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Engineering and Systems   > Home   > Thermodynamics of Interfaces and Fluid Mechanics   > Issue 1   > Article

Drop vaporization frequency response: an approximate analytical solution for mixed injection regimes

Réponse en fréquence de l’évaporation des gouttes : une solution analytique approximative pour les régimes d’injection mixtes


Kwassi Anani
University of Lomé
Togo

Roger Prud’homme
Sorbonne University / Centre National de la Recherche Scientifique
France

Mahouton Norbert Hounkonnou
University of Abomey-Calavi
Republic of Benin



Published on 29 October 2021   DOI : 10.21494/ISTE.OP.2021.0748

Abstract

Résumé

Keywords

Mots-clés

This work is devoted to a theoretical analysis of evaporating mass frequency response to pressure oscillations of a spray of repetitively injected drops into a combustion chamber. A single stationary spherical droplet continuously fed with the same liquid fuel, so that its volume remains constant in spite of the evaporation, the so-called ‘mean droplet’ in the Heidmann analogy, represents this vaporizing spray of droplets. The feeding is realized with a liquid-liquid heat transfer coefficient by using a source point placed at the mean droplet centre, in such a way that only radial thermal convection and conduction effects are allowed inside the droplet during the process. This feeding procedure is now viewed as a proper boundary condition that is a mixed or a generalized feeding regime controlling the whole process of liquid fuel injection into the combustion chamber. Drawing upon a linear analysis based on the Rayleigh criterion, the evaporating mass response factor is evaluated. Effects due to the variation of the heat transfer coefficient and of the process characteristic times are analysed. Especially, an abrupt increase in the response function is related to the influence of the value of a particular fuel thermodynamic coefficient.

This work is devoted to a theoretical analysis of evaporating mass frequency response to pressure oscillations of a spray of repetitively injected drops into a combustion chamber. A single stationary spherical droplet continuously fed with the same liquid fuel, so that its volume remains constant in spite of the evaporation, the so-called ‘mean droplet’ in the Heidmann analogy, represents this vaporizing spray of droplets. The feeding is realized with a liquid-liquid heat transfer coefficient by using a source point placed at the mean droplet centre, in such a way that only radial thermal convection and conduction effects are allowed inside the droplet during the process. This feeding procedure is now viewed as a proper boundary condition that is a mixed or a generalized feeding regime controlling the whole process of liquid fuel injection into the combustion chamber. Drawing upon a linear analysis based on the Rayleigh criterion, the evaporating mass response factor is evaluated. Effects due to the variation of the heat transfer coefficient and of the process characteristic times are analysed. Especially, an abrupt increase in the response function is related to the influence of the value of a particular fuel thermodynamic coefficient.

combustion instability heat exchange ratio truncated expansion double confluent Heun equation transfer function.

combustion instability heat exchange ratio truncated expansion double confluent Heun equation transfer function