## 2 Materials and Methods
### Experimental Setup
These were ceramic capacitive pressure sensors which can register pressures up to 2 bar, and their response time is 1 ms.  
Calibration tests were performed to ensure that the flame reached the position where the flap valve was mounted. Infrared photodiodes, with response time of under 5 ms were  
Figure 3: Technical drawing of duct configurations used: (**a**) straight duct, (**b**) including 90\({}^{\circ}\) bends. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & \\ \hline \multirow{2}{*}{**Test**} & **Dust** & \multirow{2}{*}{**Dust Length (m)**} & \multirow{2}{*}{**Dust Length (m)**} & \multirow{2}{*}{**Vessel**} & \multirow{2}{*}{**I\({}_{1}\)} & \multirow{2}{*}{**I\({}_{2}\)**} & \multirow{2}{*}{**P\({}_{1}\)**} & \multirow{2}{*}{**P\({}_{2}\)**} & \multirow{2}{*}{**P\({}_{3}\)**} & \multirow{2}{*}{**F\({}_{1}\)**} & \multirow{2}{*}{**F\({}_{2}\)**} & \multirow{2}{*}{**F\({}_{3}\)**} \\  & **Type** & & & & & & & & & & & & \\ \hline Al-3-1 & \multirow{2}{*}{Al} & \(1.1\pm 8\) & \(1.13\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.13\pm 9\) \\ Al-3-2 & \multirow{2}{*}{Al} & \(2.27\pm 9\) & \(1.34\pm 9\) & \(1.09\pm 9\) & \(1.23\pm 9\) & \(1.23\pm 9\) & \(2.29\pm 9\) & \(0.11\pm 9\) & \(1.29\pm 9\) & \(2.27\pm 9\) \\ \hline MS-3-2 & \multirow{2}{*}{MS} & \(1.1\pm 8\) & \(1.13\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) \\ MS-3-3 & \multirow{2}{*}{MS} & \(2.27\pm 9\) & \(1.34\pm 9\) & \(1.09\pm 9\) & \(1.23\pm 9\) & \(1.23\pm 9\) & \(2.29\pm 9\) & \(0.11\pm 9\) & \(1.29\pm 9\) & \(2.29\pm 9\) \\ \hline W-3-1 & \multirow{2}{*}{WF} & \(1.1\pm 8\) & \(1.13\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) & \(1.1\pm 9\) \\ W-3-2 & \multirow{2}{*}{WF} & \(1.27\pm 9\) & \(1.28\pm 9\) & \(1.33\pm 9\) & \(1.01\pm 9\) & \(1.50\pm 9\) & \(1.27\pm 9\) & \(0.11\pm 9\) & \(1.53\pm 9\) & \(2.24\pm 9\) \\ W-3-3 & \multirow{2}{*}{3.47} & \multirow{2}{*}{W} & \(1.23\pm 9\) & \(1.23\pm 9\) & \(1.23\pm 9\) & \(2.29\pm 9\) & \(0.11\pm 9\) & \(1.29\pm 9\) & \(2.27\pm 9\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the tests performed for the curved duct with a R/D ratio of 0.6 and 1.5.  
installed at similar positions to the pressure sensors to determine the speed of the flames (Tables 2 and 3). In every test, the flap of the valve stayed open using calibrated magnets and was then released due to the pressure produced in the dust explosion. The total amount of dust used was 0.35 kg, 1.2 kg and 5 kg for Al, MS and WF, respectively. In every test, the dust was placed in an air-pressurised container at 20 bar. Dust injection was controlled using a solenoid valve which was operated with specific software used to run the tests automatically. The injected dust was dispersed as it passed through a nozzle. All the dust explosions carried out were vented using venting panels mounted in the vessel on the opposite side to the duct and opened at 200 mbar (P\({}_{\text{stat}}\)). A commercial 5 kJ pyrotechnical ignitor was used for ignition. Each test was repeated at least three times. Flame speed was obtained by measuring the time the flame needs to pass through the locations where two consecutive flame sensors were mounted and wave propagation was calculated by taking into account the time when the overpressure reached 100 mbar for each consecutive pressure sensor and the distance between them. Finally, Tables 2 and 3 summarise the different test configurations and measurements.