Os custos econômicos e perdas potenciais de vidas humanas resultantes de falhas em sistemas de drenagem de águas pluviais podem ser enormes, aumentando a necessidade da busca de melhores métodos de dimensionamento destes. Os métodos baseados na precipitação de projeto são os mais usados para a estimativa do hidrograma de projeto em bacias urbanas, devido às facilidades que os mesmos apresentam em relação aos outros métodos. Entretanto, estes métodos têm suas limitações e incertezas, que podem influenciar as características do hidrograma de projeto resultante, incertezas que são, em consequência, transferidas ao dimensionamento hidráulico das obras propostas. No presente trabalho, foram avaliados os efeitos da discretização espacial da bacia, da discretização temporal e da posição do pico do hietograma de projeto, sobre as principais características do hidrograma de projeto. Esses efeitos foram ainda avaliados no dimensionamento hidráulico do sistema de macrodrenagem dos bairros de Mavalane “A” e Maxaquene “A”, localizados na cidade de Maputo em Moçambique. Para avaliar os referidos efeitos, a bacia foi discretizada em 1, 5, 7 e 12 sub-bacias. O intervalo de tempo do hietograma de projeto foi discretizado em 1, 2, 3, 4 e 5 minutos, sendo calculados para cada discretização e intervalo de tempo, hietogramas com pico no início, 25%, 50%, 75% e final do evento com duração correspondente a 90 minutos e 24 horas. Os hietogramas foram transformados em vazão no programa IPHS1, a qual foi propagada no sistema de macrodrenagem usando o modelo EPA SWMM 5.0, sendo obtidos os hidrogramas de projeto resultantes. O exutório da bacia e o trecho C19 localizado na região central da bacia foram escolhidos para análise dos resultados. Os resultados obtidos mostram uma influência importante dos efeitos avaliados nas características do hidrograma de projeto: vazão de pico, tempo de pico e volume parcial e, consequentemente, no dimensionamento da rede de macrodrenagem, sendo o efeito da discretização da bacia o mais influente, seguido dos efeitos da posição do pico da chuva e intervalo de tempo. / The economic costs and potential losses of human lives due to failure in stormwater drainage systems can be significant, calling for an improvement in methods used for its design. The design storm approach, also known as “single-event design-storm” is widespread used in formulating design hydrograph from historical rainfall data in urban watersheds, due to its relative advantages when compared to other methods. Therefore, this approach has its uncertainties which can affect the resulted design hydrograph, and consequently affect the hydraulic design of proposed structures. In this study is presented an assessment of the adopted values in design criteria, during the estimation of design hydrograph used in hydraulic design of stormwater drainage systems. In particular, are assessed the effects of spatial discretization of the watershed, the temporal discretization and peak position of the design hyetograph, in the main features of the resulted design hydrograph. The same effects are then assessed in the hydraulic design of the major stormwater drainage system of Mavalane “A” and Maxaquene “A” neighborhoods, located in Maputo city in Mozambique. To assess these effects, the watershed was discretized into 1, 5, 7 and 12 sub-watersheds. The time step of the design hyetograph was discretized into 1, 2, 3, 4 and 5 minutes, and then computed for each discretization and time step, hyetographs with peak positioned in the beginning, 25%, 50%, 75% and the end of the duration of 90 minutes and 24 hours. The hyetographs were converted into runoff in IPHS1, wish was dynamically routed in the drainage system, using EPA SWMM 5.0. The watershed outlet and conduit C19 were used to analyze the results. The results show an important influence of the assessed effects on the design hydrograph features: hydrograph peak, time to peak and partial volume and, consequently, on the hydraulic design of the major stormwater drainage system, being the effect of spatial discretization of the watershed, the most important, followed by hyetograph peak position and time step.

Preconditioners based upon sweeps and diffusion-synthetic acceleration (DSA) have been constructed and applied to the zeroth and first spatial moments of the 1-D transport equation using SN angular discretization and a strictly positive nonlinear spatial closure (the CSZ method). The sweep preconditioner was applied using the linear discontinuous Galerkin (LD) sweep operator and the nonlinear CSZ sweep operator. DSA preconditioning was applied using the linear LD S2 equations and the nonlinear CSZ S2 equations. These preconditioners were applied in conjunction with a Jacobian-free Newton Krylov (JFNK) method utilizing Flexible GMRES. The action of the Jacobian on the Krylov vector was difficult to evaluate numerically with a finite difference approximation because the angular flux spanned many orders of magnitude. The evaluation of the perturbed residual required constructing the nonlinear CSZ operators based upon the angular flux plus some perturbation. For cases in which the magnitude of the perturbation was comparable to the local angular flux, these nonlinear operators were very sensitive to the perturbation and were significantly different than the unperturbed operators. To resolve this shortcoming in the finite difference approximation, in these cases the residual evaluation was performed using nonlinear operators "frozen" at the unperturbed local psi. This was a Newton method with a perturbation fixup. Alternatively, an entirely frozen method always performed the Jacobian evaluation using the unperturbed nonlinear operators. This frozen JFNK method was actually a Picard iteration scheme. The perturbed Newton's method proved to be slightly less expensive than the Picard iteration scheme. The CSZ sweep preconditioner was significantly more effective than preconditioning with the LD sweep. Furthermore, the LD sweep is always more expensive to apply than the CSZ sweep. The CSZ sweep is superior to the LD sweep as a preconditioner. The DSA preconditioners were applied in conjunction with the CSZ sweep. The nonlinear CSZ DSA preconditioner did not form a more effective preconditioner than the linear DSA preconditioner in this 1-D analysis. As it is very difficult to construct a CSZ diffusion equation in more than one dimension, it will be very beneficial if the results regarding the effectiveness of the LD DSA preconditioner are applicable to multi-dimensional problems.

Os custos econômicos e perdas potenciais de vidas humanas resultantes de falhas em sistemas de drenagem de águas pluviais podem ser enormes, aumentando a necessidade da busca de melhores métodos de dimensionamento destes. Os métodos baseados na precipitação de projeto são os mais usados para a estimativa do hidrograma de projeto em bacias urbanas, devido às facilidades que os mesmos apresentam em relação aos outros métodos. Entretanto, estes métodos têm suas limitações e incertezas, que podem influenciar as características do hidrograma de projeto resultante, incertezas que são, em consequência, transferidas ao dimensionamento hidráulico das obras propostas. No presente trabalho, foram avaliados os efeitos da discretização espacial da bacia, da discretização temporal e da posição do pico do hietograma de projeto, sobre as principais características do hidrograma de projeto. Esses efeitos foram ainda avaliados no dimensionamento hidráulico do sistema de macrodrenagem dos bairros de Mavalane “A” e Maxaquene “A”, localizados na cidade de Maputo em Moçambique. Para avaliar os referidos efeitos, a bacia foi discretizada em 1, 5, 7 e 12 sub-bacias. O intervalo de tempo do hietograma de projeto foi discretizado em 1, 2, 3, 4 e 5 minutos, sendo calculados para cada discretização e intervalo de tempo, hietogramas com pico no início, 25%, 50%, 75% e final do evento com duração correspondente a 90 minutos e 24 horas. Os hietogramas foram transformados em vazão no programa IPHS1, a qual foi propagada no sistema de macrodrenagem usando o modelo EPA SWMM 5.0, sendo obtidos os hidrogramas de projeto resultantes. O exutório da bacia e o trecho C19 localizado na região central da bacia foram escolhidos para análise dos resultados. Os resultados obtidos mostram uma influência importante dos efeitos avaliados nas características do hidrograma de projeto: vazão de pico, tempo de pico e volume parcial e, consequentemente, no dimensionamento da rede de macrodrenagem, sendo o efeito da discretização da bacia o mais influente, seguido dos efeitos da posição do pico da chuva e intervalo de tempo. / The economic costs and potential losses of human lives due to failure in stormwater drainage systems can be significant, calling for an improvement in methods used for its design. The design storm approach, also known as “single-event design-storm” is widespread used in formulating design hydrograph from historical rainfall data in urban watersheds, due to its relative advantages when compared to other methods. Therefore, this approach has its uncertainties which can affect the resulted design hydrograph, and consequently affect the hydraulic design of proposed structures. In this study is presented an assessment of the adopted values in design criteria, during the estimation of design hydrograph used in hydraulic design of stormwater drainage systems. In particular, are assessed the effects of spatial discretization of the watershed, the temporal discretization and peak position of the design hyetograph, in the main features of the resulted design hydrograph. The same effects are then assessed in the hydraulic design of the major stormwater drainage system of Mavalane “A” and Maxaquene “A” neighborhoods, located in Maputo city in Mozambique. To assess these effects, the watershed was discretized into 1, 5, 7 and 12 sub-watersheds. The time step of the design hyetograph was discretized into 1, 2, 3, 4 and 5 minutes, and then computed for each discretization and time step, hyetographs with peak positioned in the beginning, 25%, 50%, 75% and the end of the duration of 90 minutes and 24 hours. The hyetographs were converted into runoff in IPHS1, wish was dynamically routed in the drainage system, using EPA SWMM 5.0. The watershed outlet and conduit C19 were used to analyze the results. The results show an important influence of the assessed effects on the design hydrograph features: hydrograph peak, time to peak and partial volume and, consequently, on the hydraulic design of the major stormwater drainage system, being the effect of spatial discretization of the watershed, the most important, followed by hyetograph peak position and time step.

Liquid jet atomisation has a wide variety of application in areas such as injectors in automobile and launch vehicle combustors, spray painting, ink jet printing etc. Understanding physical mechanisms involved in the primary regime of atomisation in combustors is extremely challenging due to the lack of experimental techniques that can reliably provide measurements of gas and liquid velocity fields in this region. Experimental studies have so far been mostly restricted to conditions at atmospheric conditions rather than technically relevant operating pressures. We present a computational fluid dynamics based modelling approach that can capture the evolution of the flow field in the dense primary atomization region of the spray as part of the present thesis work. A fully compressible 3D flow solver is coupled with an interface tracking solver based on level set method. A generalised mathematical formulation for thermodynamic models is implemented in flow solver enabling easy switching between various equations of states. Solvers are parallelised to run on large number of processors and are shown to have good scalability. A modification to the level set method which greatly reduces mass conservation inaccuracies when compared with existing state-of-art baseline schemes has been developed during this work. The Ghost uid Method is used for applying matching conditions at the Interface. The liquid and gas phases are modelled using the perfect gas and Tait equations of state respectively. Several validation studies have been carried out to ensure quantitative accuracy of the solver implemented. Results from canonical Rayleigh Taylor instability simulations shows good agreement with reported results in literature. Finally, results for unsteady evolution of a water-air jet at a liquid to gas density ratio of 10 are shown. Physical mechanisms causing the initial droplet formation are discussed in detail. Droplet feedback is identified as one of the important mechanisms in triggering liquid core instabilities. Comparisons between droplet size distributions obtained from computations are carried out. Vorticity dynamics is used to understand hole and ligament formation from liquid core. Effect of numerical droplets on the simulation results is also looked at in detail.

Os custos econômicos e perdas potenciais de vidas humanas resultantes de falhas em sistemas de drenagem de águas pluviais podem ser enormes, aumentando a necessidade da busca de melhores métodos de dimensionamento destes. Os métodos baseados na precipitação de projeto são os mais usados para a estimativa do hidrograma de projeto em bacias urbanas, devido às facilidades que os mesmos apresentam em relação aos outros métodos. Entretanto, estes métodos têm suas limitações e incertezas, que podem influenciar as características do hidrograma de projeto resultante, incertezas que são, em consequência, transferidas ao dimensionamento hidráulico das obras propostas. No presente trabalho, foram avaliados os efeitos da discretização espacial da bacia, da discretização temporal e da posição do pico do hietograma de projeto, sobre as principais características do hidrograma de projeto. Esses efeitos foram ainda avaliados no dimensionamento hidráulico do sistema de macrodrenagem dos bairros de Mavalane “A” e Maxaquene “A”, localizados na cidade de Maputo em Moçambique. Para avaliar os referidos efeitos, a bacia foi discretizada em 1, 5, 7 e 12 sub-bacias. O intervalo de tempo do hietograma de projeto foi discretizado em 1, 2, 3, 4 e 5 minutos, sendo calculados para cada discretização e intervalo de tempo, hietogramas com pico no início, 25%, 50%, 75% e final do evento com duração correspondente a 90 minutos e 24 horas. Os hietogramas foram transformados em vazão no programa IPHS1, a qual foi propagada no sistema de macrodrenagem usando o modelo EPA SWMM 5.0, sendo obtidos os hidrogramas de projeto resultantes. O exutório da bacia e o trecho C19 localizado na região central da bacia foram escolhidos para análise dos resultados. Os resultados obtidos mostram uma influência importante dos efeitos avaliados nas características do hidrograma de projeto: vazão de pico, tempo de pico e volume parcial e, consequentemente, no dimensionamento da rede de macrodrenagem, sendo o efeito da discretização da bacia o mais influente, seguido dos efeitos da posição do pico da chuva e intervalo de tempo. / The economic costs and potential losses of human lives due to failure in stormwater drainage systems can be significant, calling for an improvement in methods used for its design. The design storm approach, also known as “single-event design-storm” is widespread used in formulating design hydrograph from historical rainfall data in urban watersheds, due to its relative advantages when compared to other methods. Therefore, this approach has its uncertainties which can affect the resulted design hydrograph, and consequently affect the hydraulic design of proposed structures. In this study is presented an assessment of the adopted values in design criteria, during the estimation of design hydrograph used in hydraulic design of stormwater drainage systems. In particular, are assessed the effects of spatial discretization of the watershed, the temporal discretization and peak position of the design hyetograph, in the main features of the resulted design hydrograph. The same effects are then assessed in the hydraulic design of the major stormwater drainage system of Mavalane “A” and Maxaquene “A” neighborhoods, located in Maputo city in Mozambique. To assess these effects, the watershed was discretized into 1, 5, 7 and 12 sub-watersheds. The time step of the design hyetograph was discretized into 1, 2, 3, 4 and 5 minutes, and then computed for each discretization and time step, hyetographs with peak positioned in the beginning, 25%, 50%, 75% and the end of the duration of 90 minutes and 24 hours. The hyetographs were converted into runoff in IPHS1, wish was dynamically routed in the drainage system, using EPA SWMM 5.0. The watershed outlet and conduit C19 were used to analyze the results. The results show an important influence of the assessed effects on the design hydrograph features: hydrograph peak, time to peak and partial volume and, consequently, on the hydraulic design of the major stormwater drainage system, being the effect of spatial discretization of the watershed, the most important, followed by hyetograph peak position and time step.

名古屋大学博士学位論文 学位の種類:博士(工学) 学位授与年月日:平成19年9月28日

The present study in this thesis has attempted to resolve one of the key aspects of enhancing predictability of macroscopic behavior of Shape Memory Alloy (SMA) wire by considering variation of local phase inhomogeneity. Understanding of functional fatigue and its relation with the phase distribution and its passivation is the key towards tailoring thermal Shape Memory Alloy actuators’ properties and performance. Present work has been carried out in two associated areas. First part has covered solving a coupled thermo-mechanical boundary value problem where initial phase fractions are prescribed at the gauss points and subsequent evolution are tracked over the loading cycle. An incremental form of a phenomenological constitutive model has been incorporated in the modelling framework. Finite element convergence studies using both homogeneous and inhomogeneous SMA wires are performed. Effects of phase inhomogeneity are investigated for mechanical loading and thermo-electric loading. Phase inhomogeneity is simulated mainly due to process and handling quality. An example of mechanical boundary condition such as gripping indicates a negative residual strain at macroscopic behavior. Simulation accurately captures vanishing local phase inhomogeneity upon multiple cycles of thermo-mechanical loading on unconstrained straight SMA wire. In the second part, a phase identification and measurement scheme is proposed. It has been shown that by employing variation of electrical resistivity which distinctly varies with phase transformation, martensite phase volume fraction can be quantified in average sense over the length of a SMA wire. This can be easily achieved by using a simple thermo-mechanical characterization setup along with resistance measurement circuit. Local phase inhomogeneity is created in an experimental sample, which is subjected to electrical heating under constant mechanical bias load. The response shows relaxation of the initial shrinkage strain due to local phase. Results observed for thermo-electric loading on the inhomogeneous SMA wires compliment the results observed from the simulated loading cases. Several interesting features such as shrinkage of the inhomogeneous SMA wire after first loading cycle, relaxation of the residual strain over multiple loading cycles due to the presence of inhomogeneity are captured. This model promises useful applications of SMA wire in fatigue studies, SMA embedded composites and hybrid structures.

A high resolution spectrally accurate three-dimensional flow solver is developed in order to simulate convection dominated fluid flows. The governing incompressible Navier Stokes equations along with the energy equation for temperature are discretized using a second-order accurate projection method which utilizes Adams Bashforth and Backward Differentiation formula for temporal discretization of the non-linear convective and linear viscous terms, respectively. Spatial discretization is performed using a Fourier/Chebyshev spectral method. Extensive tests on three-dimensional Taylor Couette flow are performed and it is shown that the method successfully captures the different states ranging from formation of Taylor vortices to wavy vortex regime. Next, the code is validated for convection dominated flows through a comprehensive comparison of the results for two dimensional Rayleigh Benard convection with the theoretical and experimental results from the literature. Finally, fully parallel simulations, with efficient utilization of computational resources and memory, are performed on a model three-dimensional axially homogeneous Rayleigh Benard convection problem in order to explore the high Rayleigh number flows and to test the scaling of global properties.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.