Dynamics of chocolate fountains

We present a three-dimensional direct numerical simulation of a heated chocolate fountain using both dynamical and thermal properties of melted chocolate (60 C) flowing in an ambient atmosphere (20 C). We solve both the Navier-Stokes and the energy equation using a front-tracking-based multiphase method that accounts for both the Newtonian (ambient air) and Non-Newtonian (melted chocolate) fluids, and a direct forcing method technique for the rotational motion of a vertical Archimedes screw. Our numerical framework circumvents numerous meshing issues normally associated with constructing complex geometries within typical computational fluid dynamics packages. The considered device in the present work is composed of a static (motionless) chocolate fountain structure with a fast-rotating vertical Archimedes Screw in it; both of these are constructed via a module that defines solid objects by means of distance functions, which are positive for the fluid part and negative for the solid part. The construction combines primitive objects, such as cylinders, planes, and ellipsoids and combined with simple geometrical operations such as union and intersection. Finally, within a single simulation, we will highlight the multitude of classical flows such as falling film, interfacial singularities, and coiling liquid films.