Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-24T23:49:12.526Z Has data issue: false hasContentIssue false
  • English
  • Français

Sheath vaporization of a monodisperse fuel-spray jet

Published online by Cambridge University Press:  17 March 2011

J. ARRIETA-SANAGUSTÍN ,
A. L. SÁNCHEZ ,
A. LIÑÁN  and
F. A. WILLIAMS
J. ARRIETA-SANAGUSTÍN
Affiliation:
Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, Leganés 28911, Spain
A. L. SÁNCHEZ*
Affiliation:
Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, Leganés 28911, Spain
A. LIÑÁN
Affiliation:
ETSI Aeronáuticos, Plaza de Cardenal Cisneros 3, Madrid 28040, Spain
F. A. WILLIAMS
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093-0411, USA
*
†Email address for correspondence: asanchez@ing.uc3m.es
Get access Rights & Permissions [Opens in a new window]

Abstract

The group vaporization of a monodisperse fuel-spray jet discharging into a hot coflowing gaseous stream is investigated for steady flow by numerical and asymptotic methods with a two-continua formulation used for the description of the gas and liquid phases. The jet is assumed to be slender and laminar, as occurs when the Reynolds number is moderately large, so that the boundary-layer form of the conservation equations can be employed in the analysis. Two dimensionless parameters are found to control the flow structure, namely the spray dilution parameter λ, defined as the mass of liquid fuel per unit mass of gas in the spray stream, and the group vaporization parameter ϵ, defined as the ratio of the characteristic time of spray evolution due to droplet vaporization to the characteristic diffusion time across the jet. It is observed that, for the small values of ϵ often encountered in applications, vaporization occurs only in a thin layer separating the spray from the outer droplet-free stream. This regime of sheath vaporization, which is controlled by heat conduction, is amenable to a simplified asymptotic description, independent of ϵ, in which the location of the vaporization layer is determined numerically as a free boundary in a parabolic problem involving matching of the separate solutions in the external streams, with appropriate jump conditions obtained from analysis of the quasi-steady vaporization front. Separate consideration of dilute and dense sprays, corresponding, respectively, to the asymptotic limits λ ≪ 1 and λ ≫ 1, enables simplified descriptions to be obtained for the different flow variables, including explicit analytic expressions for the spray penetration distance.

JFM classification

Multiphase and Particle-laden Flows: Gas/liquid flow Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 435 - 464
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.Google Scholar
Aggarwal, S. K., Fix, G. J. & Sirignano, W. A. 1985 Two-phase laminar axisymmetric jet flow: explicit, implicit and split-operator approximations. Numer. Meth. Partial Differ. Eq. 1, 742–756.CrossRefGoogle Scholar
Annamalai, K. & Ryan, W. 1992 Interactive processes in gasification and combustion. 1. liquid-drop arrays and clouds. Prog. Energy Combust. Sci. 18, 221–295.CrossRefGoogle Scholar
Bermúdez, A., Ferrín, J. L. & Liñán, A. 2007 The modelling of the generation of volatiles, H2 and CO, and their simultaneous diffusion controlled oxidation, in pulverized coal furnaces. Combust. Theor. Model. 11, 949–976.CrossRefGoogle Scholar
Blazek, J. 2001 Computational Fluid Dynamics: Principles and Applications. Elsevier.Google Scholar
Chen, G. & Gomez, A. 1997 Dilute laminar spray diffusion flames near the transition from group combustion to individual droplet burning. Combust. Flame 110, 392–404.CrossRefGoogle Scholar
Chiu, H. H., Ahluwalia, R. K., Koh, B. & Croke, E. J. 1978 Spray group combustion. AIAA Paper 78-75 (presented at the 16th Aerospace Sciences Meeting, Huntsville, AL).Google Scholar
Chiu, H. H., Kim, H. Y. & Croke, E. J. 1982 Internal group combustion of liquid droplets. Proc. Combust. Inst. 19, 971–980.CrossRefGoogle Scholar
Chiu, H. H. & Liu, T. M. 1977 Group combustion of liquid droplets. Combust. Sci. Technol. 17, 127–142.CrossRefGoogle Scholar
Correa, S. M. & Sichel, M. 1982 a The boundary layer structure of a vaporizing fuel cloud. Combust. Sci. Technol. 28, 121–130.CrossRefGoogle Scholar
Correa, S. M. & Sichel, M. 1982 b The group combustion of a spherical cloud of monodisperse fuel droplets. Proc. Combust. Inst. 19, 981–991.CrossRefGoogle Scholar
Crane, L. J. 1972 Boundary layer flow on a circular cylinder moving in a fluid at rest. Z. Angew. Math. Phys. 23, 201–212.CrossRefGoogle Scholar
Crowe, C., Sommerfeld, M. & Tsuji, Y. 1998 Multiphase Flows with Droplets and Particles. CRC.Google Scholar
Dukowicz, J. K. 1980 A particle–fluid numerical model for liquid sprays. J. Comput. Phys. 35, 229–253.CrossRefGoogle Scholar
Faeth, G. M. 1983 Evaporation and combustion of sprays. Prog. Energy Combust. Sci. 9, 1–76.CrossRefGoogle Scholar
Glauert, M. B. & Lighthill, M. J. 1955 The axisymmetric boundary layer on a long thin cylinder. Proc. R. Soc. Lond. A 230, 188–203.Google Scholar
Godsave, G. A. E. 1953 Studies of the combustion of drops in a fuel spray – the burning of single drops of fuel. Proc. Combust. Inst. 4, 818–830.CrossRefGoogle Scholar
Karpetis, A. N. & Gomez, A. 2000 An experimental study of well-defined turbulent nonpreximed flames. Combust. Flame 121, 1–23.CrossRefGoogle Scholar
Kim, H. Y. & Chiu, H. H. 1983 Group combustion of liquid fuel sprays. AIAA Paper 83-0150 (presented at the 21st Aerospace Sciences Meeting, Reno, NE).Google Scholar
Labowsky, M. 1980 Calculation of the burning rates of interacting fuel droplets. Combust. Sci. Technol. 22, 217–226.CrossRefGoogle Scholar
Labowsky, M. & Rosner, D. E. 1978 Group combustion of droplets in fuel clouds. I. Quasi-steady predictions. In Evaporation–Combustion of Fuels (ed. Zung, J. T.), pp. 63–79. American Chemical Society.CrossRefGoogle Scholar
Lasheras, J. C. & Hopfinger, E. J. 2000 Liquid jet instability and atomization in a coaxial gas stream. Annu. Rev. Fluid Mech. 32, 275–308.CrossRefGoogle Scholar
Lee, D., Kim, H. Y., Yoon, S. S. & Cho, C. P. 2010 Group combustion of staggeringly arranged heptane droplets at various Reynolds numbers, oxygen mole-fractions, and separation distances. Fuel 89, 1447–1460.CrossRefGoogle Scholar
Liñán, A. 1985 Theory of droplet vaporization and combustion. In Modélisation des Phénomènes de Combustion (ed. Borghi, R., Clavin, P., Liñán, A., Pelcé, P. & Sivashinsky, G. I.), pp. 73–103 (CEA-EDF INRIA 59). Editions Eyrolles.Google Scholar
Luo, K., Pitsch, H., Pai, M. G. & Desjardin, O. 2011 Direct numerical simulations and analysis of three-dimensional n-heptane spray flames in a model swirl combustor. Proc. Combust. Inst. 33, 2143–2152.CrossRefGoogle Scholar
Reveillon, J. & Vervisch, L. 2005 Analysis of weakly turbulent dilute-spray flames and spray combustion regimes. J. Fluid Mech. 537, 317–347.CrossRefGoogle Scholar
Russo, S. & Gomez, A. 2006 Physical characterization of laminar spray flames in the pressure range 0.1–0.9 MPa. Combust. Flame 145, 339–356.CrossRefGoogle Scholar
Sichel, M. & Palaniswamy, S. 1984 Sheath combustion of sprays. Proc. Combust. Inst. 20, 1789–1798.CrossRefGoogle Scholar
Sirignano, W. A. 1983 Fuel droplet vaporization and spray combustion theory. Prog. Energy Combust. Sci. 9, 291–322.CrossRefGoogle Scholar
Sirignano, W. A. 1999 Fluid Dynamics and Transport of Droplets and Sprays. Cambridge University Press.CrossRefGoogle Scholar
Tanehill, J. C., Anderson, D. A. & Pletcher, R. H. 1984 Computational Fluid Mechanics and Heat Transfer. Taylor and Francis.Google Scholar
Williams, F. A. 1985 Combustion Theory, 2nd edn. Benjamin Cummings.Google Scholar