1、NASA CONTRACTORREPORTNASA CR-2440VISCOSITY ANDTHERMAL CONDUCTIVITY COEFFICIENTSOF GASEOUS AND LIQUID OXYGENby H. J. M. Hanley, R. D. McCarty, and J. V. SengersPrepared byUNIVERSITY OF MARYLANDCollege Park, Md. 20742for Lewis Research CenterNATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D.
2、 C. AUGUST 1974Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1. Report No.NASA CR-24404. Title and Subtitle2. Government Accession No.VISCOSITY AND THERMAL CONDUCTIVITY COEFFICIENTSOF GASEOUS AND LIQUID OXYGEN7. Author(s) H. J. M. Hanley, R. DStand
3、ards, Boulder, Colorado;of Maryland9. Performing Organization Name and AddressUniversity of MarylandCollege Park, Maryland 20742McCarty, National Bureau ofand J. V. Sengers, University12. Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationWashington, D.C. 2054615. Supplem
4、entary Notes3. Recipients Catalog5. Report DateAugust 197*+No.6. Performing Organization Code8. Performing Organization Report No.None10. Work Unit No.11. Contract or Grant No.NGL-2 1-002-34413. Type of Report and Period CoveredContractor Report14. Sponsoring AgencyFinal Report. Project Manager, Rob
5、ert J. Simoneau, Physical Science Division,CodeNASA LewisResearch Center, Cleveland, Ohio16. AbstractThe report presents equations and tables for the viscosity and thermal conductivity coefficientsof gaseous and liquid oxygen at temperatures between 80 K and 400 K for pressures up to 200 atm.and at
6、temperatures between 80 K and 2000 K for the dilute gas. A description of the anomalousbehavior of the thermal conductivity in the critical region is included. The tabulated coefficientsare reliable to within about 15% except for a region in the immediate vicinity of the criticalpoint. Some possibil
7、ities for future improvements of this reliability are discussed.17. Key Words (Suggested by Author(s)Correlation length; Critical phenomena;Intermolecular potential; Oxygen; Thermalconductivity; Transport properties; Viscosity19. Security Classif. (of this report)Unclassified18. Distribution Stateme
8、ntUnclassified - unlimitedCategory 3320. Security Classif. (of this page) 21. No. of PagesUnclassified 7722. Price*$4.00* For sale by the National Technical Information Service, Springfield, Virginia 22151Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,
9、-,-TABLE OF CONTENTSPageSectionI. Introduction 1II. Experimental information 52.1 Dilute gas 52.2 Dense gas and liquid 7III. Transport properties of the dilute gas 103.1 Equation for viscosity 103.2 Equation for thermal conductivity 123.3 Intermolecular potential function 23.4 Application to oxygen
10、14IV. Transport properties of the dense gas and liquid 184.1 Excess functions 184.2 Application to oxygen 8V. Thermal conductivity in the critical region 235.1 Behavior of the transport properties near thecritical point 235.2 Equation for A A 45.3 Correlation length 265.4 Application to oxygen 8VI.
11、Results 32illProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-VII. Remarks 45Appendix A. Dilute gas properties of oxygen 7A.I Introduction , , 47A.2 Second virial coefficient ,.,. 47A. 3 Thermal diffusion factor , , 49Appendix B. Critical enhancement
12、of thermal conductivity . . . , 52B.I Introduction ,.,., 52B.2 Carbon dioxide , , , 52B.3 Other gases ,., , , , 54References , . 62IVProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LIST OF TABLESTable PageI. Adjusted experimental viscosities for oxyg
13、en at lowpressures 8II. Parameters for oxygen used in this report 34III. Viscosity and thermal conductivity of gaseous oxygen asa function of temperature 35IV. Viscosity of compressed oxygen (r in milligram/cm.s) . 38V. Thermal conductivity of compressed oxygen(A in milliwatt/m.K) 40VI. Thermal cond
14、uctivity of oxygen in the critical region(A in milliwatt/m.K) 42VII. Viscosity and thermal conductivity of oxygenat saturation 3VIII. Conversion factors 44IX. Properties of CO , Ar, N and CH 53X. Comparison between experimental and calculated valuesfor the total excess thermal conductivity A.(p,T) -
15、 A0 (T)of nitrogen in the critical region 61Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LIST OF FIGURESFigure Page1. Schematic representation of the thermal conductivity(p,T) as a function of the density p at three super-critical temperatures T 0
16、, the excess value AX (p) in (Ib) is the differ-ence between the values represented by the dashed curves in Fig. 1 andX0(T), and the term A X(p,T) represent the additional contribution to beCadded to account for the effect of the vicinity of the critical point.In Fig. 1 we have indicated explicitly
17、these three contributions atp=p and T=T,.c 1Our method for calculating the dilute gas values r)0 (T) and X0 (T) isbased on the kinetic theory of gases and is described in Section III.The excess values Ar)(p) and AX (p) will be represented by an empiricalequation discussed in Section IV. A method for
18、 estimating the criticalenhancement A X(p,T) in the thermal conductivity is described in Section V.This method is based on an empirical extension of the ideas presented in apreceding NASA Contractor Report 2. Although a critical enhancementA r|(p,T) in the viscosity does exist, it is much smaller th
19、an the corre-sponding effect in the thermal conductivity and it will be neglected forthe purpose of this report.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Figure 1. Schematic representation of the thermal conductivity A(p,T)as a function of the
20、density p at three supercritical temp-eratures T UDw0)tnnsCn1 after a collision is related to thepotential by 39 dr* n b* $* .X = TT-2b*/ 1 - r C4)r*cwhere the variables are reduced according to the relations: b* = b/a,r* = r/a, r* r /a, $* = $/E. Integration of y over all values of b*c cyields the
21、cross section, Q*f- cos x)b*db* C5)1 (1 + (-1)*)2 1 +()*Q is dimensionless and has been reduced by the corresponding valuefor molecules interacting with a hard sphere potential .J Finally, integrationof Q*over all values of g* gives/ f C6)/ O *and n follows when ,s are both set equal to 2.11Provided
22、 by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-3.2 Equation for thermal conductivity.In order to calculate the thermal conductivity coefficient X0 (T) inequation (Ib) for a polyatomic gas we use the kinetic theory expressionderived by Mason and Monchick 410
23、(T) = 7 H0 + PD0c“O V A frt O O .- TTZwhere c “ is the internal specific heat per molecule of the dilute gas,Z the rotational collision number (defined as the number of collisionsneeded to relax the rotational energy to within 1/e of its-equilibriumvalue, where e is the natural logarithm base), and
24、D0 a diffusion co-efficient for internal energy. In practice, D0 is approximated by theself diffusion coefficient to be obtained from= 3 (mnkT)1/2 . (8)“-8 mrV11*Here S7 is the collision integral for diffusion, given by equation (6)with ,s set equal to 1. It is also noted that equation (7) has beenl
25、inearized by neglecting terms in the denominator of the third term thatdepend on the rotational collision number Z.3.3 Intermolecular potential function.It is apparent from equations (2-8) that, given c “ and Z, the cal-culations for the viscosity and thermal conductivity coefficients arestraight fo
26、rward once the function $(r) is known. Unfortunately, obtaining, -PX XO 0)w(U-PWnS CCri-Ho 3OS-r5 c.10d i,u a) T3s(00)0)3i“b4J(dC 4- cu id enH2CD (d ft 4-* 4 -na) a) t!.Q(Tj0)0) x! u 4J rfi 0) 4-1 wg0)w(0CnM(V0) ii4-1H-4-(NO-!OO+J CN“ Io 0)-Po OC. M r-lCD i i00) 0)r-l0) iCD-0) r-lO-Hc oQ Q0)316Provi
27、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-method to generate a table of values for T (T) and A (T) (Table III inSection VI).The uncertainty in the data and the . approximations in the calculationsmake it difficult to assign an accuracy to the tabula
28、ted coefficients. Onthe basis of the deviation curves, however, we attribute an estimateduncertainty of 3% to the viscosity values at temperatures up to 1000 K,while the error could be as large as 5% at temperatures between 1000 Kand 2000 K. The possible uncertainty in the thermal conductivity value
29、sis estimated to be 5% at all temperatures.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-IV. Transport properties of the dense gas and liquid.4.1 Excess functionsAs a next step we need to estimate the excess functions Ari(p) andAA(p), introduced in
30、 equations (1), which account for the behavior ofthe transport coefficients of the dense gas and liquid at temperaturesand densities away from the critical point. Many investigators havenoted that these excess functions for fluids other than helium andhydrogen are nearly independent of temperature w
31、hen plotted as a functionof density 1,48. Thus a considerable amount of data obtained atdifferent densities and temperatures can be represented to a first approx-imation by a single curve as a function of density, including data for thesaturated vapor and liquid. Conversely, use of the excess functi
32、ons Ar|(p)and AX(p) enables us to estimate values for the transport coefficientsover a wide range of experimental conditions from experimental data ina narrow range of conditions.f4.2 Application to oxygen.The correlation technique used in this report is to fit selectedexperimental data with the ass
33、umption that outside the critical regionThe empirical rule that the excess functions are independent of thetemperature is only approximately true. A small temperaturedependence of the excess functions does exist which becomes morepronounced at large densities such as densities twice the criticaldens
34、ities. It turns out that at large densities C3An/3T) is negative1,48. The rule breaks down for the thermal conductivity in thecritical region where an additional anomalous contribution must betaken into account as discussed in Section V. In this latter casethe more detailed equations (la),Qb) have t
35、o be considered.18Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-the excess functions An(P) and AA(p) are independent of the temperature.The excess viscosity Ari(p) was represented by the following twoequationsFor p 0.932 g/cmAn(P) = 0.47293P - 0.17
36、410P2 + 0.59995P (11)and for p 0.932 g/cmAn(P) = 0.6539P + 0.000029886exp(9.25p-1.0)where p is expressed in g/cm and ri in milligram/cm.s. These functionswere chosen on the basis of the excess viscosity values deduced from thedata of Grevendonk 30 and presented in Fig. 5. Data from ref. 4 and31 were
37、 also used to check that in the limit of low densities Ai|(p)approached zero in a consistent manner. The excess viscosity wasrepresented by the two equations in (11), because of the sharp increaseof the slope at a density twice the critical density.An equation for the excess thermal conductivity AA(
38、p) was obtainedby fitting a polynomial to the excess values deduced from the experimentaldata of Ziebland and Burton 32.AA(p) = 62.808p - 49.337p2 + 252.43p3 - 515.28p4+ 544.61p5 - 189.91p6 (12)where p is expressed in g/cm and A in milliwatt/m.K. The excessthermal conductivity is shown in Fig. 6.I s
39、hould be emphasized that equations (11) and (12) are empirical19Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-IDCJm ,._Q inaoenC)ininorOqrOCMs-ujo/ 6qCMIT)6C0)SIa-PHWC0)ao 1-1CrHo -H-PC0 OC -HP -p(XJO10)Wnj toPC C0) 0)Oitof tt)X OOt0)M-l MO0)-C O1
40、i-P4J-HWf)OGUidUJH , , Omw wDtn20Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-roc0)(0-PCJN:oEoCOLJOroCMC00COoCVJO0)rtf4JniTlIVO -UJ/M 01 xV21Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-represen
41、tations for interpolating the experimental data. The kinetictheory of gases predicts that the transport properties are nonanalyticfunctions of the density and that the density expansions for viscosity2and thermal conductivity should contain terms such as p Inp. However,the questions of how important
42、 such terms are in practice is presentlyunresolved 49,50.The excess values, Ari(p) and AA (p), calculated from equations (11)and (12) were added to the dilute gas values, )10 (T) and A0 (T) , res-pectively, obtained in Section III. The densities were converted intopressures and vice versa using the
43、equation of state. A discussion ofthe equation of state of oxygen is beyond the scope of this report.All calculations of the equilibrium properties in this report arebased on the equation of state developed by Stewart, Jacobsen andMyers 51.22Provided by IHSNot for ResaleNo reproduction or networking
44、 permitted without license from IHS-,-,-V. Thermal conductivity in the critical region.5.1 Behavior of the transport properties near the critical point.A survey of the behavior of the transport properties of fluids inthe critical region was presented by one of us in a preceding technicalreport 2. In
45、 order to account for this behavior we introduced inequations (1) anomalous contributions A l“|(p,T) and A A(p,T) defined asc cAcn(p,T) = n(P,T) - n0(T) - An(p) , U3a)AcX(p,T) = X(p,T) - X0(T) - AX(p) , (I3b)where Ari(p) and AX(p) are the temperature independent excess functionsdiscussed in Section
46、IV.The viscosity appears to exhibit a weak anomaly and A n increaseslogarithmically as the critical point is approached 52. However, theeffect can only be noticed very close to the critical point and may beneglected for most engineering purposes 53. The thermal conductivity,however, exhibits a stron
47、gly anomalous behavior which can be noticed ina large range of densities and temperatures around the critical point 53J,In a previous technical report we have argued that on approachingthe critical point the asymptotic behavior of A X (p,T) may be representedcbykT23Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
