Toward predictive simulations of pool fires in mechanicallyventilated compartments

S. Suard a,b,n, M. Forestier a, S. Vaux a,b

a Institut de Radioprotection et de Sûreté Nucléaire (IRSN), Laboratoire de l'Incendie et des Explosions (LIE), BP 3, 13115 St Paul-Lez-Durance Cedex, Franceb ETIC Laboratory, IRSN-CNRS-UAM(I, II), 5, Rue Enrico Fermi, 13453 Marseille Cedex 13, France

a r t i c l e i n f o

Article history:Received 5 December 2012Received in revised form27 May 2013Accepted 4 August 2013

Keywords:Predictive simulationsCompartment firesUnder-ventilated firesCFD model

a b s t r a c t

The objective of this work is to propose an effective modeling to perform predictive simulations of poolfires in mechanically ventilated compartments, representative of a nuclear installation. These predictivesimulations have been conducted using original boundary conditions (BCs) for the fuel mass loss rate andthe ventilation mass flow rate, which depend on the surrounding environment. To validate the proposedmodeling, the specific BCs were implemented in the ISIS computational fluid dynamics (CFD) tool,developed at IRSN, and three fire tests of the PRISME-Door experimental campaign were simulated. Theyinvolved a hydrogenated tetrapropylene (HTP) pool fire in a confined room linked to another one by adoorway; the two rooms being connected to a mechanical ventilation system. The three fire scenariosoffer different pool fire areas (0.4 and 1 m2) and air change rates (1.5 and 4.7 h�1). For the one squaremeter pool fire test, the study presents, in detail, the effects of the boundary conditions modeling.The influence of the ventilation and fuel BCs is analyzed using either fixed value, or variable, function ofthe surrounding environment, determined by a Bernoulli formulation for the ventilation mass flow rateand by the Peatross and Beyler correlation for the fuel mass loss rate. The results indicate that a fullcoupling between these two BCs is crucial to correctly predict the main parameters of a fire scenario asfire duration, temperature and oxygen fields, over- and under-pressure peaks in the fire compartment.Variable BCs for ventilation and fuel rates were afterward both used to predictively simulate the fire testswith a pool surface area of 0.4 m2. The predicted results are in good agreement with measurementssignifying that the model allows to catch the main patterns characteristic of an under-ventilated fire.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. General context and motivations

One of the aims of fire safety engineers is definitely to performpredictive simulations of complex fire scenarios. In accordance withthe terminology used in the fire community, the term “predictive”simply means that the user must only specify the configurationstudied, namely the geometry of the fire compartment, the wallthermo-physical properties, the nominal level of the mechanicalventilation system and the fuel available. Technically, to conduct suchnumerical studies, the boundary conditions describing the timevariation of the fuel mass loss rate as well as of the mass flow ratethrough the ventilation system must be accurately described andcoupled to the system of equations solved within the computationaldomain. Therefore, these boundary conditions are not fixed but are

updated during the simulation. The present paper deals with thistopic and is part of an effort that is underway at the French Institutde Radioprotection et de Sûreté Nucléaire (IRSN) to performpredictive fire simulations in confined and mechanically ventilatedcompartments. The first step of this ambitious project is to simplifyas far as possible the complexity of the scenario while maintainingthe same phenomenology as observed in typical industrial fires.In this objective, the numerical studies presented here concern onlypool fires inside a sealed compartment equipped with a mechanicalventilation network. This configuration is certainly the simplestconcerning the phase change process modeling as well as thecombustion phenomenon. However, the wide variety of liquidsallows to illustrate some behaviors in terms of fire power, gastemperature, radiative heat flux, which are close to those encoun-tered in the case of real fires.

Concerning the prediction of the fuel mass loss rate boundarycondition, several methods are beginning to be used in fire safetystudies. The simplest is to set the fuel mass loss rate to a constantvalue. In this regard, a practical way to determine the mass loss rateof large pool fires was first described by [30] and then by [5] where itwas shown that the fuel mass loss rate in an open-atmosphere

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n Corresponding author at: Institut de Radioprotection et de Sûreté Nucléaire(IRSN), Laboratoire de l'Incendie et des Explosions (LIE), BP 3, 13115 St Paul-Lez-Durance Cedex, France. Tel.: +33 442199265, fax: +33 442199161.

E-mail address: sylvain.suard@irsn.fr (S. Suard).

Fire Safety Journal 61 (2013) 54–64

system can be estimated with a simple correlation that only requiresthe knowledge of hydrocarbon properties. The second stage in firebehavior modeling involves correlations or empirical methods tocorrect the imposed mass loss rate value function on ambientconditions, namely oxygen concentration. In that context, the corre-lation, obtained from a steady-state combustion regime by Peatrossand Beyler [17], provides fuel mass loss rate against oxygen con-centration measured at the flame base for large-scale fire compart-ments. The next step concerns global and analytical formulations ofthe fuel mass loss rate and a first attempt can be found in [9] where aglobal modeling was proposed to determine the fuel mass loss rate infree atmosphere whatever may the pool fire diameter be. Based onthis modeling which deals with the burning rate in an open-atmo-sphere, a theoretical model presented in [19,29] includes fuelresponse to vitiated air along with burning enhancement due tohot gases and confinement. Validation of this approach has only beenconcerned about small-scale heptane pool fire experiments. Morerecently a theoretical formulation predicting the rate of vaporizationof large pool fires in confined environment was developed in [14,28].Based on an energy balance equation at the pool fire surface, thesestudies have focused on the determination of the total heat fluxcomponents on the pool for under-ventilated fires in a closedenvironment taking into account the air vitiation effect. The morecomplex modeling concerns the complete coupling between theliquid/solid and gas phases. Only few predictive CFD studies [16,25]have been published, in which the burning rates are adequatelyreproduced in the wide range from small to large pool sizes, in freeatmosphere. Therefore, no predictive fire simulations in confinedcompartments, using this method, have been reported yet. Due tothe great complexity of this full coupling modeling, specially for largescale fires, one of the objectives of this study is to test a compromiseapproach, based on a simple correlation [17].

The ventilation mass flow rate boundary conditions can also betreated by different ways. First, the nominal mass flow rate at inletand (or) exhaust branches without any coupling with the fire

growth can be imposed. In this case an air leakage is often addedto the enclosure for ensuring mass balance equation. Second, aboundary condition as a generalized Bernoulli equation may beused to couple the mass flow rate variation to the rising pressureinside the compartment, due to the fire growth. This modeling wasalready applied for zone fire simulations in mechanically venti-lated compartments and numerical results were in good agree-ment with measurements [27]. More recently, this method hasbeen implemented with success in the ISIS fire code anda validation was performed on a pool fire located in a mechanicallyventilated compartment [26]. This approach, also known as HVACnetwork modeling, gave encouraging results in [8] for fire simula-tions in confined spaces but still needs to be further consolidatedand expanded to fire problems in severe confined environments. Itis one of the aims of the present study.

Based on these literature findings, it appears that few researchworks deal with the coupling effect of the fuel mass loss rateand ventilation mass flow rate on the fire scenario. Therefore,the purpose of this work is to propose and validate a simple CFDmodeling which tends to perform predictive fire simulations inconfined and mechanically ventilated compartments without tak-ing into account a full modeling of the heat feedback to the poolfire surface.

1.2. Outline of the paper

Section 2 presents the physical modeling and numerical meth-ods implemented in the ISIS code [26] and used in this study.Furthermore, this part describes in detail the boundary conditionmodeling for the fuel mass loss rate and the ventilation mass flowrate. Section 3 presents the fire experiment PRISME-Door andspecifies the conditions of three tests involving different airchange rates through the ventilation branches and different poolfire areas. Numerical results are given in Section 4. In the first part,several comparisons are shown between simulations involving

Nomenclature

cp specific heat capacity, J/(kg K)G incident radiation, W/m2

g gravitational accelerationm/s2

gz vertical component of the gravity vector, m/s2

h enthalpy, J/kgI identity tensork turbulent kinetic energy, m2/s2

_m mass loss rate, kg/sp dynamic pressure, PaP turbulent production term, kg/(m s3)Pth thermodynamical pressure, PaPt total pressure, PaQ mass flow rate, kg/sqr radiative heat flux, W/m2

R universal gas constant, J/(mole K)R aerodynamic resistance, m�4

s mass stoichiometric ratioS source termT temperature, Kv velocity vector, m/sW molecular weight, kg/moleX mole fractionY mass fractionz mixture fraction; altitude, m

Greek symbols

Γ turbulent diffusion coefficient, Pa sΔHc heat of combustion, J/kgϵ turbulent dissipation rate, m2/s3

κ absorption coefficient, 1/mμ viscosity, Pa sρ density, kg/m3

s turbulent Prandtl/Schmidt number; Stefan–Boltzmannconstant, W/(m2 K4)

τ Reynolds stress tensor, Paχa combustion efficiency_ω turbulent reaction rate, kg/(m3 s)

Subscripts

0 reference stateb buoyancy effecte effectiveF fuelg gaslam laminarO oxygenr radiatives soott turbulent

S. Suard et al. / Fire Safety Journal 61 (2013) 54–64 55

different levels of complexity for the modeling of the boundaryconditions, where coupled and uncoupled BCs have been tested.The second and last part of Section 4 is an additional validationphase of the proposed modeling. The comparisons are performedwith two supplementary fire tests involving weakly ventilated andunder-ventilated fire scenarios.

2. Description of the fire field model ISIS

This open-source software [10,26], developed by IRSN, is a low-Mach number computational tool dedicated to simulate fire inopen or confined environments.

2.1. General physical modeling

Because fires are described as low speed flows with importantbuoyancy effects, the equations are written for a weakly compres-sible flow, using the low Mach number assumption [12]. For thistype of flows a density change is only due to a temperature or gasmixture variation. The total pressure Pt is then splitted into threeparts following the relation:

Pt ¼ Pth þ pþ ρ0gzz ð1Þwhere the static pressure, defined as the thermodynamic pressurePth, is constant in space, the dynamic pressure p is space and timedependent and the hydrostatic pressure ρ0gzz is function of thealtitude z.

Turbulence is treated by using the Favre-averaging methodwhich is a well-known variant of the Reynolds-Averaged-Navier–Stokes (RANS) modeling [7,15]. Furthermore, as the flow is notstatistically stationary, an unsteady RANS method is used tocapture unsteady phenomena at a time scale larger than thecharacteristic time involved by the time-averaging process. Theturbulent additional terms introduced by this approach anddescribing the Reynolds stress tensor and turbulent scalar fluxesare modeled using the eddy viscosity hypothesis. This results, forthe ISIS code, by using the k�ϵ model which is known as a first-order model with two balance equations. Standard wall functionsare used to take into account the boundary layers as the two-equations closure model is not valid near the wall where viscouseffects are dominant. Turbulent combustion is based on the fastchemistry conserved scalar approach using the mixture fractionand the reaction rate, controlled by the turbulent flow mixing,which is modeled by the Eddy Break-Up (EBU) formulation,modified for non-premixed flames [7]. For this study a one-stepirreversible combustion reaction for an hydrocarbon fuel is con-sidered and involves oxygen and products in the presence of aneutral gas. The soot production and transport can be modeled bydifferent approaches in ISIS but the simplest modeling defining asoot conversion factor in the combustion reaction [16] was usedfor this study. Radiation transfers are treated either by the P-1model [23] or the Finite Volume method [6,20]. Particularlysuitable for modeling environments with very high particle levels,the P-1 model was chosen for simulating fire in this study. Thismethod is nowadays a popular method extensively used in compu-tational fluid dynamics for different and complex situations. A majoradvantage of this model is that it requires little computing time. Thegas absorption coefficient of the mixture depends on gas tempera-ture and composition, according to experimentally established cor-relations [24] for the weighted sum of gray gases model (WSGGM)and the soot absorption coefficient is related to the soot volumefraction according to the Mie theory. The wall conduction is takeninto account through the 1D Fourier's equation. The convective flux isgiven by standard wall laws based on laminar and turbulent Prandtlnumbers [7].

The governing balance equations solved by ISIS for the simula-tion of this sensitivity analysis are the following (usual turbulentnotations have been removed for more compactness):

Mass :∂ρ∂t

þ ∇ � ρvð Þ ¼ 0

Momentum :∂ðρvÞ∂t

þ∇ � ρv � vð Þ ¼ �∇pþ∇ � τð Þ þ ρ�ρ0� �

g

Kinetic energy :∂ðρkÞ∂t

þ ∇ � ρvkð Þ ¼∇ � Γk∇kð Þ þ Sk

Viscous dissipation :∂ðρϵÞ∂t

þ ∇ � ρvϵð Þ ¼∇ � Γeps∇ϵ� �þ Sϵ

Fuel mass fraction :∂ðρYF Þ∂t

þ ∇ � ρvYFð Þ ¼∇ � ΓYF∇YF� �þ SYF

Mixture fraction :∂ðρzÞ∂t

þ ∇ � ρvzð Þ ¼∇ � Γz∇zð Þ

Enthalpy :∂ðρhÞ∂t

þ∇ � ρvhð Þ ¼∇ � Γh∇hð Þ þ Sh

Radiation : ∇ � 13κ

∇G� �

¼ κ G�4sT4� �

ð2Þ

The diffusion coefficient Γϕ is defined by μe=sϕ and the sourceterms Sϕ are listed in Table 1 with other relations and definitions.

2.1.1. Modeling ventilation mass flow rateThe thermodynamic pressure Pth, following the low-Mach

number approximation, is constant in space and may be a functionof time for closed or confined domains. For example, the over-pressure peak, usually observed in confined fire scenarios [18,26],is mainly due to the gas expansion mechanism caused by the heatof combustion release inside the enclosure. Moreover, thesepressure changes are also accompanied by reversal flow rate inthe ventilation network of the compartment. To take into accountthese phenomena as a whole, the thermodynamic pressure isexpressed through the following overall mass balance equation:ZΩ

∂∂t

PthWRT

!þ∑

iQ i ¼ 0 ð3Þ

where Qi represents the mass flow rate of the ventilation networkat each branch i of the compartment. To solve the i+1 unknowns(Pth and Qi), the system described by Eq. (3) is supplemented witha momentum balance equation, following the general Bernoulliformulation, for each branch of the ventilation network:

LiSi

∂Qi

∂t¼ Pt�Pt

ext;i�f ð4Þ

where Pt and Ptext;i represent the total compartment pressure and

the total external pressure respectively located at the extremity ofthe branch i. The head loss f is due to friction and is a function ofan aerodynamic resistance R (f ¼ sgnðQiÞRQ2

i =ρ). The geometricaldimensions Li and Si are respectively the length and the surface ofthe branch i.

Table 1Variables, diffusion coefficients, source terms and main relations used for simulat-ing fire scenarios.

Viscosity: μe ¼ μlam þ μt ; μt ¼ ρcμk2=ϵ

Momentum: τ ¼ μeð∇v þ ∇tv�2=3ð∇ � vÞIÞ�2=3ρkI

State law: ρ¼ ðPthW Þ=ðRTÞ; W�1 ¼∑Nk ¼ 1Yk=Wk ,

Kinetic energy: Sk ¼ P þ Pb�ρϵ; P ¼ τ � ∇v; Pb ¼�μt=ðρsbÞ∇ρ � gViscous dissipation: Sϵ ¼ ϵðc1P þ c3 max ðPb;0Þ�c2ρϵÞ=kFuel mass fraction: SYF ¼ _ωF ; _ωF ¼�CRρðϵ=kÞmin ðYF ; YO=sÞEnthalpy: Sh ¼ dPth=dt�∇ � qr ; qr ¼�1=ð3κÞ∇G; κ¼ κg þ κsTemperature: h¼ cpðT�T0Þ þ χaΔHcYF

Constants: cμ ¼ 0:09; c1 ¼ c3 ¼ 1:44; c2 ¼ 1:92; sk ¼ 1; sϵ ¼ 1:3,CR ¼ 4; sh ¼ sz ¼ sYF ¼ 0:7; sb ¼ 0:7

S. Suard et al. / Fire Safety Journal 61 (2013) 54–6456

2.1.2. Modeling fuel mass loss rateIn case of large pool fire in normal oxygen concentration

(XO2 ¼ 21%), the mass loss rate may be given by the Zabetakis'correlation [30] which had been generalized by Babrauskas [5]with the following expression:

_m″0 ¼ _m″1ð1� exp ð�kβDÞÞ ð5Þwhere _m″1 is a reference mass loss rate (kg/s/m2), D is the pooldiameter (m) and kβ (m�1) is a fuel constant parameter, product ofthe absorption-extinction coefficient k (m�1) by a “mean beamlength corrector” β. More recently, Peatross and Beyler [17] haveperformed compartment fire experiments using a mechanicalventilation network to assess air vitiation effect on the firebehavior. The main results have shown that the fire compartmentcan be assimilated to a well-mixed compartment in terms ofdistribution of oxygen concentration. By contrast, the temperatureprofiles exhibit a constant gradient with respect to compartmentheight. From their experimental results, the authors have thendeveloped a relationship between the fuel mass loss rate and theoxygen concentration at the flame base:

_m″¼ _m″0ð10XO2�1:1Þ ð6Þwhere _m″0 is the mass loss rate of the considered fire in a wellventilated environment and XO2 is the oxygen mole fractionmeasured at the flame base. Moreover, this linear correlation hasbeen recently used in [13] to predict fuel mass loss rate variation ofa HTP pool fire in a large-scale mechanical ventilated compart-ment. It was found that in the absence of external heat flux due togas or wall radiation and provided that the well-mixed compart-ment assumption was valid, the results given by Eq. (6) were ingood agreement with experimental measurements. From thesefindings, Eq. (6) was implemented in ISIS as a boundary conditionfor the fuel mass loss rate and the oxygen mole fraction at theflame base has been adapted to take into account an averagevalue:

_m″¼ _m″0ð10XO2�1:1Þ ð7Þwhere XO2 stands for a volume average of the oxygen mole fractionin a region near the flame and _m″0 is a reference mass loss rategiven by Eq. (5). In the case of a fire with a high ventilation systemin the compartment, the oxygen concentration exhibits a one-layer environment and the determination of the mass loss rateusing Eq. (7) is weakly dependent of how the average oxygenconcentration is computed.

2.2. Numerical methods

The system (2) is composed of two distinct groups of partialdifferential equations: firstly, the balance transport equations forscalar fields and secondly, the hydrodynamic relationships composedof momentum and mass balances, also called Navier–Stokes equa-tions. The first group is discretized in space using the classical finitevolume method in order to obtain numerical schemes that lead to agood compromise between cost and accuracy. The employed time-space discretizations ensure positivity and stability for scalars in sucha way that variables remain bounded within their physical bound-aries. Spatial approximations use second-order upwinding techni-ques to accurately take into account the fast spatial variations ofvariables without stability loss. The hydrodynamic problem isdiscretized in space using a finite element technique that satisfiesthe compatibility properties between velocity and pressure necessaryfor stability. To ensure coherence with the finite volume discretiza-tion, the approximation selected is low-order and non-conforming[21]. Convective terms in momentum equations were approximatedusing an original method allowing the conservation of kinetic energy.This method is particularly efficient for numerical simulations of low

viscosity flows [1]. The time integration is performed using afractional and semi-implicit scheme, solving the balance equationsin sequence from turbulence and combustion equations, to theenergy equation and then to Navier–Stokes equations. On thissubject, a projection method described in [1,4] was implementedto solve both the velocity and dynamic pressure fields.

3. Fire experiments

Three fire tests are chosen from the PRISME-Door experimentalprogramme which was part of the OECD/NEA PRISME1 Project[22]. This international programme consists of a series of fire andsmoke propagation tests in the DIVA IRSN facility, shown in Fig. 1.The main aims are to investigate the heat and smoke propagationthrough openings such as doorways, leaks or ventilation branches,the effect of a ventilation network on the fire growth and theresulting thermal stresses to sensitive safety equipment. Somereferences can be found in [3,11].

The configuration of the studied fire tests has involved tworooms linked by an open door, see Fig. 2 for the schematic of thefire compartments. The dimensions of the identical rooms are5�6�4 m3. The walls were made with concrete blocks of thick-ness 0.3 m and the ceiling was insulated with rock-wool of 50 mmthick. The compartments were connected to a mechanical ventila-tion system with inlet and exhaust branches of surface 0.18 m2

and situated in the upper part of the two rooms, near the ceiling.The pool fire, located at the center of the compartment and placed0.4 m above the floor, was filled with an hydrocarbon namedhydrogenated tetrapropylene (HTP). The locations of the thermo-couple trees and gas sampling measurements are shown in Fig. 2.Gas temperatures were measured with vertical thermocoupletrees, located at different compartment corners and in the centerof the two rooms and of the doorway. Each tree, composed of 18thermocouples (1.5 mm diameter), was installed at vertical spa-cing of 0.25 m. Species concentrations were measured both in onecorner of the two rooms, near the floor and near the ceiling, andnear the pool fire. Wall temperatures and heat fluxes weremeasured on each side of the walls. Following [2], the relativeexperimental measurement uncertainties have been estimated tobe 10% for gas temperature, 2% for oxygen concentration, 10% foradmission flow rates and 30% for pressure (essentially due to therepeatability of the phenomenon). For a complete description ofthe instrumentation, the reader should refer to [11]. The scenariosof the three fire tests in terms of initial ventilation flow rate, poolfire area and aeraulic conditions are described in Tables 2–4.

4. Simulation results

Three tests (PRS-D2, D3, D5) of the PRISME-Door experimentalprogramme are considered to validate the performance of theproposed modeling. The methodology developed to achieve pre-dictive simulations is detailed step by step in the first part of thissection for PRS-D5. First, the effects of modeling the ventilationBCs are presented. The simulations have been performed witha fixed mass flow rate or with a Bernoulli formulation forthe ventilation network, the fuel mass loss rate being fixed to itsexperimental value. Second, the importance of modeling the fuelBCs is addressed. The ventilation flow rates are thus specified witha Bernoulli formulation and the fuel mass loss rate is either fixedto a value which does not include the confinement effects, or

1 The acronym PRISME comes from the French phrase “Propagation d'unIncendie pour des Scénarios Multi-locaux Élémentaires”, which in English can betranslated as “Fire propagation in elementary multi-room scenarios”.

S. Suard et al. / Fire Safety Journal 61 (2013) 54–64 57

determined, according to ambient conditions, with the Peatrossand Beyler correlation [17]. The second part of this section aimsat expanding the validation of the predictive modeling using boththe Bernoulli formulation and the Peatross and Beyler correlation.Two other fire experiments, tests PRS-D2 and PRS-D3, have beenchosen. As shown in Table 2, they involved different pool fire areasand renewal ventilation rates, thus leading respectively to stronglyunder-ventilated and weakly ventilated fires.

4.1. Influence of boundary conditions modeling

4.1.1. Effect of the ventilation boundary conditionTwo types of BCs for the ventilation branches are analyzed and

compared in the framework of the PRS-D5 scenario. Their effect onpressure, gas concentration, intake and exhaust flow rates predic-tions is reported in order to exhibit the most efficient modeling forthe ventilation branches. Table 5 summarizes the BCs used in thetwo simulations compared in this part.

Simulation named Model 1 is undoubtedly the simplest sincethere is no coupling between the fire development and theventilation of the compartment. An inflow boundary condition is

used at the admission branches and the inlet mass flow rate isdetermined from the nominal conditions of the ventilation net-work, given by the air change rate of the scenario. To ensure massconservation, the extraction branches are modeled with an out-flow boundary condition which consists of a mixed conditioncombining an inlet or outlet condition, depending on if the fluidenters or leaves the computational domain. With this type ofmodeling, the domain is considered as an open domain and the

Fig. 1. DIVA facility.

Fig. 2. Schematic of the two rooms, noted L1 and L2, and instrumentation.

Table 2Characteristics of the selected PRISME-Door tests.

Test Pool area (m2) Air change rate (h�1)

PRS-D2 0.4 1.5PRS-D3 0.4 4.7PRS-D5 1 4.7

Table 3Initial total pressure (Pa) in the ventilation network. The total pressure differencebetween L1 and L2 is due to the height of the measurement point (0.8 m for L1 and1.8 m for L2).

Test L1 L2 adm. L1 adm. L2 ext. L1 ext. L2

PRS-D2 �131 �117 490 489 �172 �171PRS-D3 �92 �78 441 439 �518 �514PRS-D5 �97 �83 410 408 �508 �506

Table 4Ventilation network resistivity (m�4).

Test adm. L1 adm. L2 ext. L1 ext. L2

PRS-D2 203,533 222,924 13,444 18,540PRS-D3 17,425 17,524 13,957 14,763PRS-D5 16,576 16,065 13,465 13,824

Table 5Boundary conditions for the two first simulations.

Name Admission Extraction Pool fire

Model 1 fixed to exp. values outflow fixed to exp. valuesModel 2 Bernoulli Bernoulli fixed to exp. values

S. Suard et al. / Fire Safety Journal 61 (2013) 54–6458

thermodynamic or static pressure, with the low-Mach numberformulation, remains constant in time and thus is equal tothe external pressure. As a consequence, the overpressure peaknaturally observed in the growth phase of a confined fire cannotbe exhibited by Model 1. Simulation named Model 2 takes intoaccount, through the coupling of Eqs. (3) and (4), the effects of theincrease of gas temperature due to the heat release and of theincrease of the thermodynamic pressure due to the confinedenvironment and the ventilation network. With this modeling, afixed external pressure and a fixed aeraulic resistance have beendetermined using the nominal conditions of each scenario.For these two approaches, the fuel mass loss rate is determinedfrom the experimental measurements. The experimental errors,noticed in Section 3, have been reported in this part.

Fig. 3 depicts the time evolutions of the relative pressure in thecompartments and mass flow rate at intake branch of the fireroom. The experimental measurements and numerical results ofModel 1 and Model 2 are reported. As noticed above, the relativepressure given by Model 1 is set to zero as the computationaldomain is open and the intake mass flow rate at admission(Fig. 3b) is a constant value given by nominal conditions, beforepool fire ignition. On the other hand, the Bernoulli condition usedin Model 2 yields accurate informations about the pressureevolution in the compartments (Fig. 3a). The predicted overallresponse of the pressure is in good agreement with the measure-ments accounting for measurement uncertainties. The meanpressure level during the quasi-steady state is well reproducedby the simulation and the numerical overpressure peak isalso in agreement with the experimental results, with an

underestimation of the order of 25%. This difference is consideredacceptable in view of the large scatter already observed for thesame type of scenario [2] and also from the fact that a steadyformulation of Eqs. (3) and (4) is considered. Furthermore, theaerodynamic resistance in Eq. (4) is determined before the fireoccurs and is kept constant during the whole simulation. Inaddition to this encouraging model behavior, Fig. 3b showsaccurate results on the intake mass flow rate obtained with Model2. The specific BC used for this simulation enables to catch the flowinversion observed at the beginning of the fire test. The ventilationlevel during the quasi-steady state phase of the fire is also wellrepresented and falls in the range covered by the measurementuncertainties. An accurate prediction of this phenomenon isessential for a fire model because, in such a scenario, somehazardous materials may be transported to other compartmentsvia the reverse flow in the ventilation network.

Fig. 4 presents time evolutions of the exhaust mass flow ratesof room L1 and L2. The results indicate that Model 1 overestimates(resp. underestimates) the exhaust mass flow rate of room L1(resp. L2) while the results of Model 2 are similar to experimentaldata for both the rooms. The solution given by Model 1 in the L1room, shown in Fig. 4a, is approximately twice the experimentalvalue. In room L2, this model exhibits in Fig. 4b a bidirectional flowthrough the exhaust vent with an average value reaching zeroduring the quasi-steady state. The consequences of such differ-ences for the prediction of the ventilation flow rate are notnegligible: the combustion products quantity leaving the fire roomthrough the exhaust is higher in Model 1 than in Model 2, and as aconsequence, the quantity of gas leaving L1 through the doorway

Fig. 3. Time evolutions of the (a) relative pressure and (b) mass flow rate at intake branch of room L1. Comparisons between the experimental value and numerical resultsobtained in Model 1 and Model 2.

Fig. 4. Time evolutions of the mass flow rates at exhaust branch of room (a) L1 and (b) L2. Comparisons between the experimental value and numerical results obtained inModel 1 and Model 2.

S. Suard et al. / Fire Safety Journal 61 (2013) 54–64 59

is less important. The gas temperature in the L2 room determinedby Model 1 is then lower than in Model 2 and the air vitiation islower in Model 1 than in Model 2 for the two rooms, as depicted inFig. 5. The mean value of oxygen concentration during the quasi-steady state, determined at a lower position in L2, in Fig. 5b, andleaving this room through the doorway to feed the pool fire in L1is around 15.2% in Model 1, 13.8% in Model 2, and 13.4% in theexperimental case. From these results, the combustion regime inModel 1 occurs in an oxygen-enriched air of more than 10% incomparison to Model 2.

These simulations clearly show that Model 2 gives satisfactoryresults concerning the calculation of the time evolution of thepressure, ventilation mass flow rates and oxygen concentrations.Thereafter, the Bernoulli formulation will thus be used for thedetermination of the ventilation mass flow rate.

4.1.2. Effect of the fuel mass loss rate boundary conditionEffects of the fuel BC are analyzed and its influence on pressure,

intake mass flow rates, oxygen concentrations and fuel mass lossrate predictions is investigated. Similar to the preceding section,Table 6 summarizes the BCs used for the two simulations com-pared in this part. On the basis of the previous results, theventilation BC for the two cases is fixed and used the Bernoulliequation given by Eq. (4). The fuel mass loss rate BC is eitherdetermined with the Zabetakis' formulation [30] according toEq. (5) or with the Peatross and Beyler's correlation [17] followingEq. (6). More specifically, Model 3, using the Zabetakis' formula-tion, has a constant fuel mass loss rate, whereas the fuel BC inModel 4 is a function of the oxygen concentration near the poolfire. With this modeling, the goal is to relate the dependence of theheat release rate of the fire with the ventilation of the compart-ment since the boundary condition takes into account the vitiationlevel of the surrounding air near the pool.

Fig. 6 shows time evolutions of the fuel mass loss rate predictedin Models 3 and 4 and measured during the fire test. To accountfor the unsteady state phase at the beginning of the fire and tooffset the fact that Zabetakis' formulation used a constant value, ageneral exponentiation function was used. Based on the pool fire

area and on the initial fuel mass, this function was validated onexperimental data obtained in open atmosphere. The time evolu-tion of the fuel mass loss rate determined in Model 3 exhibits, first,this unsteady state phase until t ¼ 205 s and then a constant valueof 41.7 g/s as shown in Fig. 6. Due to the non-coupling to theventilation BC, the mass loss rate is not reduced when the oxygenconcentration decreases near the pool and the fire extinguishesquickly by a lack of fuel. The predicted fire duration is thus lesserthan the experimental value with a relative error around 60%. Thetime evolution of the predicted fuel mass loss rate given by Model4 shows globally a satisfactory agreement with experimental data.The predicted result increases until reaching a peak value and thendecreases significantly due to the oxygen depletion near the poolfire. From t ¼ 400 s, the response reaches a quasi-constant valuecorresponding to the adaptation of the fuel mass loss rate tothe ventilation mass flow rate. This value is very well predicted bythe model and the calculated fire duration is about 1200 s whereasthe fire test duration is about 1300 s. The linear decrease of theexperimental mass loss rate, not predicted by the model, is mainlydue to a reduction of the pool surface area, caused by the thermalexpansion of the bottom of the tank.

Fig. 7 shows time evolutions of the oxygen concentration at theupper location in the L1 room and the lower location in the L2room. The general appearance of the predicted results by Model3 and Model 4, depicted in Fig. 7a, differs considerably. WithModel 3, the oxygen concentration decreases from 21% to 0% at thetime t ¼ 300 s, remains zero until t ¼ 500 s and then increasesfrom this time because fire extinction occurs. The oxygen concen-tration determined with Model 4 decreases around 11% to reach a

Fig. 5. Time evolutions of the oxygen concentration in (a) L1 room at the upper position and (b) L2 room at the lower position. Comparisons between the experimental valueand numerical results obtained with Model 1 and Model 2.

Table 6Boundary condition for the third and fourth simulations.

Name Admission Extraction Pool fire

Model 3 Bernoulli Bernoulli Zabetakis' formulationModel 4 Bernoulli Bernoulli Peatross and Beyler correlation

Fig. 6. Time evolutions of the fuel mass loss rate. Comparisons between theexperimental value and numerical results obtained with Model 3 and Model 4.

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quasi-steady value whereas the measured oxygen concentration isabout 9%. Given that the predicted mass loss rate has a constantvalue from t ¼ 400 s until the extinction, the shape of the oxygenconcentration in Model 4 is also constant and increases only afterthe fire extinction due to the supply of air by the ventilationnetwork. In general, the oxygen concentration predicted by Model4 is higher than that predicted by Model 3 because the mass lossrate of Model 3 is much higher than that of Model 4.

The same comments can be made for the general trends of theoxygen concentration results at the lower location in the L2 room,shown in Fig. 7b. Globally, oxygen levels in the L2 room are moresignificant than in the L1 room and the predicted results arearound 7% in Model 3 and 15% in Model 4 during the steady-state.The measured value being approximately 13% on this state, therelative error is 45% for Model 3 and 15% for Model 4. Thisdifference between the two predicted results is important andhas consequences for the calculation of the entire flow in the fireroom. Indeed, the vitiated air, coming from the L2 room at a lowlocation and going to the L1 room through the doorway, behavesas a volume of ambient gas which will be entrained in the fireplume. The composition of this specific vitiated air is then crucialfor the combustion process and any other quantities.

Time evolutions of the relative pressure in the compartmentare shown in Fig. 8a. The overpressure peak is well reproduced byboth Model 3 and Model 4 with respective computed values of18.5 hPa and 14.5 hPa, close to the experimental (� 16:5 hPa).The time delay between the predicted results and the measureddata, of around 25 s, is mainly due to a steady formulation ofEq. (4) used with a constant aeraulic resistance. The main

difference between the predicted results is observed neart ¼ 300 s when strong pressure oscillations occur in Model 3.Close to that time, Model 3 yields either over- or under-pressurebehavior with respect to the exterior environment. These oscilla-tions are due to the combustion process which seems to stopsuddenly from lack of oxygen near the pool fire as previously seenin Fig. 7a. Time evolutions of the mass flow rate at the intakebranch in the L1 room are shown in Fig. 8b for both calculations.Due to the accurate concordance of the pressure peak in thecompartment in Models 3 and 4, the intake mass flow rate is wellreproduced by the two approaches. The reversal flow at thebeginning of the fire growth period is also well forecast by themodels. As observed for the time evolution of the relativepressure, an oscillatory behavior is obtained for the intake massflow rate predicted in Model 3. These instabilities producea reversal flow which tends to increase the phenomenonuntil the fire extinction. In contrast, the intake mass flow ratepredicted in Model 4 during the quasi-steady state matches theexperimental data.

4.2. Application to other fire scenarios

Due to promising results, the Model 4 is validated on two otherscenarios characterized by a pool fire area of 0.4 m2 and air changerates of 1.5 h�1 for PRS-D2 and 4.7 h�1 for PRS-D3. Using theglobal equivalence ratio (GER) to describe the ventilation condi-tions of these fire tests and whereas PRS-D5 has a “a priori” GER of3.33, PRS-D2 and PRS-D3 have respectively a GER of 8.7 and 2.7.In other words, these last two tests represent fire scenarios

Fig. 7. Time evolutions of the oxygen concentration in (a) L1 room at the upper position and (b) L2 room at the lower position. Comparisons between the experimental valueand numerical results obtained with Model 3 and Model 4.

Fig. 8. Time evolutions of the (a) relative pressure and (b) mass flow rate at intake branch of room L1. Comparisons between the experimental value and numerical resultsobtained with Model 3 and Model 4.

S. Suard et al. / Fire Safety Journal 61 (2013) 54–64 61

in strongly under-ventilated (PRS-D2) and weakly ventilated (PRS-D3) environment conditions.

4.2.1. Mass loss rate predictionFig. 9 shows the time evolution of the measured and predicted

mass loss rate for PRS-D2 and PRS-D3. From these results, the twosimulations underestimate the peak value of the fuel mass loss rateby 20%. Two main reasons can be given to explain this discrepancy.On one hand, at the beginning of the fire, the generic curve, used tosimulate the open mass loss rate, gives lower values than thosemeasured during PRS-D2 and PRS-D3. On the other hand, thecalculated average value of the oxygen concentration near the pool,

used in Eq. (6), decreases relatively quickly and thus tends todecrease the predicted confined mass loss rate. Extinction of thefires occurs in PRS-D2 using a critical mass loss rate of 10 g/s/m2 andin PRS-D3 due to the total fuel mass consumption. The fire durationis obtained with a relative error of less than 20% and the shapes ofthe two numerical curves reproduce quite correctly the measuredvariations for the two tests.

4.2.2. Oxygen concentration predictionFig. 10 shows the time evolutions of the measured and predicted

oxygen concentration at the upper position in the L1 room for PRS-D2and PRS-D3. Globally, the numerical results are close to the

Fig. 9. Time evolutions of the measured and predicted fuel mass loss rate for (a) PRS-D2 and (b) PRS-D3.

Fig. 10. Time evolutions of the measured and predicted oxygen concentration in high position in L1 room for (a) PRS-D2 and (b) PRS-D3.

Fig. 11. Time evolutions of the measured and predicted relative pressure for (a) PRS-D2 and (b) PRS-D3.

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measurements. The overestimation of the calculated oxygen concen-tration around t ¼ 350 s is principally due to the underestimation ofthe fuel mass loss rate by the boundary conditions modeling. After thefire growth phase, when the smoke and combustion products fill thecompartment, the oxygen level is correctly determined by the model.

4.2.3. Aeraulic predictionFigs. 11 and 12 respectively compare the time evolutions of the

predicted and measured values of the relative pressure and intakemass flow rate for fire tests PRS-D2 and PRS-D3. Globally, therelative pressure during the whole fire duration is correctlysimulated for the two tests. The predicted overpressure peakduring the unsteady phase is underestimated for PRS-D2 but isin good agreement with measurements for PRS-D3. The quasi-stationary phase is also well reproduced for the two tests.Concerning the intake mass loss rate depicted in Fig. 12, thebeginning of the fire is, once again, much more difficult to simulatethan the quasi-steady period. The reversal flow observed in PRS-D2 could not have been determined numerically and differencesbetween predicted and measured values in PRS-D3 are important.The main explanation for these discrepancies is that the intakemass flow rate is fully coupled to the compartment pressure, anddue to the used boundary condition for the fire, also to the fuelmass loss rate.

5. Conclusion

A numerical study has been conducted in order to show thatpredictive simulations of fires in mechanically ventilated compart-ments can be performed using specific boundary conditions forthe ventilation mass flow rate and the fuel mass loss rate. Theventilation BCs, known as the Bernoulli conditions, have beencoupled to the overall mass balance equation to take into accountthe pressure rise in the compartment mainly due to the heatreleased by combustion of the fuel and to the ventilation networkresistance. The fuel mass loss rate BC, based on the Peatross andBeyler correlation, takes into account the air vitiation effect nearthe pool fire by averaging oxygen concentration at the flame base.The model validation has been performed by simulating the threeunder-ventilated fire tests and numerical results are particularlyencouraging since main quantities of interest as gas temperature,oxygen concentration and pressure have been determined withsufficient agreements compared to measurements. It is shown thatthe coupling of these two BCs leads to high-quality resultscompared to those obtained with simpler BCs.

However, two major features described as unsteady combus-tion phases, namely the fire growth and the fire extinction, have

not been addressed in this study. Ignition, flame propagation onthe pool fire and fire growth are clearly out of the scope of thisstudy as they do not involve air vitiation effect. Fire extinction isalso complex and cannot be totally modeled by the Peatross andBeyler correlation as this formulation was established understationary combustion regime. Nevertheless, the modeling ofthese two unsteady combustion phases remains necessary toperform fully predictive simulation and should be the subject offuture studies.

Acknowledgments

The authors wish to thank F. Babik and C. Lapuerta for theirsupport in the development and validation of the ISIS code. Theyalso would like to acknowledge the support of the Office forEconomic Cooperation and Development and of the NuclearEnergy Agency for the PRISME program.

References

[1] G. Ansanay-Alex, F. Babik, J.-C. Latché, D. Vola, An L2-stable approximation ofthe Navier–Stokes convection operator for low-order non-conforming finiteelements, International Journal for Numerical Methods in Fluids 66 (5) (2010)555–580.

[2] L. Audouin, L. Chandra, J.L. Consalvi, L. Gay, E. Gorza, V. Hohm, S. Hostikka,T. Itoh, W. Klein-Hessling, C. Lallemand, T. Magnusson, N. Noterman, J.S. Park,J. Peco, L. Rigollet, S. Suard, P. Van-Hees, Quantifying differences betweencomputational results and measurements in the case of a large-scale well-confined fire scenario, Nuclear Engineering Design 241 (2011) 18–31.

[3] L. Audouin, H. Pretrel, W. Le Saux, Overview of the OECD PRISME project—main experimental results, in: 12th International Seminar on Fire Safety inNuclear Power Plants And Installations (SMIRT 21—Post Conference Seminar),vol. 21, Munich, Germany, 2011.

[4] F. Babik, T. Gallouet, J.-C. Latché, S. Suard, D. Vola, On two fractional step finitevolume and finite element schemes for reactive low Mach number flows, in:The International Symposium on Finite Volumes for Complex Applications IV—Problems and Perspectives, Marrakech, 4–8 July, 2005, pp. 505–514.

[5] V. Babrauskas, Estimating large pool fire burning rates, Fire Technology 19(1983) 251–261.

[6] J.C. Chai, H.S. Lee, S.V. Patankar, Finite volume method for radiation heattransfer, Journal of Thermophysics and Heat Transfer 8 (1994) 419–425.

[7] G. Cox, Combustion Fundamentals of Fire, Academic Press, 1995.[8] J. Floyd, Coupling a network HVAC model to a computational fluid dynamics

model using large eddy simulation. In: Fire Safety Science—Proceedings of the10th International Symposium. International Association for Fire SafetyScience, 2011.

[9] A. Hamins, J.C. Yang, T. Kashiwagi, A Global Model for Predicting the BurningRates of Liquid Pool Fires. Technical Report NISTIR-6381, National Institute ofStandards and Technology, 1999.

[10] C. Lapuerta, S. Suard, F. Babik, L. Rigollet, Validation process of isis cfd softwarefor fire simulation, Nuclear Engineering and Design 253 (2012) 367–373.

[11] W. Le Saux, H. Pretrel, S. Moreau, L. Audouin, The OECD PRISME fire researchproject: experimental results about mass loss rate and soot concentrationin confined mechanically ventilated compartments, in: 11th International

Fig. 12. Time evolutions of the measured and predicted intake mass flow rate in L1 room for (a) PRS-D2 and (b) PRS-D3.

S. Suard et al. / Fire Safety Journal 61 (2013) 54–64 63

Seminar on Fire Safety in Nuclear Power Plants And Installations (SMIRT20—Post Conference Seminar), vol. 20, Helsinki, Finland, 2009.

[12] A. Majda, J. Sethian, The derivation and numerical solution of the equations forzero mach number combustion, Combustion Science and Technology 42(1985) 185–205.

[13] S. Melis, L. Audouin, Effects of vitiation on the heat release rate inmechanically-ventilated compartment fires. In: Fire Safety Science—Proceed-ings of the Ninth International Symposium, vol. 9, International Associationfor Fire Safety Science, 2008, pp. 931–942.

[14] A. Nasr, S. Suard, H. El-Rabii, L. Gay, J.-P. Garo, Fuel mass-loss rate determina-tion in a confined and mechanically ventilated compartment fire using aglobal approach, Combustion Science and Technology 183 (12) (2011)1342–1359.

[15] V. Novozhilov, Computational fluid dynamics modeling of compartment fires,Progress in Energy and Combustion Science 27 (6) (2001) 611–666.

[16] V. Novozhilov, H. Koseki, Cfd prediction of pool fire burning rates and flamefeedback, Combustion Science and Technology 176 (2004) 1283–1307.

[17] M.J. Peatross, C.L. Beyler, Ventilation effects on compartment fire characteriza-tion, in: I.A. for Fire Safety Science (Ed.), International Symposium of FireSafety Science, vol. 5, 1997, pp. 403–414.

[18] H. Pretrel, J.M. Such, Effect of ventilation procedures on the behaviour of a firecompartment scenario, Nuclear Engineering and Design 235 (2005) 2155–2169.

[19] J.G. Quintiere, A.S. Rangwala, A theory for flame extinction based on flametemperature, Fire and Materials 28 (2004) 387–402.

[20] G.D. Raithby, E. HChui, A finite-volume method for predicting a radiant heattransfer in enclosures with participating media, Journal of Heat Transfer(Transactions of the ASME) 112 (1990) 415–423.

[21] R. Rannacher, S. Turek, Simple nonconforming quadrilateral Stokes element,Numerical Methods for Partial Differential Equations 8 (1992) 97–111.

[22] L. Rigollet, N. Noterman, E. Gorza, A. Siccama, J. Peco, T. Ito, M. Rowekamp,A. Bounagui, G. Lamarre, L. Gay, L. Audouin, R. Gonzalez, H. Pretrel, S. Suard,2012. OECD/NEA PRISME Project Application Report. Application Report NEA/CSNI/R(2012)14, NEA/CSNI (OECD).

[23] R. Siegel, J. Howell, Thermal Radiation Heat Transfer, Taylor & Francis, 1992.[24] T.F. Smith, Z.F. Shen, J.N. Friedman, Evaluation of coefficients for the weighted

sum of gray gases model, Journal of Heat Transfer (Transactions of the ASME)104 (1982) 602–608.

[25] A.Y. Snegirev, Statistical modeling of thermal radiation transfer in buoyantturbulent diffusion flames, Combustion and Flame 136 (2004) 51–71.

[26] S. Suard, C. Lapuerta, F. Babik, L. Rigollet, Verification and validation of a CFDmodel for simulations of large-scale compartment fires, Nuclear Engineeringand Design 241 (9) (2011) 3645–3657.

[27] S. Suard, S. Mélis, F. Babik, P. Querre, C. Lapuerta, L. Audouin, L. Rigollet, Statusof IRSN fire codes development and validation, in: 10th International Seminaron Fire Safety in Nuclear Power Plants And Installations (SMIRT 19—PostConference Seminar), vol. 19, Oshawa, Canada, 2007.

[28] S. Suard, A. Nasr, S. Melis, J.P. Garo, H. El-Rabii, L. Gay, L. Rigollet, L. Audouin,Analytical approach for predicting effects of vitiated air on the mass loss rateof large pool fire in confined compartments, in: Fire Safety Science—Proceed-ings of the 10th International Symposium. International Association for FireSafety Science, 2011.

[29] Y. Utiskul, Theoretical and experimental study on fully-developed compart-ment fires, Fire engineering, University of Maryland, USA, 2006.

[30] M.G. Zabetakis, D.S. Burgess, Research on the Hazards Associated with theProduction and Handling of Liquid Hydrogen. Technical Report R.I. 5707,Bureau of Mines, Pittsburgh, 1961.

S. Suard et al. / Fire Safety Journal 61 (2013) 54–6464