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1 I ISECURITYMARKINGThe classified or limited status of this repoit appliesto each page, unless otherwise page printoutsMUST be marked DOCUMENT CONTAINS INFORMATION AFFECTING THE NATIONAL Defense OFTHE UNITED STATES WITHIN THE MEANING OF THE ESPIONAGE LAWS, TITLE 18, , SECTIONS 793 AND 794. THE TRANSMISSION OR THE REVELATION OFITS CONTENTS IN ANY MANNER TO AN UNAUTHORIZED PERSON IS PROHIBITED : When government or other drawings, specifications or otherdata are used for any purpose other than in connection with a defi-nitely related government procurement operation, the U. S. Governmentthereby incurs no responsibility, nor any obligation whatsoever; andthe fact that the Government may have formulated, furnished, or in anyway supplied the said drawings, specifications, or other data is notto be regarded by implication or otherwise as in any manner licensingthe holder or any other person or corporation, or conveying any rightsor permission to manufacture, use or sell any patented invention thatmay in any way be related , m( a ( mNOLTR 67-32 MOLLIER DIAGRAM FOR NITROGENNOL4 MARCH 1967 UNITED STATES NAVAL ORDNANCE LABORATORY, WHITE OAK, MARYLANDIICMJ--z0 Distribution of this document is unlimited.))

2 'A ___ _ sNOLTR 67-32 Aerodynamics Research Report No. 285 MOLLIER DIAGRAM FR 11 ITROGENbyRichard L. Humphrey and Carolyn H. PiperABSTRACT: Thermodynamic dat a ""or nitrogen are presented inMollier diagram form covering the temperature range of 30*Kto 15,OOO&K and the density range of 10~ to w aagat. Datafor the solid and liquid regions are included. 7he diagram-contains all available data of interest to the w'.rker in fluid-mechanics and aerodynamics. Speed of sound data are prisentedon separate charts.:10U.* S. NAVAL ORDNANCE L&BOR&TORYW hite Oak, Silver Spring, Maryland i AiI NOLTR 67-32 14 March 1967I ollier Diagram for NitrogenI This report brings together in one large scale diarfam mostof the available data for nitrogen. The temperatu7.'e rangecovered is 30*K to 15,000 K while densities from 33-7 to 103are represented.

3 This diagram is especially recomended foraerodynamicists and those engaged in aerodynamic authors acknowledge the assistance of Mr. Jhn R. Bottwho did the lettering of the diagram F. SCHREI'.TRCaptain, USFC ommanderUL. HABtISBy directionIIIIii(|IOLTR 67-32 CONTENTSPage~~~INTRODUCTION ..SOURCES FOR THE DIAGRAM .. 2 COMPILING THE NITROGEN 1 IOLLIER DIAGRAM .. 5 USING THE MOLLIER DIAGRAM .. 5 SOLRCES FOR THE ACOUSTIC VELOCITY CHARTS .. 6 REFERENCES ..7 APPENDI)X A -SYMBOLS LIST .. A-IAPPENDIX B -STANDARD PROPERTIES AND CONVERSION FACTORS .. B-iAPPENDIX C -DENSITIES CORRESPONDING TO THE DIAGRAMMEDARGUMENTS .. C-1 APPENDIX D -CONVERSION FACTORS FOR F. DIN (REF. (lc)) .. D-1 ILLUSTRATIONSPageFigure I -Skeleton Diagram Showing Sources of Data .. 3 Figure 2 -Index to the Nitrogen Mollier DiagramFigures 3-22 -The Mollier DiagramFigure 23 -Acoustic Velocity for Low Density NitrogenFigure 24 -Acoustic Velocity for high Density NitrogenFigure 25 -Acoustic Veloci%"y for high Temperature NitrogeniANINNOLTR 67-32lNTRODUiCrIONThe demand for high Mach number low altitude flight simulationin wind tunnels increased in recent years.

4 Wind tunnel supplytemperatures and pressures have increased tremendously. Tunnsl'now being planned require pressures to 5000 atmospheres and temira-tures to 28000 K. At conditions such as these there are vide devia-tions from the ideal gas and such things as variable specific heatand intermolecular forces must be need for adequate thermodynamic property data under theseconditions is evident. The past ten years have seen an outpouringof works on the thermodynamic properties of air and these propertiesmay now be considered to be well documented. However, the study ofthe properties of nitrogen has only recently resulted in adequatetables for high diagrams have several advantages over tabulatedtables. One of the principal advantages is convenience. The dia-gram allows trends to be seen at a glance and presents masses ofdata in a few sheets.

5 The required information on most commonthermodynamic processes can be obtained from the diagram withouttedious interpolation in tables. In most cases the accuracy ofthe diagram is sufficient for engineering making of thermodynamic diagrams for gases has been apopular activity among thermodynamicists and chemists for the past60 to 70 years. Din (ref. (1)) in his three volume work on gasesfor industrial use gives an excellent historical and criticalreview of such diagrams In general (ref. (la)) and for partIculargases as he discusses them individually. Generally, industrial andchemical users have preferred the temperature-entropy diagram, forexample references (1) and (2), while aerodynamicists and power plantengineers used the Nollier or enthalpy-entropy diagram (refs. (3)-(7)). The many isenthalpic and isentropic processes encountered influid dynamics make the ollier diagram popular in this of the existing diagrams for nitrogen are limited intheir coverage.

6 Almost all do not include the high density-hightemperature region that is now of growing interest. A recent reportby Grabau and Brahinsky (ref. (8)) gives calculated properties ofnitrogen for densities to 1000 awagat. This filled in a region forwhich no adequate data had been 67-32 IThe large amount of recent data that is now available and thelimited scepe of other diagrams made it advisable to compile a newdiagram which would include as much of the available data as possi-ble. It also afforded the opportunity to co-pare and study thevarious sources of thermodynamic properties. The new diagram ispresented in this report. It covers a range from 30*K to 15,000-Kand a density range from log p/p to ; data for the solid,liquid, and vapor regions have been sources, the compilation, and the use of the diagram willbe discussed.

7 Appendices containing inforzation helpful in theuse of the diagram have been FOR THE DIAGRAMA great many sources were used in the preparation of the each source covered only a limited region. In some casesunits and reference points had to be converted. Figure 1 gives askeleton chart showing the scope of the diagran and reference numbersfor each region. In some areas the regions overlap and severalsources were bulk of the data from 100 to 1500 K and a density rangefrom log plp to was taken from Little and Neel (ref. (9)).Their tables incorporate the work of Din (ref. (1c)) and Hilsenrath,et al (ref. (10)) for pressures down to 10-2 atmospheres. They useda perfect gas extrapolation for pressures below 1072 the high densities, the tabulated pressures range from 10' atmos-pheres at 3000K to 102 atmospheres at ]500 tables of Din are based on the best available experimentaldata.

8 Din believes that his worst points are no more than per-cent in error while most of the tables are good to within made an extensive coparison of the work of -any experimentersand from these chose the best data for calculating his 1000K the ideal gas thermodynamic functions for molecularnitrogen of Hilsenrath, et al (ref. (1)) were used to determineenthalpy levels at zero pressure and entropy values at at-ospherlcpressure. Temperature lines were found by assurAng that (WH/ap) values of entropy at low pressures were found from the modifiedperfect gas relationship.(S/R)T (S/R)T -In pp-lat2M 67-M-2II s1 310B24rr10-iNOLT 67-32 The line coanecting the critical point and the triple pointwas taken from Din (ref. (1c)). Some pressare and density linesnear thi region were taken from reference (2)- This regiondefinues the bounds between the saturated vapor and thesaturatedliquid.

9 It is equivalent to the zero moisture line on a steamI ollter d. Mrom the triple poInt to lower pressures the lineIof equilibrium between the solid and vapor phass (zero vapor line)S was defined by the expression from Din (ref. (lc)) converted fromR -Hg to atmospheres:( )lo p- -I where T is in discrepancy exists between the ideal gas data of reference (10)Iand the ezperiuental triple point obtained from Din (ref. (1c)). Thej difficulty has not been resolved and caution should be used in inter-I preting the diagram near the zero vapor boundzry below 100K. Awayfrom the boundary the ideal gas data should be for the melting solid and the freezing liquid were takenfrom Din (ref. (Ic)) and from reference (2). Extrapolations wereade to extend these data to 1000 amagat (iog pip- ). Propertiesat pressures above the critical point were taken from Mui (ref.)

10 (2))and from -ttle and Neel (ref. (9)). The trend of the data In thisreggion indlcates that a point is reached about 1000 asagat where thesolid and the liquid regions for the high temerature low density region weretaken from the tables of ilsenrath and Klein (ref. (11)). Thesetables include the effects of dissociation, lonlzatlon, and inter-molecular forces. Intermolecular forces are included to the secondvirll correction. Bl1senrath and Klein use the well-known procedureof listing all of the iortant chemical -eactions talin place,determinin the amount of reactants preent at each condition andcalculating the thermodynAmic properties of the mixture. Theseproperties are then corrected for the intermolecular forces. The-tables have been widely used and are accepted as and Brahinsky (ref. (8)) recently coiled a set oftables for high density nitrogen (to 1000 azagat) which includesthird vIrial corrections.