Reactive flows modelling, problems

Analytically Reduced Mechanisms Some problems can be described by models that involve a full reaction mechanism in combination with simplied fluid dynamics. Other applications may involve laminar or turbulent multidimensional reactive flows. For problems that require a complex mathematical flow description (possibly CFD), the computational cost of using a full mechanism may be prohibitive. An alternative is to describe... 

The intent of this was to start with a useful calculation, which could not be done using brute force techniques, and demonstrate the importance of optimizing the numerical implementation of a reactive flow model to run on a vector computer. As similar problems in combustion become more extensive and intricate, it behooves us to utilize computers in the most efficient manner possible. It is no longer feasible to continue to "ask the computer to do more and more work, without thought as to how a particular problem is to be implemented. The number of problems for which one would like to use a computer, as well as the complexity of these problems, is increasing at an astronomical rate. The other side of the coin, of course is that computers, and especially central processors (CPU s) are becoming cheaper. 

Another particularly important topic in the modeling of strongly nonlinear phenomena is the occurrence of multiple fronts. For instance, in a supersonic reactive flow problem the position and speed of propagation of the shock wave and reaction front are different. 

Groundwater remediation is the often expensive process of restoring an aquifer after it has been contaminated, or at least limiting the ability of contaminants there to spread. In this chapter, we consider the widespread problem of the contamination of groundwater flows with heavy metals. We use reactive transport modeling to look at the reactions that occur as contaminated water enters a pristine aquifer, and those accompanying remediation efforts. 

At the same time, reaction modeling is now commonly coupled to the problem of mass transport in groundwater flows, producing a subfield known as reactive transport modeling. Whereas a decade ago such modeling was the domain of specialists, improvements in mathematical formulations and the development of more accessible software codes have thrust it squarely into the mainstream. 

Mechanism reduction, nevertheless, may be necessary in some applications — for example, to model multidimensional reactive flows. Even the fastest computers today cannot handle such problems using detailed mechanisms in a reasonable time frame. It must be recognized, however, that models that utilize reduced mechanisms would have a far narrower range of applicability than the ones that use comprehensive reaction mechanisms. Furthermore, models that are based on reduced mechanisms cannot be expected to be valid outside the limits set in the mechanism reduction step. 

In bringing the models to a non-dimensional form, the presence of dominant Peclet and Damkohler numbers in reactive flows is observed. The problems of interest arise in complex geometries-like porous media or systems of capillary tubes. 

The techniques just described have been extensively used in modeling reactive flow problems at NRL. Efficient solution of the coupled ordinary differential equations associated with these problems has enabled us to perform a wide variety of calculations on H2 °2 anC Ha/Oo mixtures which have greatly extended our understanding of tne combustion and detonation behavior of these systems. In addition numerous atmospheric problems have been studied. Details on these investigations are provided in references (7) and (9). 

Figure 15 Porosity structure of a high-resolution single-channel calculation for an upwelling system undergoing melting by both adiabatic decompression and reactive flow (see Spiegelman and Kelemen, 2003). Colors show the porosity field at late times in the run where the porosity is quasi steady-state. The maximum porosity at the top of the column (red) is 0.8% while the minimum porosity at the bottom (dark blue) is 10 times smaller. Axis ticks are height and width relative to the overall height of the box. In the absence of channels this problem is identical to the equilibrium one-porosity transport model of Spiegelman and Elliott (1993). Introduction of channels, however, produces interesting new chemical effects similar to the two porosity models.

The design of a complete set of governing equations for the description of reactive flows requires that the combined fluxes are treated in a convenient way. In principle, several combined flux definitions are available. However, since the mass fluxes with respect to the mass average velocity are preferred when the equation of motion is included in the problem formulation, we apply the species mass balance equations to a (/-component gas system with q — independent mass fractions Wg and an equal number of independent diffusion fluxes js. However, any of the formulations derived for the multicomponent mass diffusion flux can be substituted into the species mass balance (1.39), hence a closure selection optimization is required considering the specified restrictions for each constitutive model and the computational efforts needed to solve the resulting set of model equations for the particular problem in question. 

The statistical description of multiphase flow is developed based on the Boltzmann theory of gases [37, 121, 93, 11, 94, 58, 61]. The fundamental variable is the particle distribution function with an appropriate choice of internal coordinates relevant for the particular problem in question. Most of the multiphase flow modeling work performed so far has focused on isothermal, non-reactive mono-disperse mixtures. However, in chemical reactor engineering the industrial interest lies in multiphase systems that include multiple particle t3q)es and reactive flow mixtures, with their associated effects of mixing, segregation and heat transfer. 

Many other methods for solving flow problems can be devised. It is impossible to describe all of them here. In this book, emphasis is placed on describing elements of particular pressure-based methods originally developed for incompressible flows. The basic methods are extended and used to simulate reactive flows. The standard algorithms used to solve multi-fluid models are extensions of particular pressure-based methods for single phase flows. 

Figure 1. Initial and boundary conditions for the model problem. Undersaturated flow enters from the left, causing the reaction front to migrate gradually downstream. Shaded portion of the aquifer contains 5% reactive cement, resulting in a porosity of 5% and a permeability of 1 millidarcy. Upstream of the reaction front the porosity is 10% and the permeability is 10 millidarcies.

The original code is called SAGE. A later version with radiation is called RAGE. A recent version with the techniques for modeling reactive flow described in Chapters 1 through 4 is called NOBEL and was used for modeling many problems in detonation physics some of which are described later in this chapter. 

The problem of reactive turbulent flow is then reduced to the computation of the p.d.f. of the fluctuations of a single inert scalar diffusing into the turbulent flow. That problem, however, was not adressed by specialists of turbulence, at the time of Toor s studies it has been studied since that, and now we have at our disposal some modelled balance equations for P(d>) itself as P is usefull even when the chemistry is not very fast, we will consider this problem with this more general case. 

Remember that the volume Flows and chemical reactions comprised three parts 1. Fluid media with a single component, 2. Reactive mixtures, and 3. Interfaces and lines, that the volume Flows and Chemical Reactions in Homogeneous Mixtures comprised 1. Pipe flows, 2. Chemical reactors, and 3. Laminar and turbulent flames, and that the volume Flows and Chemical Reactions in Heterogeneous Mixtures comprised 1. Generation of multi-phase flows, 2. Problems at the scale of a particle, 3. Simplified model of a non-reactive flow with particles, 4. Simplified model of a reactive flow with particles, and 5. Radiative phenomena. 

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