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Keywords:

  • smoothed particle hydrodynamics;
  • mixing;
  • Lyapunov Exponents;
  • Twin Cam mixer;
  • chaotic transport

Abstract

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian, particle-based method that is well suited to industrial mixing simulations. Mass transport is simply the motion of the particles, and its grid-free nature means that it can easily accommodate complicated geometries involving moving parts and sharp corners. This article describes 2D SPH simulations of a Twin Cam mixer and compares the results against experimental data and results from two published finite element method (FEM) simulations. To analyze the mixing processes in the Twin Cam mixer, we present a method for calculating the Finite-Time Lyapunov Exponent (FTLE) using SPH particle data. The FTLEs can be used to locate the unstable and stable manifolds in the flow and indicate where mixing is either promoted or inhibited in the flow. We also present a local measure of how two or more fluids are “mixed” at a point in the domain. This is used to find the time-scales of mixing over different regions in the domain and at different length-scales. The purpose of the article is to evaluate the effectiveness of SPH, FTLEs, and our mixing measure in simulating and analyzing the mixing in a typical industrial mixer. © 2008 American Institute of Chemical Engineers AIChE J, 2008