The Effect of Nozzles and Extensions on Detonation Tube Performance

Abstract

The effect of nozzles on the impulse obtained from a detonation tube has been the focus of many experimental and numerical studies. We develop a partial-fill model to predict the impulse obtained from a detonation tube containing an extension (considered a partially-filled detonation tube). The experimental impulse values are found to be linearly dependent on the fraction of the tube volume filled with the explosive mixture. Data from numerical simulations were used to predict the impulse for small fill fractions not experimentally tested. The analytical Gurney model provides a method for correcting the experimental data for the tamping provided by diaphragms of a finite mass. A thermodynamic cycle analysis of a detonation is conducted to evaluate the fraction of stored chemical energy in an explosive mixture that can be converted into mechanical work. It is found that approximately 46%-64% of the ideal work from a detonation can be converted into impulse. This fraction increases with increasing nitrogn dilution. The partial-fill model is validated with multi-cycle experimental data and numerical simulations. We compare the partial-fill model with experimental data of diverging nozzles. Ideal ideal detonation efficiency calculated from Jacobs cycle Isp detonation efficiency based on predicted specific impulse ρ 1 density of reactants ρ air density of air mixture in extension

Impulse Correlation for Partially Filled Detonation Tubes

“…For small tubes, even very thin diaphragms can equal a significant fraction of the initial explosive mixture mass, increasing the tamping effectiveness. 7 Based on information of the diaphragms provided by the researchers, 1,2,4,8 we use the Gurney model (see Ref. 7) to correct the measured impulse values for the diaphragm effect as described by Cooper and Shepherd.…”

“…7) to correct the measured impulse values for the diaphragm effect as described by Cooper and Shepherd. 8 Briefly, the Gurney model assumes a linear velocity gradient in the expanding product gases that are sandwiched between the driven mass (the detonation tube) and the tamper mass (the diaphragm). The final velocity of the driven mass is determined from the conservation equations and depends on the available chemical energy of the explosive.…”

“…Previous studies of the application of MHD to engine inlets have shown that the MHD action increases flow compression and mass flow rate. 4,8,9 However, the resulting improvements in flow parameters were incremental. It was also proposed to use MHD to decelerate the flow in front of the combustion chamber of the scramjet engine, with subsequent acceleration of the flow after the chamber.…”

Impulse Generation by an Open Shock Tube

“…Cooper [6] predicted that the specific impulse will approach a limiting value on the basis of a simple model, but it is experimentally difficult to approach this limit in the detonation case. Other approximate models [5,8,[11][12][13] have also been proposed to predict the specific impulse dependence on the fill fraction when the fill fraction is close to 1. We examine both limits experimentally, carry out detailed numerical simulations, and compare the results to the approximate analytical models.…”

“…OTIVATED by recent interest in pulse detonation engines [1], a number of researchers [2][3][4][5][6][7][8][9][10][11][12] have studied the impulse from a partially filled detonation tube. In these experiments and analyses, a portion of the detonation tube near the closed end (thrust surface) contains the combustible mixture whereas the remaining portion of the tube up to the open end contains an inert gas mixture, for example, air.…”