Fire propagation within buildings Bristol study group April 19, - - PowerPoint PPT Presentation

Problem description Kyoto model ODE model PDE model Conclusions

Fire propagation within buildings

Bristol study group

April 19, 2013

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Outline

◮ Problem description ◮ Kyoto model ◮ ODE model ◮ PDE model

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

• 1. Current model:

Large scale, grid-based model for urban areas that ignores the effects of individual buildings.

• 2. Study group objective

◮ Determine estimates for the rate of fire development, spread

and decay in a building.

◮ Subject to:

minimal building information.

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Parameters to consider

• 1. Building:

◮ Dimensions ◮ Shape (N-sided, e.g. L-shape, U-shape) ◮ Usage (e.g. office, warehouse) ◮ Windows (for ventilation) ◮ Internal layout ◮ Internal firebreaks

• 2. Room

◮ Dimensions ◮ Fuel loading Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Development of fire

Figure 1: Fire growth curve

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Fire spread model

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Kyoto model

dmi dt = ˙ mF,i −

• j

( ˙ mi,j − ˙ mj,i) (1) dQi dt = ( ˙ QB,i + cp ˙ mF,iTp) −

• i

( ˙ QL,i +

• j

(cp ˙ mi,pTi − cp ˙ mj,iTj)) (2) d dt (miYX,i) = ˙ ΓX,i −

• j

( ˙ mi,pYX,i − ˙ mp,iYX,i) (3)

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Kyoto model

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

ODE model

Air Temperature Oxygen Fuel Ti−1 Oi−1 Fi−1 Wall Temperature Wi−1 Di−1 Ti Oi Fi Wi Door Function Di Ti+1 Oi+1 Fi+1 Wi+1 dTi dt =µe−Tm/Ti OiFi + λ[Di−1(Ti−1 − Ti) − Di(Ti − Ti+1)] − λW [Ai(Ti − Wi) + Si(Ti − Wi)H(Tp − Wi) + Si(Ti − Tp)H(Wi − Tp)] dWi dt =[Ai(Ti − Wi) + Si(Ti − Wi)]H(Tp − Wi) dOi dt = − ˆ αe−Tm/Ti OiFi + λ[Di−1(Oi−1 − Oi) − Di(O1 − Oi+1)] dFi dt = − ˆ βe−Tm/Ti OiFi + ˆ βSi(Ti − Tp)H(Wi − Tp) + λ[Di−1(Fi−1 − Fi) − Di(Fi − Fi−1)] ε dDi dt =(D0 − Di)H(Wi − Wc)

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Numerical results

2 4 T 2 4 W 0.6 0.8 1 O 1 2 F 2 4 6 8 10 1 2 D Time

(1) Numerical results (2) Parameters

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

PDE model

Simple combustion model (Margolis, Matkowsky, Forbes, Norbury) F + O2

k(T)

− − − → burned product and released heat Evolution equations for

◮ Fuel F(x, y, t) ◮ Oxygen O(x, y, t) ◮ Temperature T(x, y, t) ◮ Porosity (void fraction= 1-solid fraction (wall structure) )

0 ≤ φ(x, y, t) ≤ 1

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

∂F ∂t = −k(T)FO (5a) ∂O ∂t = DO∇ · (φ∇O) − k(T)FO (5b) ∂T ∂t = DT∇ · (φ∇T) + αk(T)FO (5c) ∂φ ∂t = βk(T)(1 − φ) (5d) k(T) =

• T < Tign

1 T > Tign (5e) where k(x) = λexp(− K

T ), K and α are constants. DO and DT are

the diffusion coefficients for oxygen and temperature, respectively.

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Numerical results

◮ planar fronts hitting different sides of the building will yield

different “burn-through” times based on interior wall structure...

◮ point ignition at different sites also.... (simulation with

break-down of walls)

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Ignition points

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Conclusions

• 1. There is a large literature, that we have partly reviewed.
• 2. The mass transfer is the key mechanism and not radiation or

convection.

• 3. Blockages (e.g. fire doors) appear to be primary impediments.
• 4. There is a comprehensive NIST model.
• 5. Intermediate scale Kyoto model more tractable.
• 6. Derived simplified ODE and PDE models.

Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions

Thank you! QUESTIONS?

Bristol study group Fire propagation within buildings