## 3 Results and Discussion
### Influence of R/D Ratio on Flame Speed, Pressure and Wave Propagation  
Finally, the effect of the R/D ratio on flame speed, pressure and wave propagation at 100 mbar was evaluated. For this analysis, aluminium was selected due to the more intense explosion produced. In Figure 8, the trend in pressure is shown using a straight duct, bends with a R/D ratio of 0.6, usually considered as short radius bends, and ones with a ratio of 1.5, typically considered as long radius bends.  
As in the case of bends with a R/D ratio of 0.6 (Section 3.2), the use of bends showed higher pressure in all locations where the sensors were: in the vessel, in the middle of the duct and in the valve. Moreover, as expected, the pressure in the valve was higher than that in the vessel. The highest results were obtained using bends with a R/D ratio of 1.5, more than those with a straight duct configuration. This can be explained in the same way as for a R/D ratio 0.6 (see Section 3.2). The bend contributed by reflecting the wave and the accumulate dust. This in turn enhanced combustion, and the more combustion gases there were, the more compressed they were. As a result, there was a rise in overpressure. Regarding flame speed (Figure 9), the same behaviour as commented in Section 3.1 was observed. The bends led to a significant increase in flame velocity (58 \(\pm\) 2 and 82 \(\pm\) 18 m/s for straight and bent ducts, respectively). These outcomes could be explained as in Section 3.1. The bends enhanced turbulence as well as the mass burning rate, which led to an increase in the flame speed. Concerning the propagation of the pressure wave shown in Figure 10, higher pressures were obtained in the second section of the duct. It can be concluded that the second part of the duct (between the third bend and the valve) had more influence on the pressure increase. Regarding the first section of the duct, pressures levels were similar when using straight and bent ducts (around 247 \(\pm\) 28 m/s for the straight duct and 201 \(\pm\) 21 m/s for the bent duct).  
Then, the influence of the R/D ratio of the duct was evaluated. An R/D ratio of 0.6 showed a higher rise in pressure and blast wave propagation (Figures 8 and 10) along the duct than a R/D ratio of 1.5. A short radius (R/D = 0.6) meant there was a sharper turn which may have led to a higher drop in pressure than with a long radius (R/D = 1.5). A shorter radius might imply a more intense reflection of the pressure wave. It should also be noted that the space for releasing the combustion gases would be lower. Therefore, this could cause a higher compression of the gases and the pressure signal. However, long radius bends obtained the highest flame velocity (81 \(\pm\) 19 m/s) (Figure 9), which could be explained by its lower pressure drop. In addition, another observation was that the turbulence effect was more remarkable for long radius R/D bends.  
Finally, as can be seen, both long and short radius bends showed remarkable effects on rises in pressure and flame speed. Thus, flap valves should be tested using all types of bends considering their intended use in industry.  
In Table 4 deviations in pressures and flame velocities can be seen, as well as the environmental conditions for the different tests with the R/D ratio for the bends and different dusts tested.  
Figure 7: Influence of bends on the propagation of pressure waves for Al and MS along ducts: (**a**) Wave propagation speed between position 1 and 2, (**b**) Wave propagation speed between position 2 and 3.  
Figure 8: Influence of R/D ratio on pressure for aluminium dust explosions: (**a**) Vessel pressure (P\({}_{1}\)), (**b**) pressure in the middle of duct (P\({}_{2}\)), (**c**) valve pressure (P\({}_{3}\)).  
Figure 10: Influence of R/D ratio on pressure wave propagation for aluminium explosions along ducts: (**a**) Wave propagation speed between position 1 and 2, (**b**) Wave propagation speed between position 2 and 3.  
Figure 9: Influence of R/D ratio on flame speed between position 1 and 2 for aluminium dust explosions.