The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 1: Transient analysis and explosion limits

Liñán, A.; Moreno-Boza, Daniel; Iglesias, Immaculada; Sánchez, Antonio L.; Williams, Forman A.

doi:10.1080/13647830.2016.1236987

Cited by 5 publications

(18 citation statements)

References 9 publications

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“…Since the duration of the heating period needed to increase the gas temperature in the container to values close to the wall value depends fundamentally on / I , lower values of / I result in larger ignition times, as was verified in additional computations. Nevertheless, the explosion limits, measured by the critical Damköhler number Da c , were found to be independent of the selection of / I for all / I 6 0, in agreement with our previous results for buoyancy-free systems [5].…”

Section: 32supporting

confidence: 91%

“…Dimensionless variables / ¼ bðT À T o Þ=T o andq ¼ bðq À q I Þ=q I are introduced for the temperature and density, as is appropriate for studying the slowly reacting mode of combustion. As noted in [5,21], in rigid confined vessels the changes of the density are restricted to ensure that the mean spatial value of the density remains equal to q I , resulting in temporal variations of the pressure of order p o =b, much larger than the spatial variations of the pressure associated with the low-Machnumber buoyancy-induced gas motion. These temporal changes of the pressure, which had been overlooked in previous numerical studies [15][16][17], are taken into account here when writing the energy balance and the equation of state with use made of the order-unity variablepðtÞ…”

Section: Formulation For the Transient Slowly Reacting Mode Of Combusmentioning

confidence: 99%

“…Additional symbols that appear in (6) and 7are defined in the following paragraph. In this near-explosion regime, associated with small density differences of order q I =b, the contribution of the temporal density variation to mass conservation gives a higher-order correction, of order ðb RaÞ À1 , which has been neglected in (5). Also, leaving out terms of order 1=b, variations of transport coefficients and specific heat from their values evaluated for T ¼ T o and q ¼ q I have been omitted in (6) and (7).…”

Section: Formulation For the Transient Slowly Reacting Mode Of Combusmentioning

confidence: 99%

“…Computation of the transient evolution requires specification of the initial conditions. In the following, we consider an initially cold stagnant gas mixture at temperature [5], the analysis becomes somewhat more complicated when the wall-temperature rise is larger, such that T o À T I $ T o , in which case the heating of the gas by heat conduction from the wall, which proceeds initially with negligible chemical reaction, involves relative variations of the density, temperature, and pressure of order unity.…”

Section: Formulation For the Transient Slowly Reacting Mode Of Combusmentioning

confidence: 99%

“…This success has motivated recent extensions of the early theory incorporating realistic chemistry in descriptions of hydrogen-oxygen systems that have been shown to predict explosion conditions in spherical vessels in excellent agreement with experiments [3], including critical pressures along the so-called third-explosion limit [4]. The FK problem was recently revisited in [5] to investigate influences on ignition times of initial conditions and of temporal pressure variations in spherical vessels with fixed walls.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: 32supporting

confidence: 91%