S. Jackson

Analytical Model for the Impulse of Single-Cycle Pulse Detonation Tube

An analytical model for the impulse of a single-cycle pulse detonation tube has been developed and validated against experimental data. The model is based on the pressure history at the thrust surface of the detonation tube. The pressure history is modeled by a constant pressure portion, followed by a decay due to gas expansion out of the tube. The duration and amplitude of the constant pressure portion is determined by analyzing the gasdynamics of the self-similar flow behind a steadily moving detonation wave within the tube. The gas expansion process is modeled using dimensional analysis and empirical observations. The model predictions are validated against direct experimental measurements in terms of impulse per unit volume, specific impulse, and thrust. Comparisons are given with estimates of the specific impulse based on numerical simulations. Impulse per unit volume and specific impulse calculations are carried out for a wide range of fuel–oxygen–nitrogen mixtures (including aviation fuels) of varying initial pressure, equivalence ratio, and nitrogen dilution. The effect of the initial temperature is also investigated. The trends observed are explained using a simple scaling analysis showing the dependency of the impulse on initial conditions and energy release in the mixture.

Direct Experimental Impulse Measurements for Detonations and Deflagrations

Direct impulse measurements were carried out by using a ballistic pendulum arrangement for detonations nand deflagrations in a tube closed at one end. Three tubes of different lengths and inner diameters were tested nwith stoichiometric propane– and ethylene–oxygen–nitrogen mixtures. Results were obtained as a function of ninitial pressure and percent diluent. The experimental results were compared to predictions from an analytical nmodel and generally agreed to within 15% (Wintenberger, E., Austin, J., Cooper, M., Jackson, S., and Shepherd, nJ. E., “Analytical Model for the Impulse of a Single-Cycle Pulse Detonation Engine, AIAA Paper 2001–3811, nJuly 2001). The effect of internal obstacles on the transition from deflagration to detonation was studied. Three ndifferent extensions were tested to investigate the effect of exit conditions on the ballistic impulse for stoichiometric nethylene–oxygen–nitrogen mixtures as a function of initial pressure and percent diluent.

Initiation Systems for Pulse Detonation Engines

A device capable of creating a collapsing toroidal detonation wave front has been designed and constructed. The goal is to generate pressures and temperatures at the focal region of the collapsing detonation wave that will be sufficient to initiate detonations in insensitive fuel-air mixtures inside of a detonation tube without blocking the flow path and causing associated losses in propulsive efficiency. This toroidal initiator uses a single spark and an array of small-diameter channels to generate and merge many detonation waves to create a single detonation wave with a toroidal front. The development process of the initiator system is described. Steps investigated involve detonation propagation through small tubes, development of a planar initiator capable of initiating a planar detonation wave from a single weak spark, and design and testing of the toroidal initiator. Results presented include the temporal history of pressure at locations near the focus of the collapsing torus and images of the front luminosity. The symmetry of the implosion and practical considerations related to repetitive operation are discussed.

WAVE IMPLOSION AS AN INITIATION MECHANISM FOR PULSE DETONATION ENGINES

A device has been developed which uses shock focusing to enhance the transmission e‐ciency of an initiator tube when used with pulse detonation engines. The initiator is capable of initiating detonations in ethylene-air and propane-air mixtures using less initiator fuel than is used in a conventional initiator tube. This toroidal initiator uses a single spark and an array of small-diameter channels to generate and merge many detonation waves to create a single detonation wave with a toroidal front. The collapsing front generates a high-temperature and pressure focal region. This region of high energy density is used to facilitate more e‐cient transmission of the detonation wave from the initiator into the fuel-air mixture.

Detonation Initiation in a Tube via Imploding Toroidal Shock Waves

The effectiveness of imploding waves at detonation initiation of stoichiometric ethylene- and propane–oxygen– nnitrogen mixtures in a tube was investigated. Implosions were driven by twice-shocked gas located at the end of a nshock tube, and wave strength was varied to determine the critical conditions necessary for initiation as a function of ndiluent concentration for each fuel. Hydrocarbon–air mixtures were not detonated due to facility limitations, nhowever, detonations were achieved with nitrogen dilutions as large as 60 and 40% in ethylene and propane nmixtures, respectively. The critical-energy input required for detonation of each dilution was then estimated using nthe unsteady energy equation. Blast-wave initiation theory was reviewed and the effect of tube wall proximity to the nblast-wave source was considered. Estimated critical energies were found to scale better with the planar initiation nenergy than the spherical initiation energy, suggesting that detonation initiation was influenced by wave reflection nfrom the tube walls.

Detonation Initiation via Imploding Shock Waves

An imploding annular shock wave driven by a jet of air was used to initiate detonations ninside a 76 mm diameter tube. The tube was filled with a test gas composed of either nstoichiometric ethylene-oxygen or propane-oxygen diluted with nitrogen. The strength of nthe imploding shock wave and the sensitivity of the test gas were varied in an effort to nfind the minimum shock strength required for detonation of each test mixture. The results nshow that the minimum required shock strength increases with mixture sensitivity and nsuggest that impractically large shock driver pressures are required to initiate detonations nin ethylene-air or propane-air mixtures when using this technique.

Toroidal Imploding Detonation Wave Initiator for Pulse Detonation Engines

Imploding toroidal detonation waves were used to initiate detonations in propane-air and ethylene-air mixtures inside of a tube. The imploding wave was generated by an initiator consisting of an array of channels filled with acetylene-oxygen gas and ignited with a single spark. The initiator was designed as a low-drag initiator tube for use with pulse detonation engines. To detonate hydrocarbon-air mixtures, the initiator was overfilled so that some acetylene oxygen spilled into the tube. The overfill amount required to detonate propane air was less than 2% of the volume of the 1-m-long, 76-mm-diam tube. The energy necessary to create an implosion strong enough to detonate propane-air mixtures was estimated to be 13 % more than that used by a typical initiator tube, although the initiator was also estimated to use less oxygen. Images and pressure traces show a regular, repeatable imploding wave that generates focal pressures in excess of 6 times the Chapman-Jouguet pressure. A theoretical analysis of the imploding toroidal wave performed using Whithams method was found to agree well with experimental data and showed that, unlike imploding cylindrical and spherical geometries, imploding toroids initially experience a period of diffraction before wave focusing occurs. A nonreacting numerical simulation was used to assist in the interpretation of the experimental data.

Erratum for "Analytical Model for the Impulse of Single-Cycle Pulse Detonation Tube"

I N the original evaluation of our analytical model for the singlecycle impulse of a pulse detonation tube,1 we approximated the detonation product isentrope as having a frozen composition with a corresponding polytropic exponent γ f . As discussed in the accompanying comment by Radulescu and Hanson and our response,2 for many situations, it is more appropriate to use an equilibrium approximation to the isentrope. This implies a different value of the polytropic exponent γ = γe and a new computational procedure for computing the plateau pressure P3 and results in revised values for the predicted impulse. Although the general equations and the qualitative conclusions drawn in our paper are unchanged, the revised numerical values of the predicted impulse differ up to 9.5% for stoichiometric fuel– oxygen mixtures and less than 1.3% for fuel–air mixtures at standard conditions. In this Errata, we present a revised set of data along with a short description of the calculations. The choice of the isentropic exponent, issues associated with chemical equilibrium, and the relevance to impulse calculations are discussed in the associated comment by Radulescu and Hanson and in our response to them. The input parameters of our impulse model consist of the external pressure P0, the detonation velocity UCJ, the equilibrium speed of sound behind the detonation front c2, the Chapman–Jouguet (CJ) pressure P2, and an approximation to the equilibrium polytropic exponent γe for the adiabatic expansion of the detonation products. All parameters were computed using numerical equilibrium calculations3 performed with a realistic set of combustion products. Instead of the analytic computation used in our original paper, our revised properties at state 3 (behind the Taylor wave) are now calculated by numerically integrating the Riemann invariant along the equilibrium isentrope until the plateau region of no flow is reached, ∫ P2

Planar Detonation Wave Initiation in Large-Aspect-Ratio Channels

In this study, two initiator designs are presented that are able to form planar detonations with low input energy in large-aspect-ratio channels over distances corresponding to only a few channel heights. The initiators use a single spark and an array of small channels to shape the detonation wave. The first design, referred to as the static initiator, is simple to construct as it consists of straight channels which connect at right angles. However, it is only able to create planar waves using mixtures that can reliably detonate in its small-width channels. An improved design, referred to as the dynamic initiator, is capable of detonating insensitive mixtures using an oxyacetylene gas slug injected into the initiator shortly before ignition, but is more complex to construct. The two versions are presented next, including an overview of their design and operation. Design drawings of each initiator are available elsewhere [7]. Finally, photographs and pressure traces of the resulting planar waves generated by each device are shown.