Dynamics of oblique detonations in ram accelerators

Time-accurate numerical simulations are used to study the dynamic development of oblique detonations on accelerating projectiles in ram accelerators. These simulations show that the oblique detonation can be stabilized on the projectile. The high pressure generated behind the detonation can result in accelerations up to 10⁶G and propel the projectile to velocities higher than 4.0 km/s. The detonation structure on the projectile is sensitive to the projectile geometry. A small change in the projectile shape is sufficient to alter the overall detonation structure and significantly affect the pressure distribution on the projectile. In order to maximize the thrust, an appropriate projectile shape has to be chosen to generate the detonation structure just behind the widest part of the projectile body. The projectile acceleration also has strong effects on the flow field and the detonation structure. During the acceleration, the location of the oblique detonation moves upstream from one reflected shock to another. However, one the detonation is stabilized behind the upstream shock, it remains at the new location until the transition to the next upstream shock occurs. In the simulations, the Non-Inertial-Source (NIS) technique was used to accurately represent of the projectile acceleration. Also, the Virtual-Cell-Embedding (VCE) method was employed to efficiently treat the complex projectile geometry on cartesian grids.     

Visualization of turbulent combustion of TNT detonation products in a steel vessel

Mixing and afterburning of TNT detonation products in a steel vessel are recorded by the use of the Schlieren visualization system and high speed photography. The vessel is filled with air or 50% oxygen enriched air. Overpressure histories at the vessel wall are also recorded by using pressure transducers. In these experiments nitrogen, air or 50% oxygen enriched air are used as vessel fillers. The Oppenheim-Kuhl theory of thermodynamics of closed systems is applied to estimate the released energy on the basis of pressure histories. Received 29 August 1999 / Accepted 21 January 2000     

Effects of nitrates on hydrocarbon-air flames and detonations

Abstract. The subject of hydrocarbon sensitization by nitrates under conditions of a heterogeneous spray has been of interest due to its applicability in promoting ignition. To gain insight into the mechanisms of the nitrate sensitization effect, the present work was limited to vapour phase studies at elevated temperatures in order to avoid the influence of heterogeneous factors. The experiments performed included studies of flammability, flame propagation, shock ignition and detonation. The mixtures used were composed of air, hexane, and isopropyl nitrate (IPN) with IPN concentrations ranging from 0 to 100 mole % in hydrocarbon-IPN. In addition, methane and propane were also included in the flame experiments. For the shock ignition and detonation experiments, the measured ignition delay and detonation cell size had minimum values for IPN-air and maximum values for hexane-air. With increases in the IPN concentration, the ignition delay and detonation cell size fell monotonically between the values for hexane and IPN. This monotonic behaviour was explained to be the result of mixing the hydrocarbon with the more sensitive nitrate whose energetics are larger than or comparable to the hydrocarbon when mixed with air. For the slow combustion mode, the results also confirmed the monotonic behavior and showed that the lean flammability limit and the flame velocity fell between those of the hydrocarbon and IPN. Received 10 September 1999 / Accepted 27 July 2000     

Direct initiation of detonations in unconfined gasoline sprays

Large scale experiments on detonation initiation in gasoline-air by two different sources were carried out at stoichiometric conditions. Unconfined clouds of volume generated by a special facility had a shape of semicylinder of 15–17 m in length and 6–8 m in radius. Both the charge of condensed HE and the charge of stoichiometric propane-air were used to initiate detonation in the mixture. In case of initiation by a propane-air charge the critical initiation energy was up to 7 times as large as that for HE initiation. The detonation cell size for gasoline-air was determined as 0.04–0.05 m. It was shown, that the well-known correlation between the critical energy of point blast initiation and the cell size failed for this system. The cell size obtained is close to one of propane-air, but no direct transfer of detonation from one mixture to another was observed. Received 10 March 1995 / Accepted 12 March 1995     

Two-dimensional numerical simulations of multi-headed detonations in oxygen-aluminum mixtures using an adaptive mesh refinement

Abstract. Two-dimensional numerical simulations of detonations in two-phase lean mixtures of aluminum particles and pure oxygen have been performed. The computational procedure adopts an adaptive mesh refinement methodology in order to increase spatial resolution in the most interesting parts of the flow field. A one-step heterogeneous reaction describes the evaporation and combustion of aluminum. Depending on the gas-phase temperature, the combustion product is aluminum oxide or aluminum monoxide. The results show that the heterogeneous detonations resemble gaseous single-phase ones although the scale of the phenomena is very different. The detonation of aluminum dust evolves into the 2-headed mode of propagation with the characteristic detonation cell width equal to cm. For aluminum dust the cellular structure is much finer. The detonation initially propagates in the 11-headed mode with the characteristic cell width equal to cm and evolves into the 8.5-headed mode with the characteristic cell size $\lambda_{\rm cell}$ equal to cm. Received 7 May 2001 / Accepted 25 March 2002 Published online 23 January 2003 Correspondence to: K. Benkiewicz (e-mail: kbenk@cow.me.aoyama.ac.jp)     

Theoretical considerations on shock reflections and their implications on the evaluation of air intake performance

Many theoretical studies have shown the existence of a hysteresis effect in the solution of oblique shock reflections. In fact, a wide domain of free-stream Mach number and shock angle values exists where regular reflection and Mach reflection are both possible solutions for the same flow conditions. Part of this domain overlaps the typical operating conditions of supersonic air intakes, and therefore it is of practical interest to obtain a deeper understanding of the theoretical problem. Indeed, although both solutions are theoretically possible, they yield very different flowfields and consequently large discrepancies in the evaluation of the air intake performance. Numerical solutions for steady configurations have been carried out and compared with the flow evolution obtained for time-dependent cases. The results have confirmed numerically the existence of the multiple solution domain where hysteresis takes place in time-dependent simulations. The analysis of the physical and numerical problems encountered has provided indications for a correct simulation in practical applications. Received 10 August 1999 / Accepted 6 October 2000     

A numerical study of the mechanisms of self-reignition in low-overdrive detonations

Below a threshold in overdrive, both stability analysis and numerical simulations predict that one-dimensional detonations in high activation energy mixtures behave as a chaotic sequence of failures followed by reignition. Instead, less chaotic, cellular detonations almost invariably occur in experiments. Numerical simulation, based on the Euler equations with single step chemistry, shows that a ZND detonation initially fails in that regime. The detonation splits into a weaker shock, a surface discontinuity separating reacted from unreacted fluid, and a rarefaction wave. However, the detonation is eventually reignited by the explosion of a small gas pocket, in a process reminiscent of deflagration to detonation transition. In the fluid heated by the leading shock, the chemical reaction occurs slowly at first, but becomes faster as heat is released, until the pocket explodes. Small differences in initial temperature result in large enough differences in reaction time sufficient for one pocket of fluid to explode. In two dimensions, the explosion occurs earlier because an oblique shock structure develops which unevenly heats the fluid that passes through the leading shock. Hence, pockets that underwent more heating will explode sooner. As it moves upstream, the two-dimensional explosion, meets the leading shock and the detonation quickly develops a transverse wave structure. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995.     

Research on the motion of particles in the turbulent pipe flow of fiber suspensions

The motion of fibers in turbulent pipe flow was simulated by 3-D integral method based on the slender body theory and simplified model of turbulence. The orientation distribution of fibers in the computational area for different Re numbers was computed. The results which were consistent with the experimental ones show that the fluctuation velocity of turbulence cause fibers to orient randomly. The orientation distributions become broader as the Re number increases. Then the fluctuation velocity and angular velocity of fibers were obtained. Both are affected by the fluctuation velocity of turbulence. The fluctuation velocity intensity of fiber is stronger at longitudinal than at lateral, while it was opposite for the fluctuation angular velocity intensity of fibers. Finally, the spatial distribution of fiber was given. It is obvious that the fiber dispersion is strenghened with the increase of Re numbers.     

Investigation of the detonation regimes in gaseous mixtures with suspended starch particles

The existence of a secondary discontinuity at the rear of a detonation front shown in experiments by Peraldi and Veyssiere (1986) in stoichiometric hydrogen-oxygen mixtures with suspended 20-m starch particles has not been explained satisfactorily. Recently Veyssiere et al. (1997) analyzed these results using a one-dimensional (1-D) numerical model, and concluded that the heat release rate provided by the burning of starch particles in gaseous detonation products is too weak to support a double-front detonation (DFD), in contrast to the case of hybrid mixtures of hydrogen-air with suspended aluminium particles in which a double-front detonation structure was observed by Veyssiere (1986). A two-dimensional (2-D) numerical model was used in the present work to investigate abovementioned experimental results for hybrid mixtures with starch particles. The formation and propagation of the detonation has been examined in the geometry similar to the experimental tube of Peraldi and Veyssiere (1986), which has an area change after 2 m of propagation from the ignition point from a 69 mm dia. section to a 53 mm 53 mm square cross section corresponding to a 33% area contraction. It is shown that the detonation propagation regime in these experiments has a different nature from the double-front detonation observed in hybrid mixtures with aluminium particles. The detonation propagates as a pseudo-gas detonation (PGD) because starch particles release their heat downstream of the CJ plane giving rise to a non-stationary compression wave. The discontinuity wave at the rear of the detonation front is due to the interaction of the leading detonation front with the tube contraction, and is detected at the farthest pressure gauge location because the tube length is insufficient for the perturbation generated by the tube contraction to decay. Thus, numerical simulations explain experimental observations made by Peraldi and Veyssiere (1986). Received 5 July 1997 / Accepted 13 July 1998     

The influence of detonation cell size and regularity on the propagation of gaseous detonations in granular materials

This paper presents results from an experimental study of transmission of gaseous detonation waves through various granular filters. Spherical glass beads of 4 and 8 mm diameter and crushed rock of 7.5 mm volume averaged diameter were used as filter material. Varying the initial pressure of the detonating gas mixture controlled the detonation cell size. Dilution with argon was used to vary the detonation cell regularity. The complete range from almost no detonation velocity deficit to complete extinction of the combustion wave was observed. The existing correlation for gaseous detonation velocity deficit where is the critical diameter for the gaseous detonation and is the pore size, is found to be applicable for both smooth spherical particles and irregular crushed rock when considering irregular detonation structures. Soot films and pressure measurements show that as the detonation cell size is increased, reinitiation of a reanular filter until it finally no longer occurs at . Complete extinction of the combustion wave occurs at . These two limits appear to be about the same for irregular and regular detonation cell structures. For irregular structures without argon dilution, can be found for detonation wave failure, and can be found for complete extinction of the combustion wave. For argon dilution these limits are changed to and , respectively. The data are a bit scarce as a basis for proposing a new correlation for regular structures, but as a first approximation log is suggested for regular structures. The detonation or combustion wave is found to approach a constant velocity in the granular filter if not extinguished. Received 31 October 2001 / Accepted 15 July 2002 Published online 4 November 2002 Correspondence to: T. Slungaard (e-mail: slung@maskin.ntnu.no) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001     

Detonation and deflagration initiation at the focusing of shock waves in combustible gaseous mixture

Abstract. Detonation and deflagration initiation under focusing conditions in a lean hydrogen-air mixture was experimentally investigated. The experiments were carried out in a shock tube equipped with the laser schlieren system and pressure transducers. Two-dimensional wedges (53° and 90°), semi-cylinder and parabola, were used as the focusing elements. The peculiarities of mild and strong ignition inside the reflector cavity were visualized. A hydrogen-nitrogen mixture was taken for comparison between reactive and inert mixture. It was found that mild ignition inside the reflector cavity can lead to detonation initiation outside the cavity. Schlieren pictures of the process were obtained and the dependence of the distance of detonation initiation on Mach number of the incident shock wave was established. Received 30 August 1999 / Accepted 23 February 2000     

Detonation in heterogeneous mixtures of liquids and particles

The mechanisms of detonation propagation in heterogeneous systems comprising closely packed particles and a liquid explosive are not fully understood. Recent experimental work has suggested the presence of two distinct modes of detonation propagation. One mode is valid for small particles (which is the regime we will address in this paper) with another mode for large particles. In this work we model numerically the detail of the wave interactions between the detonating liquid and the solid particles. The generic system of interest in our work is nitromethane and aluminium but our methodology can be applied to other liquids and particles. We have exercised our numerical models on the experiments described above. Our models can now qualitatively explain the observed variation in critical diameter with particle size. We also report some initial discrepancies in our predictions of wave speeds in nominally one dimensional experiments which can be explained by detailed modelling. We find that the complex wave interaction in the flow behind the leading shock in the detonating system of liquid and particles is characterised by at least two sonic points. The first is the standard CJ point in the reacting liquid. The second is a sonic point with respect to the sound speed in the inert material. This leads to a steady state zone in the flow behind the leading shock which is much longer than the reaction zone in the liquid alone. The width of this region scales linearly with particle size. Since the width of the subsonic region strongly influences the failure diameter we believe that this property of the flow is the origin of the observed increase in failure diameter with particle size for small inert particles. Received 3 December 1999 / Accepted 5 July 2000     

Experimental and numerical investigation of the shock-induced fluidization of a particles bed

An experimental study on unsteady two phase flow is conducted in a vertical shock tube. Shock Mach numbers range from 1.3 to 1.5 in 1 bar. The particles are initially positioned in horizontal beds of various thicknesses. Our research covers a large domain of void fraction from 1 (single particles) to 0.35 (compact beds). The experiments provide shadowgraph images for the recording of particle trajectories (effect of the gas on the particles) and side-wall pressures (action of the particles on the gas). A dense two phase flow model has been elaborated and numerically solved using a finite difference scheme with pseudoviscosity. The simulated shock-induced fluidization of a 2 cm thick bed of 1.5 mm diameter glass particles is compared to the experiment. Received 10 September 1996 / Accepted 4 January 1997     

On the RR→MR transition of asymmetric shock waves in steady flows

In this paper, RR→MR transition of asymmetric shock waves has been theoretically studied. The transition can occur between the sonic-point and maximum-deflection criteria due to the the effects of expansion fans which are inherent flow structures. Comparison shows a better agreement among experiments and the analytical results. Some discrepancies reported in previous studies among experiments and theory have also been explained based on the threshold for RR→MR transition.      

Shock wave interaction with a cloud of particles

The present paper is devoted to experimental and theoretical investigation of the shock wave (SW) propagation in a mixture of gas and solid particles in the presence of explicit boundaries of the two-phase region (cloud of particles). The effect of the qualitative change in the supersonic flow behind the SW in a cloud of particles within the range of the volume concentration of the disperse phase 0.1-3% is experimentally shown and theoretically grounded. Received 15 April 1996 / Accepted 3 June 1996     

Kinetic theory of interacting particles in dilute suspensions of mineral waste

A kinetic theory of interacting spherical particles in dilute suspension is developed which results in a Boltzmann transport equation. This equation is solved in the relaxation time approximation to calculate the settling velocity of fine particulates in the steady state. The theory is applied to the suspended Jamaican bauxite waste and kaolinite particles. The experimental settling velocity compares well with the calculated values at low concentrations. This treatment can form the basis for a more rigorous theory applicable to denser systems and non-spherical particulates.     

Dynamics of short fiber suspensions in bounded shear flow

We have studied the dynamics of non-colloidal short fiber suspensions in bounded shear flow using the Stokesian dynamics simulation. Such particles make up the microstructure of many suspensions for which the macroscopic dynamics are not well understood. The effect of wall on the fiber dynamics is the main focus of this work. For a single fiber undergoing simple shear flow between plane parallel walls the period of rotation was compared with the Jeffrey’s orbit. A fiber placed close to the wall shows significant deviation from Jeffrey’s orbit. The fiber moving near a solid wall in bounded shear flow follows a pole-vaulting motion, and its centroid location from the wall is also periodic. Simulations were also carried out to study the effect of fiber–fiber interactions on the viscosity of concentrated suspensions.     

Measurement and imaging of supersonic combustion in a model scramjet engine

Results of tests performed in a free-piston shock tunnel on a model scramjet engine are presented. Two conditions which differed in Mach number were tested. Flow at the lower Mach number condition was achieved using a variable-angle diffuser. Shadowgraph images and floor static pressure measurements were obtained, the latter used as the basis of a finite-difference calculation of flow properties in the scramjet. Received 9 May 1998 / Accepted 30 September 1998     

Three-dimensional propagation of the transmitted shock wave in a square cross-sectional chamber

An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.PACS: 43.40.Nm