## 2 Materials and Methods
### Experimental Setup  
Figure 2 shows the experimental test setup used in this work, the aim of which is to reflect the specified intended use of the flap valve. This includes the minimum volume of the enclosure that can be protected, the geometrical configuration of the duct and the distance for installing the flap valve. In this research, three bends in the duct were included in order to evaluate their influence on explosion propagation and the functionality of the flap valve (Tables 2 and 3). Tests were carried out using:  
* A straight duct (Figure 3a);
* A curved duct using three 90\({}^{\circ}\) bends with a R/D (curvature radius/duct diameter) ratio of 0.6 (Figure 3b);
* A curved duct using three 90\({}^{\circ}\) bends with a R/D ratio of 1.5 (Figure 3b). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Raw Material** & **Concentration (g/m\({}^{3}\)) * & **K\({}_{\text{st}}\) (bar\(\cdot\cdot\)m/s)** & **P\({}_{\text{max}}\) (bar)** \\ \hline Al & 1000 & 304 & 9.9 \\ MS & 500 (\({}^{1}\)) & 135 (\({}^{2}\)) & 9.5 (\({}^{3}\)) \\ WF & 500 & 93 & 7.6 \\ \hline \hline \end{tabular}  
* Optimum dust concentration which provides the maximum value of K\({}_{\text{st}}\); \({}^{(1)}\) \({}^{(2)}\) K\({}_{\text{st}}\) of MS has been calculated in a vessel of 1 m\({}^{3}\) at 25 \({}^{\circ}\)C. (\({}^{3}\)) P\({}_{\text{max}}\) of MS has been obtained from IFA [20].  
\end{table} 
Table 1: Dust characterisation. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & \\ \hline \multirow{2}{*}{**Test**} & **Dust** & **Duct Length** & **N\({}^{\circ}\) of** & **Vessel** & **I\({}_{1}\)** & **I\({}_{2}\)** & **P\({}_{1}\)** & **P\({}_{2}\)** & **P\({}_{3}\)** & **F\({}_{1}\)** & **F\({}_{2}\)** & **F\({}_{3}\)** \\  & **Type** & **(m)** & **Rends** & **Vessel** & **Volume (m\({}^{3}\))** & **Vessel** & **I\({}_{1}\)** & **I\({}_{2}\)** & **P\({}_{1}\)** & **P\({}_{2}\)** & **P\({}_{3}\)** & **F\({}_{1}\)** & **F\({}_{2}\)** & **F\({}_{3}\)** \\ \hline Al-0-1 & & & & & & & & & & & & & & \\ Al-0-2 & Al-0-3 & & & & & & & & & & & & & \\ \hline MS-0-1 & & & & & & & & & & & & & & \\ MS-0-2 & MS & 13 + V + 3.47 & 0 & 1 & z1 & 3.56 & 7.26 & 0.1 & 7.26 & 12.9 & 0.1 & 6.13 & 12.9 \\ MS-0-3 & & & & & & & & & & & & & \\ \hline WF-0-1 & & & & & & & & & & & & & \\ WF-0-2 & WF & 13 + V + 3.47 & 0 & 1 & z1 & 3.56 & 7.26 & 0.1 & 7.26 & 12.9 & 0.1 & 6.13 & 12.9 \\ WF-0-3 & & & & & & & & & & & & & \\ \hline \hline \end{tabular}  
* V: valve position; I\({}_{k}\): additional injection bottles; P\({}_{k}\): pressure detector; F\({}_{k}\): flame detector; Z1: Position of the ignitor (in the middle of vessel) according to EN 16447 [13].  
\end{table} 
Table 2: Summary of the tests performed for the straight duct. Figure 2: Test setup for a DN500 flap valve mounted at a distance of 10.2 m measured from the 1 m\({}^{3}\) vessel, in a duct with three short radius bends (R/D = 0.6). Figure 3 presents a technical drawing with the different geometrical configurations of the ducts used. It also shows the location of the different sensors mounted to register flame and pressure signals. Organic and metal dust were tested to compare the results regarding the reactivity of the dust. The duct diameter was DN500. The ignition source on the 1 m\({}^{3}\) vessel was located at a distance of halfway between duct entrance and opposite end of the test vessel, or the Z1 position according to EN 16447 [13]. In addition, in order to ensure the correct flame propagation, additional injection of dust was considered along the ducts (Figure 3). All of the tests were recorded using a high-speed camera at 1000 frames per second allowing observation through windows of the duct of whether the flames had reached the flap valve and whether this was blocked or not. Regarding pressure measurements, sensors were mounted in the vessel in the middle of the duct and just before the flap valve. Their exact locations are shown in Tables 2 and 3.