Numerical Study of Spheroidal Particles with Non-Uniform-Varied Temperature Settling in a Viscous Flow

The fully resolve simulation of heat transfer from the non-spherical rigid particles settling in a viscous flow is performed by the discrete forcing immersed boundary (IB) method. The method is employed to represent the hydrodynamic interactions of fluid-solid phases and a volume of fluid (VoF) approach is applied to account the heat transfer both inside and outside the solid particles. The Boussinesq approximation is used for the coupling of momentum and energy equations. The effects of solid to fluid thermal conductivity ratios (kr) ranging between 0.1 to 10 and different Grashof numbers (Gr) up to 5000 are examined to study the behavior of a single spheroidal particle with variable temperature and aspect ratios of 1/3 (oblate), 1 (sphere) and 3 (prolate). The simulations show that for the same thermal condition, the cooling/heating time of oblate particles is greater than the prolates in the free falling processes and the perfect spheres have the lowest cooling/heating time. Furthermore, we identify that for the non-spherical particles and the Grashof and Galilean (Ga) numbers less than 5000 and 50, respectively, the threshold of kr to solve the energy equation inside the particles is kr = 0.1 and for the thermal conductivity ratio higher than this value, the heating/cooling of the particles is fast enough to assume that the temperature over the solid particle changes uniformly.

Keywords:

fully resolved simulation , heat transfer , free falling , non-spherical particles , variable temperature