ICCD camera for
Chapter 5 Highly Unstable Detonation
5.4 Collision process
5.4.1 Shear layers
As discussed in Section 4.1.1, “keystones” are formed in weakly unstable fronts due to spatial oscillations in the lead shock strength. The triple point analysis shows that the shear layers form the boundary between fluid particles that have passed through the strong portion of the lead shock front (Mach stem) and react relatively quickly, and particles that have passed through the weak portion of the front (incident wave) and the transverse wave and react more slowly.
Transverse wave
Shear layer (previous cycle)
Incident wave
Mach stem Shear layer (current cycle)
2mm
(a) (b)
Figure 5.10: Images from two separate experiments in 2H2-O2-17Ar, P1=20 kPa. Det- onation propagates left to right. (a) Transverse wave has interacted with the wave of opposing family at the end of previous cell cycle. The refracted wave propagates up- wards, interacting with the shear layer from the previous cycle (Shot nc83). (b) Overlaid fluorescence and schlieren images indicating reaction of unreacted gas occurs behind the transverse wave (Shot nc82).
Shear layer instabilities are observed in schlieren images of weakly unstable fronts. In Fig. 5.10 (a), the shear layer attached to the leading shock (current cycle) appears unsta- ble. In Fig. 5.10 (b), shear layer (previous cycle) appears unstable while in Fig. 5.10 (a), the shear layer from the previous cycle appears to become unstable after interaction with the transverse wave. The instability is not evident in the corresponding fluorescence im-
instabilities in fluorescence images to the resolution of the study (at best 50 µm/pixel).
In N2-diluted 2H2-O2 mixtures, shear layer instabilities are observed in schlieren im- ages and also in OH fluorescence images from both facilities, Fig. 5.11. Features com- monly associated with Kelvin-Helmholtz instability are evident. The vortical structures have the expected rotation as the fast stream occurs behind the transverse wave where the gas is unreacted while slow stream occurs behind the Mach stem where the gas has reacted. In the GDT experiment, Fig. 5.11 (a), the cell location is unknown. In the NC experiment, Fig. 5.11 (b and c), the shear layer is not at the triple point of the dominant cellular instability, but at an intermediate triple point in the front. The appearance of unstable shear layers in PLIF images shows that, in these fronts, the instability may occur with a large difference in OH concentration across the shear layer.
(a) (b) (c)
Figure 5.11: Images of unstable shear layers in (a) 2H2-O2-7.7N2, taken in the 150x150 mm test section of the GDT (Shot gdt1598), (b) schlieren and (c) OH fluo- rescence image in 2H2-O2-5.6N2 in the NC facility. (Shot nc110)
Local triple point calculations (Section 4.1.1) may be used to estimate thermodynamic properties across the shear layers, Table 5.3. Velocity differences across the shear layers are calculated to be 233 to 364 m/s, with the greatest value for N2-diluted H2-O2. The
Mixture ∆ (P3−P2)/P2 u3 u4 ρ3 ρ4 τ3 τ4 2H2-O2-17Ar 1.4 0.32 623 390 1.03 1.09 5.8 2.7 2H2-O2-5.6N2 1.4 0.37 716 352 0.89 0.98 7.9 2.5 C3H8-5O2-9N2 1.7 0.39 554 269 1.70 1.89 5.8 1.6
Table 5.3: Calculated properties across a triple point contact surface for sample mixtures from this study. State 3 is behind the incident and transverse waves and state 4 is behind the Mach stem (Schematic is shown in Fig. 5.12). ∆ is the induction length behind the incident wave (state 2). τ is the induction time. These parameters are calculated using a constant volume explosion assumption, as discussed in Section 4.1.1, using the detailed Konnov mechanism. The incident wave velocity wave is taken to be 0.9UCJ, representative of conditions near the end of the cell. In calculating the transverse wave strength, the track angle is assumed to be 33◦.
induction time ratio, τ3/τ4, is larger for the N2-diluted H2-O2 than for the Ar-diluted H2- O2. This calculation indicates that the shear layer separates reacted and unreacted gas over a greater length in the N2-diluted H2-O2, increasing the likelihood of observing the instability in that portion of the shear layer. In contrast, shear layer instability in weakly unstable fronts appears most likely to occur either in reacted gas or at an unresolvable scale for the present experiment.
In C3H8-5O2-9N2, regions of intense chemiluminescence have been observed, Fig. 5.13.
From the schlieren images, it can be determined that these regions correspond with the location of shear layers. The detonation appears to have locally decoupled at the end of the cell cycle, but the transverse wave collision has not yet occurred. If the shock and reaction front decouples at the end of the cell, the shear layer separates reacted and unreacted gas over a considerable length. With the increase in surface area in an unstable shear layer, we may speculate that local “hot spots” may be formed due to mixing of hot products and cold reactants, and possibly contribute to the re-ignition process at the end of the cell. This is a “turbulent” combustion mechanism that is not included in traditional detonation models based on shock-induced explosion.
2 1 3
4
Mach stem
Incident wave Transverse wave
Figure 5.12: Cartoon showing states at triple point configuration. For each mixture in Table 5.3, the triple point configuration is calculated using shock polars, as discussed in Section 4.1.1. Induction times τ are calculated by taking particle paths through the three-shock configuration and using a constant volume explosion assumption.
(a) (b)
Figure 5.13: Chemiluminescence images in C3H8-5O2-9N2, P1=20 kPa. (a) Shot nc205 and (b) Shot nc206. Image height is 65 mm.