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Pressure gradients due to gas expansion in the boundary layer combustion of a condensed fuel

Druckgradienten aufgrund von Expansion bei der Grenzschichtverbrennung eines festen Brennstoffes

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Abstract

Ignition and combustion of a condensed fuel in a gaseous high temperature oxidizing boundary layer flow is analyzed on the basis of higher order boundary layer theory. First order effects due to displacement thickness are taken into account and the pressure gradients generated in the outer potential flow are included in the numerical solution of the governing equations. The strong positive pressure gradients which are induced by expansion in front of the flame generate a low velocity region which facilitates a longitudinal diffusion of heat and mass.

Zusammenfassung

Es wird die Zündung und Verbrennung eines festen Brennstoffs in einer heißen gasförmigen oxidierenden Grenzschichtströmung auf der Grundlage der Grenzschichttheorie höherer Ordnung untersucht. Effekte erster Ordnung aufgrund der Verdrängungsdicke werden berücksichtigt und Druckgradienten, die in der äußeren Potentialströmung erzeugt werden, sind in der numerischen Lösung der Bestimmungsgleichungen eingeschlossen. Die starken positiven Druckgradienten, die durch die Expansion vor der Flamme induziert werden, erzeugen ein Gebiet niedriger Geschwindigkeit, was einen Wärme- und Stofftransport entgegen der Hauptströmungsrichtung ermöglicht.

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Abbreviations

A :

preexponential factor for the gas-phase chemical reaction

D *± :

diffusion coefficient of speciesα

Ec :

Eckert number defined in Eq. (12)

f :

non-dimensional stream function introduced in Eq. (34)

L :

non-dimensional latent heat of vaporization defined in Eq. (42)

L *c :

characteristic length given in Eq. (40)

P :

non-dimensional pressure defined in Eq. (7)

Pr :

Prandtl number Pr=μ *∞ c *p /λ*

Q :

non-dimensional heat release defined in Eq. (23)

R :

Reynolds number R=ϱ *∞ u *∞ L *c /μ *∞

S :

non-dimensional coordinate defined in Eq. (23)

Scα :

Schmidt number for speciesα Scα=μ *∞ /ϱ*D *α

T *a :

activation temperature of the gas-phase chemical reaction

T*:

temperature

u *i :

cartesian components of the fluid velocity

V :

non-dimensional transversal fluid velocity

ωα :

generation rate of speciesα in mol per unit time unit volume

Wa :

molecular weight of speciesα

x*:

longitudinal coordinate

x *i :

cartesian coordinates

Yα :

mass concentration of speciesα

yα :

reduced mass concentration of speciesα defined in Eq. (35)

δ ij :

Kronecker delta; 0 fori ≠j, 1 fori =j

η :

non-dimensional similarity coordinate defined in Eq. (34)

λ*:

coefficient of thermal conduction

μ*:

coefficient of viscosity

vα :

stoichiometric coefficient of speciesα

ρ*:

gas density

ø :

non-dimensional temperature defined in Eq. (35)

Φ :

dissipation function

φ :

stream function defined in Eq. (30)

∞ :

free stream

α :

refers to species

∼:

outer flow

*:

dimensional variable

References

  1. Liñán, A.; Williams, F. A.: Theory of ignition of a reactive solid by constant energy flux. Combust. Sci. Technol. 3 (1971) 91

    Google Scholar 

  2. Niioka, T.; Williams, F. A.: Ignition of reactive solid in a hot stagnation-point flow. Combust. Flame 29 (1977) 43

    Google Scholar 

  3. Lisitskii, V. I.; Merzhanov, A. G.: ? Fiz. Goreniya Vzryva 1 (2) (1965) 62

    Google Scholar 

  4. Anderson, R.; Brown, R. S.; Shannon, L. S.: Ignition theory of solid propellants. AIAA paper (1964) 64–156

  5. Waldman, C. H.; Summerfield, M.: Theory of propellant ignition by heterogeneous reaction. AIAA J. 4 (1969) 1354

    Google Scholar 

  6. Kindelán, M.; Williams, F. A.: Radiant ignition of a combustible solid with gas-phase exothermicity. Acta Astronautica 2 (1975) 955

    Google Scholar 

  7. Krishnamurthy, L.: On gas-phase ignition of diffusion flame in the stagnation-point boundary layer. Acta Astronautica 3 (1976) 935

    Google Scholar 

  8. Kashiwagi, T.; McDonald, B. W.; Isoda, H.; Summerfield, M.: Ignition of a solid polymeric fuel in a hot oxidizing gas stream. Thirteenth Symposium (Int.) on Combustion. The Combustion Institute, Pittsburgh. PA (1971) 1973

    Google Scholar 

  9. Kashiwagi, T.; Summerfield, M.: Ignition and flame spreading over a solid fuel: Non-similar theory for a hot oxidizing boundary layer. Fourteenth Symposium (Int.) on Combustion. The Combustion Institute, Pittsburgh. PA (1973) 1235

    Google Scholar 

  10. Kashiwagi, T.; Kotia, G. G.; Summerfield, M.: Experimental study of ignition and subsequent flame spread of a solid fuel in a hot oxidizing gas stream. Combust. Flame 24 (1975) 357

    Google Scholar 

  11. Hirano, T.; Kanno, Y.: Aerodynamics and thermal structures of the laminar boundary layer over a flat plate with a diffusion flame. Fourteenth Symposium (Int.) on Combustion. The Combustion Institute, Pittsburgh. PA (1973) 391

    Google Scholar 

  12. Treviño, C.; Fernández-Pello, A. C.: Gas-phase ignition of a solid combustible in a convective flow. Latin American J. Heat Mass Transfer 9 (1985) 131

    Google Scholar 

  13. Van Dyke, M.: Perturbation methods in fluid mechanics. Stanford: Parabolic Press 1975

    Google Scholar 

  14. Lighthill, M. J.: Contribution to the theory of heat transfer through a laminar boundary layer. Proc. Royal Society A202 (1950) 359

    Google Scholar 

  15. Schlichting, H.: Boundary layer theory. New York: McGraw Hill 1978

    Google Scholar 

  16. Seshadri, K.; Williams, F. A.: Structure and extinction of counter flow diffusion flames above condensed fuels: Comparison between poly(methyl methacrylate) and its liquid monomer, both burning in nitrogen-air mixtures. J. Polym. Sci. 16 (1978) 1735

    Google Scholar 

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Authors and Affiliations

  1. Division de Ing. Mecánica y Eléctrica Facultad de Ingenieria, UNAM, Mexico D.F., Mexico

    C. Treviño

  2. Institut für Technische Mechanik, RWTH Aachen, D-5100, Aachen, FRG

    W. Stüttgen & N. Peters

Authors
  1. C. Treviño
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  2. W. Stüttgen
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  3. N. Peters
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Treviño, C., Stüttgen, W. & Peters, N. Pressure gradients due to gas expansion in the boundary layer combustion of a condensed fuel. Wärme- und Stoffübertragung 25, 309–319 (1990). https://doi.org/10.1007/BF01780744

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  • DOI: https://doi.org/10.1007/BF01780744

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