Radiative Heat Transfer in CFAST Martin Clouthier Introduction
Radiative Heat Transfer in CFAST
Concepts Conservation Equations
Martin Clouthier
Mass Species Energy Assumptions & Limitations
January 2013
Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Outline Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations Mass Species Energy Assumptions & Limitations Assumptions
1 Introduction 2 Concepts 3 Conservation Equations
Mass Species Energy 4 Assumptions & Limitations
Assumptions
Veri ication
5 Veri ication
Radiative heat transfer
6 Radiative heat transfer
Conclusions
7 Conclusions Martin Clouthier
Radiative Heat Transfer in CFAST
The purpose of this presentation is to provide… Radiative Heat Transfer in CFAST Martin Clouthier
1
Understanding of basic concepts underlying a zone ire model
2
Exposure to conservation equations and submodels
3
Knowledge of the major assumptions and limitations
4
Familiarity with veri ication of CFAST, and results for Version 6.2.0
5
Awareness of how CFAST deals with radiative heat transfer
Introduction Concepts Conservation Equations Mass Species Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
What is CFAST? Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations Mass Species Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer
CFAST is a two-zone ire model developed by NIST, used to calculate the evolving distribution of smoke, ire gases and temperature throughout compartments of a building during a ire. The software solves conservation equations for mass and energy in two control volumes Accounts for the effects of User speci ied ire(s) in multiple connected compartments Natural low between compartments through vents Mechanical ventilation Heating and ignition of objects
Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Extensive validation from literature and comparisons with experiments Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations Mass Species Energy Assumptions & Limitations Assumptions Veri ication
Predictions of HGL temperature, HGL height, ceiling jet temperature, plume temperature, lame height, gas concentration, smoke concentration, and room pressure are typically within or near experimental uncertainty Zone model predictions of target/wall lux or target/wall temperature require care and an understanding of the capabilities and limitation of zone models when used for analysing ire scenarios
Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
A zone model divides the compartment into control volumes Radiative Heat Transfer in CFAST Martin Clouthier
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Introduction Concepts Conservation Equations
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Mass Species Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer
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Figure 1: Control volumes selected in zone ire modelling
Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Conservation Equations Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations
Governing equations based on First law of thermodynamics (energy conservation)
Mass
Continuity equation (mass conservation)
Species
Newton’s second law of motion → Bernouilli’s equation (momentum)
Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Conservation of mass Radiative Heat Transfer in CFAST Martin Clouthier
∑ d ˙j=0 A (ρzl ) + m dt J
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Introduction Concepts
j=1 (net out)
Conservation Equations �̇
Mass Species Energy Assumptions & Limitations Assumptions Veri ication
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dml ˙ in − m ˙ out − m ˙e =m dt
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.
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Figure 1: Control volumes selected in zone ire modelling
dmu ˙e+m ˙f−m ˙u =m dt
Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Conservation of Species Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations Mass Species
dYi ∑ ˙ j (Yij − Yi ) = ω˙ i ρzl A + m dt J
j=1
Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Conservation of Energy Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations Mass Species Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer
rate of change of { } enthalpy energy of the =+ low in layer { } enthalpy − low out heat + transferred to the layer { } work done − by the layer
Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Conservation of Energy Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations Mass Species Energy
∑ dT dp ˙ j (Tj − T) = ω˙ F ∆H − Q˙ net loss ρcp zl A − zl A + cp m | {z } dt dt J
j=1 (net out)
Assumptions & Limitations Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
submodels
Major Assumptions Radiative Heat Transfer in CFAST Martin Clouthier Introduction
1
Gas is treated as ideal gas with constant values for molecular weight and speci ic heats (i.e., cp and cv ).
2
Exchange of mass at free boundaries is due to pressure differences or shear mixing effects.
3
Combustion is treated as a source of mass and energy.
4
Plume instantly arrives at the ceiling. Transport times are not explicitly accounted for in zone modelling.
5
Pressure is considered uniform in the energy equation, but hydrostatic variations account for pressure differences at free boundaries.
6
Mass low into the ire plume is to to turbulent entrainment.
Concepts Conservation Equations Mass Species Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Veri ication vs. Validation Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations Mass Species Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer Conclusions
ASTM E 1355 Standard Guide for Evaluating the Predictive Capability of Deterministic Fire Models Veri ication—the process of determining that the implementation of a calculation method accurately represents the developer’s conceptual description of the calculation method and the solution to the calculation method. Is the Math right? Validation—the process of determining the degree to which a calculation method is an accurate representation of the real world from the perspective of the intended uses of the calculation method. Is the Physics right?
Martin Clouthier
Radiative Heat Transfer in CFAST
Veri ication of proper installation Radiative Heat Transfer in CFAST Martin Clouthier
Table : Results at
Introduction Concepts Conservation Equations Mass Species Energy Assumptions & Limitations Assumptions
Value
C Upper Temp. C Upper Temp.
Units ∘
∘
C C
Case
Version . . . .
seconds Case
Version . . . .
Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Case
Version . . . .
CFAST simulations show the effects of increased soot yield Radiative Heat Transfer in CFAST Martin Clouthier Introduction
Table : Single Compartment at
Concepts Conservation Equations Mass Species Energy Assumptions & Limitations
Value
Upper Temp Lower Temp
Units ∘
∘
C C
Methane �̄ =
Absorbtion incorrect
Absorbtion corrected
s
Methane �̄ = . kg/kg
Absorbtion incorrect
Absorbtion corrected
Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Radiation network for two zones Radiative Heat Transfer in CFAST
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Martin Clouthier
�walls
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Introduction
�walls
Concepts Conservation Equations
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Mass Species Energy Assumptions & Limitations Assumptions Veri ication
,walls
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Figure 1: Control volumes selected in zone ire modelling
Radiative heat transfer
�walls to
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loor
to w alls r to
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� loor � loor .�
, loor
Figure 2: Radiation network
Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
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,
Equations used by CFAST to calculate radiative heat transfer Radiative Heat Transfer in CFAST Martin Clouthier
Q˙ net loss = hAs (Tgu − Twu ) + q˙ CV1 to Walls + q˙ CV1 to Floor {z } | {z } | radiative
convective
Introduction Concepts Conservation Equations
q˙ CV1 to Walls =
Ebgu − Ebw Rwg + Rw
Mass Species Energy
Rwg = (Aw Fwg ϵgu )−1 ,
Rw =
Assumptions & Limitations Assumptions Veri ication
q˙ CV1 to Floor =
Radiative heat transfer Conclusions
Ebgu − Ebflr Rflrg + Rflr
Rflrg = (Aflr Fflrg ϵgu )−1 , Martin Clouthier
1 − ϵw ϵw Aw
Rflr =
1 − ϵflr ϵflr Aflr
Radiative Heat Transfer in CFAST
Equations used by CFAST to calculate gas layer emissivity Radiative Heat Transfer in CFAST Martin Clouthier
ϵgu = 1 − e−Km S + ϵg e−Km S
Introduction Concepts Conservation Equations
Km = 3.72
Mass
Co fv Tgu C2
Species Energy Assumptions & Limitations
fv =
˙ s ∆t ¯ysoot m ρsoot (WLzl )
Assumptions Veri ication Radiative heat transfer
ϵg ≈
Conclusions
1 ϵH2 O + ϵCO2 |{z} 2
code error
Martin Clouthier
Radiative Heat Transfer in CFAST
Put simply Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations Mass Species
Q˙ net loss = f(Tg , Tw , ¯ysoot , zl , ϵg , ϵw , ϵflr )
Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
There was a coding subscript error in CFAST Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations
Source code from the SVN repository, ‘radiation.f90’
Mass Species Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
Conclusions Radiative Heat Transfer in CFAST Martin Clouthier Introduction Concepts Conservation Equations Mass Species
Soot yield has an important effect on upper layer gas temperature and radiative heat loss.
Energy Assumptions & Limitations Assumptions Veri ication Radiative heat transfer Conclusions
Martin Clouthier
Radiative Heat Transfer in CFAST
