1、rO“/q, _o_d,oitO Q3 22 id7_/NtA TR R-132i_ II -_.: “ - =AUJ:Iu=A=D- - -. “ “f,7 _.1962Foe redo by tim Supe_intendent of Dosumon_, U.8. Governmen$ Prfntf_ Omcn“ Washington, D.C., 20402. Yearly subscription, $15t.foreign) $19;slm_esupy.pekevnriasaeewding tosbe - Price $1.00Provided by IHSNot for Resal
2、eNo reproduction or networking permitted without license from IHS-,-,-TECHNICAL REPORT R-132ESTIMATED VISCOSITIES AND THERMAL CONDUCTIVITIESOF GASES AT HIGH TEMPERATURESBy ROGER A. SVEHLALewis Research CenterCleveland, OhioProvided by IHSNot for ResaleNo reproduction or networking permitted without
3、license from IHS-,-,-TECHNICAL REPORT R-132ESTIMATED VISCOSITIES AND THERMAL CONDUCTIVITIESHIGH TEMPERATURESBy ROGER A. SVEHLAOF GASES ATSUMMARYViscosities and thermal conductivities, suitablefor heat-transfer calculations, were estimated forabout 200 gases in the ground state from 100 to5000 K and
4、1-atmosphere pressure. Free radicalswere included, but vxcited states and ions were not.Calculations for the transport coel_wients were basedupon the Lennard-Jones (12-6) potential for allgases. This potential was selected because: (1) Itis one of the most realistic models available and(2) intermole
5、cular force constants can be estimatedfrom physical properties or by other techniqueswhen experimental data are not available; suchmethods for estimating force constants are not asreadily available for other potentials.When experimental viscosity data were available,they were used to obtain the forc
6、e constants; other-wise the constants were estimated. These constantswere then used to calculate both the viscosities andthermal conductivities tabulated in this report.For thermal conductivities of polyatomic gases anEucken-type correction was made to correct orexchange between internal and transla
7、tional energies.Though this correction may be rather poor at lowtemperatures, it becomes more satisfactory withincreasing temperature. It was not possible toobtain .force constants from experimental thermalconductivity data except .for the inert atoms, becausemost conductivity data are available at
8、low. tempera-tures only (200 to 400 K), the temperature rangewhere the Eucken correction is probably most inerror.However, if the same set of force constants is used/or both viscosity and thermal conductivity, there isa large degree of cancellation of error when theseproperties are used in heat-tran
9、sfer equations suchas the Dittus-Boelter equatio n. It is thereforeconcluded that the properties tabulated in this reportare suitable/or heat-transfer calculations of gaseoussystems.INTRODUCTIONIn designing rockets, heat-transfer calculationsmust be made for gases in turbulent flow at hightemperatur
10、e. Many commonly used heat-transfercorrelations for turbulent flow involve dimen-sionless groups, which in turn involve the trans-port properties, viscosity and thermal conductivity.Experimental data for these transport propertiesare available for most gases .which exist at roomtemperature, and for
11、some gases which are liquidsor solids at room temperature, but boil within afew hundred degrees of room temperature. How-ever, the availability of data diminishes rapidlyat higher temperatures. For example, there areexperimental viscosity data for only nine gasesabove 1000 K, and for no gases above
12、2000 K.Thermal conductivity data are even less available.In addition, the problem is complicated by theformation of free radicals at high temperatures forwhich virtually no experimental data are available.Therefore, it would be desirable to have tabulatedviscosities and conductivities for a :.arge n
13、umberof gases, which are found in rocket exhaust gases,with an accuracy suitable for heat-transfercalculations.In this report data for about 200 molecules andfree radicals are calculated from 100 to 5000 Kat 100 K intervals and 1-atmosphere pressure.(The data may also be used for the condition ofhig
14、h pressure and high temperature; but for thecondition of high pressure and low temperature1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 TECI-tNICAL REPORT R-132_NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONa pressure correction is necessary.) Th
15、e data are Q_for pure gases in the ground state. Excitedstates, which become important at high tempera- Rtures, have not been considered in calculating the rtransport properties, insofar as the collision crosssections are concerned. However, excited states rma_have been included in calculating the h
16、eat capaci-ties of monatomic and some diatomic gases inorder to make use of the best heat-capacity data 7available. (Heat capacities enter into the thermal Sconductivity calculation.) The heat-capacity sdata were obtained at the NASA Lewis ResearchCenter. Programs for the IBM 704 computer Twere made
17、 available to the author for calculating T_heat capacities from spectroscopic constants. T_TsubSYMBOLS T*A constant in inverse exponential repulsion upotential Vba0 Bohr radius of hydrogen atom, V,_0.5292 X 10-8 cm Wb constant in inverse exponential repulsion Zpotential ab0 second virial coefficient
18、 for rigid spheres,7rNa 3, cm3/(g-mole)C_ heat capacity at constant pressure, _“g-cal/(g-mole) (K)C_ heat capacity at constant volume,g-cal/(g-mole) (K) 7/c constant in Sutherland potential )D inner diameter of conduit, cmcoefficient of diffusion, sq cm/sec )7E(r) Slater and Kirkwood dispersion ener
19、gy Xptbetween two atoms, ergse electronic charge, statcoulombsh heat-transfer coefficient, Pg-cal/(sq cm) (sec) (K)K constant in inverse power repulsion _(r)potential _(2.2_,k Boltzmanns constant,1.38X 10 -18 ergs/KM molecular weight, g/g-moleN Avogadr0s number,6.023 X 10 _3molecules/g-molen n.umber
20、 of electrons in highest quantumstaten* effective principal quantum numberP_ critical pressure, atmp_ probability of colliding molecules follow-ing potential energy path iQ mean collision cross section, sq cmcollision cross section along potentialenergy path i, sq cmgas constant, 1.98726 g-cal/(g-mo
21、le)(K)intermolecular separation of collidingmolecules, Avalue of r corresponding to the infinitepotential barrier in modified Bucking-ham (exp-6) potential, Amean radius of a Slater orbital, ASutherland constantconstant in inverse-power repulsion po-tentialtemperature, Kboiling-point temperature, Kc
22、ritical temperature, Ksublimation temperature, Kreduced temperature, k T/elinear velocity in conduit, cm/secmolar volume at boiling point, cu cmmolar volume at melting point, eu cmscreening constantatomic numberpolarizability of molecule, cu cmconstant in modified Buckingham (exp-6)potentialG,IGmaxi
23、mum energy of attraction betweencolliding molecules, ergscoefficient of viscosity, g/(cm) (sec)coefficient of thermal conductivity,g-cal/(cm) (sec) (K)coefficient of translational thermal con-ductivity, g-eal/(cm) (sec) (K)coefficient of internal thermal conduc-tivity, g-cal/(cm) (sec) (K)density, g
24、/cu cmlow-velocity collision diameter, Apotential energy of interaction, ergsreduced collision integralMETHOD OF CALCULATIONThe equation used to calculate the coefficient ofviscosity is_6 26.693 _/_/IT_?z_lu = _-_2.-_ (1)where nXlO 8 is the viscosity in micropoises, T isthe absolute temperature in K
25、, M is the molec-ular weight, _ is the collision diameter in ang-stroms, and _(2._). is the reduced collision integral.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-VISCOSITIESAND THERMAL CONDUCTIVITIES OF GASES AT HIGH TEMPERATURES 3These collisio
26、n integrals in turn depend upon theintermolecular forces of the gas molecules, so thatit is necessary to know the potential energy ofinteraction of the colliding molecules. For thisreport the Lennard-Jones (12-6) potential hasbeen assumed. Collision integrals for thispotential were obtained from ref
27、erence 1, pages1126-1127, where they are tabulated as a functionof the reduced temperature kT/e. A discussion ofa number of different potentials and the reasonsfor selecting the L, .mard-Jones (12-6) over theother potentials are discussed in appendix A.The equation used to calculate the thermalcondu
28、ctivity isR 2J (_X10_)= (x+k“) X10 _ (2)where, e 15Rh 10 :_-_- (,X106) (3)and, 8 R C_ hfx 10 =1.32 (,X108) (4)In equation (2) k is the translational thermalconductivity, X“ is the internal thermal conductiv-ity, and X is the total thermal conductivity, all ing-cal/(em) (sec) (K). A discussion of equ
29、ation (2),including the assumptions in its derivation, isgiven in appendix B.In order to calculate the viscosity and thermalconductivity using equations (1) and (2), respec-tively, it is necessary to know the force constantsa and e/c of the Lennard-Jones (12-6) potentialfor each molecule considered.
30、 These constantsmay be obtained directly from either experimentalviscosity or thermal conductivity data, or theymay be estimated from physical properties orempirical rules when experimental data areunavailable. In this report, when experimentaltransport data were available, the viscosity data_ere us
31、ed to obtain the force constants, and thisset of force constants was then used to calculateboth the viscosity and thermal conductivity. Adiscussion of the various methods used to obtainthe constants a and e/k is given in appendix C,and a summary of these methods together withthe constants selected f
32、or each molecule is givenin table I.Conversion units are given in table II. Calcu-lated values of viscosity and thermal conductivity,using the constants of table I, are given in tableIII. Some additional calculated viscosities aregiven in table IV. It will be observed that thereare some omissions fo
33、r low-temperature propertiesof some molecules. This was because these lowtemperatures corresponded to reduced tempera-tures which were outside the range of the tabulatedcollision integrals of reference 1, pages 1126-1127.CONCLUDING REMARKSThe transport properties pr.esented in this reportare believe
34、d to be suitable for most engineeringcalculations, such as for heat transfer in rocketexhaust gases. For example, in forced-convection,turbulent-flow heat transfer in a circular conduit,a commonly used correlation of dimensionlessgroups is the Dittus-Boelter equation:D_o.o23 “ .,-7-/ (5)Combining al
35、l transport properties on the rightside of equation (5) shows that the heat-transfercoefficient h is a function of ),6/v4. It can beseen that the uncertainty in the heat-transfercoefficient is less than that of the transportproperties, because the exponent on each transportcoefficient is less than u
36、nity. In addition to this,it can be shown (ref. 2) that, if the same set offorce constants is used to calculate both viscosityand thermal conductivity, the errors in eachproperty tend to be in the same direction. There-fore, since there is a ratio of the two transportproperties, there is a certain a
37、mount of cancellationof error. To illustrate, consider the extreme casewhere each transport property enters to the samepower, such as in the Prandtl number. Whenthe same force constants are used, equation (2)may be used to write the Prandtl number asfollows:c,_ c_ (6)_-_/j!Thus, it can be seen that
38、by using a consistentset of constants the Prandtl number is independ-ent of the intermolecular potential. The resultof these two effects is that large uncertainties inthe transport properties give only small errors inthe heat-transfer coefficient.Provided by IHSNot for ResaleNo reproduction or netwo
39、rking permitted without license from IHS-,-,-4 TECHNICAL REPORT R-132_NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONThe properties calculated in this report are allfor pure gases, whereas properties of mixtures ofnonreacting gas systems are often desired. Rigor-ous mixing equations are available (ref
40、. 1, pp.531-538) but require considerable computation forall but the simplest systems. Equations havebeen proposed which approximate these rigorousequations. They have shown good agreementwith the rigorous equations, yet require consider-ably less computational work. A set of alinementcharts has bee
41、n prepared based upon these approx-imate equations (ref. 3), which can be used toreduce the calculations considerably for a multi-component system.Heat capacities and thermal conductivities havelarger values for reacting gas systems than fornonreacting systems. The explanation for this isas follows:
42、 If local chemical equilibrium is assumed,concentration gradients occur because the composi-tion varies with temperature. These gradientscause the transfer of chemical enthalpy by diffu-sion of the molecules. Rigorous equations havebeen derived which express the thermal conduc-tivity for a reacting
43、gas system (ref. 4). As inthe case of nonreacting systems, the calculationsfor reacting systems are tedious for anything butthe simplest systems. Since all reacting systemswill lie between a frozen state (nonreacting) andchemical equilibrium, depending upon the kineticsof the various reactions invol
44、ved, the thermalconductivity and heat capacity will lie betweenthese two extremes. Each system will be differ-ent, and no generalization can be made. How-ever, it has been shown (ref. 4) that the ratio ofthe equilibrium conductivity to equilibrium heatcapacity is about equal to the ratio of the froz
45、enconductivity to the frozen heat capacity. There-fore, equilibrium conductivities may be estimatedusing this relation for use in heat-transfer calcu-lations. When equilibrium conductivities areused, equilibrium heat capacities must also beused to obtain the correct result. Therefore, it isconcluded
46、 that the transport properties presentedin this report are suitable for making heat-transfercalculations in any type of unexcited or unionizedgas system.LEWIS RESEARCH CENTERNATIONAL AERONAUTICS AND SPACE ADMINISTRATIONCLEVELAND, OHIO, October 5, 1961Provided by IHSNot for ResaleNo reproduction or n
47、etworking permitted without license from IHS-,-,-APPENDIX ADISCUSSION OF POTENTIAL FUNCTIONSAll transport data above 2000 K (with the ex-ception of the thermal conductivity of argon)must be extrapolated from experimental data orestimated without the benefit of experimentaldata. Therefore, a theoreti
48、cal basis is necessaryin order to provide a reasonable means for cal-culating data outside the range of experimentaldata. In order to do this it is first necessary toknow the potential energy of interaction of thecolliding molecules. (If the gas is dilute, onlybinary collisions need be considered. T
49、his as-sumption is valid for this report, because the trans-port properties are calculated only for gases at1-atm pressure.) Three potentials which haveshown success in correlating experimental dataare the Sutherland model, the Lennard-Jones(12-6) potential, and the modified Buckingham(exp-6) potential. These three potentials aredepicted qualitatively in
