Predicting the vaporization rate of a spreading cryogenic liquid pool on concrete using an improved 1-D heat conduction equation

Abstract

The accidental spilling of cryogenic liquid leads to formation of a spreading pool, which may result in pool fires, BLEVE(boiled liquid evaporate vapor explosion) or vapor cloud fire, such as liquefied natural gas, is flammable. The key aspect of evaluating the consequence of such a disaster is to predict vaporization rate of the spreading cryogenic liquid pool. In this study, an empirical function was established to predict the temperature gradient of concrete. Afterwards an improved 1-D heat conduction equation was established to predict heat conduction of the spreading cryogenic liquid, and then vaporization rate was measured. In addition, to validate accuracy of the improved 1-D heat conduction equation, small-scale experiments were conducted to calculate vaporization rate for a spreading cryogenic liquid pool. The resulting vaporization rate decreased with discharge time, and increased with spill rate. The established empirical function was used to predict the temperature gradient displayed satisfactory accuracy with absolute average relative errors (AAREs) less than 10%; the improved 1-D heat transfer model AAREs were less than 13% compared with the experimental value. In summary, the improved 1-D heat transfer model can be applied to predict vaporization rate if the spill rate and discharge time are confirmed.

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Abbreviations

r :

pool radius, m

u :

radial liquid velocity at the edge, m/s

q s :

spill rate, kg/s

\( {M}_s^{mass} \) :

weight of the released liquid , kg

Δt :

discharge time, s

t st :

starting time, s

t end :

end time, s

ρ :

liquid density, kg/m3

H :

depth of the pool, m

h c,∞ :

minimum depth of the pool, m

α i :

molecular weight liquid, kg/mol

p i :

vapor pressure above the pool, N/m2

u * :

atmospheric friction velocity above the pool, m/s;

n :

wind profile index

m m,V :

mole fraction of vapor above liquid pool surface, mol/mol;

v :

kinematic viscosity , m2/s;

D :

diffusion coefficient, m2/s.

T :

temperature

t :

time, s

q :

heat flux, W/m2

A :

pool area, m2

L C :

characteristic length, m

λ :

thermal conductivity, W/(K·m)

C p :

specific heat capacity of air, J/(kg·K)

η :

dynamic viscosity, Pa·s

L :

latent heat of vaporization, J/kg

a :

thermal diffusivity, m2/s

u w,10 :

wind speed at 10 m height, m/s

g :

Acceleration of gravity, 9.8m/s2

E :

vaporization rate, kg/(m2·s)

L :

Liquid phase

a :

Ambient

v :

Vapor phase

b :

Boiling point

w :

Concrete ground

t :

Turbulence flow

L :

Laminar flow

Nu :

Nusselt number

Re :

Reynolds number

Sc :

Schmidt number

Pr :

Prandtl number

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Acknowledgements

This paper was supported by a Nanchong Technology Bureau Project Award under grant number 18SXHZ0021 and the National Natural Science Foundation of China under grant number 51474184.

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Correspondence to Chengjun Jing.

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Dong, J., Jing, C., Wen, H. et al. Predicting the vaporization rate of a spreading cryogenic liquid pool on concrete using an improved 1-D heat conduction equation. Heat Mass Transfer (2021). https://doi.org/10.1007/s00231-021-03018-9

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Keywords

  • Cryogenic liquid
  • Spill on concrete
  • Spreading pool
  • Vaporization rate
  • 1-D heat conduction model
  • Temperature gradient