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Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

OISHI, C. M.; MARTINS, F. P.; TOME, M. F.; CUMINATO, J. A.; MCKEE, S.
Fonte: ELSEVIER SCIENCE BV Publicador: ELSEVIER SCIENCE BV
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
65.92%
In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP - Fundacao de Amparo a pesquisa do Estado de Sao Paulo[04/16064-9]; FAPESP - Fundacao de Amparo a pesquisa do Estado de Sao Paulo[2009/15892-9]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico[304422/2007-0]; CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico[470764/2007-4]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico[477858/2009-0]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Royal Society of Edinburgh; Royal Society of Edinburgh

An implicit technique for solving 3D low Reynolds number moving free surface flows

OISHI, Cassio M.; TOME, Murilo F.; CUMINATO, Jose A.; MCKEE, Sean
Fonte: ACADEMIC PRESS INC ELSEVIER SCIENCE Publicador: ACADEMIC PRESS INC ELSEVIER SCIENCE
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
65.98%
This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP (Fundaqdo de Amparo a pesquisa do Estado de Sao Paulo)[03/12612 - 9]; FAPESP (Fundaqdo de Amparo a pesquisa do Estado de Sao Paulo)[04/16064 - 9]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); CNPq (Conselho Nacional de Desen-volvimento Cientifico e Tecnologico)[300106/2005-0]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq (Conselho Nacional de Desen-volvimento Cientifico e Tecnologico)[474040/2003 - 8]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq (Conselho Nacional de Desen-volvimento Cientifico e Tecnologico)[523141/94]; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); CAPES (Coordenacao de Aperfeicoa-mento de Pessoal de Nivel Superior)[136/05-CAPES/GRICES]; CAPES (Coordenacao de Aperfeicoa-mento de Pessoal de Nivel Superior)[0121/07 - 0]; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

TOME, M. F.; PAULO, G. S.; PINHO, F. T.; ALVES, M. A.
Fonte: ELSEVIER SCIENCE BV Publicador: ELSEVIER SCIENCE BV
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
65.96%
This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien-Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the FIT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is reported. (C) 2010 Elsevier B.V. All rights reserved.; FAPESP - Fundacao de Amparo a pesquisa do Estado de Sao Paulo[04/16064-9]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico[304422/2007-0]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico[470764/2007-4]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); GRICES; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); CAPES/GRICES[136/5]; GRICES; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); GRICES/CAPES[4.1.3]; FCT[PTDC/EQU-FTT/71800/2006]; Fundação para a Ciência e a Tecnologia de Portugal (FCT); FCT[PTDC/EQU-FTT/70727/2006]; Fundação para a Ciência e a Tecnologia de Portugal (FCT)

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

TOME, Murilo F.; SILVA, Renato A. P.; OISHI, Cassio A.; MCKEE, Sean
Fonte: GLOBAL SCIENCE PRESS Publicador: GLOBAL SCIENCE PRESS
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
65.92%
This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP[04/10988-4]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP[04/16064-9]; FAPESP[03/12612-9]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); CAPES[BEX 012070]; CAPES[BEX 1837/06-0]; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); CNPq[304422/2007-0]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A marker-and-cell approach to free surface 2-D multiphase flows

Santos, Fernando Luiz Pio dos; Ferreira, Valdemir Garcia; Tomé, Murilo Francisco; Castelo Filho, Antonio; Mangiavacchi, Norberto; Mckee, Sean
Fonte: John Wiley and Sons; Malden, Ma Publicador: John Wiley and Sons; Malden, Ma
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
65.9%
This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the NavierStokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright (c) 2012 John Wiley & Sons, Ltd.; Brazilian funding agency CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico [300479/2008-5...

Numerical investigation of three dimensional viscoelastic free surface flows: impacting drop problem

Figueiredo, Rafael Alves; Oishi, Cassio Machiaveli; Cuminato, José Alberto; Azevedo, José Manuel Cruz; Afonso, Alexandre Miguel Prior; Alves, Manuel António Moreira
Fonte: International Association for Computational Mechanics (IACM); European Community on Computational Methods in Applied Sciences (ECCOMAS); Barcelona Publicador: International Association for Computational Mechanics (IACM); European Community on Computational Methods in Applied Sciences (ECCOMAS); Barcelona
Tipo: Conferência ou Objeto de Conferência
ENG
Relevância na Pesquisa
65.92%
This work presents a numerical investigation of three dimensional viscoelastic free surface flows. In particular, using two different numerical methodologies, we have simulated a typical free-surface benchmark flow problem: the impact of a viscoelastic fluid droplet with a rigid boundary. The numerical method was recently proposed by Figueiredo et al. [1] and has been implemented in a in-house viscoelastic flow solver. In this methodology, a finite difference scheme is adopted combining the Marker-And-Cell (MAC) method with a Front-Tracking strategy. In order to preserve mass conservation properties for transient viscoelastic fluid flows, we have modified the methodology in [1] to include an improvement on the MAC discretization of the velocity boundary conditions at free-surfaces. The code is verified by solving the drop impact problem for a Newtonian fluid. After this verification, we employ the Oldroyd-B model to assess the differences between the methodologies, and compare our results with the ones in the literature. Finally, a detailed study of the influence of the relevant rheological parameters of the non-linear viscoelastic models (Giesekus and XPP) is reported, regarding the deformation and spreading of the viscoelastic fluid drop after impacting on a rigid surface.; FAPESP (processos nos. 2011/09194-7...

Estratégias "upwind" e modelagem k-epsilon para simulação numérica de escoamentos com superfícies livres em altos números de Reynolds; Upwind strategies and k-epsilon modeling for numerical simulation of free surface flow at high Reynolds numbers

Brandi, Analice Costacurta
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 13/06/2005 PT
Relevância na Pesquisa
65.92%
Este trabalho é dedicado à análise e implementação de esquemas "upwind" de alta ordem modernos e o modelo de turbulência k-epsilon padrão no Freeflow-2D; um ambiente integrado para simulação numérica em diferenças finitas de problemas de escoamentos incompressíveis com superfícies livres. O propósito do estudo é a simulação de escoamentos de fluidos newtonianos incompressíveis, bidimensionais, confinados e/ou com superfícies livres e a altos valores do número de Reynolds. O desempenho do código Freeflow-2D atual é avaliada na simulação do escoamento numa expansão brusca e de um jato livre incidindo perpendicularmente sobre uma superfície rígida impermeável. O código é então aplicado na simulação de um jato planar turbulento em uma porção de fluido com superfície livre e estacionário. Os resultados numéricos obtidos são comparados com dados experimentais, soluções analíticas e soluções numéricas de outros trabalhos.; This work is devoted to the analysis and implementation of modern high-order upwind schemes and the standard k-epsilon turbulence model into the Freeflow-2D; a finite difference integrated environment for the numerical simulation of incompressible free surface flow problems. The purpose of this study is the two-dimensional simulation of high-Reynolds incompressible newtonian confined and/or free surface flows. The performance of the current Freeflow-2D code is assessed by applying it to the simulation of flow over a backward facing step and of an impinging free jet onto an impermeable rigid surface. The code is then applied to a turbulent planar jet into a pool. The numerical results are compared with experimental data...

Análise e implementação de métodos implícitos e de projeção para escoamentos com superfície livre.; Analysis and implementation of implicit and projection methods for free surface flows

Oishi, Cássio Machiaveli
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 05/08/2008 PT
Relevância na Pesquisa
66%
No contexto do método MAC e baseado em esquemas de diferenças finitas, 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 discretiza ção 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 fluidos 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...

Desenvolvimento de um método numérico implícito para a simulação de escoamentos viscoelásticos com superfícies livres; Development of an implicit numerical method for the simulation of viscoelastic free surface flows

Martins, Fernando Pacanelli
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 18/08/2009 PT
Relevância na Pesquisa
65.96%
O tema deste trabalho é o estudo de métodos numéricos para a simulação de escoamentos incompressíveis com superfície livre a baixos Reynolds, por meio da metodologia GENSMAC e suas formulações explícita e implícita. Neste contexto, temos especial interesse na formulação implícita, objetivando o enfraquecimento da restrição de estabilidade parabólica no passo temporal em escoamentos com superfície livre. O trabalho pode ser dividido em duas partes: na primeira, algumas modificações são discutidas, propostas e testadas com o objetivo de tornar a formulação implícita mais eficiente e precisa; em seguida, aproveitamos os resultados obtidos e generalizamos o método numérico existente para simular escoamentos viscoelásticos modelados pela equação constitutiva SXPP. Em ambos os casos, a formulação explícita também é usada para comparação e teste. Resultados que demonstram a eficiência e robustez das técnicas desenvolvidas são apresentados por meio da simulação numérica de complexos problemas envolvendo superfície livre.O tema deste trabalho é o estudo de métodos numéricos para a simulação de escoamentos incom- pressíveis com superfície livre a baixos Reynolds, por meio da metodologia GENSMAC e suas formulações explícita e implícita. Neste contexto...

Estudos de métodos numéricos para a simulação de escoamentos viscoelásticos com superfície livre; Numerical methods for viscoelastic free surface flows

Figueiredo, Rafael Alves
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 29/08/2011 PT
Relevância na Pesquisa
65.92%
Neste projeto, é apresentado um método numérico com uma abordagem do tipoMAC para a simulação de escoamentos viscoelásticos incompressíveis tridimensionais com superfície livre governados pelo modelo de fluido SXPP. A formulação apresentada nesse trabalho é uma extensão dos resultados obtidos por Oishi et al. (2011), sobre o estudo de métodos numéricos para a simulação de escoamentos incompressíveis viscoelásticos com superfície livre a baixos números de Reynolds, para o caso bidimensional. No contexto de problemas transientes, metodologias explícitas para solução numérica das equações governantes apresentam restrições de estabilidade muito severas para a definição do passo temporal, acarretando em um custo computacional relativamente alto. Sendo assim, utilizamos um método implícito para resolver a equação de conservação da quantidade de movimento, eliminando assim, a restrição de estabilidade parabólica e diminuindo significativamente o custo computacional. Mas tal estratégia acopla os campos de velocidade e pressão. Dessa forma, para desacoplar esses campos, foi utilizado uma abordagem que combina método de projeção com uma técnica implícita para o tratamento da pressão na superfície livre. A equação constitutiva foi resolvida pelo método de Runge-Kutta de segunda-ordem. A validação do método numérico foi realizada utilizando refinamento da malha no escoamento em um canal. Como aplicação...

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

Oishi, C. M.; Martins, F. P.; Tome, M. F.; Cuminato, J. A.; McKee, S.
Fonte: Elsevier B.V. Publicador: Elsevier B.V.
Tipo: Artigo de Revista Científica Formato: 165-179
ENG
Relevância na Pesquisa
65.92%
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Processo FAPESP: 04/16064-9; Processo FAPESP: 09/15892-9; In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

A marker-and-cell approach to free surface 2-D multiphase flows

Santos, F. L. P.; Ferreira, V. G.; Tome, M. F.; Castelo, A.; Mangiavacchi, N.; McKee, S.
Fonte: Wiley-Blackwell Publicador: Wiley-Blackwell
Tipo: Artigo de Revista Científica Formato: 1543-1557
ENG
Relevância na Pesquisa
65.9%
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the NavierStokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright (c) 2012 John Wiley & Sons, Ltd.

Numerical assessment of mass conservation on a MAC-type method for viscoelastic free surface flows

Martins, Fernando P.; Oishi, Cassio M.; Sousa, Fabricio S.; Cuminato, Jose A.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 6545-6562
ENG
Relevância na Pesquisa
65.97%
A numerical study of mass conservation of MAC-type methods is presented, for viscoelastic free-surface flows. We use an implicit formulation which allows for greater time steps, and therefore time marching schemes for advecting the free surface marker particles have to be accurate in order to preserve the good mass conservation properties of this methodology. We then present an improvement by using a Runge-Kutta scheme coupled with a local linear extrapolation on the free surface. A thorough study of the viscoelastic impacting drop problem, for both Oldroyd-B and XPP fluid models, is presented, investigating the influence of timestep, grid spacing and other model parameters to the overall mass conservation of the method. Furthermore, an unsteady fountain flow is also simulated to illustrate the low mass conservation error obtained.

Three-dimensional transient complex free surface flows: Numerical simulation of XPP fluid

Figueiredo, R. A.; Oishi, C. M.; Cuminato, J. A.; Alves, M. A.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Artigo de Revista Científica Formato: 88-98
ENG
Relevância na Pesquisa
65.99%
In this paper we present a finite difference MAC-type approach for solving three-dimensional viscoelastic incompressible free surface flows governed by the eXtended Pom-Pom (XPP) model, considering a wide range of parameters. The numerical formulation presented in this work is an extension to three-dimensions of our implicit technique [Journal of Non-Newtonian Fluid Mechanics 166 (2011) 165-179] for solving two-dimensional viscoelastic free surface flows. To enhance the stability of the numerical method, we employ a combination of the projection method with an implicit technique for treating the pressure on the free surfaces. The differential constitutive equation of the fluid is solved using a second-order Runge-Kutta scheme. The numerical technique is validated by performing a mesh refinement study on a pipe flow, and the numerical results presented include the simulation of two complex viscoelastic free surface flows: extrudate-swell problem and jet buckling phenomenon. © 2013 Elsevier B.V.

Application of the PTT Model to Axisymmetric Free Surface Flows

Merejolli, R.; Paulo, G. S.; Tome, M. F.; Simos, T.; Psihoyios, G.; Tsitouras, C.
Fonte: Amer Inst Physics Publicador: Amer Inst Physics
Tipo: Conferência ou Objeto de Conferência Formato: 220-223
ENG
Relevância na Pesquisa
65.94%
This work is concerned with numerical simulation of axisymmetric viscoelastic free surface flows using the Phan-Thien-Tanner (PTT) constitutive equation. A finite difference technique for solving the governing equations for unsteady incompressible flows written in Cylindrical coordinates on a staggered grid is described. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are applied. The numerical method is verified by comparing numerical predictions of fully developed flow in a pipe with the corresponding analytic solutions. To demonstrate that the numerical method can simulate axisymmetric free surface flows governed by the PTT model, numerical results of the flow evolution of a drop impacting on a rigid dry plate are presented. In these simulations, the rheological effects of the parameters epsilon and xi are investigated.

Acceleration of Gas Bubble-Free Surface Interaction Computation Using Basis Preconditioners

Tan, Kiok Lim; Khoo, Boo Cheong; White, Jacob K.
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Tipo: Artigo de Revista Científica Formato: 130737 bytes; application/pdf
EN_US
Relevância na Pesquisa
65.92%
The computation of gas bubble-free surface interaction entails a time-stepping algorithm whereby a linear system is solved at each time-iteration. In our investigation, the linear systems are derived from a desingularized boundary integral formulation and are poorly conditioned. This leads to poor convergence rates when Krylov subspace methods are used to solve these systems. The convergence rates may however be improved with proper preconditioning. We limit our investigation to gas bubbles initiated at depths sufficiently small such that a spike forms on the free surface during the later stages of evolution. Bubble dynamics dictate that for gas bubbles initiated at such depths, the stages through which the gas bubble and free surface evolve are similar. Based on this fact, we propose to perform one computation run for a gas bubble initiated at one particular depth, obtain a judicious set of a priori basis preconditioners from this run and thereafter, use this set of preconditioners on computation runs for gas bubble initiated at different depths. The computation time taken by the proposed method is, in general, 50% and 20% of the time taken by the present method (without preconditioning) with terminating criteria of 1.0e-5 and 1.0e-7 in the infinity-norm respectively using the Bi-conjugate Gradient Stabilized solver. The present method further enables computation to an infinity-norm terminating criterion of 1.0e-10 in a shorter time compared to the present method with a criterion of 1.0e-5.; Singapore-MIT Alliance (SMA)

Free surface flow past topography: A beyond-all-orders approach

Lustri, C.; McCue, S.; Binder, B.
Fonte: Cambridge Univ Press Publicador: Cambridge Univ Press
Tipo: Artigo de Revista Científica
Publicado em //2012 EN
Relevância na Pesquisa
65.94%
The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck, (2006) Exponential asymptotics and gravity waves. J. Fluid Mech. 567, 299–326, the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of inclination. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase...

Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

Binder, B.; Blyth, M.; McCue, S.
Fonte: Oxford Univ Press Publicador: Oxford Univ Press
Tipo: Artigo de Revista Científica
Publicado em //2013 EN
Relevância na Pesquisa
66%
An efficient numerical method to compute nonlinear solutions for 2D steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free surface a priori and solve for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify 11 basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free surface, given the free surface shape itself.; Benjamin J. Binder, M. G. Blyth and Scott W. McCue

Enhanced SPH modeling of free-surface flows with large deformations

Marrone, Salvatore
Fonte: La Sapienza Universidade de Roma Publicador: La Sapienza Universidade de Roma
Tipo: Tese de Doutorado
EN
Relevância na Pesquisa
65.99%
The subject of the present thesis is the development of a numerical solver to study the violent interaction of marine flows with rigid structures. Among the many numerical models available, the Smoothed Particle Hydrodynamics (SPH) has been chosen as it proved appropriate in dealing with violent free-surface flows. Due to its Lagrangian and meshless character it can naturally handle breaking waves and fragmentation that generally are not easily treated by standard methods. On the other hand, some consolidated features of mesh-based methods, such as the solid boundary treatment, still remain unsolved issues in the SPH context. In the present work a great part of the research activity has been devoted to tackle some of the bottlenecks of the method. Firstly, an enhanced SPH model, called delta-SPH, has been proposed. In this model, a proper numerical diffusive term has been added in the continuity equation in order to remove the spurious numerical noise in the pressure field which typically affects the weakly-compressible SPH models. Then, particular attention has been paid to the development of suitable techniques for the enforcement of the boundary conditions. As for the free-surface, a specific algorithm has been designed to detect free-surface particles and to define a related level-set function with two main targets: to allow the imposition of peculiar conditions on the free-surface and to analyse and visualize more easily the simulation outcome (especially in 3D cases). Concerning the solid boundary treatment...

Effects of free-surface on design charts for open channels

Rahimpour,Majid
Fonte: Water SA Publicador: Water SA
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2012 EN
Relevância na Pesquisa
65.92%
Normal depth is an important parameter for the design of channels and canals. For rectangular, trapezoidal, and circular channel sections it is possible to express normal depth by a trial-and-error procedure or analytically. However, the effects of free-surface on the design charts for determination of the normal depth are not investigated. In this paper, graphical solutions of normal depth for the rectangular, trapezoidal, and circular cross-sections have been obtained in the non-dimensional form. To evaluate the resistance effects of the free-surface in the calculation of the normal depth, the dimensionless-form of Manning';s equation with free-surface weight factor is introduced herein. The design charts reported previously were modified.