Post-Flashover compartment Fire

José L. ToreroUniversity College London

United Kingdom

Lecture - 5

Assessing Structural Behavior

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.)

Origins

o Worst Case Scenario

o Curve defined by envelope to all fires

o Required Rating defined by total fuel consumption

0

250

500

750

1000

1250

0 30 60 90 120 150 180time [minutes]

Tem

per

ature

[oC

]

Fire (BS-476-Part 8)

Increasing

Fuel Load

Restrainto Compartment allows to approximate global

structural behaviour to single element –Restraint enables effective load transfer

Restraint

Standard Fireo Furnace to reproduce compartment

o Single element tested

0

250

500

750

1000

1250

0 30 60 90 120 150 180time [minutes]

Tem

per

ature

[oC

]

Fire (BS-476-Part 8)

Critical

Temperature

Resistance

Structural Element

(Ingberg, 1928)

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!

The collapse of the WTC towers emphasizes the need for a detailed structural analysis of optimized buildings – ie. Tall Buildings

Existing Framework

1958

1962-1972 1975

1969-1976

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

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

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

Typical Compartment

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

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.

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

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

The Data

Regime IRegime II

Regime I

Regime II

Theory

Τ𝑨 𝑨𝟎 𝑯𝟎

Theory

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

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.)

Realistic Fire

Tg,max

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

Travelling Fires (Regime II)

Growing Fires (Regime II or Regime I?)

(SFPE Engineering Guide – Fire Exposures to structural Elements – May 2004)

• Quintiere• McCaffrey• Pettersson• Rockett• Tanaka, etc.

𝐴

𝐴0 𝐻0

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.

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

Fuel Degradation

Gas Phase Chemistry

Soot Production

Radiative Losses

Flame Temperature

Heat Transfer Air

Entrainment

Coupling

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.)

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

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

Compartment Fire

2222 )()( tVtVrA ffB ===

fBCfC mAHmHQ ==

22

f

2

fCfBC ttm)V(HmAHQ ===

(Quintiere, 1998)

(SFPE, 2009)

ሶ𝑸" = ∆𝑯𝑪ሶ𝒎𝒇"

o Can Models Predict this Detail?

o Can Modellers Use Available Tools for this Purpose?

(Rein et al. 2009)

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!

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

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