1、REPORT 1037GENERAL METHOD AND THERMODYNAMIC TABLES FOR COMPUTATION OF EQUILIBRIUMCOMPOSITION AND TEl!lPERATT.EtE OF CHEMICAL REACTIONS 1By EAEL h. HUFF,SANFORDand (g) i.sentropicezpammbn.to an a88ignedprewure, tempera-ture, or Mach nwnkr. Tabe8 of thermodynamicfunctionsneeded with this method are Cn
2、cludedfor 41?sub8tance8for corL-wvience in numerical computati0n8.INTRODUCTIONThe theoretics.Iperforiuance of propulsion systems havinghigh combustion temperatures can be calculated on the as-sumption that chemicaI equilibrium exists among the prod-ucts of reaction. The equilibrium composition and t
3、he tem-perature for a system “ofN products of reaction are deter-mined by the simultaneous soIution of at Ieast N+ 1 equa-t.ions invoking dissociation, mass balance, aad energy or”entropy balance. This calculation becomes increasinglydi%icult as N increases.Numerous methods for soking these equation
4、s may befound in the literature that provide a successive approxima-tion or trial-and-error process for detmmining the composi-tion at an assumed temperature and pressure. Examples ofthese methods are found in references 1 to 4. When it isdesired to tid the temperature of a system in equilibrium,wit
5、h a parametm such as entropy or enthalpy assigned, thecomposition is uswdly computed at a sequence of tempera-tures that either converge to the correct temperature or arespaced to permit interpolation to obtain the correct tem-perature.A rapidly convergent successive approximation processthat determ
6、ines composition at an assigned temperature orthat simultaneously determines both composition and tem-perature for assigned wdues of another parameter, such asenthalpy or entropy, was developed at “the NTACA LewisLaboratory during 1948 and ia presented herein. This proc-,ess aJ.so permits co-reputat
7、ion of the partial derivativesrequired to compute such thermodynamic properties asspecific heat and velocity of sound cotiesponding to ckmni-cal equilibrium. The equations are deried that are re-quired for solution of the following cases: (1) combustion atconstant pressure or volume; and (2) isentro
8、pic expansionto an assigned pressure, temperature, or Wach number.EmunpIes are- given for (1) constant-pressure adiabaticcombustion; (2) iaentropic qansiort to an assigned pres-sure; and (3) isentropic expansion to an assigned Machnumber.This method is particularly suitable for problems havinga larg
9、e number of products of reaction and for problems thatrequire determination of partial derivatiws. Although it ispossible, at least in speciacases, to devise a procedure thatinvolves less numerical computation, the method presentedis applicable in a wide variety of cases and its numericalapplication
10、 to a given process is always simple and essen-tially the same for FLUreactions.TabIes of thermodynamic functions are needed for com-puting equdibrium compositions and temperature of them- .icd reactions. Tabks containing the functions specific heatat constant pressure C:, sensibIe enthslpy HHs, and
11、molar entzopy JS$exist for at least part of t-hedesired tem-perature rsnge for most of the substances of interest-in theanalysis of aircmft-propukon systems. Several specialfunctions are required for convenient use with the methoddescribed herein; tabks were therefore prepared, horn Jan-uary to June
12、 1949, that contain, in addition to C;, HI?j,and S;, assigned values of enthalpy Wr and -dues of log Kand (logarithm of equilibrium constant and enthalpychange divided by gas constant times temperature., respec-tivey, for reaction of formation of a substance horn itseknnemk in atomic gas state).The
13、data seIected from various sources or computed bythe N7ACAhave been smoothed, interpolated to every 100,and extended to 6000 K. A high degree of self-consistencyhas been maintained in the temperature range horn 1000to 6000 K by computing from specific-heat data the valuesof the other functions, and
14、retaining, in generaI, more decimalpkes than em significant. Interpolation formulas aregiven that permit computation of self-consistent values forsll the functions at any temperature betmeen 1000 and6000 KISyedesNAATSa13, AietMfmComWtitintiEQ=Cm (b) Conservation of mass;(c) conservation of energy; (
15、d) pressure; and (e) entropy.Equations (a) and (b) are used to specify chemical equilib-rium and, when used with any two of the remaining equations,define a process.The successive approximation procedure presented hereinfor finding the simultaneous solution of a specific combinationof equations (a.)
16、 to (e) consists.of the following step thefugacity of each condensed phase is equal to 1 atmosphme;the total volume occupied by the liquids and solids is negli-gible with respect. to the volume occupied by the gases; andthe iquid and solid partic.leshave the same temperature andflow velocity as the
17、gases. .Dissociation equations.For simplicity of riomenckitmwand presentation the equations for dissociation can bewritten in terms of the atomic gas as .-afZ+bf17+ . . . +Ze; “!E;H;R1AH;hh,h”h,*kk”IJKliqMu,m.IVu withsubscript, number of atoms of each elementwithin chemicaI formula; in thermodynamic
18、tables, interpolation coefficientsmolar specfie heat at comtant pressure andstandard conditions (cal)(mole) (“K)specific heat coefficient for matrixmolar specific heat at constant olume andstandard conditionsOperator-(:$T)= ,mokw internaI energy at standard conditionsinternal energy per equivalent f
19、ormulamolar free energy at standard conditionsgas phase.of substancechemical energy afi 0 K and standard condi-tions (kmI/moIe)sum of sensible entklpy and chemical energyat temperature T and standard conditions(kcal/mole)sensible enthalpy at tempwature T andstandard conditions (kcal/moIe)enthalpy ch
20、ange due to formation of snb-stance horn its elements in atomic gasstate divided by RTenthaIpy change due to formation of sub-stance from its elements in standard state(kcal/mole)enthalpy per equivalent formula.ent,haIpycoefficient for matrixsum of heat-and kinetic energiesper equivalentformularatio
21、 of Pkmc.ks constant times velocity oflight to Boltzmanns constant, 1.43847(cm) (“K)moment of inertia n) (cmz)dime-ionel constantequilibrium constantliquid phase of substancelIach numbermolecukw weight of equivalent formulamass flow per secondnumber of products of reaction:PQ,TR.8s)Ttr., r,uTr. with
22、 subscript, matris symbolLt. 1universal gas constant, 1.98718 (cal/(mole)(K)molax entropy at standard conditions (call -(mole) (K)entropy per equivalent formula; in thermo-dynamic tables, solid phase of substanceentropy coefficient for matristemperature (“K)throat meaunit matrixvelocity of sound-roI
23、umevelocity of flowelements within representatke chemicalformulacorrection -wriablessubmatricesincrementincrement due to a temperatur chmge; withsubscript,error parametertotal-error parameterspectroscopic constfmtespectroscopic constants densitynumber of atoms tithin chemical formulafueloxidantany p
24、oint in nozzle -.number of types of gaseous moleculeinitial given conditionconstant,pressureconstant entropytemperature (?K)product rndex numbers (i) that designateatomic gases -product index numberREFERENCES1. Brinkley, Stuart R., Jr.: CalculatioII of the Equilibrium Com-position of Systems of Wany
25、 Constituents. Jour. Chem. Phys.TOL 15, no. 2, Feb. 1947, pp. 107110.2. Krieger, F. J., amd Whitel W. B.: A SimplMed Method for Com-puting the Equilibrium Compceitkm of Gaseous Systems. Jocr.Cherm Phys., I-OL16, no. 4, ApriI 194S1pp. 353-360.3. Huff, VsarI N., and Cakert, CIyde S.: Charts for the Co
26、mputationOf Eqibrim Compcwition of Chemical Reactions in the Carbon-Hydrogen-Ogen-lFitrogen System at Temperaturesfrom 2000” to 5000 K. NACA TX 1653, 1948.4. Wnternitz, Paul F.: A Method for Cavitating SimultaJWCus,Homogeneous G= Equilibria and Flame Temperatures. ThirdSymposium on Combustion and Fl
27、ame and Explosion Phenomena.The Williams k Wilkins Co. (Baltimore), 1949, pp. 623-633.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-846 REPORT 1037NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS.5. Ekmrborough,James B.: Numerioal Mathematical Analysis.
28、 JohnsHopkins Press (Baltimore), 1930, pp. 187-190.6. Crout, Prescott D,: A Short Method for Evaluating Determinantsand SoIving Systems of Linear Equations with Real or ComplexCoefficients. AIEE Trans. (Suppl.), vol. 60, 1941, pp. 123E-1241.7. Pipes, Louis A.: Applied Mathematics for Engineers aid P
29、hysi-cists, Mc.Graw-Hill Book Co., Inc. (New York and London),1946, pp. 78-79.8. Woolley, HaroId W.: Thermodynamic Functiom for MolecularOxygen in the Ideal Gas State. Nat. Bur. Standards Jour. Res.,VOL40, no. 2, Feb. 1948, pp. 163-163. .-9. DuMond, Jesse W. M., and Cohen, E. Richard: Onr Knowledgeo
30、f the Atomic Ccmstanta F, N, m, and h b 1947, and of OtherConstants Derivable Therefrom. Rev.-Modern Phys., vol. 20,no. 1, Jan. 148, pp. 82-108.,.10. Anon.: Tablea of Selected Values-of Chemical ThermodynamicProperties. Nat. Bur. Standards, Deo.-=l, 1947.11. Anon.: Tables of Selected Values of Chemi
31、cal ThermodynamicProperties. Nat. Bur. Standards, June”30, 194S.12. Rossini, Frederick D., Pitzer, Kenneth- S., Taylor, William” J.,Ebert, Joan P., Kilpatrick, John E., Beckett, Charlw W.,WiUiams, Mary G., and Werner, Helene G.: Seiected Values ofProperties of Hydrocarbons. Circular C461, Nat. Bur.
32、Standards,Nov. 1947. .13. Woolley, Harold W.: Dry Air (Ideal GcaI Metall-urgy. V. Heats of Fusion of Inorganic Substances, Bull, 393,Bur. Minw, 1936.22. Davis, William D., Mason,- h S., and Stogeman, Gebhard:Thermai Properties of Some Hydrid%.Loo0 00i150 0 .1010 I 16 0 laml m3L7.77s =+- n !-:.-1- _-
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