NUMERICAL SIMULATION OF THERMOCAPILLARY FLOW 2D AND 3D: A BI-PHASE SMOOTHED PARTICLE HYDRODYNAMICS APPROACH

Resumo

This work presents a Smoothed Particle Hydrodynamics (SPH) method for modeling the heat transfers,
natural convection, and thermal Marangoni effects at the interface with density variation and bi-phase fluid flows
in two and three dimensions. A capillary interface (surface tension) scheme was implemented with the Continuum
Surface Force (CSF) model and the approximation of the SPH to the Navier-Stokes equations for delimiting stable
interfaces and smooth bi-phase to allow the simulation of flows between liquid-liquid and liquid-gas. Moreover,
the solution strategy with SPH for the combination of temperature gradient (heat transfers), gravity, and surface

tension, as required for modeling the Marangoni forces, is verified with related cases of study. Problems of ther-
mally driven flow and Bernard convection in cavities are studied to validate the heat transfer and convection. The

solutions are displayed in respect of temperature, velocity fields, and Nusselt number, with different Rayleigh
numbers (Ra) regimes (103 ≤ Ra ≤ 106

). Thus, the bi-phase method applies the thermo-capillary flow, in the
migration rises a droplet due to a surrounding fluid with a linear temperature gradient. In these cases, different

aspects of the dynamics of the thermo-capillary flow were considered for verification. Finally, the numerical ex-
amples show that the SPH and CSF proposal is efficient, reliable, and with good precision in modeling inter-facial

flow problems under hydrodynamic and thermal influences.