Existence of travelling waves and large activation energy limits for a onedimensional thermo-diffusive lean spray flame model
Résumé
This work provides a mathematical analysis of a thermo-diffusive combustion model for lean spray flames. We prove that the large activation energy limit of the model enjoys explicit expressions of two types correponding to two distinct combustion regimes, in contrast with similar gaseous flames as studied in Berestycki-Nicolaenko-Scheurer (1985). The transition parameter is proved to be the ratio between the speed of vaporisation and the speed of combustion, and we are able to prove and estimate the thickening of the combustion zone in the case of slow vaporisation, which is again a novelty compared to purely gaseous combustion. The model at task is therefore on the one hand simple enough to allow for explicit asymptotic limits, and on the other hand rich enough to capture some particular aspects of spray combustion. Finally, we briefly consider situations where the vaporisation is infinitely fast, where the spray is polydisperse, or where the geometry of the problem is different from that of the onedimensional travelling wave.
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