### Abstract

Modelling the view factor, F, of a ‘grain-like’ observer near a tilted pool fire assumed to be cylindrical in shape, requires the observer (on the same ground level as the pool fire) to be as close as possible to the flame surface so that the flame surface is viewed as a plane. The orientation of the observer is to receive a maximum view, with the view factor integrated over the flame area seen by the observer. The derived expression for F was expressed in terms of standard functions and sensitive parameters: α defined to ensure the observer receives a maximum view of the flame surface and β the angle of inclination of the differential observer plane. Results from a planar approximation to F are compared with those of PHAST 7.2 simulated results in MATLAB. The values of the planar approximation to F was found to increase with increasing β. This suggests that the larger the value of β the more the radiation received by a near observer. For β=48.961^{∘}, horizontal distance, X=30m, α=0.01, flame length, L=12.14m, tilt angle, θ=55.17^{∘}, and pool diameter, D=5m: planar and PHAST 7.2 approximations to F were found to coincide up to 6 significant digits and differ by 3.2×10^{−8}. The close agreement between both approximations depend heavily on the choice of flame properties and sensitive parameters. Interestingly, this result may depend sensitively on the choice of parameters, leading to prediction of planar approximation to F much higher or lower than those of PHAST 7.2 approximations. The advantage of this approach is that a knowledge of the plane where the largest concentration of radiation is located will help minimise loss of lives to fire hazards and improve the efficiency of risk safety assessment/management.

Language | English |
---|---|

Pages | 23-33 |

Number of pages | 11 |

Journal | Applied Mathematical Modelling |

Volume | 65 |

Early online date | 8 Aug 2018 |

DOIs | |

Status | Published - 1 Jan 2019 |

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### Keywords

- Approximation
- Flame
- Observer
- Planar
- Pool fire
- View factor

### ASJC Scopus subject areas

- Modelling and Simulation
- Applied Mathematics

### Cite this

**Modelling the view factor of a ‘grain-like’ observer near a tilted pool fire via planar approximation approach.** / Budd, Christopher J.; Ugwu, Ugochukwu O.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Modelling the view factor of a ‘grain-like’ observer near a tilted pool fire via planar approximation approach

AU - Budd, Christopher J.

AU - Ugwu, Ugochukwu O.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Modelling the view factor, F, of a ‘grain-like’ observer near a tilted pool fire assumed to be cylindrical in shape, requires the observer (on the same ground level as the pool fire) to be as close as possible to the flame surface so that the flame surface is viewed as a plane. The orientation of the observer is to receive a maximum view, with the view factor integrated over the flame area seen by the observer. The derived expression for F was expressed in terms of standard functions and sensitive parameters: α defined to ensure the observer receives a maximum view of the flame surface and β the angle of inclination of the differential observer plane. Results from a planar approximation to F are compared with those of PHAST 7.2 simulated results in MATLAB. The values of the planar approximation to F was found to increase with increasing β. This suggests that the larger the value of β the more the radiation received by a near observer. For β=48.961∘, horizontal distance, X=30m, α=0.01, flame length, L=12.14m, tilt angle, θ=55.17∘, and pool diameter, D=5m: planar and PHAST 7.2 approximations to F were found to coincide up to 6 significant digits and differ by 3.2×10−8. The close agreement between both approximations depend heavily on the choice of flame properties and sensitive parameters. Interestingly, this result may depend sensitively on the choice of parameters, leading to prediction of planar approximation to F much higher or lower than those of PHAST 7.2 approximations. The advantage of this approach is that a knowledge of the plane where the largest concentration of radiation is located will help minimise loss of lives to fire hazards and improve the efficiency of risk safety assessment/management.

AB - Modelling the view factor, F, of a ‘grain-like’ observer near a tilted pool fire assumed to be cylindrical in shape, requires the observer (on the same ground level as the pool fire) to be as close as possible to the flame surface so that the flame surface is viewed as a plane. The orientation of the observer is to receive a maximum view, with the view factor integrated over the flame area seen by the observer. The derived expression for F was expressed in terms of standard functions and sensitive parameters: α defined to ensure the observer receives a maximum view of the flame surface and β the angle of inclination of the differential observer plane. Results from a planar approximation to F are compared with those of PHAST 7.2 simulated results in MATLAB. The values of the planar approximation to F was found to increase with increasing β. This suggests that the larger the value of β the more the radiation received by a near observer. For β=48.961∘, horizontal distance, X=30m, α=0.01, flame length, L=12.14m, tilt angle, θ=55.17∘, and pool diameter, D=5m: planar and PHAST 7.2 approximations to F were found to coincide up to 6 significant digits and differ by 3.2×10−8. The close agreement between both approximations depend heavily on the choice of flame properties and sensitive parameters. Interestingly, this result may depend sensitively on the choice of parameters, leading to prediction of planar approximation to F much higher or lower than those of PHAST 7.2 approximations. The advantage of this approach is that a knowledge of the plane where the largest concentration of radiation is located will help minimise loss of lives to fire hazards and improve the efficiency of risk safety assessment/management.

KW - Approximation

KW - Flame

KW - Observer

KW - Planar

KW - Pool fire

KW - View factor

UR - http://www.scopus.com/inward/record.url?scp=85052322426&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2018.07.037

DO - 10.1016/j.apm.2018.07.037

M3 - Article

VL - 65

SP - 23

EP - 33

JO - Applied Mathematical Modelling

T2 - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

ER -