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Comparative Analysis on Semi-empirical Models of Jet Fire for Radiant Heat Estimation

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Abstract

Sudden release of combustible/flammable materials at high pressure could result in the occurrence of a jet fire in the processing industry. Understanding the jet fire phenomenon and its mechanism could assist practitioners and researchers to predict the radiant energy transfer caused by the jet fire. Due to the dynamics of jet fire occurrence, the development of a semi-empirical model to predict thermal characteristics in different scenarios might provide huge advantages to the industry and safety practitioners as it is nonexpensive and a reliable prediction. There are four semi-empirical models for jet fire thermal radiation estimation that has been developed to date, namely, solid flame model (SFM), single-point source model (PSM), multipoint source model (MPSM), and line source model (LSM). It is the aim of this paper to explore each model applicability and approach to estimate the radiant heat flux based on the governing factors associated with the models, i.e., atmospheric transmissivity, flame length, lift-off length, flame shape, radiant heat fraction, total heat release, and receiver location. It is found that the applicability of each model and the derived parameters are largely contributed by the flame scale (small, medium, and large), flame orientation, flame length, and flame shape as well as the flame distance to the target receiver. From the discussion made, it can be suggested that for both near- and far-field measurement, the weighted MPSM is a reliable model that can be used for both vertical and horizontal orientations with some modification upon the consideration of buoyancy effect. On another note, LSM is able to provide a better prediction for linear trajectory of jet flame; however, the applicability is still limited for jet flame trajectory with buoyancy effects due to fewer data available and validation in various release conditions and scenarios.

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Abbreviations

A IR :

2D area of the flame surface

c 2 :

Constant parameter cp specific heat of air at constant pressure (kJ kg-1 K-1)

c p :

Specific heat of air at constant pressure (kJ kg-1 K-1)

C x :

Normalized incident radiation (qmeas/qmodel)

D eq :

Equivalent diameter of flame

d :

Diameter of nozzle exit (mm)

d eff :

Effective diameter

d j :

Expanded jet diameter

E :

Flame emissive power per area (kW m−2)

Fr :

Froude number

f :

Multiplying factor

f s :

Mass fraction of fuel at stoichiometric condition

G :

Initial jet momentum flux

h RC :

Distance between the flame radiant center and the ground

H :

Net calorific value of fuel (kJ kg−1)

L :

Flame length from orifice (m)

L 0 :

Flame length with zero wind

L b :

Flame length in buoyancy region

L c :

Centerline flame length

L f :

Lift-off distance (m)

L IR :

Radiant flame length

L m :

Flame length in momentum region

L n :

Nozzle length

L p :

Projection distance

m :

Mass flow rate (kg s−1)

n a :

Stoichiometric air entrained

n(N):

(Total) number of point sources

P a :

Ambient pressure

P i :

Initial pressure

P 0 :

Stagnation pressure

P out :

Pressure downstream of jet fire

Q :

Heat release rate (kW)

Q R :

Incident radiation

Q s * :

Dimensionless heat release rate

\( {Q}_{\zeta_{\mathrm{l}}}^{\ast } \) :

Dimensionless heat release rate as defined in Eq. (19)

Q T :

Net power of the flame (kW)

r(r 0):

(Maximum) flame radius (m)

R :

Distance perpendicular to flame axis (m)

Re :

Reynolds number

RH:

Relative humidity of atmosphere (%)

S :

Distance from a point within the flame to the receiver (m)

S L :

Maximum laminar burning velocity of the mixture under ambient conditions (m s−1)

T :

Temperature

T ∞ :

Ambient air temperature

\( \overline{T_{\mathrm{f},\mathrm{a}}} \) :

Mean flame temperature rise

u :

Velocity (m s−1)

u eq :

Effective exit gas velocity of the gas jet

U * :

dimensionless flow number

u j :

Expanded jet velocity (m s−1)

V :

View factor

W o :

Flame width

W n :

Nozzle width

x :

Mass percentage

X :

Distance from the flame surface to exposed target (m)

EPPLL:

Emissive power per line length

LSM:

Line source model

MPSM:

Multipoint source model

PSM:

Single-point source model

SFM:

Solid flame model

α :

Length ratio of lower flame to the whole flame

α t :

Tilt angle

α w :

Absorption factors (water vapor)

α c :

Absorption factors (carbon dioxide)

δ :

Lift angle

δ f :

Laminar flame thickness under ambient conditions (m)

ε :

Flame emissivity

σ :

Stefan–Boltzmann constant (5.67 × 10−8 W m−2 K−4)

η :

Fraction of heat radiated

η H :

Fraction of heat radiated in a horizontal orientation

η m :

Fraction of heat radiated of mixture

η G :

Fraction of heat radiated of gas

η L :

Fraction of heat radiated of liquid

η V :

Fraction of heat radiated in a vertical orientation

τ :

Atmospheric transmissivity

θ :

Angle as shown in Fig. 4

φ :

Angle as shown in Fig. 4

ρ j :

Expanded jet density (kg m−3)

ρ s :

Gas density at the jet exit

ρ ∞ :

Ambient gas density

γ :

Ratio of specific heats

ξ :

Richardson number

References

  • Bagster DF, Schubacht SA (1996) The prediction of jet-fire dimensions. J Loss Prev Process Ind 9(3):241–245

    Article  Google Scholar 

  • Baillie S, Caulfield M, Cook DK, Docherty P (1998) A phenomenological model for predicting the thermal loading to a cylindrical vessel impacted by high pressure natural gas jet fires. Trans Inst Chem Eng 76(Part B):11

    Google Scholar 

  • Becker HA, Liang D (1978) Visible length of vertical free turbulent diffusion flames. Combust Flame 32:115–137

    Article  Google Scholar 

  • Birch AD, Brown DR, Dodson MG, Swaffield F (1984) The structure and concentration decay of high pressure jets of natural gas. Combust Sci Technol 36(5–6):249–261

    Article  Google Scholar 

  • Bosch CJH, Weterings RAPM, Duijm NJ, Bakkum EA, Mercx WPM, Berg ACVD, Engelhard WFJM, Doormaal JCAMV, Wees RMMV (2005) Methods for the calculation of physical effects

  • Bradley D, Gaskell PH, Gu X, Palacios A (2016) Jet flame heights, lift-off distances, and mean flame surface density for extensive ranges of fuels and flow rates. Combust Flame 164:400–409

    Article  Google Scholar 

  • Brzustowski T, Gollahalli S, Gupta M, Kaptein M, Sullivan H (1975) Radiant heating from flares. ASME paper, (75-HT), 4

  • Chamberlain GA (1987) Developments in design methods for predicting thermal radiation from flare. Chem Eng Res Des 65(4):299–309

    Google Scholar 

  • Crocker WP, Napier DH 1988 Mathematical models for the prediction of thermal radiation from jet fires. I.ChemE. Symposium Series No. 110, 331–347

  • Dadashzadeh M, Khan F, Hawboldt K, Amyotte P (2013) An integrated approach for fire and explosion consequence modelling. Fire Saf J 61:324–337

    Article  Google Scholar 

  • Ekoto IW, Ruggles AJ, Creitz LW, Li JX (2014) Updated jet flame radiation modeling with buoyancy corrections. Int J Hydrog Energy 39(35):20570–20577

    Article  Google Scholar 

  • Geankoplis, C. J. (2003). Transport processes and separation process principles: (includes unit operations). Prentice Hall Professional Technical Reference

    Google Scholar 

  • Gómez-Mares M, Muñoz M, Casal J (2010) Radiant heat from propane jet fires. Exp Thermal Fluid Sci 34(3):323–329

    Article  Google Scholar 

  • Gopalaswami N, Liu Y, Laboureur DM, Zhang B, Mannan MS (2016) Experimental study on propane jet fire hazards: comparison of main geometrical features with empirical models. J Loss Prev Process Ind 41:365–375

    Article  Google Scholar 

  • Hankinson G, Lowesmith BJ (2012) A consideration of methods of determining the radiative characteristics of jet fires. Combust Flame 159(3):1165–1177

    Article  Google Scholar 

  • Hankinson G, Lowesmith BJ, Evans JA, Shirvill LC (2007) Jet fires involving releases of crude oil, gas and water. Process Saf Environ Prot 85(B3):221–229

    Article  Google Scholar 

  • Hawthorne WR, Weddell DS, Hottel HC (1949) Mixing and combustion in turbulent gas jets. Combustion flame and explosions phenomena, p 266–288

  • Hu L, Wang Q, Delichatsios M, Tang F, Zhang X, Lu S (2013a) Flame height and lift-off of turbulent buoyant jet diffusion flames in a reduced pressure atmosphere. Fuel 109:234–240

    Article  Google Scholar 

  • Hu L, Wang Q, Tang F, Delichatsios M, Zhang X (2013b) Axial temperature profile in vertical buoyant turbulent jet fire in a reduced pressure atmosphere. Fuel 106:779–786

    Article  Google Scholar 

  • Huang Y, Li Y, Dong B, Li J (2017) Predicting the main geometrical features of horizontal rectangular source fuel jet fires. J Energy Inst:1–11

  • Institute, A. P (2008) ISO 23251 (identical) petroleum and natural gas industries, Pressure-relieving and depressuring systems. API Publishing Services, Washington, D.C

    Google Scholar 

  • Johnson AD, Brightwell HM, Carsley AJ (1994) A model for predicting the thermal radiation hazards from large-scale horizontally released natural gas jet fires. IChemE Symposium Series No. 134

  • Jujuly MM, Rahman A, Ahmed S, Khan F (2015) LNG pool fire simulation for domino effect analysis. Reliab Eng Syst Saf 143:19–29

    Article  Google Scholar 

  • Kalghatgi GT (1983) The visible shape and size of a turbulent hydrocarbon jet diffusion flame in a cross-wind. Combust Flame 52:91–106

    Article  Google Scholar 

  • Kalghatgi GT (2010) Lift-off heights and visible lengths of vertical turbulent jet diffusion flames in still air. Combust Sci Technol 41:17–29

    Google Scholar 

  • Kiran DY, Mishra DP (2007) Experimental studies of flame stability and emission characteristics of simple LPG jet diffusion flame. Fuel 86(10–11):1545–1551

    Article  Google Scholar 

  • Kohout A, Turpin T (2013) Recommended parameters for solid flame models for land based liquefied natural gas spills, Office of energy projects. Federal Energy Regulatory Commission, Washington, DC

    Google Scholar 

  • Kozanoglu B, Zárate L, Gómez-Mares M, Casal J (2011) Convective heat transfer around vertical jet fires: an experimental study. J Hazard Mater 197:104–108

    Article  Google Scholar 

  • Laboureur DM, Gopalaswami N, Zhang B, Liu Y, Mannan MS (2016) Experimental study on propane jet fire hazards: assessment of the main geometrical features of horizontal jet flames. J Loss Prev Process Ind 41:355–364

    Article  Google Scholar 

  • Lowesmith BJ, Hankinson G (2012) Large scale high pressure jet fires involving natural gas and natural gas/hydrogen mixtures. Process Saf Environ Prot 90(2):108–120

    Article  Google Scholar 

  • Lowesmith BJ, Hankinson G (2013) Large scale experiments to study fires following the rupture of high pressure pipelines conveying natural gas and natural gas/hydrogen mixtures. Process Saf Environ Prot 91(1–2):101–111

    Article  Google Scholar 

  • Lowesmith BJ, Hankinson G, Acton MR, Chamberlain G (2007) An overview of the nature of hydrocarbon jet fire hazards in the oil and gas industry and a simplified approach to assessing the hazards. Process Saf Environ Prot 85(B3):207–220

    Article  Google Scholar 

  • Lyons KM (2007) Toward an understanding of the stabilization mechanisms of lifted turbulent jet flames: experiments. Prog Energy Combust Sci 33(2):211–231

    Article  Google Scholar 

  • Markstein GH, Ris JD (1990) Wall-fire radiant emission. Part 1: slot-burner flames, comparison with jet flames. Twenty-Third Symposium (International) on Combustion/The Combustion Institute, p 1685–1692

  • Mccaffrey BJ (1989) Momentum diffusion flame characteristics and the effects of water spray. Combust Sci Technol 63(4–6):315–335

    Article  Google Scholar 

  • Miller D (2017) New model for predicting thermal radiation from flares and high pressure jet fires for hydrogen and syngas. Process Saf Prog 36(3):237–251

    Article  Google Scholar 

  • Mogi T, Horiguchi S (2009) Experimental study on the hazards of high-pressure hydrogen jet diffusion flames. J Loss Prev Process Ind 22(1):45–51

    Article  Google Scholar 

  • Molina A, Schefer RW, Houf WG (2007) Radiative fraction and optical thickness in large-scale hydrogen-jet fires. Proc Combust Inst 31:2565–2572

    Article  Google Scholar 

  • Molkov V, Saffers J-B (2013) Hydrogen jet flames. Int J Hydrog Energy 38(19):8141–8158

    Article  Google Scholar 

  • Mousavi J, Parvini M (2016) Analyzing effective factors on leakage-induced hydrogen fires. J Loss Prev Process Ind 40:29–42

    Article  Google Scholar 

  • Palacios A, Casal J (2011) Assessment of the shape of vertical jet fires. Fuel 90(2):824–833

    Article  Google Scholar 

  • Palacios Rosas A (2011) Study of jet fires geometry and radiative features. Doctor of Philosophy, Universitat Politècnica de Catalunya

  • Palacios A, Muñoz M, Casal J (2009) Jet fires: an experimental study of the main geometrical features of the flame in subsonic and sonic regimes. AICHE J 55(1):256–263

    Article  Google Scholar 

  • Palacios A, Munoz M, Darbra RM, Casal J (2012) Thermal radiation from vertical jet fires. Fire Saf J 51:93–101

    Article  Google Scholar 

  • Palacios A, Bradley D, Hu L (2016) Lift-off and blow-off of methane and propane subsonic vertical jet flames, with and without diluent air. Fuel 183:414–419

    Article  Google Scholar 

  • Peter N, Williams FA (1983) Liftoff characteristics of turbulent jet diffusion flames. Am Inst Aeronaut Astronaut J 21(3):423–429

    Article  MATH  Google Scholar 

  • Raj PK (2007) LNG fires: a review of experimental results, models and hazard prediction challenges. J Hazard Mater 140:444–464

    Article  Google Scholar 

  • Rajendram A, Khan F, Garaniya V (2015) Modelling of fire risks in an offshore facility. Fire Saf J 71:79–85

    Article  Google Scholar 

  • Rohsenow, W. M., Hartnett, J. R. and Cho, Y. I. (1998). Handbook of heat transfer. (Third edition). McGraw-Hill Companies

  • Røkke NA, Hustad JE, Sønju OK (1994) A study of partially premixed unconfined propane flames. Combust Flame 97(1):88–106

    Article  Google Scholar 

  • Santos A, Costa M (2005) Reexamination of the scaling laws for Nox emissions from hydrocarbon turbulent jet diffusion flame. Combust Flame 142:160–169

    Article  Google Scholar 

  • Schefer R, Houf B, Bourne B, Colton J (2004) Experimental measurements to characterize the thermal and radiation properties of an open-flame hydrogen plume. 15th NHA Meeting, p 26–30

  • Schefer RW, Houf WG, Williams TC, Bourne B, Colton J (2006) Characterization of high-pressure, underexpanded hydrogen-jet flame. Int J Hydrog Energy 32:2081–2093

    Article  Google Scholar 

  • Sivathanu YR, Gore JP (1993) Total radiative heat loss in jet flames from single point radiative flux measurements. Combust Flame 94:265–270

    Article  Google Scholar 

  • Smith T, Periasamy C, Baird B, Gollahalli SR (2005) Trajectory and characteristics of buoyancy and momentum dominated horizontal jet flames from circular and elliptic burners. J Energy Resour Technol 128:300–310

    Article  Google Scholar 

  • Sonju OK, Hustad J (1984) An experimental study of turbulent jet diffusion flames. Am Inst Aeronaut Astronaut J

  • Studer E, Jamois D, Jallais S, Leroy G, Hebrard J, Blanchetière V (2009) Properties of large-scale methane/hydrogen jet fires. Int J Hydrog Energy 34(23):9611–9619

    Article  Google Scholar 

  • Sugawa O, Sakai K (1996) Flame length and width produced by ejected propane gas fuel from a pipe. Int Assoc Fire Saf Sci:411–421

  • Suris AL, Flankin EV, Shorin SN (1978) Length of free diffusion flame. Combust Explosion Shock Waves 13(4):459–462

    Article  Google Scholar 

  • Tao C, Shen Y, Zong R (2016) Experimental determination of flame length of buoyancy-controlled turbulent jet diffusion flames from inclined nozzles. Appl Therm Eng 93:884–887

    Article  Google Scholar 

  • UKOOA (2006) Fire and explosion guidance. Part 2: avoidance and mitigation of fires

  • Wang Q, Hu L, Zhang M, Tang F, Zhang X, Lu S (2014) Lift-off of jet diffusion flame in sub-atmospheric pressures: an experimental investigation and interpretation based on laminar flame speed. Combust Flame 161(4):1125–1130

    Article  Google Scholar 

  • Wertenbach HG (1971) Spread of flames on cylindrical tanks for hydrocarbon fluids. Gas Erdgas 112(8)

  • Zhang B, Liu Y, Laboureur D, Mannan MS (2015) Experimental study on propane jet fire hazards: thermal radiation. Ind Eng Chem Res 54(37):9251–9256

    Article  Google Scholar 

  • Zhang X, Hu L, Zhang X, Tang F, Jiang Y, Lin Y (2017) Flame projection distance of horizontally oriented buoyant turbulent rectangular jet fires. Combust Flame 176:370–376

    Article  Google Scholar 

  • Zhou K, Jiang J (2016) Thermal radiation from vertical turbulent jet flame: line source model. J Heat Transf 138(4):042701

    Article  Google Scholar 

  • Zhou K, Liu J, Jiang J (2016) Prediction of radiant heat flux from horizontal propane jet fire. Appl Therm Eng 106:634–639

    Article  Google Scholar 

  • Zhou K, Qin X, Wang Z, Pan X, Jiang J (2018) Generalization of the radiative fraction correlation for hydrogen and hydrocarbon jet fires in subsonic and chocked flow regimes. Int J Hydrog Energy 43(20):9870–9876

    Article  Google Scholar 

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Funding

The authors would like to express their appreciation for the support of the sponsors—Research University Grant (GUP) [Grant Number = Q.J130000.2546.17H82: Parametric and Thermal Investigation of Horizontal Buoyant Jet Fires Impingement Radiation on Plant Installation].

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Authors and Affiliations

  1. Energy Management Research Group, School of Chemical and Energy Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia

    Nur Shahidah Ab Aziz, Rafiziana Md. Kasmani & Mohd Dinie Muhaimin Samsudin

  2. Faculty of Chemical Engineering, Universiti Teknologi MARA, 40450, Shah Alam, Selangor, Malaysia

    Nur Shahidah Ab Aziz

  3. Institute of Future Energy, Universiti Teknologi Malaysia, 81310, Skudai, Johor, Malaysia

    Arshad Ahmad

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  1. Nur Shahidah Ab Aziz
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  2. Rafiziana Md. Kasmani
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  3. Mohd Dinie Muhaimin Samsudin
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Correspondence to Rafiziana Md. Kasmani.

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Ab Aziz, N.S., Md. Kasmani, R., Samsudin, M.D.M. et al. Comparative Analysis on Semi-empirical Models of Jet Fire for Radiant Heat Estimation. Process Integr Optim Sustain 3, 285–305 (2019). https://doi.org/10.1007/s41660-019-00081-y

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