• computational fluid dynamics
• gravity currents on slopes
• multiphase flow modeling
• Pyroclastic density currents

Pyroclastic density currents (PDCs) are moving mixtures of gas and solid particles of different sizes resulting from magma fragmentation in explosive volcanic eruptions and from gravity-driven collapse of lava domes. They are among the most dangerous and destructive natural phenomena but, because of the complexity of their dynamics and the difficulty of direct observations, they remain not completely understood and fatalities continue to result from unsuccessfully predicted flow behaviors.
Pyroclastic flows are recognized as a class of gravity currents (i.e., a fluid motion driven by density contrast in the gravity field) caused by the presence of suspended solid particles in a gas. Such currents, characterized by the propagation of a turbulent front and by a stratified structure, occur in a variety of other geophysical situations and industrial applications.
The spatio-temporal evolution of a gravity current has been analyzed extensively both theoretically and experimentally in the Boussinesq limit (i.e. for small density contrasts) in the dam-break configuration (i.e. by releasing a fixed volume of dense fluid from an enclosed lock) over flat, horizontal surfaces. However this is often not the case in a volcanological context as volcanoes show an angle of incline up to 40 degrees and large density differences exist in pyroclastic flows. From experimental and numerical analysis of gravity currents on slopes, some substantial differences against the horizontal case emerge: the front position and dimensions, which are among the most relevant parameters for a volcanic hazard prevention, reveal a strong dependence from the angle of incline.
In this work, the dynamics of PDC are studied by means of a two-dimensional computational model describing both the dilute and concentrated regime of gas-particle currents. Although the turbulence structure of gravity currents is three-dimensional, the dynamics are closely reproduced by two-dimensional simulations because the generation of the structures responsible of their motion is essentially a two-dimensional mechanism. This allows to deal with a simplified two dimensional problem as justified by the comparison with experimental results.
The PDAC numerical model, used for the analysis contained in this thesis, is a multiphase flow model: it describes particle-laden gravity currents as systems made of different phases, defined as chemical species, in solid, liquid or gas state. In order to analyze the behaviour of the whole fluid each phase is treated individually considering its mean thermodynamical and dynamical properties and the coupling terms with other phases.
In the first part of the thesis, after the description of the used numerical model, particle-driven gravity currents on flat surfaces are analyzed. The results are shown to be in good agreement with the theoretical model predictions. Then, in order to establish appropriate simulation conditions, an analysis of the influence of initial parameters is made. This analysis allows to fix the initial geometry, the appropriate spatial resolution and the turbulence and rheological models required to correctly describe the dissipative effects.
Afterward a comparison between the horizontal and the inclined flow in dilute conditions is made. It is shown that the dynamics of the flow are strongly influenced by the angle of incline: while the height of the front in the horizontal case attains a constant values, in the inclined one it drastically grows. This is due to the process of entrainment of the ambient fluid into the current, increased with respect to the horizontal case, and to the feeding of the front from the fluid layers behind, which move faster than the front itself. For the horizontal current this latter effect is not observed.
This attitude has consequences on the front velocity, and thus on the runout: in the first stage the motion on slopes is faster and reaches a larger runout but, at later times, a transition to a deceleration regime is observed. This behaviour can be attributed to the higher resistance acting on the fluid due to the growth of its front and to the consequent dilution. For highly dilute flows the horizontal currents even overtakes the inclined ones. Again a good agreement with experimental data concerning diluted gravity currents on slopes is shown.
In a further analysis the effects of the initial particles concentration and of the temperature on the currents flow have been studied. It results that currents with a larger initial solid concentration undergo a more rapid development, resulting in a greater runout. This is a direct consequence of the larger effective gravity acting on the denser currents. The flows with an high temperature appear characterized by rising convective columns that cause a drastic reduction of the front velocity and, consequently, of the runout. These features are enhanced by the presence of a slope. In this framework, the presence of a basal dense layer subject to the gravity component parallel to the slope takes an active role in the flow dynamics of a gravity current, while it is shown to have negligible consequences for flows on horizontal boundaries. Actually the presence of coarser particles accelerates the stratification process, because of the particles sedimentation, and the associated dilution in the higher layers of the current. A rapid establishment of the concentrated basal layer is clearly observed for currents constituted by coarse particles.
Finally, numerical simulations of PDC propagation along the Southern slopes of Vesuvius volcano have been performed, and the above analysis has been applied in order to provide a coherent computational framework for PDC hazard assessment.