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Nonlinear acoustic-pressure responses of oxygen droplet flames burning in gaseous hydrogen

  • Thermal Engineering · Fluid Engineering · Energy and Power Engineering
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Abstract

A nonlinear acoustic instability of subcritical liquid-oxygen droplet flames burning in gaseous hydrogen environment are investigated numerically. Emphases are focused on the effects of finite-rate kinetics by employing a detailed hydrogen-oxygen chemistry and of the phase change of liquid oxygen. Results show that if nonlinear harmonic pressure oscillations are imposed, larger flame responses occur during the period that the pressure passes its temporal minimum, at which point flames are closer to extinction condition. Consequently, the flame response function, normalized during one cycle of pressure oscillation, increases nonlinearly with the amplitude of pressure perturbation. This nonlinear response behavior can be explained as a possible mechanism to produce the threshold phenomena for acoustic instability, often observed during rocket-engine tests.

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Abbreviations

A i :

Pre-exponential factor inith reaction step

b i :

Temperature exponent inith reaction step

D j :

Diffusion coefficient ofjth species

E i :

Activation energy inith reaction step

H :

Normalized nonlinear amplification contribution as defined in Eq. (12)

h :

Specific enthalpy of mixture

h j :

Specific enthalpy ofjth species

K i :

Reaction rate constant inith reaction step

L :

Latent heat of evaporation of liquid oxygen

\(\overline M \) :

Averaged molecular weight of mixture

M j :

Molecular weight ofjth species

m :

Radial mass flux (≡ρur 2)

n s :

Number of species

p :

Pressure

Q :

Total heat-release-rate as defined in Eq. (11)

Q ′ :

Heat-release rate per unit length

Q ″ :

Heat-release rate per unit volume

R :

Gas constant

\(\overline R \) :

Universal gas constant

r :

Radial coordinate

\(\tilde r_f \) :

Flame front stand-off ratio

T :

Temperature

t :

Time

u :

Radial velocity

V c :

Correction velocity

V j :

Diffusion velocity ofjth species

w j :

Net production rate ofjth species

X :

Mole fraction

Y :

Mass fraction

Θ j :

Thermal diffusion ratio

θ:

Phase difference

λ:

Heat conductivity of mixture

ρ:

Density

φ:

Phase angle

ω:

Acoustic frequency

a :

Oscillation amplitude

B :

Saturation state of liquid

f :

Condition at flame

g :

Gaseous state

l :

Liquid state

m :

Mean

s :

Droplet surface

∞:

Ambience

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Authors and Affiliations

  1. Environment Research Center, Korea Institute of Science and Technology, Korea

    Jong Soo Kim

  2. Department of Mechanical and Aerospace Engineering, Seoul National University, 151-742, Seoul, Korea

    Hong Jip Kim, Chae Hoon Sohn & Suk Ho Chung

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  1. Hong Jip Kim
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  2. Chae Hoon Sohn
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  3. Suk Ho Chung
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  4. Jong Soo Kim
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Correspondence to Suk Ho Chung.

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Kim, H.J., Sohn, C.H., Chung, S.H. et al. Nonlinear acoustic-pressure responses of oxygen droplet flames burning in gaseous hydrogen. KSME International Journal 15, 510–521 (2001). https://doi.org/10.1007/BF03185112

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  • DOI: https://doi.org/10.1007/BF03185112

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