Lecture 3 Fire Plumes and Flame Heights
BLDG 465/6651 – Fire and Smoke Control in Buildings
Instructor: Dr. Liangzhu (Leon) Wang
Concordia University
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Outline
 Review of Last Lecture
 This Lecture
 Background and Terminology
 Fire Flame: Determination of Mean Flame Height
 Fire Plume
 Ceiling Jet Flows
 Pressure Profile and Vent Flow in the Well-mixed
Compartment
 Pressure Profile and Vent Flow in the Stratified
Compartment
 Special Case: Vent Flow Through a Ceiling Vent
 Examples
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Review
 Terminology
 Energy Release Rate or Heat Release Rate (HRR)
 Burning Rate and Mass Loss Rate
 Complete Heat of Combustion, Effective Heat of Combustion,
and combustion efficiency
 Heat of Gasification
 Determine HRR by burning rate
 Determine HRR by oxygen consumption
HRR (kW) = consumed oxygen mass rate (kg/s) × 13,100 kJ/kg
 Understand T-squared fire for the growth phase
 Determine the constant maximum HRR for the steady phase
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Background
 Fire Plume: the buoyant flow, which is caused by
temperature/density difference about a fire source, including
any flames, is referred to as a fire plume.
 The properties of fire plumes are important because they are
closely related to:
 Fire detection
 Fire heating of building structures
 Smoke filling rates
 Fire venting and fire suppression system design
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Background (cont’d)
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Terminology
 Axisymmetric plume
A fire plume is symmetrical about its vertical centerline so
the air is entrained horizontally from all directions.
As a comparison, a non-axisymmetric plume can be a “line
plume” from a rectangular burner.
Axisymmetric burner
Line burner
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Terminology
 Turbulent Flame
3-dimensional, randomly fluctuating flame with a frequency
of the order of 1-3 Hz (one to three times per second).
Time:
tn
tn+1
*video from FDS simulation of a simple pool fire
tn+2
tn+3
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Terminology
 Mean Flame Height (L) unit: meter.
The time-average height of a fire plume, which is the height
at which the intermittency (denoted as I) is 0.5, i.e. the
height above which flame appears half the time.
*adapted from SFPE Handbook (2002)
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Terminology
 Non-dimensional Parameters and Similarity
 Physics parameters can be grouped to form the parameters
without dimensions.
 These dimensionless parameters can reflect the
fundamental physics of a phenomena and relate to each
other for the development of empirical formulas based on
experimental data.
 Two physical models are considered “similar” when these
dimensionless parameters are kept as the same values.
For example:
Reynolds number (Re) – ratio of inertia force over viscous force;
when Re is small enough, it is laminar flow
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Non-dimensional Parameters and
Similarity (cont’d)
 An example of similarity study for wind engineering
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Non-dimensional Parameters and
Similarity (cont’d)
 An example of similarity for fire research
Froude Similarity (or also called
Froude modeling)
*Adapted from Chow et al. (2008)
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Determination of Mean Flame Height (L)
L is the mean flame
height; D is the fire
source diameter;
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Determination of Mean Flame Height (L)
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Example for Determination of L
 Example 3.3 and Example 4.1
L
D
Determination of HRR by Burning Rate
(From Lecture 2)
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Example for Determination of L (FDS
Simulation)
3-D View
2-D Side View
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Fire Plume
The normal plume
The Ideal Plume
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Conservation Equations for the Ideal
Plume
 Use of Plume Model is to find:
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Conservation Equations for the Ideal
Plume (cont’d)
T
 Mass Conservation
unknowns
b, u, T
 Energy Conservation
unknowns
b, u, T
 Momentum Conservation
unknowns
So Three equations and three unknowns
b, u, T
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Conservation Equations for the Ideal
Plume (cont’d)
 Solution
When α ≈ 0.15:
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Plume Equations Based on Experiments
 The Zukoski Plume
1. The only difference from the
ideal plume is the constant
“0.21” instead of “0.20”
2. All other equations are the same
3. When
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The Heskestad Plume
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The Heskestad Plume (cont’d)
 For z > L (above mean flame height)
 For z ≤ L (below the mean flame height)
where
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The McCaffrey Plume
 Approximations: fire plume includes three
regions.
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The Thomas Plume
 Applicable when the mean flame height, L, is significantly
less than the fire source diameter, D.
i.e. L/D < 1 and where the fire source is noncircular
Where
P is the fire perimeter
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Line Plumes and Bounded Plumes
 Bounded Plumes
All the above equations apply only to unbounded plumes.
For fires near walls or corners, the following assumptions
are used:
unbounded
Original Zukoski Plume
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Line Source Plumes
 Mean Flame Height (L)
Where
B is the longer side
 Plume Mass Flow Rate
applicable for L < z < 5B
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Ceiling Jet Flows
 Most fire detection and fire suppression devices are
placed near the ceiling
 It is important to study ceiling jet flows, e.g. temperature
and velocity, or flame extension under low ceilings
*adapted from SFPE handbook (2002)
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Ceiling Jet Temperature and Velocities
 For unconfined ceiling jet (as shown in the figure)
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Flame Extensions under Low Ceilings
 When H < L
1. For small flames:
2. For large flames:
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Example of Ceiling Jet Flows
With the Tmax calculated, the heat
detector response time can be
calculated based on the heat detector
equations. (SFPE 04-01, 2002)
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Pressure Profiles and Vent Flows
BLDG 465/6651 – Fire and Smoke Control in Buildings
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Outline
 Background and Terminology
 Pressure profiles and neutral plane
 The Bernoulli equation
 Vent mass flow rates
 Pressure Profile and Vent Flow in the Well-mixed
Compartment
 Pressure Profile and Vent Flow in the Stratified
Compartment
 Special Case: Vent Flow Through a Ceiling Vent
 Examples
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Background and Terminology
 Hydrostatic Pressure or Pressure Difference
Pressure or pressure difference caused by the weight of a
column of gas or liquid
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Pressure Profile in an Enclosure and
Neutral Pressure Plane
 The distributions of hydrostatic pressures inside and
outside an enclosure
hot gas
cold air
Neutral Plane: A height, at which the inside and outside
pressure difference is zero.
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H
Neutral Plane (cont’d)
P
Case a
Pa
Pg
Case b
Pg
Pa
Case c
Pg
Pa
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The Bernoulli Equation
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Flows Through Vents
d
*Picture adapted from SFPE handbook 2002
The Bernoulli Equation Applied to
Compartment Vent Flows
1
3
2
3
1
2
Note: Vg is obtained without considering the flow resistance at the vents
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The Bernoulli Equation Applied to
Compartment Vent Flows (cont’d)
 For the lower vent
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Vent Mass Flow Rates
 Mass flow rates through vents:
Cd is called “discharge coefficient”, 0.6 < Cd < 0.7
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Height of Neutral Plane
=
hl + hu = H
*Derivation to find neutral plane is required.
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Pressure Profiles in Different Fire Stages
Stage A
Stage B
*You need to know each stage and how to draw these pressure profiles
Pressure Profiles in Different Fire Stages
(cont’d)
Stage C
Stage D
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A Summary
 So far, we reviewed the terminologies, equations, and
basic methods for “pressure profiles”, “neutral plane”,
“the Bernoulli equation”, and “calculation of mass flows
through vents”
 Now, let us look at how to apply these theories to:
1. Pressure profiles and vent flows in “well-mixed
compartment”
2. Pressure profiles and vent flows in “stratified
compartment”
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Pressures and Vent Flows in Well-mixed
and Stratified Compartments
 “Well-mixed compartment” refers to the fire in a
compartment reaching the post-flashover stage,
where the hot gases are assumed to fill the enclosure
so a uniform temperature and density in the
enclosure.
 As comparison, “stratified compartment” means
there are two distinct layers in an enclosure: upper
hot smoke layer and lower cold air layer. For each
layer, uniform temperature and density are assumed.
This case is also called “two-zone model”.
For both cases, our goal is to find “mass flow rates
through vents” and “the height of the neutral plane”
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1. Well-mixed Compartment
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1. Well-mixed Compartment (cont’d)
 Integrate the equations, we can get:
 Use mass balance, we can get the height of the neutral
plane
Where H0 is the height of the vent
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1. Well-mixed Compartment (cont’d)
 A simplified expression for the vent mass flow rate in a
well-mixed compartment
Density factor
≈ 0.214
Tg/Ta
Assumptions for the above equation:
1. Tg ≥ 300 ˚C; Ta ≈ 20 ˚C;
2. ρ ≈ 1.2 kg/m3 , Cd ≈ 0.7
3. Well-mixed compartment or post-flashover
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1. Well-mixed Compartment (cont’d)
 If considering the burning rate (or mass loss rate) in the
compartment, simply apply mass balance:
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2. Stratified Compartment
Where HD is the smoke layer height; HN is the neutral plane height for the
upper layer, H0 is the vent height.
Note: for convenience, all heights are relative to the bottom of the vent.
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2. Stratified Compartment (cont’d)
To find HN
 Four equations and five unknowns so HD (smoke layer
height) is often given
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Example 1
For air:
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Example 1 (cont’d)
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Example 2 – Stratified Compartment
with A Ceiling Vent
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Example 2 (cont’d)
 Step 1: draw pressure profile inside and outside the
compartment
 Step 2: from the neutral plane find the pressure
differences across the vents
 Step 3: use orifice equation, find mass flow rates through
vents
 Step 4: use mass balance for the compartment, find the
height of the neutral plane
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Example 2 (cont’d)
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Example 3
Ac = ?
300 ˚C
5.6 kg/s
5m
ρa = 1.2 kg/m3
2.5 m
Al = 5 m2
Ac = ?
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300 ˚C
Example 3 (cont’d)
5.6 kg/s
5m
2.5 m
Al = 5 m2