# FLASHCAT for tray failures

## Secondary Combustibles#

The initial fire source may ignite electrical raceways and cables in the compartment, which are termed as secondary combustibles in this report. Despite the term “secondary,” these objects may not combust simultaneously but rather at different timings. The secondary fires can add to the heat released by the initial fires, which eventually changes the fire and temperature calculations. In order to estimate the total heat from the initial and secondary fires, the FLASH-CAT empirical methodology developed by the National Institute of Standards and Technology (NIST) [3] is adopted in this work. Circled area 1 in Figure 3 shows the application of FLASH-CAT in the scenario generation flow.

### Calculation Process#

$\mathring{a}$

$$I = \int_0^{2\pi} \sin(x) dx$$

The FLASH-CAT methodology estimates the HRR from the burning cables, the timing and duration of fire, and the length of cable burned during the initial combustion. These values are approximated from controlled fire experiments conducted by NIST. For that reason, this methodology requires certain assumptions that fit the experiment conditions to be met. The FLASH-CAT assumptions are:

• The cable trays are horizontal and stacked vertically with a spacing of less than 0.45 m (18 in)

• The cables burn in the open; that is, they are away from walls and well below the ceiling

• The cables are not exposed to elevated temperature sources except for the ignition source below

• There are no barriers separating the trays, and the tray tops and bottoms are open

• The cables are not protected with coatings, armor shielding, or thermal blankets of any kind

• There is a fire beneath the lowest tray

• The initial extent of the fire in the lowest tray is equal to the width of the source fire

• Each tray has at least a single row of cables or roughly 25 % of the NRC limit.

Under these assumptions, the fire is assumed to propagate upwards through the array of cable trays according to an empirically determined timing sequence. The length of cables within a given tray that ignite initially increases as the fire spreads upwards. Lateral spread of the fire begins as soon as the cables within the tray ignite. This produces a solid V-shaped burning pattern that expands laterally with time. As the mass of combustible material within the center of the V is consumed, the V-shape becomes an expanding, open wedge of burning cable. The fires in each tray continue to spread until the end of the tray is reached. This process is illustrated in Figure 4.

Figure 4. V-Shaped burning pattern in FLASH-CAT model.

The initial length of fire on the raceways is determined by the raceway’s vertical distance from the fire, and the order of the raceway among other raceways. For the first raceway (i.e., the raceway closest to the fire), the initial length is the same with the length of the fire itself. Once this first raceway combusts, the other raceways on top of it will eventually burn. The initial length of fire on those other raceways are calculated as:

(1)

Where L(i) denotes the fire length of the current raceway, L(i+1) is the fire length for the next raceway in the vertical order, and the hi is the vertical distance between the two raceways. The fire spreads laterally with a rate of 1.1 m/hour for thermoset cables and 3.2 m/hour for thermoplast cables. If there are multiple cable types in the same raceway, the fire spread rate is assumed to be the fastest among the cables (i.e., thermoplast).

Cables consist of metal and plastic elements. The amount of combustible mass in a raceway depends on the plastic mass of cables in it. A variable called the combustible mass per unit area mc” is calculated as:

(2)

Where j is the index of a cable in the raceway, Yp is the plastic mass fraction of the j-th cable, v is the char yield of the cable, m’ is the mass per unit length of the cable, and W is the tray’s width. The amount of combustible mass in a raceway determines how long the fire burns, which is denoted as :

(3)

Where is the heat of combustion, and is the HRR per unit area which is 150 kW and 250 kW for thermoset and thermoplast cables respectively. To calculate the time-dependent HRR profile, the raceway is divided into spatial grids, and the distance from the center of the fire is measured as x. The time when a spatial grid begins to combust, tign,i(x), is calculated as:

(4)

Where S is the fire spread rate in m/s, and is the time when the tray first ignites. If the grid is located within the original section of raceway that first ignites, the two ignition times will be the same. After calculating the combustible mass , the fire burn period , and the ignition time , each of the raceway grid will have a local HRR per unit area as shown in the Figure 5. HRR starts to increase from until reaching the peak Heat Release Rate Per Unit Area (HRRPUA) at one-sixth of later, remains stable until , and then decreases linearly to zero.

Figure 5. Time history of the local HRRPUA for each raceway grid.

Once all the HRRPUA profiles for each raceway grid have been calculated, the total HRR of the secondary combustible is calculated by summing all the local HRRPUA profiles from all raceways as follows:

(5)

Where is the total secondary combustible’s HRR, is the HRR of the initial fire, W is the raceway’s width, is the local HRRPUA, and t is the discrete observation time.

The process to initiate FLASH-CAT in our work is as follows:

1. Model the compartment, fire source(s), vent(s), cables, and raceways in FRI3D.

2. Run the initial CFAST simulation.

3. Get CFAST output of actual HRR, fire area, heat flux, and temperature at each raceway.

4. Iterate through each raceway. Check raceway geometrical coordinate if it is located above the fire source. (If a raceway is above it is conservatively included vs. the 0.45 m spacing requirement).

5. If raceway is on top of a fire source, calculate the initial length of cable that combusts. Iterate on each cable in the raceway. Check if the maximum temperature or heat flux at the raceway exceeds the cable’s combustion threshold. If it does, check the cable material properties. If the properties are not defined by the modeler in FRI3D, the default material properties are used for the cable, typically thermoplastic unless changed by the user (see Appendix B).

6. Create a one-dimensional spatial mesh along the cable’s length (dx) and calculate which mesh segments are burning at certain times (dt) by taking into account the horizontal fire spread rate.

7. Integrate the spatio-temporal heat release rate over the cable’s length to obtain the time-dependent HRR for that cable.

8. Sum the time-dependent HRR for all the cables within the raceway.

9. Repeat Step 5 until Step 7 for other raceways in the vertical stack.

10. Add the cable HRR to the initial fire’s HRR, update the CFAST input file with the new HRR, and re-run CFAST simulation.

11. Use the new CFAST results to get the temperature and heat flux at the next raceway in the iteration. Repeat from Step 4.

12. After all raceways have been evaluated, get the temperature and heat flux from the last CFAST simulation to estimate component failures.

### Data from the 3D Model#

When modeling raceways, a single raceway is typically broken up into sections wherever a cable enters or exits, which enables simple linking to the FRANX style of logic modeling. However, to calculate FLASH-CAT, the entire tray data and all cables need to be used. To enable this, each raceway has links to other raceway pieces. When the simulation indicates a particular raceway section will have secondary combustibles, the data from all linked raceways is used in the FLASH-CAT calculation. FRI3D automatically adds the links to raceways if they are touching and distinguishes between horizontal and up or down connections. Currently only horizontal connections are calculated for secondary combustion. The linking of local raceways described above is the solution chosen to ensure FLASH-CAT fire can propagate along the whole physical raceway. From the initial fire source, data for each route or path away from the fire is gathered, branches in the raceway cause additional fire propagation paths.

The raceways sections that are linked programmatically typically each contain different cables than adjacent raceways. For more realism, these differences should be accounted for to calculate the FLASH-CAT HRR. However, in the current version, a conservative simplified approach is used. Instead of calculating the HRR contribution for each raceway section, the conservative method uses the section with the largest combustible mass and HRR per unit area for the entire raceway. This could be updated in a future revision but was done currently to reduce code complexity and computation time. The combustible mass is calculated for each local raceway following Equation (2). The maximum value among all local raceways is taken as the combustible mass for all pieces of raceway in the FLASH-CAT calculation. This value is then used to calculate the burning period following Equation (3). Therefore, the burning period for each raceway grid is conservatively longer than what is expected. These local HRRPUA profiles are then summed following Equation (5) to form the overall HRR profile. As a result, the HRR profile has conservative higher gradient and the fire burns longer.

## Failure Calculations#

Users are able to specify data used in failure calculations; if no data is provided, then default parameters are used. The default parameters outlined in Appendix B are initially assigned to conservative NRC specified values, but they can be altered for plant specific needs. These sections go over the implementation of the methods implemented in FRI3D.

### Cables#

Two methods to estimate cable failures are adopted in this work, namely the heat-soak method [4] and the THIEF method [5]. The heat-soak method is the simplest out of the two. It uses a lookup table for time-to-damage as a function of constant exposure. It determines failure in a generic manner based on whether the cable is a thermoset or a thermoplastic one. For that reason, this method is selected by default when detailed data of the cable is not provided by the modeler in the FRI3D model. The method calculates a variable called the damage integral based on the time-dependent reaction rate. Damage occurs when this damage integral is greater than or equal to 1. This method can be applied using temperature or heat flux data using the lookup table to determine failure listed in Appendix B. The time of the cable failure is determined if/when the time the cable tray is above a given temperature or flux of passes the time specified in the table.

The THIEF calculation is more detailed compared to the heat-soak method. It uses the cable’s dimension and thermal data to calculate the temperature inside the cable. Assuming the heat transfer on a cable is largely in the radial direction, it calculates the one-dimensional radial conductive heat transfer with the surface boundary conditions taken as the temperature or heat flux calculated by CFAST. Cable is damaged when the internal cable temperature, after thermal attenuation from the cable’s jacket, exceeds a specific threshold for thermoplastic or thermoset. This method is more realistic compared to the heat-soak method; however, it takes more computation time and data. The method is selected when the modeler provides the cable’s data in the FRI3D model. Circled area 2 in Figure 3 shows the application of either the THIEF or heat-soak method in the scenario generation flow.

The THIEF methodology is based on several assumptions as follows:

1. The dominant heat transfer along the cable is in the radial direction, thereby the axial heat transfer can be omitted to simplify the calculation

2. The cable’s composition is homogenous

3. The thermal properties of the cable are independent of temperature

4. There is no physical decomposition within the cable during heating, ignition and burning

5. Cable fails electrically when the temperature inside the cable’s jacket reaches a threshold value.

To perform the THIEF calculation, a CFAST simulation is run to obtain the surface temperature and incident flux at a raceway. The surface temperature is then used as the boundary condition to solve the following transient conductive heat transfer equation:

(6)

Where , and k are effective density, specific heat, and thermal conductivity respectively. The equation is solved by the finite difference method. The cable’s radius R is divided into N uniformly spaced radial grids of length dr. A time step constraint dt is selected based on the value of dr as a criterion of numerical stability:

(7)

The finite difference solution to Equation (6) is given by:

(8)

The boundary condition for this solution is given by:

(9)

Where is the net heat flux at the surface due to the heat convection with the surrounding gas as follows:

(10)

Where is the emissivity of the cable surface (assumed to be 0.95 in THIEF methodology), is the Stefan-Boltzmann constant, h is the convective heart transfer coefficient (assumed to be 10 W/m2/K), and is the effective gas temperature at the n-th time step. The effective gas temperature may be approximated by the cable’s surface temperature obtained from the preliminary CFAST simulation if the radial grid is reasonably small. The cable is assumed to fail when the internal cable temperature exceeds 400°C and 200°C for thermoplast and thermoset cables respectively. The failure timing is taken when that threshold is exceeded.

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