With their higher efficiencies compared to traditional deflagration-based combustion engines, Pulse Detonation Engines (PDE) have been of interest to researchers for the past few decades. However, in view of the excessive length required for the direct initiation of a detonation wave, the PDE has not yet been commercialized. In order to achieve a more compact PDE configuration, detonation propagation within a bent tube has been proposed. This will not only yield a physically more compact PDE due to the tube bending, but will also result in an acceleration of the deflagration-to-detonation transition (DDT) process. It has been proven by Frolov [1] that by using a 180-degree bent tube, it is possible to achieve DDT if the deflagration speed is only 800 m/s.
It is generally agreed that DDT in a 180-degree bent tube arises due to compression near the outer wall, while at the same time the region near the inner wall is greatly weakened due to diffraction effects. In order to achieve a uniform wave strength, DDT using an S-shaped tube has been proposed since the rarefied flow region will subsequently undergo compression again. It is still an unresolved question whether the critical velocity for an S-shaped tube can be further decreased or not. The purpose of this paper is to answer the above question by providing experimental data on DDT using an S-shaped tube.
The valveless PDE system used in this study has previously been described in detail in [2]. As shown in Fig. 1, three different ignition locations are used to modify the wave speed prior to entering the S-shaped tube.
Experimental results have been presented in Fig. 2. We can see that despite different rates of misfire, even if the incoming shock wave speed is lower than 1500 m/s, DDT success rate is almost higher than 90% for equivalence ratios ranging from 1.0 to 1.4. Since detonation is a very stochastic phenomenon, shock waves with a wide range of velocities are generated. The experimental data has further been sorted using the incoming wave speed as shown in Fig. 3. It can be found that the minimum shock speed that is capable of successfully initiating detonation through this S-shaped tube is approximately 500 m/s.
In order to study how a reactive shock wave propagates inside this tube, CFD calculations using a similar geometry have also been conducted using ANSYS FLUENT. As can be seen from the pressure contours in Fig. 4, a low speed deflagration wave propagates into the S-shaped tube. Due to compression effects, a local overdriven detonation is formed along both the first and second outer curved walls. The one forming along the first outer curved wall region will subsequently undergo diffraction when it propagates into the second inner curved wall region, gets reflected at the S-shaped tube exit wall, and finally forms a Mach Stem before successfully undergoing transition to detonation. At the same time, the overdriven detonation forming along the second outer curved wall region has to propagate along a longer path so that it may trail behind the main Mach Stem generated previously. Therefore, the critical factors that could contribute to the DDT process are apparently the shock speed and strength at point 1 (in Fig. 1), which is formed by the previous compression at the first outer curved wall region. This could probably provide an explanation for why a shock wave having such a low speed is still able to achieve DDT through the S-shaped tube: even though the incoming shock wave before the S-shaped tube is propagating at a low velocity, as long as it can be accelerated to an overdriven detonation with a certain speed and strength before point 1, it will eventually undergo transition to detonation near the S-shaped tube exit. Experimental soot visualization results from test 1 corresponding to the same configuration have also been obtained as shown in Fig. 5 for validation. Some clear trajectories caused by the compression effect near the outer curved regions can be identified. Even though test 1 shows successful DDT, no cell structure can be found except in a small area to the right of the tube exit. Test 2 is similar to test 1 except the inlet velocity is higher than the Chapman-Jouguet velocity. As shown in Fig. 5(2), no cell structure can be found near the tube exit. These results show a comparable trend with the CFD results in that detonation initiation will only occur near or outside the S-shaped tube exit.
With the above analysis, it could be summarized that the S-shaped tube is capable of reducing the DDT inlet critical velocity to 500 m/s. Soot visualization and CFD results suggest that DDT is achievable for relatively low inlet wave speeds, possibly because of the compression process near the first outer curved wall region, diffraction of the local overdriven detonation and the subsequent reflection along the tube end wall. Further research work regarding the 180-degree bent tube and S-shaped tube on the critical velocity will be pursued for a better understanding of the DDT phenomenon in a bent tube.
References
[1] Frolov, S.M., Aksenov. V.S., Shamshin. I.O., Propagation of Shock and Detonation Waves in Channels with U-Shaped Bends of Limiting Curvature. Russian Journal of Physical Chemistry B, October 2008, Volume 2, Issue 5, pp 759-774.
[2] Li, J., Teo, C.J., Lim, K.S., Wen, C., Khoo, B.C., Deflagration to detonation transition by hybrid obstables in pulse detonation engines, AIAA paper 2013-3657.
