Numerical study of the square-root conformation tensor formulation for confined and free-surface viscoelastic fluid flows

被引：0
作者：
Palhares Junior I.L. [1 ]
Oishi C.M. [1 ]
Afonso A.M. [2 ,3 ]
Alves M.A. [2 ,3 ]
Pinho F.T. [3 ]
机构：
[1] Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista “Júlio de Mesquita Filho”, Presidente Prudente
[2] Departamento de Engenharia Química, CEFT, Faculdade de Engenharia da Universidade do Porto, Porto
[3] CEFT, Faculdade de Engenharia da Universidade do Porto, Porto
来源：
Advanced Modeling and Simulation in Engineering Sciences | / 3卷 / 1期
基金：
巴西圣保罗研究基金会; 欧洲研究理事会;
关键词：
Complex flows; Confined flows; Free-surface flows; High-Weissenberg Number Problem; Square-root formulation; Viscoelastic fluids;
D O I：
10.1186/s40323-015-0054-4
中图分类号：
学科分类号：
摘要：
We present a numerical study of a stabilization method for computing confined and free-surface flows of highly elastic viscoelastic fluids. In this approach, the constitutive equation based on the conformation tensor, which is used to define the viscoelastic model, is modified introducing an evolution equation for the square-root conformation tensor. Both confined and free-surface flows are considered, using two different numerical codes. A finite volume method is used for confined flows and a finite difference code developed in the context of the marker-and-cell method is used for confined and free-surface flows. The implementation of the square-root formulation was performed in both numerical schemes and discussed in terms of its ability and efficiency to compute steady and transient viscoelastic fluid flows. The numerical results show that the square-root formulation performs efficiently in the tested benchmark problems at high-Weissenberg number flows, such as the lid-driven cavity flow, the flow around a confined cylinder, the cross-slot flow and the impacting drop free surface problem. © 2016, Palhares Junior et al.
引用
收藏
相关论文
共 54 条
[41]  
Brown R.A., McKinley G.H., Report on the VIIIth international workshop on numerical methods in viscoelastic flows, J Non Newton Fluid Mech, 52, 3, pp. 407-413, (1994)
[42]  
Alves M.A., Pinho F.T., Oliveira P.J., The flow of viscoelastic fluids past a cylinder: finite-volume high-resolution methods, J Non Newton Fluid Mech, 97, pp. 207-232, (2001)
[43]  
Fan Y., Tanner R.I., Phan-Thien N., Galerkin/least-square finite-element methods for steady viscoelastic flows, J Non Newton Fluid Mech, 84, pp. 233-256, (1999)
[44]  
Kim J.M., Kim C., Ahn K.H., Lee S.J., An efficient iterative solver and high precision solutions of the Oldroyd-B fluid flow past a confined cylinder, J Non Newton Fluid Mech, 123, pp. 161-173, (2004)
[45]  
Hulsen M.A., Some properties and analytical expressions for plane flow of Leonov and Giesekus models, J Non Newton Fluid Mech, 30, pp. 85-92, (1988)
[46]  
Fuller G.G., Cathey C.A., Hubbard B., Zebrowski B.E., Extensional viscosity measurements for low viscosity fluids, J Rheol, 31, pp. 235-249, (1987)
[47]  
Arratia P.E., Thomas C.C., Diorio J.D., Gollub J.P., Elastic instabilities of polymer solutions in cross-channel flow, Phys Rev Lett, (2006)
[48]  
Poole R.J., Alves M.A., Oliveira P.J., Purely elastic flow asymmetries, Phys Rev Lett, 99, 16, (2007)
[49]  
Cruz F.A., Poole R.J., Afonso A.M., Pinho F.T., Oliveira P.J., Alves M.A., A new viscoelastic benchmark flow: stationary bifurcation in a cross slot, J Non Newton Fluid Mech, 214, pp. 57-68, (2014)
[50]  
Cruz D.O.A., Pinho F.T., Analytical solution of steady 2D wall-free extensional flows of UCM fluids, J Non Newton Fluid Mech, 223, pp. 157-164, (2015)
123456