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.

A new method to perform direct numerical simulations of wall-bounded flows has been developed and implemented. The method uses high-order compact finite differences in wall-normal (for channel flow) or radial direction (for pipe flow) on a collocated grid, which gives high-accuracy results without the effectfof filtering caused by frequent interpolation as required on a staggered grid. The use of compact finite differences means that extreme clustering near the wall leading to small time steps in high-Reynolds number simulations is avoided. The influence matrix method is used to ensure a completely divergence-freesolution and all systems of equations are solved in banded form, which ensures an effcient solution procedure with low requirements for data storage. The method is unique in the sense that exactly divergence-free solutions on collocated meshes are calculated using arbitrary dffierence matrices. The code is validated for two flow cases, i.e. turbulent channel and turbulent pipe flow at relatively low Reynolds number. All tests show excellent agreement with analytical and existing results, confirming the accuracy and robustness ofthe method. The next step is to eciently parallelise the code so that high-Reynolds number simulations at high resolution can be performed. We furthermore investigated rare events occurring in the near-wall region of turbulent wall-bounded flows. We find that negative streamwise velocities and extreme wall-normal velocity uctuations are found rarely (on the order of 0:01%), and that they occur more frequently at higher Reynolds number. These events are caused by strong vortices lying further away from the wall and it appears that these events are universal for wall-bounded flows. / <p>QC 20150303</p>