Thermal explosion in spherical vessels at large Rayleigh numbers

Iglesias, I. and Moreno Boza, D. and Sánchez, A.L. and Liñán Martínez, Amable and Williams, F.A. (2017). Thermal explosion in spherical vessels at large Rayleigh numbers. "International Journal of Heat and Mass Transfer", v. 115B ; pp. 1042-1053. ISSN 0017-9310.


Title: Thermal explosion in spherical vessels at large Rayleigh numbers
  • Iglesias, I.
  • Moreno Boza, D.
  • Sánchez, A.L.
  • Liñán Martínez, Amable
  • Williams, F.A.
Item Type: Article
Título de Revista/Publicación: International Journal of Heat and Mass Transfer
Date: December 2017
ISSN: 0017-9310
Volume: 115B
Freetext Keywords: Thermal explosions; Laminar reacting flows; Natural convection; Boundary-layer theory
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Mecánica de Fluidos y Propulsión Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

Full text

PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (1MB) | Preview


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 Dac 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 > Dac 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 > Dac 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 Dac 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 Dac Ra1=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 Dac ¼ 0:655Ra1=4 is found to be in excellent agreement with the results obtained by integration of the complete conservation equations for Ra 1.

More information

Item ID: 50883
DC Identifier:
OAI Identifier:
DOI: 10.1016/j.ijheatmasstransfer.2017.08.109
Official URL:
Deposited by: Memoria Investigacion
Deposited on: 01 Aug 2018 12:23
Last Modified: 04 Apr 2019 11:56
  • Logo InvestigaM (UPM)
  • Logo GEOUP4
  • Logo Open Access
  • Open Access
  • Logo Sherpa/Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Logo Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Logo de Recolecta
  • Logo del Observatorio I+D+i UPM
  • Logo de OpenCourseWare UPM