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MINISTERO DELL’INTERNO DIPARTIMENTO DEI VIGILI DEL FUOCO, DEL SOCCORSO PUBBLICO E DELLA DIFESA CIVILE DIREZIONE CENTRALE PER LA FORMAZIONE An Application In Fire Safety Engineering C. Barbera, A. Bascià, G. Di Salvo, A. Galfo, R. Lala, S. Lucidi, D. Maisano, G. Mancini, V. Puccia, F. Vorraro I e II Corso Direttori Antincendi Istituto Superiore Antincendi Roma Fire Service College Moreton-in-Marsh

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FIRE SAFETY Deterministic Approach Laws and regulations FIRE ENGINEERING APPLICATIONS In absence of specific laws and regulations When specific laws and regulations can’t be complied with Fire investigation High risk activities (safety report) Fire Engineering Approach Fire Models

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FIRE ENGINEERING: OPERATIVE VS. NUMERICAL MODELS Fitted parameters models (or operative models or zone models) Distributed parameters models (or numerical models or field models) They solve numerically (i.e., approximately) a set of exact balance equations (momentum, energy, mass) The computational domain is meshed by means of a calculation grid, whose refinement affects the accuracy of the result They yield temperature and concentration profiles as a function of time and space They solve exactly a set of simplified semi – empirical equations (momentum, energy, mass) The computational domain is divided into mixed zones, where intensive properties (i.e., P, T, concentrations) are assumed to be homogeneous They yield temperature and gases and smoke concentration in each zone

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AN OPERATIVE MODEL: CFAST Confined fires Two mixed volumes: upper layer (hot layer) + lower layer (cold layer) comb << = V / Q Hypotheses S: stoichiometric ratio air / fuel m: specific combustion rate [=] kg m -2 s -1 A: compartment section [=] m -2 m e : air mass flow rate [=] kg s -1 equivalence factor Controlling parameters Correlation equation X: output variable X 0 : X evaluated in unconfined fires : correlation parameters ventilation controlled fire Ventilation factor, Heat Release Rate (HRR)

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AN OPERATIVE MODEL: CFAST Equations mass equation pressure equation energy equation volume equationdensity equationtemperature equation

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AN OPERATIVE MODEL: CFAST Inputs Geometry (compartment dimension, ventilation surface, etc.) Material properties (thermal conductivities, etc.) Fire geometry and position HRR vs. time curve Outputs Average temperature in both layers height of layer interfacies O 2 concentration CO concentration visibility index mass and enthalpy exchange rates

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A NUMERICAL MODEL: FDS (Fire Dynamics Simulator) Both confined and unconfined fires Rate of Heat Release (HRR) not depending on O 2 concentration Hypotheses Equations Mass conservation Momentum conservation (three scalar equations) Constitutive law (nine scalar equations) Energy conservation Chemical species conservation

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Inputs Geometry (compartment dimension, ventilation surface, etc.) Material properties (thermal conductivities, etc.) Position and characteristics of ignition sources Rate of Heat Release (HRR): depends on fuel and combustion conditions Outputs Pressure, temperature, velocity and chemical species concentrations as a function of time and space Fluxes and exchange rates A NUMERICAL MODEL: FDS (Fire Dynamics Simulator)

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COMPUTATIONAL DOMAIN (D.M. 16/2/1982 All.I – act. 87) Plan Cross Section North View South View

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COMPUTATIONAL DOMAIN (D.M. 16/2/1982 All.I – act. 87) Geometry Two compartments Ventilation surfaces (2 windows + 1 external door + 1 internal door) Material properties Concrete walls ( = 2100 kg m -3 ; c p = 0.88 kJ kg -1 K -1 ; k T = 1 W m -1 K -1 ) Fire geometry and position 7 cellulosic material stacks Heat Release Rate (HRR): depends on fuel and combustion conditions

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CFAST NUMERICAL RUNS t3t3 HRR [=] MW t [=] s t2t2 t1t1 t0t0 Runs 0.0029 kW s -2 2 0.0049 kW s -2 3 0.0069 kW s -2 4 0.009 kW s -2 5 0.011 kW s -2 6 0.02 kW s -2 HRR max (MW)27.5532.8336.9040.2242.9752.39 t 0 (s)000000 t 1 (s)308025852300211019751620 t 2 (s)924077556900633059254860 t 3 (s)12320103409200844079006480 Run 1: sensitivity analysis on the role of

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A TYPICAL CFAST OUTPUT WINDOW Values Profiles

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= 0.0069 kW s -2 = 0.02 kW s -2 = 0.011 kW s -2 = 0.009 kW s -2

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OUTPUTS OF CFAST RUN 1 Run 1 0.0029 kW s -2 2 0.0049 kW s -2 3 0.0069 kW s -2 4 0.009 kW s -2 5 0.011 kW s -2 6 0.02 kW s -2 h 1 (m)1.21 h 2 (m)0.890.880.870.86 Tu 1 (°C)670654643636630610 Tl 1 (°C)585567554546538514 Tu 2 (°C)289282278275272265 Tl 2 (°C)616059 58.758 h 1 : interfacies height in compartment 1 h 2 : interfacies height in compartment 2 Tu 1 : maximum temperature in the upper layer in compartment 1 Tl 1 : maximum temperature in the lower layer in compartment 1 Tu 2 : maximum temperature in the upper layer in compartment 2 Tl 2 : maximum temperature in the lower layer in compartment 2

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CFAST NUMERICAL RUNS Run 2: sensitivity analysis on the role of ventilation factor

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OUTPUTS OF CFAST RUN 2 Run 2 ( 6 = 0.02) Vf 1 0.031 Vf 0.034 Vf 0.0366 Vf 0.046 t 600 (min)77.856.246.328.1 h 1 (m)1.21 1.221.27 h 2 (m)0.860.920.991.11 Tu 1 (°C)610665704813 Tl 1 (°C)514564596707 Tu 2 (°C)265271273282 Tl 2 (°C)58545044 t 600 : t corresponding to T u = 600 °C

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FDS NUMERICAL RUNS Operative assumptions Distributed parameters model Fire load can be splitted! 7 stacks with HRR = HRR max / 7 Fire starts from stack 1 Each stack burns when T ≥ 200°C (ignition temperature) Run1: without sprinklersRun 2: with sprinklers

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OUTPUTS OF FDS RUN 1 Ceiling temperature Ceiling temperature vs. time t (T 1max ) = 338 s Ceiling temperature distribution at t = 338 s

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OUTPUTS OF FDS RUN 1 Smoke propagation: even though at t = 180 s only one stack burns, smoke invades both the compartments.

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FDS NUMERICAL RUN 2 Sprinklers lay-out Operating pressure: 0.483 bar K: 79 l min -1 bar -1/2 Activation temperature: 74°C RTI (Response Time Index): 110 (m·s) 1/2 Sprinklers characteristics

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OUTPUTS OF FDS RUN 2 Ceiling temperature Tc1 Tc4 Tc7 Synoptic

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OUTPUTS OF FDS RUN 2 Smoke propagation and sprinkler activation: the first sprinkler activates at t = 111.6 s… … and the last one at t = 330 s

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CONCLUSIONS… Zone models are very sensitive to ventilation factor and HRR vs. time curve (controlling parameters): they are quick and simple Field models allow a more realistic and flexible problem description: accurate input estimation is required and simulations are very time expensive T vs. t curves yielded by the two models are different but similarly shaped … AND FURTHER INVESTIGATIONS A set of numerical runs has to be carried out in order to gain a deeper insight in T vs. t curves A comparison between model prediction and deterministic approach results can be performed

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