LUBRICATING OIL FIRE IN PUMP COMPARTMENT
C.3 Selection and Evaluation of Models
C.4.1 Calculation of Oxygen Availability
At the start of the scenario, the mechanical ventilation is operational, the door is closed, and the fire output immediately jumps to the peak heat release rate (HRR) with a total spill area of approximately 2.75 m2 (29.6 ft2), as shown in the hatched area of Figure C-1. The peak HRR,
, is computed from the fuel mass burning rate, , the heat of combustion, ∆ , and the specified area of the spill, :
∆ 0.039 kg/m s 46,000 kJ/kg 2.75 m⁄ 4,934 kW (C-1) The oxygen needed to sustain the fire is calculated from the following equation:
∆ O
4934 kW
13,100 kJ/kg 0.377 kg/s (C-2)
where ∆ is the heat of combustion per unit mass of oxygen consumed. The quantity of oxygen provided by the ventilation system is calculated by multiplying the oxygen content (0.23) by the density and the ventilation rate of the air:
0.23 0.23 1.2 kg/m 0.25 m /s 0.069 kg/s (C-3)
The oxygen provided by the ventilation system is much lower than the amount needed to sustain the fire. The oxygen initially in the room can provide the additional oxygen needed for combustion for a short time. The available oxygen in the room, calculated from the room dimensions (Table C-4), is:
0.23 0.23 1.2 kg/m 2.81 9.39 4.9 m 35.7 kg (C-4)
The oxygen initially in the room can sustain the fire for an amount of time equal to the oxygen quantity in the room divided by the consumption rate minus the ventilation supply rate, as shown below:
35.7 kg
0.377 kg/s 0.069 kg/s 116 s (C-5)
LUBRICATING OIL FIRE IN PUMP COMPARTMENT
Equation C-4 requires that all the oxygen within the room be consumed by the fire. This establishes an upper limit to the burning duration before the fire becomes ventilation-limited.
After 116 s, the size of the fire is maintained only by the ventilation system and is limited to:
0.069 kg/s 13,100 kJ/kg 904 kW (C-6)
These results show that the oxygen supply available to the room will only allow a fire of reduced size to burn until the door is opened (under-ventilated condition).
C.4.2 Zone Model
The following paragraphs outline the data utilized to model the scenario using MAGIC. Figure C-2 provides an illustration of the scenario, as rendered by MAGIC.
Geometry: To model this scenario with MAGIC, the pump compartment is modeled as a single compartment having the same total volume and surface area as the actual enclosure. This allows the volume in which the HGL develops and the surface area through which energy is transferred from the compartment to be maintained. Maintaining the total volume and surface area while leaving the ceiling height unchanged at 4.9 m (16 ft) yields an effective compartment size of 9.39 m (30.8 ft) by 2.81 m (9.2 ft). The modification to the geometry can be seen by comparing Figure C-1 and Figure C-2. All other aspects of the geometry are relatively unchanged.
Table C-4. Calculated input for lubricating oil fire.
Parameter Value
Effective Length 2.81 m
Effective Width 9.39 m
Fire Diameter 1.87 m
Peak Heat Release Rate 4,934 kW
Fire Duration 1345 s
Mass of Fuel (kg) 144.4
Stoichiometric Mass-Oxygen 3.5 g/g
Specific Area 513 m2/g
LUBRICATING OIL FIRE IN PUMP COMPARTMENT
Figure C-2. MAGIC view of the pump room.
Fire: For this scenario, the lubricating oil is preheated prior to the spill, such that the HRR reaches the peak immediately upon fire initiation, as shown in the HRR curve plotted in Figure C-3. The lower oxygen level is specified to be 10%. Using the specified spill area and volume, the spill depth is calculated as 0.069 m (0.23 ft).
The fire is modeled as a single circular area of equivalent diameter. The actual entrainment for the pool fire is proportional to the perimeter of the fire, which is significantly greater than the perimeter of the circular area. However, the enclosure is small and the smoke filling rates are expected to be short regardless of the fire shape.
The fire duration, ∆ , is determined from the pool depth, , density, , and burning rate, :
∆ 0.069 m 760 kg/m
0.039 kg/m /s 1345 s 22.4 min (C-7)
LUBRICATING OIL FIRE IN PUMP COMPARTMENT
Figure C-3. Heat release rate curve for lubricating oil fire.
The location of the fire is placed at the edge of the dike, closest to the target cable. The total mass of fuel is 144.4 kg, calculated from the volume multiplied by the density from Table C-2.
The stoichiometric mass-oxygen-to-fuel ratio, , is calculated using Equation 22 from Chapter 3-4 of SFPE Handbook, 4th Edition and the values from Table C-1, as follows:
∆
∆ O
46,000 kJ/kg
13,100 kJ/kg 3.5 kg/kg (C-8)
where ∆ is heat of combustion per unit mass of fuel consumed and ∆ O is the heat of combustion per unit mass of oxygen consumed. One of the inputs required by MAGIC is the specific area, s, a measure of the smoke generation, which is calculated as described in NUREG-1824 (EPRI 1011999), Volume 6, Section 3.2.7:
0.059 8,700 m /kg 513 m /kg (C-9)
where is the mass extinction coefficient and is the soot yield, as listed in Table C-2. The pyrolysis rate (g/s) is calculated for input to MAGIC by dividing the HRR values (4934 kW) at each time step by the heat of combustion (46,000 kJ/kg). Other inputs needed for MAGIC are listed in Tables 3-1, C-1, C-2, and C-4. Figure C-4 is a screenshot of the source fire in the MAGIC input file.
0 1000 2000 3000 4000 5000 6000
0 600 1200 1800 2400 3000 3600
HRR (kW)
Time (s) Heat Release Rate
Input HRR
LUBRICATING OIL FIRE IN PUMP COMPARTMENT
Figure C-4. MAGIC fire input screen for pump fire.
LUBRICATING OIL FIRE IN PUMP COMPARTMENT
In MAGIC, multi-conductor cables, composed of jacket, insulation, and conductor (copper, in this case), are modeled as single-conductor cables, as shown in Figure C-5.
Figure C-5. Modeling multi-conductor cables in MAGIC. Source: NUREG-1824 (EPRI 1011999), Volume 6, Figure 3-3.
The radius of the conductor in an equivalent single-conductor cable is needed for input to MAGIC. The mass of the conductor per unit length is calculated from the mass fraction of the conductor multiplied by the mass per unit length of the multi-conductor cable: 0.67 x 0.4 kg/m = 0.27 kg/m (values from Table C-1). To determine the conductor radius, , the mass per unit length (0.27 kg/m) is set equal to the cross-sectional area times the density of copper, 8954 kg/m3 (Table 3-1) or 0.27 . Rearranging the equation to solve for conductor radius results in the following:
0.27
8954 3.1 mm (C-10)
The insulation thickness is calculated by cable radius – jacket thickness – copper thickness = 7.5 mm – 2 mm – 3.1 mm = 2.4 mm. Since the jacket and the insulation are both composed of PE/PVC, the thicknesses are added together for a total thickness of 4.4 mm. As a result, the ERFBS protected cable raceway is modeled with three layers (Figure C-6): ceramic fiber blanket (5 cm), PE/PVC (4.4 mm), and copper (3.1 mm). The input screen for the layers of the ERFBS and the cables is shown in Figure C-7.
a Jacket
Insulation Conductor
a
LUBRICATING OIL FIRE IN PUMP COMPARTMENT
Figure C-6. Representation of the ERFBS protected cable raceway for MAGIC.
Figure C-7. MAGIC input screen for ERFBS layers.
Ventilation: Mechanical ventilation is maintained constantly during the simulation, using the values provided above. MAGIC uses circular ducts, so the rectangular ducts seen in Figure C-1 are modeled as circular areas with equivalent diameter of 0.56 m (1.8 ft). As noted above, the door is normally closed, but it is opened 10 minutes after ignition by the arriving fire brigade.
Before the door opens, leakage due to the doorway occurs via a 1.3 cm (0.5 in) gap under the door. The MAGIC input screen for the doorway is shown in Figure C-8.
Cooper Conductor Ceramic Fiber Blanket (ERFBS)
Combined Cable Jacket
LUBRICATING OIL FIRE IN PUMP COMPARTMENT
Figure C-8. MAGIC input screen for ventilation through door.
C.4.3 CFD Model
The following paragraphs outline the data utilized to model the scenario using FDS. Figure C-9 provides an illustration of the scenario, as rendered by Smokeview.
Geometry: The compartment is modeled as shown in Figure C-1, except that the pump itself is modeled as two rectangular boxes. A single uniform, rectangular mesh spans the entire
compartment, plus the hallway outside the door. The numerical mesh consists of approximately 0.2 m (0.7 ft) grid cells. A finer calculation with 0.1 m (0.3 ft) cells was performed with similar results. The latter calculation requires roughly a week of computing time on a single processor computer (2008 vintage), whereas the more coarsely gridded calculation requires about 10 hours.
Materials: All material properties are as specified above. The protected cable tray is modeled as a rectangular box with the same dimensions as the tray wrapped in a blanket. The box is made solely of 5 cm (2 in) of ceramic fiber insulation. The tray is neglected. A cable target is positioned within the box pointing downwards, as this is the hottest surface of the box. The exact dimensions of the box are not an issue; what matters is that the cable within the box is exposed to the heat that penetrates the thermal blanket. The cable temperature is computed using the Thermally-Induced Electrical Failure (THIEF) methodology (NUREG/CR-6931).
LUBRICATING OIL FIRE IN PUMP COMPARTMENT
Fire: Due to the limited amount of validation data available for scenarios of this type and the considerable uncertainties involved, the approach taken is to specify, rather than attempt to predict, the burning rate of the fuel, even though the FDS model does provide the physical mechanisms to estimate burning rates. The fire is specified in the diked area surrounding the pump. Although FDS has a liquid fuel burning model, it is not used here because there is not enough information about the fuel, and, more importantly, it lacks the exact geometry of the pump and diked area. Typically, FDS would expect that the oil has formed a relatively deep pool with relatively little influence by the surrounding solids. This is not the case here. Instead, the specified burning rate, 0.039 kg/m2/s, is applied directly to the model over an area of
2.75 m2 (29.6 ft2), yielding a burning rate of 0.107 kg/s. The density of the oil is 0.76 kg/L, which means that the oil burns at a rate of 0.141 L/s. At this rate, 190 L (50 gal) will require 1,348 s to burn out. Note that this is slightly different from the burning duration of 1345 s computed for the MAGIC input. The fire duration computation for FDS converts the mass data to volumetric data,
Figure C-9. FDS/Smokeview rendering of the pump room scenario at the early stage of the fire, before the compartment becomes under-ventilated.
LUBRICATING OIL FIRE IN PUMP COMPARTMENT
thus introducing an additional step and some rounding. The slight difference in the burning durations is due to this additional rounding and is not significant. The vaporized fuel is a mixture of various hydrocarbons, but FDS uses only one fuel molecule in the combustion sub-model.
For this calculation the fuel molecule is modeled as C14H30. Ventilation: The volume flow rates are applied as specified.
C.5 Evaluation of Results
The primary purpose of these calculations is to assess whether the Kaowool ERFBS applied to the critical cables within the pump room would be damaged in the event of a lubricating oil fire.
The results of the zone model MAGIC and the CFD model FDS are consistent in their HRR and compartment temperatures. This is expected because the models use the same specified burning rate, the same fuel stoichiometry, and the same basic rules of gas phase flame extinction based on oxygen and temperature levels in the vicinity of the fire.
Table C-5 summarizes the predicted cable temperatures from MAGIC and FDS, including an assessment of the model uncertainty. Note that the results are based only on a direct
calculation of the cable temperature and do not include an assessment of the sensitivity studies that are discussed in the next section.
Table C-5. Summary of the model predictions of the pump room scenario.
Model
The HRR curves predicted by the hand calculations and the MAGIC and FDS models are shown in Figure C-10 for the entire simulation (first plot) and the first five minutes (second plot).
The figures show the pronounced drop in the HRR soon after the start of the fire, which demonstrates that there is insufficient air (i.e., oxygen) within the compartment to sustain the postulated fire. Based on the calculations, the drop in HRR does not occur until after about 120 s, which is later than the predictions by MAGIC and FDS because the algebraic calculations allow all of the oxygen in the room to be consumed. MAGIC uses a lower oxygen limit of 10%, and FDS uses a lower oxygen limit that depends on temperature. At high temperatures, FDS expects all of the oxygen is consumed. After 120 s, but before the door is opened at 600 s, the value of the HRR calculated by the algebraic calculations (approximately 900 kW) is higher than the values predicted by MAGIC and FDS (approximately 350 kW) due to the differences in the lower oxygen level. The sudden jump in the HRR, predicted by FDS at 600 seconds, is caused by the unburned fuel igniting as the door is opened. Note that none of the models has an algorithm capable of determining whether or not the fire would be sustained at this reduced burning rate until the time when the door is opened.