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Two dimensional linear stability of premixed laminar flames under zero gravity

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Abstract

This paper reports on the numerical study of the linear stability of laminar premixed flames under zero gravity. The study specifically addresses the dependence of stability on finite rate chemistry with low activation energy and variable thermodynamic and transport properties. The calculations show that activation energy and details of chemistry play a minor role in altering the linear neutral stability results from asymptotic analysis. Variable specific heat makes a marginal change to the stability. Variable transport properties on the other hand tend to substantially enhance the stability from critical wave number of about 0.5 to 0.20. Also, it appears that the effects of variable properties tend to nullify the effects of non-unity Lewis number. When the Lewis number of a single species is different from unity, as will happen in a hydrogen-air premixed flame, the stability results remain close to that of unity Lewis number.

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Abbreviations

A f :

Frequency factor for the forward reaction

A b :

Frequency factor for the backward reaction

Y i :

Mass fraction of speciesi

\(\dot \omega _i^m \) :

Volumetric reaction rate of speciesi

c p :

Specific heat at constant pressure

D i :

Trace diffusion coefficient ofspeciesi

E :

Activation energy

h i :

Enthalpy of speciesi

h s :

Sensible enthalpy of the mixture

h ct :

Heat of combustion of the reaction

h o i :

Heat of formation of speciesi

J i,j :

Jacobian of the reactioni with respect to speciesj

k :

Wave number

Le i :

Lewis number of speciesi

M i :

Molecular weight of speciesi

ns :

Number of Species=4, here

p :

Pressure

Pr:

Prandtl number

R:

Universal gas constant

Re :

Reynolds number

s :

Stoichiometric ratio

T :

Temperature

T r :

Reference temperature = initial temperature

T ad :

Adiabatic flame temperature

t :

Time

u :

Streamwise velocity

v :

Transverse velocity

x :

Streamwise coordinate

y :

Transverse coordinate

z :

product of density andu velocity

κ :

Conductivity

τ :

Non-dimensional temperature

δ f :

Flame thickness

φ :

Disturbance function

θ :

Activation parameter

γ :

Ratio of specific heats

ρ :

Density

μ :

Laminar viscosity

ω :

Coefficient of time in the disturbance

f :

Perturbed quantity

r :

Value at reference condition

s :

Steady state

i :

Species identity, 1 for fuel, 2 for oxidizer, 3 for product and 4 for inert

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Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Science, 560 012, Bangalore, India

    H. S. Mukunda

  2. NASA Langley Research Center, Hampton, Virginia, USA

    J. P. Drummond

Authors
  1. H. S. Mukunda
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  2. J. P. Drummond
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Mukunda, H.S., Drummond, J.P. Two dimensional linear stability of premixed laminar flames under zero gravity. Appl. Sci. Res. 51, 687–711 (1993). https://doi.org/10.1007/BF00849273

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  • DOI: https://doi.org/10.1007/BF00849273

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