Detonation waves were propagated in propane-oxygen mixtures through tubes with diameters on the order of the detonation cell size of the mixture. Two test section tubes were used with inner diameters (ID) of 6.35 mm and 1.27 mm and lengths of 1.82 m and 1.50 m respectively. For experiments in the 6.35 mm ID tube, initial pressure and equivalence ratio were varied. Stoichiometric propane-oxygen mixtures were tested with initial pressures varying from 0.1 to 1 bar and the mixture equivalence ratio φ was varied from 0.3 to 3. For experiments in the 1.27 mm ID tube, the initial pressure of stoichiometric propane-oxygen mixtures was varied from 0.1 to 1.8 bar.

Wave speeds in the test section were observed to decrease significantly below the Chapman-Jouguet (CJ) velocity as initial pressure was decreased. Minimum propagation velocities of 0.4 U_CJ were observed for mixtures at initial pressures of 0.14 bar. Small velocity deficits were also detected as φ diverged from unity. The measured velocity data normalized by the U_CJ appear to collapse to a curve as shown on the right when plotted as a function of induction zone length Δ normalized by tube radius r. The induction zone length of each test mixture was calculated from the mixture initial properties and the experimentally measured wave speed.

Boundary layer growth in the detonation wave was attributed to the decreased propagation velocities. Two versions of Fay's boundary layer analysis (Fay 1959, Dupre et al. 1986) were used to quantitatively predict the expected wave velocity deficit as a function of a given tube diameter, initial gas properties and Chapman-Jouguet properties. The model from Fay (1959) was found to best fit the data from the 1.27 mm ID tube while the model used by Dupre et al. (1986) was found to best fit the data from the 6.35 mm ID tube. Analysis is ongoing.

The motivation for this study was determination of the minimum channel diameter necessary for detonation propagation. This information was necessary for the design of the planar and toroidal initiators presented below.

A wave shaping device was developed that is capable of initiating planar detonation waves in large aspect ratio channels over a short distance using a single spark plug, an array of small diameter channels and a small amount of sensitized gas. Planar detonations are created in shorter distances than required by conventional techniques such as exploding wires or spherically expanding waves from a point-source initiation. The planar wave initiator is currently in use on the Narrow Channel Facility in the GALCIT Detonation Physics Lab.

Gas is injected into the device through the hole located at the start of the main channel (left of the figure). The spark plug (not shown) is located next to this gas injection port. Just downstream of the gas injection port, a series of circular indentations have been milled into the main channel to promote DDT. Shortly after the obstacles, the main channel bifurcates into the next family of channels. There are five families of channels. The last series of channels exhausts into a test section shown on the right side of the figure. The end portion of the test section is equipped with three pressure transducers that allow measurement of the time of arrival of the resulting planar wave. A polycarbonate window and thin Teflon gasket seal the channels and provide optical access to the top of the initiator.

During testing, the initiator and test section are filled with the mixture to be studied using the method of partial pressures. Approximately one second before ignition, equimolar acetylene-oxygen gas is injected into the device just behind the spark plug. Injection continues for approximately 0.8 seconds until all initiator channels (but not the test section) are filled with the acetylene-oxygen mixture. When all channels are filled, the spark plug is fired, releasing about 30 mJ of stored energy into the initiator mixture. The resulting deflagration rapidly accelerates into a detonation over the obstacle section in the first channel. The detonation than branches out as it travels down successive channels. The detonation wavelets emerge from the small channels into the test section at the same time and combine to form a planar detonation, which is then propagated into the test section mixture. The figure at the left shows a series of images taken by an intensified CCD camera with exposure times of 100 ns. Chemiluminescence of the burning gas allows the progress of the detonation to be traced throughout the initiator channels. In the final image, the detonations in the channels have combined in the test section to form the planar detonation front. Pressure traces from the test section indicate that the resulting front in the test section is planar to within 6 mm over a distance of 15 cm. The planar initiator demonstrated the ability to create a shaped detonation wave front from a single single spark. It provided a groundwork for the design of the toroidal initiator which is discussed below.

A study was conducted to determine the possibility of increasing detonation tube initiator efficiency by using shock wave focusing. In shock focusing, a collapsing shock wave generates a high-pressure and high-temperature focal region by adiabatically compressing shocked gas as it flows into an ever-decreasing area. This compression is capable of generating regions of extremely high energy density. It is also possible to apply shock focusing concepts to detonation waves to generate high-pressure and high-temperature regions. Compressing the detonation products increases the post-detonation wave pressure higher than the CJ pressure, resulting in an increasingly overdriven detonation wave. Thus, shock focusing can be used to increase the overpressure of the shock transmitted from the initiator section into the main tube, which has been shown to facilitate detonation transmission from the initiator to the main tube. This technique is dependent only on the geometry of the initiator wave and provides the means to dramatically increase the transmission efficiency or to reduce the amount of initiator gas used.

Building on the wave shaping principles demonstrated in the development of the planar wave initiator, an imploding toroidal initiator was developed which generated imploding toroidal detonation waves from a single spark plug and an array of small diameter channels filled with a hydrocarbon-oxygen mixture. As the imploding wave converges, a region of extremely high temperature and pressure exists near the focal point. It is thought that the presence of this high energy region would aid in the initiation of detonations in insensitive mixtures. The initiator was designed to be incorporated into the walls of a detonation tube and is able to successfully initiate hydrocarbon-air mixtures.

The design of the toroidal initiator is similar to that of the planar initiator described above, only the channels are mapped to a cylindrical surface as shown in the figure. The end result is a tube with the initiator channels contained in the tube wall. Turning the detonation wave inward as it emerges from the small channels creates an implosion along the central axis of the tube.

Operation of the toroidal initiator is similar to that of the planar initiator. The initiator channels and the main tube volume are filled with a hydrocarbon-air mixture. Shortly before the spark plug is to be fired, an equimolar acetylene-oxygen mixture is injected to fill the initiator channels using the same gas injection system used to operate the planar initiator. Once the initiator channels are filled, the spark plug is fired and an imploding detonation wave is sent into the hydrocarbon-air mixture. Pressure transducers near the focus of the imploding wave measure pressures approximately 10 times the Chapman-Jouguet pressure P_CJ. Chemiluminescence imaging of the imploding wave shows that it is very regular. Using this technique, the toroidal initiator is able to initiate stoichiometric ethylene-air and propane-air mixtures.

In an attempt to experimentally validate the simulations of Li and Kailasanath (2003), an experiment was designed to generate an imploding annular shock wave in a detonation tube. The shock was driven by a jet of air and used to initiate detonations in stoichiometric ethylene-oxygen and propane-oxygen mixtures diluted with nitrogen. The experiment consisted of a detonation tube with an annular orifice inserted into the rear of a shock tube. The annular orifice was covered with a diaphragm. The detonation tube was filled with the combustible mixture and the shock tube was filled with air. Shock waves propagating though the shock tube reflected off the annular orifice located in the end flange of the shock tube. The increased pressure behind the reflected shock wave P₅ ruptured the diaphragm and sent a series of imploding shock waves into the detonation tube.

The figure shows the results for ethylene-oxygen mixtures. For sufficiently high reflected wave pressure P₅, prompt detonations were initiated near the implosion focus. As P₅ was decreased, prompt initiation no longer occurred and instead DDT was observed to occur at some location in the tube. The numbers next to the DDT data points correspond to the nearest ion probe to the DDT event for that data point. The tube was equipped with 9 equidistant ion probes. Decreasing P₅ even further resulted in no detonation initiation from the implosion, although in some cases a detonation would occur after the shock wave in the detonation tube reflected off the end flange of the detonation tube.

During testing, the strength of the imploding shock wave and the sensitivity of the test gas were varied in an effort to find the minimum shock strength required for detonation of each test mixture. The results show that the minimum required shock strength increased with mixture sensitivity and suggest that shock driver pressures in excess of the Chapman-Jouguet detonation pressure would be required to initiate detonations in ethylene-air or propane-air mixtures when using this technique.

It should be noted that the experimental conditions did not exactly simulate the situation modeled by Li and Kailasanath (2003). The experimental implosion was far from perfect. It consisted of a series of imploding waves that were disrupted by the presence of support struts and diaphragm fragments. Also the experimental detonation tube inner diameter was smaller than the tube in the simulations which could have resulted in less overdrive in the imploding shock wave.

Detonations and deflagrations were initiated by shock reflection off of a parabolic focusing wall in a tube filled with ethylene-oxygen and propane-oxygen mixtures diluted with nitrogen. The strength of the shock wave, the depth of the reflector and the sensitivity of the combustible mixture were varied experimentally. Analysis is ongoing.

A facility was constructed to simulate the flow in a pulse detonation engine. Pressurized air was expanded through a rectangular test section channel and exhausted into a dump tank. The flow was started abruptly by rupturing a diaphragm that separated the downstream end of the test section from the dump tank. Following a short transient period of a wave propagation, a quasi-steady flow was set up in the test section. Quasi-steady operation was found to last for about 0.15 s and, during that time, the flow in a test section had a Mach number of about 0.7 and a velocity of 200 m/s. The pressure and temperature in the test section could be adjusted by varying the conditions in the supply reservoir. The implementation tested used room temperature air at pressures up to 6 bar in the supply reservoir. For some tests, a fast-acting valve was installed upstream of the test section that was capable of shutting off flow to the test section.

Tests were carried out to determine the performance as a function of the pressures in the supply and receiver vessel. Measurements included pressure and temperature in the two vessels and pitot and static probe measurements of the test section flow. Flow visualization with a schlieren system was also carried out. The data were analyzed by using simple one-dimensional steady and unsteady gas dynamics. Some two-dimensional unsteady numerical simulations were also carried out to examine the influence of the diaphragm location on the flow starting process. A control-volume model was developed to predict the variation of pressure with time in the supply and receiver vessels. That model and analyses of the tests indicates that choked flow results in a constant Mach number inside the test section. The duration of the choked flow regime and the conditions within the test section were reliably estimated with the model.

Experiments were conducted with Advanced Projects Research Incorporated.

Single-cycle impulse measurements were obtained for deflagrations and detonations in hydrocarbon-oxygen-nitrogen mixtures using a tube closed at one end. Impulse was directly measured using the ballistic pendulum method. The effect of using obstacles with a blockage ratio of 0.43 inside the tube to promote deflagration-to-detonation transition (DDT) was also studied. This work led to the development of an analytical model for predicting single cycle detonation tube impulse.

Obstacles were found to reduce DDT times and enable the initiation of detonations in insensitive mixtures (up to 60% dilution in ethylene-oxygen-nitrogen mixtures) at the expense of increased drag losses. For cases where DDT occurred early in the tube, the presence of obstacles were found to reduce the measured impulse by an average value of 25% compared to the impulse obtained from the tube with no obstacles present.

Investigations were carried out to determine the flammability limits and flame speeds of rich methane-oxygen mixtures. A constant volume explosion vessel was equipped with a pressure transducer, optical windows and a schlieren system. Pressure histories and schlieren videos of the explosions were recorded. Flame speeds were extrapolated from the pressure history data using the analysis of Shepherd et al. (1997) and directly measured from the schlieren videos.

G. Dupre, R. Knystautas, and J.H. Lee, "Near-limit propagation of detonations in tubes," Progress in Astronautics and Aeronautics, 106:244-259, 1986.

J.A. Fay, "Two-dimensional gaseous detonations: Velocity deficit," The Physics of Fluids, 2(3):283-289, May-June 1959.

C. Li and K. Kailasanath, "Detonation Initiation in Pulse Detonation Engines," 41st AIAA Aerospace Sciences Meeting and Exhibit, January 6-9, 2003, Reno, NV, AIAA 2003-1170.

J.E. Shepherd, J. Krok, and J. Lee, "Jet A explosion experiments: Laboratory testing," Technical Report, Graduate Aeronautical Laboratories, California Institute of Technology, 1997.