Numerical investigation of fluid flows using finite element method combined with characteristic-based split scheme
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Data
2020-03-23
Autores
Oliveira, Ruhan Carlos Ponce de
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Universidade Estadual Paulista (Unesp)
Resumo
No presente trabalho são apresentados os fundamentos de fenômenos de transporte, algumas equações de estado termodinâmico, a formulação fraca do método dos elementos finitos aplicado à escoamento e alguns métodos para resolução dos diversos campos de análise deste, a turbulência em escoamentos incompressíveis e compressíveis, a combustão como escoamento reativo em uma mistura homogênea pré-misturada. Procede-se então à apresentação em forma resumida de uma revisão técnica de várias referências escol- hidas abordando aspectos da solução numérica, do modelo turbulento, da integração turbulência-combustão (TCI), da pré-mistura e da escolha do combustível e comburente, incluindo ainda uma tabela para que possa analisar a complexa relação entre todos esses aspectos nas publicações verificadas. O principal objetivo neste trabalho é desenvolver uma análise teórica e numérica de escoamentos incompressíveis e compressíveis turbu- lentos para diversos domínios, desenvolvendo um framework base para futuramente ser integrado a simulação de escoamentos reativos em motores à foguetes. As equações de continuidade, momentum, energia e conservação de espécies químicas são discretizadas aplicando o método de elementos finitos de Galerkin combinado o esquema de estabilização CBS (Characteristic Based-Split), para se obter os efeitos fluidodinâmicos e térmicos do processo. O processo de combustão e comportamento da frente de chama foi analisado somente teóricamente e para isso foi empregado o método de Flamelet-Progress Variable. Para a modelagem da cinética química é aplicado o software Canterar, o que utiliza o GRI-3.0, mecanismo que contém 325 reações e inclui 53 espécies químicas como produto da combustão. Para isso, foi considerado uma mistura pré-misturada de metano e oxigênio. Um framework foi desenvolvido em Python com o sistema algébrico resultante da discretização temporal e espacial de elementos finitos com aplicação de uma Programação Orientada à Objetos (POO) e paralelismo local por meio de controle de processos. Para a resolução temporal e transiente foi aplicado o esquema de Euler completamente explícito, já para a obtenção do comportamento espacial foi empregado o método de Elemento por Elemento (EbE), baseado no método de Gradiente Biconjugado para resolução de sistemas lineares, reduzindo os custos computacionais e espaço de memória associados a não utilização de matrizes esparsas. Para análise de consistência do framework é apresentado resultados para diversos escoamentos de referência da literatura.
This work presents the fundamentals of transport phenomena, some equations of thermodynamic state, the weak formulation of the finite element method applied to the flow and some methods for solving the various fields of analysis of the flow, the turbulence in incompressible and compressible flows, the combustion as reactive flow in a premixed homogeneous mixture. A technical review of several chosen references addressing aspects of the numerical solution, the turbulent model, the turbulence-combustion integration (TCI), the premixture and the choice of fuel and oxidizer, including a table so that you can analyze the complex relationship between all these aspects in publications checked. The main objective of this work is to develop a theoretical and numerical analysis of incompressible and compressible turbulent flows for several domains, developing a framework base to be integrated into the simulation of reactive flows in rocket engines in the future. The equations of continuity, momentum, energy and conservation of chemical species are discretized using the Galerkin finite element method combined with the CBS (Characteristic Based-Split) stabilization scheme, to obtain the fluid dynamic and thermal effects of the process. The combustion process and flame front behavior was only analyzed theoretically and for this, the Flamelet-Progress Variable method was employed. For the modeling of chemical kinetics, the software Canterar is applied, which uses the GRI-3.0, a mechanism that contains 325 reactions and includes 53 chemical species as a product of combustion. For this, a premixed mixture of methane and oxygen was considered. A framework was developed in Python with the algebraic system resulting from the temporal and spatial discretization of finite elements with the application of Object Oriented Programming (OOP) and local parallelism through process control. For the temporal and transient resolution, the completely explicit Euler scheme was applied, while the Element-by-Element (EbE) method was used to obtain the spatial behavior, based on the Biconjugated Gradient method for solving linear systems, reducing computational costs. and memory space associated with not using sparse arrays. For consistency analysis of the framework, results are presented for several reference flows in the literature.
This work presents the fundamentals of transport phenomena, some equations of thermodynamic state, the weak formulation of the finite element method applied to the flow and some methods for solving the various fields of analysis of the flow, the turbulence in incompressible and compressible flows, the combustion as reactive flow in a premixed homogeneous mixture. A technical review of several chosen references addressing aspects of the numerical solution, the turbulent model, the turbulence-combustion integration (TCI), the premixture and the choice of fuel and oxidizer, including a table so that you can analyze the complex relationship between all these aspects in publications checked. The main objective of this work is to develop a theoretical and numerical analysis of incompressible and compressible turbulent flows for several domains, developing a framework base to be integrated into the simulation of reactive flows in rocket engines in the future. The equations of continuity, momentum, energy and conservation of chemical species are discretized using the Galerkin finite element method combined with the CBS (Characteristic Based-Split) stabilization scheme, to obtain the fluid dynamic and thermal effects of the process. The combustion process and flame front behavior was only analyzed theoretically and for this, the Flamelet-Progress Variable method was employed. For the modeling of chemical kinetics, the software Canterar is applied, which uses the GRI-3.0, a mechanism that contains 325 reactions and includes 53 chemical species as a product of combustion. For this, a premixed mixture of methane and oxygen was considered. A framework was developed in Python with the algebraic system resulting from the temporal and spatial discretization of finite elements with the application of Object Oriented Programming (OOP) and local parallelism through process control. For the temporal and transient resolution, the completely explicit Euler scheme was applied, while the Element-by-Element (EbE) method was used to obtain the spatial behavior, based on the Biconjugated Gradient method for solving linear systems, reducing computational costs. and memory space associated with not using sparse arrays. For consistency analysis of the framework, results are presented for several reference flows in the literature.
Descrição
Palavras-chave
Characteristic-based split, Python, Método elemento por elemento, Programação paralela, Element-by-Element approach, Parallel programming