Numerical investigation of the viscoelastic fluids

Yapıcı, Kerim
Most materials used in many industries such as plastic, food, pharmaceuticals, electronics, dye, etc. exhibit viscoelastic properties under their processing or flow conditions. Due to the elasticity of such materials, deformation-stress in addition to their hydrodynamic behavior differ from simple Newtonian fluids in many important respects. Rod climbing, siphoning, secondary flows are all common examples to how a viscoelastic fluid can exhibit quite distinctive flow behavior than a Newtonian fluid would do under similar flow conditions. In industrial processes involving flow of viscoelastic materials, understanding complexities associated with the viscoelasticity can lead to both design and development of hydrodynamically efficient processes and to improved quality of the final products. In the present study, the main objective is to develop two dimensional finite volume based convergent numerical algorithm for the simulation of viscoelastic flows using nonlinear differential constitutive equations. The constitutive models adopted are Oldroyd-B, Phan-Thien Tanner (PTT) and White-Metzner models. The semi-implicit method for the pressure-linked equation (SIMPLE) and SIMPLE consistent (SIMPLEC) are used to solve the coupled continuity, momentum and constitutive equations. Extra stress terms in momentum equations are solved by decoupled strategy. The schemes to approximate the convection terms in the momentum equations adopted are first order upwind, hybrid, power-law second order central differences and finally third order quadratic upstream interpolation for convective kinematics QUICK schemes. Upwind and QUICK schemes are used in the constitutive equations for the stresses. Non-uniform collocated grid system is employed to discretize flow geometries. As test cases, three problems are considered: flow in entrance of planar channel, stick-slip and lid driven cavity flow. Detailed investigation of the flow field is carried out in terms of velocity and stress fields. It is found that range of convergence of numerical solutions is very sensitive to the type of rheological model, Reynolds number and polymer contribution of viscosity as well as mesh refinement. Use of White-Metzner constitutive differential model gives smooth, non oscillatory solutions to much higher Weissenberg number than Oldroyd-B and PTT models. Differences between the behavior of Newtonian and viscoelastic fluids for lid-driven cavity, such as the normal stress effects and secondary eddy formations, are highlighted. In addition to the viscoelastic flow simulations, steady incompressible Newtonian flow of lid-driven cavity flow at high Reynolds numbers is also solved by finite volume approach. Effect of the solution procedure of pressure correction equation cycles, which is called inner loop, on the solution is discussesed in detail and results are compared with the available data in literature.


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Citation Formats
K. Yapıcı, “Numerical investigation of the viscoelastic fluids,” Ph.D. - Doctoral Program, Middle East Technical University, 2008.