[American Institute of Aeronautics and Astronautics 33rd Joint Propulsion Conference and Exhibit -...

Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

At A A. A97-36173

AIAA 97-2864Design of a Micro Solid Rocket MotorYang Tao, Xun-bo Wu,Xiao-qian ChenDept. of Aerospace Tech.National Univ. of Defense Tech.Changsha, P.R.China

33rd AlAA/ASME/SAE/ASEEJoint PropulsionConference & Exhibit

July 6 - 9, 1997 / Seattle, WAFor permission to copy or republish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 22091


Design of A Micro Solid Rocket MotorYang Tao* , Xun-bo Wu, Xiao-qian Chen

Department of Aerospace Technology, National University of Defense Technology,Changsha, Hunan,China 410073

Abstract

This paper introduced the structural and reli-ability design of a Micro Solid Rocket Motor(also called gas generator) which was used togenerate gas so as to do work and lift something.The mathematics-physical model which de-scribed the internal flow field of the gas genera-tor and the lifting device was established, theempirical coefficient in the heat-loss model wasdetermined by experiment. The processes ofcombustion . flow and heat transfer inside thechamber of the gas generator and lifting devicewere simulated by numerical method. The theo-retical analysis guided the design of the grain,which made the gas generator satisfy the re-quirements of good performance and high reli-ability.

Introduction

Pyrotechnic elements is a kind of small com-ponent containing a small amount of powder ,explosive or pyrotechnic compound. It can giveoff a large amount of energy in a very short time,and the energy can be used to do mechanicalwork to complete certain action. Thus, it iswidely used in spacecraft 's unlocking .ejecting . separating , cutting and supplyingsmall thrust, etc. This paper introduced the de-sign of a kind of micro solid rocket motor(gasgenerator). Because of the complexity of thewhole mechanism, here only the principlescheme of the whole system is shown in Figure1. The grain of the micro solid rocket motorbums in chamber 0 and produces high tempera-ture , high pressure combustion gas, whichflows through nozzle and towards chamber 1.There is an one-way valve between chamber 1and chamber 2. When the pressure differencebetween the chamber 1 and 2 is greater than a

certain critical value, the gas in chamber 1 be-gins to enter chamber 2. chamber 2 is connectedwith chamber 3 by two small holes whose di-ameter are 2 mm. When the pressure in chamber3 is great enough to provide the force to movethe piston, the piston begins to move until itreaches the top. The function of the whole de-vice is to raise the piston to a certain top heightreliably with an acceleration lower than a certaincritical value. It is mainly realized through thedesign of the gas generator.

Fig. 1 The schematic diagram of die lifting device

The structural design and reliability design ofthe gas generator

the structural designTo see on the structure, the gas generator is a

miniature solid rocket motor. It mainly consistsof igniter , combustion chamber , grain .. thefront and aft trap as well as nozzle(as is shownin Figure 2). The size of the configuration is de-termined by the requirements of installation andthe grain design. The pressure of the combustionchamber is mainly determined for ensuring thenormal combustion of the propellant. A kind ofdouble base propellant "SG-2" is selected in thisdesign, its critical pressure of steady combustionis 3.9 MPa at -40 °C. Hence, the designed pres-sure in the chamber of the gas generator must begreater than 3,9 MPa. The grain design is mainlyto determine the shape and the grain mass tomeet the overall task's requirements. Its detailed

* Associate Professor.Copyright © 1997 by Authors. Published by the American Instituteof Aeronautics and Astronautics, Inc. with permission.


design will be given in the latter section. Herethe range of the amount of the grain is firstgiven through preliminary analysis.

2 3 7

quirement, we adopt a redundant system whichis paralleled by two gas generators. The reliabil-ity block diagram is shown in Figure 3:

Fig.2 The gas generator. 1-igniter; 2-top cap; 3-case; 4-igniterpower; 5-main grain; 6-nozzle; 7-diaphragm.

(1) Estimation of the minimum amount of thegrain

The minimum amount of the grain means thegrain mass that is enough to lift the piston to thetop height without considering any energy lossin the processes of combustion, flow, and work-ing. The loss of the energy includes the combus-tion loss > the flow loss „ the heat transfer lossand the frictional loss , among which the heattransfer loss is the most important. If neglectingthe effects of the initial air in the lifting device,the mass of the propellant, in the light of themass conversation, should be equal to the massof the combustion gas generated by the propel-lant's complete combustion. Assuming the massof the propellant to be m, the final equilibriumpressure to be p, the temperature to be T, thevolume of the inner chamber of the lifting de-vice to be V and the gas constant to be R, wecan draw the state equation:

PV = mRT (1)Because of the neglecting of the heat loss,

the gas temperature of the end state can be con-sidered approximately to be the adiabatic com-bustion temperature of the propellant Tp, whosevalue is 2348K. The equilibrium pressure can bedetermined to be 0.955 MPa according to themass of the piston. From equation (1) we canobtain that the minimum propellant is 0.8 gram.(2)Estimation of the maximum amount of thegrain

The maximum amount of the grain means thepropellant mass which is required to completethe lifting action when the heat loss is maximum.It is obvious that the heat loss is maximum whenthe temperature of the combustion gas drop tothat of the environment. If the temperature ofthe environment is 298K, then from equation(1) ,the maximum amount of the grain can bedetermined to be 6.34 gram.

the reliability analysisThe reliability index of pyrotechnic elements

is usually very high. As to the gas generator,its reliability index is 0.9999. To satisfy this re-

/

s

z

i

—

&3

/

4

aFigure 3, The reliability block diagram of the gas generatorsystem. 1,5: igniter; 2, 6: the case of gas generator; 3,7: grain;4,8: nozzle.

If we use P to stand for the reliability, the re-liability of gas generator A is Pt , then,

PA=P,P,P,Pt (2)According to the symmetry, PB = PA , hence,

the reliability of the system is:P-(2-PA)PA (3)

Obviously, when PA =0.99, the reliability ofthe system P will be 0.9999. The reliability of asingle gas generator is determined by the reli-ability of the components. The igniter is a stan-dardized component, whose reliability is greaterthan 0.995. The reliability of the other compo-nents can be calculated by stress analysis. Tak-ing the case as an example, The size of theweakest position is:Diameter: D = 1 8.6 _„ 084 mm ;Wall thickness: £=2.3_0,g4/wM ;And known condition:The maximum operating pressure:

p=8.14±0.814MPa;The strength limit of the case material:

o-6=1078±49MPoAccording to the "3a principal", the standard

deviation of the variables areap =0.087 MPa

as =0.0473/w«aR =0.007mm

In the light of the strength theory, the maxi-mum stress of the case is:

K--1Where

K=R/(R-S)The standard deviation of the stress is

(4)

(5)


Where ckr/cfr>,dcr/d8,and dcrjdR can be de-rived from equation (4).Assuming that both stress and strength obeynormal distribution, then according to the stress-strength interference theory, we have

Z= — r=-65.2

So< 7 _ 2 - < 7 *

P/=<l>(Z)<0.0000001

(7)

That isP,> 0.9999999

For the same reason we can get the reliability ofother components. At last, using equation (3),we can draw the conclusion that the reliability ofthe gas generator system is greater than 0.9999.

Simulation of the flow field

the mathematics-physical modelIn the process of the gas generator design, the

simulation of the flow field is the most impor-tant and the most difficult. Its importance lies in:(1) the simulation of the flow field is an impor-tant way to understand the mechanism of com-bustion, flow and heat transfer, and the processof energy transformation in gas generator andlifting device ; (2) the simulation of the flowfield can guide the grain design of the gas gen-erator. Its difficulty is a result of the complexityof the lifting device: the propellant grain in thegas generator is very small, but the area of theheat dissemination is quite great and difficult topreestimate accurately, any improper assump-tion may lead to quite great error.

As to the physical model shown in Figure 1,assuming the parameters of each chamber to beuniform, and taking the combustion gas in eachchamber as object, we can draw the equations ofmass . energy . state and the piston's move-ment.(1) The control equations of chamber 0

m,-mm (8)

d(p0v<tc,T<l)/dt=mtx0cpTf-mmcfT<> (9)dvJdt = Ahr (10)deldt=r (11)Po=P0RT0 (12)

Here the subscript "0" represents chamber 0,p, p, T represents pressure, density, and tem-perature, respectively, v is the free volume ofthe gas generator, mh is the gas generation rate,mm is the mass flow rate from chamber 0 tochamber 1, cy represents the specific heat atconstant volume, cf the specific heat at con-stant pressure, R and Tp are the gas constant

and the adiabatic combustion temperature, re-spectively, x0 is the coefficient of heat loss, Ab

is the burning area, r is the burning rate, e is theweb which has been burned.

In the control equations above, the burningrate is determined by the exponential burningrate formula:

' r=opl (13)If the main grain adopts r, /r, - L0 tube-

shaped grain and full-surface combustion, then ,when the burned thickness is e, the burning areais

r2) (14)

Here A^ is the initial burning area.+/-:)L0-(/-:

:-rl:)] (15)

From the instantaneous burning area, we cancalculate the instantaneous gas generation rate:

Here the p represents the propellant density.The mass flow rate can be divided into twocases: super-critical flow and sub-critical flow.From the nozzle area expansion ratio we cancalculate that the critical pressure ratio equals0.9967, thus,when

when

P,/P2<Pc

(17)

Here At is the throat area, <pm is the dis-charge coefficient of the nozzle, F is the func-tion of the specific heat ratio k ,

l)]<*tl)'2(*-') (19)

(2) The control equations of chamber 1Similarly, we can write the equations of

chamber 1 :d(plvl)/dt=mn-mlz (20)d(p]v}c,Tt)/dt=n,mcpT0-m}2cfT}-Ql (21)Pt=P,RTt (22)Here the mu is the mass flow rate of combus-

tion gas from chamber 1 to chamber 2 throughthe one-way valve, the opening process of theone-way valve is shown in Figure 4.

In the beginning, the valve is closed. Whenthe combustion gas enters chamber 1, the gaspressure pushes the piston to move towardchamber 2. When the piston moves outside ofchamber 1, the gas begins to enter chamber 2.Then the difference of pressure of the two


chambers is noted, and the distance that the pis-ton moves is equal to the thickness of the piston.By the relation of the force of the spring and itsdisplacement we can get:

F=g*/6 (23)For the thickness of the piston is 9 mm, we

can calculate the critical pressure difference us-ing the following equation:

/?„., =6g/7E/1:, (24)Here dp is the diameter of the one-way valve.When Pl -p, <Pfr-,

mu=0

When />,-/>:>/>,,:

easy to solve. After transformation we get 12ordinary differential equations.dpa/dt = (ml,-mol-p<1Abr)/vg (35)

k-\

(25)Here the port area of the combustion gas is a

ring area:Aa=xdnl (26)

Here 1 is the width (shown in Figure 4), it canbe calculated by Hooke's law. The Q} in equa-tion (21) is the heat loss of chamber 1, it mustbe determined by experiment.

Av

iVVz\,VI

q

^

i

—

Fig.4 The schematic diagram of the one-way valve

(3)The control equation of chamber 2mn-m23 (27)

,v2cJ,)/dt=mncpT,-m21cpT2 -Q2 (28)P^P^RT, (29)

(4)The control equation of chamber 3jfia (30)

mdv/dt=(p3A,-mg-paA3) (32)dv,/dt=A,v (33)P,=P,BT> (34)Here the m is the piston mass, v is the lifting

speed, A^ is the cross area, pa is the environ-ment atmospheric pressure. Equation (32) is themotion equation of the lifting device.

Up to now we have established the flow con-trol equations in each chamber. These equationsmust be solved simultaneously. First we trans-forms these equations into the forms which are

f k -kRT0mm -p0

(36)dvJdt = Atr (37)deldt = r (38)dpi/dt=(mm-mt.,)/vl (39)dT, ldt=[(cf T0 -c, T, X, -RTtmK -Q, ] / ( c , p , v, )

(40)dpjdt=(mlt-m^)/v2 (41)dv}/dt = A3v (42)

l2-T2m,,)/v2-RQJcJv: (43)p,A,v)lv, (44)

(45)dv/dt=(piA:s-mg-PaA1)/m (46)

To solve simultaneously the set of equationsabove, together with the state equations and thealgebraic relations which determine the rightfunction of the set of equations, we can calcu-late the change of pressure, temperature, density,the piston speed and acceleration vs. the time.

The Result and Analysis

The performance preestimation when single gasgenerator working

In this section we will numerically simulatethe whole process that is from the ignition of gasgenerator to the piston's movement and its arri-val to the top, and compare the numerical resultswith the experimental data as far as possible.Figure 5 through Figure 7 show the result of cal-culation.

Figure 5 shows the curves of pressure vs. timein the gas generator and the chambers of the lift-ing device, at the same time it also shows the re-sults of the experimental data. As is shown inthe figure, after the ignition of the gas generator,since the burning rate of pyrotechnic charge andblack powder is quite high, the pressure in thegas generator reach the maximum value veryquickly, this pressure peak is mainly decided bythe energy release rate of the ignition powder;when the ignition powder is burned, the pressurein the gas generator drops to the equilibriumpressure which is corresponding to the burningof the main grain. From the figure we can findthat the predicted pressure is a little lower thanthat of the measured , and the predicted burningtime is a little longer than the measured value.This is because we assume that the grain bumsaccording to the geometric law of burning inpreestimation, but in fact, at the edge of the


grain ,its burning rate is quite high because theheat transfer is very quick, which enhances therate of the energy release. Thus the pressure inthe gas generator is greater than the predictedvalue. And this difference leads to the differencebetween prestimation and experimental value ofpressure in the lifting device and acceleration ofpiston.

12.0 •

8.0 -

Propellont ma39:3qPropellent slze:12.32/1.6-15.9Loading weight:61.2kg*:Expenmenlal data

100 200 300 400Time(ms)

500 600

Fig.5 The comparison of the predicted pressurewith the experimental data.

1.6

1.2 -

!o.8-

s.a.

0.0

P2• - - P3»• • • • Experimentol Ooto

Propellent m<m:3gProponent size:12.32/1.6-15.9Loading w«ight:61.2kg

0 100 200 300 400 500 600Time(ms)

Fig.6 The pressure curves in chamber 2 and chamber 3.

As is shown in Figure 5, the pressure in thethree chambers in the lifting device is almostidentical. It is easy to understand consideringthat the required pressure difference to open theone-way valve is only 0.0277 MPa. As is shownin Figure 6, before the motion of the piston, thefree volume in chamber 3 is quite little, the pres-sure in chamber 2 and chamber 3 is in balance;as the piston begins to move upward, the gasflow from chamber 2, through two 2mm-diameter holes , to chamber 3. As the pistonmoves faster and faster, the room in chamber 3that needs replenishing gas becomes bigger andbigger, the two 2mm-diameter holes begins tothrottle. The pressure in chamber 2 is higher

than that in chamber 3, the pressure differencebetween the two chambers is decided by the re-leasing rate of the combustion gas of the gasgenerator, the higher the rate is, the greater thepressure difference is. From the figure we canfind that the pressure difference of two cham-bers is little. Hence, the way of lowering the lift-ing acceleration of the piston by means of throt-tle port is not obvious. Figure 7 presented thecomparison of the predicted acceleration andthat of the experiment.

6.0

4.0 -

Propellent moB8:3qPropellent aize:12.32/1.6-15.9Loodinq weiqht:61.2kg•:Expenmenfol data

100 200 300 400 500 600Time(ms)

Fig.7 The comparison of the predicted accelerationwith the experimental data

The performance preestimation of two gas gen-erators which work simultaneously

The calculated results are shown in Figure 8-10. the maximum pressure in chamber 3 is 1.25MPa when one gas generator works alone, andthis value will be 2.08 MPa when two gas gen-erators work together. The latter is not equal tobut lower than twice of the former, because theheat loss when gas generator working together isgreater than that of one gas generator workingalone. The case of acceleration is shown in Fig-ure 9, the maximum acceleration of one gasgenerator working alone is 0.5g, and that of twogas generators' working together is 1.5g, that is,about three times of the former. The accelera-tion of piston is calculated from equation (46),here the mass of the piston and the atmosphericpressure is constant, in the right of the equationonly the pressure of the chamber 3 is variable, itis obvious that the acceleration is not increasedin proportion to the pressure of chamber 3. Inthe Figure 10 the comparison of speed is shown.

The effect of different grain shape to the per-formance

An important task of the grain design is itsshape design, the choice of different grain shapemay control the release rate of the combustiongas. Now we will calculate on the basis of cylin-


der grain, and compare the result with that oftubular grain. The cylinder grain shape is12.32/0-17.66, the grain mass is 3.4Ig. Themain difference of the tubular and cylinder grainis the burning time and the burning area: whenthe size of the grain is the same, the burningtime of the cylinder grain is about four timesthan that of tubular grain because it has no per-foration. What is more, the burning area of cyl-inder grain is smaller than that of the tubulargrain. As the rate of energy release of cylindergrain is slower and the burning time is longer,the total energy loss is greater, the increase ofthe pressure in chamber 3 is flatter, the maxi-mum pressure is far lower than that of the tubu-lar grain(as is shown in Figure 11), and the cor-responding acceleration has the similarlaw(shown in figure 12). As is shown in figure13: To adopt cylinder grain, although theamount of grain of that is greater than that of thetubular grain, the lifting height of piston is only150mm, that is, it hasn't reached the requiredheight.

The above analysis shows that the perform-ance of the gas generator , the internal pres-

sure of the lifting device and the lifting accelera-tion of the piston is controllable, and the way tocontrol it is mainly in the design of the gas gen-erator, in other words, the choice of the grainshape and the amount of the grain.

Conclusion

The integrate mathematics-physical model ofthe internal flow field in the gas generator andthe lifting device is built, and this model can beused to analyze the mechanism of the internalworking process and to instruct the design of thegrain, the result of the experiment proves thatthe theoretical model to be reasonable.The analysis shows that the pressure in the gasgenerator and the lifting device, and the liftingacceleration of the piston is controllable, themain way is the grain design of the gas genera-tor. The heat loss of the lifting device is themain factor affecting the accuracy of preestima-tion, the heat-loss model should be determinedby the experiment.

2.5

2.0 -

o0-

-.1.5 -

• 1.0 -

m-3.0gi m=.3.0g-H3.0g

0 . 0 - 1 1 1 1 1 1 i 1 1 1 i0 200 400 600

Time(ms)BOO 1000

Fig. 8 The pressure comparison of one gas generatorwith two gas generator.

-4.0100 200_ 300 400

I ime(ms)500 600

Fig.9 The acceleration comparison of one gasgenerator with two gas generator.


0 100 200 300 400 500 600Time(rns)

Fig. 10 The lifting velocity comparison of one gasgenerator with two gas generator.

12.34/1.6-15.9. 2.99g12.32/0-17.68, 3.41g

-2.00 200 400 600 800 1000 1200

Time(ms)Fig. 12 The acceleration comparison in gas generator of

tubular with cylinder grain.

12.0

8.0 -oD.

0. 4.0 -

0.0

——— 12.34/1.8-15.9, 2.99g— - 12.32/0-17.66. 3.41g

0.30 -i

"i " 1 1 1 I I 1 1 I I i [ i i i i i m i ) i mi i i i i H i i n i i 1 1 1 1 1 i n i0 ZOO 400 _ 600 800 1000 1200

Time(ms)

Fig. 11 The pressure comparison in gas generator oftubular with cylinder grain.

—— 12.34/1.8-15.9, 2.99g- - 12.32/0-17.66, 3.41g

0.000 200 4OO 600 BOO 1000 1200

Time(tris)

Fig. 13 The-lifting height comparison in gas generatorof tubular with cylinder grain.

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