Emergence of Spatial Structures during Filtration Combustion

Ozerkovskaya, N. I.; Firsov, A. N.; Шкадинский, К. Г.

doi:10.1007/s10573-010-0067-8

Cited by 18 publications

(4 citation statements)

References 6 publications

(9 reference statements)

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“…The macrokinetic equation of chemical interaction reads as (5) where δ is a small parameter, which characterizes the weak dependence of the reaction rate on the gas pres sure except for the range of low pressures.…”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

“…The memory of the details of the nonlin ear dynamics of the process of initiation of the front (ignition stage [5]), so the focus of our analysis will be on the propagation of the high temperature zone of exothermic chemical conversion. This high tempera ture zone (cell) does not yet experience a strong influ ence of the open end, but have already forgotten the details of the initiation stage; it is such a cell will be presented in the figures.…”

Section: Calculation Algorithmmentioning

confidence: 99%

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Critical phenomena in the cellular mode of filtration combustion in the presence of heat loss

Шкадинский

Firsov

Ozerkovskaya³

2012

Russ. J. Phys. Chem. B

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Critical conditions for combustion failure due to heat loss to the environment are examined. The process of filtration combustion is considered under conditions where a cellular structure of the front is real ized, because the planar combustion front loses its stability and splits into separate cells of exothermic chem ical conversion, which propagate in self sustained mode. The size and structure of the cells of chemical inter action depend nonlinearly on the governing parameters, including the rate of heat loss to the environment. Within the framework of a mathematical model of filtration combustion, the steady state dynamics of the combustion process and the structure of the cell of exothermic chemical reaction of a powder mixture with a gaseous reagent with the formation of solid products are simulated. The specifics of the evolution of the cell before combustion failure as a function of the heat loss rate are studied.

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Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

Section: Calculation Algorithmmentioning

confidence: 99%

Critical phenomena in the cellular mode of filtration combustion in the presence of heat loss

Шкадинский

Firsov

Ozerkovskaya³

2012

Russ. J. Phys. Chem. B

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“…In the conventional cyclic sequence: Experiment → Physical Model → Mathematical model → CE → Experiment, CE occupies an important place, which, in turn, consists of several stages: CE → Model → Algorithm → Program → CE, being, generally, also a cyclic procedure. Currently, CE includes not so much the development of computational methods and its implementation on a computer [13,14], but rather planning a series of calculations with a clearly defined objective. The formulation of this goal is largely dependent on the adequacy of consideration of the theoretical model and the level of physicochemical understanding of the process.…”

mentioning

confidence: 99%

“…At the initial stage of research, the objective of CE may be to obtain interpolation formulas capable of replacing the exact analytical solution of the corre sponding mathematical models. In the case of multi parameter problems, the goal of CE may be to analyze limiting regimes determining the boundaries of rear rangement of the process when the conditions in the multidimensional parameter space change [13][14][15][16][17][18].…”

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confidence: 99%

On the design of computational experiment in combustion theory

Быков

2012

Russ. J. Phys. Chem. B

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Combustion is a complex physicochemical pro cess, which is generally characterized by a significant nonlinearity and nonstationarity, as well as by a com bination of many factors, such as chemical and phase transformations, heat and mass transfer, etc. [1]. Accordingly, the theory of combustion contains a sig nificant number of mathematical models of the pro cesses under study [2][3][4][5][6], providing a basis for a wide spread use of modern methods of computational experiment [7][8][9][10][11].In this work, we formulate, in a compact form, the concept of planning a computational experiment in combustion theory, which generalizes the accumu lated experience in mathematical modeling of com bustion processes, including the development and qualitative and numerical analysis of mathematical models and their use in studying the problems of sta bility and control combustion processes. This report is closely related to [12], where the adequacy of the experimental and theoretical models of combustion processes is considered.Computational experiment (CE) is an effective means of modern mathematical modeling [8][9][10][11]. In the conventional cyclic sequence: Experiment → Physical Model → Mathematical model → CE → Experiment, CE occupies an important place, which, in turn, consists of several stages: CE → Model → Algorithm → Program → CE, being, generally, also a cyclic procedure. Currently, CE includes not so much the development of computational methods and its implementation on a computer [13,14], but rather planning a series of calculations with a clearly defined objective. The formulation of this goal is largely dependent on the adequacy of consideration of the theoretical model and the level of physicochemical understanding of the process.According to Academician A.G. Merzhanov [12], there are the following levels of adequacy of combus tion models:(1) basic mathematical model that qualitatively reproduce a limited set of main properties of a certain class of processes;(2) mathematical models that reflect basic charac teristic dependences upon variation of the parameters that have real physicochemical sense;(3) quantitative description of some of the experi mentally observed dependences;(4) detailed mathematical models capable of quan titatively describe all the observed data with required degree of adequacy.The whole practice of theoretical and experimental studies of combustion processes has shown that a given phenomenon can be described within the framework of various mathematical models, but the adequacy of which may be different. The physicochemical ade quacy of the model implies that it can, in principle, describe an experimentally observed property of the process. The mathematical adequacy means a quanti tative description of a specific set of experimental data in accordance with a desired criterion. Basic models of combustion theory reflect a certain level of specifica tion of the physicochemical description of a given class of processes. In passing from a base to a quantita tive model for a particular proce...

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