Fire Physics, Nomenclature,
and Modeling
Focus is on internal/enclosed fire
situations. NPP applications are
emphasized.
There is one Significant Fire
Event Every 10 Reactor Years.
Arthur Ruggles, UTNE
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Outline of Material
• Basics of Fire Modeling-Intro to Concepts
• Definitions for phenomena
–
–
–
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Energy release rates and energy release vs. time
Combustion efficiency
Mass loss rate
Flash-over
• The Axi-symmetric plume
• Enclosure flows
• Smoke filling and combustion products
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Philosophy of Presentation
• The fire and fire induced plume drives the
simulation-these physics are presented first.
• The fire responds to feedback from the
enclosure such as reflected heat from walls,
or restricted air/oxygen inflow.
• Relatively simple transport models and
empirical models are introduced to develop
understanding and intuition.
• A few parameters important to Nuclear Power
Plant (NPP) Probabilistic Risk Assessment
(PRA) are presented.
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Fire and Fire Plume Attributes
Continuous Flame Height-combustion and thermal energy addition occurs in the flame
Intermittent Flame-flame is varying in time and position in this region
Mean Flame Height-time and position average for flame height needed for steady state model development, this
is where energy addition due to combustion ends, and a buoyancy driven plume begins.
Plume-buoyancy due to hot gasses from fire balanced by shear and mixing with entrained air to form a vertical
flow of air and combustion gasses in the “plume”. Momentum balance used to define plume mass flow
and diameter are considered later.
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Context of Fire and Plume to Enclosure Fire Dynamics
Fire drives the energy addition and hot gas production that causes the plume and
creates hazard to humans via smoke inhalation and heat exposure.
Mass flow in plume determines smoke filling rate in enclosure.
Temperature in plume is important to buoyancy drive for flow into and out of the enclosure
openings. Air/oxygen inflow often limits fire progression in enclosures.
Fire progression, which involves heating and vaporization of adjacent fuel, determines
energy release versus time, and fire duration.
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Approach to Fire and Plume Modeling
Energy release rate models-empirical.
examine approaches to measurement and conventions for use.
Mass Loss rate models and burn efficiency-empirical.
examine approaches to measurement and conventions for use.
Mean flame height models-empirical.
measurement method and interface with plume parameters.
Plume models, including plume mass flow, temperature and diameter-mechanistic.
mass, momentum and energy balance leading to plume models. These
are related to buoyancy driven flows from thermal science. Models
developed for the plume are quasi-steady.
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Empirical Model Development is based on Experimental Data
Mass loss rate-mass versus time
Mass flow in plume-mass flow measurement with plume capture in hood
Oxygen content-oxygen meter, air is normally 23% oxygen by mass.
Plume temperature measurement-RTDs or Thermocouples
Combustion efficiency-mass flow with mass loss rate, oxygen content and
temperature used to infer this quantity.
Temperature
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Energy Release Rate, Mass Loss Rate, Heat of Combustion
and Heat of Gasification.
Mass Loss Rate: The rate of fuel mass lost, Kg/s, some of which will combust,
and some of which is gasified but does not combust.
Combustion Efficiency: Ratio of effective (actual) heat of combustion in
the fire over the complete heat of combustion, g.
Heat of Combustion: Energy released per unit mass of fuel. There is
effective heat of combustion, DHeff , which is equal to the combustion
efficiency, g, times the complete heat of combustion, DHc .
Heat of Gassification: Gases combust in fires. Some portion of the energy
released from the fire must go back into gasification of liquid
or solid fuels, DHg.
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Energy Release Rate or Heat Release Rate
The Heat Release Rate (HRR) is the total energy per unit time released
by the fire. Units of KW are usually used in fire literature for
power, so the HRR is usually given in KW.
 DHeff  m
 gDHc
HRR  Q  m
This definition of the HRR assumes the heat of combustion includes
the energy required to gasify the fuel. In most cases 70% to
80% of the fuel combusts, placing g between 0.7 and 0.8.
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Pool Fires
• These fires are fairly common, machines with
lube oil or transformer oil are dyked.
• Dyked area determines the pool fire area, which
determines heat release rate.
• Lube oil or transformer oil inventory will fit in
dyke by design.
• Do not put tools and components inside the dyke
during component service.
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Pool Fires: Constant HRR
Large pool fire mass loss rate per unit area, m  , is larger than
that for smaller pool fires. An approximation for smaller pool
fire mass loss rate is provided below, where the parameter
kb is derived from data. The diameter of the fire, D, may be
the diameter of a circle of equivalent area when the pool
shape is not circular.
   m
  (1  e
m
 kbD
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)
HRR and mass loss data per unit area for
Common Combustible Materials: SFPE Handbook
MATERIAL
Polyethelene
Polypropolene
Kerosene
Gasoline
Transformer oil(s)
Polystyrene
Methanol
Polyurethane foams
PVC
Teflon
Mass Loss
0.026 kg/m2s
0.024
0.065
0.062
0.025-0.030
0.034
0.025
0.021-0.027
0.016
0.007 Kg/m2s
DHc
43.6 MJ/Kg
43.4
44.1
44.2
44.8
39.2
20
23.2-28.0
16.4
4.8 MJ/Kg
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kb(m-1)
3.5
2.1
0.7
infinite
Example Pool Fire
Diesel for emergency generators is compromised by a 40 year old fitting
Failure. Approximately 90 gallons are released into an area 3m by 4m.
The combustion efficiency is near 0.75, evaluate the heat release rate and
duration of this fire. Assume this is an unrestricted (open) fire.
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Fire Progression in an Enclosure, Time Varying HRR
Ignition: self sustained combustion begins, PRA may provide list of ignition
sources and probability of occurrence.
Growth: Fire grows, smoke layer forms and descends, temperature in smoke
layer increases, and fire radiative flux increases.
Flashover: Smoke layer/upper gas layer reaches 500F to 600F, and radiation
from smoke layer and fire supports rapid fire spread to entire enclosure.
Fully Developed fire: Air/oxygen limited combustion in enclosure.
Ignition
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HRR versus Time
• Experiments with common fuel sources
provide heat release rate versus time.
• NPP fuel sources include cable insulation,
paint, and various fluids (e.g., lube oil,
transformer oil, solvents, fuel).
• The HRR, along with fire base diameter,
provide information on mean flame height.
• HRR, flame height and fire base diameter
allow quantification of the plume.
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Fire Growth Phase: HRR=at2
• For Design Purposes, the growth phase is
important since this is when protection and
response systems should intervene.
• Some values for a: 1/8 inch plywood
wardrobe with clothes (.86); Easychair
23Kg (0.19)
• “Fast” growth for a greater than 0.047.
• “Slow” growth for a less than 0.003.
(NFPA 204M)
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Flame Height Modeling
• Dimensionless groups used in natural
convection flow appear in empirical models.
L is flame height, D is fire diameter at base.
 2/ 5

L  0.235(Q ) 1.02D

Q


Q 
2
  c pT D gD
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The Plume Above the Flame
• The buoyancy in the plume above the flame is
fixed if density is taken linear with temperature,
and thermal losses are neglected.
• Plume model involves a balance of buoyancy
with momentum losses due to mixing with
adjacent air.
• Mixing also cools the plume average
temperature, and increases the plume mass
flow.
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Note that average of products
is generally
not equal
to the product of averages.
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by USNRC:
EDU10-002
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Homework 1 Solution:
The first two steps follow
almost exactly the sequence
of the example earlier in the notes.
Note that the oil evaporates more
slowly than the diesel, but the
heating value per unit mass for
Diesel and the transformer oil
are similar.
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NRC has these Models
Coded into Spread Sheets
Available on-line for Free!
These spreadsheets are in use
now for NPP fire safety
assessment.
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Plume Model Assumes
Point heat source at Z=0.
floor
b
Zo
Virtual Fire at
Virtual Origin
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Enclosure Dynamics using Two Zone Model
Plume feeds hot gases to hot layer.
Hot layer fills enclosure and alters pressure distribution from that outside.
Differential pressure drives flow into and out of the enclosure
through openings.
Flow into enclosure may limit oxygen availability for fire
(ventilation controlled fire).
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Cables in Trays and Conduit are all over the Plant.
Often smaller diameter cables for instrumentation
are suspended in trays. Time to loss of cable function
is modeled in fire progression and plant response. PRA
may include cable integrity predictions. (NUREG 1805)
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Pressure Differences Drive flow Into and Out of Enclosure
Fire Induced Hot Layer Alters Pressure Gradient In Enclosure
Z+
Neutral Line
Z-
Hn
Hd
Neutral Pressure at Hn
Density Change at Hd
Define z relative to Neutral Plane
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Pressure Differences can be
related to Hot Gas
Temperature, Hot Gas Layer
Height, and Height of Neutral
Pressure
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Mass flow is reduced to account for some flow physics not captured in
Isentropic Bernoulli Model.
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Position of Neutral Pressure Plane is established using the Mass Balance
Mass flow into the enclosure must equal the mass flow out
of the enclosure. If the enclosure has only one opening, then the
Neutral pressure plane will cut through that opening, allowing both
inflow and outflow through the same opening.
Neutral Pressure Plane
door
Note Velocity Profile for Inlet Flow is not Linear,
Pressure Profile is linear, Velocity goes as
Square root of Pressure for tall openings.
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Flows Through Openings are Modeled using Form Losses
And Modified Bernoulli Equation for Horizontal flow
In Nuclear, Mechanical and Civil Engineering

v 2  
v 2  v 2
p
  p
 
2 1 
2 2
2

 l

f

C
 f

D
h


Upstream Flow is near zero, and downstream flow is
also near zero, with maximum flow kinetic energy
developed in the opening (actually just downstream of
the opening), and later lost (actually thermalized via
turbulence and shear), so our model reduces to:
p1  p2  1/ 2v C f
2
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Cfast is a Two Zone Fire Modeling Code that was
Subjected to Verification and Validation (V&V) for NRC
The code is general purpose, architectural enclosure fire modeling code
developed by NIST
The code has a primitive GUI, and solves the equations we just
covered, so a fire progression can be modeled.
The output is available in tables, or can be examined graphically using a
package called Smokeview.
Validation in this case means the code was run to predict experimental data
from situations representative of a NPP. The predictions were
compared with the test data, the outcomes reviewed, and
published.
The code was Verified during previous examinations and tests during the
development by NIST.
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