The applications of unsteady, multi-dimensional studies of detonation waves to ram accelerators

Since much of the early work on the concepts on which ram accelerators are based dates back to the 1960s, although many of these are still being actively pursued, it is difficult to formulate a completely logical approach. This situation is compounded by the use of presently unacceptable treatments of unidimensional detonations in the early work and unfortunately extended to some of the more modern treatments. My approach has been to start by dealing with the early work and recent work impinging upon it, then to re-emphasise recent work on detonations, particularly that dealing with the influence of changes in confinement on quenching and re-initiation of detonations. However, some knowledge of this is inferred in suggestions made in Part 2 for possible improvements in the techniques. Latter sections cover the development of the ram accelerator, the use of various types of projectiles, developments in experimental techniques and finally on areas in space flight where the results from ram accelerators might be utilised. Received 14 January 1999 / Accepted 16 June 1999     

Detonation properties of dense methane-oxygen-diluent gaseous mixtures: application to ram accelerators

Using a 90mm-bore, 3.15 m long detonation tube, experimental detonation characteristics (detonability limits, detonation velocities and peak pressures) of stoichiometric methane-oxygen-diluent mixtures at an initial pressure up to 3.5 MPa have been experimentally investigated. A parametric study has been carried out as a function of both amount and nature of diluent, namely carbon dioxide, nitrogen and helium. The experimental results allowed the adjustment and validation of computations of the Chapman-Jouguet characteristics by means of a thermochemical code. These experimental data associated with validated computations provide a valuable tool, among others, for the choice of the most appropriate mixture composition in the superdetonative combustion mode for ram accelerator (ramac) experiments. The investigations were organized to determine the upper detonable areas of dense ternary mixtures, and to provide detonation velocity data in order to adjust a series of intermolecular parameters involved in the thermochemical code. Received 8 May 1997 / Accepted 15 December 1997     

Experimental investigation of ram accelerator propulsion modes

Experimental investigations on the propulsive modes of the ram accelerator are reviewed in this paper. The ram accelerator is a ramjet-in-tube projectile accelerator whose principle of operation is similar to that of a supersonic air-breathing ramjet. The projectile resembles the centerbody of a ramjet and travels through a stationary tube filled with a premixed gaseous fuel and oxidizer mixture. The combustion process travels with the projectile, generating a pressure distribution which produces forward thrust on the projectile. Several modes of ram accelerator operation are possible which are distinguished by their operating velocity range and the manner in which the combustion process is initiated and stabilized. Propulsive cycles utilizing subsonic, thermally choked combustion theoretically allow projectiles to be accelerated to the Chapman-Jouguet(C-J) detonation speed of a gaseous propellant mixture. In the superdetonative velocity range, the projectile is accelerated while always traveling faster than the C-J speed, and in the transdetonative regime (85–115 % of C-J speed) the projectile makes a smooth transition from a subdetonative to a superdetonative propulsive mode. This paper examines operation in these three regimes of flow using methane and ethylene based propellant mixtures in a 16 m long, 38 mm bore ram accelerator using 45–90 g projectiles at velocities up to 2500 m/s.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Helium dilution for ram accelerator operation

Experimental detonation characteristics (detonability limits and detonation velocities) of methane-oxygen-helium mixtures at initial pressures of up to 5 MPa were measured in a 90 mm caliber, 11.7 m long (130 calibers) smooth-bore detonation tube. Stoichiometric as well as fuel-rich mixtures were investigated in order to provide performance data for ram accelerator applications. The experimental results were used to adjust and validate calculations of the Chapman-Jouguet detonation characteristics by means of a thermochemical code based on various real gas equations of state. On the basis of the detonation velocity data, a series of intermolecular parameters involved in the thermochemical code was determined. Furthermore, the investigation enabled to determine of the upper detonable area of these dense ternary mixtures under the present experimental conditions. Received 25 February 2000 / Accepted 24 January 2001     

Detonation wave initiation of ram accelerator propellants

The current ram accelerator operations have shown that data on the ability of the propellants to detonate are required. Previous studies examined the efficacy of initiation techniques based on piston impact. The purpose of the present work is to analyze the effects of detonation wave transmission from a detonating mixture into a low sensitivity mixture. One-dimensional modeling based on the analysis of pressure vs particle velocity for the mixtures is used to interpret experimental data. Furthermore, calculations based on chemical kinetics (CHEMKIN code) are provided. Experimental data together with the modeling of the detonation transmission provide some new insight into the limiting conditions necessary to establish a Chapman-Jouguet (CJ) wave in a detonable mixture. Received 11 January 2000 / Accepted 15 September 2000     

Obturator and detonation experiments in the subdetonative ram accelerator

An experimental investigation has been undertaken to improve understanding of the role of the obturator and detonations in the subdetonative ram accelerator starting process. Ram accelerator start experiments were conducted with various obturator geometries to determine the obturator dynamics and assess its effect on the outcome of a start attempt. The obturator rapidly decelerates upon entrance and then moves backwards. Reversal of direction occurs more rapidly after propellant ignition, for less massive obturators, and solid geometries. Perforated geometries and decreasing obturator mass are less conducive to igniting a given propellant, as evidenced by the flowfield and start attempt outcome data presented. Wave unstarts were observed to occur with and without detonations, indicating more than one mechanism responsible for this type of start failure. Piston-initiated detonation experiments were conducted by firing the obturators without the ram accelerator projectile. The piston experiments identified the detonation limits for a wide range of propellants, but were found to not always be indicative of the upper Mach number at which a ram accelerator can be successfully started. In some instances a successful start or wave fall-off would occur at Mach numbers above which a piston alone detonated the propellant. Thus, the projectile can play a mitigating role in detonation initiation and use of piston detonation limits to quantitatively define a detonation wave unstart limit was not realized. Received 6 April 1998 / Accepted 15 January 1999     

Real gas effects on the prediction of ram accelerator performance

The analysis of ram accelerator performance is based on one-dimensional modelling of the flow process that propels the projectile. The conservation equations are applied to a control volume travelling with the projectile, and quasi-steady flow is assumed. To date the solution obtained, namely the generalized thrust equation, has been based on the ideal gas assumption. At the high level of pressure that is encountered during the ram accelerator process, this assumption cannot be regarded as adequate. Thus, a more appropriate equation of state (EOS) should be used instead. Depending upon the level of pressure, several equations of state are available for dense gaseous energetic materials. The virial type of EOS can be more or less sophisticated, depending upon the extent of complexity of the intermolecular modelling, and turns out to be totally appropriate for most gaseous explosive mixtures that have been investigated at moderate initial pressures, i.e., less than 10MPa. In the present case the Boltzmann EOS was applied. It is based on very simplified molecular interactions, which makes it relatively easy to use in calculations. Moreover, the energetic EOS needs to be taken into account. This concerns all the calorimetric coefficients, as well as the thermodynamic parameters, which can no longer be expressed as only a function of temperature. The higher the pressure level, the more sophisticated these corrections become, but the main relationships that account for real gas effects are basically the same. These include the use of a general form of analytical operators applied to correct the thermodynamic functions and coefficients. The equations governing the one-dimensional model were taken as a basis for the real gas corrections and were solved analytically. The parameters which play the most crucial roles in this correction can thus be highlighted. A complete set of equations involving the real gas effects are presented in this paper. The QUARTET code was used in this investigation, especially for determining chemical equilibrium compositions. This more accurate model can better predict the projectile acceleration of the thermally choked propulsive mode. Although the present analysis is applied to the fuel-rich methane-oxygen-nitrogen mixture currently used in the ram accelerator experiments, its general formulation makes it readily applicable to any other mixture. The projectile velocity and acceleration histories determined by the Hugoniot analysis for the thermally choked ram accelerator mode, assuming the Boltzmann EOS, turn out to be in much better agreement with experimental observations up to the CJ detonation velocity than that when based on the ideal gas assumption. Received 9 August 1996 / Accepted 23 May 1997     

Non-equilibrium model of steady detonations in aluminum particles - oxygen suspensions

Steady-state detonation regimes are studied on the basis of the mathematical model of detonation of aluminum particles in oxygen taking into account differences in velocities and temperatures of the mixture components. The final steady state is analyzed by determining the types of final singularities in the plane of relaxation parameters (the ratios of characteristic times of thermal and velocity relaxations and combustion). The regions of existence of steady-state regimes are found numerically, depending on the detonation wave velocity and relaxation parameters. Numerical illustrations of various flow types are presented, and the properties of the detonation wave structure caused by velocity nonequilibrium are examined. Qualitative agreement of data obtained with frozen relaxation parameters and their dependence on the flow parameters is shown. Received 5 July 1997 / Accepted 13 July 1998     

A nonlinear oscillator concept for one-dimensional pulsating detonations

To interpret the results of direct numerical simulations for the one-dimensional pulsating detonation, a nonlinear oscillator model is proposed based on the integral conservation considerations. A gauging procedure is suggested in which the results from the direct numerical simulation are used to compute the coefficients of the oscillator equation. Various terms of the oscillator equation obtained are compared with those of mechanical nonlinear oscillators in order to illustrate their analogy. Among many important features captured by this nonlinear oscillator equation, the oscillatory behavior of the detonation wave front can be interpreted as resonant excitation of the chemical energy release. Received 24 March 1997 / Accepted 7 May 1998     

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     

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.     

Computational study of reacting flow establishment in expansion tube facilities

We study the temporal evolution of the combustion flowfield established by the interaction of ram accelerator-type projectiles with an explosive gas mixture accelerated to hypersonic speeds in an expansion tube. The Navier-Stokes equations for a chemically reacting gas mixture are solved in a fully coupled manner using an implicit, time accurate algorithm. The solution procedure is based on a spatially second order, total variation diminishing scheme and a temporally second order, variable-step, backward differentiation formula method. The hydrogen-oxygen-argon chemistry is modeled with a 9-species, 19-step mechanism. The accuracy of the solution method is first demonstrated by several benchmark calculations. Numerical simulations of expansion tube flowfields are then presented for two different geometries: an axisymmetric projectile and a ram accelerator configuration. The development of the shock-induced combustion process is followed. The temporal variations of the calculated thrust and drag forces on the ram accelerator projectile are also presented. In the axisymmetric projectile case, which was designed to ensure combustion only in the boundary layer, the radial extent of the flame front during the initial transient phase was surprisingly large. In the ram accelerator configuration the flame propagated upstream along both the projectile and tube wall boundary layers, resulting in unstart. Received 25 September 1996 / Accepted 15 January 1997     

Recent work on gaseous detonations

The paper reviews recent progress in the field of gaseous detonations, with sections on shock diffraction and reflection, the transition to detonation, hybrid, spherically-imploding, and galloping and stuttering fronts, their structure, their transmission and quenching by additives, the critical energy for initiation and detonation of more unusual fuels. The final section points out areas where our understanding is still far from being complete and contains some suggestions of ways in which progress might be made. Received 9 September 1999 / Accepted 10 May 2001     

Detailed flowfields of a RAMAC device in H2−O2 full chemistry

Numerical simulations of a RAMAC device were performed for a range of speeds and grid densities. For certain initial conditions the detonation was unstable and propagated ahead of the projectile in a normal detonation wave, similar to the experimental phenomenon of unstart. The unstart was observed to develop within the narrow space between projectile and tube wall (the throat), so we focus on that area. Detailed flowfield views of the throat reveal a separated flow rotating in one large vortex. The detonation is overdriven but steady for fast enough upstream velocities. The vortex has an important role in triggering off the unstart by creating a condition at the throat whereby the detonation can propagate against the flow. 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.     

Propagation mechanism of dust detonations

This paper summarizes the studies on dust detonations at the Stosswellenlabor of RWTH Aachen since 1987. The onset and propagation mechanism of heterogeneous dust detonations are similar to those of marginal gas phase detonations. A self-sustained dust detonation has transverse wave structures that provide the coupling between shock and reaction. Large transition distances and transverse wave spacings require large sized tubes for the propagation of self-sustained dust detonations. The Hugoniot analysis of the Chapman-Jouguet detonation predicts equilibrium detonation states being in reasonable agreement with the self-sustained dust detonations observed. Shock matching calculations at the triple point adequately determine the wave structures of those stable dust detonations.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Analytical study of idealized two-dimensional cellular detonations

In this study, the idealized two-dimensional detonation cells were decomposed into the primary units referred to as sub-cells. Based on the theory of oblique shock waves, an analytical formula was derived to describe the relation between the Mach number ratio through triple-shock collision and the geometric properties of the cell. By applying a modified blast wave theory, an analytical model was developed to predict the propagation of detonation waves along the cell. The calculated results show that detonation wave is, first, strengthened at the beginning of the cell after triple-shock collision, and then decays till reaching the cell end. The analytical results were compared with experimental data and previous numerical results; the agreement between them appears to be good, in general. Received 13 February 2001 / Accepted 2 August 2001     

Reignition of detonations by reflected shocks

Numerical simulations are used to study the diffraction, decay, and reignition that occurs when a detonation propagates past an increase in cross-sectional area in a rectangular tube. The computations solve the time-dependent two-dimensional equations describing a reactive flow in an argon-diluted stoichiometric hydrogen-oxygen mixture at atmospheric pressure. Previous studies have shown that soon after transmission to a larger area, the reaction front decouples from the leading shock and forms a decaying blast wave (“bubble”) in the larger tube. Then, depending on the initial conditions, the detonation either continues to decay or is reignited as the bubble reflects off confining surfaces. For a strongly overdriven initiating detonation, reignition occurs through an interaction between the bubble and the original contact surface. For a more weakly driven system, reignition can occur in two ways: either in the slip line and Mach stem of the Mach reflection formed when the bubble reflects off the bottom surface of the tube, or by multiple shock interactions that occur when the reflected bubble overtakes the initial detonation front. The computations show the evolution and development of the cellular structure of the steady detonation front. Submitted to the 14th International Colloquium on the Dynamics of Energetic and Reactive Systems, Coimbra, Portugal, August, 1993