1、THERMODYNAMIC AND TRANSPORT PROPERTIES FOR THE N2O4 -c2NO2 = 2NOtOZ SYSTEM NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. MARCH 1966 1 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB, NM Illllll1111111111 lllllIll11
2、11111lllllIllIll 0I30023 THERMODYNAMIC AND TRANSPORT PROPERTIES FOR THE N204 2N02 2N0+02 SYSTEM By Roger A. Svehla and Richard S. Brokaw Lewis Research Center Cleveland, Ohio NATIONAL AERONAUT ICs AND SPACE ADMlN ISTRATION For sale by the Clearinghouse for Federal Scientific and Technical Informatio
3、n Springfield, Virginia 22151 - Price $0.85 I. . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-THERMODYNAMIC AND TRANSPORT PROPERTIES FOR THE N204 22N02 -2N0+02 SYSTEM by Roger A. Svehla and Richard S. Brokaw Lewis Research Center SUMMARY Thermodyn
4、amic and transport properties, including enthalpy, entropy, heat capacity, molecular weight, viscosity, and thermal conductivity, have been calculated for the 2N02 equilibrium and also the N204 t 2N02 = 2NO+O2 equilibrium from 300 to N2b = 1280 K and from 0.01 to 100 atmospheres. The Prandtl number,
5、 Lewis number, isen tropic exponent, and two derivatives involving the molecular weight, pressure, and tem perature were also calculated. The Chapman-Enskog theory of monatomic gases was applied in the transport property calculations, with an Eucken-type correction to the thermal conductivity to acc
6、ount for internal degrees of freedom. An expression for the thermal conductivity due to chemical reaction was also included. The transport cross sections were calculated for the Lennard-Jones (12-6)potential, the parameters being obtained from analysis of experimental viscosity and thermal conductiv
7、ity data. Also included in the calculations is a parameter, which may be useful in analyzing to what ex tent chemical reaction in the gas phase affects thermal conduction. This parameter is tabulated over the same pressure and temperature range over which the thermodynamic and transport properties w
8、ere calculated. INTRODUCTlON The dissociation of N204 has been of interest in heat-transfer studies because the effects of chemical reaction in the gas phase occur at pressures and temperatures con venient for experimental work (refs. 1to ?). The chemical reactions describing the dissociation from t
9、he boiling point of N204 (294.3 K) to about 1300 K are given by (I) N204 2N02 (II) 2N02 2NO+O2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Reaction I goes essentially to completion before reaction 11 becomes important, At about 1300 K the NO begi
10、ns to decompose. Previous calculations are available for the thermodynamic and transport properties for this system (refs. 6 and 8). However, these previous calculations are for only a pressure of 1 atmosphere (ref. 8) or do not include the NO2 dissocation (ref. 6). Further more, new measurements of
11、 the viscosity have become available (ref. 9), allowing more accurate estimates of the interaction potentials, and from these potentials improved transport property calculations. Therefore, thermodynamic and transport properties have been calculated over a wide pressure range (0.01 to 100 atm) and u
12、p to 1280 K, at which point the NO2 is almost completely dissociated. Frozen and equilibrium properties have been calculated, first assuming only reaction I occurs, and second assuming both reactions I and 11 occur. EXPERIMENTAL DATA ANALYSIS Experimental measurements have been reported on both the
13、viscosity and thermal conductivity from room temperature to almost 500 K (refs. 9 to 12), the temperature range where reaction I is predominant. However, the experimental viscosity data of the various workers has shown some large differences. Therefore, the data of the various authors were analyzed
14、in terms of rigorous transport theory for the viscosity of gas mix tures (ref. 13) in order to clarify these differences. The analysis consisted of fitting the experimental viscosity data to the Lennard-Jones (12-6) potential, using the derived constants to calculate both the viscosity and the therm
15、al conductivity, and then comparing the experimental and calculated results. When possible, the derived constants were com pared to constants of other molecules of similar size and shape. The constants derived from the experimental viscosity data of Petker and Mason (ref. 9) appeared to be the most
16、reasonable when compared to constants of similar molecules. Furthermore, better agreement between the experimental and calculated viscosity data was found for the data of Petker and Mason than for the experimental viscosity data of references 10 and 11. That is, the constants obtained from the data
17、of reference 9 more closely reproduced the experimental data from which they were derived than did the constants obtained from the data of references 10 and 11. In the analysis two cases were considered. The gas was assumed to be composed of (1) an equilibrium mixture of NO2 and N204 and (2) an equi
18、librium mixture of NO,. - - L N204, NO, and 02. The force constants for the N204 = 2N02 equilibrium system were determined by the following procedure. For the N204-N204 interaction E/k was estimated from the following relationship (ref. 14): 2 Provided by IHSNot for ResaleNo reproduction or networki
19、ng permitted without license from IHS-,-,-f = 1.18 Tb k (Symbols are defined in appendix A. ) For the NO2-NO2 interaction E/k was assigned four trial values of 190, 210, 230, and 250. This range of 190 to 250 for E/k was se lected because it encompassed the range considered reasonable for (c/k)No No
20、2. For 2 each trial value (e/kNO was determined by the usual combining rule (ref. 13) 2- 2 4 For each trial value the three corresponding values of u, namely, u,-, u2-24, o -N o were determined simultaneously by a least-squares fit ofand u 24 24 the experimental viscosity data. The best set of const
21、ants (in a least squares sense) was then selected from among the four sets. The entire procedure was then repeated, the only difference being that uNo was determined from the combining rule (ref. 13) 2- 24 were determined by a simultaneous least-That is, only uNo 2- No 2 and u24-24 squares fit of th
22、e viscosity data, and oNo was subject to the constraint of equa 2- 2 4 tion (3). The best set of constants among these four was then selected. This then com pleted the analysis of the N204 * 2N02 equilibrium. Next the N204 P 2N02 = 2N0+02 equilibrium system was examined. For this sys tem force const
23、ant for the NO2-NO2, NO2-N204, and N204-N204 interactions were de termined the same way as for the N204 t2N02 system. Now, however, force constants for the additional interactions NO-NO, 02-02,NO2-NO, N02-02, N204-NO, N204-02, and NO-02 were also needed. For the NO-NO and 02-O2 interactions the forc
24、e constants given in reference 14 were used. These particular constants were determined from ex perimental viscosity data of pure NO and 02. In each case the experimental viscosity data used in reference 14 covered a temperature range very nearly the same as that con sidered herein, and therefore th
25、e derived constants should be appropriate for the present calculations. For the other five unlike interactions (NO2-NO, NO2-02, N204-NO, N204-02 and NO-02) the combining rules, equations (2) and (3), were used. Therefore, four different situations were examined, the equilibrium N204 = 2N02 3 I Provi
26、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-system, the equilibrium N204 t2N02 = 2NO+O2 system, and for each equilibrium two methods of determining uNo . 2- 2 4 The results showed that a slightly better fit to the viscosity data was obtained by assumi
27、ng only reaction I occurred. This was found to be true for uNo obtained 2- 2 4 from the combining rule and also for aN0 obtained by least squares. This would 2- 2 4 suggest that reaction 11 had not appreciably progressed to the right during the course of the experimental measurements. This notion is
28、 supported by experimental kinetic data (refs. 15 to l?), which indicate that the rate of decomposition of NO2 is rather slow and becomes appreciable only at the highest temperatures and pressures considered by Petker and Mason. (Their experimental viscosity data covered the range 0.5 to 5 atm and 2
29、5 to 170 C. ) However, even for the condition most favorable for decomposition from thermodynamic considerations (0.5 atm and 170 C), at equilibrium only 2 percent of the NO2 is decomposed, and for the condition most favorable from kinetic considerations, (5 atm and 170 C) NO2 decomposition is only
30、1 percent. Therefore, since it is known that reaction I reaches equilibrium very rapidly, the constants derived assuming an equi librium mixture of NO2-N204 were considered the more realistic Lennard-Jones (12-6) parameters and were used in the calculations herein. In order to compare the two method
31、s of determining uN0 ,transport proper 2- 2 4 ties were calculated using the aNo determined by both methods. Necessarily2- 2 4 the value obtained by least squares gave a better fit to the Viscosity data. The improve ment was so slight, however, that the uN0 -N determined by least squares could not 2
32、 24 be judged a better value. The thermal conductivity data calculated for each uNo 2- 2 4 TABLE I. - LENNARD-JONES (12-6) POTENTIAL FORCE CONSTANTS FOR THE NO-N02-02-N204 SYSTEM Interaction 0, c/k, Method of determination of u and e/ki ii OK NO-NO 3.492 116.7 Ref. 14 3. 6285 156. E Eqs. (2) and (3)
33、 4. 0565 201.2 Eqs. (2) and (3) 3. 47g5 111. E Eqs. (2) and (3) 3.765 a10 Least-squares fit of viscosity data for u -and c/k 4.193 270 Eqs. (2) and (3) NO2-02 3.616 149.7 Eqs. (2) and (3) 4.621 347 Least-squares fit of viscosity data for u and eq. (1) for c/k 4.044 192.4 Eqs. (2) and (3) 3.467 106.7
34、 Ref. 14 4 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-were also compared. Since the contribution of the thermal conductivity due to chemical reaction is particularly sensitive to the unlike interactions, comparison of the calculated conductivity
35、 data should provide a critical test of the relative merits of the two As was found for the viscosity, however, the two sets of calculations were“NO-NO* in close agreement. Therefore, in order to be consistent with the method of determining the constants of the other unlike interactions and to minim
36、ize the number of adjustable parameters, uNo was calculated by equation (3).2- 2O4 Table I gives a summary of the force constants used in the calculations herein and the method of determining each. When compared to constants of similar molecules, such as N20 and C02, the con stants for NO2 appear re
37、asonable. However, since it was found in the analysis that there was a range of sets of force constants, which reproduced the experimental viscosity data about equally well, these constants should not be considered the “true“ constants, but merely as suitable ones, which will reproduce the experimen
38、tal data about as well as, or better than, any other set. As expected, the constants for N204 are substantially larger than those for NO2. An approximate value of u can be estimated from the boiling point density. UsingN204 3equations proposed in references 13 (2/3 7rNo3 = 2. 0vband 14 (2/3 TN= 2. o
39、 vb - 5), and a boiling point density of 1.443 (interpolated from N204 liquid densities given in refs. 18 and 19), gives values of u of 4.66 and 4.60, respectively. Since the value given in table I lies between these two, it does appear to be reasonable. CALCULATION OF PROPERTIES The thermodynamic a
40、nd transport properties were calculated using the program de scribed in reference 20. Calculations were performed for both the equilibrium NO2-N204 system and the equilibrium N02-N204-NO-02 system from 300 to 1280 K and from 0.01 to 100 atmospheres. The properties designated as frozen are for the eq
41、uilibrium composition at the corresponding temperature and pressure. Briefly, the rigorous Chapman-Enskog theory for gas mixtures was applied for the transport property calculations herein. Though the theory assumes only binary collisions of monatomic gases, it has been shown to apply satisfactorily
42、 to the viscosity of mixtures of polyatomic gases as well as to the viscosity and thermal conductivity of mixtures of monatomic gases (ref. 21). For the thermal conductivity the contribution of the transla tional conductivity was calculated from the theory which is rigorous for a mixture of monatomi
43、c gases. A modified Eucken-type expression was added to account for the con tribution of the internal energy states, and the thermal conductivity due to chemical re action was calculated from the equation developed in references 22 and 23. 5 Provided by IHSNot for ResaleNo reproduction or networking
44、 permitted without license from IHS-,-,-TABLE II. - STANDARD STATE (ZERO PRESSURE) ENTHALPIES AT 0 AND 298.15 K (REF. 26) Molecule Standard state enthalpy, H they are also higher than that of reference 8 in the lower temperature region, where NO2 and N204 are the predominant constituents. These diff
45、erences in the transport properties are attributed to the differences in the Lennard-Jones (12-6) force constants used in the calculations, especially the constants for the NO2-NOZ and N204-N204 interactions. Whereas the force constants used herein were obtained from the experimental data of referen
46、ce 9, the data of references 6 and 8 were calculated using estimated constants (ref. 6) for the N02-N02 and N204-N204 interactions. The viscosities calculated from these estimated constants are lower than the experimental data of Petker and Mason (ref. 9). At the higher temperatures the NO2 is disso
47、ciated into NO and 02. Since the force constants used in reference 8 for the NO-NO and 02-O2 interactions and those used in the calculation of table IV are about the same, the transport properties are in sub stantial agreement at the higher temperatures. Table V, given in appendix B, presents values
48、 of a chemical kinetic parameter q 6 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-al v) U 0 for the N204=2N02 and 2N02= 2NO+02 reactions. This parameter indicates the extent to which gas phase chemical reaction affects thermal conduction or heat t
49、ransfer in re acting gas systems. It is defined as where CR is the reaction rate in either direction at equilibrium and AH is the heat of reaction at temperature T. The calculation of this parameter is discussed in appendix B. The dimensionless quantity (spQ)2, where d is a dimension characteristic of the sys tem, involves am
