Numerical analysis of surface-driven non-isothermal viscoelastic flow - Kaptan, Yalın. (Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010)
The numerical investigations of the moving edge non-isothermal viscoelastic flows are simulated by using two example problems (lid driven cavity (LDC) and rotating disc in a cylindrical enclosure (RDCE) flows) in this study. The viscoelastic behavior of the fluids is modeled by adopting three differential constitutive relations namely Upper Convected Maxwell (UCM), Oldroyd B and Giesekus models. The comparisons reveal that the Giesekus model is the most realistic one and the maximum Weissenberg number limit is higher compared to the others. Two separate solvers are used in the simulations; PETSc and IN-GMRES solvers. PETSc code is used as a solver for the Newtonian flows and a benchmark tool for the Krylov subspace methods and preconditioners. PETSc analyses reveal that BiCGStab with ILU(5) preconditioning is the most effective solver in the simulations of the Newtonian flows. IN-GMRES solver is used to simulate the non-isothermal viscoelastic flows and it is based on the matrix free preconditioned inexact Newton-Krylov methods. To obtain higher Weissenberg number limits in the simulations, the numerical tools such as the continuation, the upwind differencing scheme, the higher order discretization schemes, the slanted stencils and similar others are implemented in the IN-GMRES algorithm. In the non-isothermal part of the study, besides the advection and diffusion, the viscous dissipation is also included and it is understood that the viscous dissipation is very important in simulations of non-Newtonian flows. The viscosity is modeled as temperature dependent by adopting the approximate Arrhenius formulation and it is realized that the viscosity changes can alter the flow field. The effects of the Reynolds number, the Weissenberg number, the Prandtl number, the Brinkman number, aspect ratio and some of the material parameters are documented within this study.
Keywords: Generalized minimal residual method.; Viscoelastic materials.; Newton-Raphson method.