Effect of Motor Length and Propellant Formulation on Nozzle Less Solid Rocket Performance

Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering http://pig.sagepub.com/

Effect of motor length and propellant formulation on nozzleless solid rocket performance

S Krishnan and Rajesh Ramakrishnan Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 1999 213: 35 DOI: 10.1243/0954410991532828 The online version of this article can be found found at: http://pig.sagepub.com/content/213/1/35

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Effect of motor length and propellant formulation on nozzleless solid rocket performance S KrishnanÃ and Rajesh Ramakrishnan Department of Aerospace Engineering, Indian Institute of Technology (Madras), Chennai, India

Abstract: Experimental results are presented for four nozzleless motors of different length±diameter ( L= D) ratios using two different composite propellants. The experimental observations discussed are: the premature unchoking in motors of insufficient L= D ratios and the tendency for the propellant to extinguish under highly negative pressure gradient environment, both peculiar to nozzleless operation. A simple onedimensional numerical scheme is presented to predict the performance of a nozzleless solid motor. Erosive burning, elastic grain deformation and L= D ratio-dependent combustion efficiency are considered in the scheme. A relatively simple procedure is followed to account for the coupling effect between port gas dynamics and elastic grain deformation. The experimental results are compared with those predicted by the numerical scheme. The predictions are in reasonable agreement with the experimental values. For a composite propellant the burning rate index n can significantly vary with respect to pressure. The application of this fact plays a very important role in accurately predicting the thrust-time trace of nozzleless motors. Keywords: solid rocket motor, nozzleless motor, performance, internal ballistics

NOTATION

a A A b b1 b2 B, C C F C 1 , C 2 d h D E F G I sp K 1 to K 4 L= D m _ m m p M n p

constant in the burning rate equation r  ap n area burning area grain inner radius grain outer radius constants thrust coefficient Lame's constants hydraulic diameter bore diameter modulus of elasticity thrust mass flux specific impulse constants length±diameter ratio molecular weight of combustion gases mass flowrate mass of propellant Mach number burning rate combustion index pressure

The MS was received on 1 April 1998 and was accepted after revision for publication on 26 January 1999. Ã Corresponding author: Department of Aerospace Engineering, Indian Institute of Technology (Madras), Chennai-600 036, India.

r r 0 r sp R t T ad T 0 ur

á, â ã ç í î b r p

total burning rate burning rate under zero cross-flow ratio of nozzleless-specific impulse to referencespecific impulse arbitrary grain radius time adiabatic flame temperature stagnation temperature deflection Lenoir ±Robillard constants ratio of specific heats combustion efficiency Poisson's ratio cÃ efficiency propellant density

Subscripts

avg b c head i max n nl ref t

average value burnout chamber head end arbitrary incremental location maximum nozzled nozzleless reference value throat

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1

S KRISHNAN AND R RAMAKRISHNAN

INTRODUCTION

Although the concept of nozzleless motors is not new, it has been actively researched for only the last three decades, with the aim of producing a simpler and therefore a more cost effective rocket motor [1]. This revival of active research is mainly due to certain definite additional advantages the nozzleless concept can provide for the boosters of integral rocket ramjets. There have also been claims that this concept can form one of the effective means to reduce significantly the cost of the boosters employed for extremely large satellite launch vehicles [ 2]. A nozzleless motor, as the name implies, does not have a conventional nozzle. The motor uses a case-bonded grain having a central cavity that terminates with an exit cone at the aft end, as shown in Fig. 1. This exit cone acts as a variable configuration nozzle. As compared with the conventional rocket motor, the specific advantages that accrue on adoption of this concept are: (a) simplicity of propellant grain geometry, (b) greater loading density, (c) weight reduction and reliability enhancement due to the absence of a conventional nozzle, (d) significant decrease in the developmental and post-developmental cost and (e) performance improvement by way of enhancement of incremental velocity of up to 15 per cent because of increased propellant mass for the same àll-up mass'. Perhaps as a price for these advantages, a minimum of 15 per cent loss in the theoretical specific impulse is inevitable. This loss is due to (a) the absence of a conventional nozzle, (b) the highly regressive pressure± time history and (c) the reduced residence time of combustion gases within the motor (because of high port flow

Fig. 1

velocity). Another operational disadvantage of a nozzleless motor is that the thrust vectoring is not possible. A nozzleless motor propellant requires improved ballistic and mechanical properties [ 1]. On the point of view of the former requirement, the propellant in comparison with a nozzled motor propellant should have a higher burning rate with a lower combustion index. In addition, generally the nozzleless motor requires longer lengths (higher L= D ratios) for optimum performance. Next, on the point of view of the latter requirement, the situation can be explained as follows. The port flow velocity, beginning with a very low subsonic value near the head end, becomes supersonic in the exit cone, and the flow generally chokes at the junction at which the exit cone starts. Consequently, there is a large pressure gradient between the head end and the aft end, subjecting the grain to severe shear loads. Hence at the low temperatures experienced during initial operation, the propellant should have a superior strain capacity to allow an optimum web fraction and a greater loading density to be achieved. Furthermore, the stress capacity should also be superior towards the end of burning when the grain encounters high temperatures. It is appropriate at this juncture to review briefly previous studies on the nozzleless motor concept. Procinsky and McHale [1] were the first to give a detailed account of an experimental study on nozzleless motor performance. They projected that the nozzleless motor is better than the conventional nozzled one for application to the integral rocket ramjet booster. In a later study, Procinsky and Yezzi [3] briefly explained the features of a nozzleless performance prediction programme, but they did not give any comparison between experimental and

Nozzleless motor assembly


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EFFECT OF MOTOR LENGTH AND PROPELLANT FORMULATION ON NOZZLELESS ROCKET PERFORMANCE

theoretical results. Glick [4] developed a general methodology for predicting the maximum performance of a solid rocket motor and applied it to a nozzleless motor with a fixed port area. Chase [ 5] presented an overview of the cost goals for ongoing and future launchers for satellites, and discussed the cost drivers of current solid rocket launchers. According to him, among the future technologies required to minimize booster cost, as opposed to maximizing performance, the nozzleless and pseudonozzleless concepts are important. The development of nozzleless technology requires a detailed knowledge of erosive burning. Towards this requirement, Traineau and Kuentzmann [6], using ultrasonic transducers, measured instantaneous web thickness of propellant grains. However, they did not discuss the erosive burning characteristics of the propellant under transonic and supersonic cross-flow Mach numbers. In a related study, Waesche and O'Brien [7] determined the resolution and accuracy requirements for non-intrusive burning rate measurement systems suited for nozzleless motors. X-ray, microwave and ultrasonic systems have potential applications in tests of nozzleless motors. Ultrasonic systems have the greatest measurement accuracy but in a narrow field-of-view. Microwave and ultrasonic systems, being compact, may be suitable for flight experiments. However, the excellent resolution in a wide field-of-view of X-ray systems is unsurpassed, Waesche and O'Brien concluded. Nahon [ 8], using a one-dimensional model that ignores grain deformation, compared the predicted values with experimental pressure±time and thrust±time traces; the predicted traces were not satisfactory. Gany and Aharon [9] obtained a simple analytical modelling of internal ballistics of nozzleless motors. Their analysis consisted of a quasi steady state one-dimensional flow of a perfect gas in a constant area port. Effects of erosive burning, grain deformation and axial port area variation were neglected. They obtained closed-form expressions involving two major operating parameters: (a) p= phead and (b) pavg = pmax , where p is pressure. The maximum theoretical achievable specific impulse for nozzleless motors was found to be approximately 86 per cent of the specific impulse value in an adapted nozzled motor at the same average chamber pressure. In this study, experimental results are presented for four nozzleless motors of different L= D ratios using two different composite propellants. HTPB propellants are selected because of their extensive use in present-day solid propellant motors. The study demonstrates two design principles: (a) the propellant burning rate influences the minimum grain length required for nozzleless operation and (b) the variation of burning rate index n with respect to pressure during a run affects the thrust± time pattern. The other experimental observations discussed are the premature unchoking in motors of insufficient L= D ratios and the tendency for the propellant to extinguish under a highly negative pressure gradient environment, both peculiar to nozzleless opera-

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tion. The successful modelling of the internal ballistics of nozzleless motors and the associated performance predictions are important. The phenomena to be considered in the modelling are erosive burning, propellant grain deformation, combustion efficiency variation, combustion instability, ignition transients, flame spreading, two-phase flow and nozzle flow separation [3]. However, considering only the erosive burning, grain deformation and combustion efficiency variation, the present study evolves a relatively simple one-dimensional incremental analysis. It then compares the predicted results with the experimental ones. The predicted results are in better agreement than those possible using the available onedimensional models.

2

EXPERIMENTAL PROCEDURE

Figure 1 gives the details of the four motors of different L= D ratios used in the study. The motor casings were of thick-walled steel tubes that could withstand pressures up to 200 bar. The grain was inhibited at both ends. Two unmetallized ammonium perchlorate (AP)/hydroxyl terminated polybutadiene (HTPB) propellants with relatively high burning rates were used. The high burning rates were achieved by using fine AP powder of mass mean diameter [(Ó ni d 4i )=(Ó ni d 3i )]  18 ì m and by adding a copper chromite catalyst (CC). The formulation I propellant had the mass composition of AP:HTPB:2-ethyl hexyl adipate (DOA):toluene di-isocyanate (TDI):CC  71.54:21.17: 3.97:1.32:2.00 and the formulation II propellant had the mass composition of AP:HTPB:DOA:TDI:CC  76.44:17.25: 3.23:1.08:2.00. The burning rate equations for the two formulations were determined using a ballistic evaluation motor [10]. The equations are, for formulation I: r 0  3:073 3 10À5 p0:412 m=s (1:1 3 106 < p < 1:9 3 106 Pa) and for formulation II: r 0  4:024 3 10À6 p0:570 (0:45 3 106 < p < 1:55 3 106 Pa); and r 0  1:781 3 10À4 p0:305 m=s (1:55 3 106 < p < 4:3 3 106 Pa). Formulation I was of a slower burning rate due to a richer fuel composition. (The reason for determining the burning rate equations for formulation II for a wider pressure range is discussed subsequently.) Formulation I had a modulus of elasticity of 0.85 MPa while the other one was 3.55 MPa. These were determined at a test speed of 1 mm=min [11]. With a frangible aft-end closure, the motor was ignited by a bag-type pyrotechnic igniter containing a mixture of potassium nitrate, zirconium and black powder. Data from the thrust transducer and two pressure transducers at the head-end were acquired at a sampling rate of 200 samples per second per channel, and recorded by a computer for subsequent analyses. All pressure and thrust transducers were periodically calibrated. The errors involved were Æ0:4 bar for the pressure transducer and Æ4:45 N for the thrust transducer.

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3


NUMERICAL SCHEME

In the present nozzleless motor study, the numerical scheme for the ballistics prediction assumes: (a) onedimensional quasi steady adiabatic flow, (b) perfect gas law, (c) calorically perfect combustion gases, (d) frictionless grain port flow, (e) erosive burning, (f) elastic grain deformation and (g) combustion efficiency, çnl  K 1 ( L= D)  K 2 . For erosive burning the widely accepted Lenoir±Robillard (LR) equation [ 12] is adopted. For an estimation of the parameters á and â of the propellant a semi-empirical procedure [ 13] is used. With the hydraulic diameter as the characteristic dimension, the LR equation is r  r 0 

á G 0:8 d 0h:2





âr p r exp À G

(1)

This equation predicts satisfactorily the motor performance with erosive burning under subsonic cross-flow conditions [14]. However, despite the absence of any correlation beyond this condition, it is assumed that the equation is valid also in the transonic and supersonic flow regimes. The grain deformation strongly influences the motor performance since the throat location is within the propellant grain port. An infinitely rigid motor casing and an elastically deformable propellant are assumed for the deformation. For simplicity, viscoelastic effects are not taken into account because the motors of the present study operate only for about 2 s or less. Lame's plane strain solution [15] for thick cylinders is used as a good engineering approximation. Lame's equation is ur  C 1 R 

C 2 R

(2)

where C 1  À

p(1 À í)(1 À 2í) E [1  (1 À 2í)b22 =b21 ]

(3)

and C 2  À C 1 b22

(4)

The whole port is divided into a number of incremental volumes, with the respective port radii Ri , Ri1 , etc., known at the incremental stations i, i  1, etc., as indicated in Fig. 1. The pressures at these stations are pi , pi1 , etc., or in short pi 's. The grain deformation modifies the amount of mass added into the incremental volumes. At the entry and exit stations of each incremental volume the grain is allowed to deform according to the local static pressures. The combustion efficiency is defined as the ratio of the effective stagnation temperature to the adiabatic flame temperature. In a nozzled motor, this is çn  T 0n = T ad . This efficiency in a nozzleless motor (çnl ) is less than çn

because of the reduced residence time for combustion gases and the highly regressive pressure±time history. To account for combustion efficiency in nozzleless motors an empirical equation is used by employing the concept of the cÃ efficiency (î b  ç0n:5 ) in nozzled motors which is approximately equal to 0.98. Hence the combustion efficiency for a nozzleless motor can be written as çnl  çn çl . Here çl is a term that accounts for the additional loss in combustion efficiency due to the nozzleless configuration. It is known that a longer nozzleless motor has a higher combustion efficiency because of the extended average residence time of the combustion gases within the motor. A higher chamber pressure can also give a higher combustion efficiency, but it is also a function of motor length. Thus, it is appropriate to assume çl to be a function of the L= D ratio only. However, no quantitative data in this regard is available in the literature. Therefore, in order to introduce this qualitative experimental observation into the numerical scheme çnl is arbitrarily fixed as 0.95 at L= D ratio  9:0 and as 0.93 at L= D ratio  3:5. Taking for simplicity çl to be a linear function of the L= D ratio, çl  B ( L= D)  C . With çn taken to be 0.982 , as discussed above, the values of B and C can now be evaluated.

3.1

Method of solution

The nozzleless motor grain has generally a tapered cylindrical port, enlarging towards the aft end. Hence the port flow can be considered as a flow with simultaneous area variation and mass addition [ 16]. The inputs for the present ballistics prediction code are the initial motor geometry, and the ballistic and mechanical propellant properties (r p ; T ad , m and ã; B, C and çn ; a and n; and E and í). The spatial and the temporal step sizes for the internal ballistics calculations are chosen such that the propellant mass balance is satisfied within Æ1:0 per cent; spatial and temporal step sizes of 1 mm and 5 ms were found to be adequate. For ease of understanding the method of solution, the adopted procedure is listed below in steps. The corresponding flowchart is given in Fig. 2: Step 1. For an arbitrary time t , the calculations start with a corresponding ùndeformed' port envelope and the (1) converged pi values along the port axis for the previous time (t À Ä t ). Step 2. For the port envelope, the iterative gas dynamic procedure is as follows. At time t , the head-end trial pressure phead is taken as the previously converged phead (however, at time t  0, phead is suitably estimated) [14]. The incremental integration of subsonic flow down the port up to the throat is performed by applying the mass, momentum and energy conservation equations [16]. If the Mach number at the throat is not equal to or greater than (1 À ä) (where ä is a small number), phead is reestimated and the iteration is continued until the specified convergence of 1 . M > (1 À ä) is obtained at the throatÐnumerically M  1 cannot be reached there


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Fig. 2

39

Flowchart of the numerical scheme

and ä is typically kept at 0.01. After this convergence is obtained, the gas dynamic properties for the supersonic region down the throat are calculated incrementally, thus completing the iterative gas dynamic procedure to give (2) p i values along the entire port axis. Step 3. Now the coupling effect between gas dynamics and elastic deformation has to be accounted for. This is achieved by the following simple procedure. The static (2) pressure distribution of the pi values is compared with (1) the previous static pressure distribution of the p i values (1) (2) to find the maximum of j p i À p i j, say DELPMAX. (2) (1) After this, the pi values are set equal to the p i values. If DELPMAX is not less than or equal to å (the error (1) limit), the port is allowed to deform for the new p i values, employing the grain deformation model. (2) Step 4. For this port envelope, the new p i values are calculated following the above iterative gas dynamic procedure (step 2) until the required convergence of DELPMAX (step 3) is obtained. Step 5. On attainment of this convergence, the motor thrust is calculated for the instant t . Next the port is allowed to `spring back' to the ùndeformed' port envelope. Under the quasi steady state assumption this ùndeformed' envelope is allowed to expand to Ri  Ri  Ä t r i (where Ä t is the time increment) to arrive at the new ùndeformed' port envelope for the time ( t  Ä t ). Now for the time (t  Ä t ) , the calculations start with a corresponding ùndeformed' port envelope and the

(1)

converged p i values along the port axis for the previous time t (see step 1). Step 6. The above gas dynamics and elastic deformation coupled solution procedures (steps 1 to 5) are repeated until a minimum chamber pressure for choking is reached. In flow problems where simultaneous area variation and mass addition take place, it is not mandatory for the flow to choke always at the junction from where the exit cone starts. Such a situation exists in nozzleless motors because the nozzle is formed in the grain port. Under these considerations, the logic for throat movement can be arrived at from the influence coefficient equation of Mach number given below [17, 18]:

 

d M ãÀ1 2 (1 À M 2 ) M  M 1  d x 2 3

À

1 d A A d x

 2

 (1  ã M )

_ 1 d m _ d x m



(5)

At M  1 the term in the brackets is equal to zero. Therefore,

_ d A A d m  (1  ã) _ d x m d x

(6)

The right-hand side of equation (6) is positive and hence

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the flow should choke somewhere in the nozzle expansion cone. The solution of equation (6) gives the throat location. In a nozzleless motor, higher pressure and elevated convective heat transfer prevail at the throat compared to the conditions at the port exit region. Therefore the nozzle expansion ratio decreases with time with a reduced possibility of overexpansion; this is in spite of the highly regressive pressure± time trace.

4

RESULTS AND DISCUSSION

Figures 3 and 4 show the pressure±time and the thrust± time traces obtained for the formulation I motors with L= D ratios of 7 and 9. The other motors with L= D ratios of 3.5 and 5 were not choked; for these, the propellant burned at a pressure of around 1 atmosphere, producing practically no thrust. Figures 5 and 6 show the test results obtained for the formulation II motors with L= D ratios of 5, 7 and 9Ðhere the motor with an L= D ratio of 5 was also choked. The oscillations found in all the thrust±time traces were only due to thrust-stand vibrations. Both head-end pressure transducers picked up the same downward pressure oscillations for the L= D ratio of 9 (Fig. 5), thereby confirming this effect. The thrust±time trace also reflects this, as shown in Fig. 6. Possibly, these downward oscillations point to the tendency of the propellant to extinguish. The most important parameter for the evaluation of any rocket motor performance is its specific impulse. A

Fig. 3

reference specific impulse is required for the comparison of the nozzleless motor specific impulse with that of the nozzled motor. From the experimental pressure±time trace of a nozzleless motor, the average operating pressure can be calculated as t b

pavg 



p d t

0

(7)

t b

For the same propellant, the frozen flow theoretical specific impulse under adapted conditions can be calculated for pavg using a standard program such as CEC71 [19]. This specific impulse is taken as the reference, I sp,ref . The experimental specific impulse for the nozzleless motor is defined as t b

I sp,nl 



F d t

0

(8)

m p

Then the specific impulse ratio for nozzleless operation becomes r sp 

I sp,nl

(9)

I sp,ref

Table 1 gives the calculated performance figures for all the tests.

Predicted and experimental pressure± time traces of nozzleless motors with propellant of formulation I


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Fig. 4

Fig. 5

41

Predicted and experimental thrust± time traces of nozzleless motor tests with propellant of formulation I

Predicted and experimental pressure±time traces of nozzleless motor tests propellant of formulation II

For the formulation I propellant, the motors with L= D ratios of 7.0 and 9.0 were choked and gave r sp values of 0.733 and 0.757 respectively. The motor with L= D ratio of 7.0 had a lower pavg and hence with the approximately equal web thickness it burned for a longer duration than that with the L= D ratio of 9.0. For the formulation II propellant, the motor with the L= D ratio of 5.0 was also

choked. However, it could give an r sp value of only 0.433. This was because the motor could not remain choked for the full web burning time. The motor became `prematurely' unchoked, producing thereafter practically no thrust. For the same reason this motor, in spite of having the lowest pavg and approximately equal web thickness, had the shortest thrusting time. The faster burning formulation II

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Fig. 6

Table 1

Predicted and experimental thrust±time traces of nozzleless motor tests with propellant of formulation II

Noting that C F is essentially a constant,

Results of nozzleless motor tests

L= D ratio

Mass (kg)

I sp,nl (N s=kg)

I sp,ref (N s=kg)

r sp

F-I

7.0 9.0

1.32 1.69

1108 1245

1512 1645

0.733 0.757

F-II

5.0 7.0 9.0

0.97 1.37 1.76

733 1481 1500

1692 1829 1913

0.433 0.810 0.784

Propellant

F % K 4 D(1À2 n)=(1À n)

F-I  formulation I, F-II  formulation II.

propellant could deliver a higher specific impulse for L= D ratios of 7 and 9.

4.1

Validation

Figures 3 and 4 also show the comparisons of the predicted and experimental values. The predicted pressure± time trace is close to the experimental one, but the predicted thrust±time trace does not follow the experimental trend well. This is due to the variation of the combustion index n with pressure. The adopted burning rate equation did not take this into account for n was kept constant for the entire pressure range. The following simple argument can demonstrate this. The nozzle throat area At is proportional to D 2, and for a fixed grain length the burning area A b is proportional to D. Therefore, under the èquilibrium pressure' assumption [14],



1 pc % K 3 D

1=(1À n)

(10)

(11)

This explains the influence of the combustion index n on the shape of the thrust±time trace: for n , 0:5 the thrust is progressive and for n . 0:5 it is regressive. Many studies have reported that the combustion index n of a composite propellant is low at high pressures but high at low pressures. This is due to the equilibria attained between the competing kinetics-limited premixed flame(s) and mixinglimited diffusion flame(s) [20]. Therefore a propellant can give progressivity at high pressures but regressivity at low pressures if its n value changes significantly with pressure. This explains why the experimental thrust±time traces in Figs 4 and 6 are progressive at high pressures but regressive at low pressures. Procinsky and McHale [ 1], and Nahon [8] also reported similar experimental thrust± time traces. Therefore the burning rate equation for the formulation II propellant was determined over a wider range of pressures. By doing so, two different burning rate equations were found for the divided pressure range, as listed previously. Figures 5 and 6 show the experimental and predicted pressure±time and thrust±time tracesÐthe prediction for the L= D ratio 5.0 was not done as its r sp performance was extremely poor due to the `premature' unchoking explained previously. Compared to the predictions for the formulation I motors, those for the formulation II motors are better in predicting the thrust±time trend. This improvement is due to the use of two different burning rate equations for the divided pressure range. The present study did not include experimental erosive


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burning rate characterization of the propellants used, and consequently the constants for the LR equation were calculated using a semi-empirical procedure [13]. If these constants were obtained experimentally for the subsonic to supersonic Mach number range, the predicted results could be improved. Also, a more precise determination of n with respect to pressure would further improve the predictions. A typical variation of erosion ratio ( r = r 0 ) calculated for L= D  7 and the formulation II propellant are shown in Fig. 7. Although there are no experimental results from the present study to validate this prediction, the trend of the variation is as expected. The effect of erosive burning sets in only after a certain axial distance within the grain. The erosive burning ratio decreases with time. At least for subsonic cross-flow conditions, this trend has been experimentally shown by King [ 21, 22]. The peak erosion ratio is predicted to occur in the exit cone of the motor at M . 1. The experimental erosive burning results for cross-flow Mach numbers around one and above are not available in the open literature.

5

43

dure for nozzleless motors is presented. This takes into account the effects of erosive burning, grain deflection and combustion efficiency variation. The predicted results are in reasonable agreement with the experimental values and the agreement is seen to be better than the ones available in the open literature. For a given composite propellant the burning rate combustion index n can significantly vary with pressure; this has been reported by many studies. The application of this fact plays a very important role in accurately predicting the nozzleless motor performance. In the present numerical scheme the erosive burning characteristics under transonic and supersonic cross-flow Mach numbers are assumed to follow the Lenoir±Robillard equation. While this equation is known to truly represent the erosive burning characteristics up to high-subsonic cross-flow Mach numbers, its applicability under transonic and supersonic cross-flow Mach numbers is not known. The availability of experimental data on erosive burning under transonic and supersonic cross-flow Mach numbers will improve the performance prediction of nozzleless motors.

CONCLUSIONS

It is a known fact that a nozzleless motor using a faster burning propellant can attain its peak performance with a shorter length. The present experimental study demonstrates this in a simple way. The tendency for the propellant to extinguish under a highly negative pressure gradient environment and the premature unchoking due to insufficient L= D ratios, both peculiar to nozzleless operation, are demonstrated. A relatively simple one-dimensional prediction proce-

Fig. 7

REFERENCES 1 Procinsky, I. M. and McHale, C. A. Nozzleless boosters for integral-rocket± ramjet missile systems. J. Spacecraft and Rockets, June 1981, 18, 193± 199. 2 Albert, L. Nozzleless booster hardware demonstration progress to date. In 24th Joint Propulsion Conference, Boston, July 1988, AIAA paper 88±3366. 3 Procinsky, I. M. and Yezzi, C. A. Nozzleless performance

Variation of erosion ratio along the port axis, axial distance from the head end

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4

5

6

7

8

9

10

11

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program. In 18th Joint Propulsion Conference, Cleveland, June 1982, AIAA paper 82±1198. Glick, R. L. On the performance of nozzleless rocket motors. In 19th Joint Propulsion Conference, Seattle, June 1983, AIAA paper 83±1318. Chase, C. A. Solid booster propulsion for the late 1990s. In 22nd Joint Propulsion Conference, San Jose, June 1986, AIAA paper 86±1637. Traineau, J.-C. and Kuentzmann, P. Some measurements of solid propellant burning rates in nozzleless motors. In 20th Joint Propulsion Conference, June 1984, Cincinnati, AIAA paper 84±1469. Waesche, R. H. W. and O'Brien, W. F. Evaluation of techniques for direct measurement of burning rates in nozzleless motors. In 24th JANNAF Combustion Meeting, California, 1987, Vol. 1, pp. 281± 292. Nahon, S. Nozzleless solid propellant rocket motors experimental and theoretical investigations. In 20th Joint Propulsion Conference, Cincinnati, June 1984, AIAA paper 84 ±1312. Gany, A. and Aharon, I. Internal ballistics considerations of nozzleless rocket motors. In 31st Joint Propulsion Conference, San Diego, July 1995, AIAA paper 95± 2735. Anon. NASA space vehicle design criteria, solid rocket motor performance analysis and prediction. NASA-SP-6039, May 1971. Kelly, F. N. Solid propellant mechanical properties, testing, failure criteria, and aging. In Propellants Manufacture, Hazards, and Testing (Eds C. Boyars and K. Klager), Advances in Chemistry Series 88, 1969, pp. 188±243 (American Chemical Society). Lenoir, J. M. and Robillard, G. A mathematical method to predict the effects of erosive burning in solid propellant rockets. In Sixth International Symposium on Combustion, 1957, pp. 663± 667 (The Combustion Institute, Pittsburg, Pennsylvania).

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G02398 # IMechE 1999


Effect of Motor Length and Propellant Formulation on Nozzle Less Solid Rocket Performance

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