The evolution and cellular structure of a detonation subsequent to a head-on interaction with a shock wave

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1 Combustion and Flame 151 (2007) The evolution and cellular structure of a detonation subsequent to a head-on interaction with a shock wave Barbara B. Botros a,, Hoi Dick Ng b, YuJian Zhu a, Yiguang Ju b, John H.S. Lee a a Department of Mechanical Engineering, McGill University, Montréal, Québec, Canada b Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Received 11 October 2006; received in revised form 16 July 2007; accepted 25 July 2007 Available online 24 October 2007 Abstract This paper analyzes the results of a head-on collision between a detonation and a planar shock wave. The evolution of the detonation cellular structure subsequent to the frontal collision was examined through smoked foil experiments. It is shown that a large reduction in cell size is observed following the frontal collision, and that the detonation cell widths are correlated well with the chemical kinetic calculations from the ZND model. From chemical kinetic calculations, the density increase caused by shock compression appears to be the main factor leading to the significant reduction in cell size. It was found that depending on the initial conditions, the transition to the final cellular pattern can be either smooth or spotty. This phenomenon appears to be equivalent to Oppenheim s strong and mild reflected shock ignition experiments. The difference between these two transitions is, however, more related to the stability of the incident detonation and the strength of the perturbation generated by the incident shock The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Detonation; Cellular structure; Shock wave; Frontal collision; Chemical kinetics 1. Introduction A detonation wave possesses a three-dimensional unstable structure, characterized by a cell-like pattern that is traced out on a smoked foil in its path. The width of the cellular structure is proven to be a fundamental length scale with which different detonation dynamic parameters (e.g., initiation energy, critical tube diameter) are correlated, and its regularity can * Corresponding author. Fax: +1 (514) address: barbara.botros@mail.mcgill.ca (B.B. Botros). reflect the stability of the detonation wave [1]. For this reason, there is substantial interest in measuring the detonation cell size experimentally under different mixture conditions [2], from which improved model correlations with chemical kinetics can also be formulated [3,4]. Recently, an experimental technique was devised to study the evolution of the detonation cellular structure by perturbing it with a planar shock wave [5,6]. The technique provides a very reproducible diagnostic experiment that causes a step change in the underlying thermochemistry of the detonation to examine the coupling between gas dynamics and chemical processes. Following the collision, the detonation /$ see front matter 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi: /j.combustflame

574 B.B. Botros et al. / Combustion and Flame 151 (2007) 573 580 Fig. 1. Experimental setup.

2 574 B.B. Botros et al. / Combustion and Flame 151 (2007) Fig. 1. Experimental setup. propagates into a shocked medium with thermodynamic properties different from the pre-shock state of the reactants. A self-sustained CJ detonation will eventually re-establish itself with respect to the new downstream conditions [6]. By controlling the incident shock strength, it is possible to generate different thermodynamic conditions into which the detonation transmits and measure the resulting cell size values. Moreover, this technique also permits one to study how the detonation adjusts to a sudden change in mixture conditions. In this paper, the evolution of cellular structure subsequent to the frontal collision with a shock wave is examined by means of a smoked foil experiment. The measurements of detonation cell sizes following the collision are reported and compared with data from a chemical kinetic analysis. 2. Experimental setup Experiments were carried out in a 6-m-long and 6-cm-diameter detonation tube. The 2-m-long highpressure driver section is used to generate the incident shock wave. A thin diaphragm separates the driver and test sections. The driver section is pressurized with air and the diaphragm is ruptured by a pneumatic plunger, generating an incident shock that propagates into the test section. PCB pressure transducers mounted along the length of the shock tube measure time of arrival and pressure rise for all waves, where the signal from the first pressure transducer is used as a trigger to initiate the detonation by a spark discharge at the other end of the tube after an appropriate delay. A window section is mounted for taking streak Schlieren photographs using a high-speed camera. Thin foils initially coated with carbon soot are inserted along the tube wall to record the cellular pattern produced by the detonation. A schematic of the experimental setup is given in Fig. 1. Fig. 2. A typical streak Schlieren photograph for C 2 H 2 /O 2 at T 0 = 300 K and P 0 = 4 kpa showing the wave processes subsequent to the collision with a shock wave of M s = Results and discussion To illustrate the wave processes subsequent of the head-on collision, a typical streak Schlieren photograph is given in Fig. 2 showing the x t trajectories of different waves. As discussed in our earlier analytical and numerical study [6], a transmitted CJ detonation and a transmitted shock separated by a contact surface will result subsequent to the collision. This wave configuration can be seen clearly in Fig. 2.

B.B. Botros et al. / Combustion and Flame 151 (2007) 573 580 575 Fig. 3.

3 B.B. Botros et al. / Combustion and Flame 151 (2007) Fig. 3. A typical smoked foil for C 2 H 2 /O 2 at T 0 = 300 K and P 0 = 2 kpa showing the evolution of the detonation cellular structure from the head collision with a shock wave of M s = Fig. 4. The reduction in detonation cell size as a function of shock strength. Fig. 3 shows a typical smoked foil obtained from experiment. From this figure, the cellular pattern on the left side (darker region) corresponds to the cell size of the incident detonation propagating to the right. After colliding with the shock, the pattern evolves so that a finite transition region can be identified. It takes roughly two cell lengths of the unperturbed detonation to reach the final steady cellular pattern. Another important phenomenon observed from experiment is the significant change in the final cellular structure of the detonation wave, where its pattern is much finer than that before the head-on collision. The cell sizes of the perturbed detonation and the original detonation are measured, and their ratio is plotted as a function of incident shock strengths, as given in Fig. 4. The measurements obtained experimentally are compared with the computed results determined using the ZND chemical kinetic detonation model with an updated comprehensive mechanism for hydrogen [7] and Konnov s mechanism for acetylene reactions [8]. As a first approximation commonly considered in literature, the detonation cell size is assumed to be linearly proportional to the induction length of a steady ZND detonation ([9 12], etc.), i.e., λ = A Δ,whereA is a proportional constant. Equivalently, λ/λ 0 Δ/Δ 0, where it is assumed that the constant of proportionality A remains constant with a change in upstream conditions. It was found that the computed induction length ratio does not significantly change with the different initial pressures and mixture compositions considered in this study, and hence only one curve is shown in Fig. 4 for comparison. Further comparison of the effect of reactant mixture on the

4 576 B.B. Botros et al. / Combustion and Flame 151 (2007) Fig. 5. The variation of detonation cell size with reactant mixture conditions. theoretical cell size ratio is given in Fig. 5. It is seen that over the range of Mach numbers tested, there is very little divergence between the different curves. Despite the simplicity of the detonation model, the experimental and computational results are in good agreement. However, results for H 2 /O 2 are found to be consistently below the theoretical curve for the range of Mach numbers tested. This can be attributed to the change of the proportionality parameter A between cell size and induction zone length. In general, the parameter A is not universal and is shown to depend on the reactant thermodynamics and composition conditions [3,10 12]. For instance, in the study by Ciccarelli et al. [12], the parameter A is shown to decrease with increasing initial temperature of the H 2 /air mixtures. Equivalently, as the detonation propagates into the shocked hydrogen mixture, which has a higher initial temperature than the preshock (unperturbed) temperature of the reactants, the effect is to reduce the ratio λ/λ 0 = (A Δ)/(A 0 Δ 0 ).The observed decrease in cell size for H 2 /O 2 is thus not only due to a decrease in the computed induction zone length Δ/Δ 0, but also to the ratio of the parameters A/A 0. This would result in a lower theoretical curve than the one shown in Fig. 4 and better agreement with theory. However, this above reason only provides one preliminary explanation. It is important to point out that the initial temperature is not the only factor that affects the parameter A in this interaction phenomenon. The combined effect of pressure, temperature, mixture composition, reaction structure, and stability needs to be analyzed in more detail to understand the variation of A in the cell size correlation [3,4]. Subsequent to the collision, the detonation propagates into a mixture pre-conditioned by the incident shock. All thermodynamic properties of the mixture are raised by the adiabatic shock compression. Along with this new thermodynamic condition, there may also be a change in the fluid mechanics of the flow (i.e., detonation velocity, particle velocity). Since the induction zone length can be approximated as Δ u p τ i (where u p is the fluid particle velocity following the leading shock of the detonation in a ZND detonation-fixed reference frame and τ i is the chemical induction time), it is important to first determine if the reduction in induction length is caused by the purely chemical kinetic effect (τ i ) or fluid mechanical aspects (u p ) of the problem. This can be answered by looking at Fig. 6. The chemical induction time is first plotted as a function of the density and temperature following the collision. To determine how the particle velocity u p varies, we first note from the continuity equation that u p = ρ 1 /ρ 2 D, whered is the detonation velocity, ρ 1 is the density upstream of the detonation, and ρ 2 is the density downstream of the leading shock wave of the detonation. The values of ρ 1 /ρ 2 and D are plotted over the range of shock Mach numbers tested and are shown not to change significantly. Also plotted in Fig. 6 is the post-shock gas velocity u p. The particle velocity u p does not vary greatly over the range of incident shock strengths, compared to a larger change in the induction time. Therefore, a decrease in the reaction zone length following the collision is primarily determined by the changes in thermodynamic state of the reactants. Hence the chemical aspect appears to be the dominant factor. From purely chemical kinetic considerations, the thermodynamic parameter whose increase leads to the significant reduction in the cell size can be determined. Fig. 7 shows the computational results ob-

5 B.B. Botros et al. / Combustion and Flame 151 (2007) Fig. 6. The variation of different fluid and thermodynamics parameters as a function of incident shock strength. Fig. 7. The effect of temperature and density on the cell size reduction. tained by fixing either the density or temperature and computing the decrease in cell size. This is compare the results obtained using the post-shock condition. It becomes clear from this figure that the increase in density by the shock compression has a much more pronounced effect on the reduction in cell size than the effect of temperature. Figs. 8 and 9 illustrate the evolution of the cellular structure subsequent to the collision for the two cases studied. It appears that there are two kinds of transition processes. For the case with H 2 /O 2 and low incident shock strengths M s 1.3, as shown in Fig. 8, the transition is more smooth or gradual. In contrast, the transition for C 2 H 2 /O 2 and a larger shock strengths M s 2.0, as observed in Fig. 9, is more spotty, where new triple points or tiny reinitiation cells are being generated in localized regions. These small cells continue to develop and eventually produce a final cellular pattern. These different transitions appear to be very similar to Oppenheim s strong and mild reflected shock ignition experiments [13,14]. The analogy is thus an observation of the reestablishment mechanism upon the head-on collision to the new self-sustained CJ detonation downstream and the similar characteristic features during the transition or relaxation period [6].

578 B.B. Botros et al. / Combustion and Flame 151 (2007) 573 580 (a) (b) Fig. 8. Smoked foils showing the two different transitions for H 2 /O 2 (a) at T 0 = 300 K and M s = 1.

Table 1 Different thermodynamic and mixture properties obtained from chemical kinetics computation Cases T 0 P 0 Incident Behind incident shock detonation, χ T shock M s T shock E a / H 2 /O 2 300 K

6 578 B.B. Botros et al. / Combustion and Flame 151 (2007) (a) (b) Fig. 8. Smoked foils showing the two different transitions for H 2 /O 2 (a) at T 0 = 300 K and M s = 1.33, P 0 = 8 kpa and (b) at T 0 = 300 K and M s = 1.3, P 0 = 14.7 kpa. Table 1 Different thermodynamic and mixture properties obtained from chemical kinetics computation Cases T 0 P 0 Incident Behind incident shock detonation, χ T shock M s T shock E a / H 2 /O K 8 kpa K 24.9 C 2 H 2 /O K 1 kpa K 20.7 To understand the factors that influence the transition regime, we look first at the sensitivities of the shocked mixtures by calculating their corresponding activation energies, as given in Table 1. It is shown from the value of activation energies that the unreacted C 2 H 2 /O 2 mixture perturbed by an M s = 1.98 incident shock should be less sensitive than the unreacted H 2 /O 2 mixture shocked by a weak M s = 1.33 shock. This is in contrast to the difference in the transition regime, where C 2 H 2 /O 2 displays a transition of mild type. Hence, the sensitivity of the shocked mixture in this case does not appear to be the dominant factor that leads to the weak/strong transition. Instead, the strength of the incident shock and the stability of the incident detonation should determine the transition process. Table 1 shows the stability parameter χ, which has been shown to provide a relatively good characterization of detonation instability [15], i.e., Δ I σ max χ = ε I = εδ I Δ R u, CJ where ε I, Δ R, σ max and u CJ denote, respectively, the reduced activation energy of the induction process, main heat release zone length, maximum thermicity, and CJ particle velocity in shock-attached frame. These numbers mean that the incident C 2 H 2 /O 2 detonation, which has a larger value of χ, is more unstable than the H 2 /O 2 mixtures. In other words, the incident C 2 H 2 /O 2 detonation is more sensitive to temperature perturbations. When colliding with a strong shock, the C 2 H 2 /O 2 detonation may initially fail before the transmitted detonation re-establishes itself. The instability can manifest during the failure state and develop tiny reinitiation cells in localized regions, analogous to Oppenheim s experiment, leading to the onset of the transmitted detonation. Conversely, the incident

B.B. Botros et al. / Combustion and Flame 151 (2007) 573 580 579 (a) (b) Fig. 9. Smoked foils showing the two different transitions for C 2 H 2 /O 2 (a) at T 0 = 300 K and M s = 1.

H 2 /O 2 detonation is more stable and perturbation by the weak shock may not cause the initial failure before re-establishment of the transmitted detonation.

7 B.B. Botros et al. / Combustion and Flame 151 (2007) (a) (b) Fig. 9. Smoked foils showing the two different transitions for C 2 H 2 /O 2 (a) at T 0 = 300 K and M s = 1.98, P 0 = 1kPaand(b)at T 0 = 300 K and M s = 2.09, P 0 = 1kPa. H 2 /O 2 detonation is more stable and perturbation by the weak shock may not cause the initial failure before re-establishment of the transmitted detonation. The cellular detonation can therefore transit smoothly to the final configuration. 4. Concluding remarks In this study, the cellular structure and its evolution are studied by using a shock wave to perturb an incident CJ detonation. The shock wave modifies the thermodynamic properties of the reactant mixture, thus causing a significant change in the cellular pattern of the transmitted detonation. A significant reduction in cell size is observed, which is in good agreement with the chemical kinetic prediction, showing a decrease in the chemical induction length. By looking at the transition region subsequent to the collision in more detail, two types of transition regimes can be observed, similar to Oppenheim s reflected shock ignition experiments. However, it appears in this problem that the difference is mainly due to the stability of the incident detonation and the strength of the shock perturbation. If the incident detonation is unstable, and collides with a strong shock wave, failure can initially occur. The re-establishment of the transmitted detonation is caused by spotty re-initiation cells in localized regions. This characteristic feature is reminiscent of the propagation mechanism of a highly unstable detonation, such as that of a detonation wave propagating in a methane mixture. Acknowledgments B.B. Botros and H.D. Ng are supported by the Natural Sciences and Engineering Research Council of Canada. References [1] J.H.S. Lee, Annu. Rev. Fluid Mech. 16 (1984) [2] M. Kaneshige, J.E. Shepherd, Detonation database. GALCIT Technical report FM97, 1997 (web page at

8 580 B.B. Botros et al. / Combustion and Flame 151 (2007) [3] A.I. Gavrikov, A.A. Efimenko, S.B. Dorofeev, Combust. Flame 120 (1 2) (2000) [4] H.D. Ng, Y. Ju, J.H.S. Lee, Int. J. Hydrogen Energy 32 (1) (2006) [5] K. Terao, T. Yoshida, K. Kishi, K. Ishii, Proc. 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems, Seattle, USA, [6] H.D. Ng, B.B. Botros, J. Chao, J.M. Yang, N. Nikiforakis, J.H.S. Lee, Shock Waves 15 (5) (2006) [7] J. Li, Z.W. Zhao, A. Kazakov, F.L. Dryer, Int. J. Chem. Kinet. 31 (1999) [8] A.A. Konnov, Detailed Reaction Mechanism for Small Hydrocarbons Combustion. Release 0.5, 2000, [9] C.K. Westbrook, P.A. Urtiew, Proc. Combust. Inst. 19 (1982) [10] J.E. Shepherd, Prog. Astronaut. Aeronaut. 106 (1986) [11] D.W. Stamps, S.R. Tieszen, Combust. Flame 83 (3 4) (1991) [12] G. Ciccarelli, T. Ginsberg, J. Boccio, C. Economos, K. Sato, M. Kinoshita, Combust. Flame 99 (2) (1994) [13] J.W. Meyer, A.K. Oppenheim, Proc. Combust. Inst. 13 (1971) [14] A.K. Oppenheim, Philos. Trans. R. Soc. London Ser. A 315 (1985) [15] H.D. Ng, M.I. Radulescu, A.J. Higgins, N. Nikiforakis, J.H.S. Lee, Combust. Theory Modelling 9 (3) (2005)

Near limit behavior of the detonation velocity

Near limit behavior of the detonation velocity John H.S. Lee 1, Anne Jesuthasan 1 and Hoi Dick Ng 2 1 McGill University Department of Mechanical Engineering Montreal, QC, Canada 2 Concordia University