This research was funded in part by a Multidisciplinary Research Program of the University Research Initiative (MURI) grant from the Office of Naval Research. Previous work has shown that the strength of the leading shock front oscillates and propagates secondary shock waves transversely to the main front. 22 1.4 (a) OH number density and temperature ZND profiles for a CJ explosion. b) Induction length ∆ as a function of the pilot shock strength.
Detonation Structure
- Introduction
- Historical background
- Characterization of the front
- Detonation structure and propagation
- Detonation theory
- Chapman-Jouguet theory
- Zel’dovich-von Neumann-D¨ oring (ZND) theory
- Constant volume explosion assumption
- Stability analysis
- Numerical simulations
- Thesis Outline
However, these images are difficult to interpret, due to the three-dimensionality of the front. A key result of the Chapman-Jouguet (CJ) theory is the calculation of the blast wave velocity, UCJ. 1if the object is large relative to the length scale of the cellular instability.
Experimental Setup
Facility description
Three PCB pressure transducers are mounted along the tube and record the blast pressure and time of arrival of the wave which is used to calculate the wave speed. One of these is at the center line of the window and can be used to enable flow visualization. Pressure sensors monitored the flatness of the blast front at the exit level of the initiator.
Flow visualization
A transducer was located 21.4 mm upstream of the centerline of the window and was used to trigger the flow visualization. The alignment laser is used to align the ruby laser cavity and also the rest of the path. The height of the light sheet and the size of the image were varied from 30-80 mm.
ICCD camera for
Soot foils
- Soot transport by detonation
In the NC facility, flat soot foils are mounted on the test section wall at the window location to the and anchored at the downstream end of the channel. As a contribution to this work, a study of the transport of soot by explosion was carried out. The optical path is aligned by placing a He-Ne alignment laser in place of the flash lamp housing.
The Effect of Confinement Geometry
- Transverse wave damping
- Boundary layers
Soot foils were fitted along surface A, upstream and downstream of the replaceable section, and along surface B. Test results for the effect of the porous wall on weakly unstable detonation are shown in Fig. In this case, the structure in both planes appears significantly disturbed downstream of the porous wall.
Weakly Unstable Detonation
- Transverse waves and triple point structure
- Keystones
- Detonation in narrow channel
- Collision process
The configuration found near the apex of the cell involves only a single triple point and a transverse wave almost orthogonal to the incident shock. The analysis assumes the flow is quasi-steady in the frame of the triple point and the waves are straight in the vicinity of the triple point, see Fig. In addition, the calculation assumes that the flow is steady in the frame of the primary triple point. .
Constant volume explosion calculations were made to obtain the OH mole fraction contours in the triple point region. These calculations show quantitative agreement with the PLIF images, although the location of the shock structure in the images must be estimated. These predictions are based on the idealized model of the triple point configuration and estimates of the OH mole fraction using zero-dimensional reaction zone models, as discussed in the text.
Triplet configurations appear to be of weak type in general, regardless of location in the cell cycle. From the superimposed images of the shock configurations and the reaction front structure in Fig. Schlieren images of the front in the narrow channel show a "double" structure, detailed in Fig.
Instead, it appears that part of the transverse wave becomes more closely coupled to the reaction and a second triple point may appear at the intersection with the out-of-plane structure.
Highly Unstable Detonation
- Lead shock oscillation
- Local decoupling
- Collision process
- Shear layers
- Structure over a range of scales
- Range of length scales
The temporal oscillation of the front during one cell cycle will be discussed in section 5.2. The magnitude of the oscillation in the foreshock velocity for this numerical simulation of weakly unstable detonation in two dimensions is 0.3UCJ. They found that the magnitude of the transient oscillation in lead shock strength increased for mixtures with higher activation energy.
In the first half of the cell, x-xo/L <0.5, the lead shock is called the Mach stem. In the second half of the cell, x-xo/L >0.5, the lead shock is called the incident wave. Lead shock velocity profile along the center line of the cell through one cell cycle, Fig.
Local detachment at the end of the cell cycle is observed in images of highly unstable fronts in the narrow channel. The substructure appears in the first half of the cell in scales of gradually increasing length. The aim is to obtain a first estimate of lead shock fluctuations from fluctuations in induction time.
A probability distribution of the horizontal edge displacement around the mean is shown in Fig.
Detonation Regimes
If the lead shock oscillations are fast enough (with fluctuation rates exceeding the critical decay rate), local decoupling or quenching of the detonation results. As the axes of the diagram, we choose the size of the lead shock oscillation normalized by the local average U0/UCJ, and the size of the fluctuation in the reaction time normalized by the local average τ0/τCJ, shown in fig. UCJ is the velocity of the front calculated from the stable, one-dimensional CJ model.
For the present analysis, we are interested in the size of the fluctuation, so we define it. 1.6, the critical value of the activation energy for the occurrence of instability can be taken as an asymptote, θ ~ 4.5. Induction time can also be calculated as a function of lead impact velocity for a given mixture using the constant volume approximation and detailed mechanism kinetics (Section 1.3.3).
If the mixture chemistry is such that the induction time response is 2.5≤τ0/τCJ ≤8, coupled detonation with cellular instability occurs. If the normalized induction time fluctuation is larger, τ0 ≥ 8τCJ, local separation or damping of the front may occur. The axes are the magnitude of the lead shock oscillation normalized by the local average U0/UCJ and the magnitude of the reaction time oscillation normalized by the local average τ0/τCJ.
The boundary (En. 6.28) between coupled and uncoupled is determined by the decay rate of the lead shock front, as explained in the text.
Conclusions
- Future Work
7.1 (c) shows a superimposed schlieren and fluorescence image, which directly shows the location and structure of the lead shock and the reaction front. The sketch shows part of the keystone feature in (a). c) Superimposed Schlieren and fluorescence image (false color) showing the correspondence of the location and configuration of the bullet impact with the keystones (Shot nc74). From the shadowgraph movies made in the present study, we measure the magnitude of the temporal oscillation of the firing rate of the lead through the cell cycle.
The lead shock velocity decreases from U = 1.42UCJ at the beginning of the cell to U = 0.69UCJ at the end of the cell in a sample of highly unstable detonation in C3H8-5O2-9N2. The magnitude of the oscillation, 0.73UCJ, is about 4 times the value measured for a weakly unstable detonation in 2H2-O2-17Ar. Decoupling is also inferred from experimental images of highly unstable detonations, which show significant oscillations in the location of the response behind a smooth lead shock.
Comparison with the corresponding schlieren images shows that the hot spots in the shear layer occur near the end of the cell cycle, but before the three-point collision. This release of energy can potentially contribute to the re-ignition process at the end of the cell - a. We show that a larger range of scales of cellular instability results from the stronger dependence of the induction time on pilot shock strength.
The axes are the magnitude of the pilot oscillation normalized by the local mean U0/UCJ and the magnitude of the fluctuation in the response time normalized by the local mean τ0/τCJ.
Bibliography
In Fluid Mechanics and its Applications v.5 Dynamic structure of detonation in gaseous and dispersed media, The Netherlands, p. Kinetic modeling of the CO/H2O/O2/NO/SO2 system: Implications for the high-pressure drop in SO2+ O(+M)=SO3(+M) reaction. VIII Rate constants for O+H2=OH+H and O+D2=OD+D from measurements of O atoms in oxidation to H2 and D2 by N2O. Optical Laser Visualization of Detonating Structures.
Diplom Arbeit, Lehrstuhl f¨ur Thermodynamik: Technische Universit¨at M¨unchen / Graduate Aeronautical Laboratories: California Institute of Technology. On the nonlinear stability and detonation limit of a detonation wave for a model three-step chain-branching reaction.
Appendix A Images from Narrow Channel Experiments
Appendix B Triple Point Calculation
Two entries are required to close the system; we choose the speed of the incident wave and the angle of impact. In the analysis discussed in the main text in section 4.1.1, the incident wave velocity is obtained from two-dimensional numerical simulations by Eckett (2000). The speed of the incident wave is a function of the location of the lead shock through the cell cycle.
If the analysis is performed for comparison with a specific experimental image, the location through the cell cycle is estimated based on the measured length of the Mach stem and parts of the incident wave at the front of the image. The second input, the angle of the incident wave with respect to the current, β1, is assumed to be π/2−φ, where φ is the angle of the track or the angle of the cell pattern observed on the soot film. The analysis is sensitive to this parameter and an analysis of the implications of this is contained in the main text, Section 4.1.1.
A shock polar locus is drawn for the pilot shock of given Mach number (this is the first input). The post-shock state behind the incident wave, state 2, is found along this pole, given the value of the shock angle, β1 (the second input). The intersection of the pilot shock and transverse wave polar states 3 and 4 are found to be equivalent in the P-θ plane.
In the mixtures considered in this study, there is no crossing of the polar transverse wave and the lead wave detonation polar, and there is no detonation polar for the transverse wave.
Appendix C Mixture Parameters
Appendix D Narrow Channel Shot List
The field of view of the schlieren images was about 146 mm and of the frame camera images was about 138 mm.
