richard a. reinhardt- computer program for internal aluminum-fuel-air explosions

8/3/2019 Richard A. Reinhardt- Computer Program for Internal Aluminum-Fuel-Air Explosions

http://slidepdf.com/reader/full/richard-a-reinhardt-computer-program-for-internal-aluminum-fuel-air-explosions 1/34

NWC TP 6449

)Computer Program for Internal

Aluminum-Fuel-Air Explosions

byRichard A. Reinhardt

Naval Postgraduate School

Monterey, Californiafor the

Research Department

AUGUST 1983

NAVAL WEAPONS CENTERCHINA LAKE. CALIFORNIA 93555

'-eC 0 ...

Approved for public release; distribttion unlimited.

DTICS ELECTE

LU OCT26 IM

._j=72~

B ~~



Naval Weapons CenterAN ACTIVITY OF THE NAVAL MATERIAL COMMAND

FOREWORD

This report documents the extension of the continuing research effort oninternal blast at the Naval Weapons Center to include aluminized fuels in air. Work

was performed during the period 1978-1932.

This effort was supported by the Naval Air Systems Command (NAVAIR) andwas executed by the Naval Weapons Center under the Strike Warfare Weaponry

Technology Block Program under AIRTASK A03W-03P2/008B/2F32300-000 (appro-priation 1721319.4lAj). This airtask provides for continued explorate-, development

in the air superiority and ar-to-surface mission areas. Mr. H. B. Benefiel, AIR-350, was

the cognizant NAVAIR Technology Administrator.

This report was reviewed for technical accuracy by K. J. Graham.

Approved by Under authority ofE. B. ROYCE, Head K.A. DICKERSON

Research Department Capt., USN

5 August 1983 Commander

Released for publication by

B. W. HAYSTechnicalDirector

NWC Technical Publication 6449

Published by ................................ Technical Information Department

Collation .................................................. Cover, 16 leavesFirst printing ....................................... 200 unnumbered copies



UNCLASSIFIED

%ECUA.ITY CLASSIFICATION OF THIS PAGE (When Dote Eeiteted)

REPORT DOCUMENTATION PAGE BEFOE COMPL.ETIN~G FORMII. REPORT NUMBER 2.GV CCESSION NO. 3. RECIPIEN 1"S CATALOG NUMBER

INWC TP 6449

4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED

COMPUTER PROGRAM FOR IN1 ERNAI. Final report

ALUMINUM-FUrL-AIR EXPLOSIONS 1978-1982

6. PERFORMING ORG. RIEPORT NUMBER

7. AUTHOR(*) B. CO~NTRACT OR GRANT NUMBER(*)

Richaid A. Rein~hardt

3. PRFOMINGORGNIZTIONNAMNDADDESS10. PROGRAM ELEMENT. PROJECT. TASK9. PRFOMINGORGNIZAIONNAMEANDJADDESSAREA & WORK UNIT NUMBERS

Naval Postgraduate SchoolARTSAOWOP/8B2-O-

Mvonlerey. California

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

NavalI Weapons CenterAust18

China Lake, California 9355MBR5FPAE

14. MONITORING AGENCY NAME & ADDRESS(if different from. Controlling Office) 15. SECURITY CLASS. (of this report)

16. DISTRIBUTION STATEMENT (of this Repot)

Approved for public release. distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abstrte teod in Block"20,1!dIffereat from Rjpce)

III. SUPPLEMENTARY NOTES

19. KEY WORDS (Cota roerso side It naenty and Idontify by block number)

Aluminum Internal Explosions

Explosions Overprcssure

Internal Bast Reactive Metals

20. ABSTRACT (Continue an ueveeeo side It neceomsy snd Identify by blocA iw)

See back of form.

DDOR 12LF41340

JAN 73 VEOITN OF I NOV £5 IS OBSOLETE UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (WAR DaOte .16e0



UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE 0,4(Is o

(U) Computer Program for Intenal Alumhmi.in-el-Air l'rplosions,.

by Richard A. Reinhardt. Naval Postgraduate School. China Lake. Calif..

Naval Weapons Center, August 1983. 30 pp. (NWC TP 6449. publication

UNCLASSIFIED.)

(U) This report do,uments the intcrial explosin computer pro-

gram INAL. used to calculate overpressures. temperatures. and chem-

ical species present in the internal explosion of aluminized fuels in air.

A complete listing of the program in HP-BASIC is presented. as well as

a discussion of the function performed in each major subroutine.

UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE~Uhmm DO* Eftle1)

_ -, . - -



___ ~~tz

NWC TP 6449

CONTENTS

InProurion........................................................ 3

Minu Srogtion..................................................... 3Computat Section ................................................ 43

om pu tatio .Se..o............................................... 4

Initial Approximatiop .............................................. 5IRegimes in Akui .................. ............................... 6Label 1GM................................................... 6Exit from Alcal ............................................... 6Subroutines in A ea! ............................................ 7

Diagnostic Suabroutines............... ................................. 7

Appendix A. Program INAL.......................................... 9

Accession For

~IS GF'

DTIC? ]

DiStribution/

P A'Valablit7 Coce

II

_

- -- -A



NW C TP 6449

INTRODUCTION

This report describes a program used to calculate overpressures in internalexplosions of aluminized fuels in air. The program, formerly called INE, has beenslightly modified and is called INAL (internal explosions with aluminum). Anannotated copy of the INAL program appears in Appendix A.

The calculations are based on the assumptions that the process as a whole isadiabatic, that the products are uniformly distributed through the volume, that chem-ical and thermal equilibria prevail, and that the ideal gas law may be used throughout.The adiabatic assumption in a constant volume system is equivalent to the requirementthat there be no net change in internal energy: that is, that the ir.ternal energy of the

products (34 chemical species are considered) must be equal to that of the "Itroducedfuel (inasmuch as all the other starting materials are elements in thei- thermochemicalreference states).

A description of the program can rather logically be divided into two segments:

(I) the main program, in which the general procedure is to find, by trial and error, a

product temperature for which the adiabatic condition holds: and (2) the subroutine.called Alcal, which carries out the equilibrium calculations and then finds the internalenergy change corresponding to the equilibrium set of products.

MAIN PROGRAM

INPUT SECTION

Fuel. enter formula and internal energy of formation. Computes formula mass:

allows for zero C or If or no fuel.

Cone (accessible from line 1780) resets flags, counters, and amounts of solidsto zero. Enter concentration (kg/m 3 ) of fuel and of A]. Comput-.i moles of fuel andof atoms of Al, C, H, N, 0. Computes total initial internal energy.*



NWC TP 6449

Temp (for entering trial temperature manually) may be accessed by use ofspecial function key k4. After at !east tw o trials, Temp may be bypassed and

interpolation used to find the new temperature.

COMPUTATION SECTION

Cale calls up the compvtational subroutines Eq. Alcal. and Ex.

Eq is a subroutine of ihe main program to evaluate equilibrium constants of

formation of each of the 34 chemiral species. Kp is first computed from the storedparameters an d then converted to K. (expressed in mole numbers). Kp is defined foreach chemical species as the ratio of the activity of the species to the product of the

activities of C, Al vapor. 1-2 , N2 , and 02, each raised to the power corresponding tothe stoichiometric content of the element. In converting the Kp, the activities of

gaseous species, including the elements, are changed to mole numbers. For thecondensed species the standard state remains the pure phase, so that the activity is

unity, except for C.1

Acal is the master subroutine which carries out equilibrium an d energy

calculations. Results are displayed as "dU" (net) and "T high" or "T low"; dU = 0 is

desired for convergence. A new temperature approximation is performed automaticallyby interpolatior, based on former T and dU values, or else it is entered manually with

k4 .

Ex prepares termination of calculation. Calls up Molsum, finding the total

moles of gases.

OUTPUT

Prints results of calculations.

Cv, the molar heat capacity at constant volume, is computed by finding dU att,. nearby temperatures. An isentropic parameter, lambda, is found by using alsodnldT (change of mole number of gas with temperature).

Conclusion: various options allowed, as for new concentartions or a new fuel.

Nav4 Weapovs Ceuer. Adisatk Compsautlbn of Imau1 Infiom Aaminm.Casd Chnes inAir,by P. A. Reiahdt and A. . XacDooal, N& Postlproda School Cin Lake, Caif., NWC, January 1982.

(NWC If 6257, publicatin UNCI.SZFED.)

4

~~

E___- ~~~ jI~-.~-



NWC TP 6449

ALCAL SUBROUTINE

Alcal is the major computational subroutine wiiotv task is to find the niumbers

of moles of the products present at equilibrium at the selected temperatiure. T;e

conditions to be satisfied (other than for the trivial case of Ar) are tie atom baiance

conditions for C. 1-. N. 0. an d Al and the establishinent of chencia! equilibriumbetween each compound and its component elements in their reference states at the

prevailing temperature.

Th e master variables (all in mole nunibrs) are X = 06,1- Y = ' Z =,>

Aiv = Al metal vapor. Ace = activity of C (standard state - graplute). Of these. Y isalways computed in closed for, n. from one to four of flit, %i-mihing aster variables

are found as unknown parameters. using the Newton-Rq.phso.) method. The actual

number of unknowns is equal to four. reduced by the .ianbe:r of condensed phases

present. Possible condens.:d phases are: AiO (solid oz liquid). Al (liquid). AIN(solid), C (solid). AIjC 3 (solid). The presence or absence of each condensed plase is

indicated by a flag. to be set as de-'ribed later. The set of condensed phases isreferred to as a regime: allowance is made it the program for about 20 different

regines.

Based on the values of the master variables and the Kn of focmliatiot. the mole

number of each species is computed. Then the material balance in tile elements 0. N.

C. and Al is written in teins of these mole numbers. Thus. there results a set of up

to four simultaneous non-linear equations. It is this set which is used as the basis ofthe Newton-Raphson scheme to find the unknown paranciers.

At the conclusion of an iteration, the newly generated values of the mastervariahIlc-s are used to repeat the calculations. In favorable situations each it-:ration

results in improvement (although temporary divergence sometimes occurs). Iteration isrepeated until errors in the material balances are less than one part in te i thousand.

INITIAL APPROXIMATION

To begin the calculation, an initial approximation of the master %ariablcs ismade using the subroutine -lpprox. In this approximation an arbitrary hierarchy ofoxygen and nitrogen uptake is assumed. Oxygen is assumed to produce. in order. CO.

A120 (g), ASO20 (c). 120. CO. and 0. When there is insufficient 0 to conw.e t all

Al to AI203. AIN is assumed p.esent. If there is no t sufficient 0 to conert al l C toCO. A14C is considered if the temperature is low enough. This rather long subroutinehas given many more satisfactory initial conditions than fhe simpler scheme described

in Reference I. I is used once, or at most twice. for each new concentration that isrun.

5



NWC 1? 6449

REGIMES IN ALCAL

It is necessary to assume which condensed phases are present, then perform thecalculations previously outlined, and finally test for the presence of the cordensedphases. The following criteria must be met: (1) the quantity of the phase must be

positive and (2) the formation constant must be satisfied. The tests are carried ou tafter the convergence of the Newton's method calculation. If the tests fail. a differentregime (set of condensed phases) is tried--the assumptions now based on the currentlyif computed sets of mole numbers.

An index Nw is used to identify the regime being considered. Eleven differ-en t values of Nw are allowed, which account fo r about 20 different regimes, since formost values of Nw graphite may be present or absent. A key to the Nw values isgiven at the end of the program in Appendix A.

LABEL 110.M

The section of Alcal beginning at label Ilo is the setup for the Newton's

method calcuiation. (iiomO is merely an early entrance iltn Hom.) Dcpending on the

regime selected, ii (the number of variables) and Nw (the index identifying the 1'-.'ge)are evaluated by the subroutines liet and Nwset. The regime is established in a varietyof ways. Initially. Approx gives the first guess. Afterwards. the subroutine Alniest isused as criterion fo r all solids except AI4C3 . which is looked fo r at florn2. At Exit

and Exit) additional tests for alumina and -raphite are made.

The variou. ibdivisions of Hom are designated Nw.x. where x is partly indic-ative of the value of Nw for the regime considered. Th e correspondence is imperfectsince Nwl includes the cases of Aw = 1. 4. and 5 and Nw2 inchudes Nw = 21 and 6.

In each case. initi i approximations arc set fo r each variable to be Solved. using latestresults of the appropriate variable.

Subroutine Newt is called to carry out the calculations (except Nw = 4. for

which solution in closed form is possible;. Then either a new value of V., s used (ascalled for by Alntest and liset) or the program switches to llom2. As this point.

if A14 C. had no t been presupposed, bu t was found present, it is necessary to passonce again through Approx. Otherwise exit from the subroutine is prepared.

EXIT FROM ALCAL

At Exit and Exritl it is necessary to check for negative amounts of aluminaand graphite. If found. the appropriate flags must be reset and a return to Iom is

required. If those tests are satisfactory. next, at label Ener,. the internal energy.for each species is calculated making use of the stored parameters and the nmb-r of

moles of the species. If T = 2315 K (the melting point of alumina), the relative

6



NWC ip 6449

amounts of the tw o phases of alumina are found from the energy balance. Return to

the main program then takes place.

SUBROUTINES IN ALCAL

Alatest sets flags for AIN. A12 0 3 , Lq ( !iquid Al), and Gr (graphite) based on

the present value of the formation expression. as related to the formation constant for

the first three, and on whether Acc has been found less titan unity (indicating no

graphite).

liset and Nwse: evaluate i (the number of variables to be solved for) and Nw

(the index for the solids regime), based on the flags se t by AIntest.

Newt solves the set of simultaneous non-linear equations needed to find the

values of the master variables, using the Newton-Raphson method.

Fx gives the fitting functions for Newt. Th e subdivisions are labelled Fxy

where y is a value appropriate to that of Nw. Th e subroutine generates a variable

designated Fx (returned to Newt), which gives the fractional error in the stoichiometry

for whichever element is being considered at the moment. Since Fx calls on Spec,

mole numbers of all species are found each time.

Diff first computes all the master variables which were not found in Fx and

then calls Spec to find all the mole numbers of the gaseous species. Diff compuics

mole numbers of the condensed species; and finally the errors in the material balances

!oT 0, N, AJ . and C are returned to Fx.

Spec ccmvputes the mole numbers of all gaseous species, given the currentvalues of X. Z. Ah , a:nd Ace. Y -'-W is computed in closed form in Spec; it is

nm-ded for computations on the hydrogen-containing species. For each species the mole

number is computed by ;siing appropriate values of Kn , the formation constant.

DIAGNOSTIC SUBROUTINES

Sseil is called at the end of each run to give first a check on the materialbWance in each element and then, at Tezik, a comparison of the computed amounts

with the equilibrium con:-ants of formation of each condensed phase and of several

key gaseous spcies.

Painit . called whenever special function key kO has been depressed once. At

each emus-gencc from News the mole numbers of all species are given in a condensed

table. this is followed by Uml and Testk, which give output as previously described.

These various checks are especiall> valuable in troubleshooting.

7

........



NWC 17 6449

Depressing special function key kI will cause execution of TRACEVARIABLES Yn(*). Then during each iteration in Newt the relative error functions.used to test convergence, will be displayed. Each Yn(J) must drop below 0.0001 inabsolute value before convergence is realized. This feature may be turned off byexecuting NORMAL.

JJi

i"I

\8



IANW C 1? 6449

PROGRAM IAL

Thisprogram is written

inlfewlett-Packards

lIP-BASIC.and is intended for use} on any of the HP 9845 series computers. In addition to the mlain program. tile data

file '7111) and the key file "INEK- are neceded for operation.

A KEY FILE INEK

KEY ICheck -(Chtck-0)-Execute

'EY IRACE VARIAB4LES Y.(*)

-Execute

'YF1TrE-Execute

VEY 91-STORE

-Left arW

-Insert chparacter

KE CONT Teep

V Esec te

VEY STRACE PAUSE Iiset-Execute

KEY 6TRACE PAUSE S

-Exqcv,te

KEY 77, 3,6

REY v

KE Y 1

-Cler line

KEYI3

-Clear lineLSTV

KEY11

-Clear lane

ClI**eaned

EY0

- n cze

KEY14

-Clear an*

XEYISUdeke

KEY17O-Undfined

KEY3I -Unde'tned

9EE1S



NW C TP 6449

all.

4$_A. L.o '1 0-

0 1- 0 0 4 .4

1L~ 00

-. V DI u'J

U 0344'

3.. 14-02 0L

2 0 -,-tn. --

4. I . 0*.-20

;U.C ,0. 0

4- 00-

.22 '0 OCOC --.

0 C *1 .. ~-4I3

4M9

mc - 1. .4. -l Zc

CI - 0U20 --C C 1 0L C C+2 U. O

crcL*% zo Z..2U . V

4 J-i M Ul 3i_X C 0

a- c~r C,- 3

4-. 0 3

z-o- I.

LP_ . C 6 m. 0Cc

+-f -- c CA.0~a 1.0

o o - UcO c&Z-

Q O4j 0 C60 V .0C~ C4.

-a . I LI Sct -.x z C

CM Mx2. X <9a cp*r'*C-00*G

c c. r.. 4.lttn X V 9== ZOO - tz cV 4

-v - - c Lc OK.O L 4f44CMN M U) 0. z 4. - ;'C.

ulz1 N 1- -W 0 00 0l

c n c - _hV4.."0. V4 C2:L U2 UML4300VO D a . -Z 0UI. Ua

W q~-qut. UPZ MW C xmz.. z1.:

4 z -zo C-0.I-Z 03ew I. Cm 0

4-ow.-a a.it.-. - 0 -1-. -0 3 cc

2. . Lis 0.N

.4 ~~ ~ ~ ~ (j iI~Z0 0 .UUx

C'it it*-0 If4r, 0%*-C' f

30 0 2Ce.0 UC -



NWC TP 6449

V2

1 05

U C

L. u..

ua

LL3U IA W -

va -L VI- 0

a, C 0 *, - CL

00U4 4 00-

0.., *a Lg *

;.0* Q-C-!

C4 C.o LSC ox 11 00 04. 4- * -j

4.Ca I44U~0.. C

L.C 4L C r- 10.

4 SC 3. . "I

CS~~~a@C r.. 0

WI-I 00a c-C i ~ - 44

LA:

-. r- r

2 a .6

;- I-- - V a0

s cc I. I- - pL m

r 1 99 r C - 0c. 3. N.n z2.'

--. ZA 00 tJ

** Wr rP ax4.;t Z z- C5-0-

zL -. 00 '=. ri- IC6 r u 9-I- C' L.ZC ZI nrW2 C-"= z w a l0

I a 40- HCzz AL-' = "*iw -'

-V *0 A. C, I0 ..A. O- 00 4I-OC 0- m V

ac as4 -K. =4 Mt r~ -x -

a a- a= 2.-zUz i0 a ~ ,L " w

Cw a0 0 4Lt~t% Zuo - 0

CS- c 44 L"

o~~~~~ 4A'S- C 0 -.

C~L ~ 3~ - 2 0 .q CA - -1- c

CI. ~~ ~ ~ ~ ~ ~ 'W V..c4. - X A C1 ZX O 1

Wi-O 40 - * U i U C,' iJO0



NWC TP 6449

K S

L a

5 0

G. a-WC. L

00CC Ca;.L4

aO- y.

ac-nU L-Z

C M. _ar-. cLa 3c

V~~~ clc--rL U a a- - o-02. t,

a o me "-*4CS~rv -40t - uat

Z, (it. Ck. 1O nV VoQ a .

a wSowC -CN C-a

-; wU LC C

I. C

IL-2.-a-)w

U t L t

S.0 z0)C. - La-

-9 ws 'a w

9-a L z-. 0

4

OW 0- - L U Z zLO* f" ani- Jsm

-I 3 U U' -; 2 cP C atIllam- -. C" Mr) of - 0

a . P. - cl2 p

2 -1c -a-4QWaLM- on 2

- c c 0UMCr4 Z- ow IL Lz O SL -*

c :- 1 C. ve. u*-wO* amtz U JLZ V Cz #-0 t 403au- -IA. 9- U I- Se g2 -

Z! Oc - M Z.. *- Int.wa a-w- za0 wzIW" - " z arLS04 ^2 gum cmmoW )- t >an 0 -2r

CM4 SNIkIec il- IW 1-C~ aI 2- Ita . wo 4--.I-fl,4pq a't -c-i -I w 1,-*%. K$- X 0.119-ad4

-wp tod:aa C.. U 3 I 2It *-s -- 02misZ ca.' C UAc c - a -*-cw-..-dc

u C ~ ~ C U L)JZ(sE p4 OC OWa wol 0,010-00340 t'0

2'.- aac-z RJ tP C P2- C S,12I 0W 2 ' *0



04

CW P 644

u 0

- C,

L %: I

. Vc U 4: .

* .4 fu4- 4.

& 0 C4.44.44~ 4 0

to 06- 0A U 9£C CC04 cc

CU - 4. c0 ~ V 0

C .4 - U z .* -. C 4 **4

..CC I ' U v. 'A v ^0'.

00 2 0 30 C £4 . 4

-~ v. V4.- 0 . 4

C O - C4.4b42 3 C 2 .

U 4- -4.4 ~- 4

V 4- . 4' 4 . . 4 -.

*26a-

r3,

.4V.V.4.4

.4.4

.4.T

Ul h -L O4 C

.4.466 CT

NO-

.4.4~-.LC 0 fO C c-C ;*aa4 z -Cs"arvx%.OC4L dc -- ZI-ac ITZ

fn nN7 - OrV 94L2. 04cmF4.JZ CZ - Ie.o+a4*- 6=V v ,

v.4f- LZcz U "

oo" -ZZL01:TE0zIV ,-C -.44 -N

o. a i.4-Qi=itI-

.4'r~ C w C~z.l-=2j*6

.413



NWC TP 6449

.0

L.el . UC

0 .0 Cc

-.cww wL DOCC T ACt

A VC u C O A

c QC C3 C a

T@ r cc %A 3. r6N3OC C

of % C C CC aa C O

a. ~ 00 4-.O LA Ct'C 0.n 'a C.1 0 0 ~ A

cr zC' ;rC v. 0 zcuO .04'J a -

Z - UO..0 . 4- C0.0~ 0 .0-C V.C.C4 4

a.. 0 C ~~~~0.-- aC ~ -- o- ~ -A

-C Zo CZull a- 0 ~U - 0~~~~ 0 0 O Oo N 00 U0'

43 an 1f 11 0 0Ca4J~. Ci

Z* I (0*

C MVa - 4o 2 1.L.wa

a a - az% L- an-Z CUit 1O un

alpa -ot N 0Z iLm zm

TILref.,vur.w*um w U 2C%.U I~ e0 tv r.5 NqCO 'A' ar~

U0 .0

w z * IL 0j -

~~ w~0J0i0-0e*1" 0WW O M0fl I aaf.aI6

14



- - >2 - -

NWC iF 6449

j .CL

C

Cm a0 V.

10 c. c

0 - a a C u V

Nl *.-Lw C L 5

92 1-~ I,,* =006 a"L4 -

v2409 0 0 a 5

. 0 1J v 0 3.U.4 C C4. 200K . 0 a 4 L 1.1 U 82 z. 0

.5.C4*-V -- 4m5 %-' C

.d.0z a 4 0 4. al- 2a 4

.5 .L 4 0 %. CZ. 10

*.ONNO m L . LN .04 a r a a:c r

4.-V im. 9. a. O 4K U 4. .4. UAoa 4.. Lu 1

2 e.) 6-C -40 4.*4C 04, Cm - C

. . .-.2C4 4: 0,0 L 4.: , .

* 4-5 L) 7L CK C 0 4 2. .51VG. 644C0. .. . 8. C - .. 0 :C

C 160, WA W3, co 0N a.48 6 C. 2 2 a v

L49"SO 4.40 Cc C. 2w - L a~ CLLS.-&

044.~~cq QU02228 04.4 . 0 c La 0 u .0 4

9,.O~.@2Kc . 9 *0, -n-O1. 4 . 4 U ~ 2

9,. .4 004.£0 - 22 2 9

Lmauw .40 I.& ' 0~

040

I x U

0L am v 22C

00 pi4 -a AA ON z0 ; 2 L Z

002 K' l2 - M t

00~~ 2Kv~'4

a0;z -Wa U- "

V0- w w*(A x- 4

0*0 &.- 00wo-

vaowI 4- R "-cvw-' ,CF4 -Z-: Z3, we naUI -W3=p~

xctC cx8 Z .%.aa xU

IgUU0a .~.41-q-

00i 0 0 o bw o1dbob4Nmof 0om-m 0 0

00b a- VbIA 0

AA A

i -1

ARM=.

00 2 .4-- -~.now.



NW C TP 6449

CI.

2:6

UU

Cc 0 0 41

I. 4- V;oc Z C

Mc u A 0 .

6 0 0 0 a

NI. L. a@wo 11 01 8.1 0 -

oo ua u -- S.%I= c - . ; 3. -SOL 3 0 a. Al an0~

0 1 a 1C S.4'W'a AL . 9 C.

aC C Ni. c- C 4 ccC

a c -. a 4 Ac a, - 1 f, U- gw0 U -4 40 40 c. z2 Cl

S. Ac 3. v a1c c '0£

aC - 8. ! c* .0 10 U t 0 c439u cu .c ua , t-- a5- - - 4 .4 4 0

c00 e C- C D4 0c - 7. C

*c a I. -0 =HC U 32 2

z z

z 2

C C80

42CD 2

4.. 4.. 4.

o0 acts

ari aa 4

c M2 a Cc -g ata

x ca al-x c- SC Lcw C

0'X 0 5'- a U'x

C4-N -0-..

C~ X. ah 2X-Os0-Xc CX . c x xC

x N.Cd- -Z -0 au - UJo

I- - .f1=S.V4aJ;a -M Z- O--C 4. r. b - -- x- 5 'C.to2 EI CC XC6 -auC4

)cq'"'L 3£22 3t.X Z-4 GO- 020wq we1 4 .j=9-% wa.- -0 -%9 W fw v%4 ILu 02 -

I . *QL422-W- "a - 2 X 4b-c 3 Woa 2 -c ek e .-

A, 4-ri *l4a h

.4w &1Ww qw w0.q qp . -%" Ww "RV w ItS

~C41~-4 '0241 C.6



;S -;7hly-l

NWC 'IF 6449

- 0- CL

*$3v

a-

V C,.-S 46~

we~11 0 6. '.

-~ C -. C a

z CL' a

Ui am lopL a -

Ce C

cc V0 ~4~ ~ 0-

tv -

c

-4.

* 0-z--

z~~ zx~

.3

a qax 64 a

a.

0

17 -

Ear



NW C 71? 6449

0

a 3.

0 C

xcc w u a

*%-c e 4

4.0 a to s1. fI4 . C -20.0

Coo C C1 V L

KZuQ V

cm AC Cc c-£

414e.0

oa UcU1

. 4 U -US x. Ua All:£

CU - 4 a c 0 *0 1-c 4. K 40' - -. - - U= -I. . -W 34 :1

U O

C 1%3 goa UM0.00rjoe4

41**nuj- k %RAIL 04- X #2lartacADOt*. 1sa0

0* 4&L*0Z -Z OM

Q .-o W s-0 sW-0 ILLL96 0 0 ma WIL.#

00 ~ap.L

INIts is So-1

or

*AR



NW C 1? 6449

2-

r 03

9.4

-C0. 20

2 - *S m

C0. i

616 *W

0 - 4 U 0

a.. a .

a ~ . 5: *

-4 - U S

L C U *~*Ow

I- - w c.Vl I

z.U3 db-

-e& f cra a -4 VSC4

-. Iv = . t

:; 1' ... CC"4

*5m

C.3-*m

-006*Vi a M., M ,

6*

::cti*

6*0

-U-

* 19



NW C TP 6449

C *0. 000 Ch.

00 *4-c 0

'00 SU-

-c c.

x- 4-0 c

00 , c.

LX V

0-e o~l

CC O- I4--X,-

.4 L-

2. a. L

4'.. 04 c L a 2 U.S CL I

00 F c I fa dAL C 0m0*cma z= p

0*0t c r a.LUW00f

wo,*00 13 Cc0cz

0* w db00X t--J-? x L -

n a Q*=-

0* -0. x 5' -x X 4 ~0*= - '-I :CV--

0*o -- azx--o <C4 U

Ulh*L , .. 02t~= &0L0 -J ZP1 m-

00I4 CCD OD=DMI4D~btl0 =--04CM 0 00 j

* .3 20



cc4

NWC 1? 6449

'rL

.. o

f- CA v a 6

C ft . 0 L

a$- ,vww 1.0

f- V cc 4

*12

L~

w % . C CC

ii:-t-@-

WI

:U l

0 -.

I . w 6c - 91

10 a u Z = a

4" It& xa.- .~ Z~ -



NW C TP 6449

uU~.C

ILI

az.4b -

-46 o-ZLLs-4 C;z

V,*

to*

411FJ '* 3 g

c~a -6Saw

94. OC.0I

*b

Nz0* e - z*C

00 a= 00cc

240* wtU0*

am 0 9i eft0 w Ir

0*l M gtbf'

04*"'00 4oc

0*22



NY/C TI' 6449

4. 24

a

aa

L ca

U U a-Ca19L) 0D -

9a-4 a 0

0-= ViL :

U 0 U 0v mcx . SAC- IV

0- .8c~*2 aL 4* a I

0 -. j I 04.9

-. . L

U- ~ f.

z~ c

4.2~v a.

8~ LL

mz

R0 N

*3 OF L. ru 0at * 0 = .wc , gft ~ -e X0 *JLU .W:

3-* IL 0*N flc!-

4c-n N*"44L- t . -

.44N a- N14"0 --- n L. 40 c- xwU

top. nz Nw- 3a-m CS0

*1 N4p 2 Ll4CC

30 Ui%- LiUN "29& I- C 3w2a2z U e m-*N -

*014 L. L W~L-

341 a-me 4 .%CCJ*3 W -nIho".umqui .0*NODC

* 3in rat, 2 J X- N,

33 3 8 94~~~' 33N)*. N 8J



NWC 1? 6449

+a

C -CM

00

0.-

2

4 V . '

C* IC0 l -,j

::o 1. 4L11~

.2W- 0 You-

MM .L ..-..

MW '04 - K!t'-ED

LM, .,O

c'J I, ('

LM 2

MM 24



NWC TP 6449

0U V

t, CL

V

--

C

-Cc

20 10 Clo 0

*OZ.X~C04@3. c -

IS- * _ 0 a L.

*0 -

*U7 ~ w

CL. O

6*U V.Z- O .

*

Af6 ,h Mmm)

- - ~ - - -- - - - - - - - -

6 W~ '25



NWC TrP 6449

D)ATA FILE TIMD

E.1quilibrium Constant of F:ormation I)Jia

-2.64217215 3t95.U513M5 -i1.443163634 -7.S97i35794j1E-5S 2.49S791&243§E-13 -.5

4.IVM24?I 26%4.0692M5 1.441316479 9.72321?13E-46 9.522745371E-lS -1

-8.5121&7992 401.5374Mi -. 771591646 -1.7497U541E-14 4.Y192121 654 --S

2.2544W3379.1674 27.353411 t.I676939W2-e5 2.37493M392E-13 i

4.593131464 &1I.44364152 29.75624115 -4.72i2q5934f-S ?.17169S?764E -S .

6.7466315 1- 26641.4645 1.1U7392I -2,4367raMf-05 6.32419S771-SS I

3.1m97679 -12116.W5425 19133911 44 i.4157313t4E-IS 8.435077673ES-S .

.749*5222? -191.952495 -16.3430133692 -1 47412U147E-35 4 421654E-S I

I I I I 1 0-3.560374647t 13MA519269 13.867M?425 -5.19S32483354E-S6 4.759413387E-IS -.5

-2.m43174446 i2 .321315 S.2VOMUS2 &.nQW8347W2-35 1.95115?315844 -.

-6.14764*551A6 2615.63429 -7.41178001i6 i.146324MOM4~S~ 1.1623678SE-14 -1

.7iS133lS614 -1.1454345 7.7834427223 -?.442572-P% 3.52621675SE4 I

3.497133637 -1343U.Th60S3 9.7S11i771 6.1732276%1E-1f 6.906MYOSK51-65 *C

-5.95275582 15438.2%8UY -21.9673054972 9.14266i6521&S 1.7i2i46919LE-04 -1

-IS.Ml UN3139S354.261256 -37.26147353? -i .i73s8842-14 2.7S18632S7KE-13 -- .5

-43.697593 i54312.SI779 M9.327462644 1"29147157E-13 6.13952SME2-S3 -3Vi

-29.43593324 11U7.36593 -6.55489562564 S.0647333193SE-14 3.i35118744t-14 -3.5

I I I

SM25677ifi95 4.7683263592 -2418.3457294 4.6474Y2491E-45 1.61847?43WI--02 -.S

5.3921566319222218-146W8S -11.958115513 -i .643=57S39.-IS 2.S7767i3SilE-4 .

6.2329113 -24268.91617l -12.4711153M2 -4.29713319ff3-SS i .866173MM29-04 .5

7.54627333629343.331797 -.37142S411396 -6.6129197SBR4E-S 9.S477i$777E-S .-24.91262577M14.9524 -915163 -S1945462331-14 6.4668977746E-03 -4

MA167151 -686.7965268 -12.51659672 -7.6957594781-6 S.5396SI187E-I5

-25.741375395 96495J46919 2S62.82767313 2.86i9527614E-5 1.1561513721EM .

2.221IS4114 129.1199597 219.33512518 -S.9?6838743lE-lS 4.361151S6919E-SS I

-2.535953635? 676T.63261573£9.28584179 -i.625S53iS26E-SS 0.6624576232SE-l5 -.S

2.604367687 -11332.2018 -15.5S72441176 1.3&7217S992E-17 6.42Z26SM87E-SS I

13.94954M76 -41395.0614497 -16.1531S46361 -I.9547S2S964E-D4 3.89OIIS9iE-14 i

26



NWC TP 6449

2. Internal Energy of Formation Data

131.27691 11.599712 .66667516556 1364.276M6 6"431.8426411S.42%ff 3151159 .6621i482 -2961.6168e 16395S8.46

-5536.7S57 61.7M732 -.6603553262 -2262.9668 -411677.36

-O4940.1553 50.69532 -l.27i676803K-0 -S72.49672 1672177.44

MU M MA5235 11.395124 .66466955466 273.79376 2271419.92

-3717.719M7 P2.AM56 I I I

-0m114.54~41 31.13199 -.111024618196 -6217.8424 2373.952

-36101.3939 56.7432 .111166571624 -"6.616 1763M1.94

21092661 12.472564 6 6 6

1660438864 4.79576 -.6616U6S816 -2192.823 -76487.6

i3fisAM ~ 32.6657 .16631254 -20%5.m7 -940244.85056.641564? 63.224132 -.6663459W -45%46.68N -164717.2

644161.1319 6U.474912 -. 663681562 -90479 -39617841.9

-2245.5397 S51LU16 .664225664 3306.2632 387565.23

1150.1M1 30.619512 .116616425492 -435.42 6M62.M

3173.1226616 31.&511232 -.66173515S2 -713.7744 -657139.54

21445.6641 9.6437 .1660773M4 4427.581 2650327.36

3214.695629 29.47629 .636663662 -6264.7132 -2162256.6

-794.96 31.74619266

-29715.6292 37.56464 .661366442 -417.19548 983.36

-10349.4414 13fi.548632 II I-1471365.672 1464226 .061932994 -37420.4418 -1202S234.4

-40.173619 2Z.904059 -6113199714 3411.71336 SO2958.

1623 9476 31.550772 .31111"7412 -7102.212B -392311.512

691553.9142 33.9275 .16740337 -V192.4129 -2465757.2

75647.6269 66.61346 MOM2391 -4391.79 -2"69159.6

536354169 51.37166 -.66461466156 -6.1842463,5. t4

-3M2.911290 264.3341H9 .311306402M -31427.2M9 26311

2HM94.717U66 6P.76 -. 63296 -262S.606 -S%4719.2

36116.646937 U3.SiVx6 -.1116474082 -2923.912 -474966.3

9025.79213 6316"16 -.6631M 12 -1923.4296 -234479.2B

54534.993 6.5629 .06976 -32361.566 -1211.52

4746?.K31L 92.611V12 -.00462 ' 293.12-13652

?6m1.3m69p 43.9077 .6623163 -1615156 -32261.69

27



NWC TP 6449

3. Chemical Species Symbols

Al

ANM

AlOH

AlIU0

H0

02

A iMA133(s)

C3

28



NWC 1? 6449

INITIAL DISTRIBUTION

7 Naval Air S.stem%Command

AIk-00D4 (2)

AIR-301 (2)

AIR-350 (l)

AIR-320E (1)AIR-541 (1)

5 Chief of Naval Operation%OP-03 (2)

OP-05 (1)

OP-098 (1)OP-55 (1)

I Chief of Naval Material (MAT-05)

3 Chief of Naval Research. Arlington

ONR.102 (1)

ONB-461 (1)ONB-473 (1)

2 Naval Sea S.sem- Command (SEA-99612)

I Commander in Chief. U.S. Pacific Fleet (Code 325)

I Air Test and Evaluation Squadron 5I Commander. Third Fleet. Pearl Harbor

I Commander. Seventh Fleet. San Francisco

I David W. TP.lor Naval Ship Res-arch and Development Center. Bethesda

I Naval Air Enginvt-ring Center. lakehurN

I Naval Air Force. Atlantic Fleet

2 Naval Air Force. Pacific FleetI Naval Air Station. North Iland

I Naval Air Test Center. Patuxent River (CT-0-52. Bldg. 40 5 (Aeronautical Publications Librar.))

I Naval Avionic- Center. Indianapoli- (Technical libran)

2 Naval Civil Engineering Laboratory. Port Iluneme

W. Keenan (1)

Technical Librarv (1)1 Naval Explosive Ordnance Disposal Tchnolog, Center. Indian Hlead

I Naval Ocan Systems Center. San Diego (Code 131)

I Naval Ordnance Station. Indian Head (Technical Librar.)

28 Naval Postgraduate School. Monterey

Code 012. Dean of Research (1)

Code 06 . Dean of Science and Engineering (1)Code 1424. Library - Technical Reporti (2)

Code 33 . Veapons Engineering Program Office (1)

Code 61. Chairman. Physis and Chemistr. Department (I)

Code 61KY. G. F. Kinney (2)

Code GIRl. R. A. Rinhardt (20)

3 Naval Ship Weapon Systems Engineering Station. Port fluclme

Code 5711. Repositor. (2)

Code 5712 (1)

29



NWC TP 644

12 Naval Surface Weapons Center. IDahlgren

C10 (1)G20 (1)625. liales (2)

630 (1)G35 (1)G43 (1)

-j 651 (1)6103 (1;%12 (l)

W. Marton (1)

Technical library (1)14 Naval Surface Weapons Center. White Oak Laboratory. Silver Spring

G4 2 (1)RIO. S. Jacobs (I)

B12

If. Adloph (1)It. Berrnecker (1)K. Durrell (1)

J. Erkman (1)W . Filler (1)K. Kim (1)Roslund (1)Short (2)

R13. R. Liddiard (1)

Guided Mlisile Warhead Sct ion (1)Technical Library (1)

1 Naval War College. NewportI Office of Naval Research. Pasadena Branch OfficeI Operational Test and Evaluation Force. Atlantic

I Operational Test and Evaluation Force. Pacific

I Pacific Mlissile Test Center. Point Mlugu (Technical Librar%)

I Marine Air Base Squadron 32 . Beaufort

I Army Armament Materiel Readiness Command. Rock Isand (Technical l~ibrary)

4 Army Armament Research and Desclopment Command. Dover

DRDAR-LCt.-SS. J. Pentel (1)DRDAR.TSS. Technical Library (3)

I Aberdeen Proving Ground (D~eselopment and Proof Services)2 Army Ballistic Research Laboratory. Aberdeen Prosing Ground

DRDAR.BLT. C. KingMr (1)

I Arm). Materiel Svystesns Analysis Activit%. Aberdeen Nrosing Ground (J. Sperrazza)

I ArM% Research Office. Research Triangle Park

I Harry Diamond Laboratories. Adelphi (Technical 1.ihrar%)

I Radford Arm% Ammunition Plant

I Redstone Arsenal (Rocket Development 1.aborator%. Test and Evaluation Branch)

I Rock Isand Arsenal

I White Sands Missile Range (STEWS-A)-!.)

Yumaroving Gound%(STEYT-TE N& W Branch)

I Tactical Air Command. Langles Air Force Base (TPI..ROI).M)

I Air University librar%. Mazssell Air Force Base

I Tactical Fighter Weapons Center. Netllis Air Force Base (COA)

I 57th Fighter Weapons Wing. Nellis Air Force Base (DTOi

I 554th Combat Support Group. \elli%Air Force Base tOT)2 Defense Nuclear Agenci

Shock Ph%-sic- Directorate (1)

NM. rankel (1)12 Defense Tcchtsic-a Information Center

I Department of Defense Etplosives Salet% Board. Alexandria (Chairman)

30



I Department of Defense-Institute for Defense Analyses Monagement Office (DIMO). Aerandria1 Lewis Research Center (NASA), Cevel d

I California Institute of Technology, Jet Propulsion Laboratory. Pasadena CA2 Hercules Incorporated, Allegany Ballistics Laboratory. Cumberland. MD

I liT Research Institute, Chicago. IL (Department M. Document Librarian)2 Johns Hopkins University, Applied Physics Laboratory, Laurel, MD (Document Library)2 Johns Hopdin University. Applied Physics Laboratory. Chemical Propulsion Information Agency. Laurel, MD2 Los Alamos National Laboratory, Los Alamos, NM

C. Madr. MS 214 (1)Reports Library (1)

1 Princeton University. Forrestal Campus Library, Princeton, NJI R&D A.ociates, Marina del Rey, CA1 Stanford Research Institute, Poulter Laboratories, Menlo Park. CAI The Rand Corporation, Santa Monk, CA (Technical Library)

1 University of California. Lawrence Livermore National Laboratory, Livermore, CA

I University of Denver, Denver Research Institute, Denver. CO

?i

richard a. reinhardt- computer program for internal aluminum-fuel-air explosions

Documents