1.4. FIRE MODELING THEORY
An Educational Program to Improve the
Level of Teaching Risk-Informed,
Performance-based Fire Protection
Engineering Assessment Methods
DJ Icove & AE Ruggles
Department of Nuclear Engineering
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1.4 Fire Modeling Theory
• Fire development in
compartments is often
divided into phases
depending on the dominant
processes at any given
stage of development.
• Ignition is dictated by the
characteristics of the fuel
item being ignited (i.e.,
ignition temperature,
geometry, orientation, and
thermophysical properties)
and the strength of the
ignition source.
NUREG 1934 Scenarios
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1.4 Fire Modeling Theory (Con’t)
• Once the flames
are sustained on
a burning fuel
item, a smoke
plume develops;
transporting mass
and heat vertically
as a result of the
buoyancy of the
smoke.
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1.4 Fire Modeling Theory (Con’t)
• The plume will entrain air as it rises, causing the
smoke to cool and become diluted; as a result,
the quantity of smoke being transported will
increase with increasing elevation.
• After a smoke plume strikes the ceiling, the
smoke travels horizontally under the ceiling in a
relatively thin layer, referred to as a ceiling jet.
• As the ceiling jet travels, the smoke cools with
increasing distance from the plume impingement
point, in part because of air entrainment into the
ceiling jet as well as heat losses from the ceiling
jet to the solid ceiling boundary.
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1.4 Fire Modeling Theory (Con’t)
• The aspects of fire behavior that may
be of interest in such analyses include:
– Rate of smoke production
– Rate of smoke filling
– Properties of the ceiling jet
– Properties of the HGL
– Target response to incident heat flux via
either thermal radiation or convection
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Rate of smoke production
• Smoke is defined as a combination of the gaseous
and solid particulates resulting from the combustion
process, plus the air that is entrained into the flame
and/or smoke plume.
• The rate of smoke production at a particular height in
the plume is the combination of the generation rate
of combustion products and air entrainment rate into
the flame and/or smoke plume between the top of
the fuel and the height of interest.
• Since air entrainment rate greatly exceeds the
generation rate of combustion products, the
correlations used to estimate the rate of smoke
production are usually taken from experimental
research on entrained air.
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Rate of Smoke Filling
• The rate of smoke filling is dependent on
the rate of smoke production, the heat
release rate, floor area and height of the
space, and time from ignition.
• For a fire with a steady heat release rate,
the rate of smoke filling in a compartment
will decrease with time due to a decrease in
the smoke production rate, which decreases
as the height available to entrain air
decreases when the HGL deepens.
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Properties of the Ceiling Jet
• The ceiling jet transports smoke and heat
horizontally away from the region of plume
impact with the ceiling.
• The response of ceiling-mounted fire
detectors or sprinklers is governed primarily
by their interaction with a ceiling jet.
• The temperature and concentration of
smoke in a ceiling jet is principally
dependent on the height of the space,
distance between the impact point of the
smoke plume and the ceiling, and the heat
release rate of the fire.
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Properties of the HGL
• As smoke and heat are transported to the HGL via the
smoke and fire plumes, the properties of the HGL will
change.
• The principal properties of interest include the depth,
temperature and gas concentrations in the HGL.
• The magnitude of the properties depends on the heat
release rate of the fire, geometry of the space,
ventilation openings (permitting material from the HGL
to leave the space, providing air to the fire, and/or
causing a stirring action), yields of combustion
products, and the elapsed time after ignition.
• These changes can be tracked by considering the
conservation of energy, mass, and species relative to
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Target response to incident heat flux
via thermal radiation or convection
• The targets’ temperature will increase as a result
of receiving heat via either thermal radiation or
convection.
• Radiation heat transfer is dependent on the
intensity of thermal radiation emitted by a source,
the size of the source, and the proximity of the
target to the source.
• For this application, the flame height, the portion
of heat released from the fire as radiation, and
the distance separating the target from the flame
are the dominant parameters.
• Convection heat transfer occurs whenever the
target is submerged in the smoke plume or HGL.
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Range of Fire Models
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1.4.1 Algebraic Models
• Algebraic models may be standalone equations
found in literature or may be contained within
spreadsheets (such as the NRC’s FDTs), and can
help give a general understanding of one of the fire
environment phenomena.
• These equations are typically closed-form algebraic
expressions, many of which were developed as
correlations from empirical data.
• In some cases, they may take the form of a firstorder ordinary differential equation, and, when used
properly, can provide an estimate of fire variables,
such as HGL temperature, heat flux from flames or
the HGL, smoke production rate, depth of the HGL,
and the actuation time for detectors
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1.4.1 Algebraic Models (Con’t)
• Algebraic models are helpful because they require minimal
computational time and a limited number of input variables.
• When applying the results of the algebraic models, users
need to be aware that the development of most equations
involved assumptions to simplify the analysis.
• Other than for very simple situations, algebraic models are
useful primarily as screening tools (i.e., to provide a rough
approximation to an analysis, perhaps as a check of an
aspect of the results of the computer-based models), and
are also applicable when only one phenomenon can be
treated in isolation: for instance, plume or ceiling jet
correlations are not applicable if there is a significant HGL
unless they are modified to account for this effect.
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1.4.2 Zone Models
• A zone models calculate fire environment variables
using control volumes, or zones, of a space.
• The zones correspond to a cooler lower layer and an
HGL.
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1.4.2 Zone Models (Con’t)
• The fundamental idea behind a zone model is
that each zone is well-mixed and that all fire
environment variables (temperature, smoke
concentration, etc.) are therefore uniform
throughout the zone.
• Conditions in each zone are calculated by
applying conservation equations and the ideal
gas law. The variables in each zone change as a
function of time and rely on the initial conditions
specified by the user.
• It is assumed that there is a well-defined
boundary separating the two zones, though this
boundary may move up or down throughout the
simulation.
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1.4.2 Zone Models (Con’t)
• Zone models are most applicable in situations
involving simple geometries or where spatial
resolution within a compartment is not
important.
• The preparation of input for a zone model, the
computation time, and the amount of output
data generated are slightly more extensive
than a simple algebraic model; however, the
overall computational time cost is still low.
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1.4.3 CFD Models
• A CFD model is often useful when trying to determine fire
variables at a specific location or when there are geometric
features that are expected to play a significant role in the
results beyond what is calculated in a zone model
approximation.
• A typical CFD model consists of a preprocessor, a solver,
and a postprocessor. CFD models can provide a detailed
analysis in both simple and complex geometries. CFD
models essentially apply a series of conservation and state
equations across multiple cell boundaries in a space.
• The number of cell boundaries depends on the mesh size,
which breaks the geometry into three-dimensional
subvolumes called cells. Solutions to partial derivatives of
the conservation equations are updated as a function of
time within each numerical grid cell, with the solutions in all
cells, collectively describing the fire environment within the
geometry at the cell resolution.
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1.4.3 CFD Models (Con’t)
• CFD models have much better spatial fidelity than zone
models, being able to distinguish conditions in one part of
the space from another.
• Because of the appreciable amount of time and effort
required to apply CFD models as compared to zone models
or algebraic models, CFD models are generally applied
when:
– Spatial resolution is important, either relative to the locations of
fuel packages or targets.
– Large compartments relative to the fire size are involved.
– Compartments have complex geometries, flow connections, or
numerous obstructions in the upper part of the compartment.
– Large numbers of compartments are within the area of interest
and the presence of each compartment is expected to affect
the fire environment in the area of interest.
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1.4.3 CFD Models (Con’t)
• While CFD models provide a detailed analysis of a space,
they are costly to create, simulate and maintain. The input
files created in the preprocessing stage require a significant
effort to create. The user must understand the code syntax
and the implications and assumptions embedded in the
model.
• A firm understanding of fire dynamics is important in
providing input data that is relevant to the application. Most
CFD models have default values that must be recognized
and adjusted as necessary if the simulation is going to be
accurate.
• The relevance of the default values needs to be confirmed
for any application. User manuals and technical references
for each CFD model outline such values and may provide
recommended ranges for the parameters.
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1.4.4 V&V
• The use of fire models to support fire protection
decision making requires a good understanding of
their limitations and predictive capabilities. NFPA
805 states that fire models shall only be applied
within the limitations of the given model and shall be
verified and validated.
• Verification is the process of determining that a
model preserves the laws of science and math,
thereby assessing whether it was “built” correctly. In
this assessment, the theoretical basis of the model is
reviewed to confirm that the scientific and
mathematical foundation of the model is correct, that
is, that the laws of physics and chemistry are upheld
and proper numerical techniques are employed.
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1.4.4 V&V (Con’t)
• Validation is the process of determining that a model is a
suitable representation of the real world and is thus capable
of reproducing the phenomena of interest.
• Validating a model requires that the output of subroutines or
the entire model provide predictions that compare
reasonably well with experimental data.
• NRC RES and EPRI conducted a project for V&V of the five
selected fire models described in Sections 2.3.1 through
2.3.5 that may be used to support RI/PB fire protection and
implementation.
• The results of this project were documented in NUREG1824, Verification and Validation of Selected Fire Models for
Nuclear Power Plant Applications.
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1.5 NFPA 805
An Educational Program to
Improve the Level of Teaching
Risk-Informed, Performancebased Fire Protection Engineering
Assessment Methods
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1.5 NFPA 805 Fire Modeling
Applications
• The NFPA 805 requirements associated
with fire modeling are organized in two
sections:
– Section 4.2.4.1 describes requirements for
the implementation of a performance-based
fire modeling analysis.
– Section 2.4.1.4 describes the requirements
associated with the analytical fire modeling
tools selected for the analysis.
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1.5.1 Requirements Associated with the Implementation
of a Performance Based Fire Modeling Analysis
• NFPA 805 Section 4.2.4.1 describes the
process to follow when using fire
modeling to address variances from
deterministic requirements (VFDRs).
• VFDR is used in the fire protection
community within the commercial nuclear
industry to refer to plant conditions that
deviate from deterministic requirements
of NFPA 805 Section 4.2.3.
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NFPA 805, Section 4.2.4.1 – Variances From
Deterministic Requirements (VFDRs)
• Identify Targets (NFPA 805 § 4.2.4.1.1)
• Establish Damage Thresholds (NFPA 805 §
4.2.4.1.2)
– Damage or ignition temperature
– Damage or ignition incident heat flux
• Determine Limiting Conditions (NFPA 805 §
4.2.4.1.3)
• Establish Fire Scenarios (NFPA 805 § 4.2.4.1.4)
– Maximum Expected Fire Scenario (MEFS)
– Limiting Fire Scenario (LFS)
• Protection of Required Nuclear Safety Success
Paths (NFPA 805 § 4.2.4.1.5)
• Operations Guidance (NFPA 805 § 4.2.4.1.6)
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NFPA
805
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1.5.2 Requirements Associated with
the Selected Analytical Fire Models
• NFPA 805 Section 2.4.1.2 describes the
requirements for the use of fire models,
which include:
– The use of fire models acceptable to the
authority having jurisdiction (i.e., the US Nuclear
Regulatory Commission)
– The application of fire models within their range
and limitations. Section 2 of this document
provides guidance on ensuring the model is
within the range of limitations and what steps
are necessary if the application is outside
existing V&V data ranges
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1.5.2 Requirements Associated with
the Selected Analytical Fire Models
• NFPA 805 stipulates that the fire models
used shall be verified and validated. In the
context of this application, the specific
analytical capabilities within the fire model
need to be verified and validated.
• Model capabilities not invoked in specific
calculation are outside the scope of this
requirement.
• NUREG-1824 (EPRI 1011999) is an
example of a verification and validation
study for fire models specifically developed
for NPP applications.
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