Averaging method in calculations of the exothermal reaction in porous-body?Gas systems

Zhukova, L. A.; Khudyaev, S. I.

doi:10.1007/bf00788804

Cited by 2 publications

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“…In the particular case Ze = 0, Eqs. (13) and (14) imply the results of the Frank-Kamenetskii steady-state theory of thermal explosion [3]: A = 1.809 andFk * * = 3.52. The critical dependencesFk * * (Ze) andFk * (Ze) are presented in Fig.…”

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confidence: 74%

“…The most questionable issue was the averaging performed in [8] for temperatures and concentrations with different weight functions for different values of the thermal and diffusion Biot numbers (Bi h and Bi d , respectively). A comparison with the numerical solution of the distributed problem [13] has shown that the process is correctly described by the averaged system over a broad range of Bi h and Bi d numbers. The largest deviations of the parameters determined by the averaged and distributed systems of equations were observed for greatly different values of Bi h and Bi d .…”

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confidence: 87%

“…The effect of the diffusion of the reactants of the chemical process on the ignition regimes of the porous layer has been studied [8][9][10][11][12][13][14][15][16]. As one might expected, the main features distinguishing the thermal ignition of porous systems from that of homogeneous layers have been observed in the case of hindered diffusion.…”

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confidence: 98%

“…In the case of hindered heat transfer on the surface of the porous layer, the degeneration effect was not observed but the critical ratios of the parameters were shown to be qualitatively different for strong and weak diffusion. The unsteady problem of thermal ignition of a porous layer with temperature and concentration distributions on the spatial coordinate was studied numerically by Seleznev et al [12] and Zhukova and Khudyaev [13]. The critical parameters obtained numerically in [12] were compared with the results obtained by averaging [8].…”

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confidence: 99%

“…It was noted that the solutions of the original and averaged problems coincide for the chosen set of parameters in the region of self-oscillations and that the critical conditions also coincide for both identical and different boundary conditions for the temperature and reactant concentration. Zhukova and Khudyaev [13] performed qualitative and quantitative assessments of the accuracy of the solution for the averaged system [8] relative to the solution of the distributed problem. The most questionable issue was the averaging performed in [8] for temperatures and concentrations with different weight functions for different values of the thermal and diffusion Biot numbers (Bi h and Bi d , respectively).…”

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confidence: 99%

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Critical conditions of thermal explosion of a porous layer

Burkina

Prokof’ev

2008

Combust Explos Shock Waves

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The conditions and regimes of thermal ignition of a reactive porous layer are investigated under asymmetric conditions on its lateral surfaces and with an oxidizer supply to the layer by diffusion or filtration through the cold boundary. For a zero-order reaction, an analytical dependence of the critical value of the Frank-Kamenetskii parameter on the Zel'dovich parameter is obtained, which separates the regions of steady-state and unsteady regimes. A numerical analysis is made of the critical value of the Frank-Kamenetskii parameter on the Zel'dovich parameter, the Todes parameter, which determines the oxidizer consumption, and the parameter determining the oxidizer supply to the layer: the Lewis numbers or the filtration analog of the Peclet parameter.Key words: porous medium, natural filtration, critical conditions, thermal explosion, analytical and numerical solutions.The conditions of thermal self-ignition of reactive materials are one of the key issues of fire and explosion safety, and their investigation has therefore proceeded in parallel with the development of ignition and combustion theory, starting from the work of van't Hoff [1]. The critical conditions of thermal self-ignition of homogeneous reactive media with simple kinetics were determined and studied in the classical theories of Semenov [2] and Frank-Kamenetskii [3]. Subsequent investigation has shown that a chemical process or a thermal situation are capable, by virtue of complexity, of significantly changing the self-ignition limit [4]. The special features of chemical processes in porous materials, as was noted even by Zel'dovich [5], are related to the delivery of some reactants to the zone of localization of the chemical process and to the complex heat-transfer mechanism. The indicated specificity results in ignition regimes of porous systems qualitatively different from the ignition regimes of homogeneous media. The ignition limits and times of porous systems and the location of the ignition spot depend greatly on the conditions of the process and are determined by heat and mass transfer.Investigation of the initiation of chemical processes 1 Tomsk State University, Tomsk 634050; roza@ftf.tsu.ru.in porous media has been carried out in three directions: 1) self-ignition; 2) ignition of porous media by a hot body and radiative and convective heat flows; 3) hotspot ignition of porous media. The present paper is concerned with the processes related to the first direction. The effect of heat convection due to gas blowing through a reactive layer on the critical conditions of thermal explosion under symmetric conditions on the layer walls was studied by Eremin and Kolesnikov [6]. Steady-state temperature profiles and the dependence of the critical value of the Frank-Kamenetskii number Fk * on the Peclet parameter Pe were obtained numerically using a one-temperature model for a zero-order chemical process. The dependence for Pe < 4 was approximated by a polynomial with an accuracy of 4%. It was established that, for large values of the Peclet par...

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confidence: 74%

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confidence: 87%