## 3 Results and Discussion  
### Influence of Bends (R/D Ratio of 0.6) on Flame Speed  
Figure 4 shows the flame speed between position 1 and 2 as a function of the number of bends for wheat flour, maize starch and aluminium dusts. It can be observed that the bends led to a slight increase of the flame speed for aluminium and maize starch (from 58 \(\pm\) 2 to 62 \(\pm\) 3 m/s for Al and from 29 \(\pm\) 9 to 37 \(\pm\) 6 m/s for MS), while for wheat flour a clear downward trend was observed (from 20 \(\pm\) 6 to 8 \(\pm\) 2 m/s). These different trends can be explained by their different reactive properties. Regarding WF dust, this has the fewest explosive characteristics (Table 1), and hence led to a less severe explosion with lower pressure and with the flame taking longer to reach the sensor. According to [PERSON] et al., flame speed could decrease due to the pressure drop experienced along the duct and the presence of bends [21]. Note that the pressure drop experienced with wheat flour should be more significant since the overpressures obtained were far less, due to its lower reactivity. However, for Al and MS dusts, the explosion pressure was more significant than pressure loss and thus, higher pressures were reached (Section 3.2). As mentioned above, for aluminium and maize starch, the bends caused a slight increase in the flame speed. These results concur with those published by [PERSON] et al. ; the presence of bends in the flame trajectory could cause the flow to reflect (moment in which the flow shocks the wall of the bend and changes its trajectory); therefore, a vortex could be formed [22]. In short, it can be considered as a loop; the bend can increase the flow distortion, which generates additional turbulence in turn improving the combustion of unburned particles due to the better dust/air dispersion and the more available air [23]. The rise in the mass burning rate caused an increase in the heat released which caused an expansion of combustion gases [24]. Thus, the expansion of combustion products may be related to higher flame speeds due to a release of energy and the formation of strong compression waves [25]. In addition, the dust combustion process can also be enhanced by the accumulation of unburned dust in the bend, approaching the stoichiometric concentration which would lead to a more optimal combustion process [24]. Finally, it could be observed that the highest speed of the flame was obtained with Al (62 \(\pm\) 3 m/s), which is in accordance with the highest K\({}_{\text{st}}\) (304 bar\(\cdot\)m/s) and P\({}_{\text{red}}\) (1253 \(\pm\) 141 mbar). In addition, a stronger explosion was observed with the third flame sensor using Al dust (Figure 3). The sensor closest to the flap valve did not detect any flame when testing Al dusts using the straight duct, and when testing MS and WF for both duct configurations, thus indicating that the flame did not reach the valve. This could be related to the weaker explosion and flame reverse (when the pressure is higher in the valve than in the explosion vessel). However, the flame sensor near the flap valve detected a signal in Al dust explosions with bends. To help understand this behaviour, Figure 5 shows the trend in flame speed along the different bends. A clear and notable increase in flame speed was obtained along the duct (from 62 \(\pm\) 3 to 80 \(\pm\) 7 m/s) for Al dust. It can be explained as described above: an increase in turbulence could be caused by the third bend and the closing of the flap valve. To ensure these protective systems work against explosions, the fact that the flames caused by Al dust went further (with bends) than the other ones (without bends) should be considered in their certification. This could imply that the flap valve takes too long to close and allows the flame to pass through the valve and hence the installation is not isolated. Thus, the minimum and maximum length of the flap valve installation should be carefully determined when using bends and highly reactive dusts such as Al.