Horizontal cable tray fire in a well‐confined and mechanically ventilated enclosure using a two‐zone model

Electrical cable trays are used in large quantities in nuclear power plants (NPPs) and are one of the main potential sources of fire. A malfunction of electrical equipment due to thermal stress for instance may lead to the loss of important safety functions of the NPPs. The investigation of such fires in a confined and mechanically ventilated enclosure has been scarce up to now and limited to nuclear industry. In the scope of the OECD PRISME‐2 project, the Institut de Radioprotection et de Sûreté Nucléaire (IRSN) conducted more than a dozen fire tests involving horizontal electrical cable trays burning either in open atmosphere or inside mechanically ventilated compartments to investigate this topic. A semi‐empirical model of horizontal cable tray fires in a well‐confined and mechanically ventilated enclosure was developed. This model is partly based on the approach used in FLASH‐CAT and on experimental findings from IRSN cables fire tests. It was implemented in the two‐zone model SYLVIA. The major features of the compartment fire experiments could then be reproduced with acceptable error, except for combustion of unburned gases. The development of such a semi‐empirical model is a common practice in fire safety engineering concerned with complex solid fuels.

loosely or tightly along the trays. Two of the three cable types were compliant with the IEEE-383 standard test. 3 The HRR peak and the fire growth rate were affected by the duration of the ignition source.
In addition, an increase of the HRR peak was observed with a loose arrangement of cables or with the use of non-compliant cables.
Large-scale experiments involving cable trays in an open atmosphere were also performed as part of the FIPEC project conducted by Grayson et al 4 in the 2000s. One of the main objectives of this project was to develop an experimental fire data base used for the validation of fire models. Tests showed that both fire ignition and fire spread significantly depend on the cable characteristics. Tests using identical cables indicated that the HRR peak increased with the power of the ignition source, as well as with the partial confinement of the fire source with the presence of walls and ceiling. Moreover, the cable arrangement was also found as one of the most sensitive parameters on the fire growth.
Within the scope of the CHRISTIFIRE program, McGrattan et al 5,6 carried out at NIST many cable tray fire tests in order to quantify the burning characteristics in an open atmosphere over a wide range of multiple cable tray configurations found in operating NPPs. Twentysix multiple tray tests involving horizontal cable trays without wall and ceiling, followed by 10 corridor tests using horizontal cable trays located near the ceiling, were carried out. One to seven horizontal ladder-type trays (2.4 and 3.6 m long) were used, with a tray spacing ranging from 0.23 to 0.45 m and tray width ranging from 0.3 to 0.9 m. Ignition was achieved by means of a sand burner (300 × 300 mm 2 ) providing a fire power of 40 kW. These tests showed that the fire spread depends on the cable type, cable loading, and operating time of the gas burner, as well as on the cable tray geometry in terms of width and spacing. The corridor tests dealt with horizontal multiple cable trays inside a fully open corridor (2.4 m width × 2.4 m high × 7.3 m long) and located at 0.3 m from the ceiling. A significant increase of the fire growth rate with the presence of the ceiling was observed; the hot gas layer accumulated under the ceiling pre-heated the cables directly upstream of the spreading fire.
Few experimental programs involving cable tray fires in confined and mechanically ventilated compartments were carried out. 7 These ones mainly aimed at studying the failure modes of electrical cables used as a target subjected to fire conditions.
Since the investigation of cable tray fires in confined and mechanically ventilated compartments has been scarce up to now, IRSN conducted, in the framework of the OECD PRISME-2 program, 8 15 mainly depending on the gas temperature and the oxygen volume fraction close to the cables.
Concerning the upward fire propagation in the cable tray stack, the FLASH-CAT modeling uses the "minute rule," 14 based on a simple and empirical law providing a time to ignite the next cable tray without any considerations about the nature of cables and the distance between cable trays for instance. In this paper, the ignition of the upper cable tray is performed by the assessment of the thermal stress on it due to the flame located on the lower tray. This new modeling was implemented in the two-zone model SYLVIA 16 and is here applied to the IRSN cable fire tests in order to validate properly the SYLVIA software. Such an approach is very useful in fire design of NPPs or some such to predict the fire spread on cable trays including both the thermal properties of cables and the distance separating each tray.

| CONFIGURATION OF THE CFS 1 TO 4 TESTS
CFS tests were carried out in the multi-room large-scale fire test DIVA facility. The DIVA facility (shown in Figure 1 Room 3 and part of the adjacent corridor. Rooms can be connected via doors, simple openings, and calibrated leak passages (to simulate leaks through an actual closed door and/or through a transfer grid between two rooms). They can also be connected with a ventilation network, with one inlet duct and one exhaust duct per room. The ventilation system of the DIVA facility consists of two separate circuits (one for inlet and one for exhaust), each equipped with fans.
Only rooms 1 and 2 were used for the CFS 1 to 4 tests. These rooms communicate through a doorway, as shown in Figure 2. The fire source was located in Room 1, against the west wall of the room, and was composed of five horizontal ladder-type trays 3 m long, 0.45 m wide, and spaced from each other by 0.3 m (see Figure 3). Each tray was filled with 32 samples of a 2.4-m-long cable. The cable types and characteristics are displayed in Table 1. For all the tests, the number of cables per tray was determined in order to ensure the same total cable surface for the five cable trays (24 m 2 ). The cable samples were packed loosely along the five trays. In addition, the five trays were set up against an insulated side wall. Ignition was achieved by means of a propane gas burner (300 × 300 mm 2 ). It was centered and located 0.  for which a correction is applied to take into account the effect of the oxygen depletion in the fire room on the fire heat release rate.

| Heat release rate
A useful correlation for estimating the HRR generated by a burning cable tray is given in NUREG-1805, 17 which specifies the state-ofart relevant to fire dynamic equations and correlations for performing fire hazards analysis for the NRC inspection program. This correlation was developed by Lee 18 who showed that the peak full-scale HRR in well-ventilated conditions can be predicted according to bench-scale HRR measurements performed on cable samples. This correlation is expressed as where _ Q fs is the peak full-scale HRR, S, the total burning area of cables involved in the fire at the peak full-scale HRR, _ q ″ bs ; the peak benchscale HRR per unit area, under 60 kW.m −2 irradiance, and 0.45, an empirical constant.    This decrease is mainly due to the reduced heat transfer from the flame to the fuel surface as the oxygen is depleted in the room, because of the air renewal rate that can be quite low compared to the kinetics of oxygen consumption by the fire source. The underoxygenation of the fire source is taken into account in the model by applying a correction factor to MLR. In these conditions, HRR is written as where ΔH c , is the effective heat of combustion and χ(O 2 ), a correction factor representative of the rate of decrease of the pyrolysis rate with oxygen depletion (see Section 4.2).

By inserting Equation 2 in Equation 3, HRR is expressed as
The difficulty in applying Equation 4 lies in the estimation of the instantaneous burning surface area of cables that depends on the horizontal fire spread along cable trays and on the vertical fire spread from one cable tray to another.

| Cable burning surface area
where n, the number of cables per cable tray, d, the diameter of cables, x b (t), the abscissa of the flame front, x e (t), the abscissa of the extinction front, and p the total perimeter of the cables in contact with the surrounding gas.
The abscissa of the flame front is given by and the abscissa of the extinction front is given by where v b (t) is the flame spread velocity, t i (x e ) denotes the crossing time of the flame front at the abscissa x e , and t e (x e ) one of the extinction fronts at the same abscissa.
At a given abscissa x, from the ignition time of this area, the extinction time corresponds to the moment when the whole fuel mass in this region is consumed. It is given by where _ m ″ c;∞ is the fuel mass loss rate per unit surface and m ′ c , the mass of the fuel per unit length.
A scheme of the modeling of the cables burning surface area is shown in Figure 4. a time dependence to the ambient gas temperature for confined fires and a correction factor (χ) to the incident heat flux from flames to fuel surface to take into account the decrease of the heat flux with the depletion of oxygen in the compartment:

| Horizontal flame spread velocity along the cable trays
where _ q ″ f;∞ is the incident heat flux from flames to the fuel surface in well-ventilated conditions, χ(O 2 ), the oxygen limiting law, δ c , the heated fuel distance, kρc p , the thermal inertia of cables, T ign , the ignition temperature of cables, and T amb , the ambient gas temperature. Cable trays were filled with a three-conductor XPE cable. 14 The lowest tray in the stack has the burning length of the characteristic length of the ignition source (see Figure 5). The burning length of the trays above is calculated using the following equation: where h is the tray elevation measured from the bottom of the lowest tray and β the fire spread angle.
Assuming that the first cable tray in a stack of horizontal cable trays is within the zone of influence of a given ignition source, the spread of the fire within the stack is assumed as follows in FLASH-CAT: • exposure source to the first tray: tray ignites at time to damage; • first tray to second tray: 4 minutes after ignition of first tray; • second tray to third tray: 3 minutes after ignition of second tray; • third tray to fourth tray: 2 minutes after ignition of third tray; • for next trays: 1 minute after ignition of the previous tray.
In a confined enclosure, this rule (known as the "minute rule") is  Table 2. Properties were only obtained at room temperature by using a helium Pycnometer for density measurement, a Perkin Elmer differential scanning calorimetry for HX þ H : → H 2 þ X : Thus, the most energetic free radicals of the flame (HO . and H . ) are replaced by X . radicals of lower energy. Here, X mainly refers to the chlorine contained in PVC cables.
The number of mineral compounds used as flame retardants is relatively small since they have to be decomposed at a relatively low temperature, which is not common for minerals. Alumina trihydrate (Al (OH) 3 ) is one of the most common mineral flame retardants because it is inexpensive and easy to incorporate into plastics. Alumina trihydrate is decomposed in a temperature range between 180°C and 200°C, as follows: Alumina trihydrate is cooled by the reaction of dehydration (endothermic reaction), which involves less volatile products released by the fuel. Moreover, aluminum oxide resulting from its dehydration forms, at the fuel surface, a protective crust against a subsequent degradation of the material. Finally, water vapor released by the reaction dilutes the gaseous phase and decreases the amount of oxygen at the fuel surface.
In terms of modeling, effects of mineral flame retardants on combustion are taken into account in the thermal inertia of the fuel.
According to Table 2, thermal inertia of mineral flame-retardant cables tested in CFS-3 and CFS-4 tests is three times higher than the one of PVC cables tested in CFS-2 test. This results in a delay in the heat up of the fuel surface and, then, to a slower flame spread velocity. The mass loss due to the dehydration reaction is not modeled in SYLVIA.
The chlorine contained in the PVC cables causes a reduction of the effective heat of combustion due to the inhibition reactions occurring in the flame that consume oxygen (flame poisoning).
Chemical reactions occurring during the burning of cables are complex. They depend on the nature of the fuel as well as on the oxygen content in the gas close to the fuel. In SYLVIA, a one-step irreversible combustion reaction, expressed in terms of mass, is used as It is assumed that the fuel is homogeneous and that chemical reactions  Table 3 for the CFS cable fire tests performed in DIVA). Since the amount of water vapor is not measured experimentally (condensable species), the coefficient related to this species is determined by the mass balance of the reaction. Yield of oxygen consumption is given by where ΔH O2 is the heat released per kilogram of consumed oxygen (set to 13.1 MJ kg −1 23 ) and ΔH c , the effective heat of combustion (user data).
A correction factor, η, is applied to the yield of oxygen consump-  The fire design of the SYLVIA software belongs to the well-known two-zone fire modeling. 24,25 In such software, each compartment is described with two Lagrangian control volumes separated by a thermal interface (see Figure 6)  Since the cable samples were packed loosely along the trays in the CFS tests, no correction factor is applied to the total burning surface area of the cables to take into account the staking density of the cables (α = 1). The mass per unit length of the cable components are reported in Table 4.
Bench-scale HRR measurements performed on cable samples 32 and full-scale heat of combustion in open atmosphere are reported in Table 5.
Thermal inertia of PVC cable samples tested in CFS-1 test is not known. This one was fitted in a way to reproduce the kinetics of the   gas temperature increase in the fire room (see Figure 10). A value of 0.10 kW 2 .s.m −4 .K −2 was found.

| Results and discussion
The results of the CFS test simulations for the heat release rate, pressure, and mean gas temperature in the fire room are presented in Figures 9-11. These results are compared to experimental data, including experimental uncertainties.
The relative uncertainty of the measurement, e u; of a temperature, pressure … or that of the assessment of a fire characteristic, such as the heat release rate, may be defined as followed: where, u is the uncertainty (standard deviation) of the measurement or assessment and R its result expressed in the corresponding unit. u is estimated by combining the individual standard uncertainties, such as the instrument uncertainty and the repeatability, using the usual method called the "law of propagation of uncertainty." 33,34 Furthermore, the uncertainty is often expressed in terms of an expanded uncertainty, in which the confidence level that the measurement or the assessment falls within the expanded bounds is high. 33 For an expansion factor (or coverage factor) of 2, here considered, the expanded relative uncertainty of the measurement or assessment, ǔ, is thus related to two relative standard deviations (2·e u) and the confidence level corresponds to 95%. Table 6 gives the expanded relative uncertainty evaluated or assessed for some measurements and assessments carried out as part of the PRISME-2 CFS test campaign. 36 The evaluation of the uncertainty for the HRR is detailed in Zavaleta and Audouin 11 for the CFS-3 and 4 fire tests and in Zavaleta 12 for the CFS-1 and CFS-2 fire tests.
The comparison of the predicted HRR with the experimental data shows a good agreement for the CFS-2 test (except for the fire duration) and deviations for the three other tests, as shown in  The comparison between the CFS-1 and CFS-3 experimental data and numerical results ( Figure 9) appears to be satisfactory about up to 1000 and to 5000 s for CFS-1 and CFS-3, respectively. Beyond these times, the HRR are significantly overestimated because no modeling is used to predict the fire extinction due to a lack of oxygen, as observed during the fire tests (see Table 7). Indeed, this extinction can be explained by the low ventilation rate of the fire compartment.
Moreover, only 82% and 73% of mass loss were burned during the CFS-1 and CFS-3 experiments, respectively, while all the mass of combustible is consumed in the simulations.
Pressure rise in the fire room mainly depends on the ratio between the fire heat release rate and the dissipated and evacuated heat rates. At the beginning of the fire, heat dissipation by walls is low because of their inertia, which results in a rise in pressure of the fire room. The resulting pressure peak is quite well reproduced by the calculations for CFS-1 and CFS-3 tests, as shown in Figure 10.
The highest pressure peak value is predicted for CFS-1 test (23 hPa in the simulation against 14 hPa experimentally), this test involving cables with the highest fire growth rate (0.14 kW.s −2