Unified, Multi-Phase, Numerical Method Using Volume-of-Fluid Transport Models

Multiphase fluid flows involving free surface fluids can be found in many space transportation and propulsion systems such as injector atomization in SSME combustors, cavitation in liquid rocket pump operations, handling of cryogenic fluids in a micro- gravity environment and the operation of cryogenic propellants on board spacecraft. The innovative feature of the proposed Phase I effort is to combine the novel feature of the Volume of Fluid (VOF) method and the Eulerian/Lagrangian method into a unified solution algorithm for efficient, time-accurate calculations of multiphase free surface flows valid at all speeds. The proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and gas) and tracks droplets on a lagrangian frame using a unified predictor-corrector technique to account for the non-linear linkages through the convective contributions of VOF. The discontinuities within the sharp interface will be modeled as a volume force to avoid stiffness. The proposed method will be implemented into the FDNS code which has three-dimensional, multi- zone and combined Eulerian-Lagrangian capabilities. Further exten sions of the current proposed algorithm for handling other flow processes such as turbulence, droplet coalescence and chemistry are extremely feasible.