American Institute of Aeronautics and Astronautics

1

Prediction of Time Variation of Ballistic Parameters For a Swirling-Oxidizer-Flow-Type Hybrid Rocket Engine

using Burning Data

Noriko Shiraishi1 JAXA, Tsukuba, Ibaraki, 305-8505,Japan

and

Saburo Yuasa2 Tokyo Metropolitan University, Hino, Tokyo, 191-0065,Japan

For hybrid rocket engines, there are some unique relationships between the parameters, such as the fuel regression rate, oxidizer mass flow rate, equivalence ratio and so on, which determine the burning properties. These relationships are strongly related to the engine performance. Our final goal of this study is to establish the optimum design method which considers the engine performance of hybrid rocket engines for practical hybrid rockets varying with time. In this paper, we focused on the time variation of ballistic parameters. First, we established the calculation method which well simulates the burning condition of the swirling-oxidizer-flow-type hybrid rocket engine. Next, we predicted the time variation of the burning properties and ballistics parameters using this calculation method and some experimental burning data. The simulation results showed little difference in the time variations of the combustion pressure and thrust from the experiment. The simulated values of the engine efficiencies of Isp, C* and CF obtained well agreed with those experimentally. The simulation method proposed here is appropriate for predication of time variation of ballistic parameters and may be useful as a design tool for hybrid rocket engines.

I. Introduction OME hybrid rocket engines succeeded in getting an adequate thrust by using unique burning methods. The swirling-oxidizer flow type which was established in Yuasa lab. is one of the successful burning method to get a

practical thrust. 1-3 The small rocket using this type of engine succeeded in launch in 2001. But there are still some problems to make practical hybrid rockets.

One of the problems is the prediction of burning properties. In hybrid rocket engines, the equivalence ratio is defined by the mass flow rate of oxidizer which is supplied from the outside to a combustion chamber and the mass flow rate of fuel burning in the chamber. Therefore, even if the oxidizer mass flow rate is constant, the equivalence ratio changes with time due to the change of the inner diameter of solid fuel. Then the ballistic parameters, such as the combustion pressure, the combustion temperature and the thrust, also change with time. These time variations should be considered to design practical hybrid rocket engines.

The final goal of this study is to establish the optimum method for the system design of hybrid rockets. In this study, as an one approach, we simulate the experimental time variation of the ballistic parameters of the hybrid rocket engine by considering the fuel regression rate behavior and equilibrium burning condition.

1 Engineer, Space Transportation Mission Directorate, Tsukuba Space Center 2-1-1, Sengen. AIAA Member. 2 Professor, Department of Aerospace Engineering, 6-6, Asahigaoka. AIAA Member.

S

46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit25 - 28 July 2010, Nashville, TN

AIAA 2010-6874

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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II. Regression Rate Relations In this study, it is assumed that the solid fuel inner shape is cylindrical at all time. The regression rate of solid

fuel of hybrid rocket engines is shown as follows;4

(1)

r& =regression rate [ ]sm

oG =oxygen mass flux ( )[ ]smkg ⋅2

a =regression rate coefficient [ ]sm n =regression rate exponent

om& =oxidizer mass flow rate [ ]skg

d =inner diameter of solid fuel [ ]m

The oxidizer mass flow rate, the burning time and the total burned fuel mass are measured in the experiment of the swirling-oxidizer-flow-type engine. Since the solid fuel inner shape is assumed to be cylindrical, the final inner diameter of solid fuel is given by Eq.(2);

(2)

fm∆ =total burned fuel mass [ ]kg

fρ =density of fuel [ ]3mkg

0d =initial inner diameter of fuel [ ]m

ed =final inner diameter of fuel [ ]m

L =cylinder length of fuel [ ]m

The regression rate varies with time according to Eq.(1), and thus the time-averaged inner diameter of solid fuel and fuel regression rate are given as follows;

(3)

(4)

In our previous experiment by using the swirling-oxidizer-flow-type engine of Fig.1 and polypropylene(PP), the regression rates were measured as shown in Fig.2. 5,6 From this results the regression rate coefficient and exponent to calculate the time-averaged fuel regression rate are obtained.

non

o dm

aaGr ⎟⎠⎞

⎜⎝⎛== 2

4π&

&

n

ave

oavenoaveave d

maaGr ⎟

⎟⎠

⎞⎜⎜⎝

⎛== 2

4π&

&

Lddm e

f

f⎟⎟⎠

⎞⎜⎜⎝

⎛−=

∆

44

20

2 ππρ

⎟⎠⎞

⎜⎝⎛ −

=2

0ddd eave

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III. Simulation Procedure for Time Variation The time variation of ballistic parameters are simulated by using the experimental oxygen mass flux and the fuel

regression rate values of a and n . The simulation is made by two steps. Step1:Calculate the equivalence ratio and the fuel mass flow rate.

From Eq.(3) and (4), an inner diameter id at an optional time it is given by using an inner diameter 1−id in an

optional time 1−it before t∆ as follows;

(5)

This equation predicts the time variation of the inner diameter of fuel, and then the time variation of the fuel mass flow rate is given by the inner diameter of fuel and the oxidizer mass flow rate as follows;

(6)

Figure 1. Experimental device of swirling-oxidizer-type hybrid rocket engine.

Nozzle(Graphite)

Grain (PP/PMMA) Igniter Pressure transducer port

600 ~ 1000 (This is a 600mm-Engine)

Unit : [mm]

φ 40

φ100

Thermocouples

GOX

φ 90

105

φ 18

.0

Graphite Thermocouple

Swirler Injector

φ 42

.0

~φ

48

)(4

2 121

1 −−

− −⎟⎟⎠

⎞⎜⎜⎝

⎛+= ii

n

i

oii tt

dm

addπ&

dLdmam f

no

f πρπ

⎟⎠⎞

⎜⎝⎛= 2

4 &&

Figure 2. Relation between fuel regression rate and oxygen mass flux for swirling-oxidizer-flow-type hybrid rocket engines.

1 10 100 1000酸化剤質量流束,Goave[kg/(m

2/s)]

燃料後退速度,rave[mm/s]

101

100

10-1

rave=0.0826Goave0.550

L=0.15～1.00[m]

Goave=8.8～144.4[kg/(m2・s)]

Oxygen Mass Flux, kg/(m2・s)

Reg

ress

ion

Rat

e, m

m/s

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fm& =fuel mass flow rate [ ]skg Here the regression rate coefficient a and exponent n are obtained by Fig.2 for many experimental data.

Therefore, for an individual experiment the total burned fuel mass calculated by integrating Eq.(6) with a and n is not equal to a fm∆ value experimentally obtained. So, the regression rate coefficient a should be corrected so as to coincide the total burned fuel mass in the simulation with that in the experiment. Using the corrected regression rate coefficient a′ , the total mass flow rate through the engine nozzle is shown as follows;

(7)

m& =total mass flow rate [ ]skg

a′ =corrected regression rate coefficient [ ]sm

Since the equivalence ratio is defined as follows;

(8)

ϕ =equivalence ratio

( )STOF =fuel/oxidizer mass ratio at stoichiometric condition the time variation of the equivalence ratio is simulated using Eq.(6) and (8). Step2: Simulate ballistic engine parameters at equilibrium burning condition From the time variation of the equivalence ratio and the

mass flow rate, the combustion temperature, the combustion pressure and the thrust are calculated at equilibrium burning condition by using the one dimensional nozzle theory. The flow chart of the program is shown in Fig.3. The

results of this program are inspected by the CEA program.7 At some conditions, the calculated results by this program are confirmed to agree with these by the CEA program. The values of the parameters using in the simulation are shown in Table 1. The thermochemical data were referred from JANAF table.8 The burned gases are assumed to expand as the isentropic equilibrium flow in the nozzle.

dLdmammmm f

no

ofo πρπ

⎟⎠⎞

⎜⎝⎛′+=+= 2

4 &&&&&

( )ST

of

OFmm &&

≡ϕ

read φt、mt

Pct=Pci

mass flow rate=input 

mt?

Calculate Tct

Pci=Pci±α

do t=t0～tend

Calculate the condition at throat 

Calculate the condition

at nozzle exit

Figure 3. Flow chart of the simulation program for ballistic engine parameters.

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IV. Calculation Results Figure 4 shows the typical simulation results using the experimental data shown in Table 2. According to Step1,

the time variation of the equivalence ratio and the mass flow rate are simulated in the left side of Fig.4. According to Step2, the time variation of the combustion temperature Tc , the combustion pressure Pc , and the thrust F are simulated in the right side of Fig.4. It is found that the mass flow rate slightly decreases with the time, and then, the equivalence ratio also slightly decreases and the combustion temperature increases. Corresponding to these, the combustion pressure and the thrust decrease with the time. Figure 5 shows the comparison of the calculation results with experimental results.

oxidizer/fuel gas oxygen/ polypropylene (PP) density of fuel

fρ ＝910 [ ]3mkg

fuel/oxidizer mass ratio at stoichiometric condition

( )STOF ＝0.29

standard heat of formation of fuel ＝○fH∆ -20.918 [ ]molkcal

pressure of the atmosphere 0P ＝0.1013 [ ]MPa

shape of chamber (Fig.1) single port cylinder diameter of nozzle throat (Fig.1)

td ＝0.018 [ ]m diameter of nozzle exit (Fig.1)

ed ＝0.042 [ ]m species of burned gas 632222 ,,,,,,,, HCHOOHOHHOCOCO

fuel regression rate coefficient and exponent a′＝0.0787×10-3 [ ]sm n＝0.55

initial inner diameter of fuel solid 0d ＝0.0048 [ ]m length of fuel cylinder L＝1.0 [ ]m burning time t＝4.79 [ ]s total burned fuel mass fm∆ ＝1.01 [ ]kg average oxidizer mass flow rate om ＝0.3875 [ ]skg

Table 1. Fuel and engine parameters using in the simulation.

Table 2. The experimental data using in the calculation of Fig.4.

Figure 4. Calculation results.

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

0 1 2 3 4 5time, s

Mas

s Fl

ow R

ate,

kg/

sE

quiv

alen

ce R

atio ϕ

m&m&m& o

f

0

1000

2000

3000

4000

5000

0 1 2 3 4 5time, s

Com

bust

ion

Pre

ssur

e, k

Pa

Com

bust

ion

Tem

pera

ture

, KTh

rust

, N

Pc

F

Tc

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V. Discussion

A. Engine Efficiencies Since the total mass flow rate in the simulating program is assumed to coincide with experimental one, the

theoretical values of the engine efficiencies with regard to Isp, C* and CF can be predicted using the simulation results shown in Fig.4. Table 3 shows the predicted values of the engine efficiencies. The values were confirmed to well agree with those estimated experimentally by measuring the combustion chamber pressure and the thrust as shown in Table.3. This suggests that the simulation procedure is fit to predict the burning process of hybrid rocket engines.

B. Difference between Calculation and Experiment In the theory if the oxidizer flow rate is constant, the

inner diameter of solid fuel increase with time, and thus the regression rate decrease. Figure 6 shows the simulation results of the time variation of the inner diameter of solid fuel and regression rate. Corresponding to these variations, the mass flow rate and the equivalence ratio decrease with time, resulting in that the combustion pressure and the thrust also decrease. The simulation results shown in Fig.5 fit this prediction, but the experimental results showed conversely tendencies.

This difference may be explained in terms of the fuel inner shape. In our simulation the inner shape of fuel solid is assumed to be cylindrical during burning, but in the experiment the inner diameter change by the position from the grain leading edge.6 Near the oxidizer entrance at the grain leading edge, a lot of fuel is consumed due to impinging jet flames by the swirling oxidizer flow. In this region, our experimental results revealed that the fuel regression rate was considerably large and was independent of burning time and thus inner diameter. This implies that the fuel mass flow rate increases with time in proportion to an increase of the inner surface area burning in the strong swirling flow region at the grain leading edge. Corresponding to this, therefore, the camber pressure and thrust also increase. The deference behavior between the simulation and the experiment suggests the possibility that the burning

simulation experimentefficiency of Isp 86.8％ 88% efficiency of CF 98.6％ 99% efficiency of C* 88.0％ 89%

Table 3. Engine efficiencies.

Figure 5. Comparison of calculation results with experimental results.

0

1000

2000

3000

4000

5000

0 1 2 3 4 5

Thru

st, N

time, s

Experiment

Calcuration

0

500

1000

1500

2000

0 1 2 3 4 5

Com

bust

ion

Pre

ssur

e, k

Pa

time, s

Experiment

Calcuration

Figure 6. Time variation of fuel regression rate and fuel inner diameter.

Reg

ress

ion

Rat

e, m

m/s

time, s

Fuel

inne

r di

amet

er, mr&

d

0.00

0.05

0.10

0.15

0.20

0.0 

0.5 

1.0 

1.5 

2.0 

0 1 2 3 4 5

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mechanism in the leading edge region of the fuel grain with strong oxidizer swirling motion differs in the rear region of the fuel grain.

C. Maximum Engine Performance For PP, the optimum equivalence ratio to obtain a maximum Isp is about 1.4. Therefore in the experimental

condition of Table.2, the oxidizer mass flow rate should be increased to make the equivalence ratio decrease during burning. One optimum design case with the equivalence ratio of 1.4 at the initial time is calculated as shown in Table.4. Although we have not carried out the burning test at this high pressure and oxidizer mass flow rate, the theoretical calculation shows that this performance is able to attain using the same size engine. However as shown in Fig.6 the equivalence ratio is varied with time, in order to establish an optimum design process with a maximum engine performance, it is necessary to examine the time dependencies of the engine parameters more in detail and clearly.

VI. Conclusions We simulated the time variation of ballistic parameters of the swirling-oxidizer-flow-type hybrid rocket engine by

using the experimental oxygen mass flow rate and fuel regression rate values. The simulated values of the engine efficiencies well agreed with those experimentally. Therefore the simulation procedure is fit to predict the burning process of hybrid rocket engines. On the other hand, the deference tendencies of ballistic parameters between the simulation and the experiment suggests the possibility that the burning mechanism in the leading edge region of the fuel grain with strong oxidizer swirling motion differs in the rear region of the fuel grain. To establish an optimum design process of hybrid rocket engines, it is necessary to examine the burning mechanism in the fuel grain and the time dependencies of engine parameters more in detail and clearly.

Acknowledgments This research is supported by the Hybrid Rocket Research Working Group (HRrWG) of Institute of Space and

Astronautical Science, Japan Aerospace Exploration Agency. The authors express thanks to the members of HRrWG for their helpful discussion and to the students of Yuasa lab. for their cooperation in conducting this study.

References 1Yuasa, S., Shimada, O., Imamura, T., and Yamamoto, K., “A Technique for Improving the Performance of Hybrid Rocket

Engines” 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Los Angeles, California, June 1999. 2Tamura, T., Yuasa, S., and Yamamoto, K., “Effects of Swirling Oxidizer Flow on Fuel Regression Rate of Hybrid Rockets”

35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Los Angeles, California, June 1999. 3Yuasa, S., Yamamoto, K., Hachiya, H., and Kitagawa, K., “Development of a Small Sounding Hybrid Rocket with a

Swirling-Oxidizer-Type Engine” 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Salt Lake City, Utah, July 2001.

4Ronald W. H., Gray N. H., and Wiley J. L., Space Propulsion Analysis and Design, The McGraw-hill Companies, Inc. Primis Custom Publishing, New York, 1995.

5Sakurazawa, T., Kitagawa, K., Hira, R., Matsuo, Y., Sakurai, T., and Yuasa, S., “Development of a 1500N-thrust Swirling-Oxidizer-Flow-Type Hybrid Rocket Engine”, AJCPP, Gyeongju, Korea, March 2008.

6Yuasa, S., Sakamoto, M., Sezaki, T., Sakurai, T., Shiraishi, N., and Shimada, T., “Fuel Regression Rate Behavior in Swirling-Oxidizer-Flow-Type Hybrid Rocket Engines”, 8th International Symposium on Special Topics in Chemical Propulsion, Cape town, South Africa, November 2009.

7McBride, B.J., Gordon, S., “Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications II,” NASA PR 1311, 1996.

8Chase, M.W., NIST-JANAF Thermochemical Tables Forth Edition, New York, American Institute of Physics, 1998.

equivalence ratio at initial time ϕ =1.4 oxidizer mass flow rate om =0.6988 [ ]skg combustion presser Pc =6877 [ ]kPa combustion temperature Tc =3644 [ ]K thrust F =2879 [ ]N

Table 4. Estimated optimum engine parameters.