KSME International Journal

, Volume 18, Issue 8, pp 1338–1348

# Simplified Modeling of Deflagration in Vessels

Article

## Abstract

A simplified method that models the deflagration process occurring in closed or vented vessels is described. When combustion occurs within the spherical or cylindrical vessels, the flame moves spherically or segmentally to the vessel periphery. The volume and area of each element along the propagating flame front are calculated by using simple geometrical rules. For instabilities and turbulence resulting in enhanced burning rates, a simple analysis results in reasonable agreement with the experimental pressure transients when two burning rates (a laminar burning rate prior to the onset of instability and an enhanced burning rate) were used. Pressure reduction caused by a vent opening at predetermined pressure was modeled. Parameters examined in the modeling include ignition location, mixture concentration, vented area, and vent opening pressure. It was found that venting was effective in reducing the peak pressure experienced in vessels. The model can be expected to estimate reasonable peak pressures and flame front distances by modeling the enhanced burning rates, that is, turbulent enhancement factor.

## Key Words

Deflagration Explosions Flame Gas Dynamics

## Nomenclature

A

Surface area

Aυ

Vent area

CD

Outflow coefficient

D

Diameter

H

Enthalpy

L

Length

m

Mass

p

Pressure

R

Distance to the flame front, R2=s2+r2

r

Distance to the flame front touched at the wall

St

Turbulent burning velocity

Su

Laminar burning velocity

s

T

Temperature

t

Time

V

Volume

## Greek Symbols

α, β

Empirical parameters

λ

Specific heat ratio

ρ

Gas density

φ

Turbulent correction factor

ϕ

Equivalence ratio

ν

Mole fraction

ξ

Heat formation

## Subscripts

b, u

Burned/unburned gas state

υ

Vented gas state

o

Standard gas state

f

Flame state

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