scholarly journals Bifurcation curves in a combustion problem with general Arrhenius reaction-rate laws

2016 ◽  
Vol 62 (2) ◽  
pp. 337-371
Author(s):  
Kazuaki Taira
1992 ◽  
Vol 296 ◽  
Author(s):  
M. D. Fayer ◽  
Andrei Tokmakoff ◽  
Dana D. Dlott

AbstractA theoretical model is developed to describe multiphonon up-pumping of internal vibrations. The dominant mechanism for up-pumping is anharmonic coupling of excited phonon modes with low frequency molecular vibrations, termed doorway modes. Quantitative calculations were performed which show the extent and rate of multiphonon up-pumping caused by shock excitation. The time dependence of chemical reactivity behind the front is calculated using reaction rate laws for the decomposition of nitramine explosives. A mechanism for hot spot formation, based on defect induced local increases in anharmonic coupling, is discussed.


2021 ◽  
pp. 17-35
Author(s):  
Luis Arnaut
Keyword(s):  

The conductive theory of thermal explosion in its original form (Frank-Kamenetskii, Acta phys. -chim . URSS (1939)) expresses the balance between heat generation and heat conduction in terms of the dimensionless parameter δ = [QEA a 2 0 c n 0 exp ( - E/RT a )]/ K RT 2 a Stability is lost when δ exceeds a critical value which, in this approximation, depends only on the geometry of the system. Matters are usually more complicated than this. First, heat transfer is often impeded both in the interior (by conduction) and at the surface; the relative importance of these impedances is expressed by the Biot number B i = X a o / K - Second, the temperature dependence of reaction rate may not be well enough represented by the 'exponential approximation’ (which simply implies a doubling of rate every so many degrees). The natural and convenient dimensionless measure here is the parameter ϵ = RT a /E. In the present paper, critical values for the parameter δ and for the dimensionless central-temperature excess Ɵ o have been evaluated for the whole range of Biot number from the uniform case (Semenov extreme, B i → 0) to the Frank-Kamenetskii extreme (B i →∞). The procedures can handle any temperature-dependence of rate and are illustrated here for the Arrhenius and 'bimolecular’ forms for which, k∝ exp ( — E /RT ) and k ∝T ½ exp ( - E /R T ) respectively. When E /RT a is not large, criticality is lost at ϵ = ϵ tr ≤ ¼. Such transitional values for the reduced ambient temperature ϵ, for the critical value of δ, and for the dimensionless central temperature excess Ɵ 0 have also been obtained. They are represented both graphically and numerically. The present results are also compared with earlier work.


1998 ◽  
Vol 43 (Supplement) ◽  
pp. S1-S8
Author(s):  
塚田 雅夫 ◽  
西村 英俊

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