Toroidal Initiator

Efficiently initiating detonations in insensitive HC-air mixtures (such as JP10-air or C3H8-air) is deemed essential to the success of PDEs. Existing PDEs (Brophy et al., 2002) use an initiator tube to initiate detonations in HC-air mixtures. The initia- tor tube contains a sensitive mixture such as propane-oxygen that transitions from a deflagration to a detonation sufficiently quickly after ignition by a weak spark. The fully developed detonation wave in the initiator then propagates into an insensitive hydrocarbon-air mixture. If the transmitted shock Mach number and the post-shock flow duration are sufficient (Murray et al., 2003), the detonation wave will be suc- cessfully transmitted into the HC-air mixture.

initiator tube detonation tube reactant inlet detonation tube initiator tube reactant inlet spark point products outlet

Figure 3.1: The geometry of a typical initiator tube. The detonation wave is created in the initiator tube and diffracts into the detonation tube.

Current initiator tube technology has several drawbacks. Typically, the initiator tube is located at the head of the main detonation tube (Fig. 3.1) on the central axis, resulting in drag as air flows into the main tube. Furthermore, use of a tube initiator requires an amount of energy to be stored on-board during flight. This energy can be stored either electrically in batteries and capacitors or thermodynamically in a sensitive initiator mixture. Given the state of current technology, it is more efficient to store the energy on-board in the form of an initiator mixture, carrying only enough battery power to periodically ignite the mixture with a weak spark. While the initiator mixture is lighter than large banks of batteries, the stored gas still takes up payload weight, decreasing engine performance. Therefore, the tube initiator should use as little gas as possible in order to maximize the engine performance. To reduce the amount of initiator gas, the efficiency of the initiator tube must be maximized by using advanced technologies such as shock 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 (Whitham, 1958). This rapid gas compression generates regions of extremely high energy-density. The focusing of detonation waves also generates high-pressure and high-temperature regions similar to those generated by shock fo- cusing (Lee and Lee, 1965, Jiang and Takayama, 1998, Takayama et al., 1987, Devore

(a) (b) (c) initiator test-section tube obstacle focus annular wave initiator test-section tube focus obstacle focus toroidal wave

Figure 3.2: Shown are three different cross-sectional schematics of axisymmetric wave implosion experiments discussed in the text. (a) The setup tested by Murray et al. (2000). The wave enters the initiator tube from the left. (b) A similar setup tested at Caltech. As with the previous geometry, the wave enters the initiator tube from the left. (c) The concept of the toroidal initiator where an imploding toroidal wave is propagated into the test-section tube from an annular slot in the tube wall.

and Oran, 1992, Oran and Devore, 1994, Terao et al., 1995, Akbar, 1997). Compres- sion of the detonation products generates post-detonation wave pressures in excess of the CJ pressure, resulting in an increasingly overdriven detonation wave. Thus, wave focusing can be used to increase the strength of the shock wave that is trans- mitted from the initiator section into the engine, facilitating more efficient detonation initiation.

Murray et al. (2000) noted that wave focusing could promote detonation initiation while conducting experiments measuring the transfer of a detonation wave from a smaller diameter initiator tube to a larger diameter test-section tube (Fig. 3.2a). The initiator tube and test-section tube were both filled with a hydrogen-air mixture and several different obstacles were placed at the interface between the two tubes. The effect of these obstacles on the detonation wave transmission was measured in terms of their transmission efficiency. Values of the transmission efficiency above unity represent situations where the obstacle allowed detonation transfer from the initiator tube to the test-section tube for mixtures with larger cell sizes than in the case where

no obstacles were used. Conversely, values of the transmission efficiency below unity required that smaller cell size mixtures be used (compared to the no-obstacle case) to transfer the detonation wave between the initiator tube and the test-section tube. Murray et al. (2000) noted a substantial increase in the transmission efficiency when the obstacle was a circular plate. Such a geometry created an annular orifice that generated an imploding toroidal wave at the entrance of the test-section tube. The region of high energy-density at the focus of this imploding toroid was capable of evolving into a self-sustaining detonation wave. In particular, the annular orifice allowed successful detonation transmission for tubes with diameters 2.2 times smaller than cases where no obstacles were located at the interface (Murray et al., 2000).

Thus, the geometry of the wave emerging from the initiator tube has been shown to have a significant effect on the initiation process in the test-section tube (Murray et al., 2000). The appropriate wave geometry could dramatically increase the transmission efficiency and reduce the amount of initiator gas used during detonation initiation. Research at Caltech extended this concept by evaluating the transmission efficiency with a similar experimental design (Fig. 3.2b). Unlike the experiments of Murray et al. (2000), the initiator section was filled with a more sensitive gas than the gas in the test section. Using this technique, detonations were initiated in test section mixtures of C3H8-air at room temperature (298 K), but it was not possible to initiate detonations at elevated temperatures (373 K) in the C3H8-air or JP10-air mixtures. This loss in performance was attributed to the decrease in energy-density of the initiator- and test-gas mixtures due to gas expansion during heating.

The toroidal initiator was designed to create a stronger wave focus than the ex- perimental setup of Murray et al. (2000). The device created an imploding toroidal detonation wave, which was propagated into the test-section tube from the tube wall in an effort to minimize the amount of diffraction that occurred prior to wave im- plosion. The toroidal initiator was intended to create the imploding wave in HC-air mixtures at elevated temperatures with a minimum amount of HC-O2 initiator gas, and using only a single 46 mJ spark. In order to minimize the required amount of initiator gas, the internal volume of the initiator channels was minimized based on