post-flashover compartment fire - princeton universitystandard fire. o furnace to reproduce...
TRANSCRIPT
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Post-Flashover compartment Fire
José L. ToreroUniversity College London
United Kingdom
Lecture - 5
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Assessing Structural Behavior
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Fire Resistance
o Current approach is “Fire Resistance” (Ingberg S.H., “Fire loads: Guide to the application of fire safety engineering principles,” Quarterly Journal of the National Fire Protection Association, 1, 1928.)
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Origins
o Worst Case Scenario
o Curve defined by envelope to all fires
o Required Rating defined by total fuel consumption
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0 30 60 90 120 150 180time [minutes]
Tem
per
ature
[oC
]
Fire (BS-476-Part 8)
Increasing
Fuel Load
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Restrainto Compartment allows to approximate global
structural behaviour to single element –Restraint enables effective load transfer
Restraint
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Standard Fireo Furnace to reproduce compartment
o Single element tested
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0 30 60 90 120 150 180time [minutes]
Tem
per
ature
[oC
]
Fire (BS-476-Part 8)
Critical
Temperature
Resistance
Structural Element
(Ingberg, 1928)
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Large Safety Factor?
o Poor understanding of material behaviour at high temperatures
o Poor understanding of fire dynamics
o Fire Resistance embedded into Codes & Standards which represent societies responsibility to guarantee safety – i.e. Large Safety Factors!
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The collapse of the WTC towers emphasizes the need for a detailed structural analysis of optimized buildings – ie. Tall Buildings
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Existing Framework
1958
1962-1972 1975
1969-1976
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Back to the basics …
Fire Dynamics
Heat Transfer
𝜌𝐶𝑝𝜕𝑇
𝜕𝑡= 𝑘
𝜕2𝑇
𝜕𝑥2
−𝑘 ቤ𝜕𝑇
𝜕𝑥𝑥=0
= ሶ𝑞"𝑁𝐸𝑇
ቤ𝜕𝑇
𝜕𝑥𝑥=𝑥𝑆
= 0
𝑇 𝑡 = 0 = 𝑇0
Structural Analysis
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Net Heat Flux?
ሶ𝑄𝑜𝑢𝑡 = 𝐴𝑊 ሶ𝑞"𝑟 +ඵ ሶ𝑚(𝑦, 𝑧)𝐶𝑝𝑇 𝑦, 𝑧 𝑑𝑦𝑑𝑧
ሶ𝑄𝑖𝑛 = ሶ𝑚𝐶𝑝𝑇∞
ሶ𝑄𝑁𝑒𝑡
ሶ𝑄𝑔𝑒𝑛 = ∆𝐻𝐶 ሶ𝑚𝑓
ම𝑚𝐶𝑉𝐶𝑝𝑇 𝑥, 𝑦, 𝑧 𝑑𝑥𝑑𝑦𝑑𝑧
𝑑
𝑑𝑡ම𝑚𝐶𝑉𝐶𝑝𝑇 𝑥, 𝑦, 𝑧 𝑑𝑥𝑑𝑦𝑑𝑧 = ሶ𝑄𝑔𝑒𝑛 + ሶ𝑄𝑖𝑛 − ሶ𝑄𝑜𝑢𝑡 − ሶ𝑄𝑁𝑒𝑡
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The Compartment Fire
o It was understood that solving the full energy equation was not possible
o The different characteristic time scales of structure and fire do not require such precision
o Looked for a simplified formulation: The Compartment Fire
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Typical Compartment
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Thomas & Heselden (1972)
Regime I Regime II
Thomas, P.H., and Heselden, A.J.M., "Fully developed fires in single compartments", CIB Report No 20. Fire Research Note 923, Fire Research Station, Borehamwood, England, UK, 1972.
o Realistic scale compartment fires (~4 m x 4 m x 4 m) aimed at delivering average temperatures
o Simple instrumentation: Single/Two thermocouples
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Assumptions – Regime Io The heat release rate is defined by the complete consumption of all oxygen
entering the compartment and its subsequent transformation into energy, ሶ𝑄 = ሶ𝑚𝑌𝑂2,∞∆𝐻𝑐𝑂2. o Eliminates the need to define the oxygen concentration in the outgoing combustion products o Eliminates the need to resolve the oxygen transport equation within the compartment. o Limits the analysis to scenarios where there is excess fuel availabilityo Chemistry is fast enough to consume all oxygen transported to the reaction zoneo The control volume acts as a perfectly stirred reactor. o The heat of combustion is assumed to be an invariant/ the completeness of combustion is
independent of the compartment.
o Radiative losses through the openings are assumed to be negligible therefore ሶ𝑄𝑜𝑢𝑡 is treated as an advection term (3% of the total energy released
(Harmathy)).o There are no gas or solid phase temperature spatial distributions within the
compartment. o Mass transfer through the openings is governed by static pressure differences
( ሶ𝑚 = 𝐶𝐴𝑂 𝐻𝑂) o all velocities within the compartment to be negligible o Different values of the constant were derived by Harmathy and calculated by Thomas for different
experimental conditions.
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Maximum Compartment Temperature
Tg,max
T∞
Tg,max
ሶ𝑄𝑖𝑛 = ሶ𝑚𝐶𝑝𝑇∞
ሶ𝑄𝑜𝑢𝑡 = ሶ𝑚𝐶𝑝𝑇𝑔,𝑚𝑎𝑥
ሶ𝑄𝑁𝑒𝑡
ሶ𝑄𝑔𝑒𝑛 = ∆𝐻𝐶 ሶ𝑚𝑓
𝑚𝐶𝑉𝐶𝑝𝑇𝑔,𝑚𝑎𝑥
𝑑
𝑑𝑡𝑚𝐶𝑉𝐶𝑝𝑇𝑆 = ሶ𝑄𝑔𝑒𝑛 + ሶ𝑄𝑖𝑛 − ሶ𝑄𝑜𝑢𝑡 − ሶ𝑄𝑁𝑒𝑡
S.S. ሶ𝑄𝑖𝑛 ≪ ሶ𝑄𝑜𝑢𝑡
ሶ𝑚𝑖𝑛 = ሶ𝑚𝑜𝑢𝑡 = ሶ𝑚=𝐶𝐴𝑂 𝐻𝑂
H0
ሶ𝑄𝑔𝑒𝑛 = ሶ𝑚𝑌𝑂2,∞∆𝐻𝑐𝑂2
ሶ𝑄𝑁𝑒𝑡 = 𝐴𝑘𝑇𝑔,𝑚𝑎𝑥 − 𝑇∞
𝛿
ሶ𝑄𝑜𝑢𝑡 = ሶ𝑚𝐶𝑝𝑇𝑔,𝑚𝑎𝑥
d
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Maximum Compartment Temperature
Tg,max
T∞
Tg,max
ሶ𝑄𝑖𝑛 = ሶ𝑚𝐶𝑝𝑇∞
ሶ𝑄𝑜𝑢𝑡 = ሶ𝑚𝐶𝑝𝑇𝑔,𝑚𝑎𝑥
ሶ𝑄𝑁𝑒𝑡
ሶ𝑄𝑔𝑒𝑛 = ∆𝐻𝐶 ሶ𝑚𝑓
𝑚𝐶𝑉𝐶𝑝𝑇𝑔,𝑚𝑎𝑥
0 = ሶ𝑄𝑔𝑒𝑛 − ሶ𝑄𝑜𝑢𝑡 − ሶ𝑄𝑁𝑒𝑡
𝑇𝑔,𝑚𝑎𝑥 =1 +
𝑇∞𝑇𝐶𝐷
1 +𝑇𝐹𝑇𝐶𝐷
𝑇𝐹
𝑇𝐹 = Τ𝑌𝑂2,∞∆𝐻𝑐𝑂2 𝐶𝑝
𝑇𝐶𝐷 =𝐶𝑌𝑂2,∞∆𝐻𝑐𝑂2
Τ𝑘 𝛿
𝐴𝑂 𝐻𝑂
𝐴
Substituting and solving for Tg,max
d
H0
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The Data
Regime IRegime II
Regime I
Regime II
Theory
Τ𝑨 𝑨𝟎 𝑯𝟎
Theory
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Design Method
T [oC]
t [min]tBO
Heating
CoolingR = 0.1 A0H0
1/2 (kg/s)
Kawagoe (1958)Thomas & Heselden (1972)
𝑡𝐵𝑂 =𝑀𝑓
𝑅
(Law, M., “A Basis for The Design of Fire Protection of Building Structures,” Struct. Eng., no. February, pp. 25–33, 1983.)
Tg,max
Φ = 𝐴0 𝐻0
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Parametric Fires
o Recorded temperature evolution – effect of structural heating
o Average temperature – single thermocouple rack (6 – TC)
ሶ𝑄𝑁𝑒𝑡(Pettersson, O. Magnusson, S. E. and Thor, J. “Fire Engineering Design of Steel Structures,” Stockholm, Jun. 1976.)
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Realistic Fire
Tg,max
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Regime II?
o Data scatter is very large
o Factors such as aspect ratio, nature of the fuel and scale were shown by Thomas & Heseldento have a significant effect on the resulting temperatures
o The relationships between Tg,max and R with
Τ𝐴 𝐴0 𝐻0 and 𝐴0 𝐻0 are no longer valid
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Travelling Fires (Regime II)
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Growing Fires (Regime II or Regime I?)
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(SFPE Engineering Guide – Fire Exposures to structural Elements – May 2004)
• Quintiere• McCaffrey• Pettersson• Rockett• Tanaka, etc.
𝐴
𝐴0 𝐻0
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Summary
o An elegant framework was established that provided an “answer” to a “fundamental question”
o Assumptions were clearly established
o Limitations were clearly established
o A simple design methodology was developed that provided a “worst case: Tg,max vs t” curve for the purposes of structural analysis.
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Complex problems require detailed solutionso Only CFD provides temporal and
spatial resolution requiredo Precision, robustness and
uncertainty need to be consistent with the requirements of the problem
o Validation & Verification need to be consistent with the complexity of the model
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Fuel Degradation
Gas Phase Chemistry
Soot Production
Radiative Losses
Flame Temperature
Heat Transfer Air
Entrainment
Coupling
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Complexity
Complexity of Chemistry
Complexity of Turbulence and Flow
Fans
1
2
345
6
1 2
3
4
56
Ld
L/d≈ 1
(Pope, Proceedings of Combustion Institute v. 34, 2012.)
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Incompatibility of Scales
Sullivan, A., “A Review of Wildland Fire Spread Modelling, 1990-Present, 1:Physical and Quasi-Physical Models”, arXiv:0706.3074v1[physics.geo-ph] (2007).
Type Time Scale (s)
Vertical Scale (m)
Horizontal scale (m)
Combustion 0.0001 –0.01
0.0001 – 0.01 0.0001 – 0.01
Fuel particles - 0.001 – 0.01 0.001 – 0.01Fuel complex - 1 – 20 1 – 100Flames 0.1 – 30 0.1 – 10 0.1 – 2Radiation 0.1 – 30 0.1 – 10 0.1 – 50Conduction 0.01 – 10 0.01 – 100 0.01 – 0.1Convection 1 – 100 0.1 – 100 0.1 – 10Turbulence 0.1 – 1,000 1 – 1,000 1 – 1,000Spotting 1 – 100 1 – 3,000 1 – 10,000Plume 1 – 10,000 1 – 10,000 1 – 100
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Classic Scaling-Upo Uncouple processes
o Develop simplified models
o Feed Models with experimental data
VBO
VS
D
Ignition, Flame Spread (VS) & Burning rate models (VBO)
Gas Phase Combustion/Transport
Models ( ሶ𝑄, 𝐷) (Morvan et al. 2009)
ሶ𝑸, 𝑫
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Compartment Fire
2222 )()( tVtVrA ffB ===
fBCfC mAHmHQ ==
22
f
2
fCfBC ttm)V(HmAHQ ===
(Quintiere, 1998)
(SFPE, 2009)
ሶ𝑸" = ∆𝑯𝑪ሶ𝒎𝒇"
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o Can Models Predict this Detail?
o Can Modellers Use Available Tools for this Purpose?
(Rein et al. 2009)
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What went wrong?o Experimental uncertainty?
o Repeatabilityo Nature of the tests over emphasized
secondary ignitiono Models are not good enough?o Modellers are not good enough?
o Despite the precautions - tests of this nature provide little insight to improve models or the modelling exercise – too many variables!
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What is next?
o Fire models are not ready for validation & verification tests
o To improve fire models it is necessary to develop an experimental data base
specifically designed for CFD model validation
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What is next?
o Comprehensive Fire Models will not be a viable solution for a very long time
o Fundamental understanding of the different processes involved and their couplings can enable formulations consistent with the modelling domain
o The simplified formulations need to be specifically designed for the purpose of CFD based scaling-up of the fire