Effects of combined natural and forced convection on thermal explosion in a spherical reactor

Liu, Ting-Yueh; Cardoso, Silvana S. S.

doi:10.1016/j.combustflame.2012.08.012

Cited by 7 publications

(30 citation statements)

References 45 publications

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“…[9,10] Thep recise definition of ac hemical clock is am atter of debate.S ome have argued for ad efinition that restricts ac lock reaction to an abrupt increase in the concentration of one or more products owing to the total consumption of alimiting reagent, [11] while others argue that it is not the details of the kinetics but the phenomenology that is important. [15,16] In the case of our scenario,t he concept of ac hemical clock is based upon the chemicalgarden reaction acting as atimer, the period of which we can control. [13,14] But it is inarguable that the classic clock reactions are timers:they have an induction period that may be very long followed by asharp change,often acolor change, at agiven moment, and this induction time can be controlled and predicted by altering the quantities of reagents.Examples in gaseous combustion have shown the dependence of the induction time before explosion on the transport rates of chemicals and heat.…”

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“…[13,14] But it is inarguable that the classic clock reactions are timers:they have an induction period that may be very long followed by asharp change,often acolor change, at agiven moment, and this induction time can be controlled and predicted by altering the quantities of reagents.Examples in gaseous combustion have shown the dependence of the induction time before explosion on the transport rates of chemicals and heat. [15,16] In the case of our scenario,t he concept of ac hemical clock is based upon the chemicalgarden reaction acting as atimer, the period of which we can control. Herein we describe and analyze the clock-reaction explosion of ac hemical garden when confined to two dimensions.…”

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Exploding Chemical Gardens: A Phase‐Change Clock Reaction

et al. 2019

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Chemical gardensand clockreactions are two of the best-known demonstration reactions in chemistry.U ntil now these have been separate categories.W eh ave discoveredt hat ac hemical garden confined to two dimensions is ac lock reaction involving aphase change,sothat after areproducible and controllable induction period it explodes.Supportinginformation and the ORCID identification number(s) for the author(s) of this article can be found under: https://doi.

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Exploding Chemical Gardens: A Phase‐Change Clock Reaction

et al. 2019

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“…Because of the presence of backflow, the character of the resulting boundary-layer problem changes from parabolic to elliptic. The associated boundary-value problem requires consideration of the specific conditions found near the bottom h ¼ p. There, the flow exhibits a self-similar solution, with the core temperature vanishing on approaching h ¼ p according to the power law / c ¼ Aðp À hÞ k , consistent with the local scalings U / ðp À hÞ 1þk=2 and y / ðp À sÞ Àk=4 , where the value of the exponent k ¼ 8=5 is determined from the convective-reactive balance (19). Writing (12)- (14) in terms of the local coordinate n ¼ A 1=4 ðp À hÞ 2=5 y, stream function w ¼ A 1=4 ðp À hÞ 12=5 b F ðnÞ, and temperature incre-…”

Section: / 1=4mentioning

confidence: 88%

“…The flow was found to remain laminar for values of Ra < 10 6 . More recent numerical work by this same research group includes investigation of combined natural and forced convection on thermal explosions [19] as well as consideration of non-isothermal walls by use of a Robin condition including a heat-transfer coefficient [20].…”

Section: Introductionmentioning

confidence: 99%

Thermal explosions in spherical vessels at large Rayleigh numbers

Iglesias

Moreno-Boza

Sánchez

et al. 2017

International Journal of Heat and Mass Transfer

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This paper investigates effects of buoyancy-driven motion on the ''slowly reacting" mode of combustion, and its thermal-explosion limits, of an initially cold gaseous mixture enclosed in a spherical vessel with a constant wall temperature. As in Frank-Kamenetskii's seminal analysis, the strong temperature dependence of the effective overall reaction is modeled with a single irreversible reaction with an Arrhenius rate having a large activation energy. Besides the classical Damköhler number Da, measuring the ratio of the heat-release rate by chemical reaction evaluated at the wall temperature to the rate of heat removal by heat conduction to the wall, the solution is seen to depend on the Rayleigh number Ra, measuring the effect of buoyancy-induced motion on the heat-transport rate. For values of Da below a critical value Da c the system evolves in a slowly reacting mode where the heat losses to the wall limit the temperature increase associated with the chemical reaction, whereas for Da > Da c the initial stage of slow reaction ends abruptly at a well-defined ignition time, at which a thermal runaway occurs. Transient numerical integrations of the initial stage of slow reaction, formulated in the distinguished limit Da $ 1 and Ra $ 1 with account taken of the effects of the temporal pressure variation, are used to investigate influences of natural convection on thermal-explosion development, including changes in ignition times for Da > Da c and modified explosion curves. Our analysis reveals that Frank-Kamenetskii's criterion for the determination of critical explosion conditions, based on the investigation of existence of steady solutions, provides values of Da c ðRaÞ that are identical to those extracted from the transient computations. Specific consideration is given to the structure of the steady solution in the asymptotic limit Ra) 1 in which the flow includes a thin chemically frozen near-wall boundary layer of downward moving cold gas bounding a central inviscid region of slowly rising reacting flow driven by the boundary-layer entrainment, with the critical explosion conditions predicted to occur for Da c $ Ra 1=4. The mathematical structure of the resulting boundary-layer problem is fundamentally similar to that found in the unrelated problem of flow in curved pipes at large Dean numbers. As in that similar problem, the boundary layer exhibits a region of recirculating flow, so that the problem must be formulated as a boundary-value problem accounting for the self-similar local solutions that exist near the upper and lower stagnation points. The problem is solved with use made of an approximate integral method. The resulting asymptotic prediction for the critical Damköhler number Da c ¼ 0:655Ra 1=4 is found to be in excellent agreement with the results obtained by integration of the complete conservation equations for Ra) 1.

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“…But it is inarguable that the classic clock reactions are timers: they have an induction period that may be very long followed by a sharp change, often a color change, at a given moment, and this induction time can be controlled and predicted by altering the quantities of reagents. Examples in gaseous combustion have shown the dependence of the induction time before explosion on the transport rates of chemicals and heat . In the case of our scenario, the concept of a chemical clock is based upon the chemical‐garden reaction acting as a timer, the period of which we can control.…”

Section: Figurementioning

confidence: 99%