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 dm i � dt = ˙ ( ˙ m i , j − ˙ m j , i ) (1) m F , i − j dQ i dt = ( ˙ � ( ˙ � Q B , i + c p ˙ m F , i T p ) − Q L , i + ( c p ˙ m i , p T i − c p ˙ m j , i T j )) (2) i j d dt ( m i Y X , i ) = ˙ � Γ X , i − ( ˙ m i , p Y X , i − ˙ m p , i Y X , i ) (3) j 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 Wall Temperature W i − 1 W i W i +1 Air Temperature T i − 1 T i +1 T i Oxygen O i − 1 O i O i +1 F i − 1 F i F i +1 Fuel Door Function D i − 1 D i d T i = µ e − T m / T i O i F i + λ [ D i − 1 ( T i − 1 − T i ) − D i ( T i − T i +1 )] dt − λ W [ A i ( T i − W i ) + S i ( T i − W i ) H ( T p − W i ) + S i ( T i − T p ) H ( W i − T p )] d W i =[ A i ( T i − W i ) + S i ( T i − W i )] H ( T p − W i ) dt d O i α e − T m / T i O i F i + λ [ D i − 1 ( O i − 1 − O i ) − D i ( O 1 − O i +1 )] = − ˆ dt d F i dt = − ˆ β e − T m / T i O i F i + ˆ β S i ( T i − T p ) H ( W i − T p ) + λ [ D i − 1 ( F i − 1 − F i ) − D i ( F i − F i − 1 )] ε d D i =( D 0 − D i ) H ( W i − W c ) dt Bristol study group Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions Numerical results 4 T 2 0 4 W 2 0 1 0.8 O 0.6 2 1 F 0 2 D 1 0 0 2 4 6 8 10 Time Bristol study group (1) Numerical results (2) Parameters Fire propagation within buildings

Problem description Kyoto model ODE model PDE model Conclusions PDE model Simple combustion model (Margolis, Matkowsky, Forbes, Norbury) k ( T ) F + O 2 → 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 = D O ∇ · ( φ ∇ O ) − k ( T ) FO (5b) ∂ T ∂ t = D T ∇ · ( φ ∇ T ) + α k ( T ) FO (5c) ∂φ ∂ t = β k ( T )(1 − φ ) (5d) � 0 T < T ign k ( T ) = (5e) 1 T > T ign where k ( x ) = λ exp ( − K T ), K and α are constants. D O and D T 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