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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 ~~
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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
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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
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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)
_ -, . - -
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___ ~~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
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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.*
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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
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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
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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
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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
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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
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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
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KE CONT Teep
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VEY STRACE PAUSE Iiset-Execute
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NW C TP 6449
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NWC TP 6449
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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
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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
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MA167151 -686.7965268 -12.51659672 -7.6957594781-6 S.5396SI187E-I5
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2.221IS4114 129.1199597 219.33512518 -S.9?6838743lE-lS 4.361151S6919E-SS I
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13.94954M76 -41395.0614497 -16.1531S46361 -I.9547S2S964E-D4 3.89OIIS9iE-14 i
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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
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-36101.3939 56.7432 .111166571624 -"6.616 1763M1.94
21092661 12.472564 6 6 6
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i3fisAM ~ 32.6657 .16631254 -20%5.m7 -940244.85056.641564? 63.224132 -.6663459W -45%46.68N -164717.2
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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
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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
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2HM94.717U66 6P.76 -. 63296 -262S.606 -S%4719.2
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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
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NWC TP 6449
3. Chemical Species Symbols
Al
ANM
AlOH
AlIU0
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C3
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NWC TP 644
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