NASA TN D-6807

download NASA TN D-6807

of 62

Transcript of NASA TN D-6807

  • 7/31/2019 NASA TN D-6807

    1/62

    - --T E C H N I C A L N O T E

    ni0I

    wLOAN COPY: R E h i AFWL (D O E=

    i KIRTLAND A F E ~ Z S- 2-LN D RELATED COEFFICIENTS

    Robert C . Hendricks, Ildiko C, Peller,n d A n n e K . Baron

    Research CenterOhio 44135 . .

    I O N A L A E R O N A U T IC S A N D S P AC E A D M I N I S T R A T I O N W A S H I N G T O N , D . C . J U L Y 1972

  • 7/31/2019 NASA TN D-6807

    2/62

    - -. .1. Report No. 2. Government Accession No.NASA TN D -68 07

    4. Tit le and Subt i t leJOULE-THOMSON INVERSION CURVES AND RELATED

    7. Au tho r (s )Robert C. Hendri cks, lldiko C. Peller, and Anne K. Baron

    ~~

    9. Performing Organization Name and AddressLewis Research CenterNational Aeronautics and Space Adminis tratio nCleveland, Ohio 44135

    ' 2 . Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationWash ingt on, D. C. 20546

    5. Supplementary Notes

    -~ . ..6. Abstract

    I 3. Recipient 's Catalog No.5. Report DateJuly 1972

    8. Performing Organizat ion Report No.E- 6786- 10 . Work Un i t No .113-31

    11. Contract or Grant No.

    13 . Type of Report and Period CoveredIechnica l NoteI 14. Sponsoring Agency Code

    The equations of sta te (PVT rela tion s) fo r methane, oxygen, argon, carbon dioxide, carbonmonoxide, neon, hydrogen, and helium were used to esta bli sh Joule- Thomson inve rsion cur vesfor eac h fluid. The princi ple of correspond ing states was applied to the inversion cur ves, anda generalize d inversi on curve for fluids with sma ll acen tri c facto rs was developed. The quantum fluids (neon, hydrogen, and helium) were excluded from the gener alizati on, but availabledata for the fluids xenon and krypton wer e included. The crit ical isenthalpic Joule-Thomsoncoefficient pc was determ ined; and a simplified approximation pc 3 Tc/6 Pc was foundadequate, where Tc and Pc are the t empera tu re and p re s su r e at the thermodynamic crit icalpoint. The maximum inversio n te mp er at ur es wer e obtained from the second virial coefficient(maximum (B/T)).

    7. Key Words (Suggested by Aut hor(s1 ) Dist r ibut ion StatementThermodynamics Unclassified - unlimited

    9. Security Classif. (of this report) 20. Security Classif. (of this page) 21 . No. of Pages 22 . Price'~~nclassified I . Unclassified 60 $3.00

    'For s a l e by th e N a t i o n a l T e c h n i c a l I n f o rm a t i o n S e r vi c e, S p r i n g f i e l d , V i r g i n i a 22151

  • 7/31/2019 NASA TN D-6807

    3/62

    JOULE-THOMSON INVERSION CURVES AND RELATED COEFFICIENTS FOR SEVERAL SIMPLE FLUIDS

    by Robert C. He nd ricks , I idik o C. Pe l ler, a nd A n n e K. B a r o n Lewis Research Ce nter

    S U M M A R Y The pressure-volume- tempe rature (PVT) relatio ns for sev er al fluids (methane,

    oxygen, argon , carbon dioxide, neon, carbon monoxide, fluorine, hydrogen,have been used to study the behavior of the isen thalpic Joule-Thomson coef

    and in particular the invers ion curve. Some attention is al so given to Joule-on re fri ge ra to rs and liquifiers. For the fluids methane, nitrogen, oxygen, argon,

    , and neon the calcula tions involved extrapolation of the equation of st at eIn all ca se s the PVT extrapolations and the derivaP and ( a P / a ~ ) ~ , here p is density, appeared to be natura l extensions ofower press ure and temperature results. These res ults for nitrogen were com

    d to the PVT rela tion of Coleman and Stewart, which w a s developed for nitrogen andss ur es to 1000 atmospheres and temp eratur es to 1000 K . The comparisons

    From these results a Joule-Thomson inversion curve w a s calculated for each fluid.were compared to existing data with favorable r es ult s for all but carbon

    oxide, where sizable deviations from the data were noted for temp eratures above atempe rature TR of 3 . An approximation for the critical isenthalpic Joule-on coefficient pc was developed. This simple formula, pc = Tc/6Pc, w a s found

    od agreem ent with the data of Roebuck and Os terberg and Coleman and Stewartnitrogen. Reduced Joule-Thomson data w e r e determ ined for eight fluids and plotted

    a function of reduced temp eratur e for various i sob ars (reduced pre ssu res ).The inversion curve and the isotherm al Joule-Thomson coefficient are shown to

    y with the principle of corresponding st at es . The isenthalpic Joule- Thomson var does not. Nevertheless, the reduced invers ion curves are useful when data aret and for grouping data in fluid-to- fluid comparisons.The inversion temp eratur e and the Boyle tempera ture as calculated from the secondcoefficient B wer e al so found to be in agreement with values found in the litera

    Finally, a revised form of the generalized inversion curve is presented. The fluidsm, hydrogen, and neon were not included in the generaliza tion because of the irtum effects. Carbon dioxide was al so excluded from the generalization because of

    high ace ntri c factor . Available low- temperature- fluorine data w e r e included.

  • 7/31/2019 NASA TN D-6807

    4/62

    I I IIIIIIIIIIIlllllI~1ll1111l11l111I

    INTRODUCTIONJoule-Thomson expansion is widely used for liquification of gases and for refrigera

    tion. There are no moving part s, maintenance is minimal, and reliability is high.Joule-Thomson expansion is usually used in the lowest temperature portion of a liquification or refrigeration cycle; however, when coupled with a pump, a complete cycle isformed. The Joule- Thomson liquification and refrig eration p roc esse s are discussed inappendix D along with so me indication of how the figure of mer it (cost of producing aunit of liquid or cooling) influences the cycle design. It should be noted that the maximum refrigeration o r liquification does not correspond to minimum cost. A var iety ofspecific cooling and liquification applications can be found in re ferenc e 1 .

    Under certain conditions a Joule- Thomson expansion will produce heating ra therthan cooling; consequently, determining these conditions is important to the design ofcryogenic equipment. In the Joule-Thomson experiment, the gas is expanded isenthalpically through a porous plug, and the slope of the isenthalpic curve (constant H) in thepressure- temperature (P-T ) plane is called the Joule- Thomson coefficient p

    (All symbols are defined in appendix F. ) The unique locus of points where the isenthalpis a maximum is called the inversion curve. Thus, fo r a certain temperature, the reexists a pr es su re beyond which p < 0 and isenthalpic expansion causes a temperaturerise. However, at lower pr essures , p > 0 and cooling re su lt s from isenthalpic expansion. The maximum isenthalpic cooling occurs when conditions on the high-pressureside of the plug (or valve) fall on the inversion locus (appendix D ).

    While the Joule-Thomson effect has been experimentally determined for s everalfluids (e. g. , ref s. 2 to 7 ), it is not only a very difficult experiment but requir es p rec isePVT data for cr os s interpolation. Thus, when acc ura te exper imental data for a particular gas a re either inadequate or nonexistent, it becomes necessary to estimate theinvers ion curve. While the principle of corresponding states has been applied to theinversion curve by s eve ral authors (e.g., refs. 8 and 9), Gum, Chueh, and Prausnitz(ref. 10) reexamined both the experimental and calculated Joule-Thomson "data" forargon , xenon, nitrogen, carbon monoxide, methane , ethylene, neon, helium, hydrogen,and some mixtures (see al so appendix A). Quantum gas es (helium, hydrogen, and neon)do not follow the corresponding s ta te s principle except at high temperatu res and, consequently, were correlated separately. The inversion curve for the remaining gase s

    2

  • 7/31/2019 NASA TN D-6807

    5/62

    e- 5c E8 3 -= 3 8F 2 -E

    o Carbon monoxide (ref. 24)v Methane (ref. 23)Gunn's inve rs ion cu rv e

    2 4 6 8 10 12Reduced pres sure , PRFigure 1 - Generalized reduced inversion curve for several corre

    sponding states f luid s as determined by Gunn . Chueh. Prausni tz(ref. 101.

    1) w a s well represented in te rm s of reduced tempera ture (TR = T/Tc) and re(PR= P/Pc) by

    O 1 a 2 O3 O4 a 57 1 . 5 9 8 I - 4 1 . 5 6 7 1 1 . 8 2 6 - 1 . 6 7 2 1 0 . 0 9 1 1 6 7

    Gunn, Chueh, and Prausnitz (ref. 10) al so concluded that Joule-Thomson coeffints calculated with an accurate equation of sta te should be more accurate than those

    red experimentally. It must be remembered that accuracy in measuring the presdrop in an isenthalpic experiment and interpolating these data to determine

    is very difficult to obtain.Recently, accurate PVT data on methane and oxygen have been acquired (refs. 1112). Coleman and Stewart (ref. 13) have reexamined all the available nitrogen data

    ented an equation of state that is valid over a considerable range of pressure.(ref. 14) reported an accurate equation of state for five fluids: methane, nitro

    3

  • 7/31/2019 NASA TN D-6807

    6/62

    gen, oxygen, argon, and carbon dioxide. Hendricks, Baron, Peller, and P e w (ref. 15)developed a computer program to calculate the thermodynamic and transp ort propert iesfor eight fluids. The pri ma ry equation selected in this program w a s the Bender equation, because it covered five fluids of considerable int eres t with a consistent curve f i t .Carbon monoxide, neon, and helium were a ls o included in refe rence 15 by using equations formulated at NBS-Boulder (see ref. 15). In addition, the Coleman and Stewartequation for nitrogen (ref. 13), because of its extended pres su re range, w a s als o included in the program of reference 15.

    For most fluids, neither the equation of state nor the data cover the extremepressu re-temperatur e ran ges required to obtain the Joule- Thomson curve and relatedresu lts . The only equation used in refe renc e 15 which w a s originally f i t to the very highpressures required to determine the inversion curve was the Coleman and Stewart equation for nitrogen (ref. 13). Consequently, the first topic of this report is a discussionof the validity of the PVT resul ts obtained when the equations of s ta te for the eight fluidsas defined in reference 15 are extrapolated to the high pressure required to compute theJoule- Thomson inversion curve.

    Second, by using the computer program of reference 15, the work of reference 10is extended to present inversion curves and related Joule-Thomson results for the fluidsmethane, nitrogen, oxygen, carbon dioxide, argon, carbon monoxide, neon, and helium.Limited resu lt s for hydrogen, fluorine, and some noble gases ar e also included.

    The next topic covered is the calculation of inversion temperatures by using thesecond virial coefficient of the equation of state programmed in reference 15.

    Finally, the principle of corresponding states as applicable to the inversion curveand the crit ica l isenthalpic Joule- Thomson coefficient is discussed.

    H I G H - P R E S S U R E PVT EXTENS IONSIn order to extrapolate Bender's equation of state (ref. 14) to higher pr es sur es and

    temperatures, it is first necessary to examine the extended isochores. The numericalvalues of the extended isochore s for each fluid of figure 2 were based on the followingincrem ents of the crit ica l isochore: 0.5 pc, 1.0 pc, 1.25 pc, 1. 5 pc, 2.0 pc, 2.5 pand 3.0 pc. The iso chore s of figure 2 a r e bounded above by a pressure of 100 MN/mand from the right by a temperature around 600 K . While these bounds may at firstseem arbitrary, they were established to encompass most of the Joule-Thomson loci andin the case of nitrogen to compare the extrapolated isoch ores as predicted by Bender(ref. 14) to those predicted by Coleman and Stewart (ref. 13).

    The equations of state for the fluids methane, nitrogen, oxygen, argon, carbon diox

    4

  • 7/31/2019 NASA TN D-6807

    7/62

    .. . .: ---

    - -

    12ot 12o+1.5 Pc 3 . 0 ~ 2 . 5 ~ ~ 1.54 Pc 1.25 pc.(0.241 1 . 2 5 ~ ~ (0 .98 (0.78) 2.0 Pc (0.47) . (0.39)(0.20) (0.62)

    1.0 Pc. '(0.311. ... _ ... _ . . . 0.5 Pc. . ' (0.16)

    IO0 200 300 40 0 500 600la1 Methane. T = 190.77 K; P = 4.627 MN/m2; pc = 0.162 g/cm3. lb) Nit rog en (based on ref. 14). T = 126.3 K; P, = 3.417 MN/m2;pc = 0.3105 g/cm3.

    3 . 0 ~ ~ .2.5pC 1.5 Pc(0.931 (0.781 2.0 Pc ,LO.471 ' (0.39110.621 180

    1.5 Pc 1.25 pc(0.64) (0.591

    . .. . . .. . i' . : . .. . .' . . i . .: ., . ' . . 0.5 Pc.,.

    :> ..i. . . ..

    ..."../ . ' (0. 21) . .. . ...'..'. . . / . : ,,;p/;..-.:/,/ .. . .:&p:__-.. .L - . , . - . . . ._ . *

    1 00 200 300 40 0 500 I 00 200 300 40 0 500Ic I Nitrogen (based on ref. 13; not a high pressure -temper ature exten- ( dl Oxygen. T = 154.78 K; P, = 5.083MN/m2; p = 0.4325 g/cm3.sion]. T = 126.3K; P, ~ 3.417 MN/m2; pc = 0.3105g/cm3.

    120t l2QI2.5 Pc

    I 00I (1.33) 2. 0 p(1.067

    . . - . . _ . . . . I300 400 500 600 700 EO0Temperature, K(e1 Argon. T, = 150.7 K; P, = 4.865 MN/m2; pc = 0.531 g/cm3. If1 Carbon dioxide. Tc = m . 2 1 K; P = 7. 3835MN/m2; pc = 0.464 g/cm3

    Figure 2. - PVT extensions along selected isochores for several fluids as calculated from referen ce 15, for var ious values of cr iti cal tempera ture Tcrit ical pressure P,, and crit ica l density pc

    5

  • 7/31/2019 NASA TN D-6807

    8/62

    . . .

    . l . opc(0.30) 1.0Pc' (0.48)

    .. .. 0. 5 P. .. : . . ' (0.24). ... ... .... i. . .. . .. . .., . :.,..'. .. . . . . . ..":;,..i./. ,.;/. . . .

    0 10 0 200 300 400 500 600 0 200 PO 0Temperature, K(g ) Carbon monoxide. T = 132.91 K ; P = 3.4986 MN/m2; p = 0.2997 g/Cm3. ( h l Neon. T = 44.4 K; P, = 2.6537 MN/m2; p = 0.483g/cm3.

    3.0 pc 2.5 pc 2.0 pc 1.50 Pc 1.25 pc(0.21) (0: 17) (0 . 14) (0.10) (0.09)

    0.5 pc(0.031

    I .I .0 53 1 3 2 15: 213 253 300 350 490 45 0 500Temperature. K

    ( i ) Helium. T = 5.2 K ; P, = 0.72764 MN/m2; p = 0. 0693g/cm3.Figure 2 - Concluded.

    6

    0

  • 7/31/2019 NASA TN D-6807

    9/62

    carbon monoxide, and neon1 were all fitted for pres sur es less than 40 MN/m2, andfor helium for pressures less than 10 MN/m 2 (ref. 15). Nevertheless, the extrapo

    isochores appear linear, continuous, and a natural extension from the lower presregime.

    The slopes (aP/aT)P as presented i n figure 3 indicate the linear ity of the isochores.P curves a r e nearly constant for densities to p/p, * 2. Howat higher densities, that is , p/pc of 2.5 and 3.0, the (aP/aT)P exhibits a highat low tem peratu res and tends toward a constant at higher temper

    The derivatives ( a P / a ~ ) ~ ,or various fluids, are not as eas ily compared. However,w e r e noted for densiti es to p/pc of approximately 2 (perhaps 2.5), even

    were not established.Due to the linear nature of the isoc hores in the P-T plane, the behavior of the se

    is not unusual; and, as such, one would expect the extrapolated PVT resu lt s,of data, to be fairly good. A second reason for investigating the behavioris that they a r e used in the calculation of the Joule-Thomson coef

    The Coleman-Stewart equation of state for nitrogen (ref. 13) is valid to 100 MN/m 2K (this region includes the inversion curve). The extrapolated values of Ben

    r' s equation in figures 2(b) and 3(b) for nitrogen should agree with those calculated bytewart equation, in order to have gre ate r confidence in the extrapo

    ed resu lts.Apart from a slight shift of the high-density isochore as shown in figure 4, the iso

    In general, (aP/aT)P' as calcu13 and 14 by refe rence 15, are in good agreement (fig. 5).In view of these r es ul ts , one can expect the extrapolated PVT res ul ts to be a reason

    it becomes available).

    'Preliminary Joule- Thomson points for fluorine are al so presented; however, dueme unexpected curvature in the isoc hores and deviations in the enthalpy calculation,

    w a s not calculated herein.7

  • 7/31/2019 NASA TN D-6807

    10/62

    1 ' 5 p c

    '"t

    ___L_ . . . . . . . . .I". '*I ' _2_ . .2.0P,. . . . . . . . . . . . /1.0P. . . . . . . . . . . . . . . . . . . . . . . .I .LO. 16Y .5- - . . . . . . . . . .1.5 pc (0.47;3;;y;70.62)__ . . . . . . . . . . . . . .. . . . . . . . . . . . _r0.5 Oe - . . . . . . . . . . . . . . .. . . __A ' '(0.08i . O . - . . . . . . < : : : : i : : : : i : 0.5 pc (0:08).oIO0 200 300 40 0 500 600 0 IO0 200 300 40 0 500 600

    (a)Methane. pc = 0. 162g/cm3. (b l Nitr ogen (based on ref. 14). pc = 0.3105 g/cm3.

    -.&. 2.0 Pc 2 5 P c621 "---(1071

    / - - - - - ' . . . . . 1.5 Pc ,-1.25 pc- . . . . . . . ' '(0.471 ;(0.39). . l < 1.0Pc- . . . . . . . . . /' . (0.311 ,I.5 pc (0. @!/I. 25 Pc (0.54). . . 10.16) . . . . . o. 5 pc (0.21)0 IO 0 20 0 300 400 500 600 0 100 200 so 0 40 0 500(c) Nitrogen (based on ref. 13; not a high pressure-temperature exten (dl Oxygen. pc = 0.4325 g/cm?sion). pr = 0.3105 g/cm?

    . . .'el.OPc (0.43)- . . . . . . . . . .,r 0.58 Pc . . . . .r. . . . .:::[.... 1.6 2.5 Pc''1 ~ ( 1 .6)......".. 2 5 p c.........1 331

    L O PLO 93Y4 _ _. . . . . . . . . . . . . . . . . . . . . ' 10.801 ,-1.25pc. ,' (0.66). . . . . . . . . . . ,.OPC .1.25 pc (0.58)._._ . . . . . . . . . . .I' . (0.531 1 Opc (0.46)._ . . ,

  • 7/31/2019 NASA TN D-6807

    11/62

    --

    7.. 3.0 pC(1: 4516

    2. 5 p(0.75Y

    > .

    1.5 Pc(0.45) , ,rl.Opc (0.3). , . 8 - - + :

    , , 1.5pc 1 25pc (0.601.. . :. : :(1.7z1 , 110 pc (0.481__---___ . ,. ... . . . . .: , 1 I_ 0.5pc (0.25)30 0 350 A 00 A5 0 50 0 550 610 ZOO 40 0Temperature, K

    lg ) Carbon monoxide. pc = 0.2997 g/cm3. (h l Neon. pc = 0.483g/cm3.1 . 0 - 3.0 Pc(0.211.9..

    .e..2.5 Pc.7.. 10 17)

    .6 c $ .5..s

    .A,. 1.5 pC

    . J - 10.101 1.25 pc(0.091

    .2 - 1.0 Pc(0.071..., 0.5 pC(0.031J . ~ . . 0 50 IO0 I50 200 250 SO0 A0 40 0 450 500

    (i )Helium. pc = 0.0693g/cm3.Figure 3. -Concluded.

    9

  • 7/31/2019 NASA TN D-6807

    12/62

    2.5 Pc(0.781 isochore1.6 2.5 Pc(0.78) isochore

    Calcu la ted fo rn i t rogen based onequat ion o f -Bender ( ref . 14)0 Coleman and

    1.2 Stewart (ref . 13)Calcu la ted fo r n i t rogena t h i g h p re s s u re b a s ed

    60 1 o n e q u a t io n o f -N Bend er (ref . 14)

    0 Coleman and S tewartz (ref . 13) -a5 .8-!za

    40 ~- . 6 1.5 Pc,30 - . 4 - (0.47) isochore

    0 n20- . 2 0 . 5 p(0.167 i sochore

    0 100 200 300 40 0 500 600 700Tempera ture , KFigure 5. - Comp arison of part ial derivat ive (dP/dTlp based on refe rence 13a n d

    the ex tended PVT resu l t s based on re ference 14. Cri t ica l densi ty, pc. 0.3105Tempera ture , K g/cm3.

    F igure 4 . - Compar i son o f p ressure- tempera ture p lane fo r se lec ted i sochoresbased on re fe rence 13 and the ex tended PVT resu l t s based on re ference 14.Cr i t ic al densi ty, pc, 0.3105 g/cm3.

  • 7/31/2019 NASA TN D-6807

    13/62

    J OULE-TH OMSON EFFECTSInversion Curves

    The i enthalpic Joule-Thomson coefficient, defined as t h slope of an isenthalp inP plane, can be written as

    P = L[.PCP P - 1is defined as the locus of maxima of the se isenthalps in the T - P

    Th is locus of points, whe re y = 0, can be calculated by determining the maximaore simply from

    A discussion of the rela tion between the isenthalpic and iso thermal Joule- Thomsonents and the ir relation to the principle of corresponding states is found in appenA . As pointed out in appendix A, the isenthalpic Joule-Thomson coefficient y isa corresponding states variable. However, the isot her mal Joule-Thomson coeffi

    ga is a corresponding states variable. They are relate d byga = - N p (A3)

    q = 0 y = 0 since CP # 0; and consequently, the principle can be applied toy = 0.The following discuss ion of invers ion cur ves includes the nonreduced and reduced

    s. Two fluids, nit rogen and oxygen, because they are well repre sente d with redata and J- T data in the literature, are treate d in both forms . Reduced

    are presented for the eight fluids of re ferenc e 15 along with some p reliminary

    11

  • 7/31/2019 NASA TN D-6807

    14/62

    ---

    Calcu la t ed f o rn i t ro gen based ond a ta f r o m r e f e r e n c e 0 5,60 1314V 16A 17A 18a 190 20a C r i t i c a l;I:o i n t-(Pc -- 3.417M N l m , Tc - 126.3 K)- G u n n ' s i n v e r s io n c u r v e(ref. 10)

    2 (a ) Ca lcu la t i ons based o n PVT ex t ens ions o f re f e rence 14.em

    Calculated forn i t rogen based onda t a f rom re f e rence 0 59 60 1417 16A 17A 18a 190 Ma C r i t i c a l p o i n t ( P c = 3 .4MN/m2; Tc = 126.2 K )- G u n n ' s i n v e r s io n c u r v e(ref. 10)- _ - Ref. l3

    0 10 20 30 40Pressure , MN/ m2(b )Calcu la t i ons based o n re f e rence 13.

    F igu re 6. - J o u l e -T h o m s o n i n v e r s i o n c u r v e f o r n i t r o g e n . C u r v e a n d s e le ct ed i s e n th a l p s c a lcu la t ed from re f e rence 15; da ta a re f rom re f e rences 5 6, an d 14 to 20.

    12

  • 7/31/2019 NASA TN D-6807

    15/62

    N o n r ed u ce d I n v e r s i o n C u r v e s for Nitrogen a nd OxygenNitrogen is a very useful research fluid and thus several sets of data for the inver

    n the literature. The experimental Joule-Thomson inversion curvedata of Roebuck and Osterberg (ref. 5), Deming and Shupe (refs. 16 and 17),

    hels, and Wolkers (ref. 18), Dean and Mann (ref. 19), and Din (ref. 20),with the inversion curve calculated from the equation of refe rence 10, a r e plotted

    figures 6(a) and (b). The inversion curve as calculated by using the Coleman-Stewartstate (ref. 13) is illustrated as a set of data points in figure 6(a) in or der toit from the inversion curve calculated by using the extrapolated Bender equa

    state (ref. 14), which is plotted as a dashed line. As can be seen, the agreementween the data and the calculated inversion curve is quite good, indicating that such

    fo r other fluids should, in the absence of data, be reasonably good approxins. Also plotted are selected enthalpies to illustrate their gener al behavior in the

    T plane and in particu lar nea r the inversion and saturation curves.In figure 6(b) the exercise of figure S(a) is repea ted by using the Coleman-Stewartstate (ref. 13) to genera te the dashed line. As can be seen, the inversion

    are in good agreement, as are the selec ted isenthalps. This lends a great dealconfidence to the extrapolated PVT res ult s.

    Oxygen has significant applications in the nation's space program and in industr ialThe recent PVT data of Weber (ref. 1 2) ar e very accurate, and a portion of the

    w a s defined by W e b e r (ref. 12) . The inversion curve calculated by usthe extrapolated PVT res ul ts of Bender (ref. 14) and the data of Weber (ref. 1 2 ) are

    figure 7. As can be seen, the agreement is quite good; however, there is nothe high- tem peratu re portion of the invers ion curve. Again selec ted enare overlaid on figure 7 to ill ustr ate isenthalpic behavior fo r oxygen in the

    13

  • 7/31/2019 NASA TN D-6807

    16/62

    I

    F i g u r e 7. - J o u l e -T h o m s o n i n v e r s i o n c u r v e f o r o x yg e n. Cu rve an d se lec ted i sen t ha lps based on PV Tex t ens ions as ca l cu la t ed f rom re f e rence 15; data f rom reference 12.

    Reduced Inversion CurvesIn references 8 to 10, to cite a f ew, the principle of corresponding states w a s used

    to group the inversion curves. (See appendix A on the applicability of the principle. )Fur the rmo re, Gunn, Chueh, and Prausn itz (ref. 10) found that seve ra l fluids (nitrogen,argon, xenon, carbon monoxide, methane, and ethylene) could be represen ted by asingle inversion curve, while quantum fluids such as neon, hydrogen, and helium wouldnot f i t the pattern.

    Since the principle of corresponding s ta te s should be applicable at high temperatures, Gunn, Chueh, and Prausnitz (ref. 10) force-fit the inversion data for hydrogenand helium to make their maximum inversion temperature coincide with that of the otherfluids, and thereby defined pseudocrit ical values fo r the two fluids (refs. 10 and 21).

    The inversion curves for methane, nitrogen, oxygen, argon, carbon dioxide, car bon monoxide, neon, nitrogen (Coleman and Stewart, ref. 13), and helium were calculated by using the extrapolated PVT re su lt s and plotted in reduced coordinates as figures 8 and 9. The invers ion curve for hydrogen (fig. s ( ~ ) )nd portions of the inversion14

  • 7/31/2019 NASA TN D-6807

    17/62

    ----

    0 A 040 V bA

    \

    (a 1 Methane. Pc = 4.627 MN/m2; Tc = 190.77 K.TR

    Data fromreference 5. 6121617182022

    Maximum invers iont e m w r a t u r e

    ( b ) Nitrogen. Pc = 3.417 MN/m2; T - 126.3 K.61I II I I 1

    \ \ \\

    ee &-&=e0 2 4 10 12 8 10 12

    -cl Nitroge n (basedon ref. 13; not a hi gh pressure- temperat ure ex - (d l Oxygen. Pc = 5. 083MN/m2; T 154.78 K.tension) Pc = 3.4 MNlm2; Tc = 126.2 K.Figure 8. - Reduced Joule-Thornson inversi on curv e for several f luids, at various crit ic al pressures Pc and crit ical temperatures T basedo n PVT extensio ns as calcula ted from referenc e 15. Available data included for comparison.

    15

  • 7/31/2019 NASA TN D-6807

    18/62

    0 2 4 6 8 10 12(e )Argon. P, = 4.865 MN/mZ; T = M . 7 0 K . ( f ) Carb on dioxide. P, = 7.3835 MN/m2; Tc = 304.21 K.

    6

    Data from reference 50 4.7e 27,28

    0 a 10 (Kihara4 potential)0 23+ 23 (extrapolated

    data)24 to 26TR 300 29A Maximum inversion2 temperature

    1 -c-0 2 4 6 8 10 12

    PR(gl Carbon monoxide. P, 3.4986 MN/m2; Tc = 132.91 K.

    Figure 8. - Concluded.

    16

  • 7/31/2019 NASA TN D-6807

    19/62

    12

    1c

    8

    TR 6

    4

    2

    (

    ( a ) H e l i u m . P c =

    D a t a f r o m r e f e r e n c e 1931323340 41 42,43 ( as rea d f r o m f ig . 5)

    A x i m u m i n v e r s io n t e m p e r at u re--P- G u n n ' s i n v e r s i o n c u r v e ( re f. 10)

    PR0 .22746 MN/m 2 ; Tc = 5 .2 K.

    (b) R e d uc e d h e l i u m i n v e r s i o n c u r v e b a se d o n p s e ud o -c r i t i c a l v a l u e s of r e f e r e n c e 10. I n v e r s i o n c u r v ep r e s e n t e d in r e f e e n c e 10 i n c l u d e d f o r c o m p a r is o n .P = 0.549 M N l mi; T = 9.4 K.F i g u r e 9 . - R e d uc e d J o u l e - T h o m s o n i n v e r s i o n c u r v e s f o r t h e q u a n t u m f l u i d s h e l i u m , h y d r o g e n a n dneon, f o r v a r i o u s v a l u e s o f c r i t i c a l p r e s s u r e Pc a n d c r i t i c a l t e m p e r a t u r e T c.

    17

  • 7/31/2019 NASA TN D-6807

    20/62

    t

    I

    4T R

    3

    2

    1

    0

    D a ta f r o m r e f e r e n c e n 190 3 10 3 20 3 3V 400 4 1A 4 2 , 4 3 ( a s r e a d

    f r o m f i g . 5)A M a x i m u m i n v e rs i o n t e m p e ra t u re

    -CF G u n n ' s i n v e r s i o n c u r v e (r ef . IO )

    !6 8 1

    PR( c ) H y d r o g e n . P c = 1.294 M N l m 2 ; T c = 3 2 . 9 8 4 K.

    -4 8 1( d ) R e d uc e d h y d r o g e n i n v e r s i o n c u r v e b a s e d on p s e u d o c r i t i c a l v a l u e s o f

    r e f e r e n c e 10. I n v e r s i o n c u r v e r e s en t e d in r e f e r e n c e 10 i n c l u d e d f o rc o m p a r i s o n . Pb = 1.554 MNlm? TL = 41.4 K.

    F i g u r e 9. - C o n t i n u e d .18

  • 7/31/2019 NASA TN D-6807

    21/62

    t

    4

    TR ?

    2

    1

    0

    6

    5 \

    4

    T k 3

    2

    D a ta f r o m r e f e r e n c e n 190 3 1 0 3 2 0 3 3 V 400 4 1 A 4 2 , 4 3 ( a s r e a d

    f r o m fi g. 5 )A M a x i m u m i n v e r s i o n t e m p e ra t u re

    -c- G u n n ' s i n v e r s i o n c u r v e ( re f. 10)

    6 1PR

    ( e ) N e o n . P c = 2 . 6 5 3 7 M N / m 2 ; T c = 44.40 K.

    \

    1-/ /0 I I ( f ) R e d uc e d n e o n i n v e r s i o n c u r v e b as ed on p s e u d o c r i t i c a l v a lu e s o f

    r e f e r e n c e 10. Pk = 2 . 7 0 5 M N / m 2 ; Tk = 4 5 . 3 K.F i g u r e 9. - C o n c l u d e d .

    19

  • 7/31/2019 NASA TN D-6807

    22/62

    curves for xenon and krypton are presented (figs. 10 and 11). The helium, hydrogen,and neon2 pseudoreduced plots as suggested by Gunn, Chueh, and Prausnitz (ref. 10)are also presented for comparison (figs. 9(b), (d), and (f)). The maximum inversiontemperature (above which expansion produces heating at all pressures) as calculated inappendix B and summarized in table I is plotted on the inversion curve fo r each fluid.The Boyle tempera ture TB and the low-density Joule inversion tempera ture TBmaxare al so discussed in appendix B and tabulated in table I. However, for fluids consider ed herein, no calculated T was found. The behavior of these tem perature s isBmaxrelevan t to the second virial coefficient B and its relation to the principle of cor responding states (see appendixes A and B).

    Corresponding States FluidsIn figure 8 (a) the inversion curve f or methane is in good agreement with the limited

    methane data of Tester (ref. 22), except near the knee of the curve . As the isenthalpsar e extremely flat in this region, small er ro rs in PVT and in the par tial derivatives canresu lt in large shifts in the inversion curve . A s the PVT data used here are from reference 14, it is assumed that the inversion locus is more accurate than that of Tester(ref. 22).

    In figures 8(b) to (d) the nitrogen and oxygen inve rsion curves and data a re replottedin reduced coordinates. The agreement has been discussed previously.

    In figure 8(e) the inversion curve for argon is plotted along with the data of Roebuckand Osterber g (refs. 4 and 7); Grossman, McCarty, and Hust (ref. 23); and Michelse t al. (refs. 24 to 26); and the Kihara potential as calculated by Gunn (ref, 10). Theagreement is quite good up to TR = 3. From TR = 3 to the maximum inversion temperature the relative e rr or is at most 5 percent with resp ect to the res ult s of re fe rence 23. Since the calculated data points of reference 23 and the invers ion curve of figure 8(e) are both based on an extrapolation of the equation of state, the deviations seemquite reasonable. A s such, the relative e r r o r could be used as an indicator of the confidence which can be placed in the maximum inversion temperature.

    In figure 8(f) the inversion curve f o r carbon dioxide is in good agreement with thedata of Roebuck, Murre ll, and Miller (ref. 27) and Newitt, Pai, Kuloor, and Hu'ggill(ref. 28). Note that the shape of the reduced inversion curve deviates significantly fromthat of argon (fig. 8(e)). We also note that the acentric factor for argon is -0.002 and

    2The quantum fluids, helium, hydrogen, and neon, are treated separately. Neon isconsidered a weak quantum fluid.20

  • 7/31/2019 NASA TN D-6807

    23/62

    0

    8 F igure 10. - Reduced Jou le -Thomson invers io n data f o r k ryp t on f romre f e rence 44. Cr i t i ca l p ressure , Pc = 5.502 MNlm; cr i t i ca l t em -perature, Tc = 209.4 K.

    1 0

    8 9 10 F igure 11. - Reduced Jou le -Thomson invers io n da ta f o r xenon f romre f e rence 45.

    21

  • 7/31/2019 NASA TN D-6807

    24/62

    --

    --

    TABLE I. - FIXED- POINT TEMPERATURES RELATED TOSECOND VIRIAL COEFFICIENT B

    . . - _.Fluic Maximum inversior Low-density Joule Boyle tempera- Reduced temperatures

    temperature inversion tem- ture (B = 0),(B/T=.maximum), perature (B =

    TBT ~ ,nv TR, B

    maximum ),I _ _ TBmax1008.55626.78798.98815.061387.78236.0355.13

    647.51644.4

    aFrom ref. 14.'From re f. 13.

    518.9 5.2867 2.72321.4 4.9627 2.544403.3 5.162 2.606412.7 5.4085 2.738725.8 4.5619 2.386122.9 5.316 2.76727.5 10.601 5.292

    347.9 4.872 2.618329.8 5.102 2. 61

    -

    TABLE 11. - COMPARISON OF CRITICAL ISENTHALPIC JOULE- THOMSON COEFFICIENTSAS CALCULATED FROM REFERENCE 15 AND pc = Tc/6Pc

    - - _Fluid Acentric Critical pressure, Pr Zritical tem- Critical Crit ical i senthalpic Joule-Thomson coefficien

    factor ____- ~ perature, density !T

    w g/cm 6PcK/MN/m 2- (from ref. 15)- ~ .

    CH4 10.013 45.66 4.627 190.77 0.162 6. 87 6.88aN2 +. 04 33.72 3.417 126.3 .3105 6. 16 5.91+. 02 1 50.16 5.083 154.78 .4325 5.08 5. 18Ar - . 002 48.01 4.865 150.7 .531 5. 16 5.58c02 +. 42 72.87 7.3835 304.21 .464 6.87 5.56Ne 0 26.19 2.6537 44.4 .483 2.79 4co +. 041 34.53 3.4986 132.91 .2997 6.33 3.96He 0 2.245 .227464 5.2 .0693 3. 81 7 .9

    3N2 +. 04 33.56 3.4 126.2 .3053 6.19 6.22Xe +. 002 58 5. 877 289.75 1.1052 8.22Kr - .002 54.3 5.502 209.4 .908 6.34HZ- 0 1 2 . 7 7 1.294 32.984 .03077 4.248

    (ref. 50). atm M N / ~ ~ TC PC p =c,

    aFrom ref. 14.bFrom ref. 13.

    0 2

  • 7/31/2019 NASA TN D-6807

    25/62

    for carbon dioxide is 0.42 (table II and appendix C), which means that carbon dioxIn figure 8(g) the inversion cu rve for carbon monoxide depar ts significantly from

    e data of Leah (ref. 29); however, the departure is not quite s o significant for the dataf Michels, Lunbeck, and Wolkers (ref. 30). The most troublesome asp ect of these ex

    ated result s is the significant departure from the general form of the inversioncorresponding states fluids. The re su lt s of Leah (ref. 29) and those of

    ence 15 were compared in depth, and are discussed in appendix E. There do seeme systematic deviations in the re su lt s of Leah (ref. 29) and those of reference 15;

    er, the deviations pre si st into the regime where reference 15 is more accurateref erence 29. Thus, the inversion curve is questionable at high temp eratu res.

    states form is definitely favored.

    Quantum FluidsHelium, hydrogen, and neon are quantum fluids and, as such, depart from a correding st at es treatm ent . However, neon app ear s to behave mo re like a normal fluid

    d is usually considered to be a weak quantum fluid.The inversion curve for helium and the data of Baehr (ref. 31), Keesom (ref. 32),

    d Hill and Lounasmaa (ref. 33) are plotted in figures 9(a) and (b), In general, the datare in good agreem ent with the curve; however, one data point of Baehr (ref. 31) seems

    be out of line. The maximum invers ion temp erature of helium has been calculated byral rese arche rs: Beattie (ref. 34) and Keyes (ref. 35), 45 K; Kirkwood and Keyes

    f. 36), 54 K; Roebuck (ref s. 2 and 3) estimated 23.6 K by using the reduced temperof 4.55 K for air; Gunn, Chueh, and Prausnitz (ref. l o ) , 47.7 K; and an observed

    K as list ed by Crawford (ref. 37). Dean and Mann (ref. 19) use 55 K in theirof the Joule-Thomson refr ige rat or. The maximum inversion temp eratu re of

    II (appendix C) is 55 K. The agreement of the curve with reference 19 is not suras the equation of st ate used in referenc e 15 is that of Mann (ref. 38). The re

    (fie. 9(b)) is based on the pseudocritical parametersc = 9.4 K and Pc = 0.5492 MN/m 2 as suggested by Gunn, Chueh, and Prausn itz

    f. 10). Superimposed on this figure is the helium inve rsion curve determined in refce 10 for comparison. Generally, the discrepancies are large on the upper p ar t of

    as would be expected from the lack of agreement in the maximum

    3Gunn, Chueh, and Prausnitz (ref. 10) developed thr ee distinct curves: one fo r heone for hydrogen, and one for the corresponding states fluids.

    23

  • 7/31/2019 NASA TN D-6807

    26/62

    inversion temperature, 47.7 K (ref. 10)to 55 K (appendix A and table I). This wouldmean that the pseudocritical temp erature would have to be 10.8 K in order to forceagreement with the general reduced inversion temperature of 5.095 K (ref. 10).

    In figure 9(c), the inversion curve fo r hydrogen w as determined by using the program of Goldberg and Haferd (ref. 39), which is based on the PVT f i t of Roder, W e b e r ,and Goodwin (ref. 40). The data of Michels , DeGraaf, and Wolkers (ref. 41)are generally in good agreement with the curve; however, they appear high. The lower temperature data of reference 40 are in good agreement, as would be expected. In figure 9(d),the reduced hydrogen inversion curve is based on the pseudocr itical values of reference 10, Tc = 41.4 K and Pc.= 1.854 MN/m 2 . As might be expected, the agreement between the curves of Gunn, Chueh, and Prausnitz (ref. 10)and the invers ioncurves is quite good as they came from the equivalent data sets.

    In figure 9 (e) the reduced inversion curve for neon agrees very well with thesmoothed data of McCarty and Stewart (ref. 42)and Michels and Gibson (ref. 43). Thisis not too surprising since the maximum inversion temperature was used as a constraintin determining the equation of state (ref. 42). In figure 9(f) the reduced neon curve isbased on the pseudoc ritical values Tc = 45.3 K and Pc = 2.705 MN/m 2 (ref. 10).In comparing the cur ves (figs. 9(e) and (E)) the re app ears to be little difference betweenthem. (Recall that neon is considered a w e a k quantum fluid. )

    Other Joule-Thomson DataThe data of Trappeniers, Wasse naar, and Wolkers (ref. 44) and Michels,

    Wassenaar, DeGraaf, and Wolkers (ref. 45)were used to obtain portions of an inversioncurve fo r krypton and xenon, respectively (figs. 10 and 11). The general trends of thedata appear to be in good agreement with oth er fluids and are included in orde r to forma mor e general reduced inversion curve applicable to sev eral fluids, as discussed later.

    Equations for Inversion CurvesThe reduced inversion curves fo r methane, nitrogen, oxygen, carbon dioxide, car

    bon monoxide, argon, neon, helium, and hydrogen have been fitted by using a least-squ are s technique from TR = 0.9 (PR - 2 ) to the maximum inversion temp era ture witha polynomial

    6i=O

    24

  • 7/31/2019 NASA TN D-6807

    27/62

    TABLE 111. - POLYNOMIAL COEFFICIENTS OF REDUCED INVERSION CURVES OF SEVERAL FLUIDS

    L i = O JFluid lumber of AO A1 A2 A3 A4 A5 iverage sumspoints of square of

    used in residuals,each fit, ErX1OO

    nMethane 28

    1 .Nitrogen 37'Nitrogen 22Oxygen 34Argon 30Carbon 26

    dioxideNeon 30Carbon 32

    monoxidcHydrogen 21Helium 26General'

    'From ref. 14.bFrom ref. 13.

    -31.2651873 60.3026109 -32.9452935 9.29996645 - 1.50083567 1.12645882 .O. 0041500129 0.59-32.2267981 64.2512980 -37.7834485 11.966361 -2.29966244 .25510747 -.012830057 .58-35.7879152 72.8486137 -45.631724t 15.2554526 -2.90682623 .28560901 -.010865648 1.1-36.2893677 75.0939713 -48.741621 17.2310336 -3.57529548 .40633931 -. 01973906 * 77-25.2735214 47.0015602 -22.247918t 5.10306394 - .67161214 .054807958 -.0025724488 .31-49.6820235 106.352075 -72.1171474 25.3427205 -5.00402093 .51606354 -.021543775 .9-41.3301625 86.5178852 -59.0821381 21.5253196 -4.46121949 .49273197 -.02267271 7.6-24.5141408 44.1764731 -18.5476855 3.23409545 -.26868672 ,014909515 -. 001050672 1.5- 15.5988252 26.0321395 - 9.745901: 2.4207304 - .49105816 .05932495 .002913248 .18-9.50023901 13.4661013 -2.199775f .14814825 - . 01540754 .00173746 -.7093585xlO-~ 1.1

    PO p1 p2 P3 p4 P5 '-32.5209374 65.6922312 -39.738430( 12.9300299 -2.46176904 I. 25378553 -0.010986565

    'For fluids with small acentric factors. Helium, hydrogen, and neon ar e not included due to quantum effects.

  • 7/31/2019 NASA TN D-6807

    28/62

    The coefficients for these fluids are given in table III, along with the average sumsof the squares of the residuals

    E =' x ( ' R - 'R, datal2r nGenera l ized Reduced Inve rs ion C u w e

    In forming a generalized reduced inversion cu rve, inversion data for the fluidsargon, methane, oxygen, and nitrogen and the data for fluorine (ref. 46), xenon, andkrypton were weighted equivalent. The carbon monoxide data of Leah (ref. 29) andMichels, Lunbeck, and Wolkers (ref. 30) and points from the inversion locus of figure 8(g) were weighted equivalent but not used in the f i t ; however, they a r e centeredabout the gene ral inve rsion curve . The fluids helium, hydrogen, and neon were not usedbecause of the quantum effects cited previously. Carbon dioxide w a s not used becauseof its large acentric factor (0 .4 2 , table 11and appendix C). Within these res tra int s, andrecalling that much of the curves were calculated from extrapolated PVT data as discussed previously, the locus of points in figure 1 2 is a least-squares representation ofall the data for the corresponding states fluids. The generalized inversion curve isdescribed by

    6PR = x P i T k

    i=O

    The coefficients Pi a r e tabulated in table III. The agreement between the general reduced inversion curve presented herein and that of Gunn, Chueh, and Prausnitz (ref. 10)is quite good for TR < 3, as can be s een from figure 12.

    Although the quantum fluids and thei r isotopes should be handled separa tely (e. g. ,refs. 10 and 21) , the reduced invers ion c urves could probably be brought together byfinding (empirically) the suitable pseudocritical tempera ture and pr es su re for each fluid,Figure 13 ill us tra tes the pseudoreduced inversion curv es for the quantum fluids relativeto the generalized reduced inversion curve of figure 12.

    26

  • 7/31/2019 NASA TN D-6807

    29/62

    0 v00I>aoAb

    M e t h a n e ( r e f. 22) A r g o n ( r e fs . 4, 7, 10, 23 to 26)Oxygen (ref. 12)Carbon monox ide ( f ig . Ug) ) Ni t rogen ( re f s. 5 16to 18, a n d 20) K r y p t o n ( r e f. 44) Xenon ( re f . 45) Carbon monox ide ( re f. 30) Carbon monox ide ( re f. 29) F l u o r i n e ( r e f. 46) G u n n ' s i n v e r s io n c u r v e ( re f. 10) G e n e r a l i n v e r s i o n c u r v e ( t h i s r e p o r t )

    I I I I I I I TrrmlTi

    s>

    12

    F i g u r e 12. - G e n e r a li z e d re d u c e d J o u l e - T h a n s o n i n v e r s i o n c u r v e for severa l co r respond ing s t a t es fl u ids , based on the PVT e x t e n s i o n sand data. Cu rve of re f e rence 10 i n c l u d e d f o r c o m p a ri s on .

    27

  • 7/31/2019 NASA TN D-6807

    30/62

    ----6 - G e n e r a li z e d i n v e r s i o n c u r v e\\ -_-- N e o n\ Hyd rogenHe1ium-0- He l i um ( re f . 10)

    2

    0 2 4 6. 8 10 12Pk

    F i g u r e 13. - Gene ra l i zed reduced Jou le -Thomson i nve rs i on cu rve off i g u r e 1 2 a n d p s eu d o re d u ce d i n v e r s i o n c u r v e s o f q u a n t u m f l u i d sh e l i u m , h y dr o ge n , a n d n e on . I n v e r s i o n c u r v e for h e l i u m of r e f erence 10 inc lu$ed for compar ison. (For n o n q u a n t u m f l u i d s ,T k = TR a n d PR = PR. I

    Joul e-Thomson CoefficientsW i t h the aid of a computer program (e. g. , ref. 15), the isenthalpic Joule-Thomson

    coefficients (eq. (1))can be calculated over a wide range of temperatures and pressures.Curves of ,u against T with P as a parameter, T against P with ,u as a parameter, o r various combinations can be fabricated.

    Reduced Joule-Thomson CoefficientsIn appendix Cy a technique for determining the Joule-Thomson coefficient at the

    cri tic al point is discussed

    28

  • 7/31/2019 NASA TN D-6807

    31/62

    , in normalized form, in te rm s of the dimensionless para mete r,

    is, of course, obtaining a proper derivative in the crit ica l region; anded on the work of Bender (ref. 14), Coleman and Stewart (ref. 13), and reference 15,normalized dimensionless para mete r Tc/P cpc is nearly a constant. Thus, a simied form of p, is proposed

    Pc =-T C6pC

    For the fluids discussed herein, the values of pc are tabulated (table II and appenAs can be seen the values are quite rel iab le except for helium, neon, and carbon

    The equations of s ta te fo r these fluids were f i t many years ago and shouldIt must be pointed out that the values of

    for nitrogen as calculated by refe rence 15 from the s tat e equations of Coleman and(ref. 13) and Bender (ref. 14) are 6.22 and 5.91, respective ly. Moreover,

    buck and Oste rbe rg (ref. 5) experimentally determined (pc)N2 = 5.72. The agree[(pc)N 2 -- 6.171is quite good when the d ifficu lties in calculatingare considered.

    CBy using pc = Tc/6Pc, reduced Joule-Thomson coefficients ( pR = p/pc) as funcof reduced temp eratu re TR with reduced pr es su re PR as the parameter are

    in figure 14 fo r methane, nitrogen (ref. 14), oxygen, argon, carbon dioxide,n monoxide, neon, and nitrogen (re f. 13).

    Consta nt JouIe -T homson Loc iInterpolating the p-T figure with P as the par ameter, cur ves of constant p can

    as a function of tem peratu re and pres su re . The calculated values from theequations of r ef eren ce s 13 and 14 in refer enc e 15 for nitrogen for constant p are

    with the data of Roebuck and Osterberg (ref. 5) in figure 15. As can be seen,are in good agreement; however, there is some disagreement in

    e p < 0 regime between the calculated values and data of reference 5.29

  • 7/31/2019 NASA TN D-6807

    32/62

    4 .5

    A . 0

    3. 5 ---I-I3.0

    2 . 5

    2.0

    1. 5

    1 .0

    . 5

    -. 5 [a) Methane.

    IIL.

    . - 1.5 1 . 0 1.5 2.0 2 .5 3. 0 3 .5 4. 0 L . 5 .5

    (b) Nitroge n (based on ref. 14).

    1 . u 1.5 2. 0 2.5 3.0 3 .5 4.3 4.5TR (for pR = 0. 5, 0. 75, 1.0, 1.25, 1. 5, 2. 5, and 4.0 and P = 1atm)

    (c INitr ogen (based on ref. 13). (d) Oxygen.

    Figure 14. - Reduced Joule-Thornson coeff icients as func tio n of reduced tempera ture for selected isobars.

    30

  • 7/31/2019 NASA TN D-6807

    33/62

    A. 0

    3. 5

    VR 2. 0

    0

    -.5

    ._, 5 1 . 0 . 5

    $Ele) Argon. ( f l Carbon dioxide

    2 .0 2.5 3.0 3.5 1 . 0 4.5lg l Carbon monoxide. Ih l Neon,

    .5 1. 0 1.5 2. 0 2.5 5. 0 3.5 A . 0 4 .5TR (for P R = 0. 5, 0.75, 1.0, 1.25, 1 5, 2.5, an d 4 .0 and P = 1atm)

    li l Helium.Figure 14. -Concluded.

    31

  • 7/31/2019 NASA TN D-6807

    34/62

    I I Dataf romlre f e rence -

    14_ _ _ _ 13

    300

    coef f ic ient , L - 5\

    \\ \

    '\\

    \\ ,\/

    5 7 9[

    \\'\

    8

    \,\

    Pressure, atmFigure 15. - Jou le -Thomson coe f f i c i en t con t ours based re f e rences 13 and 14, ca l cu la t ed from re f e rence 15, a s c o m pared to t h e c o n t o u r s p r e s e n te d in reference 5.

    J o u l e -T h o m s o n Ref r i g e r a t o r s a n d L i q u i f i e r sJoule- Thomson re fr ige ra to rs and liquifiers usually operate in the lowest tempera

    ture portion of the cycle. The thermodynamics and operating optimums are discussed inappendix D. It was determined that the governing equations for the optimum figure ofme ri t (compressor power input/refrigeration output) for both the re fr ige ra tor and theliquifier were of the sa me form. Fur the r, i f the amount of ga s liquified were zero , thegoverning equations for the refrigerator and liquifier were identical. Dean and Mann(ref. 19 ) solved the governing equations for helium, hydrogen, and nitrogen. Their result s and those herein point out that maximum refr ige ration (liquification) does not correspond to the maximum figure of merit, that is, optimum operating costs.

    A qualitative look at the Linde intermediate press ure cycle reveals that the optimization procedure can only se rv e as a guide to the experiment. For example, the analys is tends to indicate that the intermediate press ure should be near Pc with h2/m >32

  • 7/31/2019 NASA TN D-6807

    35/62

    0.15. In the Linde proce ss for liquifying air, the intermediate pressu re is 40 atmospheres and h2/m = 0 .2 (ref. 47).

    The operating costs can also be reduced by precooling the inlet gas and/or cascading using seve ra l single J-T cycle s with different operating fluids.

    CONCLUSIONSThe pressure-volume-temperature (PVT) relatio ns for seve ral fluids (methane,

    nitrogen, oxygen, argon, carbon dioxide, neon, carbon monoxide, fluorine, hydrogen,and helium) have been used to study the behavior of the isenthalpic and isothe rma l Joule-Thomson coefficients and in par ticular the invers ion curve . The following conclusionswere reached:

    1. Examination of the PVT data obtained by extrapolating the equation of statedescribed by Hendricks, Baron, Peller, and Pew indicates valid r esu lts fo r the high-pre ssu re and high-temperature ranges. This is further validated by the fact that thepartials ( a P / a ~ ) ~nd (aP/aT)P, where p is density, are in good agreement with otherhigh-p ressu re and -tempera ture re su lts of Coleman and Stewart. The Joule-Thomsoninversion cu rves calculated a s functions of these extrapolated PVT data ag ree w e l l withbest available J-T data.

    2. Since the Joule-Thomson invers ion curve (isenthalpic J- T coefficient p = 0)conforms to the principle of corresponding sta tes, a generalized, reduced invers ioncurve can be determined for the fluids with low acen tri c fac tors . Although the individualf i t of the invers ion curve for each fluid gives better resu lts , the generalized cu rve isuseful in the absence of data and to indicate si mi la rit ies among the fluids. The inversion curve developed herein and that presen ted by Gunn, Chueh, and Prausn itz are ingood agreement. The quantum fluids helium, hydrogen, and neon ar e best handledseparately .

    3 . A cr iti ca l isenthalpic Joule-Thomson coefficient pc can be determined and asimplified expression deduced for it:

    Even though the corresponding st at es principle does not apply to p # 0, reduced curvescan be determined and are usefu l in grouping da ta and where data are not available.

    4. The maximum inversion temperature (maximum (B/T)) and the Boyle temperature (B = 0) can be found from the second virial coefficient B of the state equations.For the fluids with inversion curves calculated herein, no maximum in B was found.

    3 3

  • 7/31/2019 NASA TN D-6807

    36/62

    5 . Joule- Thomson liquifie rs and re fri ge ra to rs operate mos t efficiently at pressuressubstantially less than those corresponding to the maximum cooling capacity.Lewis Rese arch Center,

    National Aeronautic s and Space Administration,Cleveland, Ohio, March 10, 1972,113-31.

    34

  • 7/31/2019 NASA TN D-6807

    37/62

    A P P E N D I X APRINCIPLE OF CORRESPONDING STATES A ND THE INV ERSION CURV E

    The corresponding states principle applies to molecules with spherical symmetryand a universal curve shape for the potential energy of molecular interaction. Consequently, the principle applies only to those prope rti es which depend on the intermolecular energy. As such, the reduced second virial coefficient Bpc should be a universalfunction of reduced tem perature TR. Simple substances such as the inert gas es (excluding helium, hydrogen, and possibly neon due to quantum effects), nitrogen, oxygen,carbon monoxide, and methane do conform as expected.

    The second virial coefficient, to which the principle applies, is simply related tothe isotherm al Joule- Thomson coefficient

    in the limit of zero pressure

    c p o = lim cp =-(T--d l n BP-0 T d l n T )Consequently, the principle of corresponding states is applicable to c p . Now cp isrela ted to the isenthalpic Joule- Thomson coefficient p by

    Francis and Luckhurst (ref. 48) note that the principle of corresponding s tat es inthe low-pressure limit is not applicable to specific heat CP or to the isenthalpic Joule-Thomson coefficient p, even though the i r product is a corresponding st ates variable.

    However, the application of the principle of corresponding states to the inversioncurve, for the fluids indicated previously, is valid. The inversion curve repr esents thelocus of points where

    PCP = o = l (A4)P3 5

  • 7/31/2019 NASA TN D-6807

    38/62

    This, of course, als o mean s that iso the rmal Joule-Thomson expansions for 9 < 0produce cooling and iso the rmal expansions where 9 > 0 produce heating. However,the inversion curve, common to both iso the rmal and isenthalpic expansions, re pr ese nt sa locus of minimums of the isot her ms in the entha lpy-p ressur e plane (fig. 16).

    60 3Pressure , M N / ~

    =i g u r e 16. - I so t he rma l Jou le -Thomson expans ion (cp = ( ~ H / ~ P ) T- p C p) a n d t h e i n v e r s i o n c u r v e ((p - - pC p = 0)f o r fluid oxygen.

    36

  • 7/31/2019 NASA TN D-6807

    39/62

    APPENDIX BINVE RS ION TEMPERATURES AND THE SECOND VlRlA L COEFFICIENT

    The isothe rma l and isenthalpic Joule- Thomson coefficients, as discussed in appendix A , have been used to test virial forms of the equation of state and derived properties.

    From refe renc e 15 the equation of state can be written asP = pRT + A(T)p2 + B(T)p3 + C(T)p4 + D(T)p5 + H(T)p6

    where the functions H(T) and G(T) were added to accommodate Coleman and Stewart' sequation for nitrogen (ref. 13). Expanding the exponential in a Taylor se ri es aboutp = 0 and rearr angin g, the equation of state can be written as

    n

    = l + B p + C p2 + D p3 + . . . (B2)where the first term represents a fluid with negligible molecular interaction (i.e. , idealgas). The second B, thi rd C, or fourth D, etc ., te rm s or virial coefficients represen t interactions between two, thr ee , or four molecules, etc. , respectively. As suchthe virials B, C, D, etc ., repre sent the deviation from an idea l gas state. Here weare inte rest ed in the second vir ial coefficient B = A(T)/RT, or from reference 15 withthe modifications cited,

    R T2 T3 T4 T5 T7The zero-pressur e inversion temperature (maximum inversion temperature) is

    given in terms of the second v ir ia l coefficient for the equation of st ate= l + B ' P + C ' P2 + . . .

    37

  • 7/31/2019 NASA TN D-6807

    40/62

    m1111 . . . . ...

    by the ze ro-p res sur e limit of cp (appendix A ) . Using equations (B l) and (1)we find thelimit

    lim ( -p ) = lim p C = T2 d(B/T)P-0 P-0 p dT

    Since CP > 0, p pas ses through zero at the temperature for which B/T is a max-imum. By using the second vi ri al coefficient of r ef eren ce 15 (eq. (B3)) and maximizingB/T, the zero-p ressure inversion tempe ratures Tinv esti mated by extrapolating thePVT result s to higher temperatu res are presented in table I. For the Van d er Waalequation of state

    p = - - -T aV - b v 2

    the second virial coefficient becomes

    B = b - - aRTand substituting equation (B7) into equation (B5) the maximum inversion tempera turebecomes

    - 2aTinv -zor in reduced form

    - 27T ~ ,nv -4since Van der W a a l ' s value of Tc is 8a/27Rb. Meissner in the Handbuch der Physik(1926) found TR, inv to be about 5 . 8 for all gases, which is 14 percent lower than givenby equation (B9) except, of cours e, fo r helium. However, the values presented intable I are even lower but a r e generally in good agreement with the results of Gunn,Chueh, and Prausnitz (ref. l o ) , where TR, inv is about 5.075 K. Fo r nitrogen, re ference 34 gives TR, inv = 4.75 and reference 6 gives TR, inv = 4 . 9 2 . Fo r argon, reference 6 gives TR, inv = 4.8, and reference 2 3 gives TR,inv = 5.26.

    The Joule o r fr ee expansion coefficient38

  • 7/31/2019 NASA TN D-6807

    41/62

    2 aT7 7 " p d),

    has an inversion temperature at the maximum in the second virial coefficient B forlow densit ies. While the relation between the Joule-Thomson coefficients cp and pis simple , the relation to the Joule coefficient is more complex

    qCv = T ( S L - P

    where cp = - pCP' Substituting equation (B4) into (BlO), we find for the region of lowpressure (low density) that

    ml .de that at zero pressure, 77 is zero; but for densities low enoug-- for equation (B11)to hold, the Joule coefficient has an inversion where B is a maximum. Values of thisinversion tempe rature, as listed in table I, were obtained from reference 34. B asgiven by equation (B3) does not p os se ss a maximum for T 5 4000 K. Such temperatu res a re f a r beyond the range of the curve fits and beyond the scope of the Joule-Thomson curves for fluids discus sed herein. It is also interes ting to note that this inversion tempe rature does not exist for the Van der Waal fluid, as B does not attain amaximum.

    The Boyle temperature is that temperature for which the second virial coefficientvanishes, that is , when B = 0. The Boyle temp eratu res a re a lso given in table I. Fo rthe Van der W a a l fluid, equat ions (B8) and (B9) give

    T ~ , nvT ~= ~The relation between calculated and reduced temperatures and the calculated reducedBoyle temp erature s seem to follow equation (B12) even though the Van der W a a l temperatures TB and Tinv do not.

    39

  • 7/31/2019 NASA TN D-6807

    42/62

  • 7/31/2019 NASA TN D-6807

    43/62

    - -c42 - limT C PVT-PcVcTc T

    PcVcTcwhich norma lizes the crit ical isenthalpic Joule-Thomson coefficient pc. The value of(aP/aT)p can be found from re fer enc es 14 and 15. However, for methane, nitrogen,oxygen, carbon dioxide, and argon Bender ( ref. 14) gives a nearly constant value for theproduct (T/P)(aP/aT)p v T ; that is, the normalized cri tica l isenthalpic Joulec c cThomson coefficient (eq. (C4)) is nearly a constant,

    =6

    Rearranging p C becomes

    The values of pc calculated from equation (C7) and from refe rence 15 for the fluidsconsidered here in a re given in table II.Using pc we can find the cri tica l dependency of the isothermal Joule-Thomsoncoefficient 50 and the Joule or free expansion coefficient 77 . The Joule or free expansion coefficient may be written as

    qCv = T ( Z 1 - P

    Rearranging and passing the limit

    41

  • 7/31/2019 NASA TN D-6807

    44/62

    and

    77 , =- 5pc(CY>,

    since ( c ~ ) ~s weakly divergent, qc must approach zero in a weak manner.The iso the rma l Joule-Thomson coefficient, from appendix A, is directly related to

    p through CP

    In the cri tica l region, CP diverges as IT - Tcl- 4/3, while p rema ins finite and nonzero. Consequently, 50, diverges as CP that is ,

    42

  • 7/31/2019 NASA TN D-6807

    45/62

    A P P E N D I X DJOU LE-TH OMSON L lQU lF lER AN D R EFR IGERATOR

    C YC LES AN D OPERATIN G OP TIMU MSA Joule-Thomson liquifier and refrigerator is illustrated schematically in figures 17

    and 18 (see also refs. 19 and 49). The only difference between the two devices is themakeup gas supplied to the liquifier at the compresso r; consequently, the temperatu re-entropy and enthalpy-temperature diagrams apply to eithe r proce ss.

    I r--- Makeup gas

    I l i q u i d EntropyF igu re 17. - Process d iag ram and f low schema t ic f o r a Jou le -Thomson l iqu i f i e r . Process diagramalso appl ies to Joule-Thornson re f r igerator.The compressor need not be a par t of the cycle; however, high-pressure gas mus t

    be supplied and a re tu rn provided. The Joule-Thomson process could be the last of several stages in a real ref rige rato r or liquifier of gas compresse d isothermally at ambienttemperature Ta to inlet pres sur e PI.

    Upon passing through the heat exchanger m g/sec of fluid is expanded isenthalpically such that h g/sec of the ga s a re liquified. The energy balance requ ire s

    Since we want to maximize the amount of liquid produced and the liquid re se rv oi rpressure is fixed, the only variable at our disposal is H1, which is controlled by P1

    43

  • 7/31/2019 NASA TN D-6807

    46/62

    t-----iCompressor

    ~ .~ - .Tempe rat u r e

    F i g u r e 18. - Process d iagram and flow schemat i c for J o u l e -Thomson ref r igerator . Process d iagram also appl ies to Jou le -Thomson l i qu i f i e r .

    But the latter term is the isothermal Joule-Thomson coefficient. This term is zeroonly when P and T lie on the inversion curve (appendix A). Consequently, the maximum liquification or refrigeration occurs when the process starts on the inversioncurve .

    However, the maximum liquification or refri gerati on "costs" more than operatingon a locus within the Joule-Thomson inversion curve. To see thi s, again consider theliquifier. If we let 77, represent the efficiency of the compressor, etc. , the work required to compress m g/sec of gas (isothermally) becomes

    Dividing by the amount of liquid produced (h =- h2 g/sec) gives a figure of merit for thesystem. Minimizing t h e figure of merit with respect to our only variable PI gives44

  • 7/31/2019 NASA TN D-6807

    47/62

    and from the heat exchanger load,

    which rep res ent s the second law constraint (heat flow requ ire s a positive temperaturedifference). Also, it must be noted that the proce ss is constrained to those points whereP3 is les s than Pc and p is less than zero.

    Equation (D3) is identical in form t o that of Dean and Mann (ref. 19) for Joule-Thomson ref rig era tor s. Note that equation (D4) for the Joule-Thomson liquifier readilyreduces to the heat exchanger load for the refrigeration, h2 equals zero. Dean andMann numerically solved equation (D3) with h2 replaced by m and equation (D4) with[1 - (h2/mg replaced by unity, for the fluids helium, para-hydrogen, and nitrogen, presenting curves s imi lar to that of figure 19. It is quite apparent that one should operatew e l l within the invers ion curve to minimize cost. However, other methods of reducingthe operating costs are to add intermediate cycles, as illustrated in figure 20, to precool the inlet gas, or by cascading using second single cycles with different fluids.

    Optimum:

    II n l e t p r e s s u r e , P1

    F igure 19. - Compar i son of i n v e r s io n c u r v e a n do p t i m u m ( m i n i m u m c o s t) o p e r a ti n g l o c u s forJoule-Thomson processes.

    45

  • 7/31/2019 NASA TN D-6807

    48/62

    1 3 5

    Figu re 20. - Double-cascade Jou le-Thomson l i qu i f i e r(ear l y L inde process for a i r ) .

    The energy balance, isothermal comp ressor w o r k , and heat exchanger balance become, for p > 0,

    fi2H2f = ri4H4f - (h2 - ri4)H5

    Note here that (m - h) represents the ma ss of gas returning to the c ompressor and t h a tn2 represents the gas or liquid pass ing to the second Joule-Thomson valve. Solvingfor the figure of merit,

    46

  • 7/31/2019 NASA TN D-6807

    49/62

    (%1)]

    p1In-+-In-n2 p3_ _ _W P3 m P59 = RTan4 n,

    H5 - H4fThis procedure can eas ily be extended to N-stages

    N

    k=O JEquations (D7)can be readily solved for the figure of me ri t for an N-stage Joule-Thom son pro cess ,

    wP='2N

    N - 1 *RTa[k=O2 n '2k+3 (H2Nf - H2N+1)

    N- 1'2N- 2 1H2N+1 - 7- ("2k-2 - 1'2k)H2k+lk=OThe optimization procedure becomes quite complicated and of academic in terest .For example, the optimum WP/m in equation (D6)s for h2 equals zero; that is , nofluid passing to the second J- T valve. However, the whole idea is to produce liquid, and

    the optimum curves are found by plotting those points that can be attained by expandingfrom P1 to P3. The ana lysi s can, however, se rv e as a guide to experimental testing.

    If one reflects on the previous discussion for a moment, and us es a little intuitionalong with figure 7, one would anticipate the maximum tempera ture drop to occur i f the

    47

  • 7/31/2019 NASA TN D-6807

    50/62

    process star ted at the inversion curve. Fur the rmo re, since most of the curves arequite flat nea r the inversion curve, one would expect that nearly the same amount ofrefrigeration could be obtained for a significantly lower pre ss ur e drop, at a substantialsavings in compressor power.

    48

  • 7/31/2019 NASA TN D-6807

    51/62

    A P P E N D I X EDIFFERENCES IN C AR BO N MO N O XID E PR OPERTIES

    The inversion curve of figure 8(g) as calculated from ref eren ce 15 and the res ul ts ofLeah (ref. 2 9 ) are in considerable disagreement. As the PVT data from reference 151are extrapolated considerably beyond the range of da ta used in the curve f i t (TR 2. One part of the band is formed from figure 8(g), the other from the data of Leah (ref. 29). A s can be see n, the difference increases as TR increases to 5 and PR & 6. The difference in density along theinversion curve then diminishes as pressure is reduced. Thus, the inver sion curve inthe region TR > 3 and 1 < PR < 112 seem s to have a significant departure from thatof Leah (ref. 29). However, in figure 8(g), the deviations from Leah (re f. 29) a re significant even for TR < 3 . Thus, not all the answers lie in the PVT results.

    In figure 21(b) the difference in enthalpy along the inversion curve is considerablebetween 10 < PR < 12, passes through a minimum nea r PR = 9, and increa ses as pressur e decreases. As very sm al l deviations in the enthalpy in this region will significantlyal te r the inversion locus, it appears that derived properties (i.e. , the (aP/aT)p) may bethe source of the differences.

    However, in figure 21(c) the difference i n entropy along the inversion curve is about0.9kO. 2 percent for PR < 11, which apart from the level sh i f t in So is quite reasonable. As both enthalpy and entropy require (aP/aT)P such agreement tends to exonerate the derivative (aP/aT!, .

    In figure 21(d) the d ifference i n spec ific heat at constant volume is quite large anddirectly relate d to temp eratu re level. Even in the regim e where the re su lts of refe r1ence 15 are quite accurate (TR

  • 7/31/2019 NASA TN D-6807

    52/62

    Reducedtemperature,

    TR0 2.055 0 2.806 0 3.56 A 4.31 4 5.065 -CO nvers ion(ref. 29)-- _ CO invers ion

    Temperature,T.K273 373 473 573 673

    fr om data (fig. 8(g))locus (fig. Ng))

    -.5 - .[

    1.5

    0 1.csX '= . 5

    0

    -.5

    I 1 I I (a) Relative density differences.

    I I 1 1 (b) Relative enthal py differences.

    I ~~ 1 I 1 1.50 2 4 6 8 10 12 PR

    (c ) Relative entropy differences.Figure 21. - Canpar ison of carbon monoxide propert ies as calculated fr an reference 15wi th those of reference 29, atseveral reduced pressur es for selected isotherms. Expected differences along invers ion curves (Leah's results vs.

    ref. 15)are bounded by shaded region.

    50

  • 7/31/2019 NASA TN D-6807

    53/62

    Reducedtemperature,TR

    0 2.0550 2.8060 3.56A 4.314 5.065-CO inversion(ref. 29)- -_ CO inversion

    -*L .~ I g---Zr, i ' IId) Relative specific heat at constant vo l ume differences.

    (e ) Relative specific heat at constant pressure differences.Figure 21. - Concluded.

    Temperature,T,K273313 473 573673 from data (fig. 8(9))

    locus (fig. 8(9)1

    51

  • 7/31/2019 NASA TN D-6807

    54/62

    tions in (aP/aT)P lead to sma ll shifts in the isenthalps, which in turn lead to deviationsin the invers ion curve. However, the data of Michels, Lunbeck, and Wolkers (r ef . 30)depart significantly from those of Leah (ref. 29) and to a lesser extent from the resultsof reference 15 . But these data appear to follow a curve about 5 percen t higher than theinversion curve of figure 8(g) and 10 percent lower than that of Leah (ref. 29).

    It is quite apparent tha t the carbon monoxide data need to be reevaluated and a newequation of state presented.Finally, invoking the principle of corresponding states, one would expect the inver

    sion curve to more closely follow that of Leah (ref. 29) . Therefore, the curve of figure 8(g) should be considered valid for TR < 3 and low fo r TR 2 3 .

    52

  • 7/31/2019 NASA TN D-6807

    55/62

    APPENDIX FSYMBOLS

    B' CC'cPcVDHk mNnnniPR

    U V wPTT2

    temperature functions in equation of state of ref. 15constantsconstants in Van de r W a a l equation of statesecond vir ial coefficientmodified second vir ial coefficientthird virial coefficientmodified third virial coefficientspecific heat at constant press ure, J/(g)(K)specific heat at constant volume, J/(g)(K)fourth virial coefficiententhalpy, J/gsummation indexma s s flow rate, g/secnumber of stagesnumber of pointsma ss flow rate, g/secconstan ts in equation of st ate (ref. 15) as modified to accommo

    date ref. 13 (i = 1, 2, 3, 4, 5 . . . 20, 21, 25)pressure, MN/m 2gas constant, J/(g)(K)reference entropy, J/(g)(K)interna l energy, J/gspecific volume, cm3/gcompressor or pump work, J/(sec)(W)temperature, Ktemperature, used in helium fit only, K

    53

  • 7/31/2019 NASA TN D-6807

    56/62

    11111111111111m111

    Z compressibility factor, PV/RT5 constants (i = 1, 2, . . . 5 )4 constants (i = 1, 2, . . . 7 )P density, g/cm 3cp iso thermal Joule- Thomson coefficient, cm3/g77 Joule or free expansion coefficient, (g)(K)/cm 3qe efficiencyP isenthalpic Joule- Thomson coefficient, K/( MN)(m2)w acentric factor, - [(1 loglop R ~y)TR,O. d (ref. 50)Subscripts :a ambientB BoyleC criticaldata datainv inversionf liquidm a x maximumN2 nitrogenR reducedVp vapor pressu re0 zero pressure1,2,3 . . . states on thermodynamic diagramSuperscripts:0 pseudovalue7 (see fig. 9)

    54

  • 7/31/2019 NASA TN D-6807

    57/62

    REFERENCES1. Timmerhaus, K . D., ed. : Advances in Cryogenic Engineering. Vol. 15. Plenum

    Press, 1970, sections K and L, pp. 415-475.2. Roebuck, J. R. ; and Osterberg, H. : The Joule-Thomson Effect in Helium. Phys.

    Rev., vol. 43, no. 1, Jan. 1, 1933, pp. 60-69.3. Roebuck, J. R. ; and Osterberg, H. : The Thermodynamic Properties of Helium

    Gas. Phys. Rev., vol. 45, no. 5, Mar. 1, 1934, pp. 332-340.4. Roebuck, J. R. ; and Osterberg, H. : The Joule-Thomson Effect in Argon. Phys.

    Rev., vol. 46, no. 9, Nov. 1, 1934, pp. 785-790.5. Roebuck, J. R. ; and Osterberg, H. : The Joule-Thomson Effect in Nitrogen. Phys.

    Rev., vol. 48, no. 5, Sept. 1, 1935, pp. 450-457.6. Roebuck, J. R. ; and Osterberg, H. : The Joule-Thomson Effect in Mixtures of

    Helium and Nitrogen. J. Am. Chem. SOC., vol. 60, no. 2, Feb. 1938, pp. 341351.

    7. Roebuck, J . R. ; and Osterberg, H. : The Joule-Thomson Effect in Mixtures ofHelium and Argon. J. Chem. Phys., vol. 8, no. 8, Aug. 1940, pp. 627-635.

    8. Jakob, M. : Inversion Curve of the Joule-Thomson Effect in Gases. Phys. Z e i t . ,vol. 22, Feb. 1, 1921, pp. 65-69.

    9. Watson, K . M. ; and Smith, R. L. : Generalized High Pressure Properties of Gases.Nat . Petroleum News, vol. 28, no. 27, July 1, 1936, pp. 29-30, 34-36.

    . Gunn, R. D.; Chueh, P. L. ; and Prausnitz, J. M.: Inversion Temperatures andPr es su re s for Cryogenic Gases and Their Mixtures. Cryogenics, vol. 6, no. 6,Dec. 1966, pp. 3 2 4 3 2 9 .

    . Vennix, Alan J. : Low Temperature Volumetric Proper ties and the Development ofan Equation of State for Methane. Ph. D. Thes is, Rice University, 1966.

    . Weber, L. A . : Thermodynamics and Related Properti es of Oxygen from the T rip lePoint to 300 K at Pressures to 330 Atmospheres. Rep. 9710, National Bureau ofStandards (NASA CR-99159), June 20, 1968.

    3. Coleman, T. C.; and Stewart, R. B. : Thermodynamic Properties of Nitrogen from70 K to 1000 K with Pressures to 1000 Atm. Presented at the NAS-NRC 13thInternational Congress of Refrigeration, Washington, D. C. , Aug. 27-Sept. 3,1971.

    55

  • 7/31/2019 NASA TN D-6807

    58/62

    14. Bender, E. : Equations of State Exactly Representing the Phase Behavior of PureSubstances. Proceedings of the Fifth Symposium on Thermophysical Proper tie s.ASME, 1970, pp. 227-235.

    15. Hendricks, R. C. ; Baron, A,; Peller, I. ; and P e w , K. J. : GASP - A ComputerCode for Calculating the Thermodynamic and Transport Properties for EightFluids - Helium, Methane, Neon, Nitrogen, Carbon Monoxide, Oxygen, Argon,Carbon Dioxide. Presented at the NAS-NRC 13th International Congress of Refrigeration, Washington, D. C. , Aug. 27-Sept. 3, 1971.

    16. Deming, W. Edwards; and Shupe, Lola E. : Some Physical Pro perti es of Compr es sed Gases. I. Nitrogen. Phys. Rev ., vol. 37, no. 5, M a r . 1, 1931,pp. 638-654.

    17. Deming, Edwards W. ; and Deming, Lola S. : Some Physical Prop ert ies of Compressed Gases. V. The Joule-Thomson Coefficient for Nitrogen. Phys. Rev.,vol. 48, no. 5, Sept. 1, 1935, pp. 448-449.

    18. Lunbeck, R. J. ; Michels, A. ; and Wolkers, G. J. : Thermodynamic Properties ofNitrogen as Functions of Pressure and Temperature Between 0 and 6000 Atmosph er es and -125' and +150 C. Appl. Sci. Res. , vol. A3, 1952, pp. 197-210.

    19. Dean, J. W. ; and Mann, D. B. : The Joule-Thomson Pr oc es s in Cryogenic Refrigeration Systems. Tech. Note 227, National Bureau of Standards, Feb. 14,1965.

    20. Din, F.: Nitrogen. Thermodynamic Functions of Gases. Vol. 3. F. Din, ed.,Butterworth, Inc., 1961, pp. 72- 161.

    21. Gunn, R. D.; Chueh, P. L. ; and Prausnitz, J. M. : Prediction of ThermodynamicProperties of Dense Gas Mixtures Containing One or More of the Quantum Gases.AIChE J. , vol. 12 , no. 5, Sept. 1966, pp. 937-941.

    22. Tester , H. E. : Methane. Thermodynamic Functions of Gases. Vol. 3. F. Din,ed ., Butterworth, Inc. , 1961, pp. 1-71.

    23. Grossman, A. L. ; McCarty, R. D. ; and Hust, J. G. : Thermodynamic P rope rtie sof Argon from the Triple Point to 300 K at Pressures to 1000 Atmospheres. Rep.NSRDS-NBS-27,National Bureau of Standards (NASA CR- 100532), Mar. 1969.

    24. Michels, A. ; Levelt, J. M. ; and Wolkers, G. J. : Thermodynamic Properties ofArgon at Temperatu res Between 0 C and -140' C and at Densities up to 640Amagat ( Pr es su re s up to 1050 atm.). Physica, vol. 24, 1958, pp. 769-794.

    25. Michels, A.; Lunbeck, R. J . ; and Wolkers, G. J .: Thermodynamical P rope rtie sof Argon as Function of Density and Temp eratu re Between 0 and 150' C and Densities to 640 Amagat. Physica, vol. 15, 1949, pp. 689-695.

    56

  • 7/31/2019 NASA TN D-6807

    59/62

    26. Michels, A. ; Lunbeck, R. J. ; and Wolkers, G. J. : Thermodynamical Propertiesof Argon as Function of P re ss ur e and Tempera ture Between 0 and 2000 Atmospheres and 0 and 150' C. Appl. Sci. Res., vol. A2, 1951, pp. 345-350.

    27. Roebuck, J. R.; Murrell, T. A. ; and Miller, E. E. : The Joule-Thomson Effectin Carbon Dioxide. J. Am. Chem. SOC . , vol. 64, no. 2, Feb. 1942, pp. 400-411.

    28. Newitt, D. M . ; Pai, M. V. ; Kuloor, N. R. ; and Huggill, J. A. W. : Carbon Dioxide. Thermodynamic Functions of Gases. Vol. 1. F. Din, ed., Butterworth,Inc., 1956.

    29. Leah, A. Smeeton: Carbon Monoxide. Thermodynamic Functions of Gases. Vol. 1.F. Din, ed., Butterworth, Inc., 1956.

    30. Michels, A. ; Lunbeck, R. J. ; and Wolkers, G. J. : Thermodynamic Pr ope rtie s ofCarbon Monoxide at Temperatures Between 0 and 150 C and at Press ures up to3000A tmospheres. Appl. Sci. Re s. , vol. A3, 1952, pp. 253-260.

    31. Baehr, Hans D. : Zur Kenntnis de s Joule-Thomson-Effekts und de r Molwarme vonDeuterium und Helium. Z . Electrochem., vol. 60, no. 5, 1956, pp. 515-517.

    32. Keesom, Willem H.: Helium. Els evier Publ. Co., 1942.33 . Hill, R. W. ; and Lounasmaa, 0. V. : The Thermodynamic Properties of Fluid

    Helium. Phil. Tr an s. Roy. SO C., Ser. A, vol. 252, no. 1013, Mar. 31, 1960,pp. 357-395.

    34 . Beattie, James A. : Thermodynamics and Physics of Matter. Vol. 1 of High SpeedAerodynamics and Jet Propulsion. Fre der ick D. Rossini, ed ., P rince ton Univers i t y Press, 1955, p. 249.

    35. Keyes, Frederick G. : Gas Thermometer Scale Corrections Based on an ObjectiveCorrelation of Available Data for Hydrogen, Helium and Nitrogen. Temp erature,Its Measurement and Contro l in Science and Industry. Reinhold Publ. Co rp .,1941, pp. 45-59.

    36. Kirkwood, John G . ; and Keyes, Frederick G. : The Equation of State of Helium.Phys. Rev., vol. 37, no. 7, Apr. 1, 1931, pp. 832-840.

    37. Crawford, Franzo H. : H e a t , Thermodynamics, and Statistical Physics. Harcourt,Brace & World, 1963.

    38. Mann, Douglas B. : The Thermodynamic Prop er ti es of Helium from 3 to 300' KBetween 0.5 and 100 Atmospheres. Tech. Note 154, National Bureau of Standards,Jan. 1962.

    39. Goldberg, Fredric N. ; and Haferd, Angela M. : Numerical Procedures for Calculating Real Fluid Pr op er ti es of Normal and Parahydrogen. NASA TN D-4341, 1968.

    57

  • 7/31/2019 NASA TN D-6807

    60/62

    40. Roder, H. M. ; Weber, L. A. ; and Goodwin, R. D. : Thermodynamic and RelatedProperties of Para-Hydrogen from the Triple Point to 100' K at Pressures to340 Atmospheres. Monograph 94, National Bureau of Standards (NASA CR- 64443),Aug. 10, 1965.

    41. Michels, A. ; DeGraaff, W. ; and Wolkers, G. J. : Thermodynamic Properties ofHydrogen and Deuterium at Temperatures Between -175' C and 150' C and atDensities up to 840 Amagat. Physica, vol. 25, 1959, pp. 1097-1124.

    42. McCarty, R. D. ; and Stewart, R. B. : Thermodynamic Prop er tie s of Neon from25 to 300' K Between 0.1 and 200 Atmospheres. Advances in ThermophysicalProperties at Extreme Temperatu res and Pr es su re s. Serge Gratch, ed., ASME,1965, pp. 84-97.

    43. Michels, A. ; and Gibson, R. 0. : Measurements of Isothermals (of Neon) at HighPressures. Ann. d. Physik, vol. 87, Nov. 22, 1928, pp. 850-876.44. Trappeniers, N. J. ; Wassenaar, T. ; and Wolkers, G. J. : Isotherms and Thermodynamic Properties of Krypton at Temperatures Between 0 and 150' C and atDensities up to 620 Amagat. Physica, vol. 32, 1966, pp. 1503-1520.

    45. Michels, A.; Wassenaar, T.; Wolkers, G. J .; and Dawson, J. : ThermodynamicProperties of Xenon as a Function of Density up to 520 Amagat and as a Functionof Pressure up to 2800 Atmospheres, at Temperatures Between 0 C and 150' C.Physica, vol. 22, 1956, pp. 17-28.

    46. Prydz, Rolf; and Straty, G. C. : PVT Measurements, Vir ial Coefficients, andJoule-Thomson Inversion Curve of Fluorine. J. Res. Nat. Bur. Standards, Sec.A - Phys. Chem., vol. 74A, no. 6, Nov.-Dec. 1970, pp. 747-760.

    47. Ruhemann, M. ; and Ruhemann, B. : Low-Temperature Phys ics. Cambridge Univers i ty Press , 1937.

    48. Francis, P. G. ; and Luckhurst, G. R. : Joule-Thomson Coefficients and the Frinciple of Corresponding States . Tr an s. Faraday SOC., vol. 59, 1963, pp. 667-672.

    49. Faires, V i r g i l M. : Elementary Thermodynamics. Third ed., Macmillan Co.,1957.

    50. Reid, Robert C. ; and Sherwood, Thomas K. : The Properties of Gases and'Liquids:Their Estimation and Correlation. Second ed . , McGraw-Hill Book Co., Inc.,1966.

    58

  • 7/31/2019 NASA TN D-6807

    61/62

    B IBLIOG RA PHYBudenholzer, R. A. ; Sage, B. H. ; and Lacey, W. N. : Phase Equilibria in Hydrocarbon

    Systems. Joule-Thomson Coefficient of Methane. Ind. Eng. Chem., vol. 31,no. 3, Mar. 1939, pp. 369-374.

    DeGroot, S. R. ; and Geldermans, M. : The Joule-Thomson Effect in Ethylene. Physica, vol. 13, 1947, pp. 538-542.

    Johnston, H. L. ; and White, David: V I I - A Summary of Experimental Determinationsof Joule-Thomson Effects in Gases. Trans. ASME, vol. 70, no. 6, Aug. 1948,pp. 651-654.

    Meissner, W. : Erzengungtiefer Temperaturen und Gasverflussigung. Handbuch derPhysik, 11, 1926. Referenced in Ruhemann, M. and B. : Low-Temperature Physics. Cambridge University Pr es s, 1937, p. 20.

    Sage, B. H. ; Webster, D . C. ; and Lacey, W. N. : Phase Equilibria in HydrocarbonSystems. XVl'II. Thermodynamic Pr op er ti es of Ethane. Ind. Eng. Chem.,vol. 29, no. 6, June 1937, pp. 658-666.

    Whalley, E. : Thermodynamic Properties of Argon in the Temperature Range - 100 to+600 C. and Pressure Range 0 to 80 Atmospheres. Can. J. Tech., vol. 33, 1955,pp. 111-116.

    1972- 3 3 E-6786 59

  • 7/31/2019 NASA TN D-6807

    62/62

    111m11~1ll1lll1lIII I 111111 Ill I IN A T I O N A L A E R ON A U TI CS A N D S PA CE A D M I S T R A T I O N

    W A S H I N G T O N , D . C . 20546 POST A GE A N D F EES PA I D__ N A T I ON A L A ER ON A U T I C S A N D0FFI C IA L B US I NESS FIRST CLASS MAIL SPA C E A D M I N I ST R A T I ONPEN A L T Y F OR PR I VA T E US E $300 USMAIL

    NASA 451011 001 C 1 U 33 720630 S O O 9 0 3 D S DEPT OF THE A I R FORCE AF W E A P O N S L A B ( A F S C ) TECH L I S R A R Y / k L O L / ATTN: f L O U BOWMAN, C H I E F K I R T L A N D A F B NM 87117

    POSTMASTER:

    T he aeionairtical and space activities of the United States shall becondacted so as to contribute . , . t o the expansion of human knowledge of phenoiiiena in th e a tmosphere and space. T h e Adni in is trat ionshall provid e for th e wide st practicable and appro priate disseminationof inforttiation concer ning its actizlities and th e re sd ts thereof.-NATIONALAERONAUTICSN D SPACE ACT OF 1958

    If Undeliverable (Section I5Postal Manual) Do Nor Reru

    NASA SCIENTIFIC ,AND TECHNICAL PUBLICATIONS TECHNICAL REPORTS: Scientific andtechnical information considered important,complete, and a lasting contribution to existingknowledge.TECHNICAL NOTES: 1nformation.less broadin scope but nevertheless of importance as acontribution to existing knowledge.TECHNICAL MEMORANDUMS:Information receiving limited distributionbecause of preliminary data, security classification, or other reasons.. ,CONTRA6FOR REPORTS: Scienrific andtechnical information generated under a NASAContract or grant and considered an important

    TECHNICAL TRANSLATIONS: Informationpublished in a foreign language consideredto merit NASA distribution in English.SPECIAL PUBLICATIONS: Informationderived from or of value to NASA activities.Publications include conference proceedings,monographs, data compilations, handbooks,sourcebooks, and special bibliographies.TECHNOLOGY UTILIZATIONPUBLICATIONS: Information on technologyused by NASA that may be of particularinterest in commercial and other non-aerospaceapplications. Publications include Tech Briefs,Technology Utilization Reports andTechnology Surveys.


Tn 5 Transposon

Tn 5 Transposon

murdercube.com Conversions/AR-7... · ö *970 c; „0£'0 o o o „ogo noz z . o tn ort o . 4-)tn

murdercube.com Conversions/AR-7... · ö *970 c; „0£'0 o o o „ogo noz z . o tn ort o . 4-)tn

Brochure harissa tn

Brochure harissa tn

Application of a three-dimensional viscous transonic inverse method to NASA rotor … · 2015. 7. 19. · Application of a three-dimensional viscous transonic inverse method to NASA

Application of a three-dimensional viscous transonic inverse method to NASA rotor … · 2015. 7. 19. · Application of a three-dimensional viscous transonic inverse method to NASA

Notice de montage - KelElek.com · TN402 Notice de montage TN131 TN001S TN 0 01S TN 001S TN 001S TN103S 1 6T 6200c ¢ Coffret VDI basique semi-équipé 2R-20M Grade 1 TN 10 3S TN103S

Notice de montage - KelElek.com · TN402 Notice de montage TN131 TN001S TN 0 01S TN 001S TN 001S TN103S 1 6T 6200c ¢ Coffret VDI basique semi-équipé 2R-20M Grade 1 TN 10 3S TN103S

Tn sept 1978

Tn sept 1978

TN 411 Grade 1 TN 413 Grade 3 - DBM-energie

TN 411 Grade 1 TN 413 Grade 3 - DBM-energie

Panenome voilure tournante en 1949 19740009679 trad NASA

Panenome voilure tournante en 1949 19740009679 trad NASA

TN Configuration 2

TN Configuration 2

Chauffe-eau Thermodynamique CET 200/300 TN - … · 1 CET 200/300 TN – Notice d’installation et fonctionnement Chauffe-eau Thermodynamique CET 200/300 TN NOTICE D’INSTALLATION

Chauffe-eau Thermodynamique CET 200/300 TN - … · 1 CET 200/300 TN – Notice d’installation et fonctionnement Chauffe-eau Thermodynamique CET 200/300 TN NOTICE D’INSTALLATION

Sec1 Mod8 Data Tn 71713

Sec1 Mod8 Data Tn 71713

à la terre TN .

à la terre TN .

Française de Cardiologie 10de Cardiologie Pratique · Abid L TN Ajmi Th TN Aloui H TN Attia N TN Belhadj Z TN Ben Ghorbel I TN Ben Halima A TN Ben Khalfallah A TN Ben Miled M TN

Française de Cardiologie 10de Cardiologie Pratique · Abid L TN Ajmi Th TN Aloui H TN Attia N TN Belhadj Z TN Ben Ghorbel I TN Ben Halima A TN Ben Khalfallah A TN Ben Miled M TN

TN tong hop

TN tong hop

Norges Bergverksdrift 1910 - Forside - SSB · dtr, hv ndhld v nltl vr tn jnnntl rl, tn 0. Jr n. Vd N ... dt ndl drft d frhldv tl trt ndp, n dn lr væntlt btt ndrøl frbrdl. dr nd

Norges Bergverksdrift 1910 - Forside - SSB · dtr, hv ndhld v nltl vr tn jnnntl rl, tn 0. Jr n. Vd N ... dt ndl drft d frhldv tl trt ndp, n dn lr væntlt btt ndrøl frbrdl. dr nd

TN 208 - Lecture 2

TN 208 - Lecture 2

TN-72 pp.01-05

TN-72 pp.01-05

BILAN DE L ACTIVITE BOURSIERE - Challenges TN

BILAN DE L ACTIVITE BOURSIERE - Challenges TN

Voyager Estate 2009 Cabernet Sauvignon Merlot TN - HO

Voyager Estate 2009 Cabernet Sauvignon Merlot TN - HO

D DPT T pLNT D B...NVTNT N TN T N BLTN DNTRPR dbr 86 (vlr d rltn n llr d dllr NTRPR Dntn t nrl d rvlln Hldn .. n rprtnr Prrrth n. pr rptl Lttnbr n. rdnrprvl l tl n. tdnt Ln rtn tn

D DPT T pLNT D B...NVTNT N TN T N BLTN DNTRPR dbr 86 (vlr d rltn n llr d dllr NTRPR Dntn t nrl d rvlln Hldn .. n rprtnr Prrrth n. pr rptl Lttnbr n. rdnrprvl l tl n. tdnt Ln rtn tn