Comparison of FDS predictions by different combustion models with measured data for enclosure fires

Fire Safety Journal 45 (2010) 298–313

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Fire Safety Journal journal homepage: www.elsevier.com/locate/firesaf

Comparison of FDS predictions by different combustion models with measured data for enclosure fires D. Yang a,b, L.H. Hu a,n, Y.Q. Jiang a, R. Huo a, S. Zhu a, X.Y. Zhao a a b

State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, China Faculty of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400045, China

a r t i c l e in f o

a b s t r a c t

Article history: Received 15 May 2009 Received in revised form 11 May 2010 Accepted 3 June 2010 Available online 1 July 2010

The performance of mixture fraction models FDS4 and FDS5 is investigated under different global equivalence ratios (GER). Predictions of heat release rate (HRR), upper-layer temperature, and CO yield are compared with measurements considering their sensitivities to the lower limit of fuel, mixing time scale, and turbulence model constants. When using FDS4, the inclusion of an extinction model can result in significant variations in both total and volumetric HRR prediction. When using FDS5, the mixing model constant has significant effects on volumetric HRR prediction. At low GER (o 0.23), the prediction of upper-layer temperature shows dependency on both the lower fuel limit and the mixing model constant, but the predicted temperature is always lower than measured temperature, with deviations in excess of 30%. At higher GER (0.53 o GER o 0.81), the upper-layer temperature prediction shows significant dependency on the mixing model constant but can be over-predicted, with deviations up to 24%. The variations of CO yield prediction with lower fuel limit or with the mixing model constant show an opposite trend to that of upper-layer temperature. Furthermore, the prediction of CO yield shows a much greater dependency on the Smagorinsky constant and on the turbulent Schmidt number than do those of HRR and upper-layer temperature. & 2010 Elsevier Ltd. All rights reserved.

Keywords: FDS Enclosure fire Combustion model Heat release rate CO yield GER

1. Introduction Fire dynamics simulator (FDS) codes, developed by the National Institute of Standards and Technology (NIST), USA, have been widely used in the community of fire simulation. FDS4 is prevalent in both fundamental research areas and practical engineering applications, although FDS5 is being increasingly used by fire researchers and engineers. For turbulence modeling, the large eddy simulation (LES) approach was demonstrated to produce encouraging results and has become the focus of fire modeling in recent years [1–3]. FDS contains LES and uses the classical Smagorinsky model as its sub-grid scale (SGS) model for turbulence modeling [4]. A combustion model is crucial for fire simulation. The eddy break-up (EBU) model [5,6] and the laminar flamelet model [7] are the two most widely used combustion models. The EBU model is widespread in commercial CFD packages due to its simplicity of implementation; however, it may overestimate key parameters such as temperature [8]. Another promising approach is the flamelet approach, which provides the advantage of separating the solution for the turbulent flow and the mixture fields from the

n

Corresponding author. Tel.: +86 551 3606446; fax: + 86 551 3601669. E-mail addresses: [email protected] (D. Yang), [email protected] (L.H. Hu).

0379-7112/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.firesaf.2010.06.002

chemistry solution. The flamelet approach can also include the modeling of transient effects, with the scalar dissipation rate as another variable [9]. The inclusion of the classical flamelet model may raise the computational cost to an undesirable level for typical fire simulation. Thus, the combustion model applicable to fire simulation must not only include the necessary mechanisms to describe the combustion process but also be able to reduce the overall computational expense. The combustion model used by FDS4 is one such model. It is based on the assumption that the combustion is mixing-controlled and that the reaction of fuel and oxygen is infinitely fast [4]. This combustion model uses the single mixture fraction as its conserved scalar and is conventionally called as a mixture fraction model [4]. The concentrations of major species (such as fuel, oxygen, and combustion products) are related to this single mixture fraction variable. Previous studies have indicated that FDS4 with the mixture fraction model obtains encouraging results in certain fire scenarios, e.g., free fire plumes [2,10]. Although promising, the mixture fraction model used by FDS4 still has limitations. Firstly, the combustion chemistry is simplified by FDS4 as an infinitely fast single-step reaction. This could result in the over-prediction of reaction rates and of local temperatures [2,10]. Secondly, the under-ventilated fires are associated with sub-critical oxygen concentrations and consequent flame extinction. However, the state relations for a single

D. Yang et al. / Fire Safety Journal 45 (2010) 298–313

mixture fraction do not account for the possibility of extinction. Thirdly, the mixture fraction model used by FDS4 cannot consider the effects of the ventilation condition on products yields. The yields of partially oxidized products, such as CO, are specified, rather than predicted, by FDS4. In reality, the CO yield is usually not constant but rather a function of the equivalence ratio [11–13]. These limitations motivate the inclusion of a new combustion model into the FDS codes (i.e., FDS5) [14]. The FDS developers carried out a series of validation studies to examine the capabilities of FDS5 for enclosure fire prediction [15,16]. In these studies, the predictions for concentrations of major species (such as CO, O2, and CO2), temperatures and doorway velocities were compared against the NIST reduced scale enclosure (RSE) tests [17,18]. Although the FDS developers conducted many validation works on FDS5, some of the model aspects remain unclear, such as the effects of combustion model constants, the capabilities of the two-step reaction model on overall CO yield prediction, and the quantification of the difference in predicted heat release rate (HRR) between using a single-mixture-fraction model (i.e., FDS4) and using a multiple-mixture-fraction model (i.e., FDS5). The above information is useful for the community of FDS users, thus motivating the studies presented here. To clarify these issues, three different types of combustion models with different model constants are considered in this work: FDS4 (single-step reaction with a single mixture fraction variable), FDS5 (including both a single-step reaction model with two mixture fraction variables and a two-step reaction model with three mixture fraction variables). This study compares several crucial parameter predictions (including heat release rate, upper-layer temperature, and CO yield) by different combustion models with corresponding series of measured data. Heat release rate is a very important parameter in enclosure fire dynamics. The investigation of the capability of FDS for HRR prediction remains limited, especially for under-ventilated fires, where a considerable amount of combustion occurs outside the enclosure via the vents in addition to that inside the enclosure. In this work, the performance on the prediction of HRR is considered under such a condition. The two-step model predictions of upperlayer temperature are also investigated at different global equivalence ratios (GER), including a higher GER that what would indicate under-ventilated fires. The sensitivities of the upperlayer temperature prediction to two important input constants of the current version of FDS are considered. The first one is the flammable fuel concentration limit, which affects the prediction of flame extinction and is not considered by the previous versions of FDS. The second one is the mixing model constant, which affects the mixing rate of fuel and oxygen and consequently the fuel consumption rate. In fundamental combustion studies, mixing rate is usually obtained from empirical models combined with sensitivity calculations [19–21]. The mixing model constant is not universal and has been found to have a significant effect on the evolution of the scalar field [22,23]. These studies indicate that the mixing rate model remains an open issue. Therefore, FDS5 also uses an empirical model to evaluate the mixing time scale, which includes a model constant derived from numerical tests in comparison with flame height correlations [14]. This implies that the flame height in an open environment can be well predicted by using this mixing model constant. However, the effects of the mixing model constant on other crucial parameters of fire dynamics, e.g., temperature and CO yield, were not tested, although they bear further investigation. The prediction of CO production is an important consideration for the two-step reaction scheme of FDS5. In previous validation studies, the CO concentration measured in certain locations in the upper smoke layer was compared with the FDS predictions, such

299

as those by Hu et al. [24] and Floyd and McGrattan [15,16]. However, it should be noted that the local CO concentration is controlled by two mechanisms: the CO yield through combustion and the transportation of the CO species in the smoke flow. In this view, the CO yield within the compartment has been measured to determine the combustion species transported from the compartment into the adjacent spaces [25–27]. However, to our knowledge, there have been no works testing the capability of a two-step reaction model on overall CO yield prediction, which should be considered prior to the local CO concentration. The performance of FDS5 with a two-step reaction model on CO yield prediction is investigated in this work. The measurements from 1/2-scale International Organization for Standards (ISO) 9705 enclosure tests were used as references. The dependency of CO yield prediction on the upper-layer temperature prediction is then further investigated at different equivalence ratios, varying the combustion and SGS model constants.

2. FDS combustion model Combustion models used by FDS have been presented in detail in technical reference guides [4,14] and have been discussed in previous literature [2,10,16]. In this section, only the differences between the combustion model used by FDS4 and those used by FDS5 are presented, with discussion of advantages and limitations of these models. 2.1. Combustion model used by FDS4 The combustion model of FDS4 assumes that fuel and oxidizer burn instantaneously when mixed [4]. A single-step combustion reaction is introduced, with the general form X ð1Þ vF Fuelþ vO O2 - vP,i Products i

where the stoichiometric coefficients for products are either established by using data from bench-scale tests or specified by users. The flame structure is described in terms of the single mixture fraction, which is defined as   sYF  YO YO1 vO MO Z¼ , s¼ ð2Þ vF MF sYFI þYO1 The mixture fraction satisfies the conservation law DZ ¼ rUrDrZ ð3Þ Dt Due to the infinitely fast reaction, the flame surface (flame sheet) is at the locations where fuel and oxidizer vanish simultaneously:

r

zðx,t Þ ¼ zf ,

zst ¼

YO1 þYO1

sYFI

ð4Þ

The mass fraction of oxygen is calculated based on the assumption that fuel and oxygen cannot co-exist: YO ðZ Þ ¼ YO1 ð1Z=Zf Þ, YO ðZ Þ ¼ 0, Z 4Zf

Z o Zf , ð5Þ

The mass fractions of other species are correlated with the mixture fraction through the state relations, which were illustrated by McGrattan [4]. In FDS4, the heat release rate is derived from the oxygen consumption rate [28]: _O q_ ¼ DHO m

ð6Þ

where DHO denotes the heat release rate per unit mass of oxygen _ O is the oxygen consumed, with a default value of 13,100 kJ/kg. m

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consumption rate, as calculated by d YO  2 rZ dZ 2 2

_ O ¼ rD m

ð7Þ

Extinction may occur in an under-ventilated fire. To account for flame extinction, a simplified model derived from the concept of critical adiabatic flame temperature is incorporated in FDS4 [29,30]. This model combines the flame temperature Tst with a critical flame temperature Tc and a lower oxygen mass concentration limit YO2 ,c . Non-flammable (or extinction) conditions correspond to sub-critical flame temperatures (or sub-critical oxygen levels), i.e., Tst oTc or YO2 =YO2 ,c o ðTc T Þ=ðTc T1 Þ, where YO2 and T characterize the oxygen mass fraction and the gas temperature of the oxidizer stream, respectively. There are several obvious limitations of the combustion model used by FDS4. Firstly, the assumption of infinitely fast chemistry has the disadvantage of overestimating several important parameters, e.g., temperature. Secondly, the yields of product species (e.g., CO) are prescribed rather than calculated. Thirdly, the state relations for the single mixture fraction cease being valid under the circumstances of extinction, because the unburned fuel may be mixed with oxygen or other combustion products at those conditions. Lastly, the volumetric HRR is proportional to the gradient of Z across the flame sheet (i.e., interfaces with stoichiometric ratio of fuel to oxygen). Fairly fine grid resolution is necessary to compute the steep gradients of Z [31,32]. Due to the limited computer capability, even the grid size used in some reduced-scale fire scenarios is still too coarse to accurately compute the mixture fraction gradients, thus yielding numerical errors (e.g., ‘‘undershoot’’ [16]). The ‘‘undershoot’’ could redistribute the fuel mass across the flame sheet and result in the inaccuracy of local HRR computation.

2.2. Combustion models used by FDS5 Based on the framework of the mixture fraction approach, FDS5 introduced a two-step reaction scheme to improve its prediction capability for under-ventilated fire [14]. The singlestep reaction scheme is also included in FDS5 but has been significantly improved as compared with those used by FDS4. FDS5 decomposes the single mixture fraction Z into two components: YF Z1 ¼ I YF

ð8Þ

YCO2 WF Z2 ¼ ½xvCO ð1XH Þvs WCO2 YFI

ð9Þ

YFI

(YFI

where is fuel mass fraction at the burner surface would be 1 in the cases without diluent gas species), x denotes the number of carbon atoms in the fuel molecule, and xvCO ð1XH Þvs thus denotes the number of carbon atoms in the fuel molecule that are oxidized. It is indicated that Z ¼Z1 + Z2. Due to decomposition of the mixture fraction, the state relations of FDS5 can include the circumstance of extinction. Z1 is used to track the unburned fuel, as explained in works coauthored by McGrattan [14,33]. Another advantage of this decomposition approach is that there is no need to determine the locations of ‘‘flame sheets’’ or to compute the mixture fraction gradients. The local volumetric HRR is directly computed from the conversion rate of fuel to products; thus, numerical problems such as the ‘‘undershoot’’ could be eliminated [16]. The local heat release rate is computed as [14] _F q_ ¼ DHF m

ð10Þ

_ F is computed as The volumetric fuel consumption rate m   min rYF , srYO2 _F¼ m ð11Þ

t

where t is a mixing time scale and is given by 2=3

t¼

C ðdxdydzÞ DLES

ð12Þ

where C is an empirical model constant that is taken as 0.1 by default [14]. This model constant has a considerable effect on the predictions, which will be discussed in the following sections. Despite these improvements, this single-step reaction scheme still cannot predict the CO production in ventilation-limited fires. A two-step reaction scheme is incorporated by FDS5 to account for CO production in ventilation-limited fires [14,16]: Step 1 : Fuelþ O2 -COþ Other products

ð13Þ

1 O2 -CO2 ð14Þ 2 Eqs. (13) and (14) are rewritten in terms of all of the species:

Step 2 : CO þ

Cx Hy Oz Na Mb þ nO2 O2 -nH2 O H2 O þ ðnuCO þ nCO ÞCO þ nS soot þ nN2 N2 þ nM M

ð15Þ

nuCO



 1 CO þ O2 -nuCO CO2 2

ð16Þ

The stoichiometric coefficient of CO in the first step consists of two components, including the so-called ‘‘well-ventilated’’ stoichiometric coefficient nCO and nuCO , which can potentially be converted to CO2. The first step is a ‘‘fast’’ reaction and occurs as it does for the two-parameter mixture fraction. If fuel, oxygen and CO exist in a grid cell where flammability is viable, step 1 is followed by the instantaneous conversion of CO to CO2 if there is sufficient remaining oxygen and if the upper bound in the volumetric heat release rate has not been reached. Away from the flame (such as within the upper smoke layer), a finite-rate reaction computation is performed to convert CO to CO2: kðTÞ ¼ 2:53  1012 e199:547=RT cm3 =mol s

ð17Þ

For the two-step scheme, three components of the mixture fraction are required: one to account for the amount of unburned fuel, one to account for CO, and one to account for CO2: Z1 ¼

YF YFI

ð18Þ

Z2 ¼

WF YCO ½xð1XH Þvs WCO YFI

ð19Þ

Z3 ¼

YCO2 WF ½xð1XH Þvs WCO2 YFI

ð20Þ

It is indicated that Z¼ Z1 + Z2 + Z3. The following transport equations were derived for these three mixture fraction variables: DZ1 _ 000 ¼ rUDrrZ1 þ m F,1 Dt

ð21Þ 000

_ CO,2 WF m DZ2 _ 000 ¼ rUDrrZ2 m F,1 þ Dt vCO WCO

ð22Þ

_ 000 WF m DZ3 CO,2 ¼ rUDrrZ3  Dt vCO WCO

ð23Þ

For both the single-step reaction and the two-step reaction model of FDS5, an empirical model is used to decide whether or not step 1, the oxidation of fuel to products, can occur. At each time step of the calculation, state relations are used to extract the individual species mass fractions from the multiple mixture fraction variables. The extinction model is then used to decide

D. Yang et al. / Fire Safety Journal 45 (2010) 298–313

whether the reaction of fuel can occur. The empirical extinction model used by FDS5 is also derived from the concept of critical adiabatic flame temperature [14]; however, for the current version of FDS5, both the lower mass concentration limit of oxygen, YO2 ,c , and that of fuel, Yf,c, are used to evaluate whether the local environment can support the combustion. Non-flammable (or extinction) conditions correspond to sub-critical oxygen level or sub-critical fuel level, i.e., YO2 =YO2 ,c o   ðTc To Þ=ðTc T1 Þ or Yf =Yf ,c o Tc Tf =ðTc T1 Þ, where YO2 and Yf characterize the oxygen concentration level for the oxidizer stream and the fuel concentration level for the fuel stream, with To and Tf characterizing the temperatures of the oxidizer stream and the fuel stream, respectively. Besides the differences in physical effects on flame extinction, there are also differences in numerical implementation between the extinction model of FDS4 and that of FDS5. The characterized oxygen mass concentration (i.e., YO2 ) for a particular cell is assumed by FDS4 to be the one in the grid cell with the lowest fuel concentration level from among the current grid cell and its neighboring cells. However, these gas species concentrations may not be reliably calculated because the state relation of FDS4 excludes the circumstance of extinction. However, for any particular grid cell, the extinction model of FDS5 can directly take the characterized oxygen mass concentration, YO2 , and the characterized fuel mass concentration, Yf , as their maximum corresponding values around its neighboring cells. In other words, the extinction model of FDS5 presumes that ignition will always occur for a particular grid cell if there is adequate oxygen and fuel supply from any of its neighboring cells. At the grid cell where reaction occurs, combustion depletes either fuel or oxygen, combined with the conversion of Z1 to Z2. These mixture fractions are updated according to the transport equations (e.g (e.g., Eqs. (21)–(23) for the two-step reaction), at which point, the next time step of calculation continues. Additional details about the combustion model used by FDS5 are given by Floyd and McGrattan [16].

3. Experimental data Predictions were compared against three sets of enclosure fire experiments. The first set of experiments was conducted by NIST in a 2/5-reduced-scale International Organization for Standards (ISO) 9705 room [17] (RSE for simplicity). The internal dimensions of the RSE enclosure were 0.95 m wide  1.42 m long  0.98 m tall. The standard opening was 0.81 m high  0.48 m wide, and centered horizontally on the 0.95-m front wall. Additional details on the RSE experiments are given by Bundy et al. [17]. The measured data of total HRR from Test #3 were used as the input HRR in FDS simulations. The differences in total and volumetric HRR predictions between different combustion models using different model constants were investigated. Lee’s tests measured the HRR inside the enclosure and the vertical temperature distributions [34,35]. The enclosure of Tests #1–4 and 9–12 in Lee’s tests [35] was cubic with dimensions of 0.5 m on each side. Both RSE Test #3 [17] and Lee’s Tests #1–4 and #9–12 [35] were used to investigate the capability of the twostep reaction model on upper-layer temperature prediction. In this work, the global equivalence ratio (GER) [36,37] is used to characterize the ventilation conditions:   _ f= m _ a YO2 ,a ð24Þ f ¼ sm where s is the stoichiometric ratio of oxygen to fuel for complete _a reaction, YO2 ,a is the oxygen mass fraction in ambient air, and m represents the mass pffiffiffiffi inflow rate, which is based on the empirical correlation 0:5A H kg=s [38] in this work. The GER concept has been used in the representation of the combustion condition for

301

enclosure fires in many previous studies [3,12,13,34]. Some researchers have proposed that the GER concept needs to be modified to incorporate the temperature-dependent kinetics and the enclosure flow patterns [18,26]. Although the mass inflow rate pffiffiffiffi can be estimated by FDS, the approximation of 0:5A H kg=s is used in this work to calculate GER, with the lack of prior knowledge of temperature or detailed flow patterns before simulation. In this work, fires with GER of less than unity were identified as ventilation-limited fires [17], and those with GER larger than unity were identified as under-ventilated fires. The RSE experiments have GER values from 0.1 to 0.82, whereas Lee’s experiments represent under-ventilated fires with GER from 1.1 to 6.1 [34,35]. In Lee’s tests, the supplied fuel cannot be entirely consumed inside the enclosure due to oxygen deficiency. The excess fuel exits the enclosure through the opening, with a significant portion of combustion heat being released in the form of external flame. This indicates that the total HRR could be divided into the HRR inside the enclosure and that outside the enclosure. Under such a condition, the prediction of upper-layer temperature can only be done in the context that the HRR inside the enclosure is well predicted. Lee and his co-workers proposed a simple but effective approach to distinguish the HRR inside the enclosure from the total HRR by using the oxygen consumption calorimetry method [34,35,39], with the measurement uncertainty reported to be approximately 10% [34,40]. Additional details about the measurement approach were reported by Lee [34]. These measured data were used to investigate the performance of FDS5 with a two-step reaction scheme on the prediction of HRR inside the enclosure at higher GER. Wieczorek and his co-workers measured the yields of carboncontaining species in the Virginia Tech 1/2-scale ISO 9705 compartment under different ventilation conditions [25,26]. The interior compartment dimensions were 1.17 m wide  1.78 m deep  1.17 m high. The doorway height was 0.82 m with widths of 0.165, 0.33, or 0.66 m. The measured data from these experiments were used to investigate the capability of FDS5 on CO yield prediction.

4. FDS simulation setup 4.1. Simulation scenarios Four sets of FDS scenarios were established in this work. The first set of scenarios was used to investigate the differences in both total and local volumetric HRR predictions by using different combustion models combined with different model constants. The effects of the individual extinction models on HRR prediction were also discussed. The second set of scenarios was used to investigate the upperlayer temperature prediction by the two-step reaction model. Both ventilation-limited (GERo1) and the under-ventilated (GER41) fires were considered. For the ventilation-limited fires, the sensitivities of upper-layer temperature prediction to the lower limit of fuel and mixing model constant were investigated. For the under-ventilated fires with higher GER, the upper-layer temperature predictions were compared with measured data combined with the discussion of the prediction of HRR inside the enclosure. The third set of scenarios was used to investigate the performance of the two-step reaction model at CO yield prediction. The sensitivities of CO yield prediction to the lower flammable limit fuel mass fraction and to the mixing model constant were also investigated.

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D. Yang et al. / Fire Safety Journal 45 (2010) 298–313

Table 1 Summary of simulation scenarios and corresponding tests. Scenario no.

Combustion model

Input parametera

Test name

Scenario description

Parameters investigated

1

For FDS5 Y_F_LFL¼ 0.028 or 0.0; C_EDC ¼0.1; SOOT_YIELD ¼0.015

RSE Test#3

Y_F_LFL¼0. C_EDC ¼ 0.1; CO_YIELD ¼0.002; SOOT_YIELD ¼0.024

Lee’s Test#1–4; #9–12

3

FDS5 two-step reaction

Y_F_LFL¼0.032 or 0.0; C_EDC¼ 0.1 or 0.45; CO_YIELD ¼0.002; SOOT_YIELD ¼0.024

VT 1/2-scale ISO 9705

4

FDS5 two-step reaction

Y_F_LFL¼0.028 or 0.0; C_EDC¼ 0.1 or 0.45; CO_YIELD ¼0.0; SOOT_YIELD ¼0.015

RSE

Fuel is natural gas; HRR are 75, 116, 180, 265 and 410 kW; Vent dimension is 0.48  0.81 m2 Fuel is propane; HRR are 30, 40, 50, 60 kW; vent dimensions are 0.2  0.2 m2 (#1–4), 0.075  0.2 m2 (#9–12) Fuel is propane; HRR are 107, 204 kW for the vent width 0.33 m; 204, 266 and 379 kW for the vent width 0.165 m Fuel is natural gas; HRR are 75, 150, 180, 265, 410, 500 and 600 kW; vent dimension is 0.48  0.81 m2

Total HRR; upper-layer temperature

2

FDS4; FDS4 without extinction model; FDS5 single-step reaction; FDS5 two-step reaction FDS5 two-step reaction

HRR inside the enclosure; upper-layer temperature

CO yield

CO yield; upper-layer temperature

a Y_F_LFL was derived from the volume concentration flammability limit, as given by the Ref [30]. For natural gas, it was taken as that of methane for approximation. CO_YIELD of the two-step reaction scheme represents the ‘‘well-ventilated’’ CO yield given by the Ref [41].

The fourth set of scenarios was similar to the first one (RSE tests) but with a different focus, investigating the dependency of CO yield prediction on temperature. Table 1 summarizes the simulation scenarios, corresponding tests, combustion models with the important input parameters, and the investigated parameters. 4.2. Numerical mesh It is suggested by McGrattan et al. [42] that the mesh size must be no larger than 0.1D* to guarantee the reliable operation of FDS. D* represents the characteristic length scale for a fire plume and is written as !2=5 Q_ D* ¼ ð25Þ r1 T1 cp g 1=2 The value of 0.1D* has also been confirmed by Merci’s study [43] to be reasonable for FDS simulation. In this study, for the simulations corresponding to the RSE tests (i.e., Scenarios #1 and 4), the computational domain and grid system were similar to those used by Floyd and McGrattan [15], which were 0.95  2.44  1.50 m3 with 40  100  72 cells. Grid sensitivity studies on this grid system have been performed, as reported by Floyd and McGrattan [15]. For the smallest fire size in Lee’s tests, 30 kW, the value of 0.1D* is about 0.025 m. To avoid treating the vents as pressure boundaries, The computational domain was extended to 1.0  0.5  1.0 m3. For the simulations corresponding to the Virginia Tech 1/2-scale ISO 9705 compartment, the computational domain size was 1.17  2.78  1.69 m3. Grid sensitivity studies were carried out for the two scenarios, as shown in Fig. 1. Finally, in this work, a more restrictive grid system than that used by Floyd and McGrattan [15], i.e., uniform grid cells with a size of 0.01  0.01  0.01 m3, was used for the simulations corresponding to Lee’s tests (e.g., Scenario #2), and a grid with cells of 0.02  0.02  0.023 m3 was used for the Virginia Tech tests. As shown in Fig. 1, the grid sizes used in this work were demonstrated to be appropriate. 4.3. Other simulation details The Smagorinsky constant Cs, turbulent Prandtl number Pr and turbulent Schmidt number Sc are related to the SGS turbulence

modeling and are assumed to be constant in a given scenario. The default values of Cs, Pr, and Sc are suggested to be 0.2, 0.5, and 0.5, respectively. Previous study [44] indicated that the results vary significantly with the choice of Pr and Sc for the free-reacting buoyant plumes. In this work, the effects of Cs, Pr and Sc on enclosure fire predictions were also investigated. Radiation was computed by a finite volume method combined with a gray gas approach, which is the default model of FDS. The absorption coefficients were computed using RADCAL [45]. The readers are referred to the technical reference guide for more details [14]. For both the front and the back solid surface, the thermal boundary conditions were treated by the combination of convective heat transfer and radiation heat transfer to the solid boundaries. The thermal properties of walls and ceilings were set by referring to the corresponding experimental reports [17,27,34], which have been demonstrated by the previous studies [15] to have little impact on the quasi-steady predictions. The velocity condition at the solid surface was treated as default conditions of FDS [14], i.e., ‘‘half-slip’’ condition; the tangential components of velocity were assumed to be one-half of the values corresponding to the first layer of gas phase grid cells above the solid surface. Each of the simulation scenarios was simulated for 300 s using an acceleration approach [16]. All of the predictions in this work were taken as time-averaged results during the quasi-steady burning state.

5. Results and discussion 5.1. Heat release rate Scenario #1 was set up to test different combustion models of FDS (including FDS4, FDS5 with a single-step reaction model and FDS5 with a two-step reaction model) on HRR prediction to observe the effects of their individual extinction models and of the mixing model constants. The limiting critical oxygen volume fraction at the ambient temperature was set to be 0.15 for both the extinction model of FDS4 and that of FDS5. FDS5 accounts for the effects of fuel mass fraction on flame extinction. In this section, both the case considering the lower fuel limit (Y_F_LFL¼0.028, derived from the volume concentration flammability limit of methane, as reported by Beyler [30]) and that

D. Yang et al. / Fire Safety Journal 45 (2010) 298–313

303

0.50 1cm∗1cm∗1cm (This work)

0.45

0.7cm∗0.7cm∗0.7cm 2cm∗2cm∗2cm

0.40

Height (m)

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0

100

200

300

400

500

600

700

800

900 1000 1100 1200

Temperature (°C) 700 2cm∗2.3cm∗2.3cm (This work) 1.3cm∗1.5cm∗1.5cm

600

4cm∗4.6cm∗4.6cm

Temperature (°C)

500

400

300

200

100

0 0.3

0.4

0.5

0.6 0.7 Height (m)

0.8

0.9

1.0

Fig. 1. Grid sensitivity studies for Lee’s tests and Virginia Tech tests using temperature. (a) Lee’s tests (30 kW, Opening Width 0.2 m, back corner thermocouple tree) and (b) Virginia Tech tests (107 kW, Opening Width 0.33 m, back wall thermocouple tree).

without considering the lower fuel limit (i.e., Y_F_LFL¼0.0) were included in these two-step reaction simulations. To investigate the effects of the mixing model constant on the HRR prediction, the mixing model constant for FDS5 was specified as either the default value of 0.1 or a larger value of 0.45. The influences of SGS turbulence model parameters (i.e., Cs, Pr, and Sc) on the total HRR predictions were also tested. The measured total HRR from Test #3 of RSE experiments [17] were used as references, with values of 75, 115, 180, 265, and 410 kW with uncertainty reported by Bundy et al. [17]. The fire sizes were prescribed to be similar to the measurements in the FDS simulations.

Firstly, the influences of SGS turbulence model parameters on the predictions were investigated. Table 2 presents the total HRR predictions (i.e., HRR integrated in the computational domain) obtained from different turbulence model parameters for the 410-kW fire, by varying one of these three parameters while maintaining the other two at their default values. These turbulent model parameters were selected with reference to previous works that have simulated different types of turbulent flows [46–48]. In these simulations, the two-step reaction model with a default mixing model constant (i.e., 0.1) was used. The maximum relative deviation was less than 10%, which occurred in the case with a

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Table 2 Summary of predictions obtained from different values of SGS model constants for a 410-kW RSE fire.

Cs ¼ 0.1 Cs ¼ 0.15 Cs ¼ 0.2 (default) Cs ¼ 0.25

Pr ¼ 0.3 Pr ¼ 0.4 Pr ¼ 0.5 (default) Pr ¼ 0.7

Sc ¼0.4 Sc ¼0.5 (default) Sc ¼0.7 Sc ¼1.0

HRR

Rear upper layer temperature Pr ¼0.5 (default)

Front upper layer temperature Sc ¼0.5 (default)

CO yield

366 385 391 395

1072 1119 1100 1099

1193 1195 1190 1194

0.170 0.130 0.112 0.108

Cs ¼0.2 (Default)

Sc ¼0.5 (Default)

1092 1094 1100 1098

1198 1196 1190 1190

Cs ¼0.2 (default)

Pr ¼ 0.5 (default)

1105 1100 1074 1050

1202 1190 1182 1163

385 389 391 393

396 391 379 365

0.112 0.113 0.112 0.112

0.104 0.112 0.134 0.178

Table 3 Summary of predictions of total HRR by different combustion models for the RSE tests. Measured total HRR (uncertainty)a Predicted total HRR (kW)

FDS4 FDS4 FDS5 FDS5 FDS5 FDS5 FDS5 FDS5

With extinction model Without extinction model One-step Y_F_LFL ¼0.028 C-EDC¼ 0.1 Two-step Y_F_LFL¼ 0.0 C-EDC ¼0.1 Two-step Y_F_LFL¼ 0.028 C-EDC ¼ 0.1 Two-step without extinction C-EDC ¼0.1 Two-step Y_F_LFL¼ 0.028 C-EDC ¼ 0.45 Two-step without extinction C-EDC ¼0.45

75 (10)

115 (25)

180 (25)

265 (14)

410 (55)

67.2 73.4 67.2 75 66.5 75 47 75

71 111 115 115 115 115 80 –

103 168 178 180 169 180 143 179

173 247 256 – 264 265 228 261

325 367 398 410 391 410 330 375

a The unit of both measured total HRR and uncertainty is kW; the lower limit of oxygen volume concentration is specified as 0.15 (mol/mol) for both the extinction model of FDS4 and that of FDS5, if extinction is considered in the simulation.

lower CS (i.e., CS ¼0.1). This indicates that turbulence model parameters Cs, Pr, and Sc have no significant influence on the total HRR prediction. Table 3 presents the total HRR predictions obtained from different combustion models with different fire sizes using default turbulence model constants (i.e., Cs¼0.2, Pr ¼0.5, and Sc ¼0.5). As shown in Table 3, the predictions obtained from FDS4 with the extinction model were lower than those obtained from FDS4 without extinction, with a relative deviation up to 39%, indicating that a smaller amount of fuel was consumed in the computational domain. This also implies that consideration of flame extinction could result in significant variations in local volumetric HRR predictions within the computational domain if the single mixture fraction model, FDS4, is used. As shown in Fig. 2, for the results obtained from FDS4, the inclusion of the extinction model resulted in lower volumetric HRR predictions in the upper regions of the enclosure. The unburned fuel would be expected to flow out of the computational domain. However, nearly no fuel was observed to flow through the open boundaries of the domain when FDS4 with the extinction model was used. As discussed above, once flame extinction occurs, the state relations for the single mixture fraction become invalid for the value of Z below Zst because fuel may now be mixed with oxidizer or combustion products. As shown in Fig. 3, the fuel volume concentration falls to a negligible level once the single mixture fraction Z falls below its stoichiometric value. This may be the reason that inclusion of extinction model results in significant variation in both total and volumetric HRR prediction when using FDS4. As shown in Table 3, by using either FDS5 with an one-step scheme or FDS5 with a two-step scheme, the lower flammable

limit of fuel mass fraction has no considerable effect on the total HRR prediction when the fire size is larger than 115 kW. For smaller fires (e.g., 75 kW), due to the lower fuel supply rate and consequent lower local fuel concentrations, the specification of a lower limit of fuel mass concentration can result in local extinction within the computational domain and consequently in a lower prediction of total HRR. Without the consideration of flame extinction, the mixing model constant seems to have no considerable effects on total HRR prediction at fire sizes of less than 265 kW, as shown in Table 3. However, significant differences in local volumetric HRR prediction can be identified by using different values of mixing model constant. As shown in Fig. 2, a larger mixing model constant can result in a smaller portion of fuel being consumed near the burner but a larger portion of fuel being consumed outside the enclosure. This is due to the larger mixing model constant corresponding to a lower mixing rate between fuel and oxidizer. For fires with a size of 410 kW, using a larger mixing model constant (i.e., C_EDC¼0.45), the supplied fuel was not entirely consumed in the computational domain, corresponding to a lower total HRR than that obtained from C_EDC¼0.1. At a higher mixing model constant, the effects of the extinction model on total HRR prediction seem to be more significant. For small fires (e.g., 75 kW), the relative deviation between the total HRR predicted by the two-step reaction with the extinction model and that predicted by the one without the extinction model can be up to 46%. This is because a larger mixing model constant can result in lower local temperatures (which will be discussed in the following section) and thus raise the possibility of local extinction. The excessive fuel was

D. Yang et al. / Fire Safety Journal 45 (2010) 298–313

-0.5

-0.5

-0.5

0

0

0

0.5

0.5

0.5

305

1

1

0.5

0.5

0

0

1

-0.5

0

0.5

1

1

1

0.5

0.5

0

0

1

-0.5

0

0.5

1

1

1

0.5

0.5

0

0

1

-0.5

0

0.5

1

Fig. 2. Comparison of HRR distributions predicted by different combustion models at the symmetry plane for a 265-kW fire (unit: kW/m3). (a) FDS4 without extinction, (b) FDS4 with extinction, (c) FDS5 two-step without extinction (C_EDC¼ 0.1), (d) FDS5 two-step (Y_F_LFL¼ 0.028, C_EDC ¼0.1), (e) FDS5 two-step without extinction (C_EDC ¼0.45) and (f) FDS5 two-step (Y_F_LFL¼0.028, C_EDC ¼ 0.45).

observed to flow out of the computational domain, the amount of which in terms of the combustion heat was verified to be nearly equal to the difference between the predicted total HRR and the prescribed one (e.g., for the 265-kW fire simulated by Y_F_LFL¼0.028 and C-EDC¼0.45, the fuel mass outflow rate through the domain boundaries was integrated to be approximately 0.0007 kg/s, with the combustion enthalpy of about 34 kW being nearly equal to the deviation between the predicted total HRR and the prescribed one). As shown in Fig. 3, differences between the state relations for the multiple mixture fraction model and those for the single mixture fraction model can be observed; e.g., by using FDS5, a considerable amount of fuel remains in the regions with the mixture fraction below its stoichiometric value. This indicates that the co-existence of fuel and oxygen can be considered by the multiple mixture fraction model.

By using the multiple mixture fraction model, the extinction model has a smaller influence on the volumetric HRR prediction within the upper regions of the enclosure, as compared with the predictions obtained from the single mixture fraction model. This is attributed to their differences in local volumetric HRR computation and to the use of different extinction models.

5.2. Upper-layer temperature The capability of the two-step reaction scheme for upper-layer temperature prediction was investigated at different GER (including under-ventilated fires with higher GER). Two sets of experiment data were used as references: the RSE tests [17] and Lee’s test [35]. The sensitivities of temperature prediction both to combustion model constants (e.g., lower limit of fuel mass

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1.5

1

1

0.5

0.5

0

0

Z > Zst

Z < Zst

-0.5

0

0.5

-0.5

1

0

0.5

1

1

1

0.5

0.5

0

0

Z > Zst

Z < Zst

-0.5

0

0.5

1

-0.5

0

0.5

1

Fig. 3. Comparison of mixture fraction/fuel volume concentration distributions predicted by FDS4 and FDS5 with a two-step reaction (Zst ¼ 0.057, FDS5 two-step reaction: Z¼ Z1 + Z2 +Z3, Y_F_LFL ¼0.028, C_EDC ¼0.45). (a) FDS4 with extinction: mixture fraction, (b) FDS4 with extinction: fuel volume concentration (mol/mol), (c) FDS5 with extinction: mixture fraction and (d) FDS5 with extinction: fuel volume concentration (mol/mol).

fraction and mixing model constant) and to turbulence model parameters (i.e., Cs, Pr, and Sc) were considered. The RSE tests were identified as ventilation-limited fires. Firstly, the influences of turbulence model parameters on the upper-layer temperature predictions were investigated. Table 2 presents the predictions with different turbulence model parameters for the fire with a size of 410 kW. The results obtained using different values of turbulence model parameters differ only slightly from the results obtained using the default values, both at the front and at the rear. This indicates that Cs, Pr, and Sc have little influence on the upper-layer temperature predictions for enclosure fires. Fig. 4 presents the predicted upper-layer temperatures and the measured data of the RSE tests for different fire sizes, varying the selected lower flammable limits of fuel or the mixing model constant. As shown in Fig. 4, the specification of the lower limit of fuel can result in a lower upperlayer temperature than that obtained without consideration of the lower limit of fuel, with a relative deviation of, e.g., 11% for the 75 kW fire. The lower limit of fuel seems to have a far smaller impact on the temperature prediction for larger fires (e.g., ones larger than 410 kW), as shown in Fig. 4, because the local fuel mass fractions are unlikely to fall below the flammability limits due to the abundant fuel supplied by the fires with larger GER. For fires smaller than 115 kW (GERo0.23), it is seen that the upper-layer temperatures were under-predicted for the cases with C_EDC¼0.1 and without consideration of the lower limit of fuel, both at the front and the rear. The maximum relative difference is about 17% with consideration of measurement uncertainty, occurring at the front of the 75 kW fire. For such cases with a larger mixing model constant (C_EDC ¼0.45), the degree of under-prediction seems to be higher than for those obtained from C_EDC ¼0.1 with relatively small fires; e.g., the relative difference between the prediction and the measurement exceeds 39% for the fire with a size of 75 kW. This is due to a

higher mixing model constant leading to a lower reaction rate of fuel and consequent lower local temperatures. In contrast to those of small fires, the rear temperatures of large fires (e.g., fires larger than 264 kW or GER larger than 0.64) were over-predicted, rather than under-predicted, both for the cases with C_EDC¼0.1 and for those with C_EDC ¼0.45, as shown in Fig. 4. For the rear temperature of the 410-kW fire, the result obtained from the case with C_EDC¼0.1 is higher than the measurements by 37%. The degree of over-prediction can be decreased by using a larger mixing model constant; the relative deviation between prediction and measurement decreased to 24% when C_EDC was increased to 0.45. The above discussion concerns the ventilation-limited fires with the range of GER from 0.1 to 0.81. For under-ventilated fires with GER higher than unity (such as Lee’s enclosure fire experiments with the range of GER from 1.1 to 6.1 [34,35]), due to the existence of external combustion, the prediction of upperlayer temperature can only be done if the HRR inside the enclosure is well predicted. The two-step reaction predictions were compared against the measured data from Tests #1–4 and 9–12 of Lee’s work [35]. The mixing model constant was used at its default value (i.e., 0.1), and the lower limit of fuel mass concentration was not considered. Prior to testing the temperature prediction, the predictions of HRR inside the enclosure were compared against the measured data. Table 4 presents the predictions of HRR inside the enclosure and the measured data of Lee’s tests during the quasi-steady period. It is seen that the two-step reaction scheme performs well for the prediction of HRR inside the enclosure for fires with the range of GER from 1.5 to 4.0. For a fire with GER larger than 5.0, the predictions seem to be lower than the measured data. In general, the two-step reaction model predictions for the HRR inside the enclosure are acceptable. The measured gas temperatures inside the enclosure at high GER during the quasi-steady period, as indicated by Lee [34,35],

D. Yang et al. / Fire Safety Journal 45 (2010) 298–313

307

1400

Front side upper layer temperature (°C)

1300 1200 1100 1000 900 800 700 600 RSE Test#3 Front

500

FDS5 Y_F_LFL=0.028 C-EDC=0.1

400

FDS5 Y_F_LFL=0.0 C-EDC=0.1

300

FDS5 Y_F_LFL=0.028 C-EDC=0.45

200

0

50

100 150 200 250 300 350 400 450 500 550 600 650 Fire size (kW)

1200

Rear side upper layer temperature (°C)

1100 1000 900 800 700 600 500

RSE Test#3 Rear FDS5 Y_F_LFL=0.028 C-EDC=0.1

400

FDS5 Y_F_LFL=0.0 C-EDC=0.1 FDS5 Y_F_LFL=0.028 C-EDC=0.45

300 200 0

50

100 150 200 250 300 350 400 450 500 550 600 650 Fire size (kW)

Fig. 4. Comparison of the upper-layer temperatures predicted by the two-step reaction model with the measured data from the RSE experiments. (a) Front side and (b) Rear side.

Table 4 Comparison of HRR inside the enclosure predicted by FDS5 with the measured data. Test no.

Total HRR (kW)

GER

Predicted HRR inside the enclosure (kW)

Measured HRR inside the enclosure (kW)

Relative deviation (%)

Opening dimension (m2)

1 2 3 4 9 10 11 12

30 40 50 60 30 40 50 60

1.1 1.5 1.9 2.3 3.0 4.0 5.0 6.1

20.9 22.7 23.6 26.2 9.2 9.8 7.1 6.7

26.7(7 2.7) 26.7(7 2.7) 26.7(7 2.7) 26.7(7 2.7) 10.1(7 1) 10.1(7 1) 10.1(7 1) 10.1(7 1)

 21  15  11 1 8 2  29  33

0.2  0.2 0.2  0.2 0.2  0.2 0.2  0.2 0.075  0.2 0.075  0.2 0.075  0.2 0.075  0.2

were uniform from the top to the floor inside the enclosure. The temperatures in Lee’s tests were measured by shielded thermocouples with a diameter of 1.5 mm [34]. There were differences

between the true gas temperatures and shielded thermocouple measurements due to the radiation exchange between the thermocouple and the surrounding environment [49]. Based on

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the models proposed by Blevins and Pitts [49], the estimation of the measurement uncertainty requires information regarding the effective surroundings temperature. For these thermocouples installed at the corners of the enclosure, the effective surrounding temperature can be characterized by both the temperature of the inner surface of the enclosure wall and the gas temperature at the locations that can be monitored by the thermocouple of interest. In Lee’s tests, the gas temperatures were measured to be nearly uniform from the top to the bottom inside the enclosure, and the inner surface temperature was measured to be nearly equal to these gas temperatures [34]. Thus, it is estimated that the effective surroundings temperatures were quite close to those measured by shielded thermocouples. Based on the models derived from energy balance (e.g., the model proposed by Blevins

and Pitts [49]), the differences between the shielded thermocouple measurements and the true gas temperatures were negligible for Lee’s tests. Therefore, this work compared the FDS predicted gas temperatures against the shielded thermocouple measurements. Both the measured vertical temperature distributions and the predictions are shown in Fig. 5. For the fire with the size of 30 kW (GER of about 1.1), the predicted upper-layer temperatures agree very well with the measured data at both the front corner and the back corner. For the fire with the size of 60 kW (GER is about 2.3), the predictions seem to be slightly lower than the measured data, especially at the back corner. The relative deviations between the predictions and the measurements were in the range of 12–17% at the back corner.

0.6

0.5

Height (m)

0.4

0.3

0.2 Lee Test#1 Front (30kW) FDS5 Test#1 Front (30kW)

0.1

Lee Test#4 Front (60kW) FDS5 Test#4 Front (60kW)

0.0 0

100

200

300

400 500 600 700 Temperature (°C)

800

900

1000 1100

0.6

0.5

Height (m)

0.4

0.3

0.2 Lee Test#1 Back (30kW) FDS5 Test#1 Back (30kW)

0.1

Lee Test#4 Back (60kW) FDS5 Test#4 Back (60kW)

0.0 0

100

200

300

400

500 600 700 800 Temperature (°C)

900 1000 1100 1200

Fig. 5. Comparison of vertical temperature distributions predicted by the two-step reaction model with the measured data from the Lee’s experiments. (a) Front corner and (b) Back corner.

D. Yang et al. / Fire Safety Journal 45 (2010) 298–313

5.3. Carbon monoxide yield inside the enclosure 5.3.1. Comparison with 1/2-scale ISO 9705 compartment measurements For those fires with a well-mixed and uniform upper layer, the CO yield can be obtained based on the single point measurement, as in, e.g., Gottuk’s experiments [13]. However, spatial variation in the species levels is expected within the upper layer for a typical building enclosure, as observed in the NIST RSE [18] and Virginia Tech tests [25,26]. The CO yield inside the enclosure during the quasi-steady burning state can be obtained from i R hR , , 1 Aout ryi vUds dt T T mi Yi ¼ ¼ ð26Þ _f mf m _ i is time-averaged mass outflow rate of gas species where m through the compartment opening during the quasi-steady period , in kg/s, yi , r, and v are the mass fraction of gas species, gas density, and velocity at a particular cell of the opening plane, and the subscript i denotes different species. Aout denotes the opening _ f is the time-averaged mass burning rate of fuel inside the area. m enclosure (not including the amount that flows out of the enclosure) in kg/s. T denotes the duration of the quasi-steady state. The normalized yield, fi, is calculated by dividing the species yield by the maximum theoretical yield [13,36]: fi ¼

Yi ¼ Yi =ki ki

ð27Þ

f ¼ fCO þ fCO2 þ fsoot ¼ 1

ð28Þ

where ki denotes the theoretical maximum yield of species i and f is the sum of the normalized yield of carbon-containing products. The conservation of carbon requires that f is equal to unity. The two-step predictions of both the normalized CO yield and the normalized CO2 yield were compared against measured data from the Virginia Tech tests. The turbulence model parameters, Cs, Pr, and Sc, were used at their default values. Two different specified values of the lower flammable limit fuel mass fraction and the two mixing model constants were considered (see Table 1). The lower flammable limit of propane mass concentration (Y_F_LFL¼0.032) has been reported by Beyler [30]. The CO yield that exists in a well-ventilated fire was specified according to the values reported by Tewarson [41]. Table 5 compares the predictions of CO yield and CO2 yield with the measured data. At lower GER (o0.26), the CO yields obtained from Y_F_LFL¼0.032 seem to be much higher than the measured data for both specified mixing model constants. At higher GER (41.36), the predictions

309

with C_EDC¼0.1 seem to be much lower than the measured data for both specified lower limits of fuel mass fraction. At this range of GER, the predictions obtained from C_EDC¼0.45 were much closer to the measurements than those obtained from C_EDC¼0.1. Furthermore, it was found that the underprediction of CO yield corresponds to the over-prediction of CO2 yield. The above results indicate that both the prediction of CO yield and that of CO2 yield were strongly dependent on the lower limit of fuel and on the mixing model constant. This may be due to the effects of these two combustion model constants on the temperature prediction, as discussed in Section 5.2. The upperlayer temperature measurements were not reported for the Virginia Tech tests. The next section further discusses the temperature effects on CO yield prediction.

5.3.2. Additional discussion of the temperature effects Temperature has an important role on the chemical kinetics of CO production in enclosure fires, as indicated by Gottuk et al. [50]. The detailed reaction mechanism is simplified to a two-step reaction scheme by FDS5. The first step represents the formation of CO, and the second one represents CO consumption. The first reaction step is always assumed to be infinitely fast, whereas the second step is assumed to be an infinitely fast reaction at the flammable regions but with a finite reaction rate at the regions outside of combustion (see Eq. (17)). Therefore, the temperature prediction would affect that of the CO yield through the second reaction step at these non-combusting regions. Scenario #4 is used to investigate the effects of temperature on the prediction of CO yield inside the enclosure, which corresponds to RSE tests. Both the measurements and the predictions for upper-layer temperature are presented in Fig. 4. In Fig. 6, the CO yield obtained from different specifications of the lower limit of fuel and the mixing model constant were plotted against the equivalence ratio. Fires ranged from 50 to 600 kW, with the equivalence ratios reported by Bryner et al. [18]. It should be noted that the equivalence ratios used in this section could be higher than those obtained from the GER concept because a considerable portion of incoming air may be directly entrained into the out-flowing gases, never reaching the reaction zone for the single-side-opened configuration [17,18]. As shown in Fig. 6, for a fire smaller than 116 kW (equivalence ratioo0.7), the predictions obtained from Y_F_LFL¼0.028 seem to be higher than those obtained from Y_F_LFL¼0.0 and even higher than those corresponding to under-ventilated fires (equivalence ratio 41.0). Several experiments reported the measurements of CO yield, e.g., those by Toner et al. [11], Beyler

Table 5 Comparison of normalized CO2 yield/CO yield predictions with the measured data. Opening width (m)

GER

Measured dataa (uncertainty)

Y_F_LFL¼ 0.032 C_EDC ¼0.1

Y_F_LFL ¼0.0 C_EDC ¼ 0.1

Y_F_LFL¼ 0.032 C_EDC¼ 0.45

Normalized CO2 yield 107 204 204 266 379

0.33 0.33 0.165 0.165 0.165

0.14 0.26 1.04 1.36 1.94

0.968( 70.50) 0.975( 70.51) 0.857( 70.44) 0.679( 70.35) 0.550( 70.28)

0.704 0.858 0.954 0.948 0.936

0.971 0.972 0.969 0.960 0.933

0.557 0.674 – 0.910 0.884

Normalized CO yield 107 204 204 266 379

0.33 0.33 0.165 0.165 0.165

0.14 0.26 1.04 1.36 1.94

0.005( 70.00) 0.006( 70.00) 0.072( 70.04) 0.195( 70.10) 0.263( 70.13)

0.273 0.123 0.026 0.029 0.051

0.001 0.001 0.006 0.018 0.050

0.424 0.304 – 0.069 0.104

HRR (kW)

a

The measurement uncertainty was provided by the Ref [27].

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Equivalence ratio

0.0 0.8

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

FDS5 Y_F_LFL=0.028 C-EDC=0.1

0.7

FDS5 Y_F_LFL=0.0

C-EDC=0.1

FDS5 Y_F_LFL=0.028 C-EDC=0.45

0.6

CO yield

0.5 0.4 0.3 0.2 0.1 0.0 0

100

200

300 400 Fire size (kW)

500

600

Fig. 6. Comparison of predictions of CO yield inside the enclosure using different specifications of the lower flammable limit fuel mass fraction and mixing time scale.

[12], Gottuk [13] and Lonnermark et al. [51]. All of these studies indicated that the CO yield inside the enclosure should be near zero at such a low equivalence ratio. The model over-prediction of CO yield was a result of over-prediction of CO production in the first step combined with the under-prediction of CO consumption in the second step. The CO formation in the first step may be over-predicted due to the use of infinitely fast reaction. An infinitely fast reaction results in a large amount of fuel being consumed near the burner with a significant portion of heat released at the same location. Consequently, the product of the first reaction step, CO, is produced at a high rate near the burner. The second reaction step, conversion of CO to CO2, is also assumed to be infinitely fast at these flammable regions. However, the upper bound in the volumetric heat release rate may prevent the instantaneous conversion of CO to CO2. Therefore, the CO species was transported to the upper layer, where a finite reaction rate was used to compute its oxidization to CO2. This can be confirmed by the CO and CO2 distributions, as shown in Figs. 7 and 8. For all three cases corresponding to the 75-kW fire, it is seen that the CO volume concentrations near the burner were predicted to be much higher than those in the upper layer. In contrast, the CO2 volume concentrations in the upper layer were predicted to be higher than those near the burner. As shown in Fig. 8, for the 75 kW fire, the case with Y_F_LFL¼0.0 and C_EDC¼ 0.1 yields the highest CO2 volume concentrations within the upper layer, followed by the case with Y_F_LFL¼0.028 and C_EDC ¼0.1 and the case with Y_F_LFL¼0.028 and C_EDC ¼0.45, in order. These discrepancies could result from the differences in temperature prediction, as shown in Fig. 4. This also implies that the CO yield is overpredicted at the expense of under-prediction of CO2 yield if the lower limit of fuel is considered. Though the lower limit of fuel should be considered from the viewpoint of physical mechanisms, specification of the lower limit of fuel can result in a dramatic variation in CO yield prediction for these small fires (equivalence ratioo0.7); e.g., at 75 kW fire, the

CO yield obtained from Y_F_LFL¼0.028 and C_EDC ¼0.1 is three orders of magnitude higher than that obtained from Y_F_LFL¼0.0 and C_EDC ¼0.1, though the temperature prediction of the former one was only 11% lower than that of the latter one. Though a larger mixing model constant (i.e., C_EDC¼0.45) results in a lower mixing rate between fuel and oxygen and consequently a lower production rate of CO in the first reaction step, it results in a higher CO yield as compared with that obtained from C_EDC¼0.45. The reason is that the consumption rate of CO can be under-predicted in a greater extend with a larger mixing model constant. With the increase in the equivalence ratio, the specification of the lower limit of fuel has a far smaller effect on CO yield prediction, as shown in Fig. 6. This may be due to the lower flammability limit becoming less frequently reached and the temperature predictions thus becoming less sensitive to the specification of the lower limit of fuel with increasing fire size. However, for large fires (equivalence ratio42.4), the mixing model constant still has a significant effect on CO yield prediction due to its strong effect on temperature prediction; e.g., for the 600-kW fire, the CO yield obtained with C_EDC¼0.45 was approximately three times as high as that obtained with C_EDC¼0.1. The variation of CO yield prediction with the mixing model constant shows an opposite trend to that followed by the upper-layer temperature. The effects of turbulence model constants on CO yield prediction were tested by using the RSE fire scenario with a size of 410 kW, as shown in Table 2. Cs¼0.1 results in a higher prediction of CO yield than that with the default value of Cs (i.e., Cs¼0.2), with a relative deviation of 52%. This is due to the slightly lower upper temperatures obtained using Cs¼0.1. Similarly, a higher value of the turbulent Schmidt number Sc (i.e., Sc ¼1.0) results in a higher prediction of CO yield than when using the default value of Sc (i.e., Sc ¼0.5), with a relative deviation of 59%. The turbulent Prandtl number Pr seems to have a much smaller effect on the CO yield prediction than do the other two turbulence model constants.

D. Yang et al. / Fire Safety Journal 45 (2010) 298–313

1.5

1.5

1.5

Y_F_LFL=0.0 C_EDC=0.1 0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002

1

0.5

0 -1

0.5

0 0

0.5

-1

1

1.5

1

0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002

0 0

0.5

1

1.5

0.5

0 -1

0.5

0

0.5

-0.5

1

0

0.5

1

1.5 0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002

Y_F_LFL=0.028 C_EDC=0.45 1

0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002

0.5

0

0

-0.5

-1

Y_F_LFL=0.028 C_EDC=0.1 1

0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002

0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002

0.5

-0.5

Y_F_LFL=0.0 C_EDC=0.1 1

Y_F_LFL=0.028 C_EDC=0.45

Y_F_LFL=0.028 C_EDC=0.1 1

-0.5

311

-1

-0.5

0

0.5

-1

1

-0.5

0

0.5

1

Fig. 7. CO distribution at the central plane (unit: mol/mol). (a) 75 kW and (b) 410 kW.

1.5

1.5

1

1 0.03 0.026 0.022 0.018 0.014 0.01 0.006 0.002

0.5

0.03 0.028 0.026 0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002

0.5

0

Y_F_LFL=0.0 C_EDC=0.1 -1

1.5

-0.5

0

0.5

0 -1

1

1.5

0.5

Y_F_LFL=0.028 C_EDC=0.1

-0.5

0

0.5

0.08 0.075 0.07 0.065 0.06 0.055 0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005

0.5

0 -1

0.08 0.075 0.07 0.065 0.06 0.055 0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005

0.5

-0.5

0

0.5

1

-1

Y_F_LFL=0.028 C_EDC=0.45

-0.5

0

0.5

1

1.5

1

Y_F_LFL=0.0 C_EDC=0.1

0

1

1.5

1

0.03 0.028 0.026 0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002

1

0 -1

0.08 0.075 0.07 0.065 0.06 0.055 0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005

1

0.5

Y_F_LFL=0.028 C_EDC=0.1 -0.5

0

0.5

1

0 -1

Y_F_LFL=0.028 C_EDC=0.45

-0.5

0

0.5

1

Fig. 8. CO2 distribution at the central plane (unit: mol/mol). (a) 75 kW and (b) 410 kW.

6. Conclusions This study investigated the performance of FDS prediction for ventilation-limited enclosure fires. The combustion models used by FDS4 or FDS5 were considered, including a single-step reaction scheme with a single mixture fraction, a single-step reaction scheme with two mixture fraction variables, and a two-step

reaction with three mixture fraction variables. The following main conclusions were reached: (1) FDS4 with the inclusion of an extinction model predicts a much lower total HRR than does the system without an extinction model for a wide range of GER (GERo0.81), with a maximum deviation of 39%. These discrepancies are

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attributed to the limitations of the state relations for the single mixture fraction. For FDS5, the specification of the lower flammable limit of fuel has significant effects on total HRR prediction for small fires (GERo0.18), with a relative deviation of 13%. A model with higher mixing corresponds to a stronger influence of the extinction model on total HRR prediction. The turbulence model parameters Cs, Pr, and Sc do not strongly affect the total HRR prediction. (2) The two-step reaction scheme of FDS5 generally under-predicts the upper-layer temperatures for small fires (GERo0.23), with a maximum deviation of about 39%, but over-predicts the upper-layer temperatures for larger fires (0.53 oGERo0.81), with a maximum deviation of about 24%. The consideration of the lower limit of fuel mass fraction could result in a lower upper-layer temperature for small fires (GERo0.23), with a maximum deviation of about 11%. The mixing time model constant affects the upper-layer temperature prediction for a wide range of GER (e.g., from 0.1 to 0.81); i.e., a higher mixing model constant always results in a lower upper-layer temperature prediction. For under-ventilated fires (GER41), the two-step reaction scheme can well predict the value of HRR inside the enclosure with the GER up to 4.0. It predicts the upper-layer temperatures well at GER up to 2.3. The turbulence model parameters Cs, Pr, and Sc have no significant influence on the upper-layer temperature prediction. (3) The CO yield prediction shows a strong dependency on the temperature prediction. For this reason, it is sensitive to the mixing time scale model constant for a wide range of equivalence ratios (equivalence ratio o3.6) and to the lower limit of fuel mass concentration at lower equivalence ratios (equivalence ratioo0.7). For small fires (e.g., equivalence ratio less than 0.7), the specification of the lower limit of fuel mass concentration results in an increase in CO yield prediction by three orders of magnitude. The effects of the Smagorinsky constant Cs and the turbulent Schmidt number Sc on the CO yield prediction also become significant due to the strong dependency of CO yield on temperature. This indicates that further studies are necessary for the improvement of combustion models applicable to fire simulations. The probability density function (PDF) approach seems to obtain encouraging results in the area of fundamental combustion; however, it could result in a dramatic increase in computational cost for typical fire simulations.

Acknowledgements This work was supported by Natural Science Foundation of China (NSFC) under Grant no. 40975005, Fundamental Research Funds for the Central Universities, and Program for New Century Excellent Talents in University under Grant no. NCET-09-0914. The authors would also like to thank Dr. Jason Floyd from the Hughes Associates, Inc., for providing the FDS5 input files of 2006 RSE tests. References [1] V. Novozhilov, Computational fluid dynamics modeling of compartment fires, Progress in Energy and Combustion Science 27 (6) (2001) 611–666. [2] Y. Xin, J. Gore, K.B. Mcgrattan, R.G. Rehm, H.R. Baum, Large eddy simulation of buoyant turbulent pool fires, Proceedings of the Combustion Institute 29 (1) (2002) 259–266. [3] Z.X. Hu, Y. Utiskul, J.G. Quintiere, A. Trouve, Towards large eddy simulations of flame extinction and carbon monoxide emission in compartment fires, Proceedings of the Combustion Institute 31 (2) (2007) 2537–2545. [4] K.B. McGrattan, Fire Dynamics Simulator (Version 4) Technical Reference Guide, National Institute of Standards and Technology, NISTIR, 2006.

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