On the properties of high-order least-squares finite-volume schemes

High-order finite-volume schemes based on polynomial least-squares methods are an active research topic for the discretization of hyperbolic equations as they allow to obtain high-order spatial discretization schemes in arbitrary meshes. However, few studies have analyzed their performance in good-quality/near-to-uniform meshes, which are commonly used as a meshing strategy in zones where turbulent effects are important. In this paper, the theoretical numerical properties of commonly used least-squares (LSQ) k-exact high-order finite volume schemes are studied in one-dimensional and in several two- dimensional meshes (with some remarks regarding their properties in three-dimensional meshes). These results are compared to those obtained using fully-constrained polynomial reconstructions only compatible with structured meshes. The numerical properties of the schemes are investigated through the von Neumann analysis methodology applied to the one-dimensional and two-dimensional finite volume formulation, including temporal discretization errors. This analysis is also extended to non-uniform and unstructured two- dimensional meshes. At last, the schemes are tested with several numerical experiments using the linear advection, the Euler equations and the Navier-Stokes equations. The analysis of both studies yields similar conclusions regarding the numerical errors and stability of the different studied schemes showing that the high-order least-squares finite volume schemes yield stable and robust results across different uniform and non-uniform unstructured meshes. However, their performance is heavily degraded in simulations with low mesh resolution compared to schemes specially catered to structured meshes. On the other hand, the latter schemes lack stability and robustness in general structured meshes and its formulation cannot be straightforwardly extended to unstructured meshes. Moreover, this work shows that the use of weighted-LSQ can drastically improve the results of LSQ schemes in under-resolved simulations

Evaluación de esquemas de alto orden para la simulación numérica de fenómenos de transporte convectivo en flujos reales

Los flujos reales están determinados por características y fenómenos físicos muy complejos. En particular, la turbulencia del movimiento fluido es indescriptible analíticamente, así que es necesario afrontar su resolución mediante métodos numéricos. En la Dinámica de Fluidos Computacional, a la hora de resolver flujos turbulentos es conveniente conocer de manera muy detallada las propiedades de los esquemas numéricos que se van a utilizar. Dos propiedades relevantes de estos esquemas son la dispersión y la difusión numéricas, que pueden ser cuantificadas mediante el análisis espectral de von Neumann. En este trabajo se explora el estudio de varios esquemas numéricos, utilizando esta metodología, para evaluar su adecuación para la resolución de problemas de turbulencia. El análisis espectral de los esquemas numéricos se complementa con el estudio de un problema unidimensional descrito por la ecuación de Burgers con término fuente, que presenta características análogas a las de las ecuaciones de Navier-Stokes. Con las conclusiones obtenidas se propone un modelo de simulación para flujos de aguas poco profundas y se evalúan sus limitaciones.<br /

Numerical modelling of suspension high velocity oxy fuel (S-HVOF) thermal spray

Suspension high velocity oxy fuel (SHVOF) thermal spray is an emerging technology used to deposit nano and submicron particles onto the surface of a component to form dense coatings with a fine microstructure. Coatings are deposited onto components to improve their performance by modifying the components surface properties. Numerical models have been employed within the open literature to improve the understanding of the process. This thesis focuses on development of a new thermal spray technology, a hybrid nozzle, that allows for the deposition of a composite coating formed from two materials with drastically different properties. Oxygen sensitive materials such as graphene nanoplatelets degrade when exposed to oxygen at high temperatures. A radial injection allows for a reduction of the time the particles are exposed to oxygen at high temperatures. A physical shroud has been designed based upon the modelling work within this thesis to prevent mixing of ambient oxygen within the jet. The physical shroud is combined with a shrouding gas to delay the mixing of oxygen. A combination of a radial injection, a physical shroud and a shrouding gas allows for a lower oxygen content within the jet and a reduction of the residence time of the particles within the jet. The axial injection within the combustion chamber can be simultaneously used for injecting a feedstock containing ceramic particles. The combined radial and axial injection are expected to allow for a significant improvement in the deposition of composite coatings. The hybrid nozzle is a completely new concept which offers fundamental changes over the traditional SHVOF thermal spray design. Numerical models employed within the literature to predict the flow behaviour within SHVOF thermal spray have suffered from a number of flaws. The prior combustion models employed over predict the gas temperature within the combustion chamber when compared to the adiabatic flame temperature. Additionally, prior combustion models demonstrate unphysical species compositions away from the flame front. This thesis employs a robust treatment to model the combustion reaction within SHVOF thermal spray to better predict the combustion chamber temperature and species composition. This approach avoids the overprediction in the adiabatic flame temperature as seen with the global single step mechanism currently employed within the literature to model SHVOF thermal spray. Additionally, the numerical models to determine the heat transfer coefficient previously employed within the literature underpredict the particle temperatures by as much as 40 % when compared to experimental measurements. This thesis evaluates the effects of the Mach number and the Knudsen number on the Nusselt number to better predict the heat transfer coefficient for the suspension particles. The models are validated against ensembled averaged inflight particle temperature measurements obtained from the commercially available Accuraspray G4 diagnostic system. It is shown that accounting for Mach number effects better predicts the particle temperature however accounting for Knudsen number effects provides the most accurate prediction of the heat transfer to particles within suspension high velocity oxy fuel thermal spray. Finally, this thesis presents the first ever high-fidelity investigation into the combustion chamber for SHVOF thermal spray using a coupled volume of fluid and discrete particle model with the large eddy simulation scale resolving method. This multiscale approach provides a significant reduction in the computational cost over the standalone volume of fluid framework and a significantly higher fidelity over the standalone discrete particle model framework. The framework has been developed to expand the understanding within an SHVOF thermal spray combustion chamber; to characterise and inform the injection for use in lower fidelity models. From this approach more representative suspension injection conditions can be used for lower fidelity DPM - RANS methods. From the numerical modelling undertaken a modified injector design is proposed to reduce clogging within the combustion chamber

Numerical modelling of suspension high velocity oxy fuel (S-HVOF) thermal spray

Suspension high velocity oxy fuel (SHVOF) thermal spray is an emerging technology used to deposit nano and submicron particles onto the surface of a component to form dense coatings with a fine microstructure. Coatings are deposited onto components to improve their performance by modifying the components surface properties. Numerical models have been employed within the open literature to improve the understanding of the process. This thesis focuses on development of a new thermal spray technology, a hybrid nozzle, that allows for the deposition of a composite coating formed from two materials with drastically different properties. Oxygen sensitive materials such as graphene nanoplatelets degrade when exposed to oxygen at high temperatures. A radial injection allows for a reduction of the time the particles are exposed to oxygen at high temperatures. A physical shroud has been designed based upon the modelling work within this thesis to prevent mixing of ambient oxygen within the jet. The physical shroud is combined with a shrouding gas to delay the mixing of oxygen. A combination of a radial injection, a physical shroud and a shrouding gas allows for a lower oxygen content within the jet and a reduction of the residence time of the particles within the jet. The axial injection within the combustion chamber can be simultaneously used for injecting a feedstock containing ceramic particles. The combined radial and axial injection are expected to allow for a significant improvement in the deposition of composite coatings. The hybrid nozzle is a completely new concept which offers fundamental changes over the traditional SHVOF thermal spray design. Numerical models employed within the literature to predict the flow behaviour within SHVOF thermal spray have suffered from a number of flaws. The prior combustion models employed over predict the gas temperature within the combustion chamber when compared to the adiabatic flame temperature. Additionally, prior combustion models demonstrate unphysical species compositions away from the flame front. This thesis employs a robust treatment to model the combustion reaction within SHVOF thermal spray to better predict the combustion chamber temperature and species composition. This approach avoids the overprediction in the adiabatic flame temperature as seen with the global single step mechanism currently employed within the literature to model SHVOF thermal spray. Additionally, the numerical models to determine the heat transfer coefficient previously employed within the literature underpredict the particle temperatures by as much as 40 % when compared to experimental measurements. This thesis evaluates the effects of the Mach number and the Knudsen number on the Nusselt number to better predict the heat transfer coefficient for the suspension particles. The models are validated against ensembled averaged inflight particle temperature measurements obtained from the commercially available Accuraspray G4 diagnostic system. It is shown that accounting for Mach number effects better predicts the particle temperature however accounting for Knudsen number effects provides the most accurate prediction of the heat transfer to particles within suspension high velocity oxy fuel thermal spray. Finally, this thesis presents the first ever high-fidelity investigation into the combustion chamber for SHVOF thermal spray using a coupled volume of fluid and discrete particle model with the large eddy simulation scale resolving method. This multiscale approach provides a significant reduction in the computational cost over the standalone volume of fluid framework and a significantly higher fidelity over the standalone discrete particle model framework. The framework has been developed to expand the understanding within an SHVOF thermal spray combustion chamber; to characterise and inform the injection for use in lower fidelity models. From this approach more representative suspension injection conditions can be used for lower fidelity DPM - RANS methods. From the numerical modelling undertaken a modified injector design is proposed to reduce clogging within the combustion chamber