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Effect of thermal convection on frequency response of a perturbed vaporizing pastille-shaped droplet

Published online by Cambridge University Press:  09 June 2011

Kwassi Anani ,
Roger Prud’homme ,
Séna Amah d’Almeida  and
Kofi Seylom Assiamoua
Kwassi Anani*
Affiliation:
Doctoral School of Mathematics and Applications, Department of Mathematics, University of Lomé, BP 1515, Lomé, Togo
Roger Prud’homme
Affiliation:
Doctoral School of Mathematics and Applications, Department of Mathematics, University of Lomé, BP 1515, Lomé, Togo
Séna Amah d’Almeida
Affiliation:
Doctoral School of Mathematics and Applications, Department of Mathematics, University of Lomé, BP 1515, Lomé, Togo
Kofi Seylom Assiamoua
Affiliation:
Doctoral School of Mathematics and Applications, Department of Mathematics, University of Lomé, BP 1515, Lomé, Togo
*
aCorresponding author: [email protected]
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Abstract

We study the dynamic response to small acoustic oscillations of a vaporizing droplet in shape of a pastille (a small liquid cylinder, called “pastille” in the sequel, the height of which being smaller than the radius of the base). Contrary to some previously proposed models, where the thermal convection effect inside the droplet is often neglected, the continuously fed pastille-shaped model takes into account the effects of both thermal convection and conduction. Curves related to different heat exchange coefficients are presented for the frequency response of the vaporization rate. The case where the feeding process at the bottom of the pastille is assumed isothermal (isothermal bottom regime) is compared to the one where the feeding process at the bottom of the pastille is adiabatic (adiabatic bottom regime). The response factor curves for the pure conduction model of the spherical droplet and for the present model of the “equivalent pastille” are also compared. The temperature field perturbation is then examined. As well as for the evaporation mass flow rate perturbation, comparisons are made between the regime with an isothermal bottom and the one with an adiabatic bottom. We find that, in spite of some divergences observed between the various cases, the frequency response of a droplet submitted to acoustic oscillations presents also some common points. It is shown that the life time (or residence time), the thermal diffusion time, and the period of the harmonic perturbation do intervene strongly in the behaviour of the vaporizing pastille. The liquid propulsion is a possible application of this basic study conducted as part of a thesis.

Keywords

Pastilleevaporationharmonic oscillationsresponse factortemperature perturbation
Type
Research Article
Information
Mechanics & Industry , Volume 12 , Issue 4 , 2011 , pp. 301 - 313
Copyright
© AFM, EDP Sciences 2011

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References

Prud’homme, R., Habiballah, M., Matuszewski, L., Mauriot, Y., Nicole, A., Theoretical analysis of dynamic response of a vaporizing droplet to a acoustic oscillation, J. Propuls. Power (0748-4658) 26 (2010) 1 Google Scholar
Bhatia, R., Sirignano, W.A., One-dimensional analysis of liquid-fuel combustion instability, J. Propulsion 7 (1991) 953–961 CrossRefGoogle Scholar
Culick, F., Yang, V., Overview of combustion instabilities in liquid-propellant rocket engines, Liquid Rocket Engine Combustion Instability AIAA 169 (1995) 3–37 Google Scholar
Delplanque, J.-P., Sirignano, W.A., Transcritical liquid oxygen droplet vaporization: effect on rocket combustion instability, Atomization and sprays 4 (1996) 325–349 CrossRefGoogle Scholar
M. DiCicco, J. Buckmaster, Acoustic instabilities driven by slip between a condensed phase and the gas-phase in combustion systems, 32nd AIAA Aerospace Sciences Meeting and Exhibit, Paper AIAA 94-0103, Reno, NV (USA), 1994, pp. 10–13
I. Dubois, M. Habiballah, R. Lecourt, Numerical analysis of liquid rocket engine combustion instability, 33rd AIAA Aerospace Sciences Meeting and Exhibit, Paper AIAA-95-0607, Reno, NV (USA), 1995, pp. 9–12
Duvur, A., Chiang, C.H., Sirignano, W.A., Oscillatory fuel droplet vaporization: driving mechanism for combustion instability, J. Propuls. Power 12 (1996) 358–365 CrossRefGoogle Scholar
D.T. Harrje, F.H. Reardon, Liquid propellant rocket combustion instability, NASA SP-194, 1972
M.F. Heidmann, P.R. Wieber, Analysis of frequency response characteristics of propellant vaporisation, NASA Technical Note D-3749, 1966
M.F. Heidmann, Frequency response of a vaporization process to distorted acoustic disturbances, NASA Technical Note D-6806, 1972
R. Prud’homme, Evaporation et combustion de gouttes dans les moteurs, Editions Techniques de l’Ingénieur, Traité de Mécanique, BM 2 521, 2009, p. 22
R. Prud’homme, Flows of reactive fluids, Book Series: Fluid Mechanics and Its applications, Springer, 2010, Vol. 94
R. Prudhomme, M. Habiballah, A. Nicole, Y. Mauriot, Instabilités liées au phénomène d’évaporation: Réponse dynamique d’une goutte à un champ acoustique, 17e Congrès Français de Mécanique, Troyes, 2005
Sazhin, S.S., Advanced models of fuel droplet heating and evaporation, Progr. Energ. Combust. Sci. 32 (2006) 162–214 CrossRefGoogle Scholar
L. Rayleigh, The theory of sound, Macmillan, 1945
Aggarwal, S.K., Tong, A.Y., Sirignano, W.A., A comparison of vaporization models in spray calculations, AIAA J. 22 (1984) 1448–1457 CrossRefGoogle Scholar
R. Prudhomme, M. Habiballah, Évaporation et combustion de gouttes: revue des hypothèses et des principaux résultats de l’analyse quasi-stationnaire, Rapport Technique ONERA N RT 1/05 424, 2001
Law, C.K., Recent advances in droplet vaporization and combustion, Proc. Energy Combustion Science 8 (1982) 171–201 CrossRefGoogle Scholar
W.A. Sirignano, J.-P. Delplanque, C.H. Chiang, R. Bhatia, Liquid-propellant droplet vaporization: a rate controlling process for combustion instability, in Liquid rocket engine combustion instability, edited by V. Yang, W.E. Anderson, Progress in Astronautics and Aeronautics 169 (1994), Publ. AIAA
M. De Benedictis, Instabilités couplées haute fréquence dans les moteurs-fusées à ergols liquides : étude du couplage chambre de combustion/système d’alimentation, Thèse, Université de Poitiers, 2007
V. Yang and W. Anderson, Liquid propellant rocket combustion instability, Progress in astronautics and aeronautics, 169, 1995