eli freedman dtic
TRANSCRIPT
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TECHNICAL REPORT ARBRL-TR-12411
* •(Supersedes BRL IMR Nos. 249, 359, and 380)
BLAKE - A THERMODYNAMICS CODE BASED ON
TIGER: USERS' GUIDE AND MANUAL
Eli Freedman
$' DTIC-t• ECTE
July 1982 tI4V 4a98
"-4 B
US ARMY ARMAMENT RESEARCH AND DEVELOPMENT COMMANDs- BALLISTIC RESEARCH LABORATORY
ABERDEEN PROVING GROL*tD; MARYLAND
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LA.J
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Additional copies of this report may be obtainedfrom the National Technical Information Service,U. S. Department of Commerce, Springfield, Virginia22161.
The findings in this report are not to be construed asan of•icial Department of the Army position, umlessso designated by other authorized docuents.
wie of tir'Wie no*o wmuffactwom Im*is'heyid'snot OMWttut. i's.*wheote ofO ., eitpr~
I NICIASSTFIFEDSECURITYr CLASSIFICAT!ON OF THIS PAGE: ^o~n 11st. fnt*#ad)
REPORT DOCUMENTATION PAGE READR INTUTONS
1. REPORT NU)MOER 2GOTAC~cESSIOAl NO. 3. RECIPIENT'S CATALOG NUMBEfl
Technical Report ARJ3RL-TR-0241 h-)2'j4, TITLE fend Subtitle) S. Tr(PE OF REPORT & PERIOD COVERED
BLAKE - A Thermodynlamics C-.)6e B::sed on TIGER: Technical ReportUsrs 6..O ndMna PEAFORMING ORG. REP.)RT NUMBER
7 AIJTHOR(e.) S. CONTRA .7 NR GRANT NUMBER(s)
Eli FreedmanS. PERFORMING ORGA4IZATtON NAME AND ADDRESS 10. PROGPAM ELEMENT. PROJECT. TASK
A'E.IA 4 WORK UtRIT HUMSERSUS Army Ballistic Reseavch LaboratoryATfN: DRDAR-BLIAberdeen Proving Ground, MD 21030S J1,1'1lA9lA
11. CONTROLLINU OFFICE NAME ANVD PVORESS 12. AE,'ORr DA-FE
US Army Armament Research ý Development CommanadJuy18US Army Ballistic Rese~rch Laboratory (DRDAR-BL) -1. iUMC-ERtOF PACES
kberdeen Proving Ground, miD. 2ltxi 1314. MONITV3RING AGCNC'? NAME & A('OREWS': dlile,.ot from Controlling Off.ce 15. SECURI' Y CI ASS. (of tlA: A.P, II UNCLASSIFIED
I~a OtCL ..SSI FlC,uTi.)Nf DOWNGRIADINGSCHEDULE
t;,. OISTRIBUUION4 S ATEMENT (of thio Report)
Approved for public r(lease, distributionulmtd
17. D!3TTt;"J1w.' !TATEMENT fof the 4betujet entered In Hlock 20, '1difiewent ~.1oa itopofl)
is. suPr'.mgirwTARy ?4oTEE
Superjedes BRL 1MRs 249, 359, and 380
19. K'Ir W040S (44m(Itnve on rwwwe~o old* It neceo4Aay anid Identify Cr block manele)
Thermodynamics piopel lantscomputers combustion gasescomputer codes no'n-~idea's gasesBLAKE.
M~ AV15rRACT (e.o(8ueO so'~ ruvw oft I wa~ew 4a. ~Cr 3?U~y bloc* mwent)
BLAKE is - geneial thermodynamics codt: derivcd from the SRI TIGER code, It
is intended primarily for making calculations on propellant gases under gunchamber conditions (temperatures between 1500 K and 4000 K and pressures up to
I700 IMPa) on the combustion gases formed by military propellants. The uniquefeaturc- of this code is th~t it eiMbodie5 a correction for non-ideal gaseffects appropriate to 'is application. It uses a truncated virial equationof state for this purpose, Thie second virial coevficient is computed using theassumption that the Liennard.-jones 6, 12 intermolecular potential applies. The
DO~S W3 mytWOeS*$LThucas" ~ e.Ntr/A 73 N C L S S I I E
.INTh ASczT-TrTTP
SECURITY CLASSIFICATION OF THIS PIAOE(Uum D*ta Entoted•
third virial coefficient is computed for a hard-sphere model. Appropriatemixing rules are used for intermolecular force constants and for thie virial':coefficients.%
Another valuable feature of the code is that it contains enthalpy data for 49of the ingredients most often found in military propellants and fol the 300nitroceiluloses with percentages of nitration between 11.00 and 14.00.
This report is a complete guide to the local implementation and use of the code.it contains illustrative examples of its use, and its application to theAUTOCAP exercise, and a discussion of its experimental validation.
UNCLASSIFIEDSSECURITY CLeAUSIFICATIO14 OF TXiS PA-GE("WlT6 Dot* Jr.er-WO
TABLE OF CONTENTS
Page
LIST OF TABLES ............. ..................... S
I. PREFACE .............. ......................... 7
A. Target ............... ....................... 7
B. Notation and Usage ........... ................. 7
C. Applicability of This Report ...... ............ 7
II. INTRODUCTION ......... ...................... . 7..
A. Some Background .......... ................... 8
B. Comments on Gaseous Equations of State .... ....... 11
C. Algebra of the Truncated Virial Equation .... ...... 11
III. COMPUTATIONAL AND EXPERIMENTAL TESTS OF 'BLAKE'. ..... 14
A. Comiputational Test ...... ................ .... 14
B. Experimental Test ........ .................. 19
IV. APPLICATION OF 'BLAKE' TO THE AUTOCAP EXERCISE ........ 20
V. SOURCES OF DATA ........ ..................... .. 32
A. Elements ......... ...................... ... 32
B. Product Species ........ ................... 32
C. Ingredients ............................ .. 33
VI. IMPLEMENTING 'BLAKE'........ ......... ............. 36
A. Machine-Dependent Features ...... ............. 36
B. User-Dependent Aspects ..... .................. 39
VII. USING 'BLAKE' ....... ... ...................... 39
A. Job Control Cards and the First Two Runs . . ...... 39
B. Comments on the Computation of Equilibrium byTIGER ....... ............................. 40
SC. General Remarks on the Instruction Set ......... .. 42
D. The Instruction Set ...... ................. ... 43
E. Error Messages ............. ........... . 57
4 3
TABLE OF CONTENTS (Continued)
Page
VII I. THE OUTPUT FROM 'B, iT'..................64
IX. ACKNOWLEDGMENTS ........... .................... b8
REFERENCES ................ ...................... 69
APPENDIX A ...................................... .. 71
APPENDIX B ................ ...................... 75
APPENDIX C ............ ....................... .. 99
DISTRIBUTION LIST ............. ............ . .. .125
4
LIST OF TABLES
Table Page
1 Formulations for Code Intercomparison ...... .......... 15
2 Comparison of BLAKE with NASA/Lewis .... ......... .... 16
3 Comparison Between ICT Code and BLAKE (Idnal Gas Case). . 18
4 Comparison of Results from the ICT Code and BLAKE(Real Gas Case) ......... ..................... 22
5 BLAKE Computations on Crow-Grimshaw's Propellants . ... 23
6 Vest's Experiments ....... .................... ... 26
7 Relative Force of AUTOCAP Propellants ...... .......... 28
8 Parametric Sensitivities of AUTOCAP Lots .... ......... 29
9 Variability of Ingredients in AUTOCAP M-6 ......... .... 30
10 Names and Abbreviations of the Pre-Stored Ingredients inBLAKE ....... ......... .......................... 34
AccossionFo .
N TTS GRA&I•-. ~DTIC TAB [
Unannounced ElJustif catIo
Distributi~n/
Availability CodesjAvail and/or
Dist j Special
Iwil
.IL
I. PREFACE
A. Target
This report is designed for YOU, the user, and is so written.
B. Notation and Usage
The numeral '0' (zero) and the letter '0' (oh) are easily confused.In this report, the character '0' is always the letter when it appearswith other letters, as in COM or ORD. if it appears with numbers, as in3.04 or 1.0. it is a numeral. In a few places where misunderstandingmay occur, the symbol '0' is used for the letter 'oh'. (This is standardBRL usage.)
In this report, certain names appear inside single quote marks, as'name2'. When this happens, you are to understand that it is the quan-tity denoted by the symbol 'name2' that is being referred to, not thecharacters themselves. (This is contrary to standard computer usage,but is adopted here in order to minimize the use of quote marks.)
In standard American English usage, punctuation marks go insidequote marks. In this report, however, the punctuation is placed outsidethe quote marks to decrease the likelihood of confusion.
C. ý2p1icability of This Report
Since lite 1978, BLAKE has printed a version designator oit everyoutput page. This report is specifically intended for use with version20S.0. Any change in the program, no matter how small, will be signalledby a change in version number.
In any case, the nature of the change or correction will be n, .edin comment cards placed in Subroutine VRSION. If necessary, chan•.s tothis manual will be noted there also.
II. INTRODUCTION
The BLAKE computer program is a general equilibrium thermodynamic'sprogram derived fr3m an older version of TIGER. Although it is applicableto a wide range of chemical equilibrium calculations, it is specificallyintended for computing the properties of gun propellants at.chamber con-ditions.
A. Some Background
Among the first chemical equilibrium programs that did not assumethe ideal gas equation were BKW and RUBY. They both employed the Becker.,Kistiakowsky-Wilson equation of state that had been developed earlierat Los Alamos for the computation of p-V-T properties behind detonationwraves in condensed explosives. RUBY apparently was difficult to use,'equiring considerable user supervision and intervention. To improvethis situation, the US Army Ordnance Corps' Ballistic Research Laborato-ries (now the Ballistic Rescarch Laboratory of the US Army ArmamentResearch and Development Command) contracted with the Stanford ResearchInstitute (now Stanford Research International) to develop an entireiynew code that would be much easier to use and that would permit theready insertion of a variety of non-ideal equations of state for thegaseous and condensed states. The TIGER code was the result. Sincethen. managerial oversight of TIGER has resided in a group representingthe Army, Navy, and Energy Departments. Under its guidance, the pro-gram has been significantly improved and its capabilities extended.
Originally TIGER incorporated only two gaseous equations of state,the ideal and the BKW, neither of which is applicable to gases at gun-chamber conditions. These Lre typically pressures up to 700 MPa andtemperatures between 1500 and 3000 K, too dense for the ideal gas equa-tion but not nearly dense enough for the BKW. A more appropriate equa-tion for such conditions is the truncated virial equation,
pV = nnT [1 + (n/V)B('r) + (n/V) 2 (1)
whose application to this problem was first described by CornerI.
Corner showed how the constants B(T) and C(TJ, the second and thirdvirial coefficients, could be computed once the intermolecular potentialwas known. The significance of this result is that iz bypasses the needfor measurements on the chamber gases, a complex mixture of some 10 to40 molecules, free atoms, and radicals, at elevated temperatures andpressures.
A code embodying Corner's results was written over 22 years ago inthe BRL by Leser 2 . Results obtained with it were summarized in a com-prehensive report by Baer and Bryson3 which is still a valuable referencework.
1J. Corner, "Theory of the Interior Ballistics of Guns," J. Wiley & Sons,NY & London (1950).
22. Leser, "High Speed Digital Calculations of the Composition and Thermo-
dynamic Properties of Propellant Gases by the Brinkley Method," BRL R1023(August 1967) (AD 156a161
3 P .GBaer and K. Bryson, "Tables of Computed Thermodynamic Propertiesof Military Gun Propellants," BRL MR 1338 (March 1961). (AD 258644)
8
S. . . . . . . . . :. . . .. .
Leser's program was written in assembly language for ORDVAC. Someyears later, Baer and Wortman produced a new version of the program ina high-level language called FORAST. The Baer-Wortman program is docu-mented in an appendix to a report by Stansbury and Shearer 4 . This latterprogram became a veritable work-horse within the BRL, but it could notbe exported because the explosive acceptance of FORTRAN negated the pos-sibility of FORAST compilers being written elsewhere.
When the use of FORAST was proscribed, the TIGER5 code was alreadyavailable. One of TIGER's many outstanding features is its modular design,which enables one to insert other gaseous equations of state by changingonly one subroutine. Rather than translate Baer-Wortman, it was decidedto take advantage of TIGER and thus gain the benefits of TIGER's otherattractive features. The result was BLAKE.
From a conmon origin in 1964 TIGER and BLAKE have proceeded alongseparate paths; both programs have changed so much that their 1979 ver-sions cannot use input cards prepared in 1964. The improvements inTIGER have always broadly emphasized the computation of detonation para-meters, including improved convergence, two-phase systems, and partially-frozen expansions. Consequently it remains the code of choice for de-tonation computations for condensed explosives. BLAKE has continued toemphasize gun propellants; in its present form, its original capabili-ties for computing Chapman-Jouguet parameters and Hugoniot curves havebeen deleted.
B. Comments on Gaseous Equations of State
The t.,,%cated virial equation is nowadays primarily of theore-ticalsignificance only. Practicing chemical engineers have at their disposalmany better equations (e.g., Benedict-Webb-Rubin, Beattie-Bridg-man).These equations cannot be used for propellant-gas computations becausethere is no feasible way of finding the values of their many parameters;the Benedict-Wcbb-Rubin equation, for instance, has 8.
4L. Stansbury, Jr. and R. B. Shearer, "Tables of Computed Thermo-dynamic Properties of Selected Liquid MonopropelZZ.nts," BRL R1579 (April1972). (AD 521326L)
5a) W. E. Wiebenson, Jr., W. H. Zwisler, L. B. Seely, and S. R. Brinkl.,j, Jr.,"TIGER Computer Program Documentation (November 1968);
b) M. Cowperthwaite and W. H. Zwisler, "TIGER Computer Program Documen-tation," SRI Publication No. Z106 (January 1973).
19
The significance of Corner's work is that, although the truncatedvirial equation is far from the best, it is exceptionally useful. Cornerused the Lennard-Jones 6,12 intermolecular potential function, 6
6 124(r) = 4(c/kT)[(o/r) -(a/r) ] (2)
where
*(r) = intermolecular potential;
c = depth of the attractive well;
a = distance at which the attraction vanishes; and
r = distance between two molecules.
h = Boltzmann constant, and
T = absolute temperature
The exponent 6 is dictated by theory; the exponent 12 was chosento give the best fit for second virial coefficients.
A drawback of the Lennard-Jones potential is that it is inherentlyincapable of representing the intermolecular potentials of either non-spherical or polar molecules, especially water. The Stockmayer poten-tial 7 , which adds the term - v2 G/r3 (v = dipole moment, and G = a functionof the angles that specify the orientation of the dipole in space) toEqn. (1), was developed to overcome this objeztion.
Unfortunately the situation is too complicated to be redeemed by asingle extra term. While the Stockmayer potential does give improvedestimates for B(T), it does not improve the estimates of C(I).
Numerically the contribution of the third coefficient is necessary-for loading densities greater than about 0.2 g/cm3 , but theory does notappear capable of giving adequate estimates for it. For this reason,BLAKE eschews the complications inherent in making extensive theoreticalestimates of C(T); instead, it follows an earlier re..vmmendation ofHirschfelder's 8 and computes the third virial coefficient with the as-sumption that the molecules are hard spheres with a radius equal to0.81 times the Lennard-Jones radius a.
6For a thorough discussion of gaseous equations of state and their re-lation to intermolecular potentials, see J.0. Hirschfelder, C.F. Curtiss,and R.B. Bird, "Molecular Theory of Fluids," John Wiley & Sons, New York(1954).
7See the discussion in ref. 6.
8 See ref. 6, p. 257 and pp. 262-263.
10
This decision was made early during the development of BLAKE. In1977 a coding error was discovered in this part of the code; in retro-spect, it would have been better to have changed the model from hardspheres to square wells at that time, but....
Corner's approach applied strictly only to A-A and B-B interactionsin a mixture of A and B; A-B interactions were ignored. Although it maybe inconsistent with the neglect of sophisticated third-virial computa-tions, the present BLAKE employs mixing rules for both the parametersof the intermolecular potential and of the virial coefficients. Theyare:
33 1 /2 3 [ 1/2
ij= i ] i
aij =0.5(oi + C.); (4)
B(T) = .XiXjBij; and (5)
C(T) =(XiCiii6)
In these equations, xi and xj are the mole fractions of species i and j(which may be the same), Bi. is the virial coefficient for the mixtureof gaseous species i and j icomputed using the parameters c.- and a-;and B(T) and C(T) are the second and third virial coefficiens of thetotal mixture.
Note that the mixing rule for the third viria] coefficient is simplya linear weighted sum, with all interactions ignored. This is consistentwith the use of the hard-sphere model.
C. Algebra of the Truncated Virial Equation
The insertion of a new gaseous equation of state into TIGER requiresthe evaluation of a number of expressions which are then programmed andput into Subroutine STATEG.
For reference purposes, these expressions are given here for thetruncated virial equation. The exposition is not to be considered aderivation.
The truncated virial equation is
2p = (RT/V)[I + (B/V) + (C/V)] (7)
for 1 mole of gas of volume V. Here R is the aniversal gas constant,and,! and C are the second and third virial constants.
II
A completely general equation of state is
p = nRT(p/M° (
If D = 1, this becomes the ideal gas equation of state; in general, €is a measure of the deviation from ideality.
In the general case, B and C are functions of temperature, but here,C will be assumed independent of temperature.
The vejume, V, is related to the reference mass, Mo, and the density,p, by
P = M /V (9)0
The following quantities will also be needed:
Xi :mole fraction of .
n. moles of i1
n total moles = Yn.
then.
B= = . B ji1 J 13
2= Y(n in I/n )B . (10)r 1 3i 1
C ((ni/n) C. (11)
P = nRw'//M°2
= (nRTp/Mo) [1 + (Bnp/Mo) + (np/Mo) C] (12)
The TIGER formalism requires the quantities 3P/ani, ri, alnO/alnT,3ln¢/alnp, alnD/3ni, 3ri/ilnT, ari/3Inp, ari/3n., e, and eT.
Some of these have already been defined, the others are
r.3 = 0jP[(M 0 /RTp)(ap/ani)-1]dp/p (13)
f (Mo/RTp) [p-(3p/3T)T]dp/p, and (14)
2 2C T =fJ (mT/Rp)(a p/3T )dp/p (15)
12
""hc origin ai. physical meanings, of all of these quantities are in
the '.IFk docomzention and will riot be duplicated here.
When the truncated virial equation (withi constant C) is substitutedinto these expressions, tedious aigebr.. lead's to the following equations:
2
p LnRTp/W.i )+ (r,/,i) 2 RT [nin. Bi03 i..nI
+ (P. 11) 0 ! n C. (16)2 2
ri'. (2pt )•n B. + (3/2)(P/Mo) n. C. (17)1 o g ij 1.-
1+ (./M n)yn.n.B. . + n(r/n) Yr. C. 1)
lnl/DJnT 7 W(/¢ /M o n)Inin.Bij
+ (2V'/M n)Lni Ci (19)
2lr.4/3n. :- (p/M ni,) 2 n.Bi j - ( In) J.nin BiJ
2 3(p/,1)[3ni - 1(i A) (20)
Bri/)lnl' = (2pT/M )7'n.3BBi.i•T (21)2 2
Miil;InP = ri + (3/2)(o/M ) n. C. (22)
2"-- ri/fn (/Mo),.i + (3P/M n. C.o. j] (23)
(Oi. is the Kronecker function, defined as
o.-..= 0 if i , j, . 1.) (24)
c= -(P/•l/ Ln. n 2'dB ./id'T
2 2 2
(T /M )Id . ./dT J (26)
I want to thank Arthur Cohen for checking the algebra (and findingan error), and Caledonia Henry for double-checking the algebra and check-ing the programming required to inject these equations into the code.
13
4
P1. COMPUTATIONAL AND) -.|ITRIM..TAI. 1'STS OF 'BLAKI.
A. Computational Test
The computational testing of BLAKIE has two .7. 1ect,. ,-e firsIt, wic .is readily accomplished, is verifying that the code produces The correctresults for thermodynamic computations on ideal gases. One could do thisby hand calculations but the ready availability of several well-validatedcodes makes this unnecessarily laborious. The NASA-Leis code, CEC'! 9 ,was taken to be the standard. Computations were run on it for five dilf-ferent propellant formulations. These five propellancs were chosen notas representative,, current, or typical, but mainly to ensure that thetemiperature range from 22_50 to 3890 K was covered, and that at least oneof them formed a condensed phase. Load-ing densities from 0.05 to 0.40 inintervals of 0.05 were used; some calculations at a loading density of"0.bO were also made. All calculations used the :.aime enthailpics of formaa-'tion as input.
A code developed by the Itnst itut fuer Che.n'e der Treib- und Fxil,'-sivstoffe was also run.
11"The results are described in another report 1 but it is very inac-cessible so they will be repeated here.
TI"he five compositions are shown in Table i. and tile resuits in Table2. The concordance is excellent. Additional evidence for the qualityof the agreement is found in the MIS calculations where BLAKr and CEC-Iboth predict the formation of liquid A!2O3 w•h nole fractions of 0.000124and 0.00012, respectively.
Tthe agreement between BLAKE and the ICT code is shown in rable 3.it is also very good, bat not quite so perfect as between NASA-Lewis andBIAKE. The reason likely is in the thc'rmodvnamic data selected for theproduct.s.
"S• r *odon ,zn- B. J. !c"..,e, "C .. o.ut.er ?oarari for ""....t J:'"n',,u"4Cx :hem,-cal -uiiU-b.-ix Crnoosi-ons. NASA :P-27' ,
!O u~ot< and h.* Bathkelt, "Ar Zi-ation o" the Viria" -u.ate in Cj L- ' tino -,'z te~ior0 3--is c Qzuarti*tiee Proe' -Z-tczr ts ai,!osIves 1. 7-14 (1976)
P-.i~eedws, "An in tercovivii-ison o-j West- ,'cr:-n and 5,S Plovel~nTh'werodyr1 .rn>- Codes," in ,lenLý of Presentations It the 25-28 A44r-11978 Meet of' the R aUd US Personnel Aenooiated with DEA o060, n .lB-V-lit (Ap~ii D?9?).
14
In-
0 Lf. tf n
1 4m 0 ) 00
00-
00
000 0--0 00
I *n re 0
'IT - *r4 V)
1-0.
CA00
ýr - n 00 C
- &flt~ -4 0 00
0
0))
ot C0)o
000 .,4 ~ ~0. ~
41~
o -4
u ~ ~ ~~t' 0'.C z u 9. 1C'z 0 z ' LM w 0 W ~
~O I 00 ~ I 0' a 0'. LI.is.
I! I
tI Ct: ' 0 0 0
E-2.ý 8fn '0I-r I r" Itn 11 n It
0101C1 080 0: ' 1 1
* * *
c.8 * 1 , " I "1 . In * I * I *
LON-m G L oIra 00 Ln C c 00 t.- OD
C- 1- ~ Tt -4-nT * Ln in4 %0 -- un t -
on 00ML o o0 0 % 0I
.416
Although they employ different fittings for them, BLAKE and CEC71both use virtually the same numbers from the JANNAF Tablesl 2 ; it is notclear which data were used in the ICT calculations.
Also, I have occasionally made spot checks of BLAKE runs against thenew TIGER code; here, too, the results are in excellent agreement.
It is concluded that BLAKE gives consistently accurate thermodynamicresults for the ideal gas case.
1The non-ideal gas case is more difficult to test because there isno generally-accepted standard code that can be used as a standard. Thebest that one can do is to compare one code against the other. The resultsare in Table 4. The agreement is surprisingly good, especially whenone considers the difference in approach between them. The maximum dis-crepancy in pressure does not exceed 3,5%, and that occurs at a loadingdensity of 0.6 g/cm3 , a figure that approaches the density of someliquids! The column labeled (P gives the ratio of the computed pressureto the ideal-gas pressure for the same conditions. At a loading densityof 0.6, 4 is 2.1; that is, the correction factor for the ideal pressureis 110%.
Klein et al.13 have proposed a new equation of state specificallyfor ballistics. Their treatment includes a term for the interactionbetween water and carbon dioxide, a specific interaction that is ignoredin BLAKE. It will be interesting to see the magnitude of the change thatthis equation will produce in ballistic calculations; unfortunately, in-serting the equation into BLAKE has turned out to be far from a routinematter 1 4 .
122D. R. Stull and H. Prophet, Eds., "JANAF Thermochemical Tables,"
2nd ed., NSRDS-NBS 37 (June, 1971); also looseleaf revisions and additionsfrom the Thermal Research Laboratory, The Dow Chemical Company, Midland,141 (M. Chase, Director).
E. G. Powell, G. Wilmot, L. Haar, and M. Klein, "Equations ofState and Thermodynamic Data for Interior Ballistics Calculations,"in H. Krier and M. Sutnmerfield, Interior Ballistics of Guns, Progressin Astronautics and Aeronautics, vol. 66, AIAA, New York (1979).
1 4 M. Klein. (National Bureau of Standards), private communication toE. Freedman. Febiuary 1980.
17
TABLE 3.
COMPARISON BETWEEN ICT CODE 6 BLAKEIDEAL GAS CASE
Name Temperature (K) Pressure (MPa) Impetus (J/g)ICT BLAKE ICT BLAKE ICT BLAKE
One
0.2 2265 2270 173.6 174.0 867.8 870.0
0.4 2284 2290 347.6 348.5 869.0 871.3
0.6 230t. 2311 522.2 523.7 870.3 872.8
Two
0.2 2558 2560 197.4 197.5 987.2 987.6
0.4 2563 2564 394.6 394.9 986.6 987.1
0.6 2568 2568 591.6 592.0 986.0 986.5
Three
0.2 3220 3223 221.8 222.0 1109. 1110.
0.4 3229 3232 444.2 444.7 1111. 1112.
0.6 3233 3236 666.7 667.6 1111. 1113.
Four0.2 3816 3814 235.7 235.7 1178 1178.
0.4 3865 3865 475.5 475.7 1189 1189.
0.6 3890 3891 716.4 716.9 1194 1195.
Five
0.2 2600 2609 192.4 193.1 962.0 965.5
0.4 2604 2613 384.6 386.1 961.6 965.3
0.6 2608 2617 576.7 579.0 961.2 965.1
"18
Pending this development, one can take some comfort from the agreementbetween ELAKE Pnd the ICT code; it would be indeed surprising if both codeswere wildly wrong. In my opinion, the agreement mostly shows the pzo-fundity of Hirschfelder's insight 8 of years ago: the computations areinsensitive to the differences in models in the range of temperaturesthat is ballistically interesting.
B. Experimental Test
The over-all conclusion must be that BLAKE results are worthy of cre-dence, but the desirability of experimental confirmation is not thereby"lessened. The principal difficulty with such a test is the determinationof the true uquilibrium pressure, the maximum pressure that would bereached in a closed bomb if there were no heat loss. This heat loss causesa drop in the measured pressure. In 1931 Crow and Grimshaw15 publishedan important paper which reported such an attempt. Their pioneering worknecessarily had to use a simplified model of the heat loss mechanism inorder to achieve results. A decade later Kent and Vintil6 commented thatthe thermodynamic calculation of the equilibrium temperature was theore-tically more sound; they used this temperature in a new model of heatloss and were thus able to compute a corrected pressure. All later workershave followed this lead.
In 1953 Vest17 reasoned that heat loss in a closed bomb should de-crease with surface-to-volume ratio. fie made measurements in bombs con--taining added metal pieces and then computed a corrected pressure byextrapolation of the measured pressures back to a surface-to-volume ratioof zero. Vest's compositions are listed in Appendix A.
Table 5 presents the final pressures computed by Crow and Grimshawfrom their measurements and the pressures computed with BLAKE for theircompositions. These compositions are also listed in Appendix A. Thesecalculations were made without considering the contribution of the ace-tylene/air igniter that was used, which would add 0.2 MPa or less to theresults.
1 5A. D. Crow and W. E. Grimshaw, "The Equation of State of Propellant
Gases," Phil. Trans. Roy. Soc. A 230 30 %1931).
16R. H. Kent and J. P. Vinti, "Cooling Corrections for Closed Chamber
Firings," BRL R 281 (September, 1942). (AD 492852)
17D. Vest, "On the Transfer of Heat in High-Pressure Combustion Chambers,"unpublished M. S. Thesis, The Johns Hopkins University, Bcalr..,rnore,Ma2yland (1953).
19
SThe agreement at loading densities above 0.07 g/cir3 is aý good as
one could ask. Crow and Grimshaw themselves noted that their treatmentof the heat loss was questionable at the lower densities. Also, Ypntand Vinti's correction is much larger in that region; their correctionis much smaller at the higher densities, and their final pressures arteonly slightly lower than Crow and Grimshaw's.
Vest's results are shown in Table 6; they are much less extensivethan Crow and Grimshaw's. The table also gives the BLAKE results. Theagreement is good only at the loading density of 0.15. The poorer agree-ment at the two lower densities may indicate a failure of Vest's model.
The present state of the art in closed-bomb experimentation makesit easier to conduct experiments at even higher pressures than thoseused by Crow and Grimshaw. Such experiments should certa:nly be under-taken; also, the Crow-Crimshaw treatment at higher loading densitiesdeserves another look.
IV. APPLICATION OF 'BLAKE' TO THE AUTOC:AP EXERCISE
An excellent example of the utility of BLAKE ;s given by its appli-cation to the AUTOCAP exercise. One of the purposes of this exercisewas to determine the effects of variation in composition on the perfor-mance of propellants. To this end, many lots of M-6 propellant weremade with deliberate changes from the accepted specification. Amongnumerous other properties, the impetuses of these lots were determined;also, the impetus of a reference lot of M-6 was measured. The ratio ofthe measured impetus of a lot to the measured impetus of a standard orreference lot is called the relative force (RF).
Table 7 gives the measured and computed impetuses and the corre--sponding relative forces. The average deviation of the 9 lots is 0.6with a standard deviation of 0.7. This means that the mean deviationis not significantly different from zero. This calculation has not beenattempted with another code; it would be interesting to do so.
Another interesting and useful application of BLAKE is the computa-tion of the effect on the impetus of small changes in composition or ofingredient properties. This quantity can be called the parametric sen-sitivity to distinguish it from other sensitivities (e.g., ignitionsensitivity) to which it is unrelated.
Mathematically this quantity is ýP/aQ, which can be approximatedby AP/AQ. Here, P is a thermodynamic property such as impetus, maximumprussure, temperature, or ratio of heat capacities, and Q is the amountof an ingredient or a property of an ingredient. Thus one can calculate
20
the rate of change of maximum pressure with respect to the amount ofdinitrotoluene, or the rate of change of the ratio of heat capacitieswith respect to the heat of formation of nitrocellulose, etc.
The partial derivative notation implies that all other constituentsare kept constant. This --.nnot actually be so, since it is only percen-tage composition that counts. Hence the partial derivative must be com-puted with the additional constraint that the sum of all of the constit-utents is a constant. In computing AP/tQ, the effect of the change inQ on the other constituents was in every case distributed over theseother materials in proportion to their percentage in the original formu-lation.
Since impetus or maximum pressure cannot be readily expressed as afunction of composition in closed form, the derivative 3P/aQ must beapproximated by a discrete formula. The simplest correct one is
P/aQ = (1/2h) [P(Q + h) - P(Q - h)], (27)
where h is a small increment in Q. This formula approximates the deri-vative at the given value of Q. In order to decrease the amount of com-putation, the simpler but les3 correct formula:
,P/aQ = (1/h) [P(Q + h) - P(Q)) (28)
was used. The increment h was generally chosen to be a convenient size,generally 10% of the V ise value of Q.
The results of the computations are given in Table 8. The sig-i1 nificance of these numbers is best seen by looking at the last columns
of this Table. It gives the approximate percentage change in impetus,F, or y that would oe brought about by a one percent change in that ingredient.In the case of the nitrogen content, the number is the percentage changein F for a change of 0.01 in the percentage of N.
Increases in either the amount of NC or the fraction of nitrogenin the NC cause an increase in the impetus; addition of all the othercomponents causes a decrease. The reason for this is clear: increasingeither NC or th. fraction of nitrogen increases the energy of the pro-
' pellant, hence the positive sign. Addition of the other substancescaused an effective decrease in the amount of NC, and hence decreasesthe impetus. Note that the magnitudes of almost all of these quantities"are not very different from each other. This also is a result of thefact that the principal effect of adding substance Q is to decrease theamotnt of NC (unless Q is itself NC).
Only th,, derivative for DNT is markedly different. This is becauseDNT is also an energetic substance, unlike the other additives. Hence,
21
44 _l
tn ~ 'JCJ NO 4 1 r - t %DO0N-Lnt
V)) :T .- 40C 0 O V)4O oonc o~.-4 0I 0A - 4C -4 r 0 C
-U 0- 0C'Li 6DI' aio 0 0 0C)O
U) 00- r- 00C) r t
L0 0'O 0 '. t)
LU -4 coc~~ C) LflC'J1
R 00 Gj 00 -4--
'-44
z cOLI)0 * -4 r- r-4 0
C14 0 *r) \* eq cl *nn ~'-4 \N0- C'J-4 r1 ~ N- 'r- -4 4
0r )r " 0t rit) L)Cr-\00 4U) L l 0 - nt
ooLUt)L 0" o( h \ D \
r1 n- Lf LU)\0 C1 O4O-j 00(M(n\-
0 0 Q)0) .*-0 oý *ý>t. .~* ~, .*
44 OO o ~ 0 O Ck 4 I.) C
22
I o i In 4 -4 cc ~ 4-4
0 - In N a) %.0 0) rN In -4 tN 01- q 't 0 N- 14 In) - r-4 Lfl N
0. -4 -4 1-4 N N CN V)
Z 0 'I N N N n %0 N1 N 0 0
:r %00 N- 04 V)& '.0 14 Nl -4
r.1 \ \0 t f V 1-4 \0 -4 -n N N N It
0.0
0 t4
Un ) Cý0k '.0 "c \0 00 '. t 0 N Nn 00)'0 N.
ul 4 L r4 - 44AC4 V
CA r- r0 00 00'0 -4 I :' I 00 1-4 -4
%D'. 00 1- in 00 CN in 00 0LU I 4 . -4 -4 '-4 C1 NVt)
00 0; 00 --rtn (
0) r40 -4 '-4 +- + + N +in+ +
z 0
ca4 -4C4 -4 - h (7 \
0 -'0.0-Ln C 0 00 \N IT \0 '0
0L r-4 +4 + +4 04 +1 re
4-4
z h00 CIS0 Nh 0-4 - 0) N 0~ O N GO0
o \0~c V) I4 N4 0 t4 '0 ý q; '.0
0 - -4 r-4 N N 4 N V)
-4
10 0 'U 0 0n N0 .n %0 '.0 IT in cctm .r-4 -4 C44 (NI N- ND Min0 C
0 d)ba 0 0 0 0 1-4 r-4 f-4 1-4 CN N4 N
23
31ý'* Oai t') q~ Ll N* ~ -4 t- N
(n 0 - r %0 \0 00 tn 0
ml In t.0) M tO I 00 -4 C% O14 r
U,00 0 \.0 10 0 0'ý C14 CAO 0
It Nl CA 10 N- 14 In e~C4 N-~ 0.-1 -4 C'4 C) ' tn tn
'I In a) 10 In Nq Il n 0 00 Nl
d\) 1 0 -4 1 0 1 - t 0 I4 '-
U) -ri'II~0 In \.0 q* fN In In In In In) t
C4 $4 o '.0 0 4 1 0 '0 a C) 1o 0 u 'S 1-'10 In N- V) r- 0 Inj CA 1') NIL .- 4 -4 C14 C14 C'4 Dr) V)In
wn tn C
Z V)co0 4 ) Ic CO0 N '- 0 It 00 '-4 N- al
U) 04 co 0; (7; '- ' O 4 '0 .z- M0 tt I- m m0 N- 4 In) m~ C) t-
o- -4 C t
.. CAD N 00 1 O V) c 4 4 -4 -
O 0 .n 14-4 C; c I
co C') In 0 CA. C' 00 \0 '0 In 00 -4
M- L10 In m 0 V) t-O N 4 In) 0CA C)0.. e4 r4 C') C' CJ 10
-4
co) a. r0 0\0 In In 0 Ic 0 C'
tn tn1 N, 0' 0 -4 In 0'. C'I N0.. (14 V') M' ' 0
aO 0 n In '0 It '0 m' (b. -4 0'.
*,q -H '0 C1) Q0 In) '0 IR ý* .- -4 NtrrCIn u C') It n N 0 W) In 00 0 C')
91. 0 0 0 0 f-4 '-4 '-4 -4 ') C') C')
24
"tn L I- It w 0 0 0 0 0
~~~~~U) L i) N tN 0N U) D % 0 -
I..,~~ ~ ~ N Li) rLi) 0 4 ID 0 V
CA N\ 00 'n 00 r- -4 Ln 0 t
J 4JZ 0) 04 0ý '-' c l N;00.- 0 i ) LI) N, 't on ) 0 LI)
'-4 N V) Li)
LLI
00 0) a)l U) L) ) N -4 i
z)c 0) '- t m t-n 00 0V0 00 1- -4 C1 t4* t
"a4 C 0 4 L'- N1 -) \0 0- \Of 1f) qU
ma - 0 ' mI N 0- 0- tn '0 0- 0 C4
o . 1'-1 V) Li) m C') 00 r) -4 '0 0 Vt)U I-4 -4 C1 N4 ViL)
000)
tf) 0 )L) LN N N) .4 00 10 \0 0)f-4 -
r- .,4 r= \0 0 0 '-; \ iNL) -
'-' M . C1 L4 N1 N V) Ln c
to 9 N 1 -4 -4 N4 -4 4 C1
o 0% Li 0 '4 0
U d~ I 2S
TABLE 6
VEST'S EXPERIMENTS
P (MPa)Vest BLAKE
Composition No. 1
P= 0.05 43.7 48.9
0.10 96.8 104.2
0.15 159.4 166.7
Composition No. 2
P 0.05 54.2 57.7
.10 117.9 122.7
".15 193.2 195.0
2
226
-ii
while adding it decreases the percentage of NC, the net decrease inpotential energy content is less because of the contribution that DNTmakes.
Knowing the parametric sensitivities is not sufficient. We alsoneed to know how closely the level of a particular ingredient can becontrolled. A measure of this control is the standard deviation ofeach ingredient in successive lots. Table 9 gives such data1 8 .
Together the numbers in Tables 8 and 9 can give an estimate of thevariance of the muzzle velocity. We consider an "ileal" gun, one thathas no energy loss due to heat conduction, engraving forces, etc., andone in which the propellant is completely burnt at shot start. For sucha gun, the muzzle velocity, V, is
V= (2cF/W(y - 1))(I - r (29)
where r is the ratio of the volume of the chamber to the volume of thegun, c/w the ratio of charge weight to projectile weight, and F is theimpetus. Variations in the components, Qi, cause variations in F andy, which in turn cause variations in V; that is,
V = V[F(Qi), Y(Qi)], (30)
where Qi stands for the amounts of each of the components. Let V° bethe average values of V. Then the effect of deviations from the averagesof the Qi can be expressed by a Taylor series:
3F 3F + 3V Q°) (3a), F 3Qi 3Y 3Qi
The variance of V is defined by the expectation of the quantity(V - V*) 2 ,
s = C(V - V) (32)
This quantity will now be calculated.
18I WW. May, (Ballistic Research Laboratory), private comwwanication
to E. F-eedman (1973).
27
F
TABLE 7
RELATIVE FORCE OF AUTOCAP FROPELLANTS
Lot RF RF Deviation
Measured Computed
A 100.98 100.25 -0.73
B 102.03 100.34 -1.69
C 100.72 99.72 -1.00
D 102.05 101.0i -1.04
E 99.78 99.40 -0.38
F 101.23 101.98 0.75
G 95.26 94.43 -0.83
H 95.08 94.80 -0.28
67994 100.54 99.29 -1.25
65306* 100.00 100.00 ---
* Reference Lot
Mean deviation = -0.6Standard deviation of mean = 0.7
28
TABLE 8
PARAWETRIC SENSITIVITIES OF AUTOCAP LOTS
Variable P__ IQ
NC 3960 -0.0012 +0.013 -0.0047
DBP -6150 •0 -0.020 '0
DPA -6970 N0 -0.022 n'0
K2 So 4 -6380 N0 -0.021 v0
H2 0 -4400 N0 -0.014 ".0
ETOH -5470 %,0 -0.018 ".0
DNT -1220 +0.0018 -0.0039 +0.0071
% N in NC +8100 'ý0 +0.026
29
t
TABLE 9
VARIABILITY OF INGREDIENTS
IN AUTOCAP M-6
Abbreviation Substance Average Sgma
% N Percent N 13.146 0.0114
NC Nitrocellulose 84.654 0.4936
DNT Dinitrotoluene 10.137 0.4930
DBP Dibutyl Phthalate 5.208 0.1478
DPA Diphenylamine 1.009 0.0644
K2SO4 Potassium Sulfate 1.086 0.1161
1H20 Water 0.5513 0.0931
ETOH Alcohol 0.365 2.2466
30
2 n F ' y io2Iv -
n r3V BF 3V aiY 3V =f DV°0
+ 2Q.F aQ + Ty ýQ. 3y TO._+ - - y- j CQi-Qi ) (Qj _-Q (33)Th Bqunity (Qi -F Qj 2y@Q
The quantity c(Q- Qi)Q 2 is the variance of Qi, denoted s2 (Qi).The quantity e(Qi - Qi*) (4j _ Qj*) is the covariance of Qi and Qj,denoted by cov(Qi, Qj).
The amounts of the several ingredients are subject to random varia-tions; hence s 2 (Qi) J 0. But there is no special reason to believe thatthere is any relation between Qi and Qp it is just as likely that oneof them will decrease while the other increases as it is that both willchange in the same direction. Hence it is a reasonable assumption toset cov(Qi, Qj) = 0.
Differentiation gives
V/aF = kfI /[2V(y - 1)], and (34)
V/ay = -kFf 2 /2V(y 1)2 1 (35)
where f1 = I - ry-I, (36)
S2 = fl + (Y - 1) (In r)ry-, (37)
and k = (2gc/W)1/ 2 (38)
There results after some algebra,
2 2 = (V/2fl) 2 1 BF 2i + f22 (-ii i) s2(Qi) (39)
A numerical example is enlightening. Choose
c = 15 kg,
W = 45 kg,
r = 0.2, y = 1.253, and
F = 106 J/kg.
31
Then V = 940 m/s, and sv = 19 m/s, or about 2%. This is a significantvariation. Examination of the numbers that go into sV shows that by farthe major contributor in this case is the variability in the alcohol.
This result may appear paradoxical since the alcohol contributesvirtually nothing to the impetus. As Sherlock Holmes might have said,that is just the point. The alcohol contributes nothing; an increase inits amount must come at the expense of the nitrocellulose, which doescontribute a great deal. If the variability of the alcohol had been only0.5 (the same as NC), the resultant sV would have been 4 m/s, or about0.4%, a tolerable amount.
V. SOURCES OF DATA
BLAKE is presently dimensioned to permit the simultaneous considera-tion of 29 gases and 10 condensed phases (liquids or solids or both) atone time; these species may contairn up to 40 elements. In practice cer-tain constraints (discussed in Sec. VII) must be considered.
A. Elements
BLAKE presently considers 16 elements: C, H, N, 0, B, Al, F, Na,Ti, He, Ar, Ba, K, S, Cl, and Pb. Users may add another 24 without havingto redimension any variables.
B. Product Species
Thermochemical data for 120 product compounds (98 gases and 22 con-densed species) are included in the library furnished with BLAKE. Thedata for these compounds are taken without exception from the JANAFTables12 . They are stored in the form of the coefficients of a linearcombination of functions of T/1000 (T = absolute temperature); these co-efficients were determined by a least-squares fitting and reproduce thedata over the range 400 K - 5000 K. (See also Sec. VII C 1.)
The Lennard-Jones parameters were taken from the compilation of Reidand Sherwood 1 9 . In the many cases when no data are available, the programautomatically substitutes c = 300 K and a = 3.5 x 10-1 meter. The usercan change these default values permanently at compile time by changingthem in Subroutine LJPAR; or temporarily at run time by using the instruc-tion LJP (Sec. VII C 2).
l jeid, R. C. and Sherwood, T.K., "The Properties of Gases and Liquids,"
2nd ed., McGraw-Hill, New York (1966).
32
C. Ingredients
BLAKE contains enthalpies of formation for 349 different species ina DATA statement. Of these, 300 are nitrocelluloses with percentages ofnitration varying from 11.00 to 14.00. These data are based on a re-working of those published by Jessup and Prosen2 0 (including the correc-tion of an obvious misprint). A least squares fitting of these data gives
Ah = -1406.22 + 6231.86 f , (40)
where
] Ah = enthalpy of formation (cal/g),IS~andIa
f = weight-fraction of nitrogen in the nitrocellulose.
Nitrocellulose with 100 f weight-percent nitrogen has the empiricalformula C6 Hl1 0_x 0 S+2xNx, where x is the number of nitrogen atoms in a
monomeric unit, given by
Sx = 162.1430 f/(14.0067 - 44.9975 f) (41)
The molecular veight corresponding to this empirical formula is
1 MW = 44.9975 + 162.3430f (42)
The combination of thesp formulas with Jessup and Prosen's data gives theenthalpies of formation of all nitrocelluloses as a function of f.
The other 50 compounds are 49 of the most common ingredients used inthe formulation of solid and liquid propellants. (One compound appearstwice.) The names of these compounds and the abbreviations or acronymsadopted for thent are listed in Table 10.
As much as possible, the acronyms or abbreviations were chosen toagree with customary and traditional usage. Ethanol appears twice, oneas ALC for those who prefer the common abbreviation, and once as ETOH forthose who appreciate the subtleties of organic nomenclature.
20 R. S. Jessup and E. J. Prosen, "Heats of Combustion and Formation
of Cellulose and Nitrocellulose (Cellulose Nitrate)," J. Res. NationalB -eau of Stds. 44, 387-393 (1950).
33
S
TABLE 10
Chemical Name Abbreviation
Acetone (dimethyl ketone) ACETONAlcohol (ethanol) ALCAmyl phthalate AMYLPHAkardite 2 AKAR2Ammonium nitrate AN
Barium oxide BAOBarium nitrate BANITRBasic lead oxide PB2CO4
Carbon (graphite) CCellulose diacetate CEDACCellulose nitrate -- see nitrocellulose ---Cellulose triacetate CETACCryolite (sodium aluminum fluoride) CRYCyclotetramethylene tetranitramine HMX
(octogen)Cyclo-l,3,5-trimethylene-2,4,6-trinitramine RDX
(hexogen)
Decalin DECADibutyl phthalate DBPDiethyleneglycol dinitrate DEGDN2,2'-dinitrodiphenylamine NNDPDinitrotoluene DNTDiphenylamine DPA
Ethanol ETOHEthanolamine nitrate EOANEther ETHEREthyl centralite ECEthylenediamine dinitrate EDDNEthylene glycol EGLYEthyl ether ETHER
Glycerin GLYGraphite C
H2 0 (water) H2 0Hexogen RDXHmi HMXHydrazine N2H4Hydrazine nitrate HNHydroxylammonium nitrate HAN
34
Chemical Name Abbreviation
Isopropylammonium nitrate IPAN
Lead oxide (see also basic leaC cx-de) PBO
Metriol METRIOMethyl centralite MC
Nitrocellulose with vw.xy NCvwxypercent nitrogen
2-nitrodiphenylamine NDPANitric acid HN03Nitrogen N2Nitroglycerin NGNitroguanidine NQ
Octogen HMXOxygen 02
Pentaerythritol pentanitrate PETNPotassium nitrate KNPotassium sulfate KSPotassium tetrafluoroborate K;!F4
RDX
Sodium aluminum fluoride CRY
Triacetin TRIACTriaminotrinitrobenzene TVBTriethyleneglycol dinitrate TEGU.NTrimethylammonium nitrate TMAN
Unsymmetrical dimethyl hydrazine UDMH
Water H20
3S
IThe formulas and enthalpies of formation of these ingredients are
listed in Appendix B. Wherever possible they were taken from the author-itative compilation of Cox and Pilcher 21 . Data for the inorganic com-pounds were taken either from the NBS compilation 22 or from Lange'sHandbook 2 3 .
VI. IMPLEMENTING 'BLAKE'
A. Machine-Dependent Features
BLAKE is written almost exclusively in the extended set of AmericanNational Standard FORTRAN. There are six functions and one feature init, however, that are system- or computer-dependent. These functions(CLOCKS, SECOND, DAY, ENCODE, DECODE, AND EOF) are used only in conveniencefeatures and can be readily omitted. The machine-dependent feature, wordlength, may cause a little more work.
1. Clock.
It is desirable but not essential that the program be capable ofobtaining the current time from the system clock. As furnished, the pro-gram contains Subroutine CLOCKS(T). This subroutine returns the time inseconds from the previous midnight. BLAKE obtains this time from a systemfunction named SECOND(T).
2. Date.
It is desirable but not essential that the program be capable ofobtaining the current date from the system clock or calendar. As furnished,the program contains Subroutine DAY(IDAY). IDAY is an array of 20 alpha-numeric characters that is later printed using a format of 20A1. BLAKEinserts the current date in the first 12 places, and blanks in the other8. It does this using the machine-dependent functions ENCODE and DECODE.If you want this feature, you will have to make appropriate implementationsof these functions.
21 J. D. Cox and G. Pilcher, "Thermochemistry of Ctrganic and Organo-metallic Compounds," Academic Press, London (1970).
22D. D. Wagman, et al., "Selected Values of Chemical Thermodynamic Proper-
ties," NBS Techrnical Note 270-3, Washington, DC (1968).
23J. A. Dean, ed., "Lange's Handbook of Chemistry," 12th ed., McGraw-
Hill, New York (1979).
36
3. EOF.
It is convenient but not necessary to check for the occurrenceof an end-of-file mark in the input. BLAKE does this in Subroutine CARDRDafter each READ instruction by use of the CDC function, EOF(LI), whereLI is the logical unit number of the input device. You will probably haveto change it for your particular computer.
The standard FORTRAN-77 statement
READ (unit, format, END=435)
is already in the program as a comment card. If your computer will rec-ognize it, by all means use it.
4. Word Length.
TIGER, and hence BLAKE, proceed by interpreting a serie3 of in-structions. The detailed form of these instructions is given in SectionVI; here it is only necessary to note that each separate field in an in-struction is converted by the program (in Subroutine CARDRD) to a realnumber containing from 2 to 12 digits (2 digits per character). Furexample, the symbols4 P, H20, 17E-3, ana K2S04$
become
30., 220229., 0107191303., and 250233290447.,
respectively. Some of theýe numbers are used as such; others, such as2202Z9 ('H20') are eventually converted back to their original alpha-numeric form for printing. The conversion routine, Subroutine CONVRT,starts by converting the real number into integer form. Depending onthe number of characters permitted, the routine may have to handle from6 to 12 digits without the loss of even the least significant digit.
CDC computers can handle 12 digits without any loss, so BLAKEis set to accept 6 characters in Subroutine CA.DRD. Most other computers
cannot handle more than 8 digits (4 characters) and hence require changesin CARDRD.
The change is simple. Line 100 currently reads
IF (IFLAG - 6) 270, 280, 290
All that is needed is to change the '6' to a '4'. If your computer canonly handle 6 or 7 digits, the '6' becomes a '3'.
37
Also, two change- are required in Subroutine LIBRAY. First, the line
immediately after statewent 1010 which now read3
IF (STR(J,2) - 3400000000.) 1020, 1020, 1060
must be changed to
IF (STR(J,2) - 30000000.) 1060, 1060, 1020
Secondly, the line immediately after statement 1120
IF (STC(J,2) - 3400000000.) 1140, 1140, 1130
must be changed to
IF (STC(J,2) - 30000000.) 1130, 1130, 1140
Two changes are needed in Subroutine BLAKEM. Statement 390 containsthe number
2318201526.
it must be changed to
231820.
Statement 420 contains the number
362332231526. ;
it must be changed to
362332.
Finally, changes will be needed in the library itself.
1. The words SOLID, LIQUID, AND CONDEN must tc changed to SOLI,LIQU, and COND, respectively.
2. Many of the constituents in the library have six-characternames; these must all be changed to four characters each. Be careful whenmaking the changes to note two things:
a. All names must be unique; it is regrettably easy to in-troduce duplicates when shortening the existing names.
b. If possible, make the changes with a computer editor.Some of the names may occur 14 times; it is so very easy to miss onemanually.
38
r
B. User-Dependent Aspects
There are some tiings in BLAKE that are matters of user- or installa-tion-preference, such as the designation of input and output units.
1. The input and output units for BLAKE are named symbolicallyLI and LO everywhere, with three exceptions. LI and LO are set equal toS and 6, respectively, in the main program. The three exceptions occurin Subroutines DVDINT, MATINV, and TICTIC, where the WRITE unit is ex-plicitly named unit 6. You may need to change these designations.
2. The program forms and then uses a binary file on unit LIB, whichis set to 7 in the main program. Again, you may prefer a different"number.
3. Tr• units for input quantities in BLAKE are:
energy: calories;
temperature: Kelvins;
density: grams per cubic centimeter;
pressure: atmospheies.
These units can be readily changed by altering one or more of the con-stants PCON, VCON, TMCON, TACON, and HCON in the main program. Theseare used throughout the program as conversion factors for pressure,volume, temperature (two factors), and energy, respectively. They arenow set to I.0, 1.0, 0.0, 1.0, and 1.0.
For example, if you wanted to change input unics from caioriesand Kelvins to joule5 and degrees Fahrenheit, the following changeswould be made before compiling the program:
HCON = 4.184,
-INCON = 0.555556, and TACON = 255.375.
VII. USING 5Bi.AKE'
A. Job Control Cards and the First Two Runs
All job control cards, system cards, or their equivalent, are theresponsibility of the user.
In what follows, it will be assumed that the program has been com-piled and loaded without error, The very first time the program isexecuted, it is necessary to form the binary library that will there-after be used in every run. Appropriate job control instructions
39
must be supplied to assign a file for this library, which the programassumes will be on unit 7, although you can readily change this assign-ment. (See Section VI.B)
The BLAKE library, which is supplied along with the program, is theinput for this first run. The output produced consists of the binarylibrary on anit 7, and a human-readable output on the chosen output device(unit 6 unless you have previously changed it). This latter output shouldbe carefully scrutinized for error messages, which will be the first partof the output. Assuming that all of the necessary changes described inSection VI were made prior to this run, there should not be any errormessages from the operating system at this point. There may, however,be error messages from the program calling attention to problems withthe library. The most common one is TWO OR MORE CONSTITUENTS HAVE THESAN1E NAME, which will occur if the reduction of the names of productsto four or fewer characters was not done carefully.
Following the error messages (if any) will be a complete listing ofthe library in human-readable form. It should be painstakingly readto guard against unexpected problems (garbaged names, for example).
If it looks good, then you are ready for the second run, which willconsist of the test cases also supplied with the program. Before run-ning them, it is necessary to insert control cards that will assign thebinary library formed in the previous run to unit 7.
The output from the test cases should be compared with the listinggiven in Appendix C of this report. Further discussion of the outputis given in Section VIII.
B. Comments on the Computation of Equilibrium by TIGER
In order to shorten the discussion required for some of the instruc-tions, a few comments are required on the philosophy of TIGER's calcula-tion of the equilibrium state. The discussion will be entirely qualita-tive; the complete technical details are in the TIGER manualsS.
TIGER proceeds by considering at first only the gaseous constituentsthat are chemically-possible Droducts of the specified mixture. Conden-sed phases are usually (not :i:s) considered later if necessary. Ateach step the program tries to work with a set of N linearly-independentconstituents that are present in the largest amounts, where N is thenumber of different elements present in the mixture. These N constituentsare called the 'components'. Mlost of the computing time is spent lookingfor the correct set of components, which may change with conditions,(e.g.,pressure or te 'eriture) even while computing a single composition.
40
In theory but not in practice the program could permute all of theconstituents present until it finds the components. The first attemptat finding the components consists of selecting the first linearly-inde-pendent set of constituents as they are retrieved from the library tape.This order was determined at the time the library tape was created andwas based on the order of the CONstituent cards. For the elements C,H, 0, and N, the components usually turn out to be COi, H20, N2 , and CO,which are therefore the first four constituents in the BMAKE library.See also the discussion of the instructions ORDer and ORC in Section VIIC 2.
If the first selection of components proves to be wrong, the programdoes some permuting among the constitutents. Since one knows chemicallythat some of the constituents will rarely if ever be present in largeenough concentrations to be components, the program makes provision forskipping them. Constituents that are never to be considered as componentshave an asterisk (*) punched as the last field in their CONstituent in-struction (See Section Vil Cl). Wh•en the program prints the list of con-stituents selected, those that cannot be components are all printed afterthose that will be. The dividing line between these two groups is calledthe 'floor'. You have the capability of raising or lowering the floor;see FLOor in Section VIi C 2).
BLAKE is presently limited to considering a maximum of 29 gaseousconstituents for any one composition. Error message No. 31 is printedif more than 29 gaseous constitutents are selected, and the case is re-jected.
The library contains thermodynamic data for a wide range of species.Consequently, compositions with five or more elements can readily havemcre than 29 constituents chosen by the program and thus will not run.This potentially embarrassing problem is solved by the REJect instruction.(See Section VII C 2).
Convergence is materially aided if you have advance knowledge of themajor constituents in the equilibrium composition. Such knowledge isoften obtained by running the same composition with another code. TheNASA-Lewis equilibrium code is recommended for this purpose. The NOTS
code used at the Naval Weapons Center also works well.
The NASA-Lewis code has the unsurpassed advantage that for a givencomposition, it can consider all of the chemically-possible species con-tained in the JANAF Tables. Thus, one can run an obstreperous formula-tion (ene containing more than six elements) with this code first, deter-mine the significant constituents, and then use this information todetermine REJect, ORDer, and ORC instructions for a subsequent BLAKE run.
41
C. General Remarks on the Instruwtion Set
BLAKE, like TIGER, proceeds by executing one by one a set of instruc-tions; the BLAKE set contains 37, of which a third are truly essential,a third serve to change default values of diverse parameters, and a thirdare frankly frills, intended to modify, expand, contract, label, title,or comment on, the output.
To a considerable extent the actual order in which the instructionsare entered by the user is immaterial. Logic, to be sure, demands thatsome orders precede others: a heat of explosion cannot be computed untila composition has been specified; but a title, for example, can be enteredlate or not at all, as you please.
The language of the descriptions of these instructions generallyassumes that they are created by being typed into an input file froma terminal, but they can just as well be entered from punched cards.
Each instruction consists of a key word or abbreviation followedby a variable number of fields containing keywords or numbers. Eachfield is set off from its neighbors by commas. The key word or abbrev-iation for the instruction itself must appear in columns 1-3 of theinstruction; otherwise the fields are arbitrary in both length and place-ment in the line.
When numbers are required in an instruction, they may be typed infree form. Thus, 69, 69., 69.0, 0.69E2, and 0.0069E04 all representthe same number in an instruction. The program decides eventually whetherit needs a real number or an integer and takes appropriate action.
The general form of an instruction is:
INStruction, PAR1, nl, PAR2, n2, PAR3, n3, . .. , (PARm, nm)
Names or letters in CAPITALS must be typed just that way; no variation ispermitted. Lower-case letters are added to some of the instruction namesfor mnemonic reasons, but are not part of the instructions name and maybe omitted. Thus, FOR, FORmula, and FORmulas are all interpreted as thesame instruction and all are valid. The comma marks the end of thisfield and separates succeeding fields from each other. In a few cases,double commas with at most blanks between them have a special significance;their use is explained in the applicable instruction.
The quantities PAR1, PAR2, PAR3, ... , represent key words or lettersand must be typed just as given for each particular instruction. Thequantities 'nI', 'n2', 'n3', ... , represent numbers that are associatedwith the keywords or parameters and may be typed as desired or needed.
42
Sometimes the parameters must appear in a specified order; othertimesorder is immaterial. When the order may be varied, this is so stated;if not, assume that the items must appear in the given order.
The ellipsis, ... , indicates that a variable number of items maybe entered. Names in parentheses are optional, as noted for individualinstructions.
D. The Instruction Set
1. Library Instructions. The library instructions are CONstituent,ELEment, PRInt, STC, STG, STR, and END. These instructions are used toform the binary library and are understood by the program only while thatoperation is proceeding. This operation in turn starts with the instruc-tion, STArt of library, which is thus not a library instruction, but whichhas no other purpose.
CONstituent, name, GAS, el, nl, e2, n2, e3, n3,
or
CONstituent, name, CONDEN, el, nl, e2, n2, e3, n3,
This library instruction defines 'name' as the official name ofa constituent. One of the parameters GAS or CONDEN (for condensed) mustappear. The quantities 'el', 'e2', etc., are the symbols of the elementsthat appear in 'name', 'nl', 'n2', etc., are the numbers of atoms of thoseelements respectively. Note that a condensed constituent may appear ineither the liquid state, the solid state, or both.
A ELEment, sym, atwt
This library instruction defines 'sym' as the official name of anelement whose atomic weight is 'atwt'. No constituent name will beaccepted by the program unless all of its constituent atoms appear inELEment instructions.
Note that if the element itself is to be allowed as a constituent,it must also appear in a CONstituent instruction.
Examples:ELEment, NA, 22.98997
CONstituent, NA, GAS, NA, 1
If the latter instruction were omitted, then sodium could appear asNaOH or NaG, etc., but not as the monatomic gas, Na.
43
END of Library
This instruction marks the end of the library deck. It must appear.As soon as it is read, the program then proceeds to sort the library cards,form the binary library tape (or its equivalent on the disk), and writesthe library listing (unless the latter is suppressed). Note that libraryinstructions may appear in any order between STArt and END; the programsorts them after the END card has been read.
STC, name, SOLID, 1, a!, a2, a3
STC, name, SOLID, 2, a4, aS, a6
STC, name, SOLID, 3, a7, a8, a9 (and similar forms for LIQUID)
The STC instruction supplies data for the equation of state of acondensed substance, either LIQUID or SOLID. The order of the cards isimmaterial, but all three must appear; if not, all of the numbers areskipped. (This will eventually lead to a run-time error, when the programtries to take the reciprocal of 'al'.) The three coefficients must appearin the correct order on a given card, however.
The coefficients themselves belong to the empirical equation
2V = A' + A2P + a3P (43)
where V is the molar volume of 'name', and the A. are given by1
A1 2 I + a2T + a3T , (44)2
A = a4 +aT+ a6T , and (4S)
A3 a7 + a8T + a99 T (46)
Here, P and T are pressure (atmospheres) and temperature (Kelvins);the ai are represented by the 'ai' in the instruction. It is unlikelythat all 9 coefficients will be known for many materials, but zeroesmust appear on the cards for all missing coefficients.
STR, name, GAS, 1, bl, b2, b3
STR, name, GAS, 2, b4, b5, b6
STR, name, GAS, 3, b7, b8, b9
These instructions introduce the thermodynamic data for 'name' intothe library. LIQUID or SOLID may appear instead of GAS. If a substanceforms only a liquid (solid), then the instructions for solid (liquid)are omitted for that substance.
44
The coefficients, 'bi', are related to the heat capacity at constantpressure, C, enthalpy, H, and entropy, S, by the empirical equations
C = 1 + b20 + b302 + b4E3 + b 5 /0 + b6 /02 + b7 /03; (47)
S = R(blln(O) + b 2 0 + b3 0 2/2.0 + b403/3.0 - b5 /0 - b6 /2.002 -
67/3.002 ); and (48)
H = [RT(b 1 + b 0/2.0 + b 3 0 2/3.0 + b4 0 3/4.0 + bsln(O)/0 -22
b6//0 - b7 /2.003) + b 8 - AH°(298.15)]/1000.0 (49)
Here,0 = T/1000,
R is the gas constant, 1.98717 cal/mole-K, and AH*(298.15) is the standard
enthalpy of formation.
These coefficients are obtained by applying least-squares techniquesto suitably-selected data, preferably those in the JANAF Tables 1 2 .BLAKE is furnished with a library containing data for 98 gases, and 22condensed phases of 16 elements. Users desiring additional data must dotheir own fittings.
PRInt the Library
This instruction creates a listing of the library on output unitLO. The listing is not printed unless this instruction is entered. Itmay appear anywhere between STArt and END. The library listing is orderedaccording to the order of appearance of the CONstituent instructions andis formatted for human reference. A copy should be made every time thelibrary is changed.
STG, name, coy, T, t, S, s
This instruction differs from the STG instruction of TIGER. Here,'name' is the legal name of a gaseous constituent as defined by a CON-stituent instruction. The quantity 'coy' is the BKW covolume of thissubstance (not to be confised with the covolume used in the Noble-Abelequation).
The quantities 't' and 's' are the two Lennard-Jones parameters,the well depth and the molecular diameter. The key letters T and S maybe replaced by either E or D, respectively, ind their order may be inter-changed. Of course, 't' and 's' must be associated with the proper keyletter.
45
It is sufficient to supply only the BKW covolume, but if one of theLennard-Jones parameters is specified, then so must the other; if not,neither one is accepted.
1 2. Computational and Control Instructions. The instructions arelisted in alphabetic order by their three-letter key.
Io•! CHOose, namel, name2, name3,
Example:
CHO, C02 ) H20, N2, CO, NH3
This instruction forces the program to consider only the named con-stituents as possible products of an equilibrium calculation. The nameslisted must be constituent names in the library. The use of this instruc-tion is recommended only in special cases.
CM2
See the discussion under COMposition.
CMT (message)
This instruction prints the word COMMENT followed by the 'message'you have typed, all on one line. It is convenient for adding notes tothe output.
Example:
CMT this is a comment card.
COMposition, namel, al, name2, a2, name3, a3, ... , (MOLE)
This instruction defines the composition of a mixture. It is anessential instruction, as all of the computational instructions are auto-matically rejected if they occur before a COM instruction.
The names 'namel', 'name2', etc., must have previously been de-fined by FORmula instructions; otherwise, the entire instruction is re-jected. The quantities al, a2, ... , are the relative amounts of eachsubstance. The order of the names is immaterial, but the correct amountmust follow each name. The amounts need not be percentages; any basisis acceptable. Regardless of how you enter the composition, however,the program will normalize it and print it in both weight-percent andmole per cent.
If you prefer to enter your composition data in moles, the keywordMOLE must also be typed.
46
All of the data must fit into one 80-column line. If this is notfeasible, use the instruction CM2 instead of COM. You may then extendthe input data over two 80-column lines. Do not repeat CM2 at the startof the second line. The MOLE designator does not apply to CM2.
Examples:
C0M, NC1325, 75, NG, 25
COMPOS, N2, 4, 02, 1, MOLE
DATe (message)
The separator (,) is not needed by this instruction. The date ofthe run is normally obtained from the operating system clock and printedon each output page. If you have trouble in obtaining this information,or if you want to print your own date, this instruction takes the last20 characters from 'message' and prints them in place of the system date.If the 'message' is blank, the system-produced date is omitted and nothingreplaces it. Once DATe has been used, you cannot return to using thesystem clock in the same run.
The regular use of this instruction is not recommended if you haveaccess to the system date. The primary purpose of the instruction is tomark special days, like one's birthday, Halloween, Friday the 13th, Bands-men's Day, etc.
Example:
DAT Fourth of July
DEBug, n
If 'n' is not 0, the debug feature is turned on; if zero, it isturned off if it was on.
The 'debug' feature was taken over from TIGER, where it was introducedfor assistance in developing Subroutine ECOMPO. When turned on, it printsthe current temperature, pressure, volume, entropy, and energy, the cur-rent mole numbers, and the current corrections to the mole numbers oneach pass through ECOMPO. In my experience it is not presently useful,and will be removed from later versions of BLAKE.
DEStroy
This instruction negates the effect of a RETain (which see) instruction.
ECHo, n
47
This instruction makes the program print out ('echo') each instructionas it is encountered. The feature is turned on when 'n' is non-zero, andturned off when 'n' is 0.
EXPlosion, V, vol, (EOF, e)
This instruction executes a constant-volume (isochoric) burning cal-culation on a previously-defined mixture. The specific volume, vol, is incubic centimetres per gram unless you have changed the volume conversionfactor (see Section IV B). Normally, the energy of formation calculatedfor the composition is used; if you want to use a different one, it isentered as e.
Example:
EXP, V, 5
EXl, P, p, T, t
This instruction is the same as EXP, except that it is for a gaseousmixture at pressure p and temperature t. The ideal gas law is used tocalculate the volume and then EXP is called automatically. The initialenergy cannot be changed.
Example:
EXl, P, 2, T, 298.15
FLOor, n
This instruction sets the level of the floor at n. See the initialdiscussion in Section IV. Sometimes, when you are having a lot of troubleforcing a particular computation to converge, it helps to raise the flpor(that is, make n a smaller number than the program value). Sometimes itdoesn't help. Once a new floor has been set, it remains at that valueuntil either a new COM or a new FLO instruction is entered.
FORmula, name, enth, elel, nl, ele2, n2, ele3, n3,
This instruction defines 'name' as the name of a reactant species;its enthalpy is 'enth' and its formula contains nl atoms of element 'elel',n2 atoms of 'ele2', etc. The symbols used for the elements must be exactlythose that appeared on ELEment cards when the library was formed. Theenthalpy of formation is entered in calories per gram-mole, not caloriesper 100 grams, and not kilocalories per mole.
In keeping with the TIGER and BLAKE conventions for put'king numbersin instructions, the numbers nl, n2, ... , may be typed in any way. Theprogram uses them as real numbers, so decimal fractions are accepted andused correctly. When the program goes to print the formula, however,
48
these numbers are converted to integer form by truncation, so that decimalfractions will not be printed properly, even though the program used themcorrectly. This causes trouble with polymers, since their formulas rarelycontain integer numbers of atoms. It is customary for polymer compositionsto be specified in units like gram-atoms per hundred grams, and with acorresponding enthalpy, but BLAKE does not accept such input data. Suchdata are easily converted to molecular formulas, but the numbers of atomsgenerally come out to be decimal fractions. This creates a small butannoying problem, since one usually prefers to have the correct formulasprinted for the input. The simplest solution is to multiply the formulasand the associated enthalpy by either 1000 or 10000.
For y, r convenience, the formulas of many common ingredients ofUS propell.ats are stored in the program, and need not be entered on aFORmula card. The names and abbreviations o2 these substances are listedin Section V.
If a FORmula instruction is mistyped, or if a duplicate formula nameis entered, the instruction is rejected and an error message is printed.If you wisi to use a different enthalpy for a substance whose formulais prestorei, you must enter a FORmula instruction for the material witha different name; the same name cannot be redefined without changingthe program and then recompiling it.
A maximum of 50 additional formulas is permitted; if you try to
enter more, they are rejected, and an error message is printed.
Examples:
FOR, DZS, -280E3, C, 18, H, 34, 0, 4
FOR, PG, -4E7, C, 4000, H, 5000, 0, 100
FREeze
Most calculations are carried out with the assumption of totaldynamic chemical equilibrium. The FREeze instruction 'freezes' allchemistry, so that all following calculations are done on a mixture ofnon-reacting gases. See also MELt.
GEO, name
Change the Gaseous Equation Of state to one of the following:
Equation of State Keyword
ideal IDEAL
truncated virial VIRIAL or LJ
B-K-W BKW
49
The default equation is the truncated virial equation. If 'name' is
mistyped, the program defaults to the truncated virial.
ixample:
GEO, VIRIAL
GRId, CENTER, P, np, ip, np, V, vl, nv, v2
or
GRId, CORNER, P, pl, ip, p2, V, vl, iv, v2
This instruction computes chemical equilibrium at a grid of pointscentered about, or cornered at, a specific point. The computations maybe done for various combinations of thermodynamic variables:
pressure, volume (P, V);
pressure, entropy (P, S);
volume, temperature (V, T);
volume, energy (V, E); and
volume, entropy (V, S).
In each of these cases, the parenthesized letters are the key lettersthat must be used in the instruction. In all cases the order must bethat given here.
The units of the extensive variables (enthalpy, energy, volume,and entropy) are specific; that is, for one gram of substance.
'pl' is the initial value of the variable (P, in this case); 'p2'is its final value. For CORNER, 'ip' and 'iv' are the sizes of the in-crements in those variables. For CENTER, 'np' and 'nv' are the numberof increments to be inserted between initial and final values. The in-crements 'ip' and 'iv' may be negative if desired.
If instead of a number 'pl', 'p2', etc., a comma (with at mostintervening blanks) is used, the program will automatically use theexisting value of that variable. See Test Case Nine for an example.
Examples:
GRID, CORNER, P, 1, 0.1, 10, V, 20, .5, 40
GRID, CENTER, P, 1, 4, 10, V, 20, 19, 40
50
GUN, s, i, f
This instruction computes the thermodynamic properties of the chambergas produced by propellant burning to equilibrium at constant volumeat loading densities between s and f, at increments in loading densityof i. A maximum of 16 different loading densities is permitted. If youtry to use more than 16, only the first 16 are computed, and the programcontinues to the next instruction.
Example:
GUN, 0.05, .05, 0.40
ISOline, T, tl, P, pl, np, p2, (LOG)
This instruction computes thermodynamic equilibrium for a set ofpoints, one of which is held constant. In addition to temperature andpressure (as shown), the same sets of variables permitted in a GRId in-struction are accepted.
The variable to be held constant is named first. 'pl' is the initialvalue of the variable being changed, 'np' is the number of increments,and 'p2' is the final value. If the optional parameter LOG appears,
logarithmic spacing is used. Logarithmic spacing is automatically usedwhen the variables are (S, V).
Example:
ISO, T, 1000, P, 10, 4, 20
LJP, namel, T, vl, S, v2, name2, T, v3, S, v4, ...
This iinstruction changes the values of the Lennard-Jones parametersfor substances 'name 1', 'name 2', etc. Of course, 'name 1' must bea legal name (one that appears in the library as a CONstituent). Theprogram checks that both parameters have been entered, even if you onlywish to change one of them. Changing only one is simplified by thefact that if two successive commas with at most blanks between them appearin place of 'vl' (or 'v2', etc.) the program will use the existing value.
The order of T and S is immaterial, but 'vl' and 'v2' must correspondto the key letters used. The key letter T may be replaced by E; and S,
by D.
If 'namel' is mistyped or is an illegal name, no action i3 takenbut a diagnostic message is printed. If two or more names appear on acard and one of them is wrong, the program will nevertheless attempt toprocess the remaining names.
51
If no COMposition card has been entered, the program will reject
an UP instruction. A suitable message is printed to add insult.
Examples:
LJP, H20, T, 600, D
LJP, NH3, D, 4, T, 350
MELt
This instruction undoes the effect of a FREeze instruction. It, too,is optional.
ORC, namel, name2, name3,
This instruction is almost identical with the ORDer instruction,except for one crucial point. ORDer applies only to gaseous constituents,while ORC applies only to condensed ones. It is not often needed, but insome cases (e.g., black powder), it is quite useful.
Example:
ORC, K2S04$
4 ORDer, namel, name2, name3, ...
This instruction makes the program chose 'name!', 'name2', etc.,as the components for the first attempt aL finding the equilibrium com-position. If these components are not all linearly independent, one ormore of them will be omitted. The names of the constituents must beexactly the same as the names used in the CONstituent instruction whenthe binary library was formed. Also, none of these substances may havebeen previously rejected by a REJect instruction. If either of theseconditions is violated, the entire case is omitted and the program con-tinues.
Example:
ORD, N2, H20, C07
POInt, P, p, T, t
This instruction computes chemical equilbrium at the point with thespecified pressure 'p' and the specified temperature 't'. The order inwhich they appear is not arbitrary; it must be (P,T), (P,V), (P,H), (P,S),(V,E), (V,T), or (V,S). If the wrong order is used, an error message isprinted and the program proceeds to the next case.
52
Example:
POINT, P, 10, T, 250o
PRLimit, CON, vl, FiT, v2, ERR, v3, PAG, v4
This i.i,;truction controls the amount of output printed by BLAKE.The order of the keywords is immaterial but they must be typed or punchedjust as shown. (For example, do net use 'PAGE' for 'PAG'.) The numbers'vI', 'v2', ... , are either 0, 1, o-r2, and have the following significance:
CON, 2: Print the list of constants fori4-t fitting of the thermo-
dynamic data of each constittent. This list is prýinted once after a COM-
position instruction is entered -orovided PRL, CON, 2 has been specified.The list is not repeated until cnother PRL, CON, 2 inztruction is gvcn.Instead the program reverts to PRL, CON, 1.
CON, 1: This is the default setting. The list of constants is notprinted but the composition of the chamber gas is printed after each GUNinstruction. PRL, CON, 2 reverts to this setting.
CON, 0: The printing of both the constants and the composition ofthe chamber gas is suppressed. Once set, this instruction remains ineffect dntil changed.
FIT, 1! Fit the four quantities, chamber pressure and temperature,and covilume and gamma of the chamber gas, to a cubic polynomial in theloadirg density. The fitting is done provided at least four loading dei-sities are called for in the GUN instruction.
FIT, 0: Suppress the fitting, no matter how man: loading densiticsare called for. Once entered, this instruction remain3 in effect untLlchanged. This is the default setting.
PAG, 1: Put each distinct part of the output from a G1JN instructionon a separate page. lTese parts are the composition (includi,.g the listof thermodynamic constants if called for), the thermodynamic functionsfor the chamber gas, and the summary. This is the default setting. Eachoutput page produced has its own title (if one was entered), the date(either from the system or from a DATe instruction), and the version de-si gnator.
PRL, 0: Do not paginate the output until a page is filled, or untila new COVqposition instruction is entered.
ERR, 1: Print each occurrence of error messages 28 and 30 as theyoccur.
153
NS
ERR, 0: Suppress the prinding of these error messages. A summaryot the total number of occurrences of each error is printed at the endof -he case. This is the default setting.
Slot all of the parameters on a PRL instruction need be specified
at once; you need only include the one(s) you want changed.
Examples:
PRL, CON, 0
PRL, CCN, 0, PAG. 0
PRL, CON, 2, FIT, 1
QEXplosion, R, r, T, t
This instruction computes the heat of explosion of a composition atloading density 'r' at five freeze-out temperatures centered around tem-perature It'.
The composition must have been entered previously. The order of'r' and 't' is unimportant, but the values entered for tr' and 't' mustcorrespond to their key letters.
The five temperatures are t - 200, t - 100, t, t + 100, and t + 200.
The algorithm used is thAt of CorievI. The program executes a POintcomputation at the volume 1/i and the chosen temperatures.
The working of the algorithm is critically der ndent upon the contentsof twn DATA statements in the subroutine thpt cont.- the names and enchal-pies of formation of stable final product3 at 298 K. This list has beenselected for compounds formed by the elements carbon, hydrogen, nitrogen,oxygen, boron, potassium, and sulfur. If additional elements are presentin a given formulation, appropriate cltanges must be made to the DATAstatements. Version 20S.0 allows zoom for seven additional compoundswithout ether programming changes being required.
!x ample:
QEXP, R, 0.2, T, 1100
oU It
This instruction should be the final one in every BLAKE run. Itcauses the program to execute a normal FORTRAN STOP. If it is omitted,the program will likely stop because it will next read an end-of-file.Using the QUIt instruction is more elegant.
IS4
RECall, namel
Example:
RECALL, NUMI
This instruction recalls the final conditions associated with thestate designated by 'namel'. If the point has not been saved (see SAVe),an error message is printed, and succeeding calculationt" are either skip-ped or done erroneously, until a new COMposition instruction is entered.
REJect, namel, name2, name3, ...
This instruction climinates from further consideration the constit-uents whose legal names are 'namel', 'name2', etc. If an illegal orundefined name is entered, it is ignored without harm. See also DEStroyand RETain. The maximum number of constituents that may be REJected is99.
Example:
REJ, C(s), C2 H, C2 N, C, CG
RETain
This instruction causes the program to retain a list of REJects fromone COMposition to another. If it is not used, an existing REJect listis automatically cancelled when a new COMposition instruction is entered.The effect of RETain is negated by DEStroy.
SAVe, name
BLAKE and TIGER start new thermodynamic calculations from the resultsof a previous one, except when initialized by a COMposition instruction.Then the program starts from a pre-set guess that may be far from thefinal composition. The convergence of a calculation can often be mademore efficient by having the program start from the results of an earliercalculation. This intent must be made known in advance by use using theSAVe instruction. The conditions (including the final concentrations)just computed are saved in memory, and the name 'name' is associated withthem. Up to 8 points may be saved in this way, and later recalled (seeRECall). If you try to save more than 8, an error message is printed,and the point is not saved, A name may be reused, however, the new pointwill then overwrite the old one.
Example:
SAV, NUMI
55
F
STArt the Library
This instruction is used to form the binary library. See Section
VI A.
TITle, (message)
This instruction causes a title to be written at the top of each pageof output. All of the characters in 'message' are centered and printed.
Example:
TIT, TIIS IS A TITLE
TIMe, t
This instruction is system-dependent (see Section VAl). If you haveimplemented it on your system, then it is used to change the default settingof the maximum time allowed for a single calculation by BLAKE. It is use-ful in the case that you want to run a number of different cases that youanticipate will require a maximum of (say) five minutes. It is unlikelythat you will want all five minutes to be devoted to one case. By settingthe TIMe instruction, you can control approximately the amount of timethe program devotes to one case before going on to the next. This timelimit is different from, and independent of, the time limit that is usuallyset at the beginning of a run by your job card (or other job control entry).
This instruction is optional. If you have implemented the CLOCKinstructions, you can then set a default time limit. For the UNIVAC 1108,2.5 minutes was a reasonable value; for the CDC 7600, 0.4 minutes is better.
The actual time that elapses before time is called by this instructionis usually greater than the value set, because the program only checks theclock at certain cycle limits.
Example:
TIM, 0.1
TRAnsport propertieE
This instruction is inactive. Someday it will cause the program tocompute approximate values for viscosity and thermal conductivity. Someday gold will fall from the sky.
UNIts, name
This instruction causes the program to include or exclude English(or conventional engineering) units for the summary output in a GUN
56
calculation. The summary output is always printed in SI units. Thiscannot be suppressed except by changing the program. If in addition,you want English units printed, this instruction will do that when 'name'is ENG. If 'name' is 'SI', the English unit print is suppressed.
Example:
UNI, ENG
E. Error Messages
There are two score plus four error messages contained in BLAKE.
Only a few of them (e.g., types 9 and 24) indicate truly serious problemsand terminate a case. Most of the others call your attention to situationsthat may need corrective action, but the program continues with the samecase. A few indicate that the program is having problems reaching equil-ibrium. Where appropriate the program prints the instruction that is thesource of a problem.
All of the error messages incorporated in the code are listed here.(Some of the error messages of TIGER were removed, hence the gaps in the
numbering.) The exact message is listed IN CAPITAL LETTERS; then theprobable cause is discussed and remedial action suggested.
Error Type 1: INPUT CARD NOT ACCEPTABLE.
The instruction entered is not one of the 37 recognized by BLAKE.The instruction is skipped and the program attempts to interpret and followthe next instruction. This message usually arises from faulty typing orpunching.
Error Type 2: TOO MANY CONSTITUENTS REJECTED.
Since up to 99 constituents may be rejected, this message is veryimprobable. It could occur towards the end of a very long run in whichyou forgot to DEStory several previous REJect lists; even this is im-probable.
Error Type 3: TOO MANY CONSTITUENTS ORDERED.
Only 25 constitutents may be ordered. The program continues butonly the first 25 constituents are ordered. There is never any need toorder as many as 10 constituents; one per element is sufficient.
Error Type 4: TOO MANY CONSTITUENTS CHOSEN.
The limit is 25. The program continues but only the first 25 con-stituents are chosen. Again, there is little reason for trying to choose26 or more constituents. As mentioned earlier, this order is better notused.
57
Error Type 6: FINDING RHO0O EXCESSIVE ITERATIONS.
This error message arises in Subroutinc FINDRH; PO and P are printedat the same time. When P = PO, a value 'o- RHO has been found, so thedifference between the two is a measure of the error at that time. Theprogram uses the last value of RHO and continues. If it converges later,this error can be safely ignored.
Error Type 7: FINDING TO EXCESSIVE ITERATIONS.
This message arises in Subroutine FINDTP; PO and P are printed at thesame time. When these two are equal, a value for TO has been found sotheir difference indicates the magnitude of the error. The program usesthe last value of TO and continues. If it later converges, this messagecan be ignored.
Error Type 8: COMPONENTS LINEARLY DEPENDENT.
This message arises in Subroutine SELECT. It usually means thatyou have CHOsen constituents unwisely or have been unlucky with an ORDerinstruction. REJect a condensed constituent and try it again.
Error Type 9: NO ACCEPTABLE COMPONENTS.
This is one of the most frustrating messages of all. It arises inSubroutine SELECT and indicates that the program cannot find a set oflinearly independent components after trying many sets above the floor.The case is rejected and the program continues. Unfortunately it doesnot give a list of the constituents it has considered nor the positionof the floor. There is no certain rrocedure to follow at this point.I usually add another REJect list, play with an ORDer or ORC instruction,or as the last resort, raise the floor.
Error Type 11: EXPLOSION STATE CARD NOT ACCEPTABLE.
This message arises in Subroutine EXPLOS. It indicates that eitherSan EXPlosion or E/X instruction has been incorrectly punched. Theoffending instruction is printed to facilitate the detection of the error.The case is rejected and the program continues.
Error Type 12: INPUT TO POINT NOT ACCEPTABLE.
This message arises in Subroutine POINNT. It indicates that an errorhas been made on either a POInt, ISOline, or GRId instruction. Generallythis means that the variables were ordered incorrectly; e.g., V, P insteadof P, V. The instruction is rejected and the. program continues.
58
4.
Error Type 13: THIS POINT NOT SAVED.
This message is printed in Subroutine RWhALL and is self-explanatory.Usually it arises from a punching or typing error. It can also occur whena previous case was rejected or failed to corverge, so the point that wasto have been saved was not computed. The program continues with thesucceeding instruction. The remedy is obvious.
Error Type 14: TOO MANY POINTS SAVED.
This message arises in Subroutino SAVE aod is self-explanatory. Thelimit is eight. The point is not saved, the program continues, and willprobably soon come to grief when you try to k$Call the unsaved point.The remedy is obvious.
Error Type 16: LIBRARY CARD NOT ACCEPTAOLE.
This message arises in Subroutine LIBRARY. It indicates that alibrary instruction has failed to pass all of the checks built into theprogram. The instruction is printed; it shobld be compared with thcprescribed format for library instructions. Punching or typing errorsare the most common causes. The program ignores the bad instruction andcontinues, but you probably will not want to use the library thus formed.The binary library cannot be corrected; it must be formed all at once.Fix the card and start again.
Error Type 17: COMPOSITION CARD NOT ACCEPTARLE.
This message arises in Subroutine COMPOs. Its most common cause isthat a formula card was either omitted entirely, or that it wai previouslyrejected by the program. Punching or typing errors are the next mostcommon causes. The offending card or instruction is printed. The pro-gram ignores the instruction and tries to continue since later COMpositioninstructions may be acceptable. The remedy if obvious.
Error Type 19: FORMULA ELEMENTS NOT IN LIBRARY.
This message arises in Subroutine FORMULA, and is self-explanatory.The program ignores the instruction and continues. If not due to a meretyping blunder, this error is difficult to fjx, since it involves adding
another element to the library, a time-consuming job.
Error Type 20: NOT ALL ORDERED CONSTITUENTS IN LIBRPRY.
This message arises in Subroutine COMPOS. It is caused by the list-ing on an ORDer or ORC instruction of a constituent that the program can-not find in the binary library. Typing or ponching errors are the firstthing to look for, but an equally likely erlor is that the substance inquestion had been previously listed in a REJect instruction. The program
59
ignores the instruction, rejects the case, and continues. The remedy isobvious although it is not always easy to decide which constituent in anORDer or ORC instruction was at fault.
Error Types 21, 22 and 23: FREEZE MATRIX SINGULAR.FREEZE FORCE ITERATION EXCEEDED.FREEZE ITERATION EXCEEDED.
All of these messages arise in Subroutine FREEZE. All three errorsare fatal to the computation being attempted. The program skips it andlooks for a new COMposition instruction. The usual causes are either thefrozen composition requested cannot exist at the point requested, or thepoint in question is too far from the last computed point.
Error Type 24: THERMO ITERATION EXCEEDED.
This message arises in Subrcutinc THERMO and is fatal. The programcontinues and looks for a new COMposition instruction. The most commoncause is that it was not working with a good set of components. (ReadSection VIIA over). The only cure is to use ORDer or ORC instructionsto rearrange the order in which components are selected, or to changethe REJect instructions, or both. It is worth trying extreme measuresto make a calculation converge somehow; once it has, that point can beSAVed and used to restart a new calculation with fewer restrictions.
Error Type 25: MELTING TEMPERATURE EXCESSIVE ITERATIONS.
This message arises in Subroutine ECOMPO. It is not a fatal errorbut indicates that the program is having some difficulty converging.Keep in mind chat the version of TIGER on which BLAKE is based oftenencountered insurmountable problems when it tried to deal with a con-stituent in the neighborhood of its melting point. The new TIGER handlessuch computations with ease. If the computation you are trying eventuallyconverges, fine; otherwise it is beyond BLAKE's capabilities.
Error Type 26: ECOMPO FORCE EXCESSIVE ITERATIONS.
This is a non-fatal error arising in Subroutine ECOMPO. It indicatesthat the program is having trouble converging. If it eventually doesconverge there is no problem; if not, you will get a different message(usually No. 24).
Error Type 27: SOLVING FOR ETAS MATRIX SINGULAR.
See No. 26.
Error Type 28: SOLVING FOR ETAS EXCESSIVE ITERATIONS.
See No. 26.
60
Error Type 29: SOLVING FOR N(I)S MATRIX SINGULAR.
See No. 26.
Error Type 30: SOLVING FOR N(I)S EXCESSIVE ITERATIONS.
See No. 26. Messages 28 and 30 are often produced during the courseof a straightforward computation that converges in a few more iterations.For this reason BLAKE generally suppresses their printing. If you wantto see them, use the instruction, PRL, ERR, 1. Note that even if theyare suppressed, a summary of the number of times each was encounteredis still printed.
It is of course possible to make the appearance of all these errormessages less likely by raising the limits of the iteration counters setin the main program. I have played this game occasionally, but whileit always used up more computer time, it rarely helped with a difficultcomputation.
Error Type 31: TOO MANY GASEOUS CONSTITUENTS.
This message arises in Subroutine COMPOS, and indicates that morethan 29 gaseous constituents have been selected from the binary library.It does not tell you which 29 they were but you can readily work thisout for yourself by reference to a library print. The program skips thiscase and continues looking for a new COMposition instruction. The onlycure is to add more REJects.
Error Type 32: TOO MANY CONDENSED CONSTITUENTS.
The limit here is 10, but experience ,hows that the program willnot converge when more than four condensed constituents have been selected.With the library furnished with BLAKE this error can arise only if youtry compositions with at least nine elements.
Error Types 33 - 37: TOO MANY ( .... ) CARDS.
All of these errors arise in Subroutine LIBRARY and are self-explan-atory. The ellipsis can be filled with ELEMENTS, CONSTITUENTS, STG, STR,or STC. The limits presently set in the program are:
ELEments: 40
CONstituents: 180
STG: 99
STR: 540
STC: 180
61
Any of these errors can be readily avoided by redimensioning the ap-propriate array in Subroutine LIBRAY. If you do, remember to change theerror messages accordingly. (This is not absolutely necessary, of course;it is likely that the error message will be encountered by someone elsewho will have no idea that it is meaningless. As booby traps go, this isa relatively harmless one.)
The last six error messages unnumbered:
TWO OR MORE (...) HAVE THE SAME NAME
The ellipsis can be either ELEMENTS or CONSTITUENTS. Both messagesarise in Subroutine LIBRAY and are self-expianatory. If you had to limitthe length of a name to four characters (see Section VI A3), you willsurely see this message unless you have scrupulously examined the librarybefore attempting to form the binary library file for the first time.The remedy is obvious.
LJP CARD IS FAULTY OR PREMATURE.
This message arises in Subroutine LJCH and is self-explanatory. Theprogram skips the instruction and proceeds.
--- DOES NOT APPEAR IN THE LIST OF GASEOUS CONSTITUENTS
The dash is filled by the name of a putative constituent from a LJPinstruction (see Section VII C2). The meaning is self-explanatory. Theprogram skips the instruction and proc~cds.
NO COMP CARD, NO CALCULATION
This message arises in Subroutine QEXP and is self-explanatory. Theprogram skips the instruction and proceeds.
CALCULATION REJECTED
This message arises in Subroutine REJECT. When either fatal error9 or 24 is encountered, the program prints the appropriate error messageand then branches to Subroutine REJECT where various counters are resetand this message is printed. The program then proceeds, but almost allfurther instructions are skipped until a new COMposition instruction isfound. Only TITle and QUIt are recognized.
It is hard to give good advice at this point; however, see the discus-sion for Error Types 9 and 24.
UNITS CARD IS FAULTY. NOTHING DONE.
62
This message arises in the main program and is self-explanatory.Only ENG or SI are recognized keywords in a UNIts instruction. The pro-gram proceeds.
GEO CARD IS FAULTY.
This message arises in the main program. Only IDEAL, L-J, BKW, andVIRIAL are recognized keywords on a GEO card. If a faulty card is entered,the program reverts to the truncated virial equation of state, and thenproceeds.
ILLEGAL INPUT FOR CJPREP. OMITTED.
This message arises in Subroutine CJPREP and indicates that an errorwas made on an EXl instruction. The instruction is skipped and the programproceeds with the next instruction.
TIME HAS BEEN CALLED. RETURN TO START. DO NOT PASS 'GO'. DO NOTCOLLECT TWO HUNDRED DOLLARS.
As mentioned in Section VI Al, the program contains the capabilityof timing a calculation independent of the total time allowed for theentire run, provided you have implemented the call to the system clock.This message is printed if the allotted time is exceeded. There are fewcalculations that will converge in a longer time if the default time isappropriate to your computer. (The BRL's experience has been that 0.4minute is a suitable limit for the CDC 7600,, and 2 minutes for a UNIVAC3108. A few extra lines of programming will readily enable you to printout the elapsed time per run if you have previously implemented the callto the system clock.)
Rather than setting a longer time limit (using the instruction TIMe,t), you should fiddle with the ORDer and REJect instructions to try tomake the calculation converge more rapidly.
DUPLICATE FORMULA CARD -- IGNORED.
This message arises in Subroutine FORMLA; it is followed by a listingof the duplicate card in question. It means that you~have entered a FORmulacard using a reserved name on the prestored list. The program checksonly on the name, not on the enthalpy. If you want to use a differententhalpy for a pre-stored formula, you must insert a new FORmula cardwith a different name.
BAD FORMULA CARD -- EITHER TOO MANY OF THEM OR THE CARD IS MTSPUNCHED.
This message arises in Subroutine FORMLA and is self-explanatory.In checking to see why the program has declared a card to be mispunched,pay particular attention to the difference between letter' 0 and numeral
63I
0. In any case the offending card is skipped and the program proceeds.Soon afterwards, you will likely get Error Type 17. Such is life.
ERROR. GUN CARD HAS MIS-FIRED.
This message arises in Subroutine GUNCAL and means that a GUN instruc-tion is faulty. The program skips it and proceeds.
AN 'EOF' HAS BEEN ENCOUNTERED. EXECUTION TERMINATED.
1his message arises in Subroutine CARDRD. On CDC computers it preventsthe program from aborting when it tries to read an end-of-file, thus sav-ing a page of incomprehensible printing, You can always end the programthis way but it is suggested that you enter a QUIt instruction instead.
These 44 messages are the total embedded in BLAKE; any others musthave come from your operating system.
VIII. THE OUTPUT FROM 'BLAKE'
SAppendix C contains the output produced by the BRL's CYBER systemfor nine different BLAKE runs. They are included here both for theirdidactic value and as comparisons for users to ensure that their computersare producing the same numbers. In making such comparisons bear in mindthat agreement for the last digit is not to be expected; discrepanciesof up to a few tenths of a percent can be expected from rounding errors.
The ECHo feature was used in all of these runs to show the instruc-tions entered. Special attention should be given to the REJect, ORDer,and ORC instructions since these potentially offer the most difficultyfor users.
The output starts with a banner page identifying the version numberand proclaiming BLAKE's relation to the TIGER program. The date isprinted next (assuming either that the system function DATE was imple-mented, or that a DATe instruction was used).
If either a CMT or ECHo instruction was entered, their output comeson the same page; neither of these instructions ever generates a pageeject.
A COMposition instruction always produces a page eject. The auto-matic page numbering starts with this next page; it cannot be suppressedor re-started within a run. If a TITle instruction was entered, the title(centered) is printed. Then comes the standard heading, THE COMPOSITIONIS, which is followed by a listing of the ingredients specified in theCOMposition instruction.
64
Each ingredient is followed by its weight and mole percent in theformulation, its enthalpy of formation, and its formula. In the testcases, note that most of the ingredients are those already stored in theprogram, and are called up by using the proper abbreviation. One excep-tion occurs in the test case two where it was desired to use potassiumcryolite as an ingredient instead of sodium cryolite. The latter isstored in the program under the name CRY; potassium cryolite must there-fore be given a different name (KCRY, in this case).
The program next prints the heat of formation of the composition onboth specific (per gram) and molar bases. (Owing to the form of theformulas used for nitrocellulose and other polymers, their mole fractionsare distorted; likewise, the molar heat of formation of the formulationis rarely meaningful.
Then the program prints the ultimate elemental composition of theformulation in mole percent.
A page eject normally occurs at this point unless it has been sup-pressed by a PRL, PAG, 0 instruction. (See, for example, the output fortest case 5.) If the list of possible products has been requested (by aPRL, CON, 2 instruction), it is now printed. See page 2 of the outputfor test case one.
After the standard heading and title (if any) are printed, theprogram prints the thermodynamic constants for the gaseous constituent5of possible products. Not all of these may ultimately appear in thefinal equilibrium composition, but no others will be considered. Theordering is the one in which these constituents appear in the binarylibrary unless an ORDer or CHOose instruction has been used.
The information printed for each constituent is as follows. Theformula of the constituent (as defined previously on a CONstituent cardwhen the binary library was formed), the BKW covolume, the two Lennard-Jones force constants, and then the 9 constants that reproduce the variousthermodynamic properties of the constituent as a fufiction of temperature.(See the discussion in Section VII Cl, under STR.)
The floor (see Section VII A) is printed.
If any condensed constituents have been selected, their thermodynamicdata are printed next. Owing to the length of the names of some of thecondensed species, some arbitrary truncation had to be imposed on them.The correct formulas are printed in the listing produced when the libraryis first formed. This is the explanation of the cryptic message FRMSIN LIB PRT that next appears. The symbols B and C are the coefficientsfor the thermodynamic data and the equation of state data for the condensedspecies. (See STR and STC in Section VII Cl.) As noted on the print, thedata are arranged in the order tbermo data for liquid, then solid, and
65
p-V-T data for liquid, then solid. If the species in question does notform a liquid (solid) phase, only zeroes appear for the liquid (solid)line.
The next part of the output depends on the computation selected.If the printing of the final equilibrium composition has not been suppres-sed, it comes next. The order is now different from that in which thethermodynamic constants were Irinted; it is essentially that of decreasingconcentration. The concentration unit printed is moles per kilogram ofstarting materials which has proved the most convenient for users. Theprogram prints the concentrations of all gaseous species first followedby the concentrations of condensed species; then it prints the totalmoles of gas. Eventually the total grams of condensed-phase materialwill be printed but this i: not now done in version 205.0.
For a GUN instruction the program next prints a summary, the outpitof most interest to ballisticians. This summary presents the propertiesof the chamber gas at equilibrium for each loading density specified inthe GUN instruction. These properties are the pressure, temperature,impetus, molecular weight of the gas, covolume, gamma, heat capacity atconstant pressure, the second and third virial coefficients, the specificgas volume, and also the entropy, enthalpy, internal energy, adiabaticexponent, and compressibility.
Most of these quantities are self-explanatory. If no condensedphase has formed then the specific gas volume is exactly the reciprocalof the loading density; if, however, some condensed material has formed,BLAKE subtracts its volume from the total (geometrical) volume and printsthe remainder. It is this remaining volume that is printed under theheading, GAS VOL.
Likewise, the heading MOL WT GAS indicates that the number thereprinted refers to the gas phase only. This point should be kept in mindwhen comparing BLAKE output with that produced by CEC71, where the mole-cular weight printed is for the entire equilbrium mixture. Also, thiscorrection carries over to the IMPETUS, which in BLAKE is computed strict-ly for the gas phase only.
The heat capacity and the gamma printed are computed with theassumption that the chemical composition of the mixture is fixed, or'frozen.' The equilibrium heat capacity is larger, since it containsthe frozen term plus a contribution arising from the effect of tempera-ture on the shifting equilibrium. This same effect makes the equilibriumgamma smaller. The difference is quite noticeable for hot propellantslike M9. The matter is discussed in mo• detail by several writers; see,for example, a paper by Pifer and Cohen". BLAKE prints only the frozen
24R. A. Fifer and A. Cohen, "High Temperature Thermal Conductivity and
Heat Transfer in Gun Propellant and Primer Combustion Gases," Proceedingsof the XIV JANNAF Combustion Meeting.
66
quantities since these are the ones that have been traditionally used inballistic performance codes. Whether this is correct or not, and the sizeof the error thus introduced if it is not, remain open questions.
The adiabatic exponent is the true equilibrium derivative -(3lnP/3lnP)s.
The quantity ý that is printed last is the ratio ef the non-idealpressure to the ideal pressure. It is thus a measure of the deviation ofthe system from ideality. The theory on which the gas pressure correction
is based may not be valid for 4 much greater than 1.5.
If the instruction UNIts, ENG, has been entered, the program now repeatsthe summary, this time using the proscribed units, pounds mass, poundsforce, pounds per square inch, cubic inches, etc.
If four or more loading densities have been requested and if a PRL,FIT, 1 instruction has been entered, the next part of the output con-sists of coefficients. These coefficients ase for cubic polynomials whoseindependent variable is the loading densicy. They are printed in orderof increasing power from 0 to 3. The quantities fitted are the impetus,chamber pressure, chamber temperature, and covolume. The coefficientsare obtained by a least-squares process and are useful from the lowestdensity up to the largest density fitted. They should not be used foreven short extrapolations.
Test cases six, seven, and eight are further examples of the use ofBLAKE for GUN calculations. Note the variations produced by the use ofdifferent PRL instructions. These cases also give interesting examplesof the application of the instructions ORDer, REJect, and ORC.
Test case nine shows a different calculation that is sometimes useful.A typical double-base propellant is first allowed to reach equilibriumat a constant volume of 5 cc/g; the resulting hot gas is then expandedadiabatically. A PRL instruction is used to control the printing of theconstituents.
The expansion calculation is ordered by the instruction
ISOline, S, , V, 5, 7, 500
Note the double , , ; this instructs the program to use the value ofentropy previously computed, a number the user does not know in advance.
The output in this case is mainly self-explanatory. ALPHA and BETA
printed here are, respectively, the quantities I 2e and 1 V.a2 p . and •-- v.
SIGMA is the Riemnann integral, - c jCdada 1
t 60
where c, = local sound speed, aAd
a = log v
OMEGA is the integral - c2da
a,
IX. ACKNOWLEDGMENTS
So many people from the Interior Ballistics Division have contributedor assisted with the development and improvement of the program that thenaming of names presents the danger of causing hurt by omission. But itwould be churlish to use this as an excuse not to try. May the omissionsbe few, and those, the forgiving ones.
My introduction to the need for and complexities of thermodynamiccomputations on real propellants came from Paul G. Baer, the co-authorof BRL 1338 and of the Baer-kortman code. It is noteworthy that Paul,an insightful modeller, is also a model of insight which he is alwayswilling to share.
Ingo May has been an enthusiastic supporter of BLAKE from the begin-ning and suggested several significant improvements, especially the pre-stored formulas. This report would not yet be written without his friendlyand unflagging encouragement.
R. D. "kndy" Aiderson has borne the burden of the systems programmingfor the last six or seven years, and has guided BLAKE from BRLESC to theUNIVAC to the present CYBER. The useful instruction ORC could not havebeen implemented without his methodical forays into the code.
Kevii, White has never been directly involved with BLAKE, but hispersistent quest for molecular interpretations forced me to a deeperunderstanding than would otherwise have existed. My orientation is still19th-century, but he changed my allegiance fronm Duhem to Boltzmann.
Last but not least, I want to express my appreciation to the authorsof the original TIGER code, especially William Zwisler, for their for-bearance and toleration while TIGER metamorphosed into BLAKE.
68
REFERENCES
1. J. Corner, "Theory of the Interior Ballistics of Guns," J. Wiley& Sons, New York & London (1950).
2. T. Leser, "High Speed Digital Calculations of the Composition andThermodynamic Properties of Propellant Gases by the Brinkley Method,"Ballistic Research Laboratories Report No. 1023 (August 19S7). (AD 156716)
3. P.G. Baer and K. Bryson, "Tables of Computed Thermodynamic Propertiesof Military Gun Propellants," Ballistic Research Laboratories Memo-randum Report No. 1338 (March 1961). (AD 258644)
4. L. Stansbury, Jr. and R.B. Shearer, "Tables of Computed ThermodynamicProperties of Selected Liquid Monopropellants," Ballistic ResearchLaboratories Report No. 1579 (April 1972). (AD 521326L)
S. a) W.E. Wiebenson, Jr., W.H. Zwisler. L.B. Seely and S.R. Brinkley,Jr., `rIGER Computer Program Documentation (November, 1968); b)M. Cowperthwaite and W.H. Zwisler, "TIGER Computer Program Documenta-tion," SRI Publication No. Z106 (January 1973).
6. For a thorough discussion of gaseous equations of state and theirrelation to intermolecular potentials, see J.O. Hirschfelder,C.F. Curtiss, and R.B. Bird, "Molecular Theory of Fluids," JohnWiley & Sons, New York, (1954).
7. See the discussion in Ref. 6.
8. See Ref. 6, p. 157 and pp. 262-263.
9. S. Gordon and B.J. McBride, "Computer Program for Computation ofComplex Chemical Equilibrium Compositions. . .,," NASA SP-273 (1971).
10. F. Volk and H. Bathelt, "Application of the Virial Equation of Statein Calculating Interior Ballistic Quantities," Propellants and Explo-sives 1, 7-14 (1976).
11. E. Freedman, "Pin Intercomparison of West German and US PropellantThermodynamic Codes," in Agenda of Presentations at the 25-28 April1978 Meeting of the FRG and US Personnel Associated with DEA 1060,p. IB-V-119, (April 1978).
12. D.R. Stull and H. Prophet, Eds., "JANAF Thermochemical Tables,"2nd ed., NSRDS-NBS 37 (June, 1971); also looseleaf revisions andadditions from the Thermal Research Laboratory, The Dow ChemicalCompany, Midland, MI (M. Chase, Director).
69
REFERENCES (Continued)
13. E.G. Powell, G. Wilmot, L. Haar, and M. Klein, "Equations of Stateand Thermodynamic Data for Interior Ballistics Calculations," inH. Krier and M. Summerfield, Interior Ballistics of Guns, Progressin Astronautics and Aeronautics, Vol. 66, AIAA, New York (1979).
14. M. Klein, (National Bureau of Standards), private communication toE. Freedman, February 1980.
15. A.D. Crow and W.E. Grimshaw, "The Equation of State of PropellantGases," Phil. Trans. Roy. Soc. A 230, 30 (1931).
16. R.H. Kent and J.P. Vinti, "Cooling Corrections for Closed ChamberFirings," Ballistic Research Laboratories Report No. 281, (September1942). (AD 491852)
17. D. Vest, "On the Transfer of Heat in High-Pressure CombustionChambers," unpublished M. S. thesis, The Johns Hopkins University,Baltimore, MD (19S3).
18. I.W. May, Ballistic Research Laboratory, private communication toE. Freedman (1973).
19. R.C. Reid and T.K. Sherwood, "The Properties of Gases and Liquids,"2nd ed., McGraw-Hill, New York (1966).
20. R.S. Jessup and E.J. Prosen, "Heats of Combustion and Formation ofCellulose and Nitrocellulose (Cellulose Nitrate)," J. Res. NationalBureau of Stds. 44, pp. 387-393, (1950).
21. J.D. Cox and G. Pilcher, "Thermochemistry of Organic and Organo-metallic Compounds," Academic Press, London (1970).
22. D.D. Wagman, et al., "Selected Values of Chemical ThermodynamicProperties," NBS Technical Note 270-3, Washington, DC (1968),
23. J.A. Dean, ed., "Lange's Handbook of Chemistry," 12th ed., McGraw-Hill, New York (1979).
24. R.A. Fifer and A. Cohen, "High Temperature Thermal Conductivity andHeat Transfer in Gun Propellant and Primer Combustion Gases," Pro-ceedings of the XIV JANNAF Combustion Meeting.
70
APPENDIX A.
COMPOSITIONS OF PROPELLANTS USED IN COMPARISON CALCULATIONS
7
N00
z0Or t
0) C -4
z
0
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S-4 '0
0.
r.1-4~310 U) r- ~ bt
0
cm **44 1-4 fIwu
73 I
APPENDIX A
COMPOSITIONS OF PROPELLANTS USED IN COMPARISON CALCULATIONS
Il. Vest
Designation: Type I Type II
Ingredient
NC 1313 83.25 ---
Nitroglycerin 10.29 20.49
Dibutylphthalate 5.14 ---
Diphenylamine 1.01 0.70
Water 0.31 0.41
NC 1323 --- 78.46
Dinitrotoluene --- 0.97
Potassium nitrate --- 0.94
Barium nitrate --- 1.36
Graphite --- 0.27
74
APPENDIX B
FORMULAS OF INCREDIENTS PRESTORED IN 'BLAKE'
51/76
BLAKE HEAT OF MOL, FORMULA
NAME FORMATION WEIGHTI ~CAL/MOLE
ACETON -,59270E+,05 58.0804 C 36H 0 1
ETOH -*66420E+05 46.0694 C 2H 60 1
EC -. Z5100E+05 268.3598 C17 H 0 1N 2
NDPA .15400Ee05 214.ZZ42 C1 H 10 2N 2
NNDP o54000E04 259.2217 C H 90 N12 9 4 3
NG -. 88600E•05 227.0872 C 3H 50 9N 3
NO -o22100E,5 104.0686 C H 0 N
NQ 1 4 24
DNT -o17100E+05 162,1360 C 7H, 60 4 N .
DBP -,20140E+06 278.3496 C16HZ .a 4
ALC -. 66420E+05 46.0694 C 2H 60 1
KS -. 34266E+06 174.2536 K S 10 4
CRY -,78900E+06 209.9413 NA 3AL IF 6
KM -,11776E+06 101.1029 K N 10 3
BANIITR -. 23706E+06 261.3498 BA N 0
DPA ,31P70E+.05 169.2267 C lN IH 1
H20 -. 68315E+05 1840154 H Z0
C 0. 12001110 C I
77
BLAKE HEAT OF MOL. FORMULANAME FORMATION WEIGHT
CAL/MOLE
KBF4 -.45100E+06 12549016 K B F
PETN -9128BOE+06 316.1386 C H 0 N5 81]2 4
RDX *14690E+05 222.1176 C H N 03 6 6 6
AMYLPH -,22090E+06 306o4036 C H 018 ab 4IN2 -. 59300E+03 28.0134 N
2
N 2H 4. ,2 2T 5OE+05 32 *0 4t54 N! H 42 t
AKAR2 -. 25500E+05 226.2790 C H N 014 14 2 1
IPAN -996400E+05 122.1250 C H 0 N3 10 32
HN03 -941610E+05 63.0129 H N 0113
PBO -e10350E+06 223.1994 PB 011
DEGDN -o10350E+06 196s1172 C H N 04 8 2 7
AN -*87370E+05 80.0432 N H 02 4 3
MC -. 1750.0E +Q05 240.3058 C H N 015 16 2
HAN -,87600E+05 96.0430 N H 02 44
TATB -*33400E+05 222.11710 C H N 03 6 6
GLY -,15978E÷06 92.0944 C H 0383
EGLY -*10873E+06 62.0688 C H 02 6
78
BLAKE HEAT OF MOL. FORMULA
NAME FORMATION WEIGHT
CAL/MOLE
CEDAC -,32300E+08 24265.0000 983 1383 692
-059300E+03 31L9988 0
02
CETAC -,37340E+08 28376.0000 C H 01179 1579 789
TEGON 13850E+06 240,1710 C H N 0-.GD 6 12 2 8
BAD -. 13100E+06 153.3394 BA 0BAO 1
METRIO -. 10600E+06 255,142%) c 5 H N 0
ETHER -,66750E+05 74.1234 C H 0
TMAN -974100E+05 122.1246 C H N 0
PBZCO4 -,21950E+÷6 490.4086 PB C 0
DECA -,55120E+05 138.2522 C HDECA 10 is
EDON -. 15620E+06 186.1242 C H N 0
HN -. 60130E+05 95,0578 N H 0-. 3 5 3
UDMH -,12690E+05 60.0986 C H N
EOAN -. 12360E+06 124.0962 C H N 0
TRIAC =. 2o18E+06 218.2070 C H 0TRAC9 14 6
HMX ,17900E+05 296.1560 C h 0 NHM .790E054 8 8 8-
NC1IO0 -. 18026E+09 250754.5000 C H 0
6000 80,31 89,39 1969
79
BLAKE HEAT OF MOL. FORMULA
NAME FORMATION WEIGHTCAL/MOLE
NC101o -. 38079E+09 25087941000 C H 0 N6000 8028 894' 1972
NC1102 -. 18072E+09 251003o'9000 C H 0 N6000 8025 8950 1975
NC1103 -*18066E+09 251128o8000 C H 0 N6000 8022 8955 1978
NC1104 -. 18059E+09 251253°8000 C 4 0 N6000 8020 8961 1980
NCI1O5 -. 18052E+09 251378,9000 C H 0 N6000 8017 8966 1983
NC1106 -. 18045E+09 2515,04.Z000 C H 0 N6000 8014 8972 3986
NC1107 -. 18038E+09 251629.6000 C H 0 N6000 8011 8977 1989
NC1108 -. 18{032E+09 251755.1000 C H 0 N6000 8008 8983 1992
NC1109 -. 18025E+09 251880.8000 C H 0 N6000 8006 8989 1994
NC1110 -. 18018E+09 252006.5000 C H 0 N6000 8003 0994 1997
NC1111 -. 18011E+09 252132.4000 C H 0 N6000 8000 9000 2000
NC1112 -. 18005E+09 252258.4000 C H 0 N6000 7997 9005 2003
NC1113 -. 17998E+09 252384,6000 C H 0 N6000 7995 9011 2005
NC1114 -. 17991E+09 252510.9000 C H 0 N6000 7992 9017 2008
NC1115 -. 17984E+09 252637.2000 C H 0 N6000 7989 9022 2011
NC1116 -. 17977E409 252763.8000 C H 0 N6000 7986 9028 2014
NC1117 -. 17970E+09 252890v4000 C H 0 N6000 7983 9033 2P17
80
BLAKE HEAT OF MOL* FORMULA
NAME FORMATION WEIGHTCAL/MOLE
%C1118 -*17964E+09 253017*2000C C H 0 N6000 7980 9039 2020
NC1119 -,17957E+09 253144,1000 C H 0 N6000 7978 9045 2022
CLz12O -*17950E+09 253271.1000 C 4 0 N6000 7975 9050 2025
NC1121 -*17943E+09 25339863000 C H 0 N6000 7972 9056 2028
tAC1122 -o17936E+09 253525o0 c 6 C H 0 N
2 26000 7969 9062 2031
NC1123 -. 179292÷09 253685300000 C 6 09 N6000 7966 9067 2034
NC1124 -,17920E+09 253480.5000 C H 0 N6000 7963 9073 2037
NC1125 -,17915E÷09 25390890-000 C 4 0 N6000 7961 9079 2039
NCl126 -. 17908E÷09 25403620000 C H 0 N6000 7950 9084 2042
NC2127 -,17902E*09 254163.90,0 C H 0 N6000 7955 9090 2045
NC1128 -,17895E+09 254292.0000 C H 0 N6000 7952 9096 2.048
NC11Z9 -,17888E+09 25493402000 C H 0 N6000 7949 9101 2053.
NC1130 -. 17881E+09 25454,8. 5000 C '4 0 N6000 7946 910? 2054
NCI.131 -. 17874E+09 254676.90•0 C '4 0 N6000 7944 9113 2056
NC1132 -,.17867E+09 254805,.5000 C H 0 N6000 7941 9119 2059
NC1133 _, 17860E6.09 254934.20OI0 C H 0 N6000 7938 9124 2062
NC'.434 -o17853E+09 255063.1000 C 0H 0 N6000 7935 9130 2065
81
BLAKE HEAT OF MOL. FORMULANAME FORMATION WEIGHT
CAL/MOLE
NC1135 -. 17846E+09 255192.0000 C H 0 N6000 7932 9136 2068
NC1136 -. 17839E+09 255321,1000 C H 0 N6000 7929 9142 2071
NC1137 -*17832E+09 255450,3000 C H 0 N6000 7926 9147 2074
NC1138 -#17825E+09 255579,7901D C H 0 N6000 7923 9153 2077
NCL139 -o17816E+09 255709.2000 C 6 4 0 N6000 7921 9159 2079
NC114•O -,17611E+09 255838.8000 C H 0 N
6000 7918 9165 2082
NC1141 -17807.E+09 255968.6000 C 4 0 N6000 7915 9170 2085
NC114•2 -. 17797E+09 256098.4000 C H 0 N6000 7912 9176 2088
NC1143 -,17790E+09 25622885000 C ti 0 N6000 7909 9182 2091
NC1146 -,17783E+09 256358.6P00 C H 0 N6000 7906 9188 2094
NC1145 -,17776E+09 256488.9000 C Hl 0 N6000 7903 9193 2097
NC1146 -*17769E+09 256619.3000 C H 0 N6000 7900 9199 2105
NC11497 -,17762E+09 25749018000 C H 0 N6000 7897 9205 2103
-•NC1l148 -. 17755E+09 25688p. •500• C H 0 N'• 6000 7695 9211 2105
NC1149 -*17748E+09 25701143000 C H 0 N- 6000 7892 9217 2108
-•:NCI150 -° 1Y'71E +09 257142.23000 C H 0 N
& 6000 7889 9222 2111
NC1151 -,17734E+09 257273.3000 C 0H 0 N86000 7886 9228 2114
•-• 82
BLAKE HEAT OF MOL* FORMULANAME FORMATION WEIGHT
CAL/MOLE
NC1152 -. 17726E+09 257404.6000 C 4 0 N6000 7883 9234 2117
NC1153 -. 17719E+09 257535.9000 C H 0 N6000 7880 9240 2120
NC1154 -. 17712E+09 257667.4000 C 4 0 N6000 7877 9246 2123
NC1155 -617705E+09 257799.0000 C H 0 N6000 7874 9252 2126
NC1156 -,17698E+09 257930.7000 C H 0 N6000 7871 9258 2129
NC1157 -*17691E+09 258062.6000 C H 0 N6000 7868 9263 2132
NC1158 -017684E+39 258194°6000 C H 0 N6000 7865 9269 2135
NC1159 -*17677E+09 258326.8000 C 4 0 N6000 7862 9275 2138
MC1160 -*17669E+09 258459.1000 C H 0 N6000 7860 9281 214%)
NC1161 -*17662E+09 258591.5000 C H 0 N6000 7857 9287 2143
NC1162 -917655E+09 258724.1000 C H 0 N6000 78!4 9293 2146
NC1163 -. 17648E+09 258856o8000 C 4 0 N6000 7851 9299 2149
NC1164 -,17641E409 258989.6000 C H 0 N6000 7848 9305 2152
NC1165 -917634E÷09 259122*6000 C H 0 N6000 7845 9310 2155
NC1166 -*17626E+09 259253.7000 C H 0 N6000 7842 9316 2158
NC1167 -,17619'.+09 259388.9000 C H 0 N6000 7839 9322 2161
NC1168 -917612E+09 259522.3000 C H 0 N6000 7836 9328 2164
83
SLAKE HEAT OF M0L FORMULA
NAME FORMATION WEIGHTCALIMOLE
NC1169 -. t7605E+09 259655,8000 C H 0 N6000 7833 9334 2167
NC1170 -. 17598E+09 259789s4000 C 4 0 N6000 7830 9340 2170
NC1171 -*17590E+09 259923.2000 C H 0 N6000 7827 9346 2173
NC1172 -,17583E+09 26005792000 C 7 N6:•00 7824 9352 2176
NCl173 -o17576E+09 26019192000 C H 0 N6000 7821 9358 2179
NL1174 -*17569E+09 260325.4000 C H1 0 N6000 7818 9364 2182
NC1175 -. 17561E+09 260459.8000 C 41 0 N6000 7815 9370 2185
NC1176 -, 175•4E+Q9 260594s3000 C H 0 N6000 7812 0376 2188
NC1177 -. 17547E+0) 260728.9000 C H 0 A6000 7809 9382 2191
NC1178 -,17540E+09 260863.6000 C 4 0 N6000 7806 93a8 2194
NC1179 -. 17532E+09 260998.5000 C H 0 N6000 7803 9394 2197
NCL180 -0175251.09 261133.6000 C H 0 N6000 7800 9400 2200
NCl1" -. 17518E +4', 261268.8000 C H 0 N6000 7797 9406 2203
NClezS -017510Er09 261404.1000 C H 0 N6000 7794 9412 2206
NC1183 -. 175u3E+09 261539,5000 C 4 0 a6000 779) 9418 2209
NC1184 -917.%96E+09 261675*1000 c H 0 N6000 7788 9424 2212
NC1185 -. 17488E÷09 251810.9000 C 4 0 N6000 7765 9430 2215
BLAKE HEAT OF NOL. FORMULA
NAME FORMATION WEIGHTCAL/MOLE
NC1186 -. 17481E+09 261946.8000 C 6 0 N" ~6000 7782 9436 2218
NclC17 -. 17474E+09 262062.8000 C H 0 N
6000 7779 9442 2221
NC1188 -*17466E+09 262218.9000 C H 0 N
6000 7776 9446 2224
NC1189 -. 07459E+09 262355.2000 C H 0 N6000 7773 9454 2227
NC1190 -017452E+09 262491.7000 C H N0
6000 7770 9460 2230
NC1196 -017407E+09 262628.3000 C H 0 N
6000 7767 9466 2233
NC1198 -. 17437E+09 262765.0000 C H 0 N
6000 7764 9472 2236
NC1193 -,174293E+09 •62901.9000 C H 0 N0 26000 7761 9478 2239
NC1194 -,174223+09 263038.9000 C H 0 N
6000) 7758 9485 2242
NC1195 -. 17415E+09 263176.1000 C H 0 N
6000 7755 9491 2245
NC1196 -. 17407E+09 26331340 000 C H 0 N6000 7752 9497 2248
NC1197 -. 17400E+09 263450.8000 C H 0 N6000 7749 9503 2251
NC1198 -. 17392E÷09 263588.4000 C H 0 N
6000 7746 9509 2254
NC1199 -. 173858+09 263756.1000 C 0 N
6000 7742 9515 2258
NC1200 -,*7377E+09 263864.0000 C '4 0 N
6000 7739 9521 2261
NCI.201 -. 17370E+09 264002.0000 C '4 O N
6000 7'36 9527 2264
NCI202 -,17363E+09 264140.2000 C H 06000 7733 9533 2267
85
BLAKE HEAT OF PIOL. FORMULA
NAME FORMATION WEIGHTCAI., MDL[
NC1L203 -917355E+09 264276.5000 C H 0 N6000 7730 9540 2270
NC1204 -*17348E+09 264417.0000 C H 0 N6000 772? 9546 2273
NC1205 - 17340E+09 26455!*60UO C H 0 N6000 7724 9552 2276
NC1206 -. 17333E+09 264694.3000 C 4 0 N6060 7721 9558 2279
NC1207 -*17325E+09 264833.200 C H 0 NI 6000 7718 9564 2282
NC1208 -*17318E+09 264972.2000 C 4 0 N6000 7715 9570 2285
MC1209 -o17310E+09 265111.4000 C 4 0 N6000 7712 9577 2288
NC1210 -017303E+09 265250.7000 C H 0 N6000 7709 9583 229i
NC1211 -. 17295E+09 265390.2000 C 4 0 N6000 7705 9589 2295
NC1212 -. 17287E+09 265529.80,0C C H 0 IN6000 77C2 9595 2298
NC1213 -. 17280E+09 265669.6000 C H a N6000 7699 qb01 2301
NC1214 -e17272E÷09 265809.5000 C H 0 N601Oe 7696 9608 2304
NC1215 -. 17265E÷09 265949.6000 C H 0 N6000 7693 9614 2307
liC2zib -. 17257E+09 266089.8000 C 4 0 46000 7690 9620 2310
NCIZ17 -. 17250E+09 266230.2000 c H 0 H6000 7687 9626 2313
NCi218 -*17242E+09 266370o7000 C .4 a N
6000 7684 9b33 2316
NC1219 -. 17234E+09 266511.3000 C H a N6000 7681 9639 2319
86
BLAKE HEAT OF WLH FORMULA
NAME FORMATION WEIGHTCALIMOLE
NC1220 -. 17227E+09 266652.1000 C H 0 N6000 7677 9645 2323
NC1221 -. 17219E+09 266793f1000 C H 0 N6000 7674 9651 2326
NC1222 -. 17212E+09 266934.2000 C H 0 N6000 7671 9j658 2329
MC1223 -. 17204E+09 267075.4000 C H 0 N6000 7668 9664 2332
NC1224 -,17196E+09 267216990P0 C H 0 N6000 7665 9670 2335
NC1225 -. 17i89E+09 26735804000 C H 0 N6000 7662 9677 2338
NC1226 -. 17181E+09 267500.1000 C H 0 4
6000 7659 9683 2341
NC122? -• 17173E+O9 267642.0000 C H 0 N
6000 7655 9689 2345
NC1228 -. 17166E+09 267784.00PP C H 0 5N6000 7652 9695 2348
NC1229 -. 17158E+09 267926.1000 C H 0 N
6000 7649 9702 2351
NC1230 -. 17150E+09 268068.40P0 C 4 0 0N6000 7646 9708 2354
NC1231 -. 17143E+09 268210,9000 C H 0 N6000 7643 9714 2357
NC1232 -,17135E+09 268353.5000 C H 0 N
6000 7640 9721 2360
HC1233 -. 17127E+@9 268496,2000 C H 0 N
6000 7636 9727 2364
NC24 -017119E+09 268639*2000 C H 0 N600: 7633 9733 2367
NC1235 -. 17112E+09 268782.2000 C H 0 N2•-• 6009 7630 9740 2310
NC1236 -,17104E+09 268925*400 0 C 0 L N2313
6000 7627 9746 2373
f• 87
BLAKE HEAT OF MOL. FORMULANAME FORMATION WEIGHT
CAL/MOLE
NC1237 -. 17096E+09 269068.8000 C H 0 N6000 7624 9753 2376
NC1238 -. 17088E+09 269212.3000 C H 0 N6000 7621 9759 2379
NC1239 -. 17081E+09 269356.0000 C 4 0 N60CO 7617 9765 2383
NC1240 -. 17073E+09 269499.8000 C 6 i 0 N6000 7614 9772 2386
NC1241 -*17065E+09 269643.8000 C H 0 N6000 7611 9778 2389
NC1242 -*17957E+09 269787.9000 C 60 0 N6000 7608 9785 2392
NC1243 -. 17050E+09 269932.2000 C I 09 N6000 7605 9791 2395
NC1245 -,17342E+09 270076.7000 C H 0 N6000 7601 9797 2399
NC1245 -. 17034E+09 Z70221e3000 C H 0 N6000 7598 9804 2402
NC1246 -. 17026E*09 270366.0000 C H 0 N
6•00 7595 981"0 2405
NC1247 -,17018E+09 270510.9000 C H 0 N6000 7592 9817 2408
NC1248 -,17010E+09 Z70656.0001 C H 0 N6000 7588 9823 2412
NC1249 -. 17003E+09 270801.2000 C H 0 N6000 7585 9830 2415
NC1250 -. 16995E+09 27P946*6900 C L 0 a6000 fb0 9836 2418
NC1251 -,16987E+09 271092.1000 C H 0 N6000 7579 9842 2•21
NC1252 -. 16979E+.09 271237.8000 C 60 0 N60C0 7576 9849 2424
NC1253 -. 16971E+09 271383.7000 C H 0 N6000 7572 9855 2428
V8
BLAKE HEAT OF MOLe FORMULA
NAME FORMATION WEIGHT
CALIMOLE
NC1254 -,16963E+09 271529.7t000 C H 0 N• ~6000 7569 9862 24131
NC1255 -. 16955E+09 271675.8000 C H 0 N• 6000 7566 9868 2434
NC1256 -,16947E+09 271822,1000 C H 0 N6000 7563 9875 2437
NC.257 -*16940E+09 271968.6000 C 6 1 0 N
6000 7559 9881 2441
NC1258 -,16932E+09 272115.2000 C H 0 N6000 7556 9888 2454
NC1259 -016920E+09 272262.1000 C 6 0 N6000 7553 9894 2447
NC1260 -. 16916E+09 272409.0000 C H 0 N6000 75409 9901 2451
NC1261 -.16908E+09 272556.1000 C H 0 N6000 7546 o 908 2454
MC1262 -. 16900E+09 272703.4000 C H 0 N6000 75273 9914 2457
NC1263 -. 16892E+09 272850.8000 C H 0 N6000 7540 9921 2470
NC1269 -.16884E+09 272998.4000 C 8 0 N6000 7536 9927 2486
4C1265 -. 16876E409 273146.1000 C H 0 N" ~6000 7533 9934 2467
I4C126b -. 16868E+09 2732q9.,0000 C H 0 N
6000 7530 9940 2470
NC1267 -• 1b860E+09 27344•2.1000 C H 0 N
6000 752"7 9947 2473
N4C1Z68 -. 16852E+09 273590.3000 C H 0 N
6000 7523 9954 2477
NC12E69 -. 16844E+09 213738.7000 C H1 0 N
• 6000 7520 9960 2480
NC1270 -. 16836E+09 273887.2000 C H 0 H
6000 7517 9967 2483
i 89
BLAKE HEAT OF MOL9 FORMULANAME FORMATION WEIGHT
CAL/MOLE
NC1271 -. 16828E+09 274036*00PO C H 0 N6000 7513 9973 2487
NC1272 -. 16820E+09 274184.8000 C H 0 N6000 7510 9980 2490
NC1273 -#16812E+09 274333.9P010 C H 0 N6000 7507 9987 2493
NC1274 -,16804E+09 27448391000 C H 0 N6000 7503 9993 2497
NC1275 -. 16796E+09 274632.40P0O C H 0 N6000 7500 10000 2500
NC1276 -*16788E+09 274781,9000 C 4 0 N6000 7497 10006 2503
NC1277 -o16779E+09 274931,60,00 C H 0 N6000 7493 10013 2507
NC1278 -. 16771E+C9 275081.5000 C H 0 N6000 7490 10020 2510
NC1279 -. 16763E+09 275231•5P0.0 C H 0 N6000 7487 10026 2513
NC1280 -@16755E+09 275381e6000 C H 0 N6000 7483 10033 2517
NC128. -, 16747E 09 275532.0t00 C H 0 N
6000 7480 10040 2520
NiC1282 -,16739E÷09 275682.5000 C 4 0 N6000 7477 10047 2523
NC1283 -*16731E+09 275833010l00 C H 0 N6000 7473 10053 2527
NC1284 -*16723E+09 275984.0000 C H 0 N6000 7470 10060 2530
NC1285 -. 16714E+09 276135. o0.010 C H 0 N6'000 7467 10067 2533
NC1Z86 -o16706E+09 276286.1000 C H 0 N6000 7463 10073 2537
NC1287 -. 16698E+09 276437•5000 C H 0 N6000 7460 10080 2540
90
BLAKE HEAT OF MOL. FORMULANAME FORMATION WEIGHT
CAL/MOLE
NC1288 -*16690E+09 276588.9000 C H 0 N6000 7457 10087 2543
NC1289 -. 16682E+09 276740.6000 C H 0 N6000 7453 10094 2547
NC1290 -. 16674E+09 276892.4000 C H 0 N6000 7450 10100 2550
NC1291 -. 16665E+09 277044.4000 C H 0 N6000 7446 10107 2554
NC1292 -916657E+09 277196.6000 C H 0 N6000 7443 10114 25•57
NC1293 -. 16649E+09 277348.9000 C H 0 N6000 7440 10121 256C
NC1294 -. 16641E+09 277501o4000 C H 0 N600P 7436 10127 2564
NC1295 -. 16632E+09 277654.1000 C H 0 N6000 7433 10134 2567
NC1296 -. 16624E÷09 277806.9000 C H 0 N60P0 7430 10141 257C
NC1297 -. 16616E+09 277959.9000 C H 0 N6000 7426 10148 2574
NC1298 -916608E+09 278113.0000 C H 0 N6000 7423 10155 2577
NC1299 -. 16599E+09 278266.4000 C H ' NS~6000 7419 10161 2581
NC1300 -. 16591E+09 278419.9000 C 4 0 N4 6000 7416 10168 2584
NC1301 -. 16583E+09 278573.6000 C H 0 NS6000 'p412 10175 2588
NC1302 -. 16574E+09 278727,4000 C H 0 N6000 74109 10182 2591
NC1303 -. 16566E+09 278881.4060 C H 0 N6000 7406 10189 2594
NC1304 -°16558E+09 27903:'.6000 C H a N6000 74,OZ 10196 2598
._;; ,•9!
SLAKE HEAT OF MOL* FORMULA
NAME FORMATION WEfGHTCALIMOL.
NC1305 -,16549E+09 279190.0000 C 6 7 0 Ne000 7399 10202 2601
NC1306 -. 16541E+09 279344.5000 C H 0 N6000 7395 10209 2605
NC1307 -. 16533E+09 279499.2000 C H 0 N6000 7392 10216 2608
NC1a08 -. 16524E+09 279654.0000 C H 0 N6000 7388 10223 2612
NC1109 -o16516E+09 2798092715000 C H 0 N6000 7385 10230 2615
NC1310 -165082E+09 28099643000 C H 0 N6000 73'82 10237 2818
NC1314 -. 16499E+09 280159o7000 C H 0 N6000 73-8 10264 2622
NC1312 -. 16491E+09 28027542000 C H 0 N
6000 7375 10251 2625
NC1313 -,16482E+09 280431.0000 C 7 0 N6000 7371 10258 2629
NC1318 -,16470E+09 28058619P1 P C H 0- N6000 7368 10264 2632
HC1315 -. 16465E+09 280742.9000 C H 0 N6000 7364 10271 2636:
NC1319 -. 164572+09 280899620o75 C H 0 N6fl00 7361 10278 2639
NC1317 -. 164492E+09 281055.6000 C H 0 N6000 7357 10285 2643
NC1318 - 16440E+09 281212, 200 C H 0 N' ~6000 7354 10292. 2646
NC1319 -. 164322 +09 281369.000C C H 0 H
6000 7350 10299 2650
HC132O -. 164232+09 2815 25.90100 C H 0 N
• 6000 7347 10306 2653
NC1321 -,16415E+09 281683.0000 C H 0 N26000 7343 10313 2657
92
BLAKE HEAT OF MOL* FORMULA
NAME FORMATION WEIGHT
CALIMOLE
NC1322 -, 16406209 261840.3000 C H 0 N6000 7340 10320 2660
MC1323 -,16398E+09 28199T4.8000 C H 0 N6000 7336 10327 2&66
HC1324 -. 16389E+09 28a-t155 .5000 C H 0 N6000 733~3 1u33 4 2667
NC 1-3 2-5 -. 16381E+09 28- "2-- #3000 C 6 4 0 N
6000 7329 10341 2671
NC1.326 -,16372E÷09 28P_.-7l.,30@ C H 0 N
6000 7326 10348 2--7•'4
NC1327 -,16364E409 282629. '•i' C H 0 N
6000 7322 10355 267-8
NC1328 -. 16355E÷09 28278-7.8000 C H 0 N
"6000 7319 10362 Z681
NC1329 -,16346E+09 2-2.946 *.4000 C H 0 N
600-0 731-5 103:69 Zfr"
NC1330 -. 16338E+09 2&3105,1000 C c H N
NC1330 -, +0 8 •,0 0 b bB8
NC1331 -,16329E+09 283-64,0000 C H 0 N
6000 7"3O 1A0"3 a&929'
NC1332 -,16321E+09 2 834523.0000 C H4 0 N
62000 730I5 •S-91 269'5
NC1333 -*16312E+09 283582.3000 C 7 0 Z
00000 72 H 0 N5 239 --&6°
NC1334 -,16303E909 283791.7004 4 H 0 2|6000 7298 i04-1 2106
NC1336 -,16286E+09 283901-!1000 C ' 0NC133 .1625E+096000 7-294 104-12 22-06
NC1336 -016286E+09 284061,1000 c -0H72" a4 l0f1 N?60•00 729w 1.0419 2F-09
NC1337 -016278E+09 284221.1000 C 6 7 04 N• 8000 7281 i1-26 2713
NC1338 -,16269E+09 284381,2000 C $ 0 N
6000 7283 104-S-3 2717
93
BLAKE U-EAT OF MOL. FORMULA
NAME FORMATION WEIGHTCAL/MOLE
NC1339 -*16260E+09 284541.5000 C H 0 N60,0 7280 10440 2720
NC1340 -.1625ZE+09 284702.0000 C H 0 N6000 7276 10447 2724
NC1341 -*16243E+09 2848b62700P c H 0 N6000 7273 10455 2727
NC1342 -016234E+09 285023o6000 C H 0 N6000 7269 10462 2731
NC1343 -e16225E+09 Z85184,7000 C H 0 N6000 7266 10469 2734
NC1344 -016217E+09 285345.9000 C H 0 N6000 7262 10476 2738
NC1345 -916208E+09 285507.3000 C H 0 N6000 7258 10483 2742
NC!.346 -. 16199E+09 285668.9000 C It 0 N"6000 7255 10490 2745
NC1347 -. 16191E+09 285830.7000 C H 0 N6000 7251 10498 2749
NC13-48 -0b16182E-+09 2 8 59q2,6000 C H 0 N6000 7248 10505 2752
NC1349 -. 116173E+09 286154.8pO C '-4 0 N"6000 7°-" 10512 2756
NC1350 -_16164E-+09 2B6311.71000 C H 0 N"6000 7240 10519 2760
NC1351 -416156E+09 2864-7-9.6000 C 6 1 T1 5 N6000 7231• 10526 2763
MC1352 -. 16147E+09 E5,66--, 3"000 C -i 0 N6000 723-3 10534 2767
NC135-3 -. 16138E+09 286810"5 °2000 C -4 0 N6000 7230 10541 2770
NC13-54, -. 1619E+09 286968. 3'0UO C ti 01 N6000 7226 10548 2774
-. 161a0E+0 287131.6P0K C H 0 NN000 7Z22 o60555 2778
94
BLAKE HEAT OF MOL. FORMULA
NAME FORMATION WEIGHTCAL/MOLE
NC1356 - 16111E+09 287295.0000 C 1 0 N6000 7219 10563 2781
NC1357 -. 16103E+09 287458.6000 C H 0 N" ~6000 72.15 10510 2785
NC1358 -. 16094E+09 287622.5000 C H 0 N6000 7211 10577 2789
NC1359 -. 16085E+09 287786.5000 C 4 0 N6000 7208 10584 2792
NC1360 -,16076E+09 287950.000 6 C H 0 N6000 7204 10592 2796
NC1361 -. 16067E+09 288115.0000 C H 0 N6000 7200 10599 2800
NC1362 -,16058E+09 28827996000 C 1 0 N6000 7197 10606 2803
NC1363 -. 16049E÷09 288444.3000 C H 0 N6000 7193 10614 2807
NC1364 -916040E+09 288609.3000 C H 0 N6000 7189 10621 2811
NC1365 -,16032E+09 288774e4000 C H 0 N6000 7186 10628 2814
NC1366 -. 16023E+09 288939o7000 C H 0 N6000 7182 10636 2818
NC1367 -- 16014E+09 289105.2000 C H 0 N6000 7178 10643 2822
NC1368 -#16005E+09 289270.9000 C H 0 N6000 7175 10650 2825
NC1369 -,15996E+09 289436.8000 C H 0 N6000 7171 10658 2829
NC.1370 -*15987E+09 289602090C0 C 0 N6000 7167 10665 2833
NC1371 -*15978E+09 289769.2000 C H 0 N6000 7164 10673 2836
SNC1372 -,15969E49 289935,6"000 C H 0 NNl 6000 7160 10680 2840
95
BLAKE HEAT OF MOLe FORMULA
NAME FORMATION WEIGHTCAL/MOLE
NC1373 -. 15960E+09 290102.3000 C H 0 N6000 7156 10687 2844
NC1374 -*15951E+09 290269e1000 C H 0 N6000 7153 10695 2847
NC1375 -,15942E+09 290436.2000 C H 0 N6000 7149 10702 2851
NC1376 -. 15933E+09 290603.4000 C H 0 N6000 7145 10710 2855
NC1377 -,15924E+09 290770.8000 C A 0 N6000 7141 10717 2859
4C1378 -*15915E+09 290938e4000 C H 0 N
6000 7138 10725 2862
NC1379 -. 15906E+09 291106.2000 C i 0 N6000 7134 10732 2866
NC1380 -*15896E+09 291274.2000 C H 0 N6000 7130 10740 2874
NC1381 -015887E+09 291442.4000 C H 0 N6000 7127 10747 2873
MC1382 -. 15878E+09 291610.0,0i0 C H 0 N"6000 7123 10754 2877
NC1383 -. 15869E+09 291779.4000 C 4 0 N6000 7119 10762 2881
MC1384 -915860E+09 291948,20PC C H 0 N"6000 7115 10769 2885
NC1385 -915851E+09 292117.2000 C 4 0 N6000 7112 10777 2888
NC1386 -. 158642E09 292286.3000 C H 0 N
6000 7108 10785 2892
NCL387 -. 15833E+09 292455.7000 C 4 0 N6000 7104 10792 2896
NC1368 -,158232+09 292625.3000 C H 0 N6000 7100 10800 2900
NC1389 -015814E+09 292795,0000 C H 0 N66000 7096 10807 2904
:J'•]-96
BLAKE HEAT OF MOL, FORMULA
= NAME FORMATION WEIGHTCALIMOLE
NC1390 -. 15805E÷09 292965.0000 C H a NN 96000 7093 10815 2907
NC1391 -. 15796E+09 29313591000 C H 0 NS~6000 7089 10822 2911
SNC1392 -. 15787E+09 293305.5000 C H 0 N
SC H 0NC1392 -. 15787E+09 2933056"0000 6000 7085 10830 2915
NC1393 -,15778E÷09 293476#0000 C H 0 N
6000 7078 10845 2922
NC1395 -o15759E+09 29381767000 C H 0 N6000 7078 10845 2922
NC1396 -. 15750E+09 29398819000 C H 0 N" ~6C00 7074 10853 2926
NC1397 -,15741E+09 29196082000 C DH C N" ~6000 7070 10860 2930
NC1398 -. 15731E+09 294331.8000 C H 701 N
6000 7062 10875 293e
NC1399 -o15722E+09 294503.5000 C H 0 N6000 7058 10883 2942
NC1400 -,15713E+09 294675°5000 C H 0 N6000 7055 10891 2945
APPENDIX C
OUTPUT FROM TEST CASEq
99/9
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