Applied Scientific Research

, Volume 51, Issue 4, pp 687–711 | Cite as

Two dimensional linear stability of premixed laminar flames under zero gravity

  • H. S. Mukunda
  • J. P. Drummond
Article

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.

Nomenclature

Af

Frequency factor for the forward reaction

Ab

Frequency factor for the backward reaction

Yi

Mass fraction of speciesi

\(\dot \omega _i^m \)

Volumetric reaction rate of speciesi

cp

Specific heat at constant pressure

Di

Trace diffusion coefficient ofspeciesi

E

Activation energy

hi

Enthalpy of speciesi

hs

Sensible enthalpy of the mixture

hct

Heat of combustion of the reaction

hio

Heat of formation of speciesi

Ji,j

Jacobian of the reactioni with respect to speciesj

k

Wave number

Lei

Lewis number of speciesi

Mi

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

Tr

Reference temperature = initial temperature

Tad

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

δf

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

Subscripts

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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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • H. S. Mukunda
    • 1
  • J. P. Drummond
    • 2
  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.NASA Langley Research CenterHamptonUSA

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