Direct numerical simulation of complex multi-fluid flows using a combined front tracking and immersed boundary method

In this paper a simulation model is presented for the Direct Numerical Simulation (DNS) of complex multi-fluid flows in which simultaneously (moving) deformable (drops or bubbles) and non-deformable (moving) elements (particles) are present, possibly with the additional presence of free surfaces. Our model combines a Front Tracking (FT) model developed by van Sint Annaland et al. (2008. Numerical simulation of dense gas–solid fluidized beds: a multiscale modeling strategy. Ann. Rev. Fluid Mech. 40, 47–70.) and an Immersed Boundary (IB) model developed by van der Hoef et al. (2008. Numerical simulation of dense gas–solid fluidized beds: a multiscale modeling strategy. Ann. Rev. Fluid Mech. 40, 47–70.) The FT part circumvents the explicit computation of the interface curvature. The IB part incorporates both particle–fluid and particle–particle interaction via a direct forcing method and a hard sphere Discrete Particle (DP) approach. In our model a fixed (Eulerian) grid is utilised to solve the Navier–Stokes equations for the entire computational domain. The no-slip condition at the surface of the moving particles is enforced via a momentum source term that only acts in the vicinity of the particle surface. For the enforcement of the no-slip condition Lagrangian force points are used, which are distributed evenly over the surface of the particle. Dissipative particle–particle and/or particle–wall collisions are accounted via a hard sphere DP approach using a three-parameter particle–particle interaction model accounting for normal and tangential restitution and tangential friction. The capabilities of the hybrid FT-IB model are demonstrated with a number of examples in which complex topological changes in the interface are encountered.