Combustion mathematical modeling

T. J. Tyson, "The Mathematical Modeling of Combustion Devices," paper presented at Proceedings of the Stationary Source Combustion Symposium, Vol. 

K. K. Boon, "A Flexible Mathematical Model for Analy2ing Industrial P. F. Furnaces," M.S. thesis. University of Newcasde, AustraUa, Sept. 1978. R. H. Essenhigh, "A New AppHcation of Perfectly Stirred Reactor (P.S.R.) Theory to Design of Combustion Chambers," TechnicalEeport FS67-1 (u), Peimsylvania State University, Dept, of Euel Science, University Park, Pa., Mar. 1967. 

C.-M. Brauner and C. Schmidt-Laine, Mathematical Modeling in Combustion and Related Topics, Martinus Hijhoff Pubhshers, Dordrecht, The Netherlands, 1988. 

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). 

Magnussen, B. F., and B. H. Hjertager. 1976. On the mathematical modelling of turbulent combustion with special emphasis on soot formation and combustion. 16th Symp. (Int.) on Combustion, pp. 719-729. The Combustion Institute, Pittsburgh, PA. 

Operability analysis and control system synthesis for an entire chemical plant Mathematical modeling of transport and chemical reactions of combustion-generated air pollutants... 

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. 

He has published over 200 papers in the fields of process control, optimization, and mathematical modeling of processes such as separations, combustion, and microelectronics processing. He is coauthor of Process Dynamics and Control, published by Wiley in 1989. Dr. Edgar was chairman of the CAST Division of AIChE in 1986, president of the CACHE Corporation from 1981 to 1984, and president of AIChE in 1997. 

The physical model serves as the platform for the mathematical model used to indirectly measure the mass flow and stoichiometry of the conversion gas, as well as the air excess numbers of the conversion and combustion system, respectively. 

For the sake of brevity the reader is referred to Paper II for the details regarding the constitutive mathematical models of the method applied to measure the mass flow and stoichiometry of conversion gas as well as air factors for conversion and combustion system. Below is a condensed formulation of the mathematical models applied. Here a distinction is made between measurands and sought physical quantities of the method. 

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. 

Stubington et al [6] presented a short descriptive model of how the ignition front rate and the combustion rate are determined. No mathematical models to calculate the ignition rate and the combustion rate are shown. However. As far as this author can understand, the calculation results are time average values, that is, no time instant values are obtained by the method used by Stubington. No uncertainty analysis was presented and no verification method was used. The methods used are unclearly defined. Consequently, the results would be difficult to reproduce. Nevertheless, the study includes interesting result. 

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). 

Figure 56 above describes the phenomenology of the char combustion regime (III). The concept of the shrinking core or shrinking particle model is usually applied in mathematical modelling of char combustion in regime (III). 

Beshty B.S., A Mathematical Model for the Combustion of a Porous Carbon Particle , Combustion and Flame 32, 295-311(1978). 

The aim of the present investigation is to create adequate semi-empirical physical and mathematical models that describe dynamics of turbulent combustion in heterogeneous mixtures of gas with polydispersed suspended particles. 

Theoretical investigations of the problem were carried out on the base of the mathematical model, combining both deterministic and stochastic approaches to turbulent combustion of organic dust-air mixtures modeling. To simulate the gas-phase flow, the k-e model is used with account of mass, momentum, and energy fluxes from the particles phase. The equations of motion for particles take into account random turbulent pulsations in the gas flow. The mean characteristics of those pulsations and the probability distribution functions are determined with the help of solutions obtained within the frame of the k-e model. 

Williams, F. A. 1988. Asymptotic methods for flames with detailed chemistry. In Mathematical modeling in combustion science. Eds. J. D. Buckmaster and T. Takeno. New York Springer-Verlag. 44-51. 

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. 

Heat Transfer by Conduction. In the theoretical analysis of steady state, heterogeneous combustion as encountered in the burning of a liquid droplet, a spherically symmetric model is employed with a finite cold boundary as a flame holder corresponding to the liquid vapor interface. To permit a detailed analysis of the combustion process the following assumptions are made in the definition of the mathematical model ... 

A Mathematical Model of Flare Plume Combustion and Radiation , NWSC/CR/RDTR-9,... 

Coal combustion processes can be classified based on process type (see Table 9.1), even though classification based on the particle size, the flame type, the reactor flow type, or the mathematical model complexity is also possible [7]. 

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