Multiphase flows comprise two or more phases of matter (solid, liquid, gas, etc) that are simultaneously present and are allowed to inter-penetrate (Prosperetti and Tryggvason, 2007). Furthermore, each phase is classed as either continuous or dispersed, where a continuous phase is a connected liquid or gas substance in which dispersed phases (comprising a finite number of solid particles, liquid droplets and/or gas bubbles) may be immersed (Crowe et al., 1998).
Fluidity features two multiphase flow models; one for incompressible flow and another for compressible flow. To enable the mixing and inter-penetration of phases, a separate velocity field (and hence a separate momentum equation) is assigned to each one and solved for. Extra terms are then included to account for inter-phase interactions. Furthermore, the models currently assume no mass transfer between phases, and a common pressure field so that only one continuity equation is used.
More details of the models' implementation can be found in the PhD thesis by Jacobs (2013):In this example, Fluidity's incompressible multiphase flow model is used to replicate a laboratory experiment of volcanic ash particles settling through a tank of water (Carey, 1997). The experiments by Carey (1997) introduced tephra particles into a 0.3 x 0.3 x 0.7 m tank, filled with water, from above using a delivery system and a particle disperser. The particles settled through the air in the tank at an approximately constant rate until they landed in the water and began to settle through the water at a much reduced velocity. While the particles in the water were sufficiently dispersed their settling velocity was that predicted by Stokes' flow (a few mm/s). However, the build-up of particles caused by the air-water interface eventually created a layer of particles and water with a bulk density so great, relative to the density of the particle-poor water beneath, as to be gravitationally unstable and promote the formation of a vertical gravity current (plumes). The settling velocity of these plumes of particles and water was observed to be an order of magnitude greater than the Stokes settling velocity of the individual particles.
Comparable results were achieved with Fluidity, and a video of a 2D version of the simulation illustrating plume formation and growth can be seen below:
Further details about these volcanic ash simulations, and the verification and validation of Fluidity's multiphase flow model in general, can be found in the following papers:
In this example, Fluidity's compressible multiphase flow model is used to simulate an explosive volcanic eruption (although note that the eruption does not correspond to a particular past eruption event). Hot ash and gas at 1,200 K are ejected at 80 ms-1 into the 7 x 7 km domain through the vent of the volcano, forming a large ash plume. The qualitative results agree well with field observations from actual volcanic eruption events. In the video below, the initial blast wave can be seen at early times, followed by plume growth and ascent. When the plume reaches a height of approximately 700 m, it collapses to form a dense pyroclastic flow that travels along the ground at high speed. A dilute convective region can also be seen that rises high above the main volcanic ash fountain due to buoyancy effects.
Further details about these simulations can be found in the following papers: