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Simplified Calculation Method for Determining Smoke Downdrag Due to a Sprinkler Spray

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Abstract

A simplified method has been developed to predict smoke behavior subject to a sprinkler spray. The method considers whether downdrag is likely to occur and the distance that smoke is then pulled down should downdrag be present. The method is validated using third party experimental data. Empirical equations are applied in the calculations to determine the heat loss from a smoke layer due to the sprinkler spray and therefore the smoke layer temperature. Comparative results show that the simplified method might expect the onset of smoke downdrag regardless the difference in temperature predictions. The empirical equation to predict the penetration depth of downdrag smoke is based on previous research and compared with third party experimental data. The predicted depths are acceptable for engineering use. For a 15 mm nominal sprinkler the water flow rate that leads to the onset of downdrag for typical smoke layers up to 2 m in depth is less than 100 L/min which leads to an operating pressure being less than 0.16 MPa. Experimentally data for sprinklers other than the 15 mm nominal sprinklers are unavailable and therefore the method should be used with care for any other sprinkler.

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Abbreviations

B 0 :

Buoyancy per unit area below the sprinkler (Pa)

B 0c :

Buoyancy per unit area under temperature T c,s (Pa)

B 0d :

Buoyancy per unit area under temperature T d,s (Pa)

C 0 :

Resistance coefficient of the different orifices

C 1 :

Coefficient for droplet velocity

C D :

Drag coefficient

C p :

Heat capacity of air (KJ Kg−1 K−1)

C sp :

Coefficient for calculating the mean droplet diameter

d d :

Diameter of the droplet (m)

d m :

Mean diameter of all droplets (m)

d n :

Diameter of the sprinkler nozzle (m)

d sp :

Distance between sprinkler and ceiling (m)

D 0 :

Drag force per unit area below the sprinkler (Pa)

D 0c :

Drag force per unit area under temperature T c,s (Pa)

D 0d :

Drag force per unit area under temperature T d,s (Pa)

E :

Coefficient of curve equation for the external shape of the spray region

g :

Acceleration due to gravity (m s−2)

h :

Depth of the smoke layer below a sprinkler, which equals to h 0 − d sp (m)

h 0 :

Depth of the smoke layer below the ceiling (m)

H :

Height of building space (m)

K :

Flow coefficient of the sprinkler (L min−1 bar−0.5)

m s :

Smoke mass flow (kg s−1)

m w :

Discharge mass flow of the sprinkler nozzle (kg s−1)

m ′ w :

Discharge mass flow divided by 20 m2 coverage (kg s−1 m−2)

P :

Operating pressure of the sprinkler (MPa)

Q :

Discharge volumetric flow of the sprinkler nozzle (L min−1)

\( \dot{q}_{s} \) :

Heat loss from smoke layer due to sprinkler spray (W or kW)

\( \dot{q}_{w} \) :

Heat loss from smoke layer to surrounding walls (W or kW)

R :

Correlative coefficient

S :

Penetration depth (moving distance) of downdrag smoke (m)

T 0 :

Ambient temperature (K)

T 273 :

Temperature of 273 K (K)

T c,s :

Average smoke layer temperature between T u,0 and T d,s (K)

T d,0 :

Downstream smoke layer temperature before sprinkler operation (K)

T d,s :

Downstream smoke layer temperature after sprinkler operation (K)

T sp,0 :

Average smoke layer temperature at sprinkler position before discharging (K)

T sp,s :

Average smoke layer temperature at sprinkler position after discharging (K)

T u,0 :

Upstream smoke layer temperature before entering the sprinkler spray (K)

We:

Weber number

ρ 0 :

Air density at ambient temperature (kg m−3)

ρ d :

Density of the water (kg m−3)

ρ g :

Density of the smoke layer (kg m−3)

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Acknowledgements

This work was supported by the Opening Fund of State Key Laboratory of Fire Science of University of Science and Technology of China under Grant No. HZ2009-KF01 and the Natural Science Foundation of China (NSFC) under Grant No. 51008251. Kai-Yuan Li is currently the Arup Fire Post-doctorate Fellow at the University of Canterbury.

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Authors and Affiliations

  1. Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand

    K. Y. Li & M. J. Spearpoint

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  1. K. Y. Li
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  2. M. J. Spearpoint
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Correspondence to K. Y. Li.

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Li, K.Y., Spearpoint, M.J. Simplified Calculation Method for Determining Smoke Downdrag Due to a Sprinkler Spray. Fire Technol 47, 781–800 (2011). https://doi.org/10.1007/s10694-010-0194-5

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  • DOI: https://doi.org/10.1007/s10694-010-0194-5

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