma ley constitutiva o reológica la transición de la fase de iniciación, donde el material se comporta como un sólido, a la fase de propagación donde el material se comporta como un fluido. En este trabajo de tesis, se propone un nuevo modelo reológico basado en el modelo viscoplástico de Perzyna, pensando a la viscoplasticidad como a la llave para poder simular tanto la fase de iniciación como la de propagación con el mismo modelo constitutivo. Con el fin de validar el modelo matemático y numérico se reproducen tanto ejemplos de referencia con solución analítica como experimentos de laboratorio. Finalmente, el modelo se aplica a casos reales, con especial atención al caso del deslizamiento de 1966 en Aberfan, mostrando como los resultados obtenidos simulan con éxito estos tipos de riesgos naturales. The study developed in this thesis focuses on the modelling of landslides propagation with the Smoothed Particle Hydrodynamics (SPH) meshless method which has the great advantage of allowing to deal with large deformation problems by avoiding expensive remeshing operations as happens for mesh methods such as, for example, the Finite Element Method. In this thesis, special attention is given to the role played by rheology and pore water pressure during these natural hazards. The mathematical framework used is based on the v - pw Biot-Zienkiewicz formulation, which represents the behaviour, formulated in terms of soil skeleton velocity and pore water pressure, of the mixture of solid particles and pore water in a saturated media. The governing equations are: • the mass balance equation for the pore water phase, • the momentum balance equation for the pore water phase and the mixture, • the constitutive equation and • a kinematic equation. Landslides, due to their shape and geometrical properties, have small depths in comparison with their length or width, therefore, the mathematical model aforementioned can then be simplified by depth integrating the equations, switching from a 3D to a 2D model, which presents an excellent combination of accuracy, computational costs and simplicity. The proposed model differs from previous depth integrated models by including a sub-model able to provide information on pore water pressure profiles at each computational step of the landslide's propagation. In an effective way, the evolution of the pore water pressure profiles is numerically solved through a set of 1D Finite Differences explicit scheme at each SPH node. This new approach is able to take into account the variation of the pore water pressure due to changes of height, vertical consolidation or changes of total stress. Concerning the constitutive behaviour, one of the main issues when modelling fast landslides is the difficulty to simulate with the same constitutive or rheological model the transition from the triggering phase, where the landslide behaves like a solid, to the propagation phase, where the landslide behaves in a fluid-like manner. In this work thesis, a new rheological model is proposed, based on the Perzyna viscoplastic model, thinking of viscoplasticity as the key to close the gap between the triggering and the propagation phase. In order to validate the mathematical model and the numerical approach, benchmarks and laboratory experiments are reproduced and compared to analytical solutions when possible. Finally, applications to real cases are studied, with particular attention paid to the Aberfan flowslide of 1966, showing how the mathematical model accurately and successfully simulate these kind of natural hazards.

Treatment of tropical forages with exogenous fibrolytiic enzymes: effects on chemical composition and in vitro rumen fermentation

The effects of three treatments of fibrolytic enzymes (cellulase from Trichoderma longibrachiatum (CEL), xylanase from rumen micro-organisms (XYL) and a 1:1 mixture of CEL and XYL (MIX) on the in vitro fermentation of two samples of Pennisetum clandestinum (P1 and P2), two samples of Dichanthium aristatum (D1 and D2) and one sample of each Acacia decurrens and Acacia mangium (A1 and A2) were investigated. The first experiment compared the effects of two methods of applying the enzymes to forages, either at the time of incubation or 24 h before, on the in vitro gas production. In general, the 24 h pre-treatment resulted in higher values of gas production rate, and this application method was chosen for a second study investigating the effects of enzymes on chemical composition and in vitro fermentation of forages. The pre-treatment with CEL for 24 h reduced (p < 0.05) the content of neutral detergent fibre (NDF) of P1, P2, D1 and D2, and that of MIX reduced the NDF content of P1 and D1, but XYL had no effect on any forage. The CEL treatment increased (p < 0.05) total volatile fatty acid (VFA) production for all forages (ranging from 8.6% to 22.7%), but in general, no effects of MIX and XYL were observed. For both P. clandestinum samples, CEL treatment reduced (p < 0.05) the molar proportion of acetate and increased (p < 0.05) that of butyrate, but only subtle changes in VFA profile were observed for the rest of forages. Under the conditions of the present experiment, the treatment of tropical forages with CEL stimulated their in vitro ruminal fermentation, but XYL did not produce any positive effect. These results showed clearly that effectiveness of enzymes varied with the incubated forage and further study is warranted to investigate specific, optimal enzyme-substrate combinations.

Use of tomato and cucumber horticulture by-products in goat diets: effects o nrumen fermentation and microbial communities in batch and continuous cultures

Two in vitro experiments were conducted to analyse the effects of replacing dietary barley grain with wastes of tomato and cucumber fruits and a 1 : 1 tomato : cucumber mixture on rumen fermentation characteristics and microbial abundance. The control (CON) substrate contained 250 g/kg of barley grain on a dry matter (DM) basis, and another 15 substrates were formulated by replacing 50, 100, 150, 200 or 250 g of barley grain/kg with the same amount (DM basis) of tomato or cucumber fruits or 1 : 1 tomato : cucumber mixture. In Expt 1, all substrates were incubated in batch cultures with rumen micro-organisms from goats for 24 h. Increasing amounts of tomato, cucumber and the mixture of both fruits in the substrate increased final pH and gas production, without changes in final ammonia-nitrogen (NH3-N) concentrations, substrate degradability and total volatile fatty acid (VFA) production, indicating that there were no detrimental effects of any waste fruits on rumen fermentation. Therefore, in Expt 2 the substrates including 250 g of waste fruits (T250, C250 and M250 for tomato, cucumber and the mixture of both fruits, respectively) and the CON substrate were incubated in single-flow continuous-culture fermenters for 8 days. Total VFA production did not differ among substrates, but there were differences in VFA profile. Molar proportions of propionate, isobutyrate and isovalerate were lower and acetate : propionate ratio was greater for T250 compared with CON substrate. Fermentation of substrates containing cucumber (C250 and M250) resulted in lower proportions of acetate, isobutyrate and isovalerate and acetate : propionate ratio, but greater butyrate proportions than the CON substrate. Carbohydrate degradability and microbial N synthesis tended to be lower for substrates containing cucumber than for the CON substrate, but there were no differences between CON and T250 substrates. Abundance of total bacteria, Fibrobacter succinogenes and Ruminococcus flavefaciens, fungi, methanogenic archaea and protozoa were similar in fermenters fed T250 and CON substrates, but fermenters fed C250 and M250 substrates had lower abundances of R. flavefaciens, fungi and protozoa than those fed the CON substrate. Results indicated that tomato fruits could replace dietary barley grain up to 250 g/kg of substrate DM without noticeable effects on rumen fermentation and microbial populations, but the inclusion of cucumber fruits at 250 g/kg of substrate DM negatively affected some microbial populations as it tended to reduce microbial N synthesis and changed the VFA profile. More studies are needed to identify the dietary inclusion level of cucumber which produces no detrimental effects on rumen fermentation and microbial growth.