Julian J. Lee

Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations

To understand the nonlinear dynamical behaviour of a one-dimensional pulsating detonation, results obtained from numerical simulations of the Euler equations with simple one-step Arrhenius kinetics are analysed using basic nonlinear dynamics and chaos theory. To illustrate the transition pattern from a simple harmonic limit-cycle to a more complex irregular oscillation, a bifurcation diagram is constructed from the computational results. Evidence suggests that the route to higher instability modes may follow closely the Feigenbaum scenario of a period-doubling cascade observed in many generic nonlinear systems. Analysis of the one-dimensional pulsating detonation shows that the Feigenbaum number, defined as the ratio of intervals between successive bifurcations, appears to be in reasonable agreement with the universal value of d = 4.669. Using the concept of the largest Lyapunov exponent, the existence of chaos in a one-dimensional unsteady detonation is demonstrated.

Doppler interferometry study of unstable detonations

Near-limit detonations are highly unstable and characterized by very large longitudinal velocity fluctuations that can range from 0.4 to 1.8 times the normal Chapman-Jouguet value. The period of the fluctuations also varies over a wide range from a few to a hundred tube diameters. In an attempt to establish a criterion for detonation limits, the velocity fluctuations of near-limit detonations are studied. A novel microwave Doppler technique based on a single coaxial mode has been developed for this purpose to give an unambiguous quasi-continuous velocity measurement of the detonation wave over the entire length of its travel. The near-limit unstable behavior in the detonable stoichiometric mixtures of hydrocarbons (C2H2, C2H4, C2H6, C3H8) with O2, air or N2O, tested in this work, have been characterized by four distinct modes of unstable behavior. This classification allows a qualitative description of the wide range of velocity fluctuations occurring near the detonation limit, including galloping waves.

Powdered Magnesium-Carbon Dioxide Propulsion Concepts for Mars Missions

The use of a fuel that can be burned directly with carbon dioxide derived from the Martian atmosphere has recently received attention as an alternative to chemical in situ propellant production strategies. Prior studies of theoretical performance (specific impulse) have identified magnesium as being one of the more promising fuels to bum with carbon dioxide, and magnesium has the additional advantages of being a dense, noncryogenic, storable, and environmentally benign fuel. While magnesium has been shown to bum in carbon dioxide, studies to date have been conducted with single particles, with little attention being paid to the details of how the metal fuel would be used in an actual rocket engine. This paper reyiews various options for a magnesium/carbon dioxide rocket (slurry, hybrid, etc.), and the concept of using compacted powder and carbon dioxide as bi-propellants is selected as being the most promising. The use of small particle size powdered magnesium in combination with an effective dispersion system has the potential to give the highest burning rates while minimizing particle agglomeration and two-phase losses. In order to obtain the greatest mass leveraging by in situ utilization, the magnesium/ carbon dioxide engine must‘ be able to stabilize combustion without the use of additional hydrocarbon fuels. The issues associated with magnesium/carbon dioxide combustion are addressed theoretically and experimentally. A laboratory powder dispersion system demonstrates the feasibility of working with pure powdered metal and is used to obtain some preliminary data on flame pfopagation in powdered magnesium suspensions in gaseous carbon dioxide at standard pressure and temperature. A flame speed of 1 m/s was observed .for magnesium in carbon dioxide at concentrations of approximately 800 g/m3. Flame propagation could not be established at lower

Effect of diethylenetriamine sensitization on detonation of nitromethane in porous media

Abstract The effect of varying the explosive sensitivity for a heterogeneous explosive formed of a packed bed of glass beads impregnated with liquid nitromethane (NM) sensitized with diethylenetriamine (DETA) is investigated. The changes in the dependence of critical charge diameter on bead size is investigated at concentrations of 5%, 10%, and 15% DETA over a range of bead diameters from 66 μm to 2.4 mm. Additional measurements are also performed on the critical diameter of the homogeneous liquid explosive itself. Three regions of behavior are identified for the bead-liquid explosive mixture. For bead sizes above approximately 1.5 mm, the critical diameter increases drastically as the amount of DETA is reduced from 15% to 10% and 5%. For bead sizes below approximately 1 mm, the critical diameter is nearly unchanged at concentrations of 10% and 15%. Between 1 and 1.5 mm, a region where the critical diameter increases sharply is found and detonation failure was observed in charge diameters of up to 60.5 mm. This transition region between the two others is found to be wider at lower DETA concentrations. This supports the previous proposition of two distinct mechanisms of detonation propagation which depend on the bead size: propagation through the pores of the media and propagation through the medium material itself.

Propagation of nitromethane detonations in porous media

The characteristics of the propagation of a detonation in chemically sensitized nitromethane in a dense porous medium are investigated. By introducing liquid NM+15% (by weight) DETA into densely packed beds of solid spherical glass beads 66μm to 2.4 mm in diameter, a highly heterogeneous explosive mixture is obtained. The critical (i.e., failure) charge diameter of this mixture is systematically measured in unconfined charges over a wide range of bead sizes. Velocity measurements are also made for the various charges. It is found that there exists a critical bead size above which the critical diameter decreases with increasing bead size and below which it decreases with decreasing bead size. This result indicates an abrupt change in the mechanism of propagation at the critical bead size. Velocity measurements further support this by emphasizing the different behavior above and below the critical point.

In-situ measurements of the onset of bulk exothermicity in shock initiation of reactive powder mixtures

The shock initiation process was directly observed in different powder mixtures that produce little or no gas upon reaction. The samples of reactive powder were contained in recovery capsules that permitted the samples to be analyzed after being shocked and that allowed the initiation of reaction to be monitored using three different methods. The microsecond time-scale processes were observed via a fast two-color pyrometer. Light intensity detected from the bottom of reactive samples was slightly greater compared to inert simulants in the first 10 μs after shock arrival. However, this light was much less intense than that which would correspond to the bulk of the material reacting. Thus it seemed that only small, localized zones, or hot spots, had begun to react on a time scale of less than 30 μs. Light emissions were then recorded over longer time scales, and intense light appeared at the bottom of samples a few milliseconds to a few hundreds of milliseconds after shock arrival at the bottom of the test ...

Two-dimensional autocorrelation function analysis of smoked foil patterns

Digital image processing techniques have been applied to the analysis of cellular smoked foil patterns from gaseous detonations. In particular, the two-dimensional autocorrelation function is applied to digital cell pattern images and an orientational correlation parameter is calculated. Taking line profiles along the directions of highest correlation provides an unbiased method of determining the mean cell size in each of the two principal directions. By analyzing the width, amplitude and angular position of the orientational correlation plots, information can be extracted concerning the cellular pattern regularity, the relative angular correlation between two sets of transverse waves in two directions, and the mean shape or elongation of the cells within the pattern. The technique is applied to smoked foils from oxyacetylene mixtures with argon dilutions ranging from 0 to 75% to quantify the increase in regularity with argon dilution. This method provides a simple and useful way of analyzing cellular patterns and constitutes a promising technique for improving smoked foil diagnostics.

Transmission of a Blast Wave Through a Deformable Layer

Experiments have been carried out to investigate the transmission of a blast wave through a deformable layer consisting of a variety of different types of foam. The shape of the stress-strain curve for a foam has a strong influence on the pressure wave transmitted through the foam. At low blast wave amplitudes, the transmitted pressure is attenuated because the strains induced in the foam fall within a relatively linear elastic region of the stress-strain curve. For high blast wave amplitudes, the transmitted pressure is strongly amplified because the foam is compressed into the densification region where the foam cells collapse almost completely and the foam material itself is compressed. A nonlinear spring-mass-damper model which incorporates the stress-strain curve as the spring force relation qualitatively reproduces the blast loading behavior observed experimentally for different blast wave amplitudes.

EFFECT OF PARTICLE MORPHOLOGY ON CRITICAL CONDITIONS FOR SHOCK‐INITIATED REACTIONS IN TITANIUM‐SILICON POWDER MIXTURES

The effect of titanium particle morphology on the shock sensitivity of titanium‐silicon powder mixtures has been investigated experimentally. The powder mixtures were tested in a planar recovery capsule, with the shock loading produced by a high explosive booster charge placed on top of the capsule and a PMMA attenuator. Reactions were not observed for equimolar mixtures of large (95 μm) spherical Ti particles with fine (15 μm) Si particles for incident peak shock pressures of up to 23 GPa, estimated with LS‐DYNA. In contrast, mixtures with fine (40 μm) spherical Ti particles or irregularly‐shaped fine (31 μm) Ti particles exhibited a threshold attenuator thickness, and hence shock pressure, for reaction initiation. Microscopy and microprobe backscatter analysis were used to identify the degree of intermixing between the particles for shock loading just below the reaction threshold. For the largest spherical Ti particles, little particle intermixing was evident. For the finer particles, penetration of Si ...