Modeling dispersed gas-particle turbulence in volcanic ash plumes

This PhD thesis focuses on numerical and analytical methods for simulating the dynamics of volcanic ash plumes. The study starts from the fundamental balance laws for a multiphase gas– particle mixture, reviewing the existing models and developing a new set of Partial Differential Equations (PDEs), well suited for modeling multiphase dispersed turbulence. In particular, a new model generalizing the equilibrium–Eulerian model to two-way coupled compressible flows is developed. The PDEs associated to the four-way Eulerian-Eulerian model is studied, investigating the existence of weak solutions fulfilling the energy inequalities of the PDEs. In particular, the convergence of sequences of smooth solutions to such a set of weak solutions is showed. Having explored the well-posedness of multiphase systems, the three-dimensional compressible equilibrium–Eulerian model is discretized and numerically solved by using the OpenFOAM® numerical infrastructure. The new solver is called ASHEE, and it is verified and validated against a number of well understood benchmarks and experiments. It demonstrates to be capable to capture the key phenomena involved in the dynamics of volcanic ash plumes. Those are: turbulence, mixing, heat transfer, compressibility, preferential concentration of particles, plume entrainment. The numerical solver is tested by taking advantage of the newest High Performance Computing infrastructure currently available. Thus, ASHEE is used to simulate two volcanic plumes in realistic volcanological conditions. The influence of model configuration on the numerical solution is analyzed. In particular, a parametric analysis is performed, based on: 1) the kinematic decoupling model; 2) the subgrid scale model for turbulence; 3) the discretization resolution. In a one-dimensional and steady-state approximation, the multiphase flow model is used to derive a model for volcanic plumes in a calm, stratified atmosphere. The corresponding Ordinary Differential Equations (ODEs) are written in a compact, dimensionless formulation. The six non-dimensional parameters characterizing a multiphase plume are then written. The ODEs is studied both numerically and analytically. Different regimes are analyzed, extracting the first integral of motion and asymptotic solutions. An asymptotic analytical solution approximating the model in the general regime is derived and compared with numerical results. Such a solution is coupled with an electromagnetic model providing the infrared intensity emitted by a volcanic ash plume. Key vent parameters are then retrieved by means of inversion techniques applied to infrared images measured during a real volcanic eruption.