# Application Assessment of Electrical Cables during Smoldering and Flaming Combustion
## 2 Materials and Methods
### Methods
Each test lasted 1000 s (unless all detectors had worked before or the fire parameters did not increase). Figure 1 presents an illustrative diagram of the experimental set-up; all distances are given in meters. Two test benches were used for smoldering combustion. The first was a heating plate with a diameter of 300 mm, which was warmed up to a maximum temperature of 650 \({}^{\circ}\)C. The radiation output of the hotplate was a maximum of 40 kW/m\({}^{2}\). The second test stand was a system with high current efficiency up to 120 A, and the cables were laid out in a meter-long fragment of the so-called fastening tray. To ignite samples during flame combustion, contaminated alcohol was used, in an amount of 150 mL, which filled a vessel with dimensions of 8 \(\times\) 8 \(\times\) 3 cm\({}^{3}\). Increased alcohol consumption resulted from the difficulty in starting the combustion of some samples and the duration of the test (about 1000 s). The alcohol was poured into a container placed under the samples attached to the steel hanger. Before starting the tests, 300 ml of contaminated alcohol was burnt in order to verify that the substance being combusted did not affect the measurement results. The detectors placed in the chamber did not react during the entire \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Detector Type** & **Installation Place in the Combustion Chamber** \\ \hline
1 & Linear detector & Height 3.8 m, \\  & & 1 m from the center of the chamber \\ \hline
2 & Linear detector & Height 2.8 m, \\  & & 1 m from the center of the chamber \\ \hline
4 & Optical detector plus CO detector & On radius R = 3 m, mounting height 3.9 m \\ \hline
5 & Optical detector plus CO detector & Height 1.8 m, \\  & & 1 m from the center of the chamber \\ \hline
6 & Suction detector (suction system) & Height 3.85 m, \\  & & 1 m from the center of the chamber \\ \hline \end{tabular}
\end{table} 
Table 2: Distribution of smoke detectors detecting smoke particles in the combustion chamber. Figure 1: Scheme of the experimental arrangement. combustion process, and the measuring equipment did not show the content of smoke particles in the chamber. The amount of cable material used for one test was:  
For each type of smoldering combustion (initiated by a heating field or by the flow of electric current through wires): 2 m test cable;  
For flaming combustion: 2 m test cable hung on a stand over a container of alcohol. Samples were placed above the flame. In the 1970s, [PERSON] derived an empirical formula for the efficiency of an ionization smoke detector. His research led to the definition of a mathematical model of the ionizing source in the form of the following equation [37]:  
\[\frac{\Delta I}{Io}=1-\frac{1}{\eta z}\big{(}1-e^{-\eta z}\big{)} \tag{1}\]  
where:  
\(\Delta I\)--the change in current due to the presence of smoke;  
\(Io\)--the current of the chamber without smoke;  
\(z\)--the aerosol particle concentration;  
\(\eta\)--the chamber constant that characterizes its sensitivity. The constant \(\eta\), for a given cell, is determined as a function of the particle and ion attachment factor, the geometric shape of the cell, and the voltage-current characteristics. In the case of parallel flat electrodes, it is expressed by the following formula [3; 38]:  
\[\eta=\frac{Io}{In}\frac{(x_{1}-x_{0})^{2}\beta(d)}{V_{o}b^{+}}\approx\frac{Io }{In}\frac{2\pi D_{i}(x_{1}-x_{0})^{2}}{V_{o}b^{+}} \tag{2}\]  
where:  
\(Io\)--the current of the chamber without smoke, with concentration of aerosol particles;  
\(In\)--the saturation current;  
\(\beta(d)\)--the ion attachment factor for particles of diameter \(d\);  
\(x_{1}-x_{0}\)--the electrode spacing;  
\(V_{o}\)--the voltage between electrodes at current \(Io\);  
\(b^{+}\)--the electrical mobility of the positive ion, 1.4/cm\({}^{2}\) Vs;  
\(D_{i}\)--the diffusion coefficient (for small ions 0.042 cm\({}^{2}\)/s);  
\(d\)--the mean particle diameter (homogeneous, isotropic particles).