Grain velocities during ignition of gun propellant

Grain velocities during ignition of gun propellant

COMBUSTION A N D F L A M E 24, 199-202 ( 1975) 199 Grain Velocities During Ignition of Gun Propellant .WILLIAM G. SOPER U. S. Naval Surface Weapons ...

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COMBUSTION A N D F L A M E 24, 199-202 ( 1975)

199

Grain Velocities During Ignition of Gun Propellant .WILLIAM G. SOPER U. S. Naval Surface Weapons Center, Dahlgren Laboratory, Dahlgren, Virginia 22448

By means of a dual-flash X-ray technique, propellant grain velocities during ignition have been determined for the Navy 5-in./38 gun. At the completion of ignition, the velocity profile along the grain bed is sharply peaked with maximun velocity at the propellant free surface.

Introduction Two previous papers [1,2] have presented data on gas pressure distribution, flame front motion, and grain free-surface motion during propellant ignition in the U.S. Navy 5-in/38 gun. It is anticipated that these data will be useful in checking the validity of interior ballistics models of grain ignition. To augment this body of information, a further series of experiments has been conducted to determine the distribution of grain velocity along the propellant bed during ignition. This paper describes the experimental technique and presents the results. In addition, a simple model is described which relates the velocity data to the pressure data reported previously.

Experiments Grain velocity was deduced from tests in which steel cubes initially positioned within the propellant bed were radiographed during grain ignition by dual-flash X-ray equipment. The cubes were positioned during loading at 2 in. intervals along a line parallel to the cartridge case centerline and about 0.5 in. from the case wall. The last cube was placed at the free surface of the propellant. Each cube had a side length of 3/16 in. and contained a cavity in one face to reduce weight. The mass of each cube, 0.0031 lb, was approximately three times the mass of a propellant grain, while the average presented areas of cubes and grains were nearly the same.

In the test setup, the cartridge case was positioned between two X-ray sources and a single film pack. The sources were separated horizontally and shielded in such a manner that the areas of film exposed by each of the sources did not overlap. Also, the case was oriented to set the radial plane containing the cubes approximately normal to the radiation, thus minimizing the shielding of cubes by propellant. The first source was triggered by a pressuresensitive switch or carbon break-rod as described previously [1 ]. Then, after a preset time delay, the second source was triggered. Cube velocity was obtained from change in position during the time interval. Prior to the firing test, a "still shot" was made with each source to establish the initial positions of all cubes. The 0.5 in. spacing of the cubes from the case wall, together with orientation of the case to minimize shielding by propellant, provided sufficient contrast on the film between the cubes and the surrounding propellant. The propellant in all experiments was U.S. Navy SPCF, or NACO. Charge dimensions and a description of the special fiberglass cartridge cases are given in the earlier paper [1 ]. Table 1 lists for the four experiments the time intervals between the triggering of the X-ray sources and the impact of the cartridge case closure plug upon the projectile. As reported previously, the impact of the cork plug produces an intense pressure spike which serves as a convenient time reference. Copyright © 1975 by The Combustion Institute Published by American Elsevier Publishing Company, Inc.

200

WILLIAM G. SOPER TABLE 1 Time Intervals from Experiments a

Test no.

1st flash

2nd flash

Mean

1 2 3 4

980 830 300 0

680 580 150 -50

830 705 225 -25

aTime is expressed in gsec prior to plug impact on the projectile. Maximum error is estimated to be -+5//see. Results The velocity data are plotted in Fig. 1 against initial cube position. Each set of data is labeled with the arithmetic mean of the two time intervals used in computing the velocity. In addition, the first radiograph of test 1 revealed that the three cubes closest to the propellant free surface were undisturbed. The resulting zero-velocity data for 980 gsec prior to impact are included in the figure. 8 -

225 I -25

225

g ~'5

% ~4 ...I Lit

3

705

830 O 0

,I I I t ~ 5 10 15 20 INITIAL DISTANCE FROM BREECH, inches

t 960 25

Fig. 1. Cube velocities during ignition at various times (/asec) prior to plug impact on projectile. Bar symbols indicate position of gas pressure wave ramp at noted times (~.sec).

Also indicated in Fig. 1 are the regions occupied by the ramp portion of the gas pressure wave [1 ] at 830,705, and 225 #sec. These were determined by plotting the cube velocities against actual position and comparing with pressure data from the earlier work. At 225 #sec before impact, the ramp region has started to cross the free surface of the propellant. The fluctuations in the data for 25 #sec after impact are believed to be due to error:; in measuring the small displacements of the lower-velocity cubes during the 50 #sec interval between radiographs. In each of the four experiments, the steel cube placed at the propellant free surface remained with the free surface during propellant acceleration. No tendency o f the cube to sink into the propellant was noted. Correlation of Pressure and Velocity Data The propellant velocities obtained from the experiments have been found to be consistent with a very simple model for propellant acceleration during ignition. Modeling of flame spreading and grain motion is still in its infancy and models under development [3, 4, 5, 6] are rather complex. A simple correlative model will now be described with the expectation that it may provide some insight into the phenomena and assist in the formulation of more complete and rigorous models. The earlier paper on NACO propellant [1 ] showed that the gas pressure wave which sweeps along the grain bed during ignition has an intensity that is nearly uniform in space but increases approximately linearly with time. We take the rate of increase to be 2000 lbf/in 2 msec and approximate the actual wave with one which originates at the breech and moves with constant velocity to the free surface of the propellant in 2.15 msec. At the front of the wave, we assume that the gas pressure is converted into an average pressure (total force/total area) in the grain bed, and that this pressure drives elastic waves into the unignited propellant. As the gas pressure wave moves through the propellant, the elastic waves travel back and forth between the gas pressure wave front and the free surface, steadily raising the velocity of the remaining unignited grains.

PROPELLANT GRAIN VELOCITIES Once the wave front has crossed a particle, however, the velocity of the particle remains constant. The calculation is carried out by the method of characteristics [7] in which pressure p, particle velocity u, bulk density Po' and wave speed c are related by dp = -Po c du along dx = cdt and dp = FoC du along dx = -cdt. Here x is a particle-fixed coordinate and t denotes time. The elastic wave speed is taken to be 1450 ft sec "~ , a constant for compressive strain not exceeding 35% [1]. The solution is obtained in the triangular region of the x, t plane bounded by the locus of the gas pressure wave front, the free surface of the propellant, and the line corresponding to initial time (when the wave leaves the breech). Along the front, pressure is a known function of time, while along the free surface, pressure is zero. Both pressure and particle velocity are zero initially. Values for p and u within the triangular region are developed from the values at the boundaries by repeated application of the basic relations along the left- and rightrunning characteristic lines. Figure 2 presents velocity distributions calculated from this model. Time prior to impact is computed from the fact that impact on the projectile occurs 228 msec after pressure begins to rise at the breech [1 ]. The position of the pressure wave front for each distribution corresponds to the point of maximum velocity.

Discussion Although the experimental data in Fig. 1 do not present a complete picture of the timewise development of velocity along the grain bed, they do indicate its general features. For early times, peak velocity occurs deep in the bed while the free surface is undisturbed. As time increases, the peak moves toward the free surface, closely associated in position with the pressure wave front. "The velocity profile along the bed when ignition is complete has a sharply peaked form with velocity a maximum at the free surface, but diminishing rapidly with distance into the bed. Comparison of Fig. 1 and 2 reveals a definite similarity between the predictions of the simple model and experiment. The success of the model

201

8 225 7

6

o" ,~ 5

_~ 4 340

r, 3

2 7O5

!

83O

0 0

m980 25 5 10 15 20 INITIAL OISTANCEFROM BREECH,inchos

Fig. 2. Propellant velocities at various times (//sec) prior to impact, as predicted by model. suggests that the propellant bed during ignition can be idealized as two regions: one behind the ignition front in which gas pressure is predominant, and one ahead of the ignition front in which only intergranular forces exist. It is believed that the two are separated by a relatively thin zone, marked by the ramp of the pressure wave, where both gas pressure and intergranular forces are important, and where the complex processes leading to ignition are taking place. A final point concerns the propellant free surface velocity at the time of plug impact on the projectile. From this series of experiments, the value is approximately 750 ft sec "1 , while in earlier work [1] it was reported to be 1300 ft sec "~ . A careful review of both sets of data has revealed no error in regard to charge make-up or data reduction. However, the nature of the velocity distribution suggests that the free sur-

202 face value may vary appreciably from charge to charge. References 1. Soper, W. G., Combust. Flame 20, 157 (1973). 2. Soper, W. G., Combust. Flame 22, 273 (1974). 3. Kuo, K. K., Vichnevetsky, R., and Summerfield, M., A I A A J. 11 (No. 4), 49 (1973). 4. Krier, H., Van Tassell, W. F., Rajah, S., and Ver Shaw, J. T., Model of Flame Spreading and Combustion through Packed Beds of Propellant Grains, Tech., Rept. AAE 74-1, Univ. of Illinois, Urbana Champaign, Illinois, 1974.

WILLIAM G. SOPER 5. Fisher, E. B., and Trippe, A. P., Mathematical Model of Center Cone Ignition in the 175mm Gun, Rept. No. VQ-5163-D-2, Calspan Corporation, Buffalo, N.Y., 1974. 6. Gough, P. S., and Zwarts, F. J., Theoretical Model for Ignition of Gun Propellant, Report SRC-R-67, Space Research Corporation, North Troy, Vermont, 1972. 7. Courant, R., and Friedrichs, K. O., Supersonic Flow and Shock Waves, Interscience, New York, 1948.

Received August 2, 1974; revised November 6, 1974