Fuel combustion, mathematical

The success of any mathematical model, and in turn the computer code, depends completely on the clarity of the conceptual model (physical model). The authors have concluded from a comprehensive literature review on the subject of solid-fuel combustion, that there is a slight conceptual confusion in parts of this scientific domain. The first example of this is the lack of distinction between the thermochemical conversion of solid fuels and the actual gas-phase combustion process, which led these authors to the formulation of the three-step model. The thermochemical conversion of solid fuels is a two-phase phenomenon (fluid-solid phenomenon), whereas the gas-phase combustion is a one-phase phenomenon (fluid phenomenon). 

The preceding sections show that catalytic fuel combustion is a process in which complex kinetics for heterogeneous and homogeneous reactions are combined with mass and heat transfer effects. This leads to difficulties in predicting the behavior of combustion catalysts under real conditions. Therefore, mathematical modeling is a powerful tool to assist experimental work, to interpret results, and to aid in the design of catalytic combustors. 

The aim with the present paper is to survey the literature on catalytic fuel combustion for high temperature gas turbine applications with emphasis on the progress during the last five years. Reference to work before 1993 can be found in an earlier review from our laboratory. Following a brief introduction to catalytic combustion and a discussion on formation and abatement of emission, state-of-the-art in materials development will be reviewed in Section 3. Recent results from mathematical modelling are covered in Section 4. An update of new concepts of catalytic combustors and advanced pilot-scale tests will be presented in Section 5, where also a case study on a recently finished European project is reported. Finally, deactivation of combustion catalysts is discussed in Section 6 and a spin-off effect of catalytic combustion is recapitulated in Section 7. 

The authors substantiated the validity of the entire methodological approach, mathematical models and computational methods on the basis of 1) the historical analysis of developing interactions between the theories of trajectories and the theories of states 2) the experience gained in the use of MEIS to study the processes of fuel combustion and processing, atmospheric pollution with anthropogenic emissions and motion of viscous liquids in multiloop hydraulic systems and 3) the establishment of mathematical relations between the applied dependences and thermodynamic principles. 

The development of combustion theory has led to the appearance of several specialized asymptotic concepts and mathematical methods. An extremely strong temperature dependence for the reaction rate is typical of the theory. This makes direct numerical solution of the equations difficult but at the same time accurate. The basic concept of combustion theory, the idea of a flame moving at a constant velocity independent of the ignition conditions and determined solely by the properties and state of the fuel mixture, is the product of the asymptotic approach (18,19). Theoretical understanding of turbulent combustion involves combining the theory of turbulence and the kinetics of chemical reactions (19—23). 

The major mechanism of a vapor cloud explosion, the feedback in the interaction of combustion, flow, and turbulence, can be readily found in this mathematical model. The combustion rate, which is primarily determined by the turbulence properties, is a source term in the conservation equation for the fuel-mass fraction. The attendant energy release results in a distribution of internal energy which is described by the equation for conservation of energy. This internal energy distribution is translated into a pressure field which drives the flow field through momentum equations. The flow field acts as source term in the turbulence model, which results in a turbulent-flow structure. Finally, the turbulence properties, together with the composition, determine the rate of combustion. This completes the circle, the feedback in the process of turbulent, premixed combustion in gas explosions. The set of equations has been solved with various numerical methods e.g., SIMPLE (Patankar 1980) SOLA-ICE (Cloutman et al. 1976). 

In this paper we attempt a preliminary investigation on the feasibility of catalytic combustion of CO/ H2 mixtures over mixed oxide catalysts and a comparison in this respect of perovskite and hexaaluminate type catalysts The catalysts have been characterized and tested in the combustion of CO, H2 and CH4 (as reference fuel). The catalytic tests have been carried out on powder materials and the results have been scaled up by means of a mathematical model of the catalyst section of the Hybrid Combustor. 

Pex, P.P.A.C. and Y.C. van Delft, Silica membranes for hydrogen fuel production by membrane water gas shift reaction and development of a mathematical model for a membrane reactor, in Carbon Dioxide Capture for Storage in Deep Geologic Formations—Results from the C02 Capture Project Capture and Separation of Carbon Dioxide from Combustion Sources, eds., D. Thomas, and B. Sally, Vol. 1, Chapter 17, 2005. 

A new system theory - the three-step model - of packed-bed combustion is formulated. Some new quantities and efficiencies are deduced in the context of the three-step model, such as the conversion gas, the solid-fuel convertibles, the conversion efficiency and the combustion efficiency. Mathematical models to determine the efficiencies are formulated. 

No explicit mathematical model of the method was presented. However, a short descriptive model was outlined For each run, the average ignition and combustion rate (expressed as weight of fuel ignited or burnt per unit bed area and unit time) were calculated by determining the time taken for the ignition front to pass down through the bed and the completion of burn-out, respectively. No discussion is presented about limitations and assumptions of the method. 

An ideal conversion system has 100 percent conversion efficiency that is, 100% of the solid-fuel convertibles go to the combustion system (Figure 14), and no fuel is lost in the ash flow. However, ideal conversion systems do not exist in reality. The concept of conversion efficiency is mathematically defined by the authors [3]. 

As illustrated in Fig. 1.2, a premixed flow of acetylene, hydrogen, and oxygen issue from a flat burner face onto a parallel, flat surface. Mathematically there is very little difference between this situation and one in which two flat burners face each other, in an opposed-flow configuration. There are many commonly used variants of the opposed-flow geometry. For example, premixed, combustible, gases could issue from both burner faces, causing twin premixed flames. Alternatively, fuel could issue from one side and oxidizer from the other, causing a nonpremixed, or diffusion, flame. 

A.B. Hedley and E.W. Jackson. A Simplified Mathematical Model of a Pulverized Coal Flame Showing the Effect of Recirculation on Combustion Rate. J. Inst. Fuel, 39 208,1966. 

Among the earliest works employing simplified kinetics and obtaining analytical approximations are those of Y. B. ZeVdovich, Zhur. Tekhn. fiz. 19,1199 (1949) [English translation, NACA Tech. Memo. No. 1296 (1950)] and of D. B. Spalding, Fuel 33,255 (1954). Chapter 7 of The Mathematical Theory of Combustion and Explosion by Y. B. Zel dovich,G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze, Moscow Nauka, 1980, treats the question of diffusion-flame structure for a one-step, second-order, Arrhenius reaction in a clear fashion. 

Numerical Procedure. This section describes an iterative numerical procedure for evaluating the mathematical model presented in this chapter for the nonsteady ignition and combustion of a fuel droplet The key step of this procedure is to match or couple the analytical equations for heat and mass transport at the liquid/gas interface by establishing the droplet surface temperature for a series of successive short time intervals. The numerical procedure for each time consists of the following steps ... 

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