Numerical simulations of a Pyroclastic Density Current: influence of turbulence, heat exchange, obstacles and ash grain size distribution. (original) (raw)
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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, in- vestigating 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 Perfor- mance 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.
ASHEE-1.0: a compressible, equilibrium–Eulerian model for volcanic ash plumes
A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydis-perse gas–particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations for a mixture of gases and solid dispersed particles, we adopt an asymptotic expansion strategy to derive a com-pressible version of the first-order non-equilibrium model, valid for low-concentration regimes (particle volume fraction less than 10 −3) and particle Stokes number (St – i.e., the ratio between relaxation time and flow characteristic time) not exceeding about 0.2. The new model, which is called ASHEE (ASH Equilibrium Eulerian), is significantly faster than the N-phase Eulerian model while retaining the capability to describe gas–particle non-equilibrium effects. Direct Numerical Simulation accurately reproduces the dynamics of isotropic, compressible turbulence in subsonic regimes. For gas–particle mixtures, it describes the main features of density fluctuations and the preferential concentration and clustering of particles by turbulence, thus verifying the model reliability and suitability for the numerical simulation of high-Reynolds number and high-temperature regimes in the presence of a dispersed phase. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce the averaged and instantaneous flow properties. In particular , the self-similar Gaussian radial profile and the development of large-scale coherent structures are reproduced, including the rate of turbulent mixing and entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of the important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal and maximum plume height. For very fine particles (St → 0, when non-equilibrium effects are negligible) the model reduces to the so-called dusty-gas model. However, coarse particles partially decouple from the gas phase within eddies (thus modifying the turbulent structure) and preferentially concentrate at the eddy periphery, eventually being lost from the plume margins due to the concurrent effect of gravity. By these mechanisms, gas–particle non-equilibrium processes are able to influence the large-scale behavior of volcanic plumes.
Multiparticle simulation of collapsing volcanic columns and pyroclastic flow
[1] A multiparticle thermofluid dynamic model was developed to assess the effect of a range of particle size on the transient two-dimensional behavior of collapsing columns and associated pyroclastic flows. The model accounts for full mechanical and thermal nonequilibrium conditions between a continuous gas phase and N solid particulate phases, each characterized by specific physical parameters and properties. The dynamics of the process were simulated by adopting a large eddy simulation approach able to resolve the large-scale features of the flow and by parametrizing the subgrid gas turbulence. Viscous and interphase effects were expressed in terms of Newtonian stress tensors and gas-particle and particle-particle coefficients, respectively. Numerical simulations were carried out by using different grain-size distributions of the mixture at the vent, constitutive equations, and numerical resolutions. Dispersal dynamics describe the formation of the vertical jet, the column collapse and the building of the pyroclastic fountain, the generation of radially spreading pyroclastic flows, and the development of thermal convective instabilities from the fountain and the flow. The results highlight the importance of the multiparticle formulation of the model and describe several mechanical and thermal nonequilibrium effects. Finer particles tend to follow the hot ascending gas, mainly in the phoenix column and, secondarily, in the convective plume above the fountain. Coarser particles tend to segregate mainly along the ground both in the proximal area close to the crater rim because of the recycling of material from the fountain and in the distal area, because of the loss of radial momentum. As a result, pyroclastic flows were described as formed by a dilute fine-rich suspension current overlying a dense underflow rich in coarse particles from the proximal region of the flow. Nonequilibrium effects between particles of different sizes appear to be controlled by particle-particle collisions in the basal layer of the flow, whereas particle dispersal in the suspension current and ascending plumes is determined by the gas-particle drag. Simulations performed with a different grain-size distribution at the vent indicate that a fine-grained mixture produces a thicker and more mobile current, a larger runout distance, and a greater elutriated mass than the coarse-grained mixture.
Coupling of turbulent and non-turbulent flow regimes within pyroclastic density currents
Volcanic eruptions are at their most deadly when pyroclastic density currents sweep across landscapes to devastate everything in their path 1,2. The internal dynamics underpinning these hazards cannot be directly observed 3. Here we present a quantitative view inside pyroclastic density currents by synthesizing their natural flow behaviour in large-scale experiments. The experiments trace flow dynamics from initiation to deposi-tion, and can explain the sequence and evolution of real-world deposits. We show that, inside pyroclastic density currents, the long-hypothesized non-turbulent underflow and fully turbulent ash-cloud regions 4,5 are linked through a hitherto unrecognized middle zone of intermediate turbulence and concentration. Bounded by abrupt jumps in turbulence, the middle zone couples underflow and ash-cloud regions kinematically. Inside this zone, strong feedback between gas and particle phases leads to the formation of mesoscale turbulence clusters. These extremely fast-settling dendritic structures dictate the internal stratification and evolution of pyroclastic density currents and allow the underflows to grow significantly during runout. Our experiments reveal how the underflow and ash-cloud regions are dynamically related—insights that are relevant to the forecasting of pyroclastic density current behaviour in volcanic hazard models. For more than 50 years, the transport and deposition of pyroclastic density currents (PDCs) have remained amongst the most hotly debated issues in volcanology 1,5–7. Due to their unpredictability and extreme violence, PDC deposits have been relied upon to infer flow dynamics 4,8. PDC deposits range from massive to highly stratified types 9,10. These extremes led to the conceptualization of two endmembers of PDC transport, one as a dry granular or gas-fluidized granular flow of high particle concentration 5,11,12 , and the other as a dilute fully turbulent gravity current 13,14. Attempts have been made to unify these endmembers, both theoretically 15 and with numerical modelling studies 16. However, large uncertainties remain about the multiphase physics of coupled concentrated/dilute particle-gas transport 17. Thus, even conceptual paradigms of the internal structure of PDCs remain highly controversial 4 , and envisage either rigid, coexisting zones of concentrated laminar and dilute fully turbulent transport regimes 6–8 , or a continuous gradation between them 9,10. Here we report on gas–particle flows produced by the gravitational collapse of 1.5 tons of volcanic material (Methods, Supplementary Fig. 1 and Supplementary Movie 1). As in nature, experimental currents of pumice, ash and air were synthesized by a t = 0.04 s t = 0.08 s t = 0.16 s t = 0.12 s t = 0.30 s t = 0.39 s t = 0.01 s C U b U C GP CL c CU Figure 1 | Synthesizing pyroclastic density currents in large-scale experiments. a, Side view of an experimental pyroclastic density current at the eruption simulator PELE. b, Lower 0.95 m of the flow at a runout distance of 3 m at diierent times. c, Passage of the head region at 3 m. Arrows highlight the interfaces between underflow (U, lower zone) and ash-cloud regions (C) (black), and between middle (CL) and upper (CU) zones of the pyroclastic density current, respectively. Rapid sedimentation of dendritic clusters of mesoscale turbulence entraps gas pockets (GP) in the underflows. Vertical scaling bars are 0.3-m long.
Volcanica, 2020
Pyroclastic density currents (PDCs) are a prominent hazard of volcanic activity; however, fully quantitative observations are lacking and little direct evidence exists to constrain the parameters controlling ash production and runout. Here, we use rotary tumbling experiments to investigate ash generation efficiency and clast morphometrics in the dense basal flow of PDCs. We observe greater ash generation with periodic ash removal and with higher starting mass. By scaling to the bed height and clast diameter we obtain a general description for ash production in all experiments as a function of flow distance that we parameterise in dimensionless space. We also show that ash production correlates with clast shape changes and with the Inertial number for our experiments. This work introduces some of the first systematic and generalizable experimental parameterizations of ash production and clast evolution in PDCs and should advance the ability to understand flow mobility and associated ...
In the framework of the IAVCEI (International Association of Volcanology and Chemistry of the Earth Interior) in-tercomparison study on volcanic plume models, we present three-dimensional (3D) numerical simulations carried out with the ASHEE (ASH Equilibrium Eulerian) model. The ASHEE model solves the compressible balance equations of mass, momentum, and enthalpy of a gas-particle mixture and is able to describe the kinematic decoupling for particles characterized by Stokes number (i.e., the ratio between the particle equilibrium time and the flow characteristic time) lower than 0.2 (or particles smaller than about 1 mm). The computational fluid dynamic model is designed to accurately simulate a turbulent flow field using a Large Eddy Simulation approach , and is thus suited to analyze the role of particle non-equilibrium in the dynamics of turbulent volcanic plumes. The two reference scenarios analyzed correspond to a weak (mass eruption rate = 1.5* 10 6 kg/s) and a strong volcanic plume (mass eruption rate = 1.5*10 9 kg/s) in absence of wind. For each scenario, we compare the 3D results, averaged in space and time, with theoretical results obtained from integral plume models. Such an approach enables quantitative evaluation of the effects of grid resolution and the subgrid-scale turbulence model, and the influence of gas-particle non-equilibrium processes on the large-scale plume dynamics. We thus demonstrate that the uncertainty on the numerical solution associated with such effects can be significant (of the order of 20%), but still lower than that typically associated with input data and integral model approximations. In the Weak Plume case, 3D results are consistent with the predictions of integral models in the jet and plume regions, with an entrainment coefficient around 0.10 in the plume region. In the Strong Plume case, the self-similarity assumption is less appropriate and the entrainment coefficient in the plume region is more unstable, with an average value of 0.24. For both cases, integral model predictions diverge from the 3D plume behavior in the umbrella region. The presented analysis of 3D numerical simulations thus enables identification of the critical hypotheses that underlie integral models used in operational studies. In addition, high-resolution 3D runs allow reproduction of observable quantities (such as infrasound signals) which can be useful for constraining eruption dynamics during real events.
The dynamics of pyroclastic density currents down volcanic slopes
2015
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...