[american institute of aeronautics and astronautics 43rd aiaa aerospace sciences meeting and exhibit...

American Institute of Aeronautics and Astronautics

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A Pulsed Detonation Tube with a Converging-Diverging Nozzle Operating at Different Pressure Ratios

E. A. Barbour*, R. K. Hanson†

High Temperature Gasdynamics Laboratory

Department of Mechanical Engineering Stanford University, Stanford, CA

C. I. Morris‡

NASA/George C. Marshall Space Flight Center

Huntsville, AL

M. I. Radulescu§

Mechanical and Aerospace Engineering Princeton University, Princeton, New Jersey

A pulsed detonation tube (PDT) is operated at initial pressures equal to and greater than 1 atm in order to evaluate the effect of these pressures on the relative gains achieved by a converging-diverging nozzle, while the ambient pressure is maintained at 1 atm. Local heat flux is measured and is determined to play a significant role in overall energy release during blowdown, especially when a converging-diverging nozzle in implemented. With the addition of the nozzle, a decrease in Isp is observed at low initial pressures (near 1 atm), whereas the nozzle becomes beneficial at higher initial pressures (above 2 atm) .

I. Introduction The pulsed detonation engine (PDE) has received much interest recently as a novel propulsion device which

offers several potential advantages over conventional propulsion concepts1-4. However, harnessing all of the available energy as work is not possible with the simple detonation tube concept because of unconfined expansion of the hot gases outside of the tube. At least two concepts exist which hope to convert thermal energy to kinetic energy during the blowdown portion of the PDE’s cycle by reducing the lateral expansion of exhaust gases at the PDE exit. One technique is the ejector5-7 which is distinguished by its inlet where ambient air is allowed to enter. Another technique is the nozzle which confines the flow leaving the engine while expanding the gases to the ambient condition8. In Ref. 9, Barbour et. al discussed (both experimentally and numerically) the effects of adding a particular converging-diverging nozzle to the end of a single-cycle pulsed detonation tube. It was found that 1) heat transfer is important during the blowdown of a PDT (see also Ref. 10), especially when a converging nozzle increases the blowdown time (defined as the time between ignition and when head pressure reaches ambient pressure, P0) and 2) it is possible for a converging-diverging nozzle to have little, and possibly adverse, effects on the single-cycle specific impulse (Isp), even for an ideal adiabatic engine. Specifically, it was found that by adding a particular converging-diverging nozzle to the tail end of the PDT, the cycle Isp dropped by approximately 7%. Based on model predictions, the cause for this drop was ascribed to heat transfer.

For an adiabatic PDT, Morris 11 suggests that the tube should be operated at lowered ambient pressures in order to reap the benefits of a converging-diverging nozzle. He also shows that blowdown time is increased by the addition of a converging nozzle due to this additional restriction. Cooper and Shepherd experimentally investigated the coupled effect of back pressure and nozzle geometry on the single-cycle impulse of a PDT12. Their detonation

* Graduate Research Assistant, Department of Mechanical Engineering, bldg 660, AIAA Student Member † Clarence J. and Patricia R. Woodard Professor, Department of Mechanical Engineering, bldg 520, AIAA Fellow ‡ Research Engineer, Propulsion Research Center, AIAA Member § Visiting Research Fellow, Department of Mechanical and Aerospace Engineering, AIAA Member

43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada

AIAA 2005-1307

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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tube was operated inside of a large tank, the pressure inside of which was adjustable. Diverging nozzles, converging-diverging nozzles and straight tube extensions were tested in environmental pressures ranging from 1.4 kPa to 100 kPa. In all cases the addition of the nozzle improved impulse over the straight-tube case. It is important to note that the diaphragm in Ref. 12 was located between the straight tube and the nozzle/extension. The presence of ambient air inside the nozzle/extension affects the Isp via the tamping effect. The diaphragm in the current study is located near the exit of the nozzle, so the entire tube and nozzle is filled with detonable mixture (see the “Experimental Setup” section).

The current paper aims to investigate the effect of pressure ratio (initial pressure, P0, to ambient pressure, P1) on PDT Isp with and without a convering-diverging nozzle. It acts as an extension to Ref. 9, which studied performance of a PDT operating with initial and ambient pressures both equal to 1 atm. Additionally, in order to substantiate the claim made in Ref. 9 that heat flux plays a major role in reducing Isp of a PDT, heat flux is experimentally measured using a novel sensor.

II. Experimental Setup Unlike previous PDE experiments carried out at Stanford (where a dynamic mixing and filling technique was

used, see for example Ref. 13), the current study necessitated the preparation of a premixed charge in order to achieve initial pressures different from that of the atmosphere. The experimental setup is shown schematically in Fig. 1. A 0.025 mm-thick Mylar diaphragm is installed at the exit plane of the 160 cm long tube, and is held in place with a 5 mm plate, thus giving the PDE an effective length of 160.5 cm. The inner diameter of the PDE is 3.81 cm. Mixtures of stoichiometric ethylene and oxygen were prepared by partial pressures in a 43 L high-pressure cylinder by injecting the gases through one hundred 1.51 mm diameter holes, spaced 4 cm apart along a pipe which is oriented along the cylinder axis . The gases were allowed to mix by diffusion for 24 hours.

The measurement station is located 144 cm from the head, where wave speed, pressure, and heat flux measurements are made. Pressure and wave speed are measured using a pair of Kistler 603B1 charge-mode piezoelectric pressure transducers (PZT), amplified by Kistler 5010 amplifiers. The PZTs used for wave speed measurements are separated by 36 cm, which results in a relative uncertainty of 1.5% in wave speed. Previous studies9 have shown that transition to detonation is achieved in the first 30 cm of the PDT. Wave speed and pressure measurements are repeated here only to ensure that a Chapman-Jouget detonation wave is achieved for each P1, which is varied from 1 to 2 atm. P0 was maintained at 1 atm.

The PDT was operated in both “straight-tube” (160 cm tube with diaphragm plate) and “straight-tube with nozzle” (148.2 cm tube with 11.8 cm nozzle and diaphragm plate) configurations. The type of nozzle being studied is converging-diverging. The area ratio of the converging section (APDT/Athroat) is 2.78 and that of the diverging (Aexit/Athroat) is 2.25. The design of the nozzle is discussed in Ref. 9. Thrust contributions from the nozzle are measured using five additional PZTs mounted along the nozzle wall.

Figure 1: Experimental setup.

III. Numerical Model

The finite-rate chemistry quasi 1-D model with heat transfer is described by Owens et al.14 The heat flux model is based on Reynold’s analogy, proposed by Edwards15 for modeling convective heat transfer behind the detonation wave. As the heat flux model is 1-D, it predicts the resulting changes in axial bulk flow properties due to radial heat flux to the wall at each axial location. In reality, energy is transferred in the 2nd (radial) dimension from the hot core to the cold wall by convective heat transfer. This cools the gas at the wall, and the radial expansion waves which accompany this ultimately reduce the pressure in the core. The model was originally calibrated by Radulescu and Hanson10 via separate experimental results where the heat flux was determined using thin platinum film gauges.

Igniter

160 cm

144 cm

Interchangeable nozzle section with 5 pressure transducers

Head pressure transducer Dum

p tank (P

0 = 1 atm, abs)

3.81 cm

Heat flux gauge

PZT pair for wave velocity measurement

Diaphragm

Mixing cylinder with axial injector


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The current model, mo dified by Morris, is described in Ref. 14. The modified model was not recalibrated, but rather makes use of the results presented in Ref. 10. All numerical results described here were performed for a 1/10th scale model, in order to save on computational cost.

IV. Heat Flux Sensor The heat flux sensor is shown schematically in Fig. 2. It makes use of a single time-varying temperature

measurement at the substrate-gas interface. For a given heat flux history and substrate thermal properties, the interface temperature will have a unique time dependence. Conversely, a measured temperature history will yield time-varying heat flux, given by the following relationship (see, for example, Ref. 16):

( )

−

−+⋅= ∫ τ

τ

τπ

ρd

t

TtTttTck

tqt

ssss 0 2

3

)()(21)(

)(& (1)

where

sq& and Ts are the instantaneous heat flux and temperature at the substrate surface, k , ρ and c are the thermal

conductivity, density and specific heat capacity of the substrate respectively, and t is time. Due to a singularity produced during integration when t =τ , the discrete data reduction scheme proposed by Cook and Felderman17 is implemented to convert from temperature to heat flux.

Fig. 2: Heat flux sensor

Sensors such as this have been used in high-temperature short duration facilities such as expansion tubes 18 and

shock tubes19. In these cases, the technique used to measure the interface temperature is by a resistive-thermal device (RTD), and thus requires extensive calibration. In the present work, a high-bandwidth (10 µs response time) E-type eroding thermocouple20 (manufactured by Nanmac) is used to measure the interface temperature using the well-characterized Seebeck coefficient for the E-type thermocouple, thus eliminating the necessity for calibration. The thermocouple’s substrate serves two purposes: 1) to hold the electrical leads and 2) to serve as the thermal energy carrier required by the heat flux sensor. The thermocouple is connected to another (low bandwidth) E-type thermocouple, which is kept at 0oC. The temperature-compensated voltage from this circuit is then recorded by the data acquisition system.

Relation (1) assumes a 1-D semi-infinite medium in the x-direction. The measurable time of the experiment is thus limited by how the interaction of heat waves within the substrate is affected by the finite length of the sensor. Schultz and Jones16 suggest a minimum length for the sensor of

testmin 4 t

ck

x⋅

=ρ

(2)

where ttest is the test time. Thus, for a zirconium substrate (k = 3 W/m·K, ρ = 5700 kg/m3, c = 590 J/kg·K) and a

test time of 10 ms, xmin is 0.094 mm, which is far exceeded by the 100 mm long substrate. The diameter of the substrate is 3.24 mm, which represents the spatial resolution of the sensor. The sensor is installed near the open end of the PDT (144 cm from the head) because, based on the current model, this is where the highest heat fluxes are expected to occur. (The spatial variation of heat flux is also discussed in Ref. 10.) These large heat fluxes lead to large wall surface temperatures, which in turn lead to higher thermocouple output. In order to reduce noise, the thermocouple signal is averaged every 20 µs, thus giving it an effective response time of 20 µs. Upon conversion to heat flux, this leads to an effective 95% settling time in heat flux of approximately 40 µs.

x

Hot, flowing gases

Temperature measurement

Zirconium substrate

Steel PDT wall

Teflon insulation


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V. Impulse Measurements

As we have done previously9, time-varying thrust is measured using an integration of pressure over the inner surface of the PDT. This thrust is then integrated over the cycle time to obtain impulse, where the cycle time is defined as the time from ignition to when the head pressure reaches P0.

VI. Results and Discussion Measured and predicted heat fluxes are shown in Fig. 3 for the straight tube configuration and P1 = 1 atm. The

initial peak following the detonation is not fully captured, and this can be attributed to the finite response time of the sensor. Once the sensor is given enough time to track the heat flux, the data match very well up to ~ 0.5 ms, the model overpredicting the measured data thereafter. Still, the trend after 0.5 ms is itself captured quite well. This observed heat loss is reflected in the Isp (both for straight tube and nozzle configurations), as was discussed in Ref. 9.

The effects of heat flux on performance have also been studied by others. Kasahara et al.21 showed experimentally that the impulse is greatly affect by the L/D ratio of a PDT, a parameter essential to the current model. This loss was ascribed to heat transfer by Kasahara et al., and was further substantiated theoretically by Radulescu and Hanson10. Edwards et al.15 measured instantaneous heat flux for 150 µs behind a detonation wave using a thin film resistive thermal device. Ajmani et al.22 measured instantaneous heat flux for the first millisecond after detonation passage in a PDE using a commercial heat flux microsensor.

Figure 3: Heat flux measurement and prediction.

Results for specific impulse for straight tube and straight tube with nozzle configurations are shown in Fig. 4.

P0 is equal to 1 atm in each case, and P1 is varied between 1 and 2 atm. (Perhaps of more practical interest are the cases where P1 is fixed at 1 atm and P0 is sequentially lowered, thus simulating high altitude flight, as was done by Cooper and Shepherd12. Nevertheless, the available model shows that the discrepancy in Isp by raising P1 as opposed to lowering P0 is less than 2.5% in all cases.) The data show that, for P1 = 1 atm, the addition of a nozzle lowers the Isp by approximately 7%. This is due to the fact that, while the nozzle itself offers very slight gains in impulse at this P1, the heat transfer losses associated with the long blowdown time caused by the converging section are more than enough to offset these gains. At higher P1 the increased impulse from the nozzle is able to overcome the heat losses, and a net increase in performance is observed for P1 = 2 atm. This increase, however, is minimal,


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measured as 3.6% and modeled as 1.3%. Further increase of P1 beyond 2 atm may lead to substantial gains in Isp. These experiments, however, were not performed due to safety concerns.

The apparent 10% offset between model and measurement in Fig. 4 is a subject of ongoing investigation. This offset was also noticed in past work, viz. Ref. 9. Previously, it was believed that the dynamic mixing and filling process may have an effect on the post-detonation state, and thus Isp. However, the current study has shown that this is not so, yielding a measured Isp below 150 s whether the tube is filled dynamically or not.

It is also worth noting that the measured cycle time increases slightly as P1 is increased from 1 to 2 atm due to the elevated chamber pressure from which the tube must blow down. This increase is 1.2% for the straight tube, and 8% for the straight tube with nozzle.

Figure 4: Isp comparisons for straight-tube and nozzle configurations. All model predictions include heat loss.

VII. Conclusions

The impact of nozzles and heat transfer on the performance of a single-cycle PDT were evaluated at various initial pressures. Time-varying heat flux was measured in order to validate a model based on Reynolds’ analogy, as well as to understand the rate of energy loss by heat from the PDT. The single-cycle Isp of the PDT was then measured and compared to model results, incorporating heat transfer losses into the predictions. It was found that at low initial pressures, a significant drop in Isp can be expected. As the pressure is increased, this penalty is reduced, until a point is reached where the nozzle begins to become beneficial.

Acknowledgements This research was supported by the Office of Naval Research, with Dr. Gabriel Roy acting as technical monitor.

References 1 Eidelman, S., “Pulse Detonation Engine - A Status Review and Technology Development Road Map,” AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA-97-2740, 1997. 2 Eidelman, S., and Yang, X., “Analysis of the Pulse Detonation Engine Efficiency,” AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA-98-3877, 1998.


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3 Bratkovich, T. E., Aarnio, M. J., Williams, J. T., and Bussing, T. R. A., “An introduction to pulse detonation rocket engines (PDREs),” AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA-97-2742, 1997. 4 Bussing, T., and Pappas, G., “An introduction to pulse detonation engines,” AIAA Aerospace Sciences Meeting, AIAA-94-0263, 1994. 5 Canteins, G., Franzetti, F., Zitoun, R., Desbordes, D., and Khasainov, B. A., “PDE Performance Improvement by the Addition of a Coaxial External Nozzle,” 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, 2003. 6 Yungster, S. and Perkins, H., “Multiple-Cycle Simulation of a Pulse Detonation Engine Ejector,” AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA-2002-3630, 2002. 7 Allgood, D., Gutmark, E., Rasheed, A., and Dean, A., “Experimental Investigation of a Pulse Detonation Engine with a 2D Ejector,” AIAA Aerospace Sciences Meeting, AIAA-2004-864, 2004. 8 Kailasanath, K., “A review of research on pulse detonation engine nozzles,” AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA-2001-3932, 2001. 9 Barbour, E. A., Owens, Z. C., Morris, C. I. and Hanson, R. K., “The Impact of a Converging-Diverging Nozzle on PDE Performance and its Associated Flowfield,” AIAA Aerospace Sciences Meeting, AIAA-2004-867, 2004. 10 Radulescu, M. I. and Hanson, R. K., “The effect of wall heat loss on the impulse generated in an open-ended detonation tube,” Journal of Propulsion and Power , Vol. 20, No. 6, 2004 (tentative). 11 Morris, C. I., “Numerical Modeling of Single-Pulse Gasdynamics and Performance of Pulse Detonation Rocket Engines,” Journal of Propulsion and Power , (in press) 2004. 12 Cooper, M. and Shepherd, J. E., “The Effect of Transient Nozzle Flow on Detonation Tube Impulse,” AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA-2004-3914, 2004. 13 Sanders, S. T., Mattison, D. W., Jeffries, J. B., and Hanson, R. K., “Time-of-flight diode-laser velocimeter using a locally seeded atomic absorber: application in a pulse detonation engine,” Shock Waves , 12: 435-441, 2003. 14 Owens, Z., Mattison, D., Barbour, E., Morris, C. and Hanson, R., “PDE Flowfield Characterization and Simulation Validation using Cesium-based Velocimetry,” 30th Symp. (International) on Combustion, (in press) 2004. 15 Edwards, D. H., Brown, D. R., Hooper, G., and Jones, A.T., “The Influence of Wall Heat Transfer on the Expansion Following a C-J Detonation Wave” Journal of Physics D: Applied Physics, Vol. 3, 1970, pp. 365-376. 16 Schultz, D. L., and Jones, T. V., “Heat-Transfer Measurements in Short-Duration Hypersonic Facilities,” AGARD-AG-165, 1973. 17 Cook, W. J. and Felderman, E. J., “Reduction of Data from Thin-Film Heat-Transfer Gages: A Concise Numerical Technique,” AIAA Journal: Technical Notes , Vol. 4, No. 3, March 1966, pp. 561 – 562. 18 Roberts, G. T., Kendall, M. A. and Morgan, R. G., “Shock-diaphragm interaction in expansion tubes,” 21st International Symposium on Shock Waves, 1997. 19 Hanson, R. K., “Experimental study of shock-wave reflection from a thermally accommodating wall,” The Physics of Fluids, Vol. 16, No. 3, March 1973. 20 Nanigian, J., “The Self-Renewing Thermocouple,” ISA Paper #91-085, 1991. 21 Kasahara, J., Tanahashi, Y., Numata, T., Matsuo, A. and Endo, T., “Experimental Studies on L/D Ratio and Heat Transfer in Pulse Detonation Engines,” 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, 2003. 22 Ajmani, K. and Breisacher, K., “Qualitative Study of Cooling Methods for a Pulse-Detonation Engine,” JANNAF Propulsion Meeting, 2002.

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