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Assessment of Fire Engineering Design Correlations Used to Describe the Geometry and Thermal Characteristics of Externally Venting Flames

Abstract

Externally venting flames (EVF) may emerge through openings in fully developed under-ventilated compartment fires, significantly increasing the risk of fire spreading to higher floors or adjacent buildings. Several fire engineering correlations have been developed, aiming to describe the main characteristics of EVF that affect the fire safety design aspects of a building, such as EVF geometry, EVF centreline temperature and EVF-induced heat flux to the façade elements. This work is motivated by recent literature reports suggesting that existing correlations, proposed in fire safety design guidelines (e.g. Eurocodes), cannot describe with sufficient accuracy the characteristics of EVF under realistic fire conditions. In this context, a wide range of EVF correlations are comparatively assessed and evaluated. Quantification of their predictive capabilities is achieved by means of comparison with measurements obtained in 30 different large-scale compartment-façade fire experiments, covering a broad range of heat release rates (2.8 MW to 10.3 MW), ventilation factor values (2.6 m5/2 to 11.53 m5/2) and ventilation conditions (no forced draught, forced draught). A detailed analysis of the obtained results and the respective errors corroborates the fact that many correlations significantly under-predict critical physical parameters, thus resulting in reduced (non-conservative) fire safety levels. The effect of commonly used assumptions (e.g. EVF envelope shape or model parameters for convective and radiative heat transfer calculations) on the accuracy of the predicted values is determined, aiming to highlight the potential to improve the fire engineering design correlations currently available.

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Abbreviations

Symbol (Units – Value):

Description

A 0 (m2):

Opening area

A v (m2):

Total area of vertical openings on all walls of the compartment

c (4.67):

Empirical factor (Eq. 19)

C p (1005 J/kg K):

Specific heat of air at ambient conditions

D v (m):

Effective diameter of the opening

d eq (m):

Characteristic length scale of an external structural element

E b (kW/m2):

Black body emissive power

g (9.81 m/s2):

Gravitational acceleration

H 0 (m):

Opening height

H u (13,100 kJ/kg O2):

Heat release of cellulosic fuels for each kilogram of oxygen consumed

h eq (m):

Weighted average of openings heights on all walls

k (m−1):

Extinction coefficient

k fuel (m−1):

Extinction coefficient for the combustion products of a specific fuel

L L_0.05 (m):

Flame height at the “continuous flame” (5% flame intermittency limit)

L L_0.50 (m):

Flame height at the “intermittent flame” (50% flame intermittency limit)

L L_0.95 (m):

Flame height at the “far-field flame” (95% flame intermittency limit)

L L (m):

Height of EVF

L H (m):

Projection of EVF

L f (m):

Flame length

l (–):

Characteristic length scale (Eq. 9)

l x (m):

Length along the EVF centerline, originating at the opening

\( \dot{m}_{a} \) (kg/s):

Air mass flow rate (entering the fire compartment)

\( \dot{m}_{f} \) (kg/s):

Fuel mass flow rate

\( \dot{m}_{{O_{2} }} \) (kg/s):

Oxygen mass flow rate

\( \dot{m}_{g} \) (kg):

Mass flow rate of unburnt gases venting outside the fire compartment

\( \dot{Q} \) (MW):

Heat Release Rate

\( \dot{Q}_{ex} \) (MW):

Excess Heat Release Rate

\( \dot{Q}_{in} \) (MW):

Average heat release rate at the interior of the fire compartment

\( \dot{q}^{\prime\prime} \) (W/m2):

Heat flux

\( \dot{q}^{\prime\prime}_{conv} \) (W/m2):

Convective heat flux

\( \dot{q}^{\prime\prime}_{rad} \) (W/m2):

Radiative heat flux

r (–):

Fuel-to-oxygen stoichiometric mass ratio

r’ (–):

Oxygen-to-fuel stoichiometric mass ratio

r 0 (m):

Equivalent radius of the opening

T z (K):

EVF centerline temperature in relation to height from the opening lintel

T amb (K):

Ambient temperature

T f (K):

“Effective” flame temperature

T 0 (K):

Temperature at the center of the opening

T wall (K):

Facade wall temperature

V (m/s):

External wind speed

\( \dot{V} \) (m3/s):

Air volumetric flow rate

W 0 (m):

Opening width

w f (m):

EVF width

w t (m):

Sum of opening widths on all walls of the fire compartment

w d (m):

Distance to any other opening

\( Y_{{{\text{O}}_{2} ,air}} \) (0.232):

Oxygen mass fraction in ambient air

z (m):

Height above the opening lintel

Z n (m):

Height of the neutral plane

a c (W/m2K):

Convective heat transfer coefficient

ΔT m (K):

Plume centerline temperature rise above ambient

ε (–):

Emissivity

ε z (–):

Local emissivity of the flame

λ (m):

Flame thickness

ρ amb (1.204 kg/m3):

Air density at ambient conditions

ρ 500°C (0.45 kg/m3):

Air density at 500°C

σ (5.67 × 10−8 kg/s3K4):

Stefan Boltzmann constant

φ f (–):

Configuration factor (radiation from fire through the opening)

φ z (–):

Configuration factor (radiation from EVF)

EVF:

Externally venting flames

FD:

Forced draught

GER:

Global equivalence ratio

HRR:

Heat release rate

NoFD:

No forced draught

VF:

Ventilation factor

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Acknowledgments

This work has been financially supported by the “Fire-Facts” project in the frame of the ARISTEIA action (operational programme “Education and Lifelong Learning”) that is co-financed by Greece and the E.U and by the E.C. in the frame of the FP7 Project “ELISSA: Energy Efficient Lightweight-Sustainable-Safe-Steel Construction” (EeB.NMP.2013, Grant No. 603086).

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Correspondence to Dionysios I. Kolaitis.

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Asimakopoulou, E.K., Kolaitis, D.I. & Founti, M.A. Assessment of Fire Engineering Design Correlations Used to Describe the Geometry and Thermal Characteristics of Externally Venting Flames. Fire Technol 53, 709–739 (2017). https://doi.org/10.1007/s10694-016-0594-2

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Keywords

  • Externally venting flames
  • Fire plume
  • Façade fire
  • Large-scale fire tests
  • Centreline temperature
  • Heat flux
  • Fire engineering design
  • Flame height
  • Flame width
  • Flame projection