NASA Technic,aLMemorandum 86885/

,/

Compute]: Prog_ramfor Calculation'..'

i_ of Complex Chemical EquilbdumCompositions andApplicationsSupp_ portP perti 'nt I--Trans ro es

l_ASk-TM-868851 COM£OTEI_ £FCGI_A_ FOil N85-1_6_3CALCOI&TICN 0¥ COMPIgX CBE_ICAi E_UIL£BBIU_

C?_OSITIC_S ANE A_LICAT_Cg-_. SUPPLESE_II. TRASS_ORT P_C_EB_IES (h_SA) 26 p Oncla£

BC A03/_ A01 CSC/ 20M G3/77 13101

: Sanford Gordon & Associates ,:.Cleveland, Ohio .:i

end

Bonnie J. McBride and Frank J. ZeloznikLewis Research Center i._

,: - • Cleveland,. Ohio

it. _, .

&, | L,

m - .• "8

1985008354

CONTENTS

Page

. SUHMARY ............................................. l

• INTRODUCTION................................ 1

APPROXIMATEMIXT_JREmETHODS ........................... 2Sources of Approximate Methods .............................. 2Se]ectton of Approximate Method ........................... 6

COMPUTERPROGRAMEORTRANSPORTPROPERIIES ................... 6Transport-PropertyQataset .......................... YSubroutine UTRAN .................................. 7Suurouttne INPUT ............................... 7Subroutine TRANP ............................... 8Entry OUT4 tn Subroutine OUT] ...................... 8

DESCRIPIION OF.PROGRAM OUTPUT ....................... 8

SELECTION OF TRANSPORTPROPERTIES ..................... 9Sources of Properties for Pure Spectes .................. 9Sources of Properties for Btnary ]nteraGtlons .............. ]2

APPENDIX - SYhBOLS .............................. 13

REFERENCES ............................... 15

" _ "''_"- " ' - " • _..... .2

1985008354-TSA03

COHPUTERPROGRAHFORCALCULATIONOF CORPLE_CHEMICAL

EQULLIBRIURCORPOSIIIONSANDAPPLICATIONS ........................................

SUPPLERENTI - TRANSPORTPROPERTIES

Sanford GordonSanford Gordon& Associates ....

Cleveland, Ohto 44121

BOnnie 3. RcBrlde and Frank 3. ZelezntkNational Aeronautics and Space AdminiStration

Lewis Research CenterCleveland, Ohio 44135

SUHHARY

An addition to the computer program of NASA-SP-273is given that permits,transport property calculations fo:r the gaseous phase. Approximate mixture t

formulas are used to obtain vlscosqty and frozen thermal conductivity. Reac-tion thermal conductivity ts obtained by the samemethod as tn NASATN 0-7056 .....

_-__ Transport properties for 154 gaseous species have been selected for use wtth_" the program.

_-_L 04, INTRODUCTION

Z!. An option for calculating the dilute-gas transport properties of complex-- chemical mixtures has been added to the chemical equilibrium program of-_" reference 1. Computer programs for c_lculattng mixture transport properties

are presently available (e.g., ref. 2). Reference 2 gives transport properties--"_ tn the form of collision integrals and uses the Htrschfelder "rigorous" method_. (ref. 3) for the viscosity and thermal conductivity of nonreactlng mixtures.

The Brokawmethod (refs. 4 and 5) ts used for the cor_trtbuttonof chemicalreaction to thermal, conductivity. The objectives are (1) to use _Lmethod for

-:" calculatlng, nonreacttng (frozen)_ mixture properties which is simpler than thatpresented tn refecence 2, Uhtle siLL1 retaining the sameaccuracy, and (2) to

_ use a simpler representation f_or the properties of pure specks and their-- binary interactions. These objectives shoul= _ubstantlalty. reduce calculation ................... times or increase the slze of the system which can-be calculated economically.

" In the new program transport properties for pure species and several I)tnary._ interactions are represented tn the functional form suggested Tn reference 6.• (See the section "TranSport-Property Oataset.") Mtxture viscosity Is Obtained

by an approximate method in a form first proposed by Sutherland (ref. $). HIX-"" . Lure f_'ozen thermal conductivity is obtained by an approximate method in the

form first proposed by WasstlJewa (ref. 8), which ls _lmtlar to Sutherland'sform for viscosity. ReaettOn thermal conductivity ts obtained In the samemanner as tn reference 2. lhe total thermal conductivity of the mixture Is

' the sumof the frozen and reaction thermal conductlvtttes.i

I lhts report does not repeat tte material presented In reference 1 (such. as) the equations and numerical techniques fer Obtaining chemical equilibrium com-

_:t positions, mixture thermodynamic properties, and various applications of theseproperties). Only additional meter_al relating to transport properties Is

_ given.=i!

I.I

-- - -- _:==l, __ ............ i • IN

'- ........"' 1985008354-TSA04

.o

APPROXIHATEHIXTUREHETHODS

Sources of A_prox_mate Hethods

_, In addttlon to the "Ttgorous" method for obtaining the mixture transportproperties mentioned tn the INTRODUCTION,numerousapproximate methodsmay be

_: found tn the ltteratu _. Someapproximate methods for mixture viscosity aredescribed tn re£erences 7 and 9 to 14, while someapproximate methods formixture frozen thermal conductivity may be found In references 8, 12, and 15

_: to 20. Host of these approximate methods have forms slmtlar to those first_:, proposed by Suther_and for vlscQslty (r_f. 7) and by _assl13ewa.for thermal;._-.. conductivity (ref. 8), which can be written as ......................

; q

_"

:. xln l_- = (I)_ nmtx!_ _

: xI + _ xj_Iji 3=I

j_..

_.- and

_, xl_ 1:_: Xmlx,fr = (2)

'!'_ X1 + _-___, xJ_IJ3=i

:, t =I J_t

;'_" where

_: n numberof gaseous species for transport calculations

xI mole fraction of species %

. nI viscosity of spe¢tes 1

_. nmtx viscosity of mixture J

i X_ thermal conductivity of species t

•: _m_x,fr frozen-thermal conductivity of mtxture

viscosity Interaction coefficient between species I and J (_1t _ _tl )

" '13 frozen, thermal conductivity Interaction coefficient between species_, I and 3 ('13 _ '31)

, The approximate methods of thts type differ only In the expressions forI, e13 an_ *t3" For example, Hlrschfelder's first approximation to htsiik

: tn equation (1) which ls used by someother authors _s a starting pointdertvlng other approximations to _tj. Hlrschfelder's e_presston (ref. 3,

=._Li:_ eq. (B.2-E6))Is equivalent to 2 b'1985008354-TSA05

\

3)" _tJ = ntJ(Mt +lM3)2 + Hi

where M1 ts the molecular wetght of spectes t, Atj ts a ratto of collisionIntegrals (deftned In ref. 3, eq. (8.2-15)), and ntj ts a quapttty which cancan be deftned tn several ways, someof whtch are discussed later. Various

expresstons..for _t3 dertved by other Investigators fromequatlon(3) or byi tndependeht analysts can be put tn the following general Formfor the put-)| pose of comparison:

r

I _13 = k13m13 (41

where

2Mj (s)m13 = Mt + H3

iand where r Is an exponent and klj Is a function having several forms.

_: Two examples are given to 111ustrate equatlon (4). For the first example,

Brokaw (ref. 12) gtves an expression for _t3 whtch t.s equivalent to thefollowing:

nt

_13 = n13 m13 (6)

In thls case r = 1 and

k13 = nl-_ (7)

As a second example, Nilke (ref. II) gLves the followlng expresslon for _13:

1 nt _ _112_IJ " _ + mij (e)I

In this case

klj =¼ 1 + k-I 19)

and r = 112.

3

V - A, h- _Jl_, : --• ,

1985008354-TSA06

A summary of _tJ for several approxlmcte, methods is given In table I.These methods dtffer from one another only tn the exponent n. The. quantity

qt3 which.appears in equation (6) can be oUt&lned tn several ways as follows.

An expression, for hi3 ls given by Hlrschfelder (ref. 3, eq. (8.2-21)):

2HtH_T26.696 (HI + Hi)_ (lOa)

ntj x 107 = o2 2.2)*13n13

n(2,2)*where "'t3 ls a collision Integral and a function_of c13. and o13 and

ct3 are Lennard-Jones interaction-potential _arameters for specte_ 1 and 3.For I = 3, equation (lOa) reduces to the following form for pure sDecles:

_ nl x 107 = 26.696 _Hll '.; ._2,2)* (lOb)

where nl = qtl' °t = °tt and _I 2'2)* = _(2,2)*' tl Hlrschfelder suggests

_ the following approximations for at3 a;,d ¢_3:

oI + o_°t3 - 2 (11)

el3 =_ (IZ)

An alternatlve expression for n13 can be derlved based on the follow_ng

approxlmatlon for _13' given by Svehla and HcBrlde (ref. 2, eq. (36)):

(0 , _jj_13=¼ tl + 2 I/_1t_j3 , _J3 " 2 (13)

where

= n(2,2) *_13 °_3 t3 (14)

The expression for n13 derived I_rom equations (lOa), (lOb), and (13) ts i

112

"i_%_L_ (15)"13 " --k13

I

_ 4

'q

] 985008354-TSA07

-q

where --.k_t ts deftned by equatlon_(g). Substitution of ntj from

; e(Luattop-(15) Into equatton (6) gtves the exact expression for etj tn_., equatton (B). Thus, tf the approximation gtven tn equatton (13) ts used,

equations (6) and (8) are Identical.i

In addttton to equations (lOa)and (15), va]ues of n_s may also be dertvedfrom expertment&l.data on mtxture viscosity. These thre_Jmethods for obtaining

. ntj generally gtve dt£ferent numerical values. Therefore, even the "rigorous"method gtves d_fferent values for mtxture viscosity depending on what value ts

: used for ntj.

Expressions for _tJ (refs. 12 and 15 to 19) are gtven In table 11. Theexpressions from references 17 and lg are the sameas that from reference 18except for the factors of 1.065 and 0.866. The formulas of Llndsay and Bromley(ref. 15) contatn parameters knownas Sutherland constants which can be estt-

= mated In vartous ways. Suthe_land constants for thts report were obtatned fromviscosity by meansof the following formula (derived In ref. 21); .......................................................

-- SI d In

The Sutherland Interaction constant SIj was obtatned from the followlngapproximation:

r._i__ $I_ = (16b)

'I.,,,._,

-,:_! In addttton to the foregoing methods there Is an "averaging" method forthermal conductivity due to Burgoyne and Netnberg (ref. 20). A gene-a]tzed

_t verston of thts method ts

- _mtx,fr = 2 xt_1 + - (17)-_. xt- i!

"j: An analogous formula for viscosity Is

tl;! 1 1t nmtx = _ Xtnl�.... (18)' n Xt

t'

i s

1985008354-TSA08

Selection of Approximate Method-.

A numberof mixture methods were tested to discover the extent each repro-duced experimental viscosity and thermal conductivity data for several binary

I: systems. The methods tested were the "rigorous" method; the approximate

i methods,whose expressionsfor _i_ and _i_ appear in tablesI and It; andi the averaging method of reference 20. All the methods reproduced the expert-

mentaldata by better than 3 percentfor at least some of the test cases.i However, each method also produced errors exceeding 7 percent In at least one(1 case.

An exampleof the spreadIn accuraciests shown In table Ill for the Ar-NH3systemusing the experimentaldata of reference22. The experimentaldata arefor eight different compositions of Ar and NH3.at a temperature of 308 K. Ca]_

cula_tons were madewtth values of ,nij from equations (lOa) and (15) and a

value of nlj = 175 derlyed from experimental data. In order to derive avalue from experimental data, It is necessary to select the £orm of the mixtureequation with which it ls to be used. For this example, the mixture method ofreference 12 was selected with k lJ from equation (7) and with the exponentr = I. As expectedtable III show_ the best resultskthat averageabsoluteerror = 0.2 percent)were obtainedusing the methodof Brokaw (ref. 12) and

tlle nlj derlvedfrom experimentaldata with the same method.

For the binarysystemstested,comparisonswith experlmentaldata showedthat no one method of calculationcould be Judged superiorto all others in allcases. The selectionof a particularmethod representsa compromisebetweenoverallaccuracyand ease of computations. To obtain viscosityof mixtures,

the expressionfor _I_ from equation(6) is used in equation(I) if values

of ni_ are availablein the datasetdiscussedin the section"Transport-

PropertyDataset". Otherwise _lJ from equatlon(B) Is used (whichimplies

using a value of nlj from eq. (15)).

Brokaw'smixturemethod for frozenthermalconductivity(ref. _6) wasselectedinasmuchas it reproducedthe experimentaldata for the test cases

slightlybetter than the other methodstried. The same values used for _I_

f_r viscosityare also used to calculate _lJ for frozen thermalconductivity.Reactionthermalconductivityis obtainedby the samemethod as used Inreferehce2.

ii COMPUIERPROGRAMFOR TRANSPORtPROPERTIES

lhe computer program was written in FORIRANIV and tested on an IBM![i 370/3033Computerat the Lewis ResearchCenter. A logicalvariableTRNSPI,was

added to NAMELIST/INPT2/Of referenceI. Transportcalculationsare carried

out only if TRNSPT= T has been included in the nameltst input. Table IV liststhe I/O (Input/Output) units used by the program. A transport-property data-set, five subroutines, and BLOCKOAIA are involved in tranSport-propertycalculations.

One of the five subroutines,SEARCH,has two purposes. One purposeis tosearch the unformattedthermodynamicdata on I/0 unit 4 for all possible

6

1985008354-TSA09

spectes In any specified chemical system and to store thermodynamic coeff.t-ctents for these posstble spectes tn a COMMONblock. A second purpose, tf]HNSP1 = 1, ts to search the unformatted transport data on I/O u_tt 8 for allposstble spectes tn any specified_chemical system and to store transport coef-ficients for these spectes on I/O unit 3. Subroutines 1RANP and INPUT and theentry OUT4 In subroutine OUT1 are used exclusively for transport-property cal-culations. BLOCKDATA contains headings for transport property output as wellas other Information requtred by the program. The fifth subroutine, UTRAN, Isused only for converting formatted transport properties to an unformatted form.

lransport-Proper_y Dataset

lransport properties for 154 pure species and several binary viscosityInteraction quantities nt_ were least-squares fltted to the following form,.used_n_reference6:

/= A in 1 + + C +

0 (19)

In

The coefficients were generated to give viscosity In untts of uP and thermalconductivity In untts of uW/cm K. The temperature range was dtvtded Into twoIntervals to be consistent with the same Intervals selected for thermodynamicproperties, namely, 300 to 1000 K and 1000 to 5000 K (although the programpermits any three Intervals for any species). Therefore, tn the present data-set, each pure spectes or btnary Interaction may have four sets of coefft-.ctents: two sets for viscosity (htgh- and low-temperature Intervals) and twosets for thermal conductivity (high- and low-temperature Intervals). If onlyviscosity or only thermal conductivity Is present, only the two sets of coeffi-cients for that property are given. The code word TRANmust precede theformatted sets of coefficients, and the code word LAST must follow. The formatfor the dataset containing these coefficients ts gtven tn table V.

Subroutine UTRAN

Coefficients for generating thermodynamic and transport properties are usedby the program tn an unformatted form tn order to reduce computer ttme constd-erably. Conversion of the coefficients for transport properties from formattedto unformatted form ts done by subroutine UTRAN. The formatted coefficientsare read tn as tnput on I/O untt 5. Subroutine UTRANconverts the formattedcoefficients and wrttes them In the unformatted form on i/O untt 8. Afterconversion, the coefficients are available for future runs tn unformatted formon I/O unit 8, and subroutine UTRANneed not be used agatn unttl the formatteddataset ts revtsed.

• Subroutine tNPU1

After composition has been determined for a specified thermodynamic datapotnt (such as an asstgned temperature and pressure), subroutine INPU1selects coefficients for a maximum of the 50 most abundant gaseous spectes for

_ that potnt from among the transport coefficients previously stored on I/O

7t

1985008354-TSA10

untt 3. Oependtngon the accuracy destred, the numberof spectes used by theprogram may often be reduced by meansof an opttonal tnput parameter TRPACC.If, for example,. TRPACCts set equal to 0.98, the programwt11 constder onlythose spectes whtch add up to 0.98 of the total molar composition (addtng Inthe order of largest to sma]lest spectes mole fraction). The defa_llt va]ue ofTkPACCts 0.99995. Th_mole fractions, of these selected spectes are ftrstnormalized to gtve a total of 1.0 before mtxture transport properties are cal-culated. The transport properties are calculated from the selected coeffi-cients at the current temperature.

Subroutine TRANP

Subroutine TRANPsets up _he.equations and solves for mtxture viscOsity,frOZen thermal conductivity, equilibrium thermal conductlvltyo and equtl.tbrlumspeclftc heat. The method and equations for obtaining equilibrium speclftcheat and the reaction contribution_to thermal conductivity are gtven tnreference 2.

Entry OUT4tn Subroutine OUT1

Entry OUT4handles the output of the transport-property calculations. A_ vartable format Is used whtch ts the sameas the format used for thermodynamic-! properties output (described In ref. 1).

i DESCRIPTIONOF PROGRAROUTPUI

"' A sample problem containing transport-property output ts gtven tn table V!Transport properties are gtven for mixtures of gases only. Therefore, for mix-tures containing condensedspectes, two values of equilibrium spectftc heat aregiven. One value (whtch Includes gaseous and condensed-species contributions)ts given wtth the output labled THERMOOYNAR]CPROPERT.[ES,whtle a second value(which contatns only gaseous-species contributions) ts gtven wtth the output

= labled TRANSPORTPROPERTIES. For each potnt a maxlmumof the 50 mosLabundant

gaseous specles ts used for calculating mtxture transport properties. Thermal :_:i conducttvtttes are gtven for the assumptions of both equilibrium and frozent gaseous compositions. V_scostty ts always gtven tn units of mP. An optton tsI, provtded tn the namellst tnput for u_tts of thermodynamicproperties. Untts

_t for thermal conductlvtty are consistent wtth the optton selected for thermo-dynamic units. That ts, therma] conductivity ts tn untts of mkl/cmsec tf_1 SIUNIT = T ts Included tn the tnput dataset and mcal/cm K sec otherwise. The

Prandtl numberhas the usual definition of Cpn/X, whtle the Lewts numberas1 defined tn reference 2. ts

Le - _reaC%,fr (20)XfrCp,reac

8

_ ,,, _ "-=',e:_."_. . .- -, ____: "/. -. : :: .... :.:::__::_;:

1985008354-TSA 11

SELECTION OF TRANSPORTPROPERTIES

Sources of Properties for Pure Species

Transport properties for all species except those discussed in the follow-ing paragraphs were taken from the compilations of Svehla (ref. 23). Forseveral species thermal conductivlttes were calculated for this report fromviscosities by m_ns of the following equations, given in reference 2:

15 R

' _tr,l = 4 Mt nt (21)

, Zro,, /V,ot. A

)'l = Xtr,l + Xtnt,t (23)

where

Clnt, t = - _ (24)

and

"i Co,rot,iCrot,t = R (25)

For atomic species, _lnt_ = 0 and _t = _tr,l. Crot,l is assumed to be 1for linear species and 1 for nonlinear species,

Argon. - References 6, 24, and 25 contain critical reviews of viscositydata for Ar. References 6 and 25 include more recently available experimentalviscosity data in their evaluation than found tn reference 24. Additionally,recommended values from references 6 and 25 are in close agreement (less than1 percent difference from 200 to 2000 K). By contrast, the values ofreference 24 agree with values from reference 25 at room temperature but differby 8.5 percent at 2000 K. Viscosities and thermal conductlvities were takenfrom reference 25 In order to have a consistent set of values.

Atomic carbon. - Collision integrals are given in reference 26 for everylO00 K from lO00 to 25 000 K. These collision integrals were extrapolateddown to 300 K and converted to viscosities. Thermal conducttvtties wereobtained by means of eouat}on (21).

Methane. - V_scostt_es selected by references 6, 24, and 27 to 30 are allin extremely close agreement (less than 1 percent difference). The tempera-ture range for v_scostty in these references _s from 200 to lO00 K, although

g

1985008354-TSA12

not every reference covers the entire range. The average of viscosities Inthese six references was selected. Thermal conductlvltles were selected to be

_: the average of the '_alues from references 27 and 30 to 32.

Carbonmonoxide. - Viscosities from references 24, 27, 33, and 34 werereviewed. The values selected by reference 27 are about 2 to 3 percent lower

• than those of the other three references tn the range from 500 to 1000 K andwere not used. The averaged values from the other three references are

:_ extremely close to the N2 viscosity values of reference 35. The reference 35N2 values were therefore selected as t;,e viscosity for CO tnasmuch as the N2

_ values are given to 2000 K. Thermal conducttvttles were selected tobe theaverage of the values in the four references 27, 31, 33, and 36.

: Carbon dioxide. - Viscosities from the five references 6, 24, 27, 37, and38 were reviewed. Only those of references 6 and 38 were used to obtain aver-

:. age values. The values tn reference 37 were not used because, according to_ figure 3 In that reference, the calculated values appear to be about 0.5 to

2 percent too high from 400 to 800 K. The older values of references 24 and: 27 were not used because they appear to be about 4 percent lower than the more! recent values tn references 6 and 38. Thermal conductlvtttes were averaged

from those given in the five references 27, 31, and 39 to 41.

_:_ Atomic hydrogen. - High-temperature viscosities (above 1000 K) were cal-_- culated from the collision Integrals given In reference 18. Low-temperature_ viscosities (200 to 500 K) were taken from reference 42. Values from 500 to

_ 1000 K were Interpolated. Thermal conducttvities were calculated by means of_ equation (21).

, Molecular hvdro_en. - Viscosities of H2 were taken to be the average of the

1 values In the four references 6, 24, 27, and 43. Thermal conductlvltles fromthe four references 27, 31, 40, and 43 were reviewed. The selected values are

t_.i as follows: from 200 to 600 K, average values from the four references; from1100 to 5000 K, reference 43 values; from 700 to 1000 K, values "faired"between the other selected values.

_a_e___L.- Viscosities a_d thermal conducttvttles from 373 to 1073 K weretaken from reference 44 and extrapolated to higher temperatures by means ofequations given tn reference 45.

[ Atomic nitrogen. - The high-temperature (.1000 to 15 000 K) collisionintegrals given in reference 46 were converted t6 viscosities and extrapolatedto lower temperatures. Thermal conducttvttles were obtained by means ofequation (21).

_ Ammonia.- Viscosities were selected to be the averages of those given tn:_ references 23, 24, and 47. Thermal condu,:tlvlttes were selected to be the

average of those in references 27, 31, 48, and 49.

Nitric oxide. - The two sets of viscosities and thermal conductlvttles forNOfrom references 2 and 24 are fairly close. The reference 2 viscosities wereselected inasmuch as a least-squares fit of these values gave less error thana similar fit of the reference 24 values. The reference 2 thermal conducttv-tries were selected tn order to be consistent with the viscosities. The

; selected transport properties are also given tn reference 50.

10

- .._ "-_, '- ., _. '. •

1985008354-TSA13

i NttroQen dioxide. - A problem in obtaining transport properties for NO2 liesin the fact that there is considerable association of NO2 to N204 in the tem-;: perature region of about 300 to 400 K. Thus experimental data are open to

interpretation as to whether measurements are f.or the pure species, an equ_lt-

brtum mixture of NO2 and N204, or some other combination of the two species.!

References 24 and 51 Interpret the experimental data of reference 52 differ-. ently. There Is close agreement for temperatures above 400 K (where the equi-

librium mixture ts 98 percent NO2) but considerable difference otherwise.'_ Inasmuch as reference 51 obtatned viscosity data for NO2 and N204 slmultane-

J ously from the reference 52 values, those results were selected for viscosity.Thermal conductivlttes were obtained from viscosities by means of equations

(21) to (23) with Zrot = ®.

ptatomtc nitrogen. - A comparison was made among the critically evaluatedand selected viscosities given In the three references 6, 24, and 35. Theagreement between the data from references 6 and 35 ls excellent (only a fewtenths of a percent difference _n the entire temperature range from 200 to2000 K). Reference 24 Is in good agreement with the_others at. low tempera-tures but differs by as much as 8 percent at 2000 K. Viscosities and thermalconducttvtttes were taken from reference 35 inasmuch as reference 6 does not

contain thermal conductlvttles.

_: Nitrous oxide. - Viscosities from references 2 and 24 for N20 are very:_! close (less than 0.6 percent difference from 200 to 1000 K). The reference 2

:_i- values were selected since they are given to 5000 K. The thermal conductiv-,: 1ttes from reference 31 appear to be closer to the experimental data than do_ those in reference 2 and also closer to one recent value given in reference 53.

.... 1he reference 31 thermal conductivtttes were selected up to 700 K Above 700 K1;, they were calculated from viscosities by means of equations (21) to (23) with_;_. Zro t = ®.

Atomic oxvqen. - Two sets of high-temperature v_scostt!es were compared(refs. 27 and 46). These agree to within 2.5 percent from 3000 to 5000 K.The viscosities of reference 46 were selected s_nce these are given from 1000to 5000 K, whereas the reference 27 values are given only above 3000 K. Low-temperature viscosities (200 to 300 K) were taken from reference 54. Vtscosi-

• ties from 400 to 900 K were interpolated. Thermal conductlvltles were obtainedby means of equation (21).

Molecular oxygen. Viscosities from references 6, 24, 27, and 35 werereviewed. The averages of.these viscosities are within 1 percent of thereference 35 values. The reference 35 values were selected. Thermal conduc-ttvittes from references 27, 31, 35, 55, and 56 were reviewed.. The averagesof these agree to within 1 percent with reference 35 from 200 to 600 K, butdiffer more at higher temperatures (3 percent from 1000 to 1300 K). Accordingto Hanley (ref. 35), "...most of the data for the thermal conductivity coeffl-

' ctent for both nitrogen and oxygen seem unreliable outside the range of 150 to600 K." Thermal conductivttes were also taken from reference 35 to be consls-tent with the selected viscosities.

• iHydroxyl radical. - Experimental transport data for the OH radical are notavailable. The collision integrals estimated in reference 57 and the rota-tional collision number Zrot = 8 estimated in reference 2 were used tocalculate viscosities and thermal conducttvtttes.

11

1985008354-TSA14

Sources of Properties for Btnary Interactions

The transport-property dataset currently provtdes coefficients for obtain-

Ing nt_ for only three patrs. These coefficients were taken dtrectly fromreference 58. Values of nt_ for other patrs are estimated tn the program bymeansof equatton (15) ustng kt_ from equa_ton (9).

1985008354-TSB01

APPENDIX - SYMBOLS

A, B, C, D coefficients In eq. (19)

All, AIj ratio of collision Integrals, dlmenslonless

Cp constant-pressure.heat capacity, J/kmol K

Clnt,i term defined by eq. (24), dimensionless

Crot,I term defined by eq. (25), dlmenslonlessc constant-pressure specific heat, J/kg K

. p

DI self.dlffuSlon coefficient, m2/sec

DIj binary diffusion coefflclent, m21sec

ktj function defined by eq.. (7) or (9), dimensionlessLe Lewis number, defined.by eq. (20), dlmenston]ess ......

M I molecular weight of species I, kg/kmol

mlj molecular weight function defined by eq. (S), dimensionlessn number of gaseous species included In transport calculations,

- dimensionless

R universal gas constant, 8314.41 3/kmol K

r exponent in eq. (4) i

SI Sutherland constant for specle_ I, K I

SIj Sutherland interaction constafitfor species I and _, K1 temperature, K

++ xI mole fraction of species i, dlmenslonless

Zrot rotational colllslon number.

_I depth of potential energy well for species i, _

_l_ quantity defined by eq. (.1.2)n.. viscosity, kg/m.sec

ni vlscos_ty of Species i, kg/m sec

+ nlj quantity defined by eqs. (I0_) and (15), kglm sec...... thermal conductivity, W/m K

" _t thermal conductivity for species t, W/m K

klj quantity in table [1, Wlm k

- 4 t molecular diameter for species t, A

o15 quantity defined In eq, (11), A

+_i _t_ viscosity interaction coefficient (eq. (6) or (8)), dimensionless:i _t_ CroZen-thermal-conducttvtty interaction coefficient (eq, (2) andi table II), dimensionless

+ *; collision integral, dimensionless

13

1985008354-TSB02

_lJ collision cross section defined In eq. (14), A2

Subscripts:

fr frozen contribution

I,_ Index for spectes

Int Internal contrlbutlon

mix.. for the mtxture

reac chemical reactlon contrlbutlon

rot rotatlonal contrlbutlon

tr translatlonal--contrlbutlon

|Ti

1

?:

= .{

2e_,Z,i

i

--' 14

1985008354-TSB03

REFERENCES

_i 1. Gordon, Sanford; and McBride, Bonnie 3.: Computer Program for Calculation

-;_ of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident

_1_! and Reflected Shocks, and Chapman-3ouguet Detonations. NASASP-273, 1976._. 2. Svehla, Roger A.; and McBride, Bonnie J.: FORTRANIV Computer Program for_t Calculation of lhermodynamtc and lransport Properties of Complex Chemical

_: Systems. NASA TN D-7056, 1973.

_ 3. Hlrschfelder Joseph 0 ; Curtlss, Charles F.; and Bird R. Byron:_ Molecular Theory of Gases and Liquids. John Wtley& Sons, inc., 1954.

4. Bu_ler, James N.; and Brokaw, Rlchard S.: Thermal Conductivity of GasMixtures In Chemical Equl!tbrlum. J. Chem. Phys., vol. 26, no. 6,. _une1957, pp. 1636-1643.

5. Brokaw, Richard S.: Thermal Conductivity of Gas Mixtures In Chemical:; Equilibrium. II. J. Chem. Phys., vol. 32, no. 4, Apr. 1960, pp. 1005-1006.

_: 6. Maitland, Geoffrey C.; and Smith, E. Brian: Crlttcal Reassessment of Vls-, coslttes of 11 CommonGases. J. Chem. Eng. Data, vol. 17, no. 2, 1972,

pp. 150-156.

7. Sutherland, William: The Viscosity of Mixed Gases. Phtl. Mag., vol. 40,1895, pp. 421-431.

8. Wassll3ewa, A.: Heat-Conduction In Gaseous Mixtures. Phys. Z., vol. 5,Nov. 1, 1904, pp. 737-742.

! 9. Kennard, Earle H.: Kinetic Theory of Gases. McGraw-Hlll Book Co., 1938.

:_ I0. Buddenberg, J.W.; and Wlike, C.R.: Calculation of 6a_ Mixture Vlsco_.Itles._ ind. Eng. Chem., vol. 41, no. 7, July 1949, pp. 1345-1347.

11. Wtlke, C.R.: A Viscosity Equation for Gas Mtxture_. J. Chem. Phys.,vol. 18, no. 4, Apr. 1950, pp. 517.519.

' 12. Brokaw, Richard S.: Approximate Formulas for the Viscosity and Thermal: Conductivity of Ga_ Mixtures. J. Chem. Phys., voI. 29, no. 2, Aug. 1958,

pp. 391-397.

13. Francls, W.E.: Viscosity Equations for 6as Mixtures. irans. Faraday Soc.,r vol. 54, i958, pp. 1492-14_7.

_ 14. Brokaw, Richard S : Predicting Iransport Properties of Dllute GasesInd. Eng. Chem. Process Des. Dev., vo1. 8_..no.2, Apr. 1969, pp. 240-253.

_!!/ 15. Llndsay, Alexander L.; and Bromley, LeRoy A: Thermal Conductivity Of GasM|xtures. Ind. Eng. Chem., vol. 42, no. 8, Aug. 1950, pp. 1508-15tl.

:_ lb. Brokaw, Richard S.: Alignment Charts for lransport Properties. Viscosity,

_-:! lhermal Conductivity, and Diffusion Coefficients for Nonpolar Gases andi ) Gas Mixtures at Low Density. NASA IR R.81, 1960.

15

1985008354-TSB04

17. Mason, E.A.; and Saxena, S.C.: Approximate Formula for the Thermal Con-ductlvlty of Gas Mixtures. Phys. Fluids, vol. 1, no. 5, Sept. to Oct.,1958, pp. 361-369.

18. Vandersllce, J.T., et al: High-Temperature Transport Properties of Dis-soctattng Hydrogen. Phys. Fluids, vol. 5, no. 2, Feb......1962, pp. 155-164.

19. london, P.K.; and Saxena, S.C.: Calculation of l hermal Conductivity ofPolar-Nonpolar Gas Mixtures. ADpl. Sct. Res., vol. 19, July, 1968,PD. 163-170.

20. B_rgoyne, J.H.; and Welnberg, ".: A Method of Analysis of a Plane Combus-tion Wave. Fourth Synlposium (International) on Combustion, Williams &Wllklns Co., ]953_pp. 294-302 ..................

21. Zeleznik, Frank J.; a_d RcBrtde, Bonnie J.: Modeltng the Internal Combus-tion Engtne. NASA RP-1094, ]984.

22. Rakshit, A.B.; Roy, C.S.; and Barua, A.K.: Viscosity of the Btnary GasMixtures Argon-Methane and Argon-Ammonia. J. Chem. Phys., vol. 59, no. 7,Oct. 1, 1973, pp. 3633-3638.

23. Svehla, Roger A.: Estimated Viscosities and Therma! Conducttvttles ofGases at H_gh Temperatures. NASA TR R-132, 1962.

24. Toulouklan, Y.S.; Saxena, S.C.; and Hestermans, P.: Thermophystcal Prop-ert_es of Matter. Vol. 11. Viscosity. IFI/Plenum, 1975.

25. Hanley, H.J.R.: The Viscosity and Thermal Conductivity Coefficients ofDilute Argon, Krypton, and Xenon. J. Phys. Chem. Ref. Data, vol. 2, no. 3,1973, pp. 619-642.

26. Btolst, LOU_S; Fenton, Jeff; and Owenson, Brtan: Transport Properties fora Rtxture of the Ablatton Products C, C2, and C3. ThermophyslcS of Atmos-pheric Entry, T.E. Horton, ed., Progress In Astronautics and Aeronautics,vol. 82, AIAA, 1982, pp. 17-36. _i

27. Vargaft_k, N.B.: Tables on the Thermophystcal Properties of Ltqutds andGases _n Normal and Dissociated States. Second ed., John Wiley and Sons,Inc., 1975.

28. Abe, Y.; Kest_n, J.; Khalifa, H.E.; and Wakeman, W.A.: The Visceslty andDiffusion Coefficients of the M_xtures of Four Ltght Hydrocarbon Gases.Phystca A, vol. 93, 1978, pp. 155-170.

29. G_ddings, John G.; KaO, James T.F.; and Kobayaski, R_kt: Development of aH_gh-Pressute Capillary-Tube V_scometer and |t_ Application to Nethane,Propane, and Thetr Mixtures In the Gaseous and Ltquld Regions. J. Chem.Phys., vol. 45, no. 2, July 15, 1966, pp. 578-586.

30. Hanley, H.J.M.; Haynes, W.M.; and McCarty, R.D.: The Vfscostty and lhermalConductivity Coefficients for Dense Gaseous and Ltquld Methane. J. Phys.Chem. Ref. Data, vol. 6, no. 2, 1977, pp. 597-609.

"i: 16

1985008354-TSB05

31. loulouktan, Y.S.; Llley, P.E.; and Saxena, S.C.: Thermophyslcal Propertiesof Matter. Vol. 3. Thermal Conduct%vtty, ]FJLPlenum, Lq70.

32. Afshar, R.; Cogley, A.C.; and Saxena, S.C.: Thermal Conductivity ofMethane at Atmospheric Pressure in the TemperAture Range of 360-1215 K. J.Heat Transfer, vol. 102_ _o..J, Feb. 1980, pp. 163-167.

33. Htl.senrath, Joseph: Tables of Thermal Properties of Gases. NationalBureau of Standards Circ. 564,_Nov. ]_ 1955.

34. Mal%nauskas, A.P.; Gooch, J.W. Jr.; Annls, B.K.; And Fuson, R.E.: Rota-tional Collision Number of N2, 02, CO, and CO2 From Thermal Transp%rat%onMeasurements. 3. Chem. Phys.......vQl ....53, no, 4, Aug. 15, 1970,pp. 1317-1324.

35. Hanley, H.J.M.; and fly, James F.: The Viscosity and Thermal ConductivityCoefficients of D%lute Nitrogen and Oxygen. J. Phys. Chem. Ref. Data,vol. 2, no. 4, 1973, pp_ 735-755 ...................

3b. Saxena, S.C.: Determination of lhermal Conductivity of Gas, by Shock-TubeStudies. High Temp. Sci., vol. 4, no. 6, 1972, pp. 517-540.

37. Ely, James F.; and Hanley, H.J.M.: The Statistical Mechanics of Non-Spherical Polyatomic Molecules. Application to the Properties of CarbonDioxide. Mol. Phys., vol. 30, no. 2, 1975, pp. 565-578.

38. Kestin, J.; Ro, S.T.; and Wakeham, W.A.: Viscosity of Carbon Dioxide inthe lemperature Range 25 - 700 °C. J. Chem. Phys., vol. 56, no. 8, Apr.15, 1972, pp. 4114-4118.

39. Chen, S.H.P.; Jain, P.C.; and Saxena, S.C.: Thermal Conductivity andLffective Diffusion Coefficient for Vlbra[tonal Energy: Carbon Dioxide(350 - 2000 K). J. Phys. B., vol. 8, no. 11, Aug. I, 1975, pp. 1962-1972.

40. LeNeindre, B.: Contribution a L'Etude Expertmentale de la Conductivitelhe_mique de Quelques Flu%desa Haute Temperature eta Halite Pre_sion.Int. J. Heat Mass lrans_, v_l. 15, no. 1, Jan. 1972, pp. 1-24, 1972. :i

41. Vines, Robert G.: Measurement of the Thermal Conductivities of Gases atH_gh Temperatures. J. Heat Transfer, vol. 82, no. I, Feb. 1960, pp. 48-52.

42. Amdur, I.: Viscosity and niffusion Coefficients of Atomic Hydrogen andAtomic Deuterium. J. Chem. Phys., vol. 4, no. 6, June 1936, pp. 339-343.

43. Hanley, J.J.H,; McCarty, R.D.; an¢ ]ntemann, H.: The Viscosity and Thermal_ Conductivity of Dilute Gaseous Hydrogen from 15 to 5000 K. J. Res. Nat.

Bur. Stands. Sect. A, vol. 74, no. 3, May-Oune 1970, pp. 331-353.

44. Meyer, C.A., et al.: Thermodynamic and Transport Properties of Steam.lhird ed. American Society of Mechanical Engineers, New YOrk, 1977.

45. Hendr%cks, R.C.; McClintock, R.B.; and S%lvestrt, G.J.: Revised inter-national Representations for the Viscosity of Water and Steam and NewRepresentations for the Surface lension of Water. J. Eng. Power, vol. 99,no. 4, Oct., 1977, pp. 664 678.

17

®

1985008354-TSB06

46. Yun, K.S.; and Mason, E.A.: Collision Integrals for the Transport Prop-erttes of Dissociating Air at High Temperatures. Phys. Fluids, vol. 5,no. 4, Apr., 1962, pp. 380-386.

47. Burch, L.G.; and Raw, C.3.6.: Transport Properties of Polar-Gas Mixtures.I. Viscosities of Ammonta-Methylamine Mixtures. 3. Chem. Phys., vol. 47,no. 8, Oct. 15, 1967, pp. 2798-2801.

48. Afshar, R.; Murad, S.; and Saxena, S.C.: Thermal Conductivity of GaseousAmmonia _n the Temperature Range 358-925 K. Chem. Eng. Commun., vol. 10,no. 1-3,1981, pp. 1-11.

49. Zeleznik, Frank 3.; and Svehla, Roger A.: Rotational Relaxatlon tn PolarGases. II. 3. Chem. Phys., vol. 53, no. 2, 3uly 15, 1970, pp. 632-646.

SO. Gordon, Sanford: Thermodynamic and Transport Combustion Properties ofHydrocarbons W_th Air. I - Properties tn SI Units. NASATP-1906, 1982.

S1. Svehla, Roger A.; and Brokaw, Richard S.: Thermodynamic and TransportProperties for the N204 2NO2 2NO , 02 System. NASATN 0-3327, 1966.

52. Petker, Ira; and Mason, David M.: Viscosity of the N204-NO2 Gas System.3. of Chem. Eng. Data, vol. 9, no. 2, Apr. 1964, pp. 280-281.

- 53. Fleeter, R.; Kest_n, 3.; and Wakeham, W.A.: The l hermal Conductivity of_:_ Three Polyatomic Gases and Air at 21.5 °C and Pressures up to 36 MPa.

Phys_ca A, vol. 103, 1980, pp. 521-542.

54. Konowalow, Dan}el D.; Hirschfelder, 3.0.; and L_nder, Bruno:Low-Temperature, Low-Pressure Transport Coefflc_ents for Gaseous Oxygenand Sulfur Atoms. J. Chem. Phys., vol. 31, no. 6, Dec. 1959, pp.1575-1579.

55. Geler, H.; and Schafer, K: Heat Conductivity of Pure Gases and GasMixtures at 0-1200 °. Allgem. WaermeteCh., vol. 10, 1961, pp. 70-?5.

56. Nestenberg, A.A,; and DeHaas, N.: Gas Thermal Conductivity Studies at

:3;;_i High Temperature. IT. Results for 02 and 02-H20 Mixtures. Phys. F1ulds,_,_ vol. 6, no. 5, May IgG_, pp. 617-620.

_ 51. Svehla, Roger A.: Thermodynamic and Transport Properties for theHydrogen..OxygenSystem. NASA SP-3011, 1964.

_':- 58. Ma}tland, Geoffrey C., and Smlth, E. Brlan: Vlscosltles of Binary Gas,_r Mixtures at High Temperatures. 3. Chem. Soc. Faraday Trans. I, vol. 70,

..../_ no. 7, 1974, pp. I191-121_.

_-_ IB

' _

J

',_rI

' ')_i_,_ ,, ._I_"-,',_r._ -- ," ........."

1985008354-TSB08

TABLE II. - EXPRESSIONSFOR _ij FOR MIXTUREFROZEN THERMALCONDUCTIVITY

Reference _ij

........- - i"2

( Si , Sij

LindsaYBromley,and_w11 + n._.i'Mj_3/4 i+-- T , 1+ Tref. 15 i kMi/ i + _jj ' Si-T. i i+ T i

•il Brokaw, _ij I + _- I +' ref. 12 i + M'jj _j 30 BAli Mi - Mj

!_ 2.54(Mi - M_)(Mi - 0.177 Mj)]- Brokaw,ref. 12 _ij 1 �.

(Mi + Mj)2

:'" L 2.41(Mi - Mj)(Mi - 0.142 Mj)-i

i

Brokaw, L" + .... 2 '_-:-_ ref. 16 _ij (Mi �Mj)]

Saxena,

.- ref. 17 i ..............._xj_.. £Mj# .

" i/2 I/4" 2

Vanderslice I_I/2 C_._) (M)et al., ref. 18 -_mij I +

t ' • ' ' "" n' '' "

i ' Mi "I/4 2Tondon and .1/2, (x___ ll2 (L _ "Saxena, 0,866 _,.,ij, 1 +

ref. 19 i " _xJ/ _kMJ/ "

'° i

:i.,,j

1985008354-TSB09

" TABLE Ill.- AVERAGEABSOLUTEPERCENTERROR FOR Ar-NH3

: . [Comparsion of eight experimental mixture viscositiesL-- from ref. 22 with correspondingcalculatedvalues.]

;2 Method.of Averageabsolutepercenterrorcalculation

_" nij = 148.2 nij = 164.8 nij = 175.0;::" (eq. (15)) (eq. (lOa)) (derivedfrom_' experimentaldata)

',_',:- Hi rschfel der 8.1 4.4 2.3"rigorous"E....

(ref. 3)

:_'-- WiIkea 5.8 5.8 5.8i-_ (ref. II)

_ ,=, , ..........

_ Brokaw 5.8 1.9 0.2_ (r = 1)_- (ref. 12)

_ Brokaw 6.9 3.I 1.0(r-- 718)

_I!T' (ref. 12)

Francis 7.3 3.4 1.4• (ref....13)

Sutherland ] 8.0 I 4.2 2.2" (ref.7)i

--j Burgoynea 12.5 12.5 12.51 !(ref. 20)

!t_ " aMethoddoes not use nij.

s

: i

!:.i

1985008354-TSB10

.

.... TABLE.IV. - INPUT/OUTPUTDATA FILES•

i IlO I Data file .....! unit l_,._ ,, q

" 3 ! Scratchunit_, (1) Used duringconversionof formattedto unformatteddata_,. (2) Unformattedcoefficientsto generatetransportpropertiesfor a

_. particularchemicalsystem

_. 4 Unformattedcoefficientsto generatethermodynamicpropertiesfor all

i_ species

5 Formattedinput. Case input (describedin ref. 1) and formattedcoefficientsto generatethermodynamicand transportproperties:(Note: Formattedcoefficientsneed to be processedonly once.Programwill write the unformattedfiles 4 and 8.)

6 Output

_IUnformattedcoefficientsto generatetransportpropertiesfor allL"

__] speciesand pairs of species

1985008354-TS B11