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Combustion of a single droplet in the presence of an oscillating flow

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Abstract

The two-dimensional, unsteady, laminar conservation equations for mass, momentum, energy and species transport in the gas phase are solved numerically in spherical coordinates. This is to study the heat and the mass transfer, and the combustion around a single spherical droplet. The droplet mass and momentum equations are also solved simultaneously with the gas phase equations in order to investigate the effects of droplet entrainment in the oscillating flow with and without a steady velocity. The numerical solution for a single droplet combustion gives the droplet diameter variation as well as the gas phase velocity, temperature and species concentrations as a function of time. The effects of frequency, amplitude of oscillating flow, velocity ratio of oscillating flow amplitude to the steady velocity, ambient temperature and initial droplet diameter on the droplet combustion are also investigated. The droplet burning history is not governed by thed 2-law in the presence of oscillating flow, unlike to the case under quiescent ambient conditions.

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Abbreviations

C p :

Specific heat

d :

Droplet diameter

D v :

Binary diffusion coefficient

E :

Activation energy

f :

Frequency

i :

Static enthalpy

k :

Thermal conductivity

K :

Frequency factor

L :

Heat of gasification for unit mass of fuel

m t :

Droplet mass

m l :

Net mass flux

P :

Pressure

Q :

Heat of combustion for unit mass of fuel

Γ:

Radial position

R a :

Universal gas constant

R e :

Reynolds number |U-v 1|D/v

Sϕ:

Source term for general variable ϕ

t :

Time

T :

Temperature

u r :

Radial velocity

uθ:

Axial velocity

U o :

Steady slip velocity

U 1 :

Acoustic peak velocity

v l :

Droplet velocity

W :

Reaction rate

W o :

Molecular weight of oxidizer

Y i :

Mass fraction of speciesi

Γϕ :

Diffusivity for general variable ϕ

σ:

Stoichiometric fuel-oxidizer mass ratio

θ:

Angular direction

μ:

Viscosity

ρ:

Gas density

ϕ:

General variable given in equation (1)

∞:

Infinity

bn :

Boiling

F :

Fuel

l :

Droplet

P :

Product

g :

Gas

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Authors and Affiliations

  1. Research Institute of Mechanical Technology School of Mechanical Engineering, Pusan National University, 30 Changjeon-Dong. Kumjeong-Ku, 609-735, Pusan, Korea

    Man Yeong Ha & Sun Kie Kim

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  1. Man Yeong Ha
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  2. Sun Kie Kim
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Ha, M.Y., Kim, S.K. Combustion of a single droplet in the presence of an oscillating flow. KSME Journal 9, 209–224 (1995). https://doi.org/10.1007/BF02953622

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