The quantitative description of fluid mixing using Lagrangian- and concentration-based numerical approaches

We report on two numerical approaches to quantify mixing-method I is based on kinematic mixing rates (i.e. the mixing, rates due to the fluid mechanic s only) and method II is based on the evolution of the concentration distri bution of a passive tracer. For method I, kinematic mixing rates are establ ished from the way infinitesimal fluid line elements are stretched by the f low and. from method II, the mixing rate is determined from the rate at whi ch the variance of the concentration of a particle cloud decreased. during the mixing process. For method II, concentrations were calculated by tracki ng a large number of diffusive particles using a Langevin-type equation (i. e. introducing a random walk term to model molecular diffusion) and by divi ding the domain into small regions. The two approaches were applied to a ca se study, oscillatory flow mixing (OFM) within baffled tubes, which is an i nertial flow that has been shown to provide an efficient alternative to con ventional mixing processes and is a viable candidate for technological appl ication. A numerical solution for this flow field was calculated by solving the full axisymmetric Navier-Stokes equations which is valid up to a value of the oscillatory how Reynolds number of order 200. The results of the tw o mixing methods are compared and their applicability and usefulness in the characterisation of the mixing ranked. The effect of fluid oscillation con ditions are also quantified, for the flow field examined. (C) 1998 Elsevier Science Ltd. All rights reserved.