Lattice Boltzmann studies of turbulence in non-Newtonian fluids

In this thesis Lattice Boltzmann method (LBM) was used to simulate laminar and turbulent channel flows with the goal of understanding the physics of polymer drag reduction. The following results were obtained: (a) We demonstrate the viability of LBM as a numerical method for channel flow. The form of the plots for the velocity fluctuations and Reynolds stress are quantitatively similar to those obtained in experiments and from simulations using Navier-Stokes equations. (b) A variant of LBM was used for the simulation of dilute polymer solution flow. Extra degrees of freedom were included in LBM to represent polymers. Our model for polymers is macroscopically equivalent to FENE-P model. This model was used for the simulations of turbulent channel flow with polymers (Retau = 209). Drag reduction was observed as in experiments. We measured averaged Reynolds stresses and other physical quantities before and after the polymer addition. The addition of polymers produces reductions in the product uv as well as fluctuations of normal velocity v and spanwise velocity w. In contrast, the streamwise component of the velocity fluctuation u grows moderately. These changes in energy dynamics reproduce the physical phenomena associated with the polymer dynamics in the channel flow. (c) The LBM was extended to simulate non-Newtonian effects of polymers by modifying the relaxation time in LBM. This modification makes the macroscopic viscosity of the fluid depend on the velocity-gradient tensor. When applied to pulsatile laminar flow of concentrated polymer solution, the calculation showed flow enhancement under certain conditions. The result obtained is in agreement with experiments. The same model was used to consider the scenario of drag reduction in turbulent channel flow by spatial modification of viscosity. The example considered is the linear increase of viscosity in a buffer layer up to the core region of the channel. (d) We investigated the effect of the diluted polymer solution on Kelvin-Helmholtz instability. We consider the simple problem of the mixing layer which consists of two horizontal layers of fluids moving relative to each other. The results show that polymers produce stabilizing effect and suppress momentum transport due to fluctuating velocity components. (Abstract shortened by UMI.)...