Development of Microwave Rocket as a Space Mass

Transportation System

Reiji KOMATSU, Masafumi FUKUNARI, Toshikazu YAMAGUCHI, Kimiya KOMURASAKI,

Yoshihiro ARAKAWA (The University of Tokyo),

Yasuhisa ODA, Keishi SAKAMOTO (Japan Atomic Energy Agency),

Ikko FUNAKI (Japan Aerospace Exploration Agency), Hiroshi KATSURAYAMA (Yamaguchi University)

Abstract — An air-breathing pulse-detonation engine powered

by microwave energy beaming, “Microwave Rocket” is considered as a future mass transportation system to space. A key

to realize Microwave Rocket is to achieve high air-breathing performance. We are now developing the system using side-wall reed valves which is expected to minimize ventilation period. A

test chamber equipped with a reed valve was fabricated and the ventilated volume flow rate was measured. CFD was also conducted. As a result, it came out that pressure oscillation

frequency inside the thruster was approximately in inverse proportion to the thruster length. It was also found that there is minimum thruster aspect ratio where complete ventilation can be

accomplished.

Index Terms — Microwave Rocket, Microwave Energy Beaming, Space Transportation, Gyrotron.

I. INTRODUCTION

In order to construct huge space infrastructures, like Space

Solar Power System (SSPS), transportation cost will be very

expensive if conventional chemical rockets are used. This is

because chemical rockets need huge amount of propellant to

be loaded and expensive equipment like turbo pump are

expended. Therefore alternative low cost space transportation

systems should be applied for transportation of these

infrastructures.

One of the prospective solutions is realizing beaming

propulsion. In the beaming propulsion, the energy necessary

for the launch is supplied from the ground by laser or

microwave beaming. The conceptual diagram of beaming

propulsion is shown in Fig. 1.

Microwave Rocket is one types of the beaming propulsion

systems. This rocket is initially proposed by Shad et al [1].

This rocket can use the atmospheric air as a propellant during

the flight in dense atmosphere. Thrust is generated by exhaust

process of the compressed air by microwave detonation.

Microwave detonation is a process in which a shockwave and

an ionization wave front propagate together. The cycle is often

discussed with analogy to that of Pulse Detonation Engine

(PDE) [2]. This process begins with breakdown in the air by

focusing a high power microwave beam generated by a

gyrotron on the ground. After the exhaust process, Microwave

Rocket refills the detonation tube with air and prepares for the

next cycle which begins with the next pulsed microwave.

Fig. 1. Conceptual diagram of the Beaming Propulsion

II. ADVANTAGE OF THE MICROWAVE ROCKET

Microwave Rocket can contribute to constructing huge

infrastructures in terms of following three points.

Firstly, specific impulse Isp of Microwave Rocket can be

much larger than that of conventional rockets by applying air-

breathing engine cycle. Because maximum Isp of conventional

chemical rockets is low, a large amount of onboard propellant

is required to reach the Geostationary Earth Orbit (GEO),

resulting in quite low payload ratio. If atmospheric air can be

used as a propellant, high Isp and high payload ratio will be

achievable.

Secondly, it is not necessary to load complex and expensive

systems like turbo pump on Microwave Rocket. This rocket

can generate thrust by using simple and cheap modules such

as detonation tube, mirrors and reed valves.

Finally, allowable level of security for Microwave Rocket is

lower than that of the other transportation systems by

specializing in massive material transportation as a mass-

driver. In order to transport people, levels of security and

reliability must be quite high because of need for redundancy,

acceleration limit, and no accident. It is not effective to

transport materials by the vehicles which are assumed to

transport people. However in a mass-driver case, since the

cost of rocket itself and importance of payload per one launch

are lower than former case, it gets possible to make trade-off

between cost and reliability.

IWPT10-2

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Fig. 2. Schematic of the Microwave rocket with reed valves

III. DEVELOPMENT OF THE MICROWAVE ROCKET

There are two modes of propulsion system, air-breathing

mode and rocket mode. In the rocket mode, Microwave

Rocket utilizes propellant such as Argon from the onboard

tank to generate the thrust at an altitude higher than roughly

60 km. However most of the flight is accomplished by air-

breathing mode. In this mode, air intake is realized by reed

valves. Reed valves are normally used as intake of two-stroke

engine [3].

Fig. 2 shows schematic of the Microwave Rocket with air-

breathing system by reed valves. It is possible to generate

thrust even in the thin air at a high-altitude up to about 60km

by applying this air-breathing system. This is because air can

be compressed by the slot between thruster body and cowl

when the reeds are closed. The rocket flies at the higher-

altitude, more strongly the air is compressed since flight Mach

number is tremendous there.

Shiraishi et al. showed that it is necessary to ventilate

almost whole thruster even in the low-altitude. This is because

thrust will decrease because of high temperature gas which is

still remained in the thruster if the air intake is insufficient [4].

So it is essential to develop high performance air-breathing

system for these two reasons.

IV. CFD CALCULATION

In order to develop high performance air-breathing system,

the reed valves must rapidly move against pressure oscillation

inside the thruster. It is useful to get the frequency of the

pressure oscillation in the thruster in advance because the

natural frequency of reeds must be much larger than pressure

oscillation frequency inside. Moreover, relationship between

pressure oscillation frequency fp and thruster length L is also

important because small fp means more ventilation time tv.

Therefore one dimensional Computational Fluid Dynamics

(CFD) was conducted to simulate the pressure oscillation

inside the thruster tube with no reed. Governing Equation is

one dimensional Euler equation. The effect of viscosity and

thermal condition is neglected because attenuation of the

oscillation is not important for developing air-breathing syste-

Fig. 3. Result of the pressure oscillation by CFD calculation and

experiment data for L = 500 mm obtained by Oda et al [5].

m. AUSM-DV scheme is applied for the solver.

As the initial parameter, pressure inside the thruster Pii = 1.5

atm, outside the thruster Pio = 1.0 atm, temperature inside the

thruster Tii = 600 K, and outside the thruster Tio = 298 K are

chosen from typical condition of the rocket. Fig. 3 shows the

comparison between result of the pressure oscillation by CFD

and typical experiment data at the thrust wall (at the top of the

thruster inside) for L = 500 mm obtained by Oda et al. [5].

It can be said that the oscillation can be well described by

CFD calculation. The maximum negative pressure which is

the pressure difference between inside and outside Pmax =

0.65 bar is also expressed by calculation.

V. EXPERIMENT

A. Measurement of Natural Frequency of a Reed

Natural frequency of a reed should be much larger than that

of pressure oscillation. By modeling a reed as cantilever, we

can estimate the natural frequency. However in the case the

reed length l is short, it is anticipated that the cantilever theory

causes error in some degree due to the range of application.

Therefore by oscillating the reed with impulse, we get its

natural frequency experimentally. The reed is made of SK-4

spring material (the Young’s modulus is about 190 GPa,

density is about 7800 kg/m3).

B. Measurement of Volume Flow Rate through a Reed Valve

The volume flow rate through reed valves must be enough to

ventilate almost whole the thruster. In order to estimate total

volume flow rate of the air-breathing system, we conducted

the measurement of the volume flow rate per a reed. The

experiment setup is described in Fig. 4.

A reed is set in the chamber and the inside pressure is

changed by opening and closing the solenoid valve which

connects chamber to the vacuum tank. The movement of the

reed is measured by the laser displacement meter (KEYENCE

LK-500). Volume flow rate qv is defined as volume of the

Pmax

D

L payload

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chamber over opening time of the reed. The volume of the

chamber is 126 cm3. Again, the reed is made of SK4 spring

material and the sizes tested are determined so that the natural

frequency is much larger than that of pressure oscillation

generated.

VI. RESULT

CFD result is shown in Fig. 5. It portrays the dependence of

the pressure oscillation frequency fp and ventilation time tv

upon thruster length L. It can be said that fp is approximately

in inverse proportion to L. This is because fp is determined by

the propagation of the expansion wave in the thruster. Since

the velocity of the expansion wave is nearly the same as the

sonic velocity and since sonic velocity is constant under the

constant temperature, the time of the propagation cycle tc is

almost proportional to L. That is why fp is approximately in

inverse proportion to L. And it is found that the frequency

ranges 3-20 Hz for length 5-30 m. The time which can be used

for ventilation tv is approximately proportional to the L

because tv is defined as half of the tc.

Fig. 6 shows the result of the natural frequency measurement

fe with theoretically calculated one ft. As we anticipated in

advance, the difference between fe and ft gets larger when l is

shorter than 70 mm. And it is found that the fe can be roughly

200 Hz which is as ten times large as 20 Hz when the reed

length l is equal to 30 mm.

Fig. 7 is experiment result of the volume flow rate

measurement. About 3.5 l/s volume flow rate is obtained for

every reed whose length is 32 mm. The reason why volume

flow rate is large when the thickness h is thin is that the

movement of the reed become large with small h. Actually,

the maximum reed tip displacement y = 1.3 mm is observed

when h = 0.3 mm while y = 1.0 mm when h = 0.35 mm.

However we must be careful that this happens when the

natural frequency of a reed should be much larger than that of

pressure oscillation.

Fig. 4. Schematic experiment setup for the measurement of the

volume flow rate through a reed valve.

VII. DISCUSSION ABOUT THE ACTUAL ROCKET

Using the results of the former section, we estimated the

volume flow rate Qv which is anticipated to be obtained by the

reed valves and Qn which is necessary for complete ventilation

for the several sizes of actual thruster.

The reed length 30 mm, width 10 mm, and thickness 0.3 mm

are applied and the number of the reeds is determined by the

Fig. 5. CFD result which shows relationship between thruster length

L, frequency of pressure oscillation fp, and ventilation time tv.

Fig. 6. Experiment Result which shows relationship between the

natural frequency of the reed fe and the reed size parameter (the reed

length l and thickness h). Lines shows natural frequency ft calculated

by cantilever theory. The width 12 mm is fixed.

0

50

100

150

200

0

5

10

15

20

25

0 10 20 30 40

Ventila

tion T

ime t

v[m

sec]

Fre

quency f

p[H

z]

Thruster Length L [m]

0

50

100

150

200

250

300

350

0 30 60 90 120

Natu

ral F

requency o

f R

eed [

Hz]

Reed Length l [mm]

fe(h=0.3)

fe(h=0.35)

fe(h=0.4)

ft(h=0.3)

ft(h=0.35)

ft(h=0.4)

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Fig. 7. Experiment Result which shows relationship between the

natural frequency of the reed fe and the reed size parameter (the reed

length l and thickness h). Lines shows natural frequency ft calculated

by cantilever theory. Length and width of the reed is 32 mm and 12

mm respectively. Obtained maximum negative pressure is 0.05 bar

Fig. 8. Relationship between partial filling rate Qn/Qv and aspect ratio

L/D.

side-thruster area St of the thruster. Here, 37 % of the side

surface area is assumed to be occupied by the reeds. And Qv is

obtained by multiplying qv= 3.5 l/s by the number of the reeds.

Because qv is constant and number of the reeds is proportional

to St, = DL, Qv is proportional to DL.

Thruster volume is calculated as the cylinder whose length is

L and diameter is D. By dividing this volume by ventilation

time tv, we can obtain Qn. Here, Qn is approximately

proportional to D2 because cylinder volume is expressed as

D2L and tv is roughly proportional to L. Therefore, it can be

predicted that Qv/Qn has linear relationship to L/D.

Fig. 8 describes the result of the estimation. As it is

anticipated, the linear relationship between Qv/Qn and L/D is

obtained. Usually Qv/Qn is called partial filling rate, and L/D is

called aspect ratio. Complete ventilation will be accomplished

when partial filling rate is larger than 1.

It can be said that aspect ratio should be larger than 11,

providing that qv = 3.5 l/s (Pmax = 0.05 bar) is constant.

However as Fig. 3 shows, in the typical experiment, Pmax =

0.65 bar is observed which means there is margin for

enlarging qv and making aspect ratio small.

VIII. CONCLUSION

CFD calculation and experiment was conducted to get the

pressure oscillation frequency inside the thruster, natural

frequency of a reed valve, and volume flow rate through a

reed. It was found that pressure oscillation frequency is

approximately in inverse proportion to the thruster length from

the CFD calculation. Moreover, it came out that there are

adequate sizes of a reed which allows it to follow the pressure

oscillation. Considering these results, estimation of the actual

volume flow rate by the air-breathing system was discussed. It

was found that there is minimum thruster aspect ratio around

11 where complete ventilation can be accomplished when

maximum negative pressure generated is about 0.05 bar.

REFERENCES

[1] J. L. Shad, J. J. Moriarty, 1965 Propulsion and Reentry: XVI

Intern. Astronaut. Congr. Athens vol. 5, pp. 175–86

[2] T. Endo, J. Kasahara, et al. ”Pressure History at Thrust Wall of

a Simplified Pulse Detonation Engine”, AIAA Journal, Vol. 42,

No. 9, September. 2004

[3] G. Blair, 1996, Design and Simulation of Two-Stroke Engines,

Society of Automotive Engineers, Inc, pp 367-370

[4] Y. Shiraishi, Y. Oda, T. Shibata, K. Komurasaki, “Air

Breathing Process in a Repetitively Pulsed Microwave Rocket”,

AIAA 2008-1085

[5] Y. Oda, K. Komurasaki, et al., “An Experimental Study on a

Thrust Generation Model for Microwave Beamed Energy

Propulsion”, AIAA 2006-0765

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 5 10 15 20

Part

ial F

illin

g R

ate

Qv/Q

n

Aspect Ratio L/D

3.3

3.4

3.5

3.6

0.28 0.3 0.32 0.34 0.36

Volu

me F

low

Rate

qv

[l/s]

Reed Thickness h [mm]

Pmax = 0.05 bar

Pmax = 0.05 bar

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