Validation Approaches to Volcanic Explosive Phenomenology

Large-scale volcanic eruptions are inherently hazardous events, hence cannot be described by detailed and accurate in situ measurements. As a result, volcanic explosive phenomenology is poorly understood in terms of its physics and inadequately constrained in terms of initial, boundary, and inflow conditions. Consequently, little to no real-time data exist to validate computer codes developed to model these geophysical events as a whole. However, code validation remains a necessary step, particularly when volcanologists use numerical data for assessment and mitigation of volcanic hazards as more often performed nowadays. We suggest performing the validation task in volcanology in two steps as followed. First, numerical geo-modelers should perform the validation task against simple and well-constrained analog (small-scale) experiments targeting the key physics controlling volcanic cloud phenomenology. This first step would be a validation analysis as classically performed in engineering and in CFD sciences. In this case, geo-modelers emphasize on validating against analog experiments that unambiguously represent the key-driving physics. The second “geo-validation” step is to compare numerical results against geophysical-geological (large-scale) events which are described ?as thoroughly as possible? in terms of boundary, initial, or flow conditions. Although this last step can only be a qualitative comparison against a non-fully closed system event —hence it is not per se a validation analysis—, it nevertheless attempts to rationally use numerical geo-models for large-scale volcanic phenomenology. This last step, named “field validation or geo-validation”, is as important in order to convince policy maker of the adequacy of numerical tools for modeling large-scale explosive volcanism phenomenology.

Computational Modeling of Gas-Solids Fluidized-Bed Polymerization Reactors

Gas-solid flows have numerous industrial applications and are also found in natural processes. They are involved in industries like petrochemical, polymer, pharmaceutical, food and coal. Fluidization is a commonly used gas-solid operation and is widely used in production of polyethylene. Polyethylene is one of the most widely used thermoplastics. Over 60 million tons are produced worldwide every year by both gas-phase and liquid-phase processes. Gas-phase processes are more advantageous and use fluidized-bed reactors (e.g., UNIPOLTM PE PROCESS and Innovene process) for the polymerization reactions. In this work a chemical-reaction-engineering model incorporating a given catalyst size distribution and polymerization kinetics along with the quadrature method of moments is used to predict the final polymer size distribution and temperature. An Eulerian-Eulerian multi-fluid model based on the kinetic theory of granular flow is used to solve the fluidized-bed dynamics and predict behavior such as particle segregation, slug flow and other non-ideal phenomena.

Quadrature-Based Moment Methods for Polydisperse Gas-Solids Flows

Classical Euler-Euler two-fluid models based on the kinetic theory of granular flows assume the particle phase to be dominated by collisions, even when the particle volume fraction is low and hence collisions are negligible. This leads to erroneous predictions of the particle-phase flow patterns and to the inability of such models to capture phenomena like particle trajectory crossing for finite Stokes numbers. To correctly predict the behavior of dilute gas-particle flows a more fundamental approach based on solving the Boltzmann kinetic equation is necessary to treat non-zero Knudsen-number and finite Stokes-number conditions. In this chapter an Eulerian quadrature-based moment method for the direct solution of the Boltzmann equation is adopted to describe the particle phase, and it is fully coupled with an Eulerian fluid solver to account for the two-way coupling between the phases. The solution algorithm for the moment transport equations derived in the quadrature-based moment method and the coupling procedure with a fluid solver are illustrated. The predictive capabilities of the method are shown considering a lid-driven cavity flow with particles at finite Stokes and Knudsen numbers, and comparing the results with both Euler-Euler two-fluid model predictions and with Euler-Lagrange simulations.

Mass and Heat Transfer Modeling

Mass and heat transfer are important to reactor modeling using CFD. Reactants (mass) move within the flow structure in order to react with other species and thereby form the products, both desirable and undesirable. This movement in mass occurs either by diffusion or by turbulent dispersion. In a similar fashion, heat is transferred from one point in the flow structure to another point by convective transfer between the phases and with the translational effect that occurs with the turbulent dispersion of the mass. In addition, heat can be transferred across the system boundary. In all these cases, fundamental mechanistic models are put forward that can be incorporated in the CFD code to calculate these transfer properties based upon the local hydrodynamic conditions. The chapter is organized such that dense phase systems are covered first and then dilute phase systems. Within each of these areas mass transfer is covered first and followed by heat transfer. The topics are covered in the following order: Diffusional mass transfer, Turbulent dispersion, Convective heat transfer between phases and Convective heat transfer at the system boundary.

CFD Modeling of Bubbling Fluidized Beds of Geldart A Powders

Fluidized beds have applications in a range of industrial sectors from oil refining and coal combustion to pharmaceutical manufacture and ore roasting. In spite of more than 80 years of industrial experience and a tremendous amount of academic attention, the fundamental understanding of fluidized bed hydrodynamics is still far from complete. Advanced modeling using computational fluid dynamics is one tool for improving this understanding. In the current chapter the focus is on the application of CFD to a particularly challenging yet industrially relevant area of fluidization: fluidized beds containing Geldart A powders where interparticle forces influence the bed behavior. A critical step in modeling these systems is proper representation of the interfacial drag closure relations. This is because the interparticle cohesive forces lead to the formation of clusters that reduce the drag below that for non-cohesive particles. The influence on the predictions of the macroscale fluidized behavior due to mesoscale phenomena such as clustering is discussed. At present in the literature, approaches to representing the reduced drag arising from mesoscale phenomena is ad hoc. There is a pressing need for an improved understanding of cluster formation and for robust models describing it that can be incorporated into coarse grid models of industrial scale fluidized beds.

Direct Numerical Simulation of Gas-Solids Flow Based on the Immersed Boundary Method

In this chapter, the Direct numerical simulation (DNS) of flow past particles is described. DNS is a first-principles approach for modeling interphase momentum transfer in gas-solids flows that does not require any further closure as the flow around the particles is fully resolved. In this chapter, immersed boundary method (IBM) is described where the governing Navier-Stokes equations are modeled with exact boundary conditions imposed at each particle surface using IBM and the resulting three dimensional time-dependent velocity and pressure fields are solved. Since this model has complete description of the gas-solids hydrodynamic behavior, one could extract all the Eulerian and Lagrangian statistics for validation and development of more accurate closures which could be used at coarse-grained simulations described in other chapters.

The Multiphase Particle-in-Cell (MP-PIC) Method for Dense Particle Flow

This chapter is a review of the multiphase particle-in-cell (MP-PIC) numerical method for predicting dense gas-solids flow. The MP-PIC method is a hybrid method such as IBM method described in the previous chapter, where the gas-phase is treated as a continuum in the Eulerian reference frame and the solids are modeled in the Lagrangian reference frame by tracking computational particles. The MP-PIC is a derivative of the Particle-in-Cell (PIC) method for multiphase flows and the method employs a fixed Eulerian grid, and Lagrangian parcels are used to transport mass, momentum, and energy through this grid in a way that preserves the identities of the different materials associated with the particles. The main distinction with traditional Eulerian-Lagrangian methods is that the interactions between the particles are calculated on the Eulerian grid. One of the main advantages of PIC methods is the accuracy of the convection algorithms (Lagrangian advection is non-diffusive) and this can be important aspect of gas-solids flows where the overall dynamics is dictated by the instabilities in the system due to sharp interfaces between the phases. Additional details about this method along with examples are provided in this chapter. In the following chapter, the application of this method to Circulating Fluidized Beds (CFBs) is described.

Coupled Solvers for Gas-Solids Flows

In recent years, the application of coupled solver techniques to solve the Navier-Stokes equations has become increasingly popular. The main reason for this, is the increased robustness originating from the implicit and global treatment of the pressure-velocity coupling. The drawback of a coupled solver are the increase in memory requirement and the increased complexity of implementation. However, fully coupled methods are reported to have an overall favorable computational cost when a suitable pre-conditioner and algorithm for solving the resulting set of linear equations are employed. In solving multi-phase flow problems, the coupled solver approach is even more advantageous than in single-phase, due to the presence of large source terms arising from the coupling of the phases. In this chapter, various strategies for the fully coupled approach are discussed. These strategies include employing artificial compressibility, applying physically consistent cell face interpolation, and applying momentum weighted cell face interpolation. The idea behind the strategies is outlined and their advantages and disadvantages are discussed. The treatment of source terms and volume fraction in coupled methods is also shown. Finally, a number of examples of implementations and calculations are presented.

Circulating Fluidized Beds

In the last 20 years, significant improvements in the computational fluid dynamics (CFD) modeling have been made that allow the simulation of large-scale, commercial CFBs. Today, commercial codes are available that can model some of this behavior in large-scale, commercial units in a reasonable amount of time. However, the hydrodynamics in a riser or fluidized bed are complex with both micro and macroscale features. From particle clustering to large streamers to the core-annulus profile, the particle behavior in these unit operations rarely behaves as a “continuous fluid.” Even the role of particle size distribution is often neglected and models that do consider particle size distribution don’t always consider the role of particle size on granular temperature. Many models use insufficient boundary conditions by assuming uniform or symmetric profiles, which is rarely the case. Furthermore, grid sizing is usually based on computer limitations instead of model limitations, and many models of commercial systems extend beyond the capability of the constitutive equations being used. Successful application of today’s CFD models requires a good understanding of the equations behind the code, the assumptions used for those equations and the capability or limitations of the code. CFD is nothing more than a guess without an understanding of the fundamentals, underlying assumptions and code limitations that are part of every model.

Interfacial Interactions

The drag interaction between gas and solids not only acts as a driving force for solids in gas-solids flows but also plays as a major role in the dissipation of the energy due to drag losses. This leads to enormous complexities as these drag terms are highly non-linear and multiscale in nature because of the variations in solids spatio-temporal distribution. This chapter provides an overview of this important aspect of the hydrodynamic interactions between the gas and solids and the role of spatio-temporal heterogeneities on the quantification of this drag force. In particular, a model is presented which introduces a mesoscale description into two-fluid models for gas-solids flows. This description is formulated in terms of the stability of gas-solids suspension. The stability condition is, in turn, posed as a minimization problem where the competing factors are the energy consumption required to suspend and transport the solids and their gravitational potential energy. However, the lack of scale-separation leads to many uncertainties in quantifying mesoscale structures. The authors have incorporated this model into computational fluid dynamics (CFD) simulations which have shown improvements over traditional drag models. Fully resolved simulations, such as those mentioned in this chapter and the subject of a later chapter on Immersed Boundary Methods, can be used to obtain additional information about these mesoscale structures. This can be used to formulate better constitutive equations for continuum models.