Parameters of front and condensation of carbon in detonation of benzotrifuroxan

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Lavrentiev Institute of Hydrodynamics, Novosibirsk, Russia

PARAMETERS OF FRONT AND CONDENSATION OF CARBON IN DETONATION OF BENZOTRIFUROXAN.

K.A. Ten

V.M. Titov

During the last 10 - 15 years, the development of the technology of particle accelerators resulted in a number of new non-contact methods for investigation into explosive processes [1-3]. They are based on dynamic raying of an object with high-energy beams of different nature. Considerable penetrability of synchrotron radiation (SR) and high temporal and spatial resolution allow, in addition to obtaining high-quality shadow images of flow under investigation, restoring the internal distribution of parameters of an object by imaging methods. Especially attractive is the possibility to measure diffraction signals (small-angle X-ray scattering, SAXS), from the distribution of which one can measure the sizes of nanoparticles that appear at condensation of carbon in the area of the chemical transformation. Currently, this is the only experimental method that allows investigation into the dynamics of carbon condensation in the detonation of oxygen-deficient explosives.

Investigation into the processes of carbon condensation in the detonation of such explosives is crucial for estimation of the amount of energy released under exothermic coagulation of carbon clusters. The published results [4] showed that an assumption of carbon condensation beyond the zone of chemical reaction allows a better description of the experimental data. Experiments with hydrogen-free explosive, С6N6O6 (benzotrifuroxan, BTF) are interesting in connection with big diamond particles that were discovered earlier in the products of BTF explosion [5], which makes the study of detonation processes in BTF important for practical application as well.

The method of measuring small-angle X-ray scattering (SAXS) is widely used in the static analysis of the structure of disperse systems. A combination of the SAXS method with the use of SR from high-power particle accelerators (VEPP-3, 2 GeV, Budker Institute of Nuclear Physics SB RAS) allows dynamic measurements of SAXS distribution with an exposure of 1 ns and periodicity of 250 ns. Analyzing the evolution of SAXS distributions, one can estimate the dynamics of the size of condensed nanoparticles in the detonation of explosives [6].

ALGORITHM OF RESTORATION OF FLOW PARAMETERS AND FINDINGS.

We investigated pressed BTF charges of 20 mm in diameter with a density of 1.81 g/cm3 and a length of 30 - 32 mm, which were initiated through an intermediate plasticized-TEN charge.

To measure the transmitted radiation we probed the detonating charge in two directions: the axis of the cylindric charge was in the plane of the SR beam and in the perpendicular direction [7, 8]. After calibrating the detector, from the measured transmitted radiation one can obtain data on the dynamics of mass distribution in the beam along the charge and in a fixed cross-section. In the first setting, the detonation velocity and density distribution in the front are determined with high accuracy (Fig. 1). For BTF, the width of the detonation front is 0.6 ± 0.1 mm and the maximum density in the front is 2.9 ± 0.1 g/cm3).

Fig. 1: (а). Relative intensity variation along the charge axis in the detonation of pressed BTF. The detector channels 0.1 mm wide are plotted along the X axis. Time between frames is 0.5 µs.

The results of the other setting are initial data for the tomography problems of reconstruction of internal flow parameters. Despite the high intensity of direct SR beam, straightforward use of data on absorption does not allow one to immediately get the required density of the explosion products. The reason is the high requirements imposed by tomography problems on the accuracy of the experimental data. One solution to this problem is the development of specialized techniques for reconstruction of the density, based on regularization of the desired solution to the density distribution problem with heavy use of a priori information about the structure of the flow under investigation. We have developed an original method for reconstructing the gas-dynamic parameters of detonation flow from X-raying experiment data. While the method has been adapted to a specific problem, it can greatly improve the accuracy of reconstruction of density [8] and determine the rest gas-dynamic characteristics: mass velocity and pressure distributions [9].

The method of restoring fields of gas-dynamic characteristics of detonation flow relies on a numerical solution to a gas-dynamic problem in a formulation corresponding to the experiment [6]. Let consider a problem of cylindrically symmetric gas flow. In this case, the equations of continuity and motion in the Euler coordinates are as follows:

where с is the density; p is the pressure; u and v are the axial and radial components of the velocity v; r and z are the radial and axial spatial coordinates; t is the time. Turning to the Lagrange coordinate system, we solve the problem of gas flow obeying the following equation of state:

(P0, , and are parameters yet to be determined). Given values of the parameters, we calculate the flow field, the density distribution in which can be compared with that obtained experimentally.

Parameters to be found were determined via minimizing a functional of standard deviations of calculated and experimental X-ray "shadows" of the flow in selected nodes of the region of computation. The dependence was approximated with a cubic spline. The emerging problem of multidimensional minimization was solved by the simplex method described and implemented in [10].

The reconstruction yields a parametric equation of state of the detonation products, which allows restoring a number of mechanical parameters of the flow not only in the field of observation of the X-ray shadow but in the entire space filled with the products of the explosion. Results for a benzotrifuroxan (BTF) charge of 20 mm in diameter are shown in Fig. 4.

Fig. 2: Spatial distributions of parameters and their values in the axis in the detonation of cylindrical BTF charge 2 µs after detonation front. A and C: the pressure; B: the density; D: unloading adiabat of the detonation products built along the flow line passing through the axis.

Besides the good consistency of the resulting equation of state (Fig. 2, D) with a polytropic-gas approximation with an adiabatic index close to 3, which is widely used for dense explosion products, this equation of state allows transition to an ideal-gas equation of state with an adiabatic index of 1.4.

The system of equations used in the reconstruction of the flow characteristics does not include the energy balance equation. This allows one to formally extend the method to the zone of chemical transformation, although these assumptions are not entirely correct in this case. In fact, the process in this area is not isoentropic and the state cannot be considered as a thermodynamic-equilibrium one. Continuing the consideration and interpreting the derivative as squared speed of sound с, we determine the position of the sonic surface from the equality |v| - с, which is the Chapman-Jouguet condition in a coordinate system moving with the velocity of the detonation front. The so-calculated sonic surface marks the boundary of the chemical reaction zone. For BTF charges, the length of the chemical reaction zone is less than the time resolution in this setting and the sonic boundary almost coincides with the boundary of the flat surface of the front.

The spatial accuracy of the restoration of the flow characteristics is rather high, 1-2 detector channels, i.e. ~ 0.2 mm. With the statistics over several experiments taken into account and an interval between frames of 0.5 µs, the resulting temporal resolution is about 0.2 µs. The accuracy of determination of the gas-dynamic characteristics is corrected with the applied laws of conservation and estimated as at least 10% in a 0.5 µs time scale.

MEASUREMENT OF SMALL-ANGLE SR X-RAY SCATTERING IN DETONATION OF BTF.

For dynamic experiments with SAXS registration we used a measurement scheme described in [6, 11]. Reflected SAXS rays were recorded by the detector DIMEX [12].

The angular range of the SAXS measurements was ~ 4*10-4 - 10-2 rad (2 - 100 channels of the detector). This range allows one to record SAXS from particles of the size [13]

Dmin = р /qmax = л/(4иmax) ? 2,0 nm

Dmax = р/qmin = л/(4иmin) = ~ 75 nm.

In a single flash, the SR detector records all the channels (forming one frame), registering the angular SAXS distribution. As the detonation front is moving along the charge with a constant rate of 8.5km/s (for BTF), after the SR pulse repetition period (250-500 ns), the detector records another SAXS distribution (another frame), forming a temporal sequence of SAXS distributions. In fact, this is an X-ray diffraction movie with a time shift of 0.5 µs and each frame 1 ns long. synchrotron radiation condensation detonation

The angular SAXS distribution (frames) vs. time in the BTF detonation is shown in Fig. 3. Frames, made with intervals of 0.5 µs, are marked with different colors. The scattering angle is given in the DIMEX detector channels (1 channel = 0.1 mrad).

Fig. 3. Dynamics of the SAXS distribution in the detonation of Trotyl-Hexogen 50/50 (left) and BTF (right). The angle of scattering is laid in the X-axis. The frame numbers correspond to different frames. Frame C11 corresponds to the passage of the detonation wave. The time interval between the frames is 0.5 µs.

The SAXS distribution obtained for BTF is intense enough to be processed with the program code GNOM [14].

Below are presented the processed results of the experiments at the time of the detonation wave passage (Fig. 4) and 3 µs (Fig. 5) after passage of the front. On the left are shown the volume distributions D (R) = 4рR3N(R)/3, where N (R) is the number of particles with the radius R. On the right is shown the graph of the relative number of particles N(R)/N with the radius R,. The N value was determined for each graph individually, i.e. the total number of particles in Fig. 4 ranging in size from 1 nm to 4 nm equals N.

Fig. 4. Volume distribution (left) and relative distribution of the scattering particles as the detonation wave passes (t = 0 - 0.5 µs). The radius of the particle in nm is laid in the X-axis.

Fig. 5. Volume distribution (left) and relative distribution of the scattering particles t = 3.0 µs after the passage of the detonation wave.

Analysis of the dependencies shows that the volume distribution of the particles, D(R), corresponds approximately to the particle sizes obtained by the Guinier formula (assuming that the particles are of the same size). The obtained size distributions have a maximum (in the particle size) smaller than that in Fig.5. 3 µs later, the distribution maximum of the scattering particles falls on R = 15 nm. The initial size R = 1.5 nm (at t = 0) in BTF is also larger than that in Trotyl-Hexogen 50/50. The total number of the particles strongly decreases with time (in the D(R) graphs, the volume decreases with time by orders of magnitude). Therefore the scattering particles can increase in size through coalescence of small nanoparticles into bigger ones. Further transition from the liquid phase to the crystalline one leads to growth of SAXS signals due to increasing "contrast" (the (?-?0)2 value gets bigger). In case of monodispersity, this can be interpreted as enlarging particles. Thus, the dynamic experiments confirm the data in [5], where remains of BTF detonation products in the explosion chamber were studied. In our experiments with BTF, the absence of hydrogen in the initial chemical composition can yield two factors influencing the process of carbon condensation: firstly, the absence of water vapor in the explosion products leads to increase in the temperature of the products, and consequently, to growth of the rate of condensation (formation) of carbon nanoparticles. Secondly, the absence of C-H radicals can fundamentally change the course of condensation. Mathematical modeling of nanodiamond formation via collision of carbon atoms [15] shows that carbon nanoparticles of 5 nm in size are formed within picoseconds. In dynamic experiments, the growth of nanoparticles is fixed within microseconds [6, 11]. One of the mechanisms explaining the lasting growth of the size of carbon nanoparticles is the presence of intermediate C-H radicals. One can solve the problem of registration of the radicals via measuring the diffraction reflections at big angles, which has not yet been performed in explosive experiments.

CONCLUSION

A parametric equation of state of explosion products in the density range of 500-2500 kg/m3 has been established.

Measurement of SR SAXS dynamics and processing with the program code GNOM made it possible to obtain size distributions of scattering nanoparticles. Within the first 3 µs after BTF detonation, the maximum in particle size (diameter) distribution increases from 3 nm to 30 nm. The work was performed with the equipment of the shared-use SCTSR, financial support of Ministry of Education of Russia, and RFBR grants № 10-08-00859 and № 11-03-00874.

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ABSTRACT

This article presents the results of measurements of transmitted and scattered synchrotron radiation in the detonation of benzotrifuroxan (BTF, С6N6O6). Processing of the results allowed us to determine parameters of the detonation products (density, pressure, and flow rate), as well as the dynamics of the particle size distribution at condensation of carbon behind the detonation front.

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