*Nt4 - apps.dtic.milBaan Pressur, at Several Discrete Values of Projectile Travel 7k"() 0.227 0.57 0.989 1.751 2.513 3.275 4.0371 ... Max Pressure 172 MPa 345 MPs 517 MPa The propellant

*Nt4

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Studies Supporting Development of a Modified Gradient Equation for Lumped-Parameter Interior Ballistic Codes¶1. PERSONAL AUTHOR(S)F. W. Robbins and G.: E. Keller

TYPE OF. REP8 13b TI&O 14. DATE OF REPORT (YearA.MonthDa) I11. PAGE COUNTmemoand I Report IFROM t 1WO~ TO Ot_198611SUP.MENTARY NOTATION

COSATI 00S 18. SUBJECT TERMS (Continue on reverse if necessary and identifyj by lo-ck number)F~l D IGROUP I SU$-GROUP

01 Gradient, Gradient Equation, Interior Ballistics, Lumped-Parameter

19% TACT (Continue~o wvepse If necessary and identifyj by block number)Pest firings of11111mm rounds we re performed to characterize effea~s due to the combustible cartridge ca-ses

used. Compa ns were made between measured ballistic parameters, especially gas pressure.s, and thosepredicted by isnulation calculations performed with interior ballistic codes. It was found that the 'iwo-phase flowgun code XOVAKTC (XKTC) modeled the gun firings very accurately. On the other hand, the results ofcalculations with IBHVG2, a lumped-parameter interior ballistic 'code, differed significantly from both themeasurements and the XKTC calculations. The difference is much larger for -,stems with large charge-mass-to-

* projectile-mass (C/M) ratios. Ballistic parameters which affect the pressure gradient, especially for large C/Mratios, are examined in detail. One parameter which is essential to good physical modeling is chambrage, thenarrowing of the case mouth of the cartridge; other potentially important parameters are identified. e_,

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TABLE OF CONTENTS

Page

I. INTRO D U C TIO N .................................................................................................. 1

II. INITLAL COMPARISONS BETWEEN EXPERIML'NT AND XKrC ....... 1

I. FIRST MODEL COMPARISONS ...................................................................... 2

IV. SECOND MODEL COMPARISONS ................................................................ 10

V. DISCUSSION AND CONCLUSIONS ............................................................... 14

REFEREN CES ........................................................................................................ 15

K A PPE N D IX A ....................................................................................................... . 16

A PPEN D IX B ........................................................................................................ . 17

D ISTRIBU TIO N .................................................................................................... . 19

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.Copy ) NTIS CRA&IOTIC TAB

UnannouncedJ"stification

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Dist Avdil aiidlor

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mei l i = m, ~~rm~~ -RUUN`LRUA £Lm.'- 'n im•LP~`i`••Lm -

LIST OF FIGURES

Figure Page

1 Comparisons Between Measurand XKTC-d.Cculated Ratios ofBreech Preimsr to Base Frssure .............................. . ............. 2

2 XKTC-Calculated Mean/Base Pressure Ratio Curves for a C/M of 1.0. ..... 6

3 XKTC-Calculated Breech/Mean Pressure Ratio Curves for a C/M of 1O. 7

4 XKTC-Calculated Mean/Base Pressure Ratio Curves for a C/M of 0.25. .. 8

5 XKTC-Calculated Breech/Mean Pressure Ratio Curves for a C/M of 0.25. 9

6 Baseline and Charabrage Configurations ............................................................. 1

7 Barrel Resistance Profile ..................................... 11

8 XKTC Baseline Calculated Breech/Base Pressure Ratio CurvesW ith A dded Com plexities ...................................................................................... 13

V

UST OF TABLES

1 zilRato of Breah Presmure to ProjectileBan Premre at Several Dicrete Values of Projwt-e Travel ........................ 2

2 Wapon Parameters for the First Series of CaIcuations .................................. 3

3 Other Parameters for the First Series of Calculations ................... 3

4 Pr"ela Therm oche is y .................................................................................. 3

5 Comparisons of Calculated Maximum Breech Pressures andMuczle Velocities for XKTC and IBHVG2 ....................................................... 4

6 Comparisons of Calculated Maximum Breech Pressures andMuzzJe Velocities for XKTC and IBHVG2 ........................................................ 12

vi

- na a a , as fl a ar -fl- f. .fn ~ ss n.!

I.IACKNOWLEDGMENTS

The authors wish to thank Dr. P. S. Gough for helpful discussions and technical insight, Mr.A W. Horst for his enthusistic technical support, Mr. R. D. Anderson for changes made toIBHVGZ and Mr. G. M. Mason for performing many computer runs.

vii

I - ARIAA MAMA S*MILEMANRIMuIam

1. INTODUCTION

In a recent study, 120-mm gun f-ings were performed to establish the ba iskiccontributions due to the combustible cases used'. Measured velocities and pressures we:ecompared with matching interior ballistic code simulations with the hope of quantifying thosecontributions. Previously, for firings for which the charge-ma3s-to-projectile-mam (C/M) ratiowas low, IBHVG2, a lumped-parameter interior ballistic code, has provided goodcomprmos 1'. Also in the past, the NOVA family of two-phae interior ballistic codes, ofwhich XNOVAKTC (XKTC) is the latest version, has been shown to be able to simulate firingswith very good sucems"' 3' 4. In this recent study, however, for which the C/M was about unity,there was a wide dislprity between the predictions of XKTC and those of IBHVG2 for the samenominal data base.

In the previous work', it was shown that XKTC could be made to mimic theexperimental 120-mm gun firings quite well. For IBHV02, however, that was not the situation.For one case, IBHVG2 gave a calculated maximum breech pressure that was 42 MPa higherthan that predicted by XKTC for the same nominal data base. It was found that a difference of14 MPa could be attributed to the fact that IBHVG2 does not model the projectile boattailintrusion, and that 3 MPa each could be attributed to the fact that IBHVG2 neither modelsflamespreading nor intergranular stres& The major difference in the predicted maximumpressures, however, was attributed to the simple physics used in the derivation of the pressuregradients allowed by IBHVG2. In XKTC, the axial pressure gradient is calculated from firstprinciples and analytic correlations; in IBHVG2, only analytical pressure gradient relations dueto Lagrange and due to Pidduck-Kent5 are available.

In this report, several ballistic parameters which might affect the pressure gradient,especially for large C/M ratios, are examined in some detail. The objective of this study was todetermine the physics that must be included in the analytic gradient equation, so that thepredictions of lumped-parameter codes can be improved.

II. INITIAL COMPARISONS BETWEEN EXPERIMENT AND XKIC

The 120-mm experimental gun firings are described in a previous paper1 . The gun tubewas instrumented with five pressure gages in the chamber: two at 95 mm, one at 286 mm(midchamber) and two at 489 mm from the rear face of the tub,. There were also sevendownbore gages, situated at 768 mm, 1048 mm, 1530 mm, 2292 mm, 3054 mm, 3816 mm, and4578 mm from the rear face of the tube. Assuming that the gages at 95 mm determine thebreech pressure accurately, that the base of the projectile before it moves is located at 541 mmfrom the rear face of the tube, and that the pressure measured as each downbore gage isuncovered is the projectile base pressure at that time, one can use the data contained inRefereace 1 to calculate the ratio of the breech pressure to the projectile base pressure forseveral discrete values of projectile travel. Table 1 presents the average pressure ratios for thethree gun firings which were performed with no cases and average pressure ratios for the threegun firings which were performed with inert cases.

'1~M 1.EzpehnmtulRatios of Breech Pressure to ProjectileBaan Pressur, at Several Discrete Values of Projectile Travel

7k"() 0.227 0.57 0.989 1.751 2.513 3.275 4.0371KNo cane 1.33 1.40 1.61 1.65 1.39 1:49 1.65

Inert cs 12 1.5 16 170 1.46 1.1 .6

The data points for the ratios of the breech to projectile base preeswr versus travel fromTable 1 are plotted against calculated curves of theme ratios from XIOTC in Figure 1. Both thecumeles gun firing series and the inet cae gun firig meines are shown. Breech and basepressure amves are added to assist in interpreting the ratio data. The XKTC calculations werepadrfmed using meawured values wherever possible and reasonable values for all other inputdata. Theme simulations gave accellent ajreement with measured pressure-time curves andpressure difference curves. The agreement between the measured values and the calculatedvalues for pressure ratios for ailbut the last two points is verygood. The reason for the lastpoints not fitting well is not known. In any case, this good agreement, at least for the majorportion of the ballistic event, should make XKTC a useful tool for studying the gradientphenomenology. With this understanding, in this report, XKTC calculations have been assumedto furnish the "correct" answers with which to compare lumped-parameter calculations.

CaselemsInert Case

We..5 00.0 4oo 0

U-0 - . -- 3000C noRXC

2AB - 0. "B 00.0

91 1

1000 00

.6T T .0 T 00 to0*.0 so 4.0 6.0 .0 10 20 no 40 5.0

Travel (motors) Trovok (motors.)

Figare 1. Comparisons Between Measured and XKTC-Calculated Ratios of Breech Pressure toBase Pressure

III. FIRST MODEL COMPARISONS

As we have shown that that XKTC could be used for accurate simulations of gun firings,we sought to perform calculations with XKTC specifically simplified so that IBHVG2calculations could be compared to them. To that end, the first series of calculations performedwith XKTC utilized data bases with (a) 7-perforated granular propellant evenly distributed alongthe length of the chamber, (b) the chamber diameter equal to the bore diameter, (c) zero barrelresistance, (d) a flat-based projectile, (e) nominal heat loss to the chamber walls, and (f) a

2

prqeilat Igi .ontnipea, ur equal t~o. thmbien tmpert~uuin tat the pixlai u' allignited at the start of caldltdons. A tqp XMTC data bam Wemd b this tudy b kiduded aAppendix A. The compnt in EBHVO2 data base ki icuded as Appendi B.

0-ins with two difterent chamber voiemm were 'mulatedi one wkh a dwmber Vokme""f 9BJ2.2 c.m and one with a chamber vme of 96322 an. Two diffeem Nt gu wversimulated in order to determine whether the dumew effects were a function d te plydcalsin o the weapon. *The other weapon parametur. tht were amoclated with-mob of them twogot arm an shown in Table 2. For each of the tWo weapons two different proctle qiotgoswere used to produce the two different C/M ratios for which calculations wera perormed,

Table .Z Weapon Parameters for the First Serim of Calcuatons

Caamber volume 98322 cm3 98&322 an3.

Travel. ' 4.572 m 1.88 mPr6tellant mass 9.8 kg 0.096 kgProjectile masses 9.8 kg and 39. ksg D.0OS kg and 0392 kSBore diameter 127.0 mm 28,65 mnm

The effects -of propellant burn rate and the maximum chamber presure were alsoexavined. Table 3 shows the parameters which were varied:

Table 3. Other Parameters for the First Series of Calculations

Burning Rate (p in MPa) 1.10519 pl. mm/s 0.40"51 pea mm/s

Max Pressure 172 MPa 345 MPs 517 MPa

The propellant thermochemistry for all calculations is shown in Table 4.

Table 4. Propellant Thermochemistry

Impetus 1136 J/g3Covolume 0.976 cm3/gGamma 1.23Flame temperature 3141 KMolecular Weight 23.0 g/g-moleDensity 1.66 g/cm3

3

l .' S. ab . bam I CdadOW Momum P prnh Prmir

mid Muh Votin ,for XO M and IIV 2

)am BHV02S.:.Lapwp Ormdti PkkJkck.KwA Gradient

C lit . C14 4 di rime MI 71M Msm m 7%m NduM ITw t&ki lim e T .1 TimeVol o.er"& vdoeki BIGm VdoIy on"% Vhdiy

.... ,. ft) (__ ) (81A_ (NO_ (MP.) (m) (r/a) (m) (Mh) (m) (r) 'm)

L 1.0 LQ- 173, 7.7 957 133 1,06 7..5 96 133 179 7.5 963 133

L 1.01.0 345 6.5 1352 10.4 346 6.31363 103 337 6.3 1356 10.3

L 1.0 1.0 511' 6. 1 1904 9.1 496 5.9 1W.O 9.1 481 59 1561 9.1L 1.025 174 8 549 2&3.7 179 155S7 233 179 1355 7 23.5

L 1.0 0.25 34S 11.2 779 1&.1 348 11.1 M 18.0 348 11.1 783 O8.0

L I. 0.25 518 10.4 887 159 518 103 891 1.5.8516 103 892 15.8S0.8 1.0 172 4.7 8O 11.2 184 4.7 892 11.2 181 4.6 894 112

. 0.8 1.0 347 3&8 12M 8.2 363 6 1260 8.2 357 3.6 161 8.2

L 0.8 1.0 517 3.4 1494 6.9 530 3.0 1487 6.9 52 3.1 1492 6.9L .8 025 177 8.3 511 19.8 179 83 515 19.7 179 8.3 513 19.7

L •, .0.8. 025 343 6,5 710 14"6 345 6.5 718 14.6 344 6.5 718 14.6

L 0.8 0.25 514 53. 8a 122 S18 S.6 856 12.2 516 5.6 856 12S 1.0 1.0 172 1.4 1130 3.5 185 1.4 1083 3.6 18! 1.. 1091 3.6

S 1.0 1.0 341 '1215.52 2.7 343 12 1511 2.7 334 12 1509 2.7

S 1.010 S516- 1.1 1M 2.3 512 1.0 1M6 2.3 496 1.0 1710 2.3S 1.0'025 172 2.6 642 6.3 179 25 630 63 179 2.5 630 6.3

S 1.0 0.25345 ' 2.1 895 4.7 347 2.1 881 4.7 347 2.1 880 4.7

S 1.0 0.25 518 1.9 967 4.1 513 1.9 975 4.1 513 1.9 975 4.1S 0.8 1.0 172 .90 1057 3.2 184 .91 1031 3.2 182 .90 1033 3.2

S0.8 1.0 341 .70 1461 2.3 358 .70 1443 2.4 353 .70 1466 2.4S 0.8 0.25 172 1.6 590 5.7 175 1.6 587 5.7 174 1.6 587 5.7

S 0.8 0.25 345 1.3 842 4.1 347 1.3 834 4.1 347 1.3 834 4.1

S 0.8 0.25 514 1.1 956 3.5 516 1.1 949 3.5 515 1.1 949 3.5

The comparison calculations performed with XKTC and with IBHVG2 (using theLagrange gradient model and the Pidduck-Kent gradient model) are summarized in Table 5 forthe variations described above. In the table, the "Ch Vol" is the chamber volume of theparticular weapon, and "BR" is the propellant burning rate, where "1.0" implies 1.10519 p1.0

mm/s and "0.8" denotes 0.408451 !).8 mm/s. The maximum breech pressure and muzzle -.'elocitywith their associated times are given in the table. For each horizontal line on this table, thepropellant web in the XKTC calculation was varied until the desired peak pressure was achieved;the propellant length was maintained between 2 and 3 times the outer propellant diameter.Then, with the same final propellant dimensions, the associated IBHVG2 Lagrange and the

4

IBHVO2 Pidduck-Kent calculations were performed.

Close inspection of this table reveals that IBHVG2 agrees with XKTC very closely whenC/M is 0.25, for both the Lagrange gradient and the Pidduck-Kent gradient, for both weaponsand for both propellant bunp rates. However, when C/M is 1., agreemcnt is not as good.

This rust comparson series of calculations with XKTC and IBHVO2 investigated theinfluence of C/M, chamber volume, propellant burning rate and maximum breech pressure onballistic performance. Figures 2 through 5 have been generated from XKTC calculations for theweapon with the hirge chamber volume. Figure 2 shows plots of the mean to projectile basepressures for C/M equal to 1.0, for increasing maximum breech pressures, and for differentburning rates. Figure 3 shows plots oi the breech to mean pressure ratios for C/M equal to 1.0,for incresing maximum breech pressures, and for different burning rates. Figure 4 shows plotsof the mean to projectllc base pressures for C/M equal to 0.25, for increasing maximum breechpressures, and for different burning rates. Figure 5 shows plots of the breech to mean pressureratios for C/M equal to 0.25, for increasing maximum breech pressures, and for differentburning rates. In each of these figures, the plots on the lett have increasingly higher maximtumbreech pressures and were performed with a burning rate of 1.10519 p1.0 mm/s, while the plotson the right have the same increasingly higher maximum breech pressures and w-'re performedwith a burning rate of 0.408451p°'s mm/s. The shape and magnitude of the plots for the smallerchamber volume were the same for the corresponding C/M, burning rates and pressures exceptthe time sxale and travel scale were about 1/3 that of the larger chamber volume calculations,so they have not been included in this report. As an aid in interpreting the ratios, the ba.e andbreech pressures are plotted on each graph.

5

Ell1 -0. -1 3.0C L :000S..BRE[ECH -0. - tac - 400.

lSA~l- • 300.0 •1.61.4 300.01.4. .-

, 1.0 100.00.200.0 1-01.0 , .0 .0 .0

.0 6.0 10.0 16.0 .0 6.0 10.0 15.0

Time (m-~ee) Time tmime)

--00.0

j .0

600

,-. EC 400.0 RECH 400.0

-". 1.. -Ao8

.[ 1~•-- O.8 , . O0.3000 " 00.0

1.0

DASE 40 .0 , .400. -.4

000 1.000. 00 0

...... r. ..

.0 6.0 30.0 16.0 0 6.0 100 1560Time (muse) Time (move)

Figure 2. XKTC-Ca0culate! Mean/Base Pressure Ratio Curves for a C/M of 1.0

IB

6F

El500.0 600.0

1.6 1.6

00.0 300.0

CL.o 200.0 . o1 :: 300.0 .100.0.0 .6 e --- .0

*.0 S.b 10.0 16.0 .0 .1%.0 10.0 16.0

Time (mccc) Tlffme (mono).........

It1.O I 500.0 m.0

BRVECH B REECH 0D.6ABE 400.0 7 . BABE 400-

L01. 201.4

1.0 :.100.0 1.0 -100.0

.-0 .6p .00 5.0 10.0 15.0 0 . 10.0 16.0

Time (mEcc) Time (mosai

9. 500.0 -.0509.0

BREECH --- - BREECH.-B. ASSE -400.0)- DAIIE 100.0 -

3000 00.1.4 lp 1.430.1.j2

.0100.0 10100.0

06 5.0.

Tina (a~e)Time (mesa)

Figure 3. XKTC-Calculated Breech/Mean Pressure Ratio Cuives for a C/M of 1.0

7

64000 6 6 --.. 0UC

-0400.0 .00.

900.0 900.0

40. 300.01

46 10. 4 100.0

.4 ..0 .0S0. 0 2..0 1,.0 .0 6.0 10.0 16.0

Tilmi (imune) Time (movei)

El*~1 00.0 0.0 6 00.0i -ll•-- 333 W- I . IUEC1.0 atc" t.: ~ i!

1 : :0.0 -. 9ac0:

goo. £000£01.4.

16 " 1 : - .0.• ~~0. ,"1-4 . o.--]

..0 .6 .0.0 &.0 10.0 111.0 .0 i.0 10.0 19.0

.Time ("%GOO) Time (mesa)

E J 1•10 0 T).0°. - D , 4 500.0

UA¶ 4(1)0. 4010C ' * 00.0

flg it. 300.0

,,.. ,, .4, ,

:Ioo.o .0oo.o

1 . ,

.0 8.0 £00 16.0 .0 8.0 10.0 18.0Time (mug.) Time (moen)

Figure 4. XKTC-Calculated Mean/Base Pressure Ratio Curves for a C/M of 0.25

8

.0 SOOO 2.0- 500.O

IL .8 1 .6

l-BREEC ,. _4 - - BRE CH

BASE 4000 7 BA3E 400.0

30(0 --" 3000

1.4 1 4SA . ._. 2000 o A . . '-•a 200 .

•". " 2 . 2 0oo

1.0.. 1000 10 - - 100.0

.a - -'' . . .0 8 , .0

0 6.0 100 10 0 0 ,.0 10.0 16.0Time (me)Tim. (miec)

50 20 0 F- 500.0

BREECH 400.0 13- REECH-40.18 IB.U •BASE BASE , .

St4 . ', .~ - 1.., t4". ,

5. .I. " '

o . oo o 12 . _2001.0 100000

1. 001.0 .j1000

. ' .0 .8 .0.0 6.0 10 150 0 5.0 100 16.0

Tim. (mac) Tim. (mmec)

4H 0 - BREECH 400.0

1w 180-)]00,. 2 2 ."BAS 2:.

.0 1 4 1 .

1 2 12 2. 0CIL. CL2

104-- ---- 1000 10.1000

- --- -------0 s 1 10 150 0 50 100 15 0

Tie (rmne--" ) Tim. (mnec)

Figure 5. XKTC-Calculated Breech/Mean Pressure Ratio Curves for a C/M of 0.25

The ratio plots in Figures 2 through 5 illustrate the complex nature of the relationshipbetween the breech, mean and base pressures. The general nature of the ratio curves is to beconstant near 1.0 for some length of time, followed by a first rise, a drop-off, a second rise andin some cases a second drop-off and another rise. The second drop-off seems to be caused by

9

the slivering phase of the propellant burning as it occurs just as XKTC indicates that slivering istaking place. Further, for low pressure callulations. for which the propellant does not sliverbefore projectile exit, the second drop-off does not occur. Calculations done with a singleperforation grain also did not show a second drop-off. The first rise and drop-off may be causedby the rarefaction wave caused by the projectile motion, the first peak corresponding to the timethat the rarefaction wave reaches the breech face and the first minimum corresponding to thetime the reflected wave reaches the base of the projectile. In all of these XKTC calculations,we observed that an ullage region opens up between the projectile base and the front end of thepropellant bed. In this ullage region, the pressure drop per unit of distance across this ullageregion is much smaller than across the propellant bed. Gough5 has speculated that theformation of an ullage region, as observed in the XKTC calculations, and the dircontinuity in gasvelocity at the propellant/ullage boundary may contribute to the undulatory shape of the meanto base press ,re ratio.

There remained the question, however, of what physical processes were responsible forthe greater than 10% maximum breech pressure differences observed between real-worldsimulations with XKTC and the equivalent IBHVG2 calculations, the differences that motivatedthis study.

IV. SECOND MODEL COMPARISONS

The second set of model comparisons included calculations at both high and low C/M,because C/M was inplicated in the lack of agreement between XKTC a id IBHVG2 in the firstcomparisons. The Lagrange gradient was used for all IBHVG2 calc ilations. Several otherparameters were also varied to determine their contribution to the problem. For thesecalculations, we modeled the weapon with the 9832.2 cm3 chamber volume, and we used aburning rate exponent of 1.0. We varied the barrel resistance for both XKTC and IBHVG2calculations, and for XKTC, introduced flamespreading and added chambrage (the necking downof the chamber to the bore diameter).

Since a constant .-hamber volume was desired, chamber length had to change whenchambrage was introduced. The chambrage was modeled as a truncated cone whose length was76.2 mm, which required the chamber length be reduced from 776.22 mm to 541.02 mm, withthe radius of the breech end of the chamber up to the beginning of the chambrage being 76.91mm. Baseline and chambrage configurptions are illustrated in Figure 6.

Flamespreading in XKTC is convectively driven, with the initial stimulus provided bysome level of modeling of igniter functioning. In these calculation, the igniter was described asventing over the rear 304.8 mm of propellant bed, causing the entire propellant bed to be ignitedwithin 2 ms. The resistance was modeled with a linearly interpolated table of travel versusresistive pressures. The resistance started at 0.690 MPa at 0-mm travel, remained constant for6.35 mm, rose to 6.90 MPa at 12.70 mm, fell to 0.690 MPa at 19.05 mm and remained constantuntil barrel exit, as illustrated in Figure 7.

10

1217.0mm

776.22 mm

76.2 mm

153.82 mm 12A . mm

T" it-

Figure 6. Baseline and Chambrage Configurations

S7-

4 /

0 5 I0 15 21 25 JO "5 JD 45Tr-nveI "rmm

Figure 7. Barrel Resistance Profile

11

The results of tHis .Acond series of calculations are given in Table 6. The propellantdimeMions selected for these calculations were those determined to achieve a peak pressure of345 MPa with XKTC, assuming zero barrel resistance, no chambrage and the propellant ignitedat time zero for the given C/M.

Table 6. Comparisons of Calculated Maximum Breech Pressuresand Muzzle Velocities for XKTC and IBHVG2

MaximumCode Variation* Breech Time Muzzle Time C/M

Pressure Velocity(MPa) (ms) (m/s) (nis)

XKTC B 345 6.5 1352 10.4 1.0IBHVG2 B 346 6.3 1363 10.3 1.0

XKTC R 363 6.5 1379 10.2 1.0IBHVG2 R 365 6.3 1387 10.2 1.0

XKTC F 332 6.0 1337 9.8 1.0XKTC C 310 6.5 1303 10.5 1.0XKTC FRC 321 6.0 1317 9.8 1.0XKTC B 345 11.2 779 18.1 0.25

IBHVG2 B 348 11.1 73 18.0 0.25XKTC R 363 11.2 792 17.9 0.25

IBHVG2 R 367 11.0 796 17.8 0.25XKTC F 347 9.3 779 16.2 0.25XKTC C 336 11.4 774 18.1 0.25XKTC FRC 351 9.7 784 16.5 0.25

B - Baseline * R = Resistance F = Flamespreading C = Chambrage

The first line of Table 6, the baseline calculation with XKTC, is the same as the XKTCcalculation on the second line of Table ). The second line of Table 6, the baseline IBHVG2calculation, is also the same as that shown on the second line of Table 5. The next two linesresult from adding bore resistance, and show the expected rise in peak pressure for both XKTCand IBHVG2. The following line results from adding just flamespreading to the XKTC baselinecalculation and documents a drop in peak pressure. The next line represents adding justchambrage to the baseline XKTC calculation -- note the huge drop in peak pressure of 35 MPa!The final calculation in the C/M = 1.0 series has flamespreading, bore resistance, andchambrage added to the baseline data base. Again, the large decrease in peak pressure isattributed primarily to the chambr-ge.

For C/M of 0.25, it is seen that bore resistance makes a significant change, but aboutthe same for both XKTC and IBHVG2. The influence of flamespreading and chambrage areabout 2/5 as great as those for the higher C/M.

12

Plots of ratios of breech pressure to base pressure from the XKTC calculations for thissecond series of comparison calculations are found in Figure 8. Plot 25 results from having

added flameapread alone to the baas,-ine. Plot 26 has resistance added to the baseline. Neither

Plot 25 nor Plot 26 shows much difference from the baseline plot. Plot 28 had addedchambrage to the baseline; Plot 29 had added chambrage, flarnespreading, ana resistance. P~oth

Plots 28 and 29 show a much lower pressure ratio at early time. Plots 27 and 30 are "full"

XKTC simulations (which now include projectile intrusion into the chamber) of the inert case

(Plot 27) and the caseless gun firings (Plot 28). The fact that the gradient curves in Figure 8

have assumed the general shape of the measu'ed curves leads us to believe that the majorinterior ballistic parameters have now been included.

800.0 -000

111.0 --- 9REEHK- RECH 400.0 2- ---:NCBASE 400.0 * A 400.0

- 3000 .h --000

0. 1.O "',-.. 0.o1. .. - 300.0. .100 00.0

1. 0. 0.

.•. 0 1--. .0 .15 .0

".0 1.0 4.0 3.0 4.10 .0 .0 1.0 .0 3. 0 ý-O 4 10

"Travel (meter.) Travel (meters)

- 6000 8000

BERECH It* - BREEC3ASE 400.0 - 400.0

30400 300

8000o 000

IL ..0 1 _ L0 0 0 o

.0 5 .0

.0 1.0 12.0 3.O 4.0 ft.0 1 0 a 0 :3 0 4 0 6.0

"Travel (motoer) Travel (meters)

2?500.0 B2., 0

B .00-3. BASE

3000 7°- 300.0

3000 2000

A 1.0 eL 1 0CL.1oo ..... . 2 1000

. .o ..... ;'- ..-- ,o -.02 0 0o_ . 0 0• 6 "• •• ~ ~.0.5 , - ,O

Figure 8. XKTC-Calculated Breech/Base Pressure Ratio Curves With A\dded Complexities.

13

V. DISCUSSION AND CONCLUSIONS

Earlier studies using the XKTC code' demonstrated that propellant packaging andboattail intrusion can have significant impact on maximum chamber pressures. The currentinvestigation reveals that flamespreading and, to an even greater extent, chambrage, can affectcalculated pressures as well, jarticularly at large C/M ratios.

In this study, we have seen that the presence of chambrage makes a significantdifference in the pr~asure gradient. The larger cross section of the chamber results in a closeraxial proximity of combustion product gases to the projectile base, with less axial motion andshorter transit times required to transfer pressures downbore. The result is a significantreduction in the pressuie gradient, as shown in plots 28 and 29 of Figure 8.

The role of flamespreading. as well, has been demonstrated in this study. The phasedignition of propellant surfaces, rather than the simultaneous ignition event assumed in mostlumped-parameter codes, can influence the overall rate of gas production, as well. as theformation of pressure waves, resulting in differences in the inbore trajectory and impactingmaximum chamber pressure. Wave dynamics associated with the rarefaction accompanyingprojectile motion may add further structure to the pressure gradient.

But a more interesting feature of the structure of the pressure gradient is shown in thisstudy to accompany the formation of a region of axial ullage between the propellant charge andthe projectile as it first moves downbore. XKTC calculations suggest that a lower gas pressuregradient exists in this ý.gle-phase region than in the two-phase region of the propellant charge,primarily because of a lower resistance to the transfer of pressure information. This resultsuggests that lumped-parameter codes might benefit from a two-region pressure gradient inorder to capture the true structure of the pressure field. Such a feature might prove to beparticularly important for simulation of stick charges, for which a well defined boundary betweenthe two regions persists throughout the interior ballistic cycle, or for highly nonuniform initialdistributions of propellant, as when firing low-zone artillery changes.

All of the above effects are exacerbated by an increase in C/M, since the projectilethen moves out more rapidly, and axial dim(: -ions and accompanying transit times are increasedat a time when significant amounts of gas are still being locally produced in the gun chamber.

We conclude from this study that lumped-parameter interior ballistic codes couldbenefit greatly from the inclusion of a new or modified gradient equation including functionaldependence on C/M, chambrage, propellant distribution and ullage; the influences offlamespreading and wave dynamics may also be included, though the basis for such terms wouldnecessarily be more heuristic.

14

REFERENCES

1. F. W. Robbins. J. A. Kudzal, J. A. McWilliams and P. S. Gough, ExperimentalDetermination of Stick Charge Flow Resistance, 17th JANNAF Combustion Meeting, CPIA.Publication 329, Vol. II, pp, 97-118, November 1980.

2. F. W. Robbins and A. W. Horst, "Detailed Characterization of the Interior Ballistics ofSlotted Stick Propellant', BRITR-2591, USA Ballistic Research Laboratory, Aberdeen ProvingGround, MD, Septembcr 1984. AD A147 499.

3. F. W. Robbins, A. A. Kozoru and T. C. Minor, "A Theoretf al and ExperimentalInterior Ballistic Characterization of Combustible Cases", 9th International Symposium onBallistics, Part 1, pp. 21-28, April 1986.

4. F. W. Robbins, "Comparison of TDNOVA Results with an Analytic Solution", ARBRI,MR-03299, USA ARRADCOM, Ballistic Research Laboratory, Aberdeen Provhig Ground, MD,July 1983. AD A132 969.

5. R. D. Anderson md K D. Fickie, "IBHVG2 -- A User's Guide," Technical Report BRL-TR-2829, US Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, July 1987.AD B117 104.

6. P. S. Gouph, personal communication, September 1986.

15

6-4

00n

0o con 00 0 *

N N N

0I

.00

*n .-4 Lno0 N 0CN

0 o0 i0 o .0 0 C0 0) 0 04

0

U) 00

0 0

0 0 4-

In 4-4 LL0 0N coL o -i * ý 0000 r 0 N *O g-

0 6 c -40( -4 .00 v 0 4

In0 0 -

40 00I 0 0'

o r4 Or-HNcN In n eq

ri 0 0 N0l 0 ý IO0%E-O 0- o6 - n ,

M 4 V- 0 In 0r

w 00 V * 0 - -0e N0N 00

E-4 r* E-4N~ 04

H- 0H -4-

00 0 00 o NC ; D t0 1 0 0 0 4 mo t

(A 0 oo I N 0~0 c 0 .4 t-0

E-4 r-4 L o *NrI 40 4 r

C., 00 16

APPENDIX B

IBHVG2 Data Base

$HEATTSHL - 0.00450 CSHL - 1848 RSHL - 0.284TWAL - 293 HO - 0.0648 HL = 1

$GUNNAME - '600 IN- TEST' CHAM - 600 TRAV - 180GRVE - 5.0 LAND - 5.0 G/L - 1. TWST - 99

* $PROJ NAME - 'FLAT' PRWT = 21.6$PDIS

SHOW-'PMAX' DECK-'OUT'$PDIS

SHOW.'CHWT' DECK-'PROP' NTH-2$PDIS

SHOW-'DIAM' DECK-'PROP' NTH-2$PDIS

SHOW-'PD' DECK-'PROP' NTH-2$PDIS

SHOW-'WEB' DECK'PROP' NTH-2$PDIS

SHOW-'VMUZ' DECK-'OUT'$PDIS SHOW-'ZMUZ(2)' DECK-'OUT'SPDIS

SHOW-'LDEN' DECK-'OUT'$RESI

NPTS - 5 AIR - 0TRAV = 0, .25, .5, .75, 180PRES = 0, 0, 0, 0, 0

$INFORUN - '16C05 ' DELT - 5E-5 DELP - 5E-5GRAD = 1 POPT = 1,1,1,0,2 SOPT - 0EPS - 0.002 CONP - 0

$RECONAME = 'NONE' RECO - 0 RCWT - 0

SPRIMNAME - 'AIR' CHWT = .01039 TEMP = 294GAMA = 1.4 FORC = 28284 COV = 27

$PROPNAME - 'JA2 7P' CHWT - 21.6 GRAN = '7PF'RHO = 0.06 GAMA - 1.23 FORC = 380000COV = 27. TEMP = 3141 EROS = 0.0NTBL=-2 EX4L=1.,1.PR4L-8000,100000 CF4L=.0003,.0003LEN = 1.25 DIAM = 0.50PD = 0.020 WEB=.11

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