Abstract
A compressible model is developed with kinetics based on the Wang–Mou five-step global kinetic scheme and used to evaluate the temperature, concentration, and velocity fields characteristic of low-temperature combustion in unstirred static reactors. This work relaxes the assumption of small exothermicity that enabled prior studies to employ the Boussinesq approximation, valid for cases where βΔT < < 1, i.e., slow reactions and cool flames. In this study, the range of validity of the model is extended to cases with large temperature excursions, including multi-stage ignition. For the weakly exothermic cases considered, including modes of slow reaction and cool flames, the Boussinesq approximation is completely adequate. However, it overpredicts the density change and underpredicts the ignition delay time for high-temperature ignitions. Qualitative comparison with experimental results acquired at microgravity conditions are also discussed.
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References
Barnard JA, Harwood BA (1974) Physical factors in the study of the spontaneous ignition of hydrocarbons in static systems. Combust Flame 22(1):35–42
Campbell AN, Cardoso SSS, Hayhurst AN (2005a) The influence of natural convection on the temporal development of the temperature and concentration fields for Sal’nikov’s reaction, P→A→B, occurring batchwise in the gas phase in a closed vessel. Chem Eng Sci 60(21):5705–5717. doi:10.1016/j.ces.2005.04.062
Campbell AN, Cardoso SSS, Hayhurst AN (2005b) A scaling analysis of Sal’nikov’s reaction, P→A→B, in the presence of natural convection and the diffusion of heat and matter. Proc R Soc, Ser A 461(2059):1999–2020
Campbell AN, Cardoso SSS, Hayhurst AN (2006) A scaling analysis of the effects of natural convection, when Sal’nikov’s reaction: P→A→B occurs, together with diffusion and heat transfer in a batch reactor. Chem Eng Res Des 84(A7):553–561
Campbell AN, Cardoso SSS, Hayhurst AN (2007) A comparison of measured temperatures with those calculated numerically and analytically for an exothermic chemical reaction inside a spherical batch reactor with natural convection. Chem Eng Sci 62(A7):3068–3082
Cardoso SSS, Kan PC, Savjani KK, Hayhurst AN, Griffiths JF (2004a) The computation of the velocity, concentration, and temperature fields during a gas-phase oscillatory reaction in a closed vessel with natural convection. Combust Flame 136(1–2):241–245
Cardoso SSS, Kan PC, Savjani KK, Hayhurst AN, Griffiths JF (2004b) The effect of natural convection on the gas-phase Sal’nikov reaction in a closed vessel. Phys Chem Chem Phys 6:1687–1696
COMSOL AB (2008) COMSOL Multiphysics reference guide, version 3.5a
Fairlie R, Griffiths JF, Pearlman H (2000) A numerical study of cool flame development under microgravity. Proc Combust Inst 28:1693–1699
Fairlie R, Griffiths JF, Hughes KJ, Pearlman H (2005) Cool flames in space: experimental and numerical studies of propane oxidation. Proc Combust Inst 30:1057–1064
Fine DH, Gray P, MacKinven R (1970) Thermal effects accompanying spontaneous ignitions in gases. II. The slow exothermic decomposition of diethyl peroxide. Proc R Soc London, Ser A 316(1525):241–254
Foster M (2006) Earth, partial, and reduced gravity experiments and numerical work on propane-oxygen cool flames at sub-atmospheric pressures. Master’s thesis, Drexel University
Foster M (2007) Low-temperature reactions and cool flames in an unstirred, static reactor at terrestrial and reduced-gravity. PhD thesis, Drexel University
Foster M, Pearlman H (2006a) Cool flames at terrestrial, partial and near-zero gravity. Combust Flame 147(1–2):108–117
Foster M, Pearlman H (2006b) Diffusion-controlled cool flame propagation speeds. In: 44th AIAA aerospace sciences meeting and exhibit, AIAA-2006-1132
Foster M, Pearlman H (2007) Cool flame propagation speeds. Combust Sci Technol 179:13–49
Frank-Kamenetskii DA (1955) Diffusion and heat transfer in chemical kinetics. Princeton University Press, Princeton
Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward CS (2005) SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Trans Math Softw 31(3):363–396
Kagan L, Beresycki H, Joulin G, Sivashinsky G (1997) The effect of stirring on the limits of thermal explosion. Combust Theory Model 1(1):97–111
Liang C, Mou C, Lee D (2003) Dynamic behavior and sensitivity of skeleton thermokinetic model for acetaldehyde oxidation. Chem Eng Sci 58:4173–4184
Pearlman H (2000) Low-temperature oxidation reactions and cool flames at earth and reduced gravity. Combust Flame 121(1–2):390–393
Pearlman H (2007) Multiple cool flames in static, unstirred reactors under reduced-gravity and terrestrial conditions. Combust Flame 148:280–284
Pearlman H, Foster M (2008) The role of diffusive transport on low and intermediate temperature hydrocarbon oxidation: closed reactor experiments using equimolar n-C4H10+O2 premixtures at reduced-gravity. Combust Sci Technol 180(2):219–229
Pearlman H, Foster M, Karakacak D (2003) Cool flames in propane-oxygen premixtures at low and intermediate temperatures at reduced-gravity. In: Seventh international workshop on microgravity combustion and chemically reacting systems, pp 193–196
Semenov NN (1935) Chemical kinetics and chain reactions. Oxford University Press, Oxford
Tyler BJ (1966) An experimental investigation of conductive and convective heat transfer during exothermic gas phase reactions. Combust Flame 10(1):90–91
Wang X, Mou CY (1985) A thermokinetic model of complex oscillations in gaseous hydrocarbon oxidation. J Chem Phys 83(9):4554–4561
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Foster, M.R., Pearlman, H. Non-Isothermal Cool Flames in Unstirred Static Reactors: A Compressible Model with Global Kinetics. Microgravity Sci. Technol. 24, 113–125 (2012). https://doi.org/10.1007/s12217-012-9302-0
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DOI: https://doi.org/10.1007/s12217-012-9302-0