An Investigation of the Behavior of Steady-State Laminar Jet Spray Flames

Noam Weinberg; J. Barry Greenberg

doi:10.1515/tjj-2018-0008

Artikel

An Investigation of the Behavior of Steady-State Laminar Jet Spray Flames

Noam Weinberg und J. Barry Greenberg

Veröffentlicht/Copyright: 3. April 2018

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Aus der Zeitschrift International Journal of Turbo & Jet-Engines Band 38 Heft 2

Abstract

The theory of steady-state laminar jet spray flames is developed in the limit of small Stokes number. The spray is modeled using the sectional approach. A similarity solution is suggested, and it is shown that for typical operating conditions the leading order small Stokes number solution suffices for determining lift-off and blow-out features of the flames. The latter are demonstrated to be strongly dependent on spray properties, in contrast to the Schmidt number dependence only which was predicted by classical laminar jet gaseous flame theory. The strong influence of the ambient oxygen content and the liquid fuel’s evaporation coefficient on flame characteristics, blow-out and lift-off are established.

Keywords: spray diffusion flames; jet flames; flame blow-out

JEL Classification: 47.70 Pq; 51.20+d; 47.55D-

Acknowledgements

JBG wishes to thank the Lady Davis Chair in Aerospace Engineering for support of this work.

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Appendix– Normalization

In this Appendix the way in which parameters used in the text are normalized is elucidated. In what follows the suffix i refers to conditions at the jet inlet (burner port).

x∗,y∗=x,y/di where di is the initial jet width.

u∗,v∗=u,v/Ui where Ui is the average axial velocity at the inlet.

ud∗,vd∗=ud,vd/Ui the average droplet velocity components.

St=τdUi/di the Stokes number with the droplets relaxation time given by τd=ρdDd2/18μ with ρd and Dd being the density of the liquid fuel and the average diameter of the fuel droplets, respectively, and μ the gas phase viscosity.

Yd∗=Yd/YF,i+Yd,i

β2∗,β3∗=β2−β2,∞β2,i−β2,∞,β3−β3,∞β3,i−β3,∞

in which:

β2,β3=YF−YO/ν,cpT+LYF/Q+1−L/QYO/ν

and β2,∞,β3,∞ are the values evaluated as y→∞,

where YF,YO are mass fractions of fuel vapor and oxygen respectively, ν is the stoichiometric coefficient, T is temperature, cp is specific heat, Q is heat of reaction and L is latent heat of vaporization.

Rei=ρUidi/μ is the Reynolds number at the inlet, with ρ the gas density. Sc=μ/ρD is the Schmidt number, with D the gas diffusion coefficient.

C∗=Cdi/Ui is the normalized sectional evaporation coefficient where C is the sectional evaporation coefficient, and:

αi=YF,i+Yd,i/β2,i−β2,∞

Received: 2018-03-08

Accepted: 2018-03-20

Published Online: 2018-04-03

Published in Print: 2021-05-26

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Artikel in diesem Heft

https://doi.org/10.1515/tjj-2018-0008

Schlagwörter für diesen Artikel

spray diffusion flames; jet flames; flame blow-out