A numerical method for solving three-dimensional generalized Newtonian free surface flows

Tomé, Murilo Francisco; Grossi, L.; Castelo, A.; Cuminato, José Alberto; Mangiavacchi, Norberto; Ferreira, Valdemir Garcia; Sousa, Fabrício S.; McKee, Sean

doi:10.1016/j.jnnfm.2004.06.012

Cited by 39 publications

(41 citation statements)

References 38 publications

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“…The value θ UU in Eq. (36) refers to the liquid volume fraction in the second upwind cell relative to face f. The original HRIC scheme further blends the interpolated values given by the scheme (35), with the UDS scheme, when the interface is not parallel to the cell's face, and when the local Courant number exceeds the threshold value 0.3. These corrections to the interpolated flux of the liquid volume aim at avoiding an artificial alignment of the interface with the numerical grid, as well as convergence issues.…”

Section: Algebraic Advection Schemementioning

confidence: 99%

“…the flow of the surrounding air is omitted). This method was used to simulate the extrudate swell and jet buckling phenomena for the generalized Newtonian fluid model [34,35], and for various viscoelastic constitutive models [36][37][38][39][40][41]. In the level-set method, the position of the interface (or the free surface) is represented with a level-set function that varies continuously across the interface [42].…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

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. Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods. Journal of Non-Newtonian Fluid Mechanics, 252, 1-18. DOI: 10.1016/j.jnnfm.2017 A B S T R A C TWe present an Eulerian free-surface flow solver for incompressible pseudoplastic and viscoelastic non-Newtonian fluids. The free-surface flow solver is based on the streamfunction flow formulation and the volume-of-fluid method. The streamfunction solver computes the vector potential of a solenoidal velocity field, which ensures by construction the mass conservation of the solution, and removes the pressure unknown. Pseudoplastic liquids are modelled with a Carreau model. The viscoelastic fluids are governed by differential constitutive models reformulated with the log-conformation approach, in order to preserve the positive-definiteness of the conformation tensor, and to circumvent the high Weissenberg number problem. The volume fraction of the fluid is advected with a geometric conservative unsplit scheme that preserves a sharp interface representation. For the sake of comparison, we also implemented an algebraic advection scheme for the liquid volume fraction. The proposed numerical method is tested by simulating the planar extrudate swell with the Carreau, Oldroyd-B and Giesekus constitutive models. The swell ratio of the extrudates are compared with the data available in the literature, as well as with numerical simulations performed with the open-source rheoTool toolbox in OpenFOAM ® . While the simulations of the generalized Newtonian fluids achieved mesh independence for all the methods tested, the flow simulations of the viscoelastic fluids are more sensitive to mesh refinement and the choice of numerical scheme. Moreover, the simulations of Oldroyd-B fluid flows above a critical Weissenberg number are prone to artificial surface instabilities. These numerical artifacts are due to discretization errors within the Eulerian surface-capturing method. However, the numerical issues arise from the stress singularity at the die exit corner, and the unphysical predictions of the Oldroyd-B model in the skin layer of the extrudate after the die exit, where large extensional deformations occur.

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Section: Algebraic Advection Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

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“…However, the level set surface generated by this method does not preserve temporal coherence due to the slow motion of the liquid. In computational physics literature, there are several papers using variations of generalized simplified MAC (GENSMAC) method to simulate viscous jet buckling in arbitrary 2D/3D domains with explicit [11][12][13] and implicit [14] free surface boundary conditions.…”

Section: Related Workmentioning

confidence: 99%

“…5). In our simulations of this problem, we use values for H, D and physical parameters consistent with the conditions described by Tomé et al [13].…”

Section: Jet Bucklingmentioning

confidence: 99%

Particle-based fluids for viscous jet buckling

Andrade

Sandim

Petronetto

et al. 2015

Computers & Graphics

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“…Reynolds são frequentes (por exemplo as aplicações em [162,161] por Prudhomme e Oden [131]. Outros estudos recentes têm sido realizados na estabilidade de esquemas implícitos aplicados às equações de Navier-Stokes: para fórmulas de diferenças atrasadas (backward dierentiation formulas) [83], para uma discretização totalmente implícita das equações de Navier-Stokes utilizando o método de Euler implícito [166], e para esquemas de Runge-Kutta [111].…”

Section: Esquemas Implícitos Na Metodologia Gensmacunclassified

Análise e implementação de métodos implícitos e de projeção para escoamentos com superfície livre.

Oishi¹

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Finalmente, e acima de tudo, a Deus pela minha vida.iii iv ResumoNo contexto do método MAC e baseado em esquemas de diferenças nitas, este trabalho apresenta três estudos: i) uma análise de estabilidade, ii) o desenvolvimento de técnicas implícitas e, iii) a construção de métodos de projeção para escoamentos com superfície livre.Na análise de estabilidade, o principal resultado mostra que o método de Crank-Nicolson torna-se condicionalmente estável quando aplicado para uma malha deslocada com a discretização explícita das condições de contorno do tipo Dirichlet. Entretanto, o mesmo método com condições de contorno implícitas é incondicionalmente estável.Para obter métodos mais estáveis, formulações implícitas são desenvolvidas para a equação da pressão na superfície livre, derivada da condição de tensão normal. Esta estratégia resulta no acoplamento dos campos de velocidade e pressão, o que exige a introdução de novos métodos de projeção.Os métodos de projeção assim desenvolvidos resultam em novas metodologias para escoamentos com superfície livre que são apropriados para o tratamento de problemas com baixo número de Reynolds. Além disso, mostra-se que os métodos propostos podem ser aplicados para uidos viscoelásticos. Novas estratégias são derivadas para obter métodos de projeção de segunda ordem de precisão para escoamentos com superfícies livres.Além dos resultados teóricos sobre a estabilidade de esquemas numéricos, técnicas implícitas e métodos de projeção, testes computacionais são realizados e comparados para consolidação da teoria apresentada. Os resultados numéricos são obtidos no sistema FREEFLOW.A eciência e robustez das técnicas desenvolvidas neste trabalho são demonstradas na solução de problemas tridimensionais complexos com superfície livre e baixo número de Reynolds, incluindo os problemas do jato oscilante e do inchamento do extrudado. In the context of the MAC method and based on nite dierence schemes, this work presents three studies: i) a stability analysis, ii) the development of implicit techniques, and iii) the construction of projection methods for free surface ows.In the stability analysis, the main result shows a precise stability restriction on the CrankNicolson method when one uses a staggered grid with Dirichlet explicit boundary conditions. However, the same method with implicit boundary conditions becomes unconditionally stable.In order to obtain more stable methods, implicit formulations are applied for the pressure equation at the free surface, which is derived from the normal stress condition. This approach results in a coupling of the velocity and pressure elds; hence new projection methods for free surface ows need to be developed.The developed projection methods result in new methodologies for low Reynolds number free surface ows. It is also shown that the proposed methods can be applied for viscoelastic uids. New strategies are derived for obtaining second-order accurate projection methods for free surface ows.In addition to the theoretical results on the stability of numeri...

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A numerical method for solving three-dimensional generalized Newtonian free surface flows

Cited by 39 publications

References 38 publications

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Particle-based fluids for viscous jet buckling

Análise e implementação de métodos implícitos e de projeção para escoamentos com superfície livre.

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