Análise de estabilidade de escoamentos do fluido viscoelástico Giesekus
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Data
2018-08-02
Autores
Furlan, Laison Junio da Silva [UNESP]
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Universidade Estadual Paulista (Unesp)
Resumo
O presente trabalho investiga a transição laminar-turbulenta devido a ondas de Tollmien-Schlichting para o escoamento de Poiseuille incompressível, bidimensional, de um fluido viscoelástico, utilizando a equação constitutiva Giesekus. A Teoria de Estabilidade Linear e a Simulação Numérica Direta são utilizadas para verificar a estabilidade de escoamentos de fluidos viscoelásticos a perturbações não estacionárias. Na análise LST a equação de Orr-Sommerfeld é modificada para um fluido viscoelástico e resolvida pelo método da estimativa (Shooting). Enquanto que, na formulação DNS, as equações de Navier-Stokes, juntamente com a equação constitutiva Giesekus, são resolvidas utilizando métodos de diferenças finitas compactas de alta ordem. Com o objetivo de avaliar as curvas neutras de estabilidade e as taxas de amplificação, diferentes simulações numéricas são realizadas variando-se os parâmetros adimensionais no modelo Giesekus e comparando com o fluido Newtoniano. As técnicas LST e DNS mostraram-se ferramentas eficientes na análise espacial da estabilidade de escoamentos viscoelásticos do tipo Giesekus, permitindo uma melhor compreensão da influência dos parâmetros adimensionais desses escoamentos e contribuindo com resultados originais na verificação da estabilidade de escoamentos viscoelásticos utilizando o fluido Giesekus.
The present work investigates the laminar-turbulent transition due to Tollmien-Schlichting waves for the incompressible two-dimensional Poiseuille flow of a viscoelastic fluid, using the Giesekus constitutive equation. Linear Stability Theory and Direct Numerical Simulation are used to verify the stability of viscoelastic fluid flows to unsteady disturbances. In the LST analysis, the Orr-Sommerfeld equation is modified to a viscoelastic fluid and solved by Shooting method. Whereas, in the DNS formulation, the Navier-Stokes equations with the Giesekus constitutive equation are solved using high-order compact finite difference methods. In order to evaluate the neutral stability curves and the amplification rates, different numerical simulations are performed by varying the dimensionless parameters in the Giesekus model and their results are compared with the Newtonian fluid. The LST and DNS techniques proved to be efficient tools to the spatial stability analysis of viscoelastic fluid flows of the Giesekus type, allowing a better comprehension of the dimensionless parameters influence of those flows, contributing with originals results to verification of the viscoelastics fluid flows stability using Giesekus fluid.
The present work investigates the laminar-turbulent transition due to Tollmien-Schlichting waves for the incompressible two-dimensional Poiseuille flow of a viscoelastic fluid, using the Giesekus constitutive equation. Linear Stability Theory and Direct Numerical Simulation are used to verify the stability of viscoelastic fluid flows to unsteady disturbances. In the LST analysis, the Orr-Sommerfeld equation is modified to a viscoelastic fluid and solved by Shooting method. Whereas, in the DNS formulation, the Navier-Stokes equations with the Giesekus constitutive equation are solved using high-order compact finite difference methods. In order to evaluate the neutral stability curves and the amplification rates, different numerical simulations are performed by varying the dimensionless parameters in the Giesekus model and their results are compared with the Newtonian fluid. The LST and DNS techniques proved to be efficient tools to the spatial stability analysis of viscoelastic fluid flows of the Giesekus type, allowing a better comprehension of the dimensionless parameters influence of those flows, contributing with originals results to verification of the viscoelastics fluid flows stability using Giesekus fluid.
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Palavras-chave
Fluido Giesekus, Transição laminar-turbulenta, Simulação numérica direta, Teoria de estabilidade linear, Laminar-turbulent transition, Giesekus fluid, Direct numerical simulation, Linear stability theory