Theoretical Analysis of Thermal Conduction Effect on Frequency Response of a Perturbed Vaporizing Spherical Droplet

Abstract

In this work, model results of the effect of thermal conduction on frequency response of a perturbed vaporizing spherical droplet are presented and discussed. The linear analysis of dynamic response to small acoustics oscillations are performed on the basis of the Rayleigh criterion for a mean spherical droplet representing the spray of repetitively injected droplets in the combustion chamber. Curves related to different heat exchange coefficients are presented for the frequency response of the vaporization rate. The not-yet-solved case of imposed temperature at the centre of the spherical droplet (isothermal centre regime or isothermal injection regime) is taking into account here. The case is now compared to the case where the feeding process at the centre of the spherical droplet is assumed adiabatic (adiabatic centre regime or adiabatic injection regime). Each feeding case here considered represents a specific boundary condition controlling the whole injection process. The temperature field perturbation inside the droplet is then examined. Comparisons are also made between the adiabatic and the isothermal injection regimes and differences are analysed. It is shown that the characteristic times of the evaporation process, the period of the harmonic perturbation and a particular parameter depending on fuel physical properties do intervene strongly in the behaviour of the vaporizing droplet. Especially, in the isothermal injection regime, due to this particular parameter, high and non-linear frequency responses may appear in the process. The results of this theoretical study may be applied in establishments of combustion systems stability limits.