Numerical Simulation of the Melting of Solid Particles in Thermal Convection with a Modified Immersed Boundary Method

A new immersed boundary method is proposed for the numerical simulation of the melting of solid particles in its own liquid at a high temperature. The main feature of the new method is the use of the modified direct-forcing immersed boundary method for the solution of the flow field and the sharp-interface immersed boundary method for the temperature field. The accuracy of the proposed method is validated via three problems: the sedimentation of a non-melting particle, the melting of a fixed particle under mixed thermal convection, and the sedimentation of a melting particle. The method is then applied to the investigation of the effects of various parameters, the particle interactions and the particle shape on the particle melting time. A correlation for the melting time of a circular particle in forced thermal convection is established as a function of the Reynolds, Prandtl, and Stefan numbers. The melting time of a particle in mixed thermal convection first increases and then decreases, as the Grashof number increases. The effects of the particle interactions on the melting time are complicated due to the natural convection between two particles. The sufficiently strong natural convection can even render the downstream particle melt faster than the single particle. For the same particle area, the elliptic particle with the aspect ratio being around 1.4 melts most slowly.