ISO/FDIS 24678-7

• Abstract:

  The requirements in this document govern the application of a set of explicit algebraic formulae for the calculation of specific characteristics of radiation heat flux from an open pool fire. This document is an implementation of the general requirements provided in ISO 16730‑1 for the case of fire dynamics calculations involving a set of explicit algebraic formulae. This document is arranged in the form of a template, where specific information relevant to the algebraic formulae is provided to satisfy the following types of general requirements: a) description of physical phenomena addressed by the calculation method; b) documentation of the calculation procedure and its scientific basis; c) limitations of the calculation method; d) input parameters for the calculation method; and e) domain of applicability of the calculation method. Examples of sets of algebraic formulae meeting the requirements of this document are provided in Annexes A and B. Annex A contains a set of algebraic formulae for radiation heat fluxes from a circular or near-circular open pool fire. Annex B contains formulae for configuration factors of a flame to a target.

• Status: Not Published
• ICS: 13.220.01 - Protection against fire in general
• Technical Committee: ISO/TC 92/SC 4 - Fire safety engineering
• Drafting Committee: ISO/TC 92/SC 4/WG 9 - Calculation methods for FSE
• Current Stage: 5020 - FDIS ballot initiated: 2 months. Proof sent to secretariat
• Start Date: 16-Sep-2026
• Completion Date: 16-Sep-2026

• Revises: ISO 24678-7:2019 - Fire safety engineering — Requirements governing algebraic formulae — Part 7: Radiation heat flux received from an open pool fire
• Effective Date: 12-Oct-2024

Overview

ISO/FDIS 24678-7:2026 is an International Standard developed by ISO for fire safety engineering, specifically focusing on the requirements governing algebraic formulae used to calculate radiation heat flux received from an open pool fire. This part of the ISO 24678 series provides a structured approach-using explicit algebraic formulae-for quantifying the thermal radiation transfer to targets surrounding an open pool fire. It serves fire safety professionals, engineers, and designers seeking performance-based evaluations for built environments, as guided by fire safety engineering principles.

This document implements the general requirements from ISO 16730-1 for fire dynamics calculations involving explicit formulae, ensuring consistency, transparency, and reliability in fire safety engineering applications.

Key Topics

• Physical Phenomena: Detailed requirements for describing the physical processes of radiation transfer from a fire, including pool fire geometry, radiative mechanisms, and the effect on different targets within the built environment.
• Calculation Guidelines: Procedures for documenting the calculation process, referencing scientific validation, addressing formula limitations, defining input parameters, and clarifying the method’s domain of applicability.
• Template-Based Structure: The document is arranged as a template, guiding users in documenting and applying sets of algebraic formulae for specific fire safety calculations.
• Examples and Annexes: Includes Annex A (formulae for circular or near-circular open pool fires) and Annex B (formulae for flame configuration factors to targets).

By following the process in ISO/FDIS 24678-7, fire safety engineers can ensure their calculations for radiation heat flux from pool fires are robust, validated, and aligned with international best practices.

Applications

• Performance-Based Fire Safety Engineering: Used during the fire safety design of buildings, ships, vehicles, and other built environments to assess and mitigate radiant heat hazards from potential pool fires.
• Hazard Assessment: Assists in evaluating risks such as thermal injury to occupants, ignition of adjacent materials, equipment malfunction, and structural degradation due to radiative heat exposure.
• Scenario Analysis: Enables quick estimation and comparison of design alternatives for fire protection strategies during the iterative engineering process.
• Regulatory Compliance: Supports designers and safety officials in demonstrating compliance with local and international fire safety codes that mandate performance-based assessments.
• Education and Training: Serves as a reference for developing training materials or courses on applied fire safety engineering, featuring calculation methods based on scientific research and industry practices.

Related Standards

For comprehensive fire safety analysis, ISO/FDIS 24678-7 should be used in conjunction with other key international standards, including:

• ISO 16730-1: Fire safety engineering - Procedures and requirements for verification and validation of calculation methods.
• ISO 24678-1: Fire safety engineering - Requirements governing algebraic formulae - Part 1: General requirements.
• ISO 16733-1: Fire safety engineering - Selection of design fire scenarios and design fires - Part 1.
• ISO 23932-1: Fire safety engineering - General principles, providing a performance-based framework for fire safety assessment.
• ISO 13943: Fire safety - Vocabulary, for standardized terminology.
• Other ISO 24678 Series Parts: For further tools and data relating to fire dynamics and heat transfer calculations.

By leveraging these international fire safety standards, practitioners ensure a holistic and systematic approach to the assessment of radiation heat flux from open pool fires, which is vital for modern fire safety engineering and the protection of life, property, and the environment.

FINAL DRAFT
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Requirements governing algebraic
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Radiation heat flux received from an
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International
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ISO/TC 92/SC 4
Fire safety engineering —
Secretariat: AFNOR
Requirements governing algebraic
Voting begins on:
formulae —
Part 7:
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Radiation heat flux received from an
open pool fire
Ingénierie de la sécurité incendie — Exigences régissant les
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Partie 7: Densité de flux énergétique rayonnée reçue d’un feu en
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Requirements governing the description of physical phenomena. 2
5 Requirements governing the calculation process. 3
6 Requirements governing limitations . 3
7 Requirements governing input parameters . 3
8 Requirements governing the domain of applicability . 3
9 Example of documentation . 3
Annex A (informative) Algebraic formulae for thermal radiation from a circular or near
circular open pool fire . 4
Annex B (informative) Configuration factors of a cylindrical flame to a target .18
Bibliography .38

iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 92, Fire safety, Subcommittee SC 4, Fire safety
engineering.
This second edition cancels and replaces the first edition (ISO 24678-7:2019), which has been technically
revised.
The main changes are as follows:
— the main body was revised to align with ISO 24678-1 on common requirements;
— some of the figures in Annex B, i.e. Figures B.3, B.14 and B.15, have been technically revised.
A list of all parts in the ISO 24678 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
Introduction
The ISO 24678 series is intended to be used by fire safety practitioners involved with fire safety engineering
calculation methods. It is expected that the users of this document are appropriately qualified and competent
in the field of fire safety engineering. It is particularly important that the users understand the parameters
within which particular methodologies may be used.
Algebraic formulae conforming to the requirements of this document are used with other engineering
calculation methods during fire safety design. Such a design is preceded by the establishment of a context,
including the fire safety goals and objectives to be met, as well as performance criteria when a trial fire
safety design is subject to specified design fire scenarios. Engineering calculation methods are used to
determine if these performance criteria are met by a particular design and if not, how the design needs to be
modified.
The subjects of engineering calculations include the fire safety design of entirely new built environments,
such as buildings, ships or vehicles as well as the assessment of the fire safety of existing built environments.
The algebraic formulae discussed in this document can be useful for estimating the consequences of design
fire scenarios. Such formulae are valuable for allowing the practitioner to quickly determine how a proposed
fire safety design needs to be modified to meet performance criteria and to compare among multiple
trial designs. Detailed numerical calculations can be carried out up until the final design documentation.
Examples of areas where algebraic formulae have been applicable include determination of convective
and radiative heat transfer from fire plumes, prediction of ceiling jet flow properties governing detector
response times, calculation of smoke transport through vent openings, and analysis of compartment fire
hazards such as smoke filling and flashover. However, the simple models often have stringent limitations
and are less likely to include the effects of multiple phenomena occurring in the design fire scenarios.
The general principles of fire safety engineering are described in ISO 23932-1, which provides a performance-
based methodology for engineers to assess the level of fire safety for new or existing built environments.
Fire safety is evaluated through an engineered approach based on the quantification of the behaviour of fire
and based on knowledge of the consequences of such behaviour on life safety, property and the environment.
ISO 23932-1 provides the process (i.e. necessary steps) and essential elements for conducting a robust
performance-based fire safety design.
ISO 23932-1 is supported by a set of available fire safety engineering International Standards on the methods
and data needed for all the steps in a fire safety engineering design as summarized in Figure 1 (taken from
ISO 23932-1:2018, Clause 4). The set includes the ISO 16730 series, the ISO 16732 series, the ISO 16733 series,
ISO/TR 16738, the ISO 24678 series, the ISO 24679 series, ISO 23932-1, ISO/TS 29761 and other supporting
documents that provide examples of and guidance on the application of these standards.
Each International Standard supporting the global fire safety engineering analysis and information system
includes language in the introduction to tie the standard to the steps in the fire safety engineering design
process outlined in ISO 23932-1. ISO 23932-1 requires that engineering methods be selected properly
with acceptable accuracy to predict the fire consequences of specific scenarios and scenario elements
(ISO 23932-1:2018, Clause 12). Pursuant to the requirements of ISO 23932-1, this document provides
the requirements governing algebraic formulae for fire safety engineering. This step in the fire safety
engineering process is shown as a highlighted box in Figure 1 and described in ISO 23932-1.

v
Figure 1 — Flow chart illustrating the fire safety engineering (FSE) design process (from
ISO 23932-1:2018)
vi
FINAL DRAFT International Standard ISO/FDIS 24678-7:2026(en)
Fire safety engineering — Requirements governing algebraic
formulae —
Part 7:
Radiation heat flux received from an open pool fire
1 Scope
The requirements in this document govern the application of a set of explicit algebraic formulae for the
calculation of specific characteristics of radiation heat flux from an open pool fire.
This document is an implementation of the general requirements provided in ISO 16730-1for the case of fire
dynamics calculations involving a set of explicit algebraic formulae.
This document is arranged in the form of a template, where specific information relevant to the algebraic
formulae is provided to satisfy the following types of general requirements:
a) description of physical phenomena addressed by the calculation method;
b) documentation of the calculation procedure and its scientific basis;
c) limitations of the calculation method;
d) input parameters for the calculation method; and
e) domain of applicability of the calculation method.
Examples of sets of algebraic formulae meeting the requirements of this document are provided in Annex A
and Annex B. Annex A contains a set of algebraic formulae for radiation heat fluxes from a circular or near-
circular open pool fire. Annex B contains formulae for configuration factors of a flame to a target.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 13943, Fire safety — Vocabulary
ISO 16733-1, Fire safety engineering — Selection of design fire scenarios and design fires — Part 1: Selection of
design fire scenarios
ISO 24678-1, Fire safety engineering — Requirements governing algebraic formulae — Part 1: General
requirements
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 13943 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp

— IEC Electropedia: available at https:// www .electropedia .org/
3.1
pool fire
burning of a horizontal, upward-facing, combustible fuel of liquids, liquefied gases or horizontally placed
melting plastic materials
3.2
open pool fire
pool fire (3.1) in open air or in a space that is very large relative to the size of the fire, where the confined
effect of the built environment on the behaviour of its flame is negligible
Note 1 to entry: The open pool fire characteristics are dependent on the outside conditions such as wind.
3.3
circular pool fire
near circular pool fire
pool fire (3.1) whose geometry can be approximated by a circular shape
Note 1 to entry: In case of an elongated pool, this approximation is valid if the ratio between the longest dimension and
[6]
the shortest dimension is not greater than 2 to 3 .
3.4
equivalent diameter
diameter of a circular pool of which the plan area is equivalent with rectangular or irregularly shaped pools
3.5
absorption coefficient
fraction of absorbed radiation intensity per unit length of radiation path
3.6
radiative fraction
ratio of the radiative heat release rate to the total heat release rate
3.7
mean flame height
time-averaged height of flames above the base of a fire, defined as the elevation where the probability of
finding flames is 50 %
3.8
atmospheric transmissivity
ratio of the transmitted radiation intensity after passing through unit length of a participating medium
(carbon dioxide, water vapour, dust and fog) to the radiation intensity that would have passed the same
distance through clean air
4 Requirements governing the description of physical phenomena
4.1 The requirements specified in ISO 24678-1:2019, Clause 4, governing the description of physical
phenomena, shall apply in addition to the requirements in the following subclauses.
4.2 Radiation heat flux from an open pool fire is a complex thermo-physical and chemical phenomenon that
can be highly transient or nearly steady-state. Radiation heat flux depends on the properties and geometry
of the combustible, and the environment between the radiation source and the "target" that receives the
heat flux. The properties of the target need to be considered when further calculations of target behaviour
are assessed, e.g. injuries to people, malfunction/damage of a piece of equipment, ignition of a combustible
material, deteriorations of structural members. The physical phenomena described in this document are
concerned with only the calculations of the radiation heat flux received by a target from an open pool fire.

4.3 General types of pool sources, pool geometry and relative positions of the considered targets (including
the position of radiation screens placed between the pool and the targets) shall be described with the aid of
diagrams.
4.4 Scenario elements, in accordance with ISO 16733-1, to which specific formulae apply shall be clearly
identified. Radiation heat flux characteristics to be calculated and their useful ranges shall be clearly
identified, including those characteristics inferred by association with calculated quantities, if applicable.
4.5 Physical phenomena (e.g. pool formation during a continuous release, interaction between fire and
extinguishing materials) to which specific formulae apply shall be clearly identified.
4.6 Because different formulae describe different pool source radiative flame characteristics (see 4.3) or
apply to different scenarios (see 4.4), it shall be shown that if there is more than one method to calculate a
given quantity, guidance shall be given on the selection of appropriate methods.
4.7 The radiative emission from flame is affected by various factors. The uncertainties in emissive power
shall be considered properly. Sensitivity analysis or conservative estimates is desirable. Sensitivity analysis
is used to identify the input variables that cause the greatest variation in the output results. For example, a
sensitivity analysis may be conducted on radiative fraction value to evaluate if a small variation may have
a significant impact on the radiated heat flux. If so, radiative fraction should be used cautiously. The use of
conservative assumptions may limit the impact of uncertainties on the final results. Safety factors and/or
margins may be applied to input or output data. Appropriate safety factors and margins are usually derived
[7]
from references on model validation and verification .
5 Requirements governing the calculation process
The requirements specified in ISO 24678-1:2019, Clause 5, governing the calculation process, shall apply.
6 Requirements governing limitations
The requirements specified in ISO 24678-1:2019, Clause 6, governing limitations, shall apply.
7 Requirements governing input parameters
The requirements specified in ISO 24678-1:2019, Clause 7, governing input parameters, shall apply.
8 Requirements governing the domain of applicability
The requirements specified in ISO 24678-1:2019, Clause 8, governing the domain of applicability, shall apply.
9 Example of documentation
An example of sets of algebraic formulae meeting the requirements in Clause 4 to Clause 8 is provided in
Annex A.
Annex A
(informative)
Algebraic formulae for thermal radiation from a circular or near
circular open pool fire
A.1 Symbols and abbreviated terms used in this annex
A plan area of a pool fire source (m )
s
D equivalent diameter of a pool fire source (m)
E emissive power of a flame (kW/m )
f
E emissive power of the luminous region of a flame (kW/m )
max
E emissive power of smoke (kW/m )
s
f configuration factor of side surface of an upright cylinder to a vertical target (−)
cyl-v
F configuration factor of a flame to a target (−)
F configuration factor of a flame to a vertical target (−)
12,v
g gravity acceleration (9,81 m/s )
H vertical distance from flame base to a target (m)
−1
k radiation absorption coefficient of a flame from various fuels (m )
L mean flame height (m)

m"
mass burning rate per unit area of a pool (kg/m ·s)
"
mass burning rate per unit area of a sufficiently large pool (kg/m ·s)

m
∞
*
m non-dimensional burning rate (−)

q″
radiation heat flux to a target (kW/m )

heat release rate from a pool fire (kW)
Q
u wind velocity (m/s)
w
u* non-dimensional wind velocity
X horizontal distance to a target from the centre of a flame (m)
−1
β radiation absorption coefficient of a flame taking the diameter as the characteristic length (m )
χ radiative fraction (−)
r
Γ heat of combustion of fuel (J/kg)
θ flame tilt angle (rad)
ρ density of normal ambient air (1,2 kg/m )
a
τ atmospheric transmissivity (−)
A.2 Description of the physical phenomena addressed by the algebraic formula set
A.2.1 General
The formulae described in this annex provide radiation heat fluxes from a pool fire to a target and can
be applicable to various locations and orientations. The set of formulae is particularly convenient for
horizontal and vertical target orientations. The formulae presented here have been validated on sooty liquid
hydrocarbon fires.
A.2.2 General description of the calculation method
Estimating the radiation heat flux received by a target from a pool fire involves the three following steps:
— determination of the characteristics of the pool fire (burning surface, mass burning rate, duration of the
fire, time to steady-state conditions, etc.);
— determination of the thermal radiation characteristics of the pool fire (flame height, flame tilt, emissive
power of the flames, etc.);
— calculation of the radiation heat flux received by a target (configuration factor of a flame to a target,
atmospheric transmissivity along radiation path).
It is very important that a single method be used for all the three steps of this process. The methods
presented in this annex constitute whole methods and its parts cannot be changed. The validation of the
whole model needs to be considered, not its components individually.
A.2.3 Scenario elements to which the set of formulae is applicable
The set of formulae is applicable to thermal radiation from quasi-steady-state pool fire flames that are
approximately circular or square in plan area in an unobstructed environment, unless otherwise stated.
A.2.4 Self-consistency of the set of formulae
The set of formulae provided in this annex has been derived and reviewed to ensure that the calculation
results from different formulae in the set are consistent (i.e. do not produce conflicts).
A.2.5 Standards and other documents where the set of formulae is used
None specified.
A.3 Documentation of the set of formulae
A.3.1 General
As shown in Figure A.1, radiation is emitted by a flame and received by a target. The heat flux received by a
target from a pool fire can be calculated with Formula (A.1):
"

qE F (A.1)
f12
Key
1 flame (surface 1)
2 target (surface 2)
3 emissions (to all directions)
4 heat flux to a target
Figure A.1 — Radiation from a flame to a target
Figure A.2 depicts the successive steps necessary for estimating the radiation heat flux received by a target
from a pool fire. From the specified burning object characteristics, the heat release rate and the diameter
of the pool, when not given, are estimated. The emissive power from the flame surface is assumed to be a
function of the diameter of the pool. The flame geometry is calculated by using the heat release rate and fire
source diameter. Finally, the configuration factor of a flame to a target is calculated. The effect of blockage
by a participation medium such as soot, water vapour and dipole gases is considered, where necessary, as
atmospheric transmissivity.
The target is considered as an infinitesimally small plane element, which is assumed to be located at the
minimum distance between the fire and the real target. Because configuration factors are also considered
in the calculations of the physical phenomena, the point is associated with an element surface. In this annex,
a solid cylindrical flame model is adopted. As presented in Figure A.2, the method is composed of different
interdependent sub-models, mean flame height, emissive power and so on.
Figure A.2 — Calculation process of radiation heat flux received by a target from a pool fire

A.3.2 Geometry and heat release rate of pool fires
A.3.2.1 Equivalent diameter of a pool fire source
The equivalent diameter of a pool fire source, D, is given by Formula (A.2):
4A
s
D (A.2)

A.3.2.2 Heat release rate

The heat release rate from a pool fire, Q , is given by Formula (A.3):


Qm A (A.3)
s
Examples of mass burning rate and net heat of combustion are shown in Table A.1. Using these values, the
[8]
mass burning rate per unit area of a pool is estimated by Formula (A.4) :


mm{e1 xp()kD } (A.4)

NOTE Formula (A.4) is valid for pool fires with D > 0,2 m.
[9]
Table A.1 — Net heat of combustion and mass burning rate of various fuels
Net heat of Mass burning rate at Radiation absorption coef-
Fuel
combustion sufficiently large pool ficient
"
−1
Γ (MJ/kg) k (m )

m (kg/m ·s)
∞
Liquid H 120 0,017 6,1
LNG 50,0 0,078 1,1
LP-gas 46,0 0,099 1,4
Methanol 20,0 0,017 —
Ethanol 26,8 0,015 —
Butane 42,7 0,078 2,7
Hexane 44,7 0,074 1,9
Heptane 44,6 0,101 1,1
benzene 40,1 0,085 2,7
Xylene 40,8 0,090 1,4
Acetone 25,8 0,041 1,9
Dioxane 26,2 0,018 5,4
Diethyl ether 34,2 0,085 0,7
Benzine 44,7 0,048 3,6
Gasoline 43,7 0,055 2,1
Kerosine 43,2 0,039 3,5
JP-4 43,5 0,051 3,6
JP-5 43,0 0,054 1,6
Transformer oil 46,4 0,039 0,7
Fuel oil, heavy 39,7 0,035 1,7
Crude oil 42,5 0,022 2,8
A.3.3 Cylindrical solid flame model and surface emissive power
A.3.3.1 Selection of methods
Several models have been developed based on the solid flame concept. The most common one is the
cylindrical solid flame model as shown in Figure A.1. This model has been chosen to represent the radiative
emitter by the lateral envelope of the flame as well as the upper disk.
There are various methods for estimating the surface emissive power. The surface emissive power is related
[10]
to the area of the cylindrical solid flame and the flame height. The Mudan-Croce’s method , Shokri-Beyler’s
[11]
method and the radiative fraction method are adopted in this annex. Each set of formulae corresponds to
a specific fuel type and a range of fuel diameter. The Mudan-Croce method is accompanied with the Thomas’
[12],[13]
formula for flame height and tilt . The Shokri-Beyler method is associated with the Heskestad’s
[14]
formula for flame height as described in ISO 24678-2. As the estimation formulae for the emissive power
is related to the surface area of flame, mixing various methods shall be avoided.
A.3.3.2 Mudan-Croce’s method
A.3.3.2.1 General
The Mudan-Croce’s method, for estimating the incident heat flux from a pool fire, suggests the following
Formulae (A.5) to (A.9) for the effective emissive power of gasoline, kerosene, and JP-4 flames, but it is
not recommended for LNG. The set of formulae uses correlations of flame height developed by Thomas
from wood crib experiments. In case of windy conditions, the flame tilt angle is calculated by correlation
developed by Thomas. This method is recommended in the range of diameter of approximately 1 m to 60 m.
A.3.3.2.2 Flame height by Thomas’ formula
[15]
In case of quiescent atmosphere, the flame height is calculated by Formula (A.5) :
L m
06, 1
42() (A.5)
D
 gD
a
NOTE Formula (A.5) is suitable for large open pool fires. See A.4.1 for details.
In the presence of wind, the flame length and tilt angle are calculated using Formula (A.6) and
[13]
Formula (A.7) :
L m
06,*70 ,21
55() ()u (A.6)
D
 gD
a
*

11()u 

cos  (A.7)

**

11/(uu  )

where the non-dimensional wind velocity is calculated using Formula (A.8):
u
* w
u  (A.8)
"/13

(/gm D  )
a
A.3.3.2.3 Emissive power by Mudan-Croce’s formula
The average and uniform emissive power at the flame surface of a pool fire, E, is given by the experimental
[10] 2 2 −1
correlation, Formula (A.9) , with E = 140 kW/m , E = 20 kW/m and β = 0,12 m . The average and
max s
uniform emissive power at the flame surface depends only on the pool diameter.

EEexp( DE){1 exp( D)} (A.9)
fsmax
The formula takes into consideration the screening effects of soot. Limitations of the uniform average
emissive power can arise when the target is close to the flame region at the rim of a pool fire where the
emissive power might be underestimated.
A.3.3.3 Shokri-Beyler’s method
A.3.3.3.1 General
The flame is assumed to be a cylindrical, homogeneous radiator with an average emissive power. Shokri’s
formula for emissive power is derived in association with the flame height by Heskestad’s formula. This
method is mostly applicable at heat fluxes greater than 5 kW/m . The pool diameter ranges from 1 m to
50 m and is mainly concerned with LNG and JP-5.
A.3.3.3.2 Flame height by Heskestad’s formula
[14]
Heskestad’s formula is applied to calculate the flame height as specified in ISO 24678-2; see Formula (A.10).
25/

LD10,,20 235Q (A.10)
A.3.3.3.3 Emissive power by Shokri’s formula
[11]
The effective emissive power of the pool fire is given by Shokri and Beyler as shown in Formula (A.11):
0,008 23D
E 58 ()10 (A.11)
f
A.3.3.4 Radiative fraction method
A.3.3.4.1 General
For relatively small pool diameters, the calculation formula is available for various fuels. The formula is a
purely geometrical representation of the redistribution of the radiant energy on a cylindrical envelope.
A.3.3.4.2 Flame height by Heskestad’s formula
The flame height is calculated by Heskestad’s formula as in Formula (A.10).
A.3.3.4.3 Emissive power by radiative fraction
The emissive power E is calculated considering a uniform distribution of the radiative fraction of the heat
release on the side and top surfaces of a cylinder, as expressed in Formula (A.12):

 Q
r
E  (A.12)
f
D
DL
where the radiative fraction of the energy released is correlated with the pool diameter as shown
[15]-[17]
in Table A.2 . Examples of radiative fraction of various fuels and liquid materials are shown in
[18]-[28]
Figures A.3 to A.6 . When the formulae do not provide conservative estimates of radiative fraction, it
is recommended to choose an appropriate value depending on the fuel type and pool diameter.

Table A.2 — Examples of calculation formulae for radiative fraction of energy release
Fuel Formulae Reference
kerosene, fuel oil, gasoline, JP-4, LNG,
[15]
 02,,10 00345DD() 0m SFPE guide
r
Methanol, Heptane, Toluene, Crude oil
[16]
 03,e50xp(,05DD)(25 0)
heptane, crude oil, kerosene McGrattan et al.
r
00, 3

03,(30DD,,22 6)

heptane  

r
05,
05,(52DD,)6

[17]
Yang et al.
00, 8

03,(20DD,)22

kerosene  

r
06,
04,(82DD )


Key
X pool diameter (m)
Y radiative fraction (−)
[18]
Koseki & Yumoto (1988)
[19]
Koseki (1989)
[20]
Koseki & Hayasaka (1989)
[21]
Hamins et al. (1991)
[22]
Klassen & Hamnis (1991)
[23]
Klassen & Gore (1994)
[24]
Buch et al. (1997)
[15]
SFPE guide (1999)
[16]
McGrattan et al. (2000)
[17]
Yang et al. (1994)
[18]-[24] [15]-[17]
Figure A.3 — Measured radiative fraction of heptane pool fires and formulae in
Table A.2
Key
X pool diameter (m)
Y radiative fraction (−)
[25]
Souil et al. (1986)
[18]
Koseki & Yumoto (1988)
[19]
Koseki (1989)
[15]
SFPE guide (1999)
[16]
McGrattan et al. (2000)
[17]
Yang et al. (1994)
[18],[19],[25] [15]-[17]
Figure A.4 — Measured radiative fraction of kerosene pool fires and formulae in
Table A.2
Key
X pool diameter (m)
Y radiative fraction (−)
[19]
JP4, Koseki (1989)
[26]
diesel oil, Munos (2007)
[19]
gasoline, Koseki (1989)
[26]
gasoline, Munoz (2007)
[15]
SFPE guide (1999)
[16]
McGrattan et al. (2000)
[19],[26] [15],[16]
Figure A.5 — Measured radiative fraction of pool fires of fuels and formulae in
Table A.2
Key
X pool diameter (m)
Y radiative fraction (−)
[19]
benzene, Koseki (1989)
[24]
methanol, Buch et al. (1997)
[23]
methanol, Klassen & Gore (1994)
[27]
methanol, Sjöström et al. (2015)
[24]
acetone, Buch et al. (1997)
[23]
toluene, Klassen & Gore (1994)
[24]
silicone oil, Buch et al. (1997)
[18]
crude oil, Koseki & Yumoto (1988)
[19]
crude oil, Koseki (1989)
[28]
crude oil, Koseki et al. (2000)
[15]
SFPE guide (1999)
[16]
McGrattan et al. (2000)
Figure A.6 — Measured radiative fraction of pool fires of miscellaneous combustible liquids
[18],[19],[23],[24],[27],[28] [15],[16]
and formulae in Table A.2
A.3.4 Configuration factors
The configuration factors are calculated by flame length, flame width, distance to target, flame tilt and
orientation of the target. The explicit calculation formulae are summarized in Annex B.
A.3.5 Atmospheric transmissivity
In most cases, the atmospheric transmissivity is approximated as unity. When it is desirable to consider
the absorption by the atmosphere between a flame and a target, the effect of the absorbing medium can
be applied. The principal constituents that absorb thermal radiation are soot (C), water vapour (H O) and
[29]
carbon dioxide (CO ) .
A.4 Scientific basis for the set of formulae
A.4.1 Flame height
The formulae for flame height (A.5) were developed by Thomas for wood crib fires and by Heskestad for
common fuels. The formulae were developed by a scaling law of fire plume, and compared with experimental
observations. Heskestad’s plume is described in ISO 24678-2:2022, Annex A.

Many investigators have developed correlations for turbulent flame heights in a quiescent air environment.
Most of them are based on the dimensional analysis of experimental data using Froude modelling principles.
Some are based on approximate theoretical models involving some empirical factors. These correlations are
generally cast in terms of a non-dimensional burning rate as shown in Formula (A.13).

m
*
m  (A.13)
 gD
a
The ratio of flame height to pool diameter is plotted versus non-dimensional burning rate in Figure A.7.
Key
X pool diameter (m)
Y flame height/pool diameter ratio (−)
Thomas Formula (A.5)
LNG pool fires on water
LNG pool fires on land
LNG pool fires on land
gasoline fires on land
kerosene fires on land
gasoline, kerosene, diesel oil
LNG, kerosene
acetone
[30]
Figure A.7 — Comparison of Thomas’ formulae with experimental data gathered by Mudan
A.4.2 Configuration factor
The formulae for configuration factors used in Formula (A.1) have been developed to describe radiation
heat transfer for general purposes not only for fire calculations. The factor is calculated only by geometrical
relationships between a flame and a target. See Annex B for detailed information.
A.5 Formula-set limitations
A.5.1 Shape of fire source
The set of formulae described in this annex assumes circular or near circular pool fires. Rectangular or
[7]
irregularly-shaped pool sources with aspect ratios greater than 2 to 3 require other models than the ones
described in this annex, as the equivalent diameter cannot be calculated by Formula (A.2).

A.5.2 Property of fuel
This annex deals with sooty hydrocarbon fires only. Fire sources affected by extinguishing agents are not
considered in this annex.
A.5.3 Emissive power
The emissive power depends largely on the pool diameter and slightly depends on the fuel type. The use of
correct values is essential for accurate calculations. It should be noted that experimental data are fitted with
the cylindrical flame model to determine surface emissivity. Thus, the emissive power is a model dependent
parameter.
A.5.4 Proximity to boundaries
The flame height is different when the pool is close to a vertical boundary. Rectangular pools, with a wall at
one or more sides and three-dimensional fire sources having restricted air access, cannot be considered in
this annex. In addition, if a fire plume is close to the enclosure boundary, reflection and re-radiation by the
wall surface need to be considered.
A.6 Formula-set input parameters
A.6.1 Heat release rate

The parameter, Q , is the rate of heat that is actually released by a fire under specific environmental
conditions, as measured by a calorimeter that is based on product gas collection to determine O , CO and
2 2
CO generation rates, or as otherwise specified. This parameter is normally obtained from a design fire
scenario. Further information on fire calorimetry is described in ISO 24473.
A.6.2 Radiative fraction
The radiative fraction of a flame, χ , is typically in the range of 0,3 to 0,4 for liquid fuels burning in a
R
relatively small pool but can decrease to 0,2 or smaller as the fire source diameter increases. Referring to
Figures A.3 to A.6, choose upper bound values than the experimental plot when you need a conservative
estimate of radiation heat flux.
A.6.3 Fire source diameter
The fire source diameter is normally obtained from a design fire scenario. For rectangular fire sources, an
equivalent diameter, D, is obtained from Formula (A.2), which uses a circular source having the same area as
the fire source.
A.7 Domain of applicability of the set of formulae
The domain of applicability of the set of formulae in this Annex can be determined from the scientific
literature references given in A.3 and A.4. As a brief summary, the domain of applicability is summarized in
Table A.3
Table A.3 — Domain of application of the three methods
Method Fuels Pool diameter
Mudan-Cross gasoline, kerosene, JP-4 1-60 m
Shokri-Beyler LNG, JP-5 1-50 m
Radiative fraction gasoline, kerosene, JP-4, LNG, metha- Applicability depends on the avail-
nol, heptane, toluene, crude oil ability of radiative fraction data in
Figures A.2 to A.6.
Configuration factors can be applied to any flame size and distance of the target to the flame as long as the
flame can be approximated by a cylinder.
A.8 Calculation examples
A.8.1 Calculation conditions
Calculate the radiation heat flux to a vertical target on the ground level at a distance of 20 m from a circular
kerosene pool fire of 10 m diameter as shown in Figure A.8.
Key
1 flame (surface 1)
2 target (surface 2)
Figure A.8 — Calculation example of the radiation heat flux to a vertical target
A.8.2 Burning and heat release rates
Using Formula (A.4), the mass burning rate per unit area is:
 kD

mm"(10e ),039 {e13xp(,5100)} ,0390 (kg/m ·s)

Using Formula (A.3), the heat release rate is:
31, 41 0


Qm A 43,,200390 132,3 (MW)
s
A.8.3 Mudan-Croce’s method
The flame height is calculated by Formula (A.5) as:

m 0,039
06,,1061
L42() D 42( ),10 0128, (m)
 gD 1,,205981100,
a
The emissive power is calculated by Formula (A.9) as:

DD
EEeE ()1e 140exp(01,)210201{exp(,01210)}},56 1 (kW/m )
fsmax
The configuration factor for this arrangement is calculated by Formula (B.2) in Annex B as:
L X 12,8 20,0
Ff ( , )(f , ),=0 092 99 (−)
12v cyl-vcyl-v
D/22D/ 10,/02 10,/02
The heat flux received by the target is calculated by Formula (A.1) as:
"
qE  F 10,,56 10,,09295 22 (kW/m )
f12v
A.8.4 Shokri–Beyler’s method
The flame height is calculated by Heskestad’s Formula (A.10) as:
25//25

LD10,,20235Q 10,,2100235 132300 16,1 (m)
The emissive power from the flame surface is calculated by Formula (A.11) as:
0,,008 23D 0008 2310
E 58()10 5810 48,0 (kW/m )
f
The configuration factor for this arrangement is calculated by Formula (B.2) in Annex B as:
L X 16,1 20,0
Ff ( , )(f , ),=0 103 (−)
12v cyl-vcyl-v
D/22D/ 10,/02 10,/02
The heat flux received by the target is calculated by Formula (A.1) as:
"

qE F 10,,48 00,,103494 (kW/m )
f12v
A.8.5 Radiative fraction method
The radiative fraction is calculated by the second formula in Table A.2 as:
 03,e50xp(,05D),0350exp(,)05 10 0,212
r
The emissive power is calculated by Formula (A.12) using the Heskestad’s flame height, Formula (A.20), as:

02, 12132300
 Q
r
E   48,1 (kW/m )
f
 31, 4
DD L 10 31,,410161
4 4
The heat flux received by the target is calculated by Formula (A.1) as:
"
qE  F 10,,48 10,,103496 (kW/m )
f 12v
==
==
Annex B
(informative)
Configuration factors of a cylindrical flame to a target
B.1 Symbols and abbreviated terms used in this annex
dA differential area of emitting surface
dA area of element j on an emitting surface [m ]
j
f configuration factor of side surface of an upright cylinder to a horizontal target (−)
cyl-h
f configuration factor of side surface of a tilted cylinder to a horizontal target (−)
cyl(θ)-h
f configuration factor of side surface of an upright cylinder to a vertical target (−)
cyl-v
f configuration factor of side surface of a tilted cylinder to a vertical target (−)
cyl(θ)-v
f configuration factor of a horizontal circular disk to a horizontal target (−)
cir-h
f configuration factor of a horizontal circular disk to a vertical target (−)
cir-v
f configuration factor of a vertical rectangular surface to a horizontal target (−)
rect-h
f configuration factor of a vertical rectangular surface to a vertical target (−)
rect-v
F configuration factor of a flame to a target at arbitrary orientation
F configuration factor of the emitting surface k to a plane perpendicular at the location of the target,
kh
(k=1,2)
F configuration factor of the emitting surface k to a plane parallel at the location of the target, (k=1,2)
kv
F configuration factor of a flame to a vertical target (−)
v
F configuration factor of a flame to a horizontal target (−)
h
h non-dimensional vertical distance from flame base to target, H/R (−)
H vertical distance from flam
...

ISO/TC 92/SC 4
Secretariat: AFNOR
ISO/TC 92/SC 4/WG 9
Date: 2026-03-2208-31
Fire safety engineering — Requirements governing algebraic
formulae — —
Part 7:
Radiation heat flux received from an open pool fire
Ingénierie de la sécurité incendie -- — Exigences régissant les formules algébriques -- —
Partie 7: FluxDensité de chaleur rayonné reçu d'unflux énergétique rayonnée reçue d’un feu en nappe ouvert
FDIS stage
ISO #####-#:####(X/FDIS 24678-7:2026(en)
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication
may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying,
or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO
at the address below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: + 41 22 749 01 11
EmailE-mail: [e-mail]
Website: www.iso.org
Published in Switzerland
© ISO #### 2026 – All rights reserved
ii
Contents
Foreword . iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Requirements governing the description of physical phenomena . 3
5 Requirements governing the calculation process. 3
6 Requirements governing limitations . 3
7 Requirements governing input parameters . 3
8 Requirements governing the domain of applicability . 4
9 Example of documentation . 4
Annex A (informative) Algebraic formulae for thermal radiation from a circular or near circular
open pool fire . 5
Annex B (informative) Configuration factors of a cylindrical flame to a target . 23
Bibliography . 51

iii
ISO #####-#:####(X/FDIS 24678-7:2026(en)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types of
ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent rights
in respect thereof. As of the date of publication of this document, ISO had not received notice of (a) patent(s)
which may be required to implement this document. However, implementers are cautioned that this may not
represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 92, Fire Safetysafety, Subcommittee SC 4, Fire
safety engineering.
This second edition cancels and replaces the first edition (ISO 24678-7:2019), which has been technically
revised.
The main changes are as follows:
— — Thethe main body was revised to align with ISO 24678-1 on common requirements.;
— — Somesome of the figures in Annex BAnnex B,, i.e. Figure B.3 ., B.3, B.14, Figure B.14 and Figure B.15
B.15,, have been technically revised.
A list of all parts in the ISO 24678 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
© ISO #### 2026 – All rights reserved
iv
Introduction
This documentThe ISO 24678 series is intended to be used by fire safety practitioners involved with fire safety
engineering calculation methods. It is expected that the users of this document are appropriately qualified and
competent in the field of fire safety engineering. It is particularly important that the users understand the
parameters within which particular methodologies canmay be used.
Algebraic formulae conforming to the requirements of this document are used with other engineering
calculation methods during fire safety design. Such a design is preceded by the establishment of a context,
including the fire safety goals and objectives to be met, as well as performance criteria when a trial fire safety
design is subject to specified design fire scenarios. Engineering calculation methods are used to determine if
these performance criteria are met by a particular design and if not, how the design needs to be modified.
The subjects of engineering calculations include the fire safety design of entirely new built environments, such
as buildings, ships or vehicles as well as the assessment of the fire safety of existing built environments.
The algebraic formulae discussed in this document can be useful for estimating the consequences of design
fire scenarios. Such formulae are valuable for allowing the practitioner to quickly determine how a proposed
fire safety design needs to be modified to meet performance criteria and to compare among multiple trial
designs. Detailed numerical calculations can be carried out up until the final design documentation. Examples
of areas where algebraic formulae have been applicable include determination of convective and radiative
heat transfer from fire plumes, prediction of ceiling jet flow properties governing detector response times,
calculation of smoke transport through vent openings, and analysis of compartment fire hazards such as
smoke filling and flashover. However, the simple models often have stringent limitations and are less likely to
include the effects of multiple phenomena occurring in the design fire scenarios.
The general principles of fire safety engineering are described in ISO 23932-1, which provides a performance-
based methodology for engineers to assess the level of fire safety for new or existing built environments. Fire
safety is evaluated through an engineered approach based on the quantification of the behaviour of fire and
based on knowledge of the consequences of such behaviour on life safety, property and the environment. ISO
23932-1 provides the process (i.e. necessary steps) and essential elements to conductfor conducting a robust
performance-based fire safety design.
ISO 23932-1 is supported by a set of available fire safety engineering International Standards on the methods
and data needed for all the steps in a fire safety engineering design as summarized in Figure 1 Figure 1 (taken
from ISO 23932-1:2018, Clause 4). The set includes the ISO 16730 series, the ISO 16732 series, the ISO 16733
series, ISO/TR 16738, the ISO 24678 series, the ISO 24679 series, ISO 23932-1, ISO/TS 29761 and other
supporting documents that provide examples of and guidance on the application of these standards.
Each International Standard supporting the global fire safety engineering analysis and information system
includes language in the introduction to tie the standard to the steps in the fire safety engineering design
process outlined in ISO 23932-1. ISO 23932-1 requires that engineering methods be selected properly with
acceptable accuracy to predict the fire consequences of specific scenarios and scenario elements (ISO 23932-
1:2018, Clause 12). Pursuant to the requirements of ISO 23932-1, this document provides the requirements
governing algebraic formulae for fire safety engineering. This step in the fire safety engineering process is
shown as a highlighted box in Figure 1 Figure 1 and described in ISO 23932-1.
v
ISO #####-#:####(X/FDIS 24678-7:2026(en)

Figure 1 — Flow chart illustrating the fire safety engineering (FSE) design process (from ISO 23932-
1:2018)
© ISO #### 2026 – All rights reserved
vi
DRAFT International Standard ISO/FDIS 24678-7:2026(en)

Fire safety engineering — Requirements governing algebraic
formulae — —
Part 7:
Radiation Heat Flux Receivedheat flux received from an Open Pool
Fireopen pool fire
1 Scope
The requirements in this document govern the application of a set of explicit algebraic formulae for the
calculation of specific characteristics of radiation heat flux from an open pool fire.
This document is an implementation of the general requirements provided in ISO 16730-1 for1for the case of
fire dynamics calculations involving a set of explicit algebraic formulae.
This document is arranged in the form of a template, where specific information relevant to the algebraic
formulae is provided to satisfy the following types of general requirements:
a) a) description of physical phenomena addressed by the calculation method;
b) b) documentation of the calculation procedure and its scientific basis;
c) c) limitations of the calculation method;
d) d) input parameters for the calculation method; and
e) e) domain of applicability of the calculation method.
Examples of sets of algebraic formulae meeting the requirements of this document are provided in
Annex AAnnex A and Annex BAnnex B. Annex A. Annex A contains a set of algebraic formulae for radiation
heat fluxes from a circular or near-circular open pool fire. Annex BAnnex B contains formulae for
configuration factors of a flame to a target.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 13943, Fire safety — Vocabulary
ISO 16730-1, Fire safety engineering — Procedures and requirements for verification and validation of
calculation methods — Part 1: General
ISO 16733--1, Fire safety engineering — Selection of design fire scenarios and design fires — Part 1: Selection of
design fire scenarios
ISO #####-#:####(X/FDIS 24678-7:2026(en)
ISO 24678--1, Fire safety engineering — Requirements governing algebraic formulae — Part 1: General
requirements
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 13943 and the following apply.
ISO and IEC maintain terminologyterminological databases for use in standardization at the following
addresses:
— — ISO Online browsing platform: available at https://www.iso.org/obp
— — IEC Electropedia: available at https://www.electropedia.org/
3.1 3.1
pool fire
burning of a horizontal, upward-facing, combustible fuel of liquids, liquefied gases or horizontally placed
melting plastic materials
3.2 3.2
open pool fire
pool fire (3.1(3.1)) in open air or in a space that is very large relative to the size of the fire, where the confined
effect of the built environment on the behaviour of its flame is negligible
Note 1 to entry: The open pool fire characteristics are dependent on the outside conditions such as wind.
3.3 3.3
circular or pool fire
near circular pool fire
pool fire (3.1(3.1)) whose geometry can be approximated by a circular shape
Note 1 to entry: In case of an elongated pool, this approximation is valid if the ratio between the longest dimension and
[5]
the shortest dimension is not greater than 2 to 3[6] .
3.4 3.4
equivalent diameter
diameter of a circular pool of which the plan area is equivalent with rectangular or irregularly shaped pools
3.5 3.5
absorption coefficient
fraction of absorbed radiation intensity per unit length of radiation path.
3.6 3.6
radiative fraction
ratio of the radiative heat release rate to the total heat release rate
3.7 3.7
mean flame height
time-averaged height of flames above the base of a fire, defined as the elevation where the probability of
finding flames is 50 %
3.8 3.8
atmospheric transmissivity
ratio of the transmitted radiation intensity after passing through unit length of a participating medium (carbon
dioxide, water vapour, dust and fog) to the radiation intensity that would have passed the same distance
through clean air
© ISO #### 2026 – All rights reserved
4 Requirements governing the description of physical phenomena
4.1 4.1 The requirements specified in Clause 4 of ISO 24678-1:2019, Clause 4, governing the
description of physical phenomena, shall apply in addition to the requirements in the following subclauses.
4.2 4.2 Radiation heat flux from an open pool fire is a complex thermo-physical and chemical
phenomenon that can be highly transient or nearly steady-state. Radiation heat flux depends on the properties
and geometry of the combustible, and the environment between the radiation source and the "target" that
receives the heat flux. The properties of the target need to be considered when further calculations of target
behaviour are assessed, e.g. injuries to people, malfunction/damage of a piece of equipment, ignition of a
combustible material, deteriorations of structural members. The physical phenomena described in this
document are concerned with only the calculations of the radiation heat flux received by a target from an open
pool fire.
4.3 4.3 General types of pool sources, pool geometry and relative positions of the considered targets
(including the position of radiation screens placed between the pool and the targets) shall be described with
the aid of diagrams.
4.4 4.4 Scenario elements, in accordance with ISO 16733-1, to which specific formulae apply shall be
clearly identified. Radiation heat flux characteristics to be calculated and their useful ranges shall be clearly
identified, including those characteristics inferred by association with calculated quantities, if applicable.
4.5 4.5 Physical phenomena (e.g. pool formation during a continuous release, interaction between fire
and extinguishing materials) to which specific formulae apply shall be clearly identified.
4.6 4.6 Because different formulae describe different pool source radiative flame characteristics (see
4.34.3)) or apply to different scenarios (see 4.44.4),), it shall be shown that if there is more than one method
to calculate a given quantity, guidance shall be given on the selection of appropriate methods.
4.7 4.7 The radiative emission from flame is affected by various factors. The uncertainties in emissive
power shall be considered properly. Sensitivity analysis or conservative estimates is desirable. Sensitivity
analysis is used to identify the input variables that cause the greatest variation in the output results. For
example, a sensitivity analysis may be conducted on radiative fraction value to evaluate if a small variation
may have a significant impact on the radiated heat flux. If so, radiative fraction should be used cautiously. The
use of conservative assumptions may limit the impact of uncertainties on the final results. Safety factors
and/or margins may be applied to input or output data. Appropriate safety factors and margins are usually
[6]
derived from references on model validation and verification[7]. .
5 Requirements governing the calculation process
The requirements specified in Clause 5 of ISO 24678-1:2019, Clause 5, governing the calculation process, shall
apply.
6 Requirements governing limitations
The requirements specified in Clause 6 of ISO 24678-1:2019, Clause 6, governing limitations, shall apply.
7 Requirements governing input parameters
The requirements specified in Clause 7 of ISO 24678-1:2019, Clause 7, governing input parameters, shall
apply.
ISO #####-#:####(X/FDIS 24678-7:2026(en)
8 Requirements governing the domain of applicability
The requirements specified in Clause 8 of ISO 24678-1:2019, Clause 8, governing the domain of applicability,
shall apply.
9 Example of documentation
An example of sets of algebraic formulae meeting the requirements in 4Clause 4 to 8Clause 8 is provided in
Annex AAnnex A.
© ISO #### 2026 – All rights reserved
Annex A
(informative)
Algebraic formulae for thermal radiation from a circular or near circular open
pool fire
A.1 Symbols and abbreviated terms used in this Annexannex
A plan area of a pool fire source (m )
s
D equivalent diameter of a pool fire source (m)
E emissive power of a flame (kW/m )
f
E emissive power of the luminous region of a flame (kW/m )
max
Es emissive power of smoke (kW/m )
f configuration factor of side surface of an upright cylinder to a vertical target (−)
cyl-v
F configuration factor of a flame to a target (−)
F configuration factor of a flame to a vertical target (−)
12,v
g gravity acceleration (9,81 m/s )
H vertical distance from flame base to a target (m)
−1
k radiation absorption coefficient of a flame from various fuels (m )
L mean flame height (m)
𝑚˙ " mass burning rate per unit area of a pool (kg/m ·s)
"
mass burning rate per unit area of a sufficiently large pool (kg/m ·s)
𝑚˙
∞
*
m non-dimensional burning rate (−)
𝑞˙ ″ radiation heat flux to a target (kW/m )
˙
heat release rate from a pool fire (kW)
𝑄
u wind velocity (m/s)
w
u* non-dimensional wind velocity
X horizontal distance to a target from the centre of a flame (m)
−1
β radiation absorption coefficient of a flame taking the diameter as the characteristic length (m )
χ radiative fraction (−)
r
heat of combustion of fuel (J/kg)
Γ
θ flame tilt angle (rad)
ρ density of normal ambient air (1,2 kg/m )
a
τ atmospheric transmissivity (−)
ISO #####-#:####(X/FDIS 24678-7:2026(en)
A.2 Description of the physical phenomena addressed by the algebraic formula
set
A.2.1 General
The formulae described in this annex provide radiation heat fluxes from a pool fire to a target and can be
applicable to various locations and orientations. The set of formulae is particularly convenient for horizontal
and vertical target orientations. The formulae presented here have been validated on sooty liquid
hydrocarbon fires.
A.2.2 General description of the calculation method
Estimating the radiation heat flux received by a target from a pool fire involves the three following steps:
— — determination of the characteristics of the pool fire (burning surface, mass burning rate, duration of
the fire, time to steady-state conditions, etc.);
— — determination of the thermal radiation characteristics of the pool fire (flame height, flame tilt, emissive
power of the flames, etc.);
— — calculation of the radiation heat flux received by a target (configuration factor of a flame to a target,
atmospheric transmissivity along radiation path).
It is very important that a single method be used for all the three steps of this process. The methods presented
in this annex constitute whole methods and its parts cannot be changed. The validation of the whole model
needs to be considered, not its components individually.
A.2.3 Scenario elements to which the set of formulae is applicable
The set of formulae is applicable to thermal radiation from quasi-steady-state pool fire flames that are
approximately circular or square in plan area in an unobstructed environment, unless otherwise stated.
A.2.4 Self-consistency of the set of formulae
The set of formulae provided in this annex has been derived and reviewed to ensure that the calculation results
from different formulae in the set are consistent (i.e. do not produce conflicts).
A.2.5 Standards and other documents where the set of formulae is used
None specified.
A.3 Documentation of the set of formulae
A.3.1 General
As shown in Error! Reference source not found.Figure A.1,, radiation is emitted by a flame and received by
a target. The heat flux received by a target from a pool fire can be calculated with Error! Reference source
not found.the following algebraic formula::
"
𝑞˙ = 𝜏𝐸 𝐹
f 12
(A.1)
© ISO #### 2026 – All rights reserved
Key
1 flame (surface 1)
2 target (surface 2)
3 emissions (to all directions)
4 heat flux to a target
Figure A.1 — Radiation from a flame to a target
Figure A.2 Figure A.2 depicts the successive steps necessary for estimating the radiation heat flux received by
a target from a pool fire. From the specified burning object characteristics, the heat release rate and the
diameter of the pool, when not given, are estimated. The emissive power from the flame surface is assumed to
be a function of the diameter of the pool. The flame geometry is calculated by using the heat release rate and
fire source diameter. Finally, the configuration factor of a flame to a target is calculated. The effect of blockage
by a participation medium such as soot, water vapour and dipole gases is considered, where necessary, as
atmospheric transmissivity.
ISO #####-#:####(X/FDIS 24678-7:2026(en)
The target is considered as an infinitesimally small plane element, which is assumed to be located at the
minimum distance between the fire and the real target. Because configuration factors are also considered in
the calculations of the physical phenomena, the point is associated with an element surface. In this annex, a
solid cylindrical flame model is adopted. As presented in Figure A.2 Figure A.2,, the method is composed of
different interdependent sub-models, mean flame height, emissive power and so on.

Figure A.2 — Calculation process of radiation heat flux received by a target from a pool fire
A.3.2 Geometry and heat release rate of pool fires
A.3.2.1 Equivalent diameter of a pool fire source
The equivalent diameter of a pool fire source, D, is given by Error! Reference source not
found.Formula (A.2)::
4𝐴
s
√
𝐷 =
𝜋
(A.2)
A.3.2.2 Heat release rate
˙
The heat release rate from a pool fire,,, 𝑄, is given by Error! Reference source not found.Formula (A.3)::
© ISO #### 2026 – All rights reserved
˙
𝑄 = 𝛤𝑚˙ ″𝐴 (A.3)
s
Examples of mass burning rate and net heat of combustion are shown in Error! Reference source not
found.Table A.1. Using these values, the mass burning rate per unit area of a pool is estimated by Error!
[7]
Reference source not found.Error! Reference source not found.Formula (A.4) ::
″
𝑚˙ ″ = 𝑚˙ {1 − exp(−𝑘𝐷)}
∞
(A.4)
NOTE Formula (A.4) (A.4) is valid for pool fires with D > 0,2 m.
[ [8]]
Table A.1 — Net heat of combustion and mass burning rate of various fuels [9]
Net heat of Mass burning rate at Radiation absorption
Fuel
combustion sufficiently large pool coefficient
"
2 −1
k (m )
Γ (MJ/kg) 𝑚˙ (kg/m ·s)
∞
Liquid H2 120 0,017 6,1
LNG 50,0 0,078 1,1
LP-gas 46,0 0,099 1,4
Methanol 20,0 0,017 —
Ethanol 26,8 0,015 —
Butane 42,7 0,078 2,7
Hexane 44,7 0,074 1,9
Heptane 44,6 0,101 1,1
benzene 40,1 0,085 2,7
Xylene 40,8 0,090 1,4
Acetone 25,8 0,041 1,9
Dioxane 26,2 0,018 5,4
Diethyl ether 34,2 0,085 0,7
Benzine 44,7 0,048 3,6
Gasoline 43,7 0,055 2,1
Kerosine 43,2 0,039 3,5
JP-4 43,5 0,051 3,6
JP-5 43,0 0,054 1,6
Transformer oil 46,4 0,039 0,7
Fuel oil, heavy 39,7 0,035 1,7
Crude oil 42,5 0,022 2,8
A.3.3 Cylindrical solid flame model and surface emissive power
A.3.3.1 Selection of methods
Several models have been developed based on the solid flame concept. The most common one is the cylindrical
solid flame model as shown in Figure A.1 Figure A.1. This model has been chosen to represent the radiative
emitter by the lateral envelope of the flame as well as the upper disk.
ISO #####-#:####(X/FDIS 24678-7:2026(en)
There are various methods for estimating the surface emissive power. The surface emissive power is related
[9]
to the area of the cylindrical solid flame and the flame height. The Mudan-Croce’s method[10], , Shokri-
[10]
Beyler’s method[11] and the radiative fraction method are adopted in this annex. Each set of formulae
corresponds to a specific fuel type and a range of fuel diameter. The Mudan-Croce method is accompanied
],[ [11,12]
with the Thomas’ formula for flame height and tilt[12] [13]. . The Shokri-Beyler method is associated with
[13]
the Heskestad’s formula for flame height[14] as described in ISO 24678-2. As the estimation formulae for
the emissive power is related to the surface area of flame, mixing various methods shall be avoided.
A.3.3.2 Mudan-Croce’s method
A.3.3.2.1 General
The Mudan-Croce’s method, for estimating the incident heat flux from a pool fire, suggests the following
formulae (A.5)Formula (A.5) to (A.9)Formula (A.9) for the effective emissive power of gasoline, kerosene, and
JP-4 flames, but it is not recommended for LNG. The set of formulae uses correlations of flame height
developed by Thomas from wood crib experiments. In case of windy conditions, the flame tilt angle is
calculated by correlation developed by Thomas. This method is recommended in the range of diameter of
approximately 1 m to 60 m.
A.3.3.2.2 Flame height by Thomas’ formula
In case of quiescent atmosphere, the flame height is calculated by Error! Reference source not found.Error!
[12]
Reference source not found.Formula (A.5) ::
𝐿 𝑚˙ ″
0,61
= 42( ) (A.5)
𝐷 𝜌 𝑔𝐷
√
a
NOTE Formula (A.5) (A.5) is suitable for large open pool fires. See A.4.1A.4.1 for details.
In the presence of wind, the flame length and tilt angle are calculated using Error! Reference source not
found.Formula (A.6) and Error! Reference source not found.Error! Reference source not found.Formula
[ 12]
(A.7) ::
(A.6)
(A.7)
𝐿 𝑚˙ ″
0,67 ∗ −0,21
= 55( ) (𝑢 )
𝐷
𝜌 √𝑔𝐷
a
(A.6)
∗
1 (𝑢 ≤ 1)
cos𝜃 = {
∗ ∗
⁄
1 √𝑢 (𝑢 > 1)
(A.7)
where the non-dimensional wind velocity is calculated using Error! Reference source not found.Formula
(A.8)::
𝑢
w
∗
𝑢 = (A.8)
" 1⁄3
˙
(𝑔𝑚 𝐷/𝜌 )
a
A.3.3.2.3 Emissive power by Mudan-Croce’s formula
The average and uniform emissive power at the flame surface of a pool fire, E, is given by the experimental
[9]
correlation, Error! Reference source not found.Error! Reference source not found.Formula (A.9), , with
© ISO #### 2026 – All rights reserved
2 2 −1
E = 140 kW/m , E = 20 kW/m and β = 0,12 m . The average and uniform emissive power at the flame
max s
surface depends only on the pool diameter.
(A.9)
𝐸 = 𝐸 exp(−𝛽𝐷) + 𝐸 {1 − exp(−𝛽𝐷)}
f max s
(A.9)
The formula takes into consideration the screening effects of soot. Limitations of the uniform average emissive
power can arise when the target is close to the flame region at the rim of a pool fire where the emissive power
might be underestimated.
A.3.3.3 Shokri-Beyler’s method
A.3.3.3.1 General
The flame is assumed to be a cylindrical, homogeneous radiator with an average emissive power. Shokri’s
formula for emissive power is derived in association with the flame height by Heskestad’s formula. This
method is mostly applicable at heat fluxes greater than 5 kW/m . The pool diameter ranges from 1 m to 50 m
and is mainly concerned with LNG and JP-5.
A.3.3.3.2 Flame height by Heskestad’s formula
[13]
Heskestad’s formulaError! Reference source not found. is applied to calculate the flame height as
specified in ISO 24678-2; see Error! Reference source not found.Formula (A.10).
2⁄5
˙
𝐿 = −1,02𝐷 + 0,235𝑄 (A.10)
A.3.3.3.3 Emissive power by Shokri’s formula
The effective emissive power of the pool fire is given by Shokri and Beyler Error! Reference source not
[10]
found. as shown in Error! Reference source not found.Formula (A.11)::
−0,008  23𝐷
𝐸 = 58  (10 ) (A.11)
f
A.3.3.4 Radiative fraction method
A.3.3.4.1 General
For relatively small pool diameters, the calculation formula is available for various fuels. The formula is a
purely geometrical representation of the redistribution of the radiant energy on a cylindrical envelope.
A.3.3.4.2 Flame height by Heskestad’s formula
The flame height is calculated by Heskestad’s formula as in Formula (A.10) (A.10).
A.3.3.4.3 Emissive power by radiative fraction
The emissive power E is calculated considering a uniform distribution of the radiative fraction of the heat
release on the side and top surfaces of a cylinder, as expressed in Error! Reference source not
found.Formula (A.12)::
ISO #####-#:####(X/FDIS 24678-7:2026(en)
˙
𝜒 𝑄
r
𝐸 =
f
𝜋𝐷
𝜋𝐷𝐿 +
(A.12)
where the radiative fraction of the energy released is correlated with the pool diameter as shown in Table A.2
]-[ [14-16]
[15] [17]Table A.2. . Examples of radiative fraction of various fuels and liquid materials are shown in
]-[ [17-27]
Figure A.3 Figures A.3 to Figure A.6 [18] [28]A.6. . When the formulae do not provide conservative
estimates of radiative fraction, it is recommended to choose an appropriate value depending on the fuel type
and pool diameter.
Table A.2 — Examples of calculation formulae for radiative fraction of energy release
Fuel Formulae Ref.Reference
kerosene, fuel oil, gasoline, JP-4, LNG,
[14]
𝜒 = 0,21 − 0,003 4𝐷               (𝐷 < 50 m) SFPE guide[15]
r
Methanol, Heptane, Toluene, Crude oil
[15]
heptane, crude oil, kerosene 𝜒 = 0,35exp(−0,05𝐷)                (2 ≤ 𝐷 ≤ 50) McGrattan et al. .[16]
r
0,03
0,33𝐷 (0,2 < 𝐷 ≤ 2,6)
heptane 𝜒 = {
r
−0,5
0,55𝐷 (2,6 < 𝐷)
[16]
Yang et al. .[17]
0,08
0,32𝐷 (0,2 < 𝐷 < 2)
kerosene 𝜒 = {
r
−0,6
0,48𝐷 (2 < 𝐷)
© ISO #### 2026 – All rights reserved
Key
X pool diameter (m)
Y radiative fraction (−)
[17] [
Koseki & Yumoto (1988) ) 18]
[18] [
Koseki (1989) ) 19]
[19] [
Koseki & Hayasaka (1989) ) 20]
[20] [
Hamins et al. (1991) ) 21]
[21] [
Klassen & Hamnis (1991) ) 22]
[22] [
Klassen & Gore (1994) ) 23]
[23] [
Buch et al. (1997) ) 24]
[14] [
SFPE guide (1999) ) 15]
[15] [
McGrattan et al. (2000) ) 16]
[16] [
Yang et al. (1994) ) 17]
[ ]-[ [17-23]] [ ]-
Figure A.3 — Measured radiative fraction of heptane pool fires [18] [24] and formulae [15]
[ [14-16]]
[17] in Table A.2 Table A.2
ISO #####-#:####(X/FDIS 24678-7:2026(en)

Key
X pool diameter (m)
Y radiative fraction (−)
[24]
Souil et al. (1986)
[17]
Koseki & Yumoto (1988)
[18]
Koseki (1989)
[14]
SFPE guide (1999)
[15]
McGrattan et al. (2000)
[16]
Yang et al. (1994)
[17,18,24] [14-16]
Figure A.4 — Measured radiative fraction of kerosene pool fires and formulae in
Table A.2
© ISO #### 2026 – All rights reserved
Key
X pool diameter (m)
Y radiative fraction (−)
Souil et al. JP4, (1986)[25]
[18]
Koseki (1989) & Yumoto (1988)[18]
[25]
diesel oil, Munos (2007)
[18]
gasoline, Koseki (1989) )[19]
[25]
gasoline, Munoz (2007)
[14]
SFPE guide (1999) )[15]
[15]
McGrattan et al. (2000) ) [16]
Yang et al. (1994)[17]
[ ],[ ],[ [18,25]]
Figure A.5 4 — Measured radiative fraction of kerosene pool fires [18] [19] [25] of fuels and
[ ]-[ [14,15]]
formulae [15] [17] in Table A.2 Table A.2
ISO #####-#:####(X/FDIS 24678-7:2026(en)

Key
X pool diameter (m)
Y radiative fraction (−)
JP4, Koseki (1989)[19]
diesel oil, Munos (2007)[26]
gasoline, Koseki (1989)[19]
gasoline, Munoz (2007)[26]
SFPE guide (1999)[15]
McGrattan et al. (2000)[16]
[ ],[ ] [ ],[ ]
Figure A.5 — Measured radiative fraction of pool fires of fuels [19] [26] and formulae [15] [16] in
Table A.2
© ISO #### 2026 – All rights reserved
Key
X pool diameter (m)
Y radiative fraction (−)
[18]
benzene, Koseki (1989) )[19]
[23]
methanol, Buch et al. (1997) )[24]
[22]
methanol, Klassen & Gore (1994) )[23]
[26]
methanol, Sjöström et al. (2015) )[27]
[23]
acetone, Buch et al. (1997) )[24]
[22]
toluene, Klassen & Gore (1994) )[23]
[23]
silicone oil, Buch et al. (1997) )[24]
[17]
crude oil, Koseki & Yumoto (1988) )[18]
[18]
crude oil, Koseki (1989) )[19]
[27]
crude oil, Koseki et al. (2000)
[14]
SFPE guide (1999)
[15]
McGrattan et al. (2000) )[28]
SFPE guide (1999)[15]
McGrattan et al. (2000)[16]
Figure A.6 — Measured radiative fraction of pool fires of miscellaneous combustible liquids
[ ],[ ],[ ],[ ],[ ],[ [17,18,22,23,26,27]] [ ],[ [14,15]]
[18] [19] [23] [24] [27] [28] and formulae [15] [16] in Table A.2 Table A.2
A.3.4 Configuration factors
The configuration factors are calculated by flame length, flame width, distance to target, flame tilt and
orientation of the target. The explicit calculation formulae are summarized in Annex BAnnex B.
A.3.5 Atmospheric transmissivity
In most cases, the atmospheric transmissivity is approximated as unity. When it is desirable to consider the
absorption by the atmosphere between a flame and a target, the effect of the absorbing medium can be applied.
The principal constituents that absorb thermal radiation are soot (C), water vapour (H O) and carbon
[28]
dioxide (CO2)[29]) .
ISO #####-#:####(X/FDIS 24678-7:2026(en)
A.4 Scientific basis for the set of formulae
A.4.1 Flame height
The formulae for flame height (Error! Reference source not found.(A.5)) were developed by Thomas for
wood crib fires and by Heskestad for common fuels. The formulae were developed by a scaling law of fire
plume, and compared with experimental observations. Heskestad’s plume is described in ISO 24678-2:2022,
Annex A.
Many investigators have developed correlations for turbulent flame heights in a quiescent air environment.
Most of them are based on the dimensional analysis of experimental data using Froude modelling principles.
Some are based on approximate theoretical models involving some empirical factors. These correlations are
generally cast in terms of a non-dimensional burning rate as shown in Error! Reference source not
found.Formula (A.13).
𝑚˙ ″
∗
𝑚 =
𝜌 𝑔𝐷
√
a
(A.13)
The ratio of flame height to pool diameter is plotted versus non-dimensional burning rate in Figure A.7
Figure A.7.
Key
X pool diameter (m)
Y flame height/pool diameter ratio (−)
Thomas Formula (A.5) (A.5)
LNG pool fires on water
LNG pool fires on land
LNG pool fires on land
gasoline fires on land
kerosene fires on land
gasoline, kerosene, diesel oil
LNG, kerosene
acetone
[ [29]]
Figure A.7 — Comparison of Thomas’ formulae with experimental data gathered by Mudan [30]
© ISO #### 2026 – All rights reserved
A.4.2 Configuration factor
The formulae for configuration factors used in Formula(A.1) (A.1) have been developed to describe radiation
heat transfer for general purposes not only for fire calculations. The factor is calculated only by geometrical
relationships between a flame and a target. See Annex BAnnex B for detailed information.
A.5 Formula-set limitations
A.5.1 Shape of fire source
The set of formulae described in this annex assumes circular or near circular pool fires. Rectangular or
[6]
irregularly-shaped pool sources with aspect ratios greater than 2 to 3[7] require other models than the ones
described in this annex, as the equivalent diameter cannot be calculated by Formula (A.2) (A.2).
A.5.2 Property of fuel
This annex deals with sooty hydrocarbon fires only. Fire sources affected by extinguishing agents are not
considered in this annex.
A.5.3 Emissive power
The emissive power depends largely on the pool diameter and slightly depends on the fuel type. The use of
correct values is essential for accurate calculations. It should be noted that experimental data are fitted with
the cylindrical flame model to determine surface emissivity. Thus, the emissive power is a model dependent
parameter.
A.5.4 Proximity to boundaries
The flame height is different when the pool is close to a vertical boundary. Rectangular pools, with a wall at
one or more sides and three-dimensional fire sources having restricted air access, cannot be considered in this
annex. In addition, if a fire plume is close to the enclosure boundary, reflection and re-radiation by the wall
surface need to be considered.
A.6 Formula-set input parameters
A.6.1 Heat release rate
˙
The parameter, ,𝑄, is the rate of heat that is actually released by a fire under specific environmental conditions,
as measured by a calorimeter that is based on product gas collection to determine O , CO and CO generation
2 2
rates, or as otherwise specified. This parameter is normally obtained from a design fire scenario. Further
information on fire calorimetry is described in ISO 24473.
A.6.2 Radiative fraction
The radiative fraction of a flame, ,𝜒 , is typically in the range of 0,3 to 0,4 for liquid fuels burning in a relatively
𝑅
small pool but can decrease to 0,2 or smaller as the fire source diameter increases. Referring to Figure A.3
figures A.3 to Figure A.6 A.6,, choose upper bound values than the experimental plot when you need a
conservative estimate of radiation heat flux.
A.6.3 Fire source diameter
The fire source diameter is normally obtained from a design fire scenario. For rectangular fire sources, an
equivalent diameter, D, is obtained from Formula(A.2) (A.2),, which uses a circular source having the same
area as the fire source.
ISO #####-#:####(X/FDIS 24678-7:2026(en)
A.7 Domain of applicability of the set of formulae
The domain of applicability of the set of formulae in this Annex can be determined from the scientific literature
references given in A.3A.3 and A.4A.4. As a brief summary, the domain of applicability is summarized in
Table A.3 Table A.3
Table A.3 — Domain of application of the three methods
Method Fuels Pool diameter
Mudan-Cross gasoline, kerosene, JP-4 1-60 m
Shokri-Beyler LNG, JP-5 1-50 m
Radiative fraction gasoline, kerosene, JP-4, LNG, Applicability depends on the
availability of radiative fraction data
methanol, heptane, toluene, crude oil
in Figure A.2 Figures A.2 to
Figure A.6 A.6. .
Configuration factors can be applied to any flame size and distance of the target to the flame as long as the
flame can be approximated by a cylinder.
A.8 Calculation examples
A.8.1 Calculation conditions
Calculate the radiation heat flux to a vertical target on the ground level at a distance of 20 m from a circular
kerosene pool fire of 10 m diameter as shown in Figure A.8 Figure A.8.
© ISO #### 2026 – All rights reserved
Key
1 flame (surface 1)
2 target (surface 2)
Figure A.8 — Calculation example of the radiation heat flux to a vertical target
A.8.2 Burning and heat release rates
Using Error! Reference source not found.Formula (A.4),, the mass burning rate per unit area is:
″ −𝑘𝐷
𝑚˙ " = 𝑚˙ (1 − 𝑒 ) = 0,039 × {1 − exp(−3,5 × 10)} = 0,039 0
∞
(kg/m ·s)
Using Error! Reference source not found.Formula (A.3),, the heat release rate is:
(MW)
3,14 × 10
˙
𝑄 = 𝛤𝑚˙ ″𝐴 = 43,2 × 0,039 0 × = 132,3
s
(MW)
ISO #####-#:####(X/FDIS 24678-7:2026(en)
A.8.3 Mudan-Croce’s method
The flame height is calculated by Error! Reference source not found.Formula (A.5) as:
(m)
𝑚˙ ″ 0,039
0,61 0,61
𝐿 = 42( ) 𝐷 = 42 × ( ) × 10,0 = 12,8 (m)
𝜌 𝑔𝐷 1,205× 9,81×10,0
√ √
a
The emissive power is calculated by Error! Reference source not found.Formula (A.9) as:
(kW/m )
−𝛽𝐷 −𝛽𝐷
𝐸 = 𝐸 𝑒 + 𝐸 (1 − 𝑒 ) = 140exp(−0,12 × 10) + 20{1 − exp(−0,12 × 10)} = 56,1
f max s
(kW/m )
The configuration factor for this arrangement is calculated by Error! Reference source not
found.Formula (B.2) in Error! Reference source not found.Annex B as:
(−)
𝐿 𝑋 12,8 20,0
𝐹 = 𝑓 ( , ) = 𝑓 ( , ) = 0,092 9
12𝑣 cyl-v cyl-v
⁄ ⁄
𝐷 2 𝐷 2 10,0/2 10,0/2
(−)
The heat flux received by the target is calculated by Error! Reference source not found.Formula (A.1) as:
"
𝑞˙ = 𝜏𝐸 𝐹 = 1,0 × 56,1 × 0,092 9 = 5,22
f 12𝑣
(kW/m )
A.8.4 Shokri–Beyler’s method
The flame height is calculated by Heskestad’s Error! Reference source not found.Formula (A.10) as:
(m)
2⁄5 2⁄5
˙
𝐿 = −1,02𝐷 + 0,235𝑄 = −1,02 × 10 + 0,235 × 132 300 = 16,1 (m)
The emissive power from the flame surface is calculated by Error! Reference source not
found.Formula (A.11) as:
(kW/m )
−0,008 23𝐷 −0,008 23×10
𝐸 = 58(10 ) = 58 × 10 = 48,0 (kW/m )
f
The configuration factor for this arrangement is calculated by Error! Reference source not
found.Formula (B.2) in Error! Reference source not found.Annex B as:
(−)
𝐿 𝑋 16,1 20,0
𝐹 = 𝑓 ( ,
...

PROJET FINAL
Norme
internationale
ISO/TC 92/SC 4
Ingénierie de la sécurité incendie —
Secrétariat: AFNOR
Exigences régissant les formules
Début de vote:
algébriques —
2026-09-16
Partie 7:
Vote clos le:
2026-11-11
Densité de flux énergétique
rayonnée reçue d’un feu en nappe
ouvert
Fire safety engineering — Requirements governing algebraic
formulae —
Part 7: Radiation heat flux received from an open pool fire
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Norme
internationale
ISO/TC 92/SC 4
Ingénierie de la sécurité incendie —
Secrétariat: AFNOR
Exigences régissant les formules
Début de vote:
algébriques —
2026-09-16
Partie 7:
Vote clos le:
2026-11-11
Densité de flux énergétique
rayonnée reçue d’un feu en nappe
ouvert
Fire safety engineering — Requirements governing algebraic
formulae —
Part 7: Radiation heat flux received from an open pool fire
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ii
Sommaire Page
Avant-propos .iv
Introduction .v
1 Domaine d’application . 1
2 Références normatives . 1
3 Termes et définitions . 2
4 Exigences régissant la description des phénomènes physiques . 2
5 Exigences régissant le processus de calcul . 3
6 Exigences régissant les limites . 3
7 Exigences régissant les paramètres d’entrée. 3
8 Exigences régissant le domaine d’application . 3
9 Exemple de documentation . 4
Annexe A (informative) Formules algébriques pour le rayonnement thermique d’un feu en
nappe ouvert circulaire ou quasi circulaire . 5
Annexe B (informative) Facteurs de configuration d’une flamme cylindrique par rapport à une
cible .21
Bibliographie .42

iii
Avant-propos
L’ISO (Organisation internationale de normalisation) est une fédération mondiale d’organismes nationaux
de normalisation (comités membres de l’ISO). L’élaboration des Normes internationales est en général
confiée aux comités techniques de l’ISO. Chaque comité membre intéressé par une étude a le droit de faire
partie du comité technique créé à cet effet. Les organisations internationales, gouvernementales et non
gouvernementales, en liaison avec l’ISO participent également aux travaux. L’ISO collabore étroitement avec
la Commission électrotechnique internationale (IEC) en ce qui concerne la normalisation électrotechnique.
Les procédures utilisées pour élaborer le présent document et celles destinées à sa mise à jour sont
décrites dans les Directives ISO/IEC, Partie 1. Il convient, en particulier de prendre note des différents
critères d’approbation requis pour les différents types de documents ISO. Le présent document
a été rédigé conformément aux règles de rédaction données dans les Directives ISO/IEC, Partie 2
(voir www.iso.org/directives).
L’ISO attire l’attention sur le fait que la mise en application du présent document peut entraîner l’utilisation
d’un ou de plusieurs brevets. L’ISO ne prend pas position quant à la preuve, à la validité et à l’applicabilité de
tout droit de brevet revendiqué à cet égard. À la date de publication du présent document, l’ISO n’avait pas
reçu notification qu’un ou plusieurs brevets pouvaient être nécessaires à sa mise en application. Toutefois,
il y a lieu d’avertir les responsables de la mise en application du présent document que des informations
plus récentes sont susceptibles de figurer dans la base de données de brevets, disponible à l’adresse
www.iso.org/brevets. L’ISO ne saurait être tenue pour responsable de ne pas avoir identifié tout ou partie de
tels droits de brevet.
Les appellations commerciales éventuellement mentionnées dans le présent document sont données pour
information, par souci de commodité, à l’intention des utilisateurs et ne sauraient constituer un engagement.
Pour une explication de la nature volontaire des normes, la signification des termes et expressions
spécifiques de l’ISO liés à l’évaluation de la conformité, ou pour toute information au sujet de l’adhésion de
l’ISO aux principes de l’Organisation mondiale du commerce (OMC) concernant les obstacles techniques au
commerce (OTC), voir www.iso.org/avant-propos.
Le présent document a été élaboré par le comité technique ISO/TC 92, Sécurité au feu, sous-comité SC 4,
Ingénierie de la sécurité incendie.
Cette deuxième édition annule et remplace la première édition (ISO 24678-7:2019), qui a fait l’objet d’une
révision technique.
Les principales modifications sont les suivantes:
— le contenu principal a été révisé pour être en adéquation avec l’ISO 24678-1 en ce qui concerne les
exigences communes;
— certaines des figures de l’Annexe B, c’est-à-dire les Figures B.3, B.14 et B.15, ont fait l’objet d’une révision
technique.
Une liste de toutes les parties de la série ISO 24678 se trouve sur le site web de l’ISO.
Il convient que l’utilisateur adresse tout retour d’information ou toute question concernant le présent
document à l’organisme national de normalisation de son pays. Une liste exhaustive desdits organismes se
trouve à l’adresse www.iso.org/fr/members.html.

iv
Introduction
La série ISO 24678 est destinée à être utilisée par les praticiens de la sécurité incendie impliqués dans les
méthodes de calcul utilisées dans l’ingénierie de la sécurité incendie. Il est attendu que les utilisateurs
du présent document possèdent une qualification et une compétence appropriées dans le domaine de
l’ingénierie de la sécurité incendie. Il est particulièrement important que les utilisateurs comprennent les
paramètres avec lesquels les méthodologies spécifiques peuvent être utilisées.
Les formules algébriques conformes aux exigences du présent document sont utilisées conjointement avec
d’autres méthodes de calcul d’ingénierie lors du dimensionnement de la sécurité incendie. Ces calculs sont
précédés par l’établissement d’un contexte, y compris les buts et objectifs de sécurité contre l’incendie à
atteindre, ainsi que par des critères de performance lorsqu’un dimensionnement de sécurité incendie d’essai
est soumis à des scénarios d’incendie de dimensionnement. Les méthodes de calcul d’ingénierie sont utilisées
pour déterminer si ces critères de performance sont satisfaits par un dimensionnement particulier et si ce
n’est pas le cas, comment il est nécessaire de modifier le dimensionnement.
Les aspects couverts par les calculs d’ingénierie incluent le dimensionnement de la sécurité incendie des
environnements bâtis entièrement neufs, par exemple les bâtiments, les navires ou les véhicules, ainsi que
l’évaluation de la sécurité contre l’incendie des environnements bâtis existants.
Les formules algébriques mentionnées dans le présent document peuvent être utiles pour estimer les
conséquences des scénarios d’incendie de dimensionnement. Ces formules sont utiles dans la mesure
où elles permettent au praticien de déterminer rapidement la manière dont il est nécessaire de modifier
un dimensionnement de sécurité incendie suggéré pour répondre aux critères de performance, et de le
comparer avec de multiples dimensionnements d’essai. Les calculs numériques détaillés peuvent être
effectués jusqu’à la documentation de dimensionnement finale. Les domaines dans lesquels des formules
algébriques se sont avérées applicables comprennent, par exemple, la détermination du transfert de chaleur
par convection et par rayonnement, des panaches de feu, la prédiction des propriétés des écoulements en
jet sous plafond régissant les temps de réponse des détecteurs, le calcul du transport de la fumée dans les
ouvertures de ventilation et l’analyse des dangers d’un feu en compartiment tels que le remplissage par la
fumée et l’embrasement généralisé. Cependant, les modèles simples ont parfois des limites contraignantes
et sont moins susceptibles d’inclure les effets de phénomènes multiples qui se produisent dans le scénario
d’incendie de dimensionnement.
Les principes généraux de l’ingénierie de la sécurité incendie sont décrits dans l’ISO 23932-1, qui fournit une
méthodologie axée sur la performance utile aux ingénieurs pour l’évaluation du niveau de sécurité incendie
des environnements bâtis neufs ou existants. La sécurité incendie est évaluée par une méthode d’ingénierie
basée sur la quantification du comportement du feu, prenant en compte la connaissance des conséquences
d’un tel comportement sur la protection des vies humaines, des biens et de l’environnement. L’ISO 23932-1
décrit le processus (c’est-à-dire les étapes nécessaires) et les éléments essentiels afin de réaliser un
dimensionnement performantiel et robuste de la sécurité incendie.
L’ISO 23932-1 s’appuie sur un ensemble de normes ISO d’ingénierie de la sécurité incendie disponibles
et portant sur les méthodes et les données requises pour toutes les étapes de conception d’un processus
d’ingénierie de sécurité incendie, résumées à la Figure 1 (extraite de l’Article 4 de l’ISO 23932-1:2018).
L’ensemble comprend la série ISO 16730, la série ISO 16732, la série ISO 16733, l’ISO/TR 16738, la série
ISO 24678, la série ISO 24679, l’ISO 23932-1, l’ISO/TS 29761 et d’autres documents de référence qui
fournissent des exemples et des recommandations relatives à l’application de ces normes.
Chaque Norme internationale se rapportant au système global d’information et d’analyse de l’ingénierie
de la sécurité incendie comprend, dans son introduction, des informations permettant de relier la norme
aux étapes correspondantes du processus de dimensionnement par l’ingénierie de la sécurité incendie
présenté dans l’ISO 23932-1. L’ISO 23932-1 exige que les méthodes d’ingénierie soient choisies correctement
pour prédire les conséquences du feu de scénarios et éléments de scénario spécifiques (ISO 23932-1:2018,
Article 12). Conformément aux exigences de l’ISO 23932-1, le présent document fournit les exigences qui
régissent les formules algébriques du dimensionnement de la sécurité incendie. L’étape correspondante
dans le processus de dimensionnement de la sécurité incendie est indiquée par la case grise à la Figure 1 ci-
dessous et décrite dans l’ISO 23932-1.

v
Figure 1 — Organigramme représentant le processus de conception par ingénierie de la sécurité
incendie (ISI) (extrait de l’ISO 23932-1:2018)

vi
PROJET FINAL Norme internationale ISO/FDIS 24678-7:2026(fr)
Ingénierie de la sécurité incendie — Exigences régissant les
formules algébriques —
Partie 7:
Densité de flux énergétique rayonnée reçue d’un feu en nappe
ouvert
1 Domaine d’application
Les exigences du présent document régissent l’application d’un ensemble de formules algébriques explicites
pour le calcul de caractéristiques spécifiques de la densité de flux énergétique rayonnée provenant d’un feu
en nappe.
Le présent document est une mise en application des exigences générales spécifiées dans l’ISO 16730-1 pour
les calculs relatifs à la dynamique du feu impliquant un ensemble de formules algébriques explicites.
Le présent document est organisé sous la forme d’un modèle dans lequel les informations spécifiques
relatives aux formules algébriques sont fournies pour satisfaire aux types suivants d’exigences générales:
a) description des phénomènes physiques abordés par la méthode de calcul;
b) documentation du mode opératoire de calcul et de sa base scientifique;
c) limites de la méthode de calcul;
d) paramètres d’entrée de la méthode de calcul; et
e) domaine d’application de la méthode de calcul.
Des exemples d’ensembles de formules algébriques satisfaisant aux exigences du présent document sont
fournis dans l’Annexe A et l’Annexe B. L’Annexe A contient un ensemble de formules algébriques portant
sur les densités de flux énergétiques rayonnées provenant d’un feu en nappe ouvert circulaire ou quasi
circulaire. L’Annexe B contient des formules pour les facteurs de configuration d’une flamme par rapport à
une cible.
2 Références normatives
Les documents suivants sont cités dans le texte de sorte qu’ils constituent, pour tout ou partie de leur
contenu, des exigences du présent document. Pour les références datées, seule l’édition citée s’applique. Pour
les références non datées, la dernière édition du document de référence s’applique (y compris les éventuels
amendements).
ISO 13943, Sécurité au feu — Vocabulaire
ISO 16733-1, Ingénierie de la sécurité incendie — Sélection de scénarios d'incendie et de feux de dimensionnement
— Partie 1: Sélection de scénarios d'incendie de dimensionnement
ISO 24678-1, Ingénierie de la sécurité incendie — Exigences régissant les formules algébriques — Partie 1:
Exigences générales
3 Termes et définitions
Pour les besoins du présent document, les termes et les définitions de l’ISO 13943 ainsi que les suivants
s’appliquent.
L’ISO et l’IEC tiennent à jour des bases de données terminologiques destinées à être utilisées en normalisation,
consultables aux adresses suivantes:
— ISO Online browsing platform: disponible à l’adresse https:// www .iso .org/ obp
— IEC Electropedia: disponible à l’adresse https:// www .electropedia .org/
3.1
feu en nappe
combustion d’un carburant combustible horizontal et orienté vers le haut composé de liquides, de gaz
liquéfiés ou de matières plastiques en fusion placées horizontalement
3.2
feu en nappe ouvert
feu en nappe (3.1) en plein air ou dans un espace très grand par rapport à la taille du feu, où l’effet confiné de
l’environnement bâti sur le comportement de sa flamme est négligeable
Note 1 à l'article: Les caractéristiques du feu en nappe ouvert dépendent des conditions extérieures comme le vent.
3.3
feu en nappe circulaire
feu en nappe quasi circulaire
feu en nappe (3.1) dont la géométrie peut être assimilée à une forme circulaire
Note 1 à l'article: Dans le cas d’une nappe allongée, cette assimilation est valide si le rapport entre la dimension la plus
[6]
longue et la dimension la plus courte ne dépasse pas 2 à 3 .
3.4
diamètre équivalent
diamètre d’une nappe circulaire dont la surface plane est équivalente aux nappes de forme rectangulaire ou
irrégulière
3.5
coefficient d’absorption
fraction d’intensité du rayonnement absorbé par unité de longueur de la trajectoire de rayonnement
3.6
fraction radiative
rapport entre le taux de dégagement thermique radiatif et le débit calorifique total
3.7
hauteur moyenne de la flamme
moyenne temporelle de la hauteur des flammes au-dessus de la base d’un feu, définie comme l’élévation où la
probabilité de trouver des flammes est de 50 %
3.8
transmissivité atmosphérique
rapport entre l’intensité du rayonnement transmise après avoir traversé une longueur unitaire d’un fluide
présent (dioxyde de carbone, vapeur d’eau, poussière et brouillard) et l’intensité du rayonnement qui aurait
parcouru la même distance dans de l’air propre
4 Exigences régissant la description des phénomènes physiques
4.1 Les exigences régissant la description des phénomènes physiques spécifiées dans l’Article 4 de
l’ISO 24678-1 s’appliquent, en complément des exigences spécifiées dans les paragraphes suivants.

4.2 La densité de flux énergétique rayonnée provenant d’un feu en nappe ouvert est un phénomène
thermophysique et chimique complexe qui peut être très transitoire ou de régime permanent. La densité de
flux énergétique rayonnée dépend des propriétés et de la géométrie du combustible et de l’environnement
entre la source de rayonnement et la “cible” qui reçoit la densité de flux énergétique. Les propriétés de la cible
doivent être prises en considération lorsque des calculs supplémentaires du comportement de la cible sont
évalués, par exemple les blessures subies par les personnes, le dysfonctionnement/les dommages sur une
partie de l’équipement, l’allumage d’un matériau combustible, les détériorations d’éléments structurels. Les
phénomènes physiques décrits dans le présent document concernent uniquement les calculs de la densité de
flux énergétique rayonnée provenant d’un feu en nappe ouvert et reçue par une cible.
4.3 Différents types de sources de feux en nappe, la géométrie de la nappe et les positions relatives des
cibles examinées (y compris la position des écrans antirayonnements placés entre la nappe et les cibles)
doivent être décrits à l’aide de diagrammes.
4.4 Les éléments de scénario, conformément à l’ISO 16733-1, auxquels s’appliquent les formules spécifiques,
doivent être clairement identifiés. Les caractéristiques de la densité de flux énergétique rayonnée à calculer
ainsi que leurs plages utiles doivent être clairement identifiées, y compris les caractéristiques présumées
par association avec des grandeurs calculées, si applicable.
4.5 Les phénomènes physiques (par exemple la formation d’une nappe pendant un dégagement continu,
l’interaction entre le feu et les matériaux extincteurs) auxquels des formules spécifiques s’appliquent doivent
être clairement identifiés.
4.6 Étant donné que différentes formules décrivent différentes caractéristiques des flammes radiatives
de la source de la nappe (voir 4.3) ou s’appliquent à différents scénarios (voir 4.4), il doit être démontré
que si plusieurs méthodes permettent de calculer une grandeur donnée, des recommandations doivent être
données pour choisir les méthodes appropriées.
4.7 L’émission radiative de la flamme est affectée par divers facteurs. Les incertitudes sur le pouvoir
émissif doivent être prises en compte de manière appropriée. Une analyse de sensibilité ou des estimations
prudentes sont souhaitables. L’analyse de sensibilité est utilisée pour identifier les variables d’entrée qui
entraînent la plus grande variation des résultats de sortie. Par exemple, une analyse de sensibilité peut
être réalisée sur la valeur de la fraction radiative pour évaluer si une petite variation peut avoir un impact
significatif sur la densité de flux énergétique rayonnée. Si tel est le cas, il convient d’utiliser la fraction
radiative avec précaution. L’utilisation d’hypothèses prudentes peut limiter l’impact des incertitudes sur les
résultats finaux. Des facteurs et/ou des marges de sécurité peuvent être appliqués aux données d’entrée
ou de sortie. Les facteurs et marges de sécurité appropriés sont généralement dérivés des références sur la
[4,7]
validation et la vérification du modèle .
5 Exigences régissant le processus de calcul
Les exigences spécifiées dans l’Article 5 de l’ISO 246781:2019 régissant le processus de calcul s’appliquent.
6 Exigences régissant les limites
Les exigences spécifiées dans l’Article 6 de l’ISO 24678-1:2019 régissant les limites s’appliquent.
7 Exigences régissant les paramètres d’entrée
Les exigences spécifiées dans l’Article 7 de l’ISO 24678-1:2019 régissant les paramètres d’entrée s’appliquent.
8 Exigences régissant le domaine d’application
Les exigences spécifiées dans l’Article 8 de l’ISO 24678-1:2019 régissant le domaine d’application s’appliquent.

9 Exemple de documentation
Un exemple d’ensembles de formules algébriques satisfaisant aux exigences des Articles 4 à 8 est fourni dans
l’Annexe A.
Annexe A
(informative)
Formules algébriques pour le rayonnement thermique d’un feu en
nappe ouvert circulaire ou quasi circulaire
A.1 Symboles et abréviations utilisés dans la présente annexe
A surface plane d’une source de feu en nappe (m )
s
D diamètre équivalent d’une source de feu en nappe (m)
E pouvoir émissif d’une flamme (kW/m )
f
E pouvoir émissif de la région lumineuse d’une flamme (kW/m )
max
E pouvoir émissif de la fumée (kW/m )
s
f facteur de configuration d’une surface latérale d’un cylindre vertical par rapport à une cible ver-
cyl-v
ticale (−)
F facteur de configuration d’une flamme par rapport à une cible (−)
F facteur de configuration d’une flamme par rapport à une cible verticale (−)
12,v
g accélération de la gravité (9,81 m/s )
H distance verticale entre la base de la flamme et une cible (m)
−1
k coefficient d’absorption de rayonnement d’une flamme pour différents combustibles (m )
L hauteur moyenne de la flamme (m)

m"
vitesse massique de brûlage par unité de surface d’une nappe (kg/m ·s)
"
vitesse massique de brûlage par unité de surface d’une nappe suffisamment grande (kg/m ·s)

m
∞
m* vitesse de brûlage non dimensionnelle (−)

q″
densité de flux énergétique rayonnée vers une cible (kW/m )

débit calorifique d’un feu en nappe (kW)
Q
u vitesse du vent (m/s)
w
u* vitesse du vent non dimensionnelle
X distance horizontale par rapport à une cible à partir du centre d’une flamme (m)
β coefficient d’absorption de rayonnement d’une flamme en prenant le diamètre comme longueur
−1
caractéristique (m )
χ fraction radiative (−)
r
Γ chaleur de la combustion du combustible (J/kg)

θ angle d’inclinaison de la flamme (rad)
ρ densité de l’air ambiant normal (1,2 kg/m )
a
τ transmissivité atmosphérique (−)
A.2 Description des phénomènes physiques abordés par l’ensemble de formules
algébriques
A.2.1 Généralités
Les formules décrites dans la présente annexe fournissent des densités de flux énergétique rayonnées
depuis un feu en nappe vers une cible et peuvent être applicables à différents emplacements et orientations.
L’ensemble de formules est particulièrement pratique pour les cibles orientées à la verticale et à l’horizontale.
Les formules présentées ici ont été validées avec des feux d’hydrocarbures liquides produisant beaucoup de
suie.
A.2.2 Description générale de la méthode de calcul
L’estimation de la densité de flux énergétique rayonnée reçue par une cible et provenant d’un feu en nappe
implique les trois étapes suivantes:
— détermination des caractéristiques du feu en nappe (surface en combustion, vitesse massique de brûlage,
durée du feu, durée jusqu’aux conditions de régime permanent, etc.);
— détermination des caractéristiques de rayonnement thermique du feu en nappe (hauteur de la flamme,
inclinaison de la flamme, pouvoir émissif de la flamme, etc.);
— calcul de la densité de flux énergétique rayonnée reçue par une cible (facteur de configuration d’une
flamme par rapport à une cible, transmissivité atmosphérique le long de la trajectoire du rayonnement).
Il est très important d’utiliser une seule méthode pour les trois étapes de ce processus. Les méthodes
présentées dans la présente annexe forment des méthodes complètes et ses parties ne peuvent pas
être modifiées. La validation du modèle complet doit être considérée, et non pas chaque composant
individuellement.
A.2.3 Éléments de scénario auxquels l’ensemble de formules est applicable
L’ensemble de formules est applicable au rayonnement thermique qui émane de flammes de feux en nappe
de régime permanent et qui sont quasi circulaires ou rectangulaires dans une surface vue en plan dans un
environnement non obstrué, sauf si indication contraire.
A.2.4 Cohérence intrinsèque de l’ensemble de formules
L’ensemble de formules fourni dans la présente annexe a été dérivé et révisé afin de garantir que les
résultats des calculs de différentes formules de l’ensemble sont cohérents (c’est-à-dire qu’ils ne forment pas
de conflits).
A.2.5 Normes et autres documents dans lesquels l’ensemble de formules est utilisé
Aucun spécifié.
A.3 Documentation de l’ensemble de formules
A.3.1 Généralités
Comme représenté à la Figure A.1, le rayonnement est émis par une flamme et reçu par une cible. La densité
de flux énergétique provenant d’un feu en nappe et reçue par une cible peut être calculée à l’aide de la
Formule (A.1):
"
qE  F (A.1)
f12
Légende
1 flamme (surface 1)
2 cible (surface 2)
3 émissions (dans toutes les directions)
4 densité de flux énergétique rayonnée vers une cible
Figure A.1 — Rayonnement d’une flamme vers une cible
La Figure A.2 décrit les étapes successives nécessaires pour estimer la densité de flux énergétique rayonnée
provenant d’un feu en nappe et reçue par une cible. Le débit calorifique et le diamètre de la nappe, s’il n’est
pas indiqué, sont estimés à partir des caractéristiques spécifiques de l’objet qui brûle. Le pouvoir émissif
émanant de la surface de la flamme est présumé être une fonction du diamètre de la nappe. La géométrie
de la flamme est calculée en utilisant le débit calorifique et le diamètre de la source du feu. Enfin, le facteur
de configuration d’une flamme par rapport à une cible est calculé. L’effet de blocage par une substance
présente, par exemple de la suie, de la vapeur d’eau et des gaz dipolaires, est considéré comme transmissivité
atmosphérique quand cela est nécessaire.
La cible est considérée comme un petit élément plan infinitésimal présumé se situer à la distance minimale
entre le feu et la cible réelle. Comme des facteurs de configuration sont également pris en compte dans les
calculs des phénomènes physiques, le point est associé à une surface de l’élément. Dans la présente annexe, un
modèle de flamme cylindrique solide est adopté. Comme présenté à la Figure A.2, la méthode est composée
de différents sous-modèles interdépendants, de la hauteur moyenne de la flamme, du pouvoir émissif, etc.

Figure A.2 — Processus de calcul d’une densité de flux énergétique rayonnée reçue par une cible et
provenant d’un feu en nappe
A.3.2 Géométrie et débit calorifique de feux en nappe
A.3.2.1 Diamètre équivalent d’une source de feu en nappe
Le diamètre équivalent d’une source de feu en nappe, D, est donné par la Formule (A.2):
4A
s
D (A.2)

A.3.2.2 Débit calorifique

Le débit calorifique d’un feu en nappe, Q , est donné par la Formule (A.3):


Qm A (A.3)
s
Des exemples de vitesse massique de brûlage et de chaleur nette de combustion sont donnés dans le
Tableau A.1. En utilisant ces valeurs, la vitesse massique de brûlage par unité de surface d’une nappe est
[8]
estimée par la Formule (A.4) :


mm 1exp kD (A.4)


NOTE La Formule (A.4) est valable pour les feux en nappe avec D > 0,2 m.

Tableau A.1 — Chaleur nette de combustion et vitesse massique de brûlage de
[9]
différents combustibles
Vitesse massique de brû-
Chaleur nette de Coefficient d’absorption du
Combustible lage d’une nappe suffisam-
combustion rayonnement
ment grande
"
−1
Γ (MJ/kg)  k (m )
m (kg/m ·s)
∞
H liquide 120 0,017 6,1
GNL 50,0 0,078 1,1
GPL 46,0 0,099 1,4
Méthanol 20,0 0,017 —
Éthanol 26,8 0,015 —
Butane 42,7 0,078 2,7
Hexane 44,7 0,074 1,9
Heptane 44,6 0,101 1,1
Benzène 40,1 0,085 2,7
Xylène 40,8 0,090 1,4
Acétone 25,8 0,041 1,9
Dioxane 26,2 0,018 5,4
Éther éthylique 34,2 0,085 0,7
Essence 44,7 0,048 3,6
Gasoil 43,7 0,055 2,1
Kérosène 43,2 0,039 3,5
JP-4 43,5 0,051 3,6
JP-5 43,0 0,054 1,6
Huile de transforma- 46,4 0,039 0,7
tion
Mazout lourd 39,7 0,035 1,7
Pétrole brut 42,5 0,022 2,8
A.3.3 Modèle de flamme solide cylindrique et pouvoir émissif de la surface
A.3.3.1 Sélection des méthodes
Plusieurs modèles ont été développés sur la base du concept de la flamme solide. Le plus courant est le
modèle de la flamme solide cylindrique représenté à la Figure A.1. Ce modèle a été choisi pour représenter
l’émetteur radiatif par l’enveloppe latérale de la flamme ainsi que le disque supérieur.
Il existe plusieurs méthodes d’estimation du pouvoir émissif de la surface. Le pouvoir émissif de la surface
est corrélé à la surface de la flamme solide cylindrique et à la hauteur de la flamme. La méthode de Mudan-
[10] [11]
Croce, la méthode de Shokri-Beyler et la méthode de la fraction radiative sont adoptées dans cette
annexe. Chaque ensemble de formules correspond à un type de combustible spécifique et à une plage de
diamètre du combustible. La méthode de Mudan-Croce est accompagnée par la Formule de Thomas pour
[12] [13]
la hauteur et l’inclinaison de la flamme. , La méthode de Shokri-Beyler est associée à la Formule de
[14]
Heskestad pour la hauteur de flamme, décrite dans l’ISO 24678-2. Comme la formule d’estimation du
pouvoir émissif est corrélée à la surface de la flamme, il doit être évité de mélanger les différentes méthodes.

A.3.3.2 Méthode de Mudan-Croce
A.3.3.2.1 Généralités
La méthode de Mudan-Croce pour l’estimation d’une densité de flux énergétique incident provenant d’un
feu en nappe suggère les Formules (A.5) à (A.9) suivantes pour le pouvoir émissif des flammes d’essence, de
kérosène et de JP-4, mais ne les recommande pas pour le GNL. L’ensemble de formules utilise les corrélations
de la hauteur de la flamme développées par Thomas à partir d’expériences sur des bûchers en bois. En cas de
vent, l’angle d’inclinaison de la flamme est calculé par la corrélation développée par Thomas. Cette méthode
est recommandée dans la plage de diamètres d’environ 1 m à 60 m.
A.3.3.2.2 Hauteur de flamme selon la Formule de Thomas
[15]
En cas d’atmosphère tranquille, la hauteur de la flamme est calculée par la Formule (A.5) :
06, 1
 

L m
 
42 (A.5)
 
D
 gD
 
a
NOTE La Formule (A.5) est appropriée pour les feux en nappe ouverts de grande taille. Voir A.4.1 pour des
informations détaillées.
En cas de vent, la longueur et l’angle d’inclinaison de la flamme sont calculés à l’aide de la Formule (A.6) et de
[13]
la Formule (A.7) :
06, 7
 
02, 1

L m
*
 
55 u (A.6)

 
D
 gD
 
a
*
11u 

cos { (A.7)
**
11/(uu  )
où la vitesse non dimensionnelle du vent est calculée à l’aide de la Formule (A.8):
u
* w
u  (A.8)
13/
"

gm D/

a
A.3.3.2.3 Pouvoir émissif selon la formule de Mudan-Croce
Le pouvoir émissif moyen et uniforme au niveau d’une surface de flamme d’un feu en nappe, E, est donné
[10] 2 2 −1
par corrélation expérimentale, Formule (A.9), avec E = 140 kW/m , E = 20 kW/m et β = 0,12 m . Le
max s
pouvoir émissif moyen et uniforme au niveau de la surface de la flamme dépend uniquement du diamètre de
la nappe.
EEexpeDE1 xp  D (A.9)
 
fmax s
La formule tient compte de l’effet de barrage de la suie. Les limites du pouvoir émissif moyen uniforme
peuvent survenir lorsque la cible est proche de la zone de la flamme au niveau du bord du feu en nappe, là où
le pouvoir émissif peut être sous-estimé.
A.3.3.3 Méthode de Shokri-Beyler
A.3.3.3.1 Généralités
La flamme est présumée être un élément rayonnant homogène et cylindrique avec un pouvoir émissif moyen.
Le pouvoir émissif selon la formule de Shokri est dérivé en association avec la hauteur de la flamme selon
la formule de Heskestad. Cette méthode est principalement applicable à des densités de flux énergétique

supérieures à 5 kW/m . Les plages de diamètres de nappe de 1 m à 50 m concernent principalement le GNL
et le JP-5.
A.3.3.3.2 Hauteur de la flamme selon la Formule de Heskestad
[14]
La Formule de Heskestad est appliquée pour calculer la hauteur de la flamme comme spécifiée dans
l’ISO 24678-2; voir Formule (A.10).
25/

LD10,,20 235Q (A.10)
A.3.3.3.3 Pouvoir émissif selon la Formule de Shokri
[11]
Le pouvoir émissif effectif du feu en nappe est donné par Shokri et Beyler comme indiqué dans la
Formule (A.11):
0,008 23D
 
E 58 10 (A.11)
 
f
 
A.3.3.4 Méthode de la fraction radiative
A.3.3.4.1 Généralités
Pour des nappes de diamètre relativement petit, la formule de calcul est disponible pour différents
combustibles. La formule est une représentation purement géométrique de la redistribution de l’énergie
rayonnée sur une enveloppe cylindrique.
A.3.3.4.2 Hauteur de la flamme selon la Formule de Heskestad
La hauteur de la flamme est calculée selon la Formule de Heskestad comme dans la Formule (A.10).
A.3.3.4.3 Pouvoir émissif selon la fraction radiative
Le pouvoir émissif E est calculé en tenant compte d’une distribution uniforme de la fraction radiative du
dégagement de chaleur sur les surfaces latérale et supérieure d’un cylindre, comme exprimé dans la
Formule (A.12):

 Q
r
E  (A.12)
f
D
DL
où la fraction radiative du dégagement d’énergie est corrélée au diamètre de la nappe, comme indiqué dans
[15]-[17]
le Tableau A.2. Des exemples de fractions radiatives de différents combustibles et substances liquides
[18]-[28]
sont représentés sur les Figures A.3 à A.6. Si la Formule ne fournit pas des estimations conservatrices
de la fraction radiative, il est recommandé de sélectionner une valeur appropriée en fonction du type de
combustible et du diamètre de la nappe.

Tableau A.2 — Exemples de formules de calcul pour la fraction radiative du dégagement d’énergie
Combustible Formules Référence
kérosène, mazout, essence, JP-4, GNL,
[15]
 02,,10 00345DD() 0m Guide SFPE
r
méthanol, heptane, toluène, pétrole brut
[16]
 03,,50exp 05DD25 0
heptane, pétrole bruit, kérosène   McGrattan et al.
r
00, 3
03,(30DD,,22 6)
heptane  {
r
05,
05,(52DD,)6
[17]
Yang et al.
00, 8
03,(20DD,)22
kérosène  {
r
06,
04,(82DD )
Légende
X diamètre de nappe (m)
Y fraction radiative (−)
[18]
Koseki & Yumoto (1988)
[19]
Koseki (1989)
[20]
Koseki & Hayasaka (1989)
[21]
Hamins et al. (1991)
[22]
Klassen & Hamnis (1991)
[23]
Klassen & Gore (1994)
[24]
Buch et al. (1997)
[25]
Guide SFPE (1999)
[16]
McGrattan et al. (2000)
[17]
Yang et al. (1994)
[18]-[24] [15]-[17]
Figure A.3 — Fraction radiative mesurée des feux en nappe d’heptane et formules
dans le Tableau A.2
Légende
X diamètre de nappe (m)
Y fraction radiative (−)
[25]
Souil et al. (1986)
[18]
Koseki & Yumoto (1988)
[19]
Koseki (1989)
[15]
Guide SFPE (1999)
[16]
McGrattan et al. (2000)
[17]
Yang et al. (1994)
[18],[19],[25] [15]-
Figure A.4 — Fraction radiative mesurée des feux en nappe de kérosène et formules
[17]
dans le Tableau A.2
Légende
X diamètre de nappe (m)
Y fraction radiative (−)
[19]
JP4, Koseki (1989)
[26]
diesel, Munos (2007)
[19]
essence, Koseki (1989)
[26]
essence, Munoz (2007)
[15]
Guide SFPE (1999)
[16]
McGrattan et al. (2000)
[19],[26]
Figure A.5 — Fraction radiative mesurée des feux en nappe de combustibles et formules
[15],[16]
dans le Tableau A.2
Légende
X diamètre de nappe (m)
Y fraction radiative (−)
[19]
benzène, Koseki (1989)
[24]
méthanol, Buch et al. (1997)
[23]
méthanol, Klassen & Gore (1994)
[27]
méthanol, Sjöström et al. (2015)
[24]
acétone, Buch et al. (1997)
[24]
toluène, Klassen & Gore (1994)
[24]
huile de silicone, Buch et al. (1997)
[18]
pétrole brut, Koseki & Yumoto (1988)
[19]
pétrole brut, Koseki (1989)
[28]
pétrole brut, Koseki et al. (2000)
[15]
Guide SFPE (1999)
[16]
McGrattan et al. (2000)
Figure A.6 — Fraction radiative mesurée des feux en nappe de divers liquides combustibles
[18],[19],[23],[24],[27],[28] [15],[16]
et formules dans le Tableau A.2
A.3.4 Facteurs de configuration
Les facteurs de configuration sont calculés avec la longueur de la flamme, la largeur de la flamme, la distance
par rapport à la cible, l’inclinaison de la flamme et l’orientation de la cible. Les formules de calcul explicites
sont résumées dans l’Annexe B.
A.3.5 Transmissivité atmosphérique
Dans la plupart des cas, la transmissivité atmosphérique est approchée comme unité. Lorsqu’il est
souhaitable de tenir compte de l’absorption par l’atmosphère entre la flamme et la cible, l’effet de la substance
absorbante peut être appliqué. Les principaux composants qui absorbent le rayonnement thermique sont la
[29]
suie (C), la vapeur d’eau (H O) et le dioxyde de carbone (CO ) .
2 2
A.4 Base scientifique de l’ensemble de formules
A.4.1 Hauteur de la flamme
Les formules pour la hauteur de flamme (A.5) ont été développées par Thomas pour les feux de bûchers en
bois et par Heskestad pour les combustibles courants. Les formules ont été développées par une loi d’échelle

du panache de la fumée et sont comparées à des observations expérimentales. Le panache de Heskestad est
décrit dans l’Annexe A de l’ISO 24678-2:2022.
De nombreux enquêteurs ont développé des corrélations pour les hauteurs de flammes turbulentes dans un
environnement d’air tranquille. La plupart d’entre elles sont basées sur l’analyse dimensionnelle des données
expérimentales utilisant les principes de modélisation de Froude. Certaines sont basées sur des modèles
théoriques approximatifs qui impliquent des facteurs empiriques. Ces corrélations sont généralement
formulées en matière de vitesse de brûlage non dimensionnelle, comme indiqué dans la Formule (A.13).

m
*
m  (A.13)
 gD
a
La Figure A.7 représente le rapport entre la hauteur de la flamme et le diamètre de la nappe tracé par rapport
à la vitesse de brûlage non dimensionnelle.
Légende
X diamètre de nappe (m)
Y rapport entre la hauteur de la flamme et le diamètre de la nappe (−)
Formule de Thomas (Formule A.5)
feux en nappe de GNL sur l’eau
feux en nappe de GNL sur terre
feux en nappe de GNL sur terre
feux d’essence sur terre
feux de kérosène sur terre
essence, kérosène, diesel
GNL, kérosène
acétone
Figure A.7 — Comparaison des formules de Thomas avec des données expérimentales collectées
[30]
par Mudan
A.4.2 Facteur de configuration
Les formules pour les facteurs de configuration utilisées dans la Formule (A.1) ont été développées dans le
but général de décrire le transfert thermique radiatif sans le restreindre aux calculs d’incendie. Le facteur
est calculé uniquement par les relations géométriques entre une flamme et une cible. Voir l’Annexe B pour
des informations détaillées.
A.5 Limites de l’ensemble de formules
A.5.1 Forme de la source du feu
L’ensemble de formules décrit dans la présente annexe présume que les feux en nappe sont circulaires ou
quasi circulaires. Des sources de nappe de forme rectangulaire ou irrégulière avec des rapports d’aspect
[7]
supérieurs à 2 à 3 exigent d’autres modèles que ceux décrits dans la présente annexe, car le diamètre
équivalent ne peut pas être calculé par la Formule (A.2).
A.5.2 Propriété du combustible
La présente annexe aborde uniquement les feux d’hydrocarbu
...