AIAA 2002-4228

Optimization of Multitube Pulse Detonation Configuration*

Houshang B. €brahimit Jacobs Sverdrup AEDC Group

Arnold Engineering Development Center Arnold Air Force Base, TN 37389

and

Abstract

Aspects of the operational characteristics of multiple-tube pulsed detonation engines (PDEs) are discussed. The study is based on a two-dimen- sional analysis of the first-pulse operation of two detonation tubes exhausting through a common nozzle. The computations use a viscous, eight- species, finite-rate transient flow-field model. Com- putations are first performed to assess single-tube behavior followed by results for six multitube flow geometries. Differences in behavior between single- and multitube PDE configurations are dis- cussed. The results indicate that the pressure spike produced in one tube by a detonation exiting an adjacent tube can be reduced by a factor of five by modifying the inter-tube geometry. Changing the nozzle throat area also affects the strength of this pressure spike. The results serve as an important precursor to understanding appropriate propellant fill procedures and shock wave propagation in multitube, multidimensional simulations.

Introduction

A pulsed detonation engine (PDE) is an inter- mittent thrust device that uses a detonation rather than a deflagration to combust the The pressure rise created by the detonation can potentially reduce pumping requirements, but per- haps more importantly, the simpler geometry and fewer parts count offers potential cost and weight benefits over the turbomachines that are tradition- ally used to increase pressure. For these reasons, PDEs have received increasing attention in the past decade as a potential new propulsion source for atmospheric or exoatmospheric travel.

Charles L. Merkld University of Tennessee Space Institute

41 1 B. H. Goethert Parkway Tullahoma, TN 37389-9700

Reviews of previous work on PDEs can be obtained from Eidelman et Bussing and Pap- pas: and Kaila~anath.~ Cambier and TegneF dis- cuss issues related to optimization of PDE perfor- mance. Current analytical studies of PDEs have dealt with topics such as the performance improve- ments provided by partial filling,’ detailed plume calculations,8 and the transition from detonation to shock at the detonation tube exitg Recent experi- mental studies have looked at performance issues1° and the detonation of liquid fuels.” Impressive pressure-time comparisons between detailed experiments12 and computations

g have

also been reported.

The simplest version of a pulsed detonation device is a long tube, closed at one end and open at the other. Periodic operation is initiated by feed- ing fresh propellant into the tube through appropri- ately positioned valves2 Once the tube is filled the valves are closed and a detonation is initiated and allowed to propagate through the tube. The high- pressure gases produced by the detonation then expand out the open end to produce thrust. Follow- ing this blowdown process, the valves are again opened to prepare for the succeeding pulse.

An isolated detonation tube, however, does not constitute a viable propulsive system. A complete engine requires an inlet and exhaust system as well as other supporting component^.'^ Further, the impulse produced by a single tube is small and steps must be taken to provide appropriate thrust levels. The time-averaged thrust of a single tube can be increased by using a larger chamber, oper- ating at higher frequencies, or increasing the pres- sure level, but most applications will require multi-

The research reporled herein was performed by the Arnold Engineering Development Center (AEDC). Air Force Materiel Command. Work and analysis for this research were performed by personnel of the University of Tennesee Space Institute and by personnel of Jacobs Sverdrup AEDC Group, technical services contractor for AEOC FuilhW reproducllori is aulhorired to satisfy weds of the U. S. Government.

Member, AIAA. # Professor, H. H. Arnold Chair in Computational Mechanics; Member, AIAA.

This paper is declared a work of the U . S. government and not subject Io copyright protection in the United States. 1

American Institute of Aeronautics and Astronautics

38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit7-10 July 2002, Indianapolis, Indiana

AIAA 2002-4228

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

ple detonation tubes. If multiple tubes are used, it appears advantageous to group several tubes into an engine module that can be fed from a common inlet and discharged into a common nozzle. Modu- larized components provide improved weight char- acteristics while also reducing the degree of unsteadiness in these components and the overall level of engine vibration.

Filling multiple detonation tubes from a common inlet reduces the drag associated with the inlet in intervals when none of the detonation tubes are being filled2 and mitigates against possible unstart. Similarly, feeding the exhaust nozzle from multiple tubes reduces the degree of unsteadiness in the thrust and can improve nozzle performance. The total pressure of the exhaust gases drops precipi- tously during the detonation cycle and while the nozzle will be choked at the beginning, it will unchoke at the end of the cycle, except at the high- est altitudes. When the nozzle unchokes, the diver- gent section will act as a diffuser and be detrimen- tal to thrust. Discharging multiple tubes into a com- mon nozzle provides higher average total pres- sures and ensures that the nozzle accelerates the flow over a larger fraction of time. The throat of the common nozzle can also provide an effective back pressure for the detonation tubes that increases their average operating pressure and enables them to generate more thrust.

The primary disadvantage of combining multi- ple tubes into a single module is that it allows cross talk between tubes. The valves prevent direct inter- action through the inlet, but the common nozzle provides a direct path for disturbance propagation between tubes. When a detonation is initiated in one tube, there is a clear path whereby this pres- sure pulse can propagate into neighboring tubes and the adjacent nozzle surfaces can enhance this interaction. It is this cross-talk aspect of the pulsed detonation engine that is investigated in this paper. The goal of this paper is to assess the magnitudes of the disturbances created in adjacent tubes and to identify the degree to which these disturbances can be controlled.

Model Formulation and Geometrical Configuration

Possible geometrical configurations for a multi- tube engine module include a cylindrical arrange- ment in which the tubes lie in a ring and exhaust through an axisymmetric nozzle,13 and a linear array followed by a rectangular nozzle. Either of these situations constitutes a three-dimensional configuration. To minimize computational require- ments in this initial investigation of the phenomenol- ogy of inter-tube interactions, we limit our attention to a two-dimensional system containing two tubes exhausting into a common nozzle. The phenome- nology of this planar configuration should be analo- gous to that of a full three-dimensional configura- tion even though the quantitative features clearly will be different. The two-dimensional analysis should give an indication of the levels of interaction that can be expected as well as the degree of con- trol that is available through geometrical modifica- tions. Three-dimensional domains allow distur- bances to decay, but three-dimensional (3-D) relief should be minimal in these constricted, internal geometries.

The specific geometry of the two-dimensional engine module consists of a pair of (planar) tubes, one above and one below the other, whose open ends are connected to a (planar) converging- diverging nozzle. For all cases, the detonation tubes were 0.1 m in length by 0.01 m in height and the spacing between them was one-half the tube height (0.05 m). The relatively short tube length minimizes the computation time needed to gener- ate inter-tube interactions. Longer lengths are not expected to change the findings qualitatively, although the tube volume can interact with the noz- zle volume and a potential exists for ‘tuning’ between the tubes and the nozzle. Also presented are results for a single tube as a reference against which the dual-tube results can be compared.

The converging-diverging nozzle used for both single and dual-tube configurations was comprised of a second-derivative-continuous, cubic contour.

2 American Institute of Aeronautics and Astronautics

In the single-tube case, the throat area was three- fourths the cross-sectional area of the tube (a throat height of 0.0075 m). The dual tube cases used throat heights of either 0.01 or 0.02 m. In all cases the length of the converging section was two tube heights, placing the throat 0.12 m from the closed end. A large, unconfined region was placed downstream of the diverging section to account for external perturbations.

To investigate the nature of the interactions between tubes, we parametrically varied the nozzle throat area and the distance to which the splitter plate between the tubes extends into the nozzle. Dual-tube PDE computations have been per- formed for six different geometries, four of which are shown in Fig. 1. The four dual-tube geometries are referred to as Cases 1, 2,4, and 6. Cases 1, 2, and 4 use the smaller (0.0075 m) throat nozzle, while Case 6 uses the larger throat.

In Case 1 at the top of Fig. 1, the splitter between the two tubes is terminated at the x = 0.1 rn location at the plane where the nozzle conver- gence starts. In Case 2 the splitter plate is extended inside the nozzle approximately one- quarter of the way to the throat, a distance of 0.008 rn. In this case the splitter plate is shaped to keep the area of both tubes constant until the end of the divider plate. Case 3 is not shown, but extends

Case 1 m Case 4 m Case 6

B Fig. 1. Diagram of Dual-Tube Configurations

three-fourths of the way to the throat. The splitter plate in Case 4 extends to the throat. With this splitter plate, the tubes contain converging sections and their cross-stream height is reduced to one- half the tube area. Finally, the splitter plate in Case 6 also extends to the throat, but in this case the height of the common nozzle has been increased so that the areas of the two tubes remain constant to the end of the splitter plate (the throat). In the geometry of Case 5 (not shown) the splitter plate extended past the throat into the divergent section; however, this additional extension had little impact. Note that extending the splitter plate increases the effective length of the tubes.

In the following sections, the computational solutions of the single-tube case are presented, fol- lowed by results for the dual-tube cases. For rea- sons of computational efficiency, the focus is on first-pulse results rather than periodic operation. Single-tube results are used to document the dom- inant characteristics of an isolated detonation tube and then are extended to a multitube PDE environ- ment. Except for the last case, dual-tube computa- tions are used for a single pulse in the lower tube and the induced reverberations in the upper tube are investigated. The final example shows a com- putation where a pulse is first initiated in the lower tube and is followed by a pulse in the upper tube is shown. The present two-dimensional, dual-tube analysis serves as a precursor for understanding the flow-field behavior in a multitube/common noz- zle system and for developing a strategy for imple- menting repetitively pulsed multitube computa- tions.

An H2/02 finite-rate chemical kinetics system7

comprised of eight chemical species (0, 02, OH, H, H02, H20, H202, and H2) and 16 reactions was used in all of the calculations. All computations were conducted at stoichiometric conditions with pure oxygen as the oxidizer and hydrogen as the fuel. Both the external, ambient pressure and the initial pressure in the tubes was chosen as 1 atm. Detonation initiation is accomplished by introduc- ing a high-pressure, high-temperature region near the closed end of the tube. Details of the computa- tional method and initiation procedure are given in Refs. 14 and 15.

3 American Institute of Aeronautics and Astronautics

Single-Tube Results

As a background for understanding the flow field in a multitube PDE, a brief look is made at rep- resentative results from a single detonation tube exhausting through a converging-diverging nozzle. The flow field can be separated into two regions, one inside the tube and the other outside. The internal flow field initially is characterized by the dynamics of the detonation as it moves from the initiation zone at the closed (left) end to the open (right) end of the tube and nozzle. At later times the internal flow is characterized by reverberation pro- cesses as the pressure seeks to equilibrate with conditions outside the tube. The external flow field is composed of the shock wave created by the det- onation and the ensuing compression and expan- sion processes. In the multitube arrangement this 'external' field is captured inside the common noz- zle, although the nozzle also produces its own external flow field.

A time sequence of the internal and external flow field of the single tube is given in Fig. 2. The plots in the upper portion of the figure show the

t ti 0.w mse

- 0.4S msec

Mach 2.2

Mach number contours. Those in the lower portion show the pressure contours. The results clearly show the approximately cylindrical shock wave that is generated as the detonation emerges from the open end of the nozzle. In general, this shock wave remains symmetric about the tube axis and its strength decreases steadily as it moves away from the tube. Note from the pressure plots that the expanding shock wave creates a subatmospheric pressure in the vicinity the nozzle exit plane. These external pressure excursions have a minor impact on the timing of the ensuing reverberation process inside the tube and the establishment of reverse flow at the exit.

Clearly the external flow calculations remain meaningful only when there are no surfaces nearby. When multiple tubes are placed in proxim- ity with each other, the expansion from one tube will impact conditions in adjacent tubes. If, in addition to being placed adjacent to each other, their exhaust is coupled into a common converging-diverging nozzle, this external flow is reflected from the noz- zle surfaces, producing additional interactions. The nozzle also causes each detonation tube to see an

.- ..

I 0.03 msec

1 "\.& !- 1

.-- I_- - t

U. 132 m6ec

I -.

4 P,Pa 1.3€+06

8.6E+06 4.6€+05

6.2€+04 '

6.2 mscc

D.45 mSec .. .

a. Mach Number b. Pressure

unsteady, fluctuating pressure and, depending on the size of the nozzle throat, raises the effective average back pressure.

Multiple-Tube Results

When the detonation reaches the exit of one tube in a multitube PDE configuration a portion of the ensuing shock propagates through the nozzle, but it also refracts around the splitter plate and propagates into the remain- ing detonation tubes where the pressure is still low. A multitube PDE involving a common nozzle causes a reverse flow to occur in the detonation tubes during some portions of the cycle, and the minimum pressure level in the cycle is higher than the cor-

Fig. 2. Time History of Pressure and Mach Number Contours in a Single- responding Tube PDE tube PDE.

for a sing1e

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Case 1 : Splitter Plate Terminated at Entrance to Nozzle

observed. Qualitatively, this frame resembles the external shock created by a detonation in a single tube, except for the containment by the adjacent surfaces. As an initial dual-tube case, Case 1 is consid-

ered. In this case, the splitter plate ends at the beginning of the convergent part of the nozzle (two tube heights upstream of the throat). For this com- putation a detonation was initiated in the lower tube, and the ensuing reverberation of the pulse in both tubes and in the converging-diverging nozzle was observed. This case represents the baseline case for dual-tube calculations. The results for Case 1 are shown in Fig. 3, and again, Mach num- ber and pressure contours are given for each of six different times. The total time simulated in this computation is 365 psec.

Frame A (0.035 msec) of Fig. 3 corresponds to the time just after the detonation has emerged from the lower tube. The contours exhibit strong two- dimensionality as the shock wave diffracts around the splitter plate, causing the flow to begin to enter the upper tube. Simultaneously, the shock wave propagates into the converging section of the noz- zle, where additional two-dimensional effects are

Frame A I 1

- -

Mach 2.2

1.5

0.7 - 0

Frame 6 shows continued propagation of the shock into the upper tube and the nozzle. In Frame C (0.07 msec), the shock in the upper tube has tra- versed about 70 percent of the tube length and is nearing the upstream end. The flow in the diver- gent section of the nozzle is asymmetric but shows a considerable amount of supersonic flow. The shock reflection from the closed end of the upper tube takes place between Frames C and D and creates a local pressure rise approximately equal to that originally used to initiate the detonation.

In Frame E, the pressure on the upstream wall of the upper tube is nearly as high as that pro- duced by the detonation in Frame A. Additional details are given below. The strength of the shock reflection off the endwall of the nondetonated tube is somewhat overstated for this relatively short tube. As the tube length is increased (with no change in the nozzle shape), expansion waves

would overtake and weaken the shock before it reflects from the head end so that this reflected pressure would be reduced. Addi- tional calculations are needed to ascertain the manner in which tube length affects the results.

In the final plot, Frame F (0.36 msec), the pressure on the upstream end of the upper tube has decayed considerably, but remains substantially above ambi- ent conditions. The results suggest that the lower tube may equilibrate to ambient conditions before the upper tube does; a situation that may impact the fill process and detonation initiation in the upper tube. It is worthwhile to attempt to modify the geometry to minimize interaction between the tubes. Geometries that will accomplish this end are helaw

a. Mach Number b. Pressure

Tihe PDE (Caw 1) Fig. 3. Time History of Pressure and Mach Number Contours for Dual-

5 American Institute of Aeronautics and Astronautics

Effect of Splitter-Plate Length: Cases 1,2, and 4

The effects of extending the splitter plate differ- ent distances into the converging section of the nozzle are shown in Fig. 4. Here results are shown at three different times for Case 1 (top), Case 2 (middle) and Case 4 (bottom). Case 1 is the case discussed above. For Case 2, the splitter plate is extended one-fourth of the way to the throat and, although the detonation tube curves slightly, its passage height remains constant. Case 4 corre- sponds to the case where the splitter plate ends at the throat. The convergence of the throat causes the passage height to decrease to one-half its orig- inal size at the throat. Again, both pressure and Mach number contours are given.

The leftmost row of frames in Fig. 4 (0.05 msec) corresponds to the time just after the detonation has emerged from the tubes. Note that the longer splitter plate in Case 4 causes the shock to enter

Case 1 1

the upper tube at a later time than in Cases 1 and 2. The relatively short extension in Case 2 yields results similar to those of Case 1.

The central row of frames in Fig. 4 shows condi- tions at 0.10 msec. Here we can clearly see that longer splitter plate extensions delay the shock in the upper tube. Except for this the results look qualitatively similar, although the end wall pressure in the lower tube in Case 4 is considerably higher than that in the other cases in this frame. This pres- sure rise occurs because the convergence at the tube exit in Case 4 reflects a compression wave back into the lower tube as the detonation exits. This pressure perturbation is therefore a ‘single’- tube phenomenon created by the internal geometry of the lower tube.

The rightmost row of frames in Fig. 4 corre- sponds to a time of 0.20 msec. At this time, the shock has reflected from the end wall of the upper

tube in all three cases. Again, the flow fields are qualitatively similar, but differ in detail. Important quantitative differ- ences between the shock reflections in the upper tube for the three cases are discussed below with the pressure line plots.

Effect of tncreasing Throat Area: Cases 4 and 6

The results in Fig. 4 show that the convergence in Case 4 introduces a compression wave that affects the pulse on the head end of the lower tube. To assess the significance of this on the overall process, the geometry of Case 4 was modi- fied by increasing the throat of the common nozzle so that the area of the two detonation tubes remained constant to the end of the splitter plate. The overall area of the throat in

i 5.i Case 2 n m

1 Mach 2.2

1 .s - 0.7

0

I

0.05 msec 0.1 msec a. Mach Number

I 1.6E+06 l . lE+% 5.98+05

.-.- -. 8.1E+04

I &r --- Casa 4

LLLL

0.05 msec 0.1 msec 0.2 msec b. Pressure

Fig. 4. Time History Comparison of Mach Number and Pressure Con- Case 6 is twice that of Case 4. tours in Cases 1, 2, and 4 (Single Detonation Pulse in Luwer The splitter plate again erlded at Tube) the throat. Both Mach number

6 American Institute of Aeronautics and Astronautics

and pressure contours for this larger throat config- uration (Case 6) are given in Fig. 5 and compared with the results of the smaller throat case (Case 4) at each of five different times.

Since the splitter plate length is identical for these two cases, the shock in the upper tube trav- els simultaneously in both cases. However, the pressure pulse observed in Case 4 is absent from - 0.5 msec

0.i rrmE

the corresponding results in Case 6evidence that, indeed, it is the tube convergence that gives rise to this pressure perturbation. In general, the larger area results in smaller supersonic regions

1

and lower Mach numbers in the divergent section. 1 The pressure decay from the dual-tube system also occurs periodically and more rapidly for this larger throat case. We would expect the larger noz- 1 zle of Case 6 to lead to lower average pressure levels in the tubes, and correspondingly larger thrust impulses. Note that the size of the external domain has been increased in Case 6.

Sequential Detonations in Both Tubes: Case 4

.

.7

I’

As a final qualitative comparison, Fig. 6 shows the results for the geometry of Case 4 with sequen- tial detonations in both tubes. The first pulse of these results is analogous to the small-throat area results in Fig. 5. The fill process for the second det-

E

I onation is initiated at approximately the time that the results in Case 4 ended. The six frames in the left column of Fig. 6 show conditions during the first pulse. The six on the right show second pulse con- ditions. Initiation for the second pulses occurs just before the first frame on the upper right.

h. Jach Number

6.1 E+05

Conditions in the frames on the left have already been discussed in reference to Fig. 5 and are omitted here. The primary distihction between the results in the right column and those in the left column is that the upper tube has been filled with a combustible mixture of hydrogen and oxygen just prior to this time frame, and disturbances remain in both tubes and the nozzle. The introduction of fresh propellants in this tube should probably be

c.- --.- delayed until the pressure level has decreased to near its original level. In both cases, the pressure

rm and Mach number contours in the upper tube indi- I cate the presence of a series of shocks traveling in

transverse directions as the result of interactions between the detonation initiated at the close end and the reaction zone created by the shock enter- ing from the open end. The effect of sequential det-

Fig. 5. Time History of Pressure and Mach Number onations in the two tubes appears to be to reduce Contours for Singlc-Pulse Detonation for

the pressure signature on the upstream end of the Smaller (Case 4) and Larger Throat Area (Case 6) upper tube as compared to the detonation of an

b. Pressure

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Second =w 0.036 m u c

I I

.-

Mach

0.40 msec

a. Mach Number b. Pressure

ME-01 8.6E-01 [ a a E n - I.OE-X)

c C

L 0.40 msoc 0.40 msec

c. Temperature d. Water (H20) Fig. 6. Time History of Pressure, Mach Number, Temperature, and Water Contours for Case 4 Configura-

tion (Sequential Detonations in Both Lower and Upper Tubes) isolated tube. In addition, one can see that two- dimensional effects are again more significant in this two-detonation problem than in the single-det- onation case of Fig. 2.

the upper and lower tubes are presented. Figure 7 shows the time histories of the pressure for Cases 1, 3, and 4, all of which have the smaller throat area. The lower curve depicts the pressure in the lower tube, while the upper curve is for the upper tube. For all three cases, the pressure in the lower tube starts with a strong, 30-atm spike that corre- sponds to the pressure used for the numerical det- onation initiation. As the detonatian propagates through the tube, the pressure on the lower end

Time History in Multitube Calculations

To provide more quantitative interpretations of the above computations, some time histories of the pressure at the mid-point of the head ends of both

8 American Institute of Aeronautics and Astronautics

4E&

3E+08

3 2E+08 P a 1E+08

f

The end wall pressure in the top tube remains at atmospheric conditions until the detonation from the lower tube has reached the splitter plate exit, refracted around the splitter, and traversed back up the upper tube. Note that the time it takes the reflected wave to arrive at the head end of the upper tube is increased as the splitter plate (as well as the effective tube length) is increased from Case 1 to Case 3 to Case 4. The rate of decay is, how- ever, quite rapid since it is a shock reflecting from the end, and not a detonation. Again, it is noted that the size of the throat area in the common nozzle will dictate the rate of decay in tubes, as well as the ultimate pressure eventually established.

- way to the throat gives the lowest pressure peak, as seen by comparing Cases 3 and 4. Case 5 (not shown) indicates that extensions into the super- sonic portion of the nozzle are counterproductive.

With the splitter plate extended to the throat (Case 4) the strength of the reflected wave has

-

c r r 3 - c l w t -

a

upper tube for this condition is only four times

o.Ooo1 O.ooo2 O.ooo9 0 . k !

OO Tim

a. Upper End Wall

/-‘ - 0

k lE4[ --

0.0001 0.0002 O.OOO3 0.oOW OO

b. Lower End Wall Fig. 8. Comparison of Time Histories of Pressure on

Centerline of Upper and Lower End Wall for Small Throat (Case 4) and Large Throat (Case 6)

In Case 1, the reflected wave is almost as strong as the original detonation initiation pulse in the lower tube. This reflected wave is considerably reduced in Case 3, but extending the splitter all the

9 American Institute of Aeronautics and Astronautics

approximately 50 percent stronger in Case 6 than in Case 4. This difference apparently comes from detailed changes in the nozzle shape. The maxi- mum overpressure in the upper tube does not appear to be reduced by opening up the throat area.

Finally, Fig. 9 shows the end wall pressures for Case 4 when detonations are initiated in first the lower and then the upper tube. Note that the reflec- tion in the upper tube is modestly larger than that in the lower one. This is probably because of the non- uniform conditions in the engine at the time of the second pulse. The calculation does not extend quite far enough to compare the impact of the deto- nation in the upper tube on the lower tube wall.

4E-l 3E-

n t In

To understand these interactions, the geometri- cal details of the splitter plate between the two tubes and its location with respect to the nozzle throat have been varied parametrically. Results from these dual-tube calculations have been com- pared with results for an isolated detonation tube. The common nozzle of the multitube PDE captures the familiar external shock that is generated behind a single-tube PDE, and reflects, refracts, and trans- mits this shock through the nozzle and into the det- onation tubes. The results show that the pressure induced in one tube by the detonation from a neigh- boring tube can be as large as that produced by the original detonation. Shocks of this magnitude are strong enough to initiate combustion in adjacent tubes, if they are filled with fresh propellants. The likelihood of this happening increases as additional

tubes are added to an engine module.

References

1. Nicholls, J. A., Wilkinson, H. R., and Morrison, R. B., "Intermittent Detonation as a Thrust-Producing Mechanism," Jet Propul-

ob .ob03 0 . k o . k 0 . b sion, Vol. 27, No. 5, 1957, pp. 534-541. Tim

a. Upper End Wall 2. Bratkovich, T. E., and Bussing, T. R. A., "A Pulse Detonation Engine Performance Model," AIM-95-31 55, July 1995.

3. Eidelman, S., Grossmann, W., and Lot- tati, I., "Review of Propulsion Applications and Numerical Simulations of the Pulse Detona- tion Engine Concept," Journal of Propulsion

n

0.0001 0.0002 0.0003 0.0004 0.0005 0.- SRdPDWH, Vd. 7, NO. 6, 1991, pp. 857-865. T i m

b. Lower End Wall 4. Bussing, T. R. A., and Pappas, G., Fig. 9. Time History Of Pressure on Centerline Of Upper "Pulse Detonation Engine Theory and Con-

and Lower End Wall Case 4 with Sequential Deto- cepts," Progress in Astronautics and Aero- nautics, edited by S. N. B., Murthy, and E. T., nations in Lower and Upper Tubes

Conclusions Curran, Vol. 165, 1996, pp. 421 -472.

5. Kailasanath, K., "Review of Propulsion Appli- cations of Detonation Waves," AlAA Journal, Vol.

The characteristics of multitube PDEs have been investigated by means of a two-dimensional computational model. The class of geometries con- 38, NO. 9,2000, pp. 1698-1708.

sidered is composed of two planar detonation tubes exhausting into a common nozzle. The focus was on identifying the level of interaction and crosstalk beween adjacent detonation tubes.

6. Cambier, J. L., and Tegner, J. K., "Strategies for Pulsed Detonation Engine Performance Optimi- zation," Journal of Propulsion and Power, Vol. 14, No. 4, 1993, pp. 489-498.

10 American Institute of Aeronautics and Astronautics

7. Li, C., and Kailasanath, K., 'Perfonnance Analysis of Pulse Detonation Engines with Partial Fuel Filling," AIAA-2002-0610, January 2002.

8. Zhang, Z.-C., Yu, S.-T., He, H., and Jorgen- son, P.C., 'Direct Calculations of Plume Dynamics of a Pulse Detonation Engine by the Space-Time CUSE Method." AIAA-2001-3614, July 2001.

9. Li, C., and Kailasanath, K., "A Nuumerical Study of Reactive Flows in Pulse Detonation Engines," AIAA-2001-3933, July 2001.

10. Schauer, F., Stutrud, J., and Bradley, R., "Detonation Initiation Studies and Performance Results for Pulse Detonation Engine Applications," AIAA-2001-1129, July 2001.

11. Brophy, C. M., and Netzer, "Effects of Igni- tion Characteristics and Geometry on the Perfor- mance of a JP-10/02 Fueled Pulse Detonation Engine," AIAA-99-2635, June 1999.

12. Sanders, S. T., Jenkins, T. P., and Hanson, R. D., 'Diode-Laser Sensor System for Multi- Parameter Measurements in Pulse Detonation Engine Flows," AIAA-2000-3529, July 2000.

13. Wu, Y., Ma, F., and Yang, V., 'System Per- formance and Thermodynamic Cycle Analysis of Air-Breathing Pulse Detonation Engines," AIAA- 2002-0473, January 2002.

14. Ebrahimi, H. B., and Merkle, C. L., 'A Numerical Simulation of the Pulse Detonation Engine with Hydrogen Fuels," AIAA-99-2259, June 1999.

15. Ebrahimi, H. B., Mohanraj, R., and Merkle, C. L., 'Multi-Level Analysis of Pulsed Detonation Engines," Journal of Propulsion and Power, Vol.18, April 2002, pp. 225-232.

11 American Institute of Aeronautics and Astronautics