https://hal.science/hal-01995198Prud'Homme, RogerRogerPrud'HommeIJLRDA-FRT - Fluides Réactifs et Turbulence - DALEMBERT - Institut Jean le Rond d'Alembert - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche ScientifiqueONERA - The French Aerospace Lab [Châtillon] - ONERA - Université Paris Saclay (COmUE)Habiballah, MohammedMohammedHabiballahONERA - The French Aerospace Lab [Châtillon] - ONERA - Université Paris Saclay (COmUE)Matuszewski, LionelLionelMatuszewskiONERA - The French Aerospace Lab [Palaiseau] - ONERA - Université Paris Saclay (COmUE)Mauriot, YvesYvesMauriotDMPE, ONERA, Université Paris Saclay (COmUE) [Palaiseau] - ONERA - Université Paris Saclay (COmUE)Nicole, AurélieAurélieNicoleONERA - The French Aerospace Lab [Châtillon] - ONERA - Université Paris Saclay (COmUE)Theoretical analysis of dynamic response of a vaporizing droplet to acoustic oscillations.HAL CCSD2010[SPI.FLUID] Engineering Sciences [physics]/Reactive fluid environment[SPI] Engineering Sciences [physics]Prud'homme, Roger2020-04-19 20:12:282021-11-16 05:05:202020-04-23 08:16:47enJournal articleshttps://hal.science/hal-01995198/document10.2514/1.39379application/pdf1This paper deals with the analysis of an unsteady evaporating droplet, in connection with combustion instabilities in rocket engines. We first present a bibliographic survey. We then obtain an analytical solution in the frequency domain using the Heidmann analogy of a spherical droplet of constant volume, which represents a mean droplet at a fixed place in a chamber, in the steady regime. For the case of a moderate characteristic time of liquid thermal conduction compared to the droplet lifetime, we show that, for small perturbations, the knowledge of the response factor makes it possible to determine exactly the amplification zone in the frequency domain. We first consider the simplification of Heidmann and Wieber, for which the droplet has a uniform temperature. We then present a new analysis, in which the finite thermal diffusivity of the liquid is taken into account. We find strong differences compared to the results of the preceding model. For the purpose of implementation in a numerical code, we derive a thermal transfer model with n discrete layers. For the case n=2 we verify that this model can be optimized by adjusting the volumetric ratios between layers. Finally, the quasi-steady equations of the gas phase are presented in the appendix.