Inertial Particle Dispersion in the Lagrangian Wake of a Square Cylinder

A numerical investigation is presented into the relation between finite sized, inertial particle transport and entrainment in the vortex-dominated wake of a square cylinder placed in a channel at two blockage ratios and Lagrangian Coherent Structures (LCS) identified with recent Lagrangian visualization techniques. The square cylinder flow is computed with the incompressible, viscous flow solver in Fluent at a Reynolds number of 150 ensuring a periodic Karman street in the cylinder’s wake. The traces of fluid and inertial particle are determined with Fluent’s Discrete Phase Model, that models finite sized particles as points. The MANGEN software is used to determine contours of the Finite Time Lyapunov Exponent (FTLE) in the fluid particle flow using time-dependent flow field data computed with Fluent as input. Fluid particle transport barriers or Lagrangian Coherent Structures that repel fluid particles as visualized by maxima in the FTLE contours determined in forward-time form lobes in front of the cylinder that entrain fluid particles into the near wake behind the square. Inertial particles having a delayed response to the fluid do not entrain into the near wake for particle response times greater than ten percent of the characteristic flow time. Inertial particles closely follow the attracting structures as visualized by the FTLE in backward time up to a Stokes number of unity, when particles focus along the transport barriers. When the particle response time is comparable to the shedding period, particles are entrained in the far wake between large coherent vortex structures. With increased blockage, transport barriers form of the walls that are convected downstream along the wall and interact with the structures in the wake of the cylinder. The fluid and inertial particles closely following the transport barriers show an enhanced mixing with increased blockage.