Fire Technology

, Volume 47, Issue 3, pp 781–800 | Cite as

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

  • K. Y. LiEmail author
  • M. J. Spearpoint


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.


Sprinkler Smoke Downdrag Smoke logging Interaction Drag force 



Buoyancy per unit area below the sprinkler (Pa)


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


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


Resistance coefficient of the different orifices


Coefficient for droplet velocity


Drag coefficient


Heat capacity of air (KJ Kg−1 K−1)


Coefficient for calculating the mean droplet diameter


Diameter of the droplet (m)


Mean diameter of all droplets (m)


Diameter of the sprinkler nozzle (m)


Distance between sprinkler and ceiling (m)


Drag force per unit area below the sprinkler (Pa)


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


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


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


Acceleration due to gravity (m s−2)


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


Depth of the smoke layer below the ceiling (m)


Height of building space (m)


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


Smoke mass flow (kg s−1)


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


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


Operating pressure of the sprinkler (MPa)


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)


Correlative coefficient


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


Ambient temperature (K)


Temperature of 273 K (K)


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


Downstream smoke layer temperature before sprinkler operation (K)


Downstream smoke layer temperature after sprinkler operation (K)


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


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


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


Weber number

Greek Symbols


Air density at ambient temperature (kg m−3)


Density of the water (kg m−3)


Density of the smoke layer (kg m−3)



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.


  1. 1.
    Li KY, Hu LH, Huo R, Li YZ, Chen ZB, Sun XQ and Li SC (2009) A mathematical model on interaction of smoke layer with sprinkler Spray. Fire Safety J 44:96–105. doi: 10.1016/j.firesaf.2008.04.003 CrossRefGoogle Scholar
  2. 2.
    Bullen ML (1974) The effect of a sprinkler on the stability of a smoke layer beneath a ceiling. Fire Research Note 1016, Fire Research Station, Borehamwood, Herts, UK, 1974, pp 1-11Google Scholar
  3. 3.
    Cooper LY (1995) The interaction of an isolated sprinkler spray and a two-layer compartment fire environment. Phenomena and model simulations. Fire Safety J 25:89–107. doi: 10.1016/0379-7112(95)00037-2 CrossRefGoogle Scholar
  4. 4.
    Cooper LY (1995) The interaction of an isolated sprinkler spray and a two-layer compartment fire environment. Int J Heat Mass Transfer 38: 679–690. doi: 10.1016/0017-9310(94)00188-2 CrossRefGoogle Scholar
  5. 5.
    Heskestad G (1991) Sprinkler/hot layer interaction. National Institute of Standards and Technology Technical Report NIST-GCR-91-590.Google Scholar
  6. 6.
    Williams C (1993) The downward movement of smoke due to a sprinkler spray. PhD dissertation, South Bank University, London, UKGoogle Scholar
  7. 7.
    Yu HZ (1986) Investigation of spray patterns of selected sprinklers with the FMRC drop size measuring system, Proceeding of first international symposium, international association for fire safety science, pp 1165–1176.Google Scholar
  8. 8.
    Sheppard DT (2002) Spray characteristics of fire sprinklers. PhD dissertation, Northwestern University, Evanston, USAGoogle Scholar
  9. 9.
    Mawhinney JR and Tamura GT (1994) Effect of automatic sprinkler protection on smoke control systems. ASHRAE Transactions, Vol. 100, No. 1, pp 494-513Google Scholar
  10. 10.
    Heselden AJM (1984) The interaction of sprinkler and roof venting in industrial buildings the current knowledge. Building Research Establishment, Borehamwood, Herts, UK, 1984Google Scholar
  11. 11.
    Li SC, Chen Y, Wei D, Yang D, Sun XQ, Huo R and Hu LH (2009) A mathematical model for cooling effect of sprinkler on smoke layer. ASME 2009 heat transfer summer conference, San Francisco, California, USA, 2009Google Scholar
  12. 12.
    NFPA 13 (2002) Standard for the installation of sprinkler systems. National Fire Protection Association, USAGoogle Scholar
  13. 13.
    NZS 4541 (2007) Automatic fire sprinkler systems, Standards New Zealand. Wellington, New Zealand, 2007Google Scholar
  14. 14.
    Li KY (2008) Study on stable character of smoke layer under sprinkler spray in fires. PhD dissertation, University of Science and Technology of China, Hefei, Anhui, ChinaGoogle Scholar
  15. 15.
    Spearpoint MJ (2008) Fire engineering design guide. 3rd Ed., CAENZ, Christchurch, New ZealandGoogle Scholar
  16. 16.
    Li KY, Spearpoint MJ, Ji J, Huo R and Li YZ (2010) A mathematical model on the drag component of a sprinkler spray to adjacent horizontal smoke venting. J. Fire Prot Eng 20:27–54. doi: 10.1177/1042391509360270 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Civil and Natural Resources EngineeringUniversity of CanterburyChristchurchNew Zealand

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