A FORTRAN program for calculating the thermodynamic and transport properties of diesel fuel

Technical Note A FORTRAN program for calculating the thermodynamic and transport properties of diesel fuel D. A. KOUREMENOS, C. D. R A K O P O U L O S A N D E. A. YFANTIS National Technical University of Athens, Mechanical Engineerin9 Department, Thermal Engineerin9 Section, 42 Patission Street, Athens 10682, Greece

Advanced models of the thermodynamic processes in internal combustion engines require the exact estimation of the thermodynamic and transport properties of combustion reactants and products. Although many works have been reported on the properties of air, fuel vapour and combustion products, a study on the properties of the fuel liquid phase seems to be lacking in the open literature. These properties are very important for simulating the fuel droplet evaporation process, which plays an important role on diesel engine combustion and emitted pollutant modelling. In the present work the values of the thermodynamic and transport properties of liquid diesel fuel are computed, as a function of pressure and temperature, by polynomial fitting against available experimental data. This is accomplished in a fraction of a second when using a personal computer with a very small error. N-Dodecane is treated in the present study, which forms a representative fuel of the diesel fuel in most diesel engine cycle simulations. The relevant computer program subroutines are given in an educational form, in FORTRAN-77 language. Key Words: properties, liquid fuel, diesel engine.

INTRODUCTION When a large number of computations are made and/or high accuracy is required, engine cycle process calculations are carried out on a computer. Relationships which model the composition and/or thermodynamic properties of unburned and burned gas mixtures have been developed for computer use. The most complete models are based on polynomial curve fits to the thermodynamic Paper accepted July 1990. Discussion closes April 1991.

190

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data for each species in the mixture. In the NASA equilibrium programs and other works x-4, the JANAF table thermodynamic data 5 have been used. Polynomial functions for various fuels (in the vapour phase) have been fitted in a functional form 6'7, giving the isobaric specific heat capacity and enthalpy in terms of temperature. Especially for pure hydrocarbon compounds, relationships have been produced by fitting to experimental data 8. The processes occuring in the cylinder of a diesel engine9'x°, such as evaporation of the liquid fuel, fuel-air mixing, friction at a gas/solid interface and heat transfer between the gas and walls are strongly influenced by the transport properties. Viscosity, thermal conductivity and mass diffusion coefficient of the gas mixture are computed for example in Refs 2, 11, 12. Reid and Sherwood 13 have presented relationships created by many workers which calculate the properties of gases and liquids in general. Borman and Johnson 14 presented relationships for isobaric specific heat capacity, density, heat of vapourization and vapour pressure of the liquid fuel based on the experimental data reported in Refs 12, 15, 16. In the present work a FORTRAN-77 program is set up to compute the thermodynamic and transport properties of the diesel fuel in the liquid phase. N-Dodecane is treated in the present study, since it forms a representative of the diesel fuel in most diesel engine cycle simulations. The relationships used here have been taken from Ref. 17 in the case of vapour pressure, liquid density, surface tension, liquid isobaric specific heat capacity and liquid thermal conductivity. In the case of heat of vapourization and liquid absolute viscosity they are based on polynomial curve fits, made in the present work, to the experimental data available from Ref. 17. The specific enthalpy was then deduced from the isobaric heat capacity relationships. Advanced models of the thermodynamic processes in diesel engines 18 22 require a detailed description of the history of the fuel droplets injected into the combustion

~ ComputationalMechanicsPublications

chamber and the exact estimation of the thermodynamic and transport properties of the liquid fuel. The present work completely covers this latter feature. The computer program is very fast and accurate and forms an important and useful tool as a part of a general package program which simulates the in-cylinder processes in a diesel engine cycle simulation.

T R B is the reduced temperature ( T / T B ) , were T B is the normal boiling point. The average error occured is 5 ~. Near the critical region, where maximum uncertainty exists, errors of up to 12 Y/oare to be expected. Equations (3a-c) have been deduced from equations (4a-c) to follow. For T = 0 K, enthalpy is set equal to 0.0 kJ/kg. Liquid specific isobaric heat capacity

DESCRIPTION OF THE MAIN PROGRAM The FORTRAN-77 program called properties is listed in Appendix A. Program PROPERTIES includes the subroutines needed for the calculation of the thermodynamic and transport properties of N-Dodecane in the liquid phase. The main program asks the user for temperature and pressure and returns the calculated values of the properties as in the example listed in Appendix B. Obviously every subroutine, if needed, can be used separately from the main program. Information such as input needed, output returned and average error occured are given as comments in the program listing. The errors presented are defined as: ERROR = ICALCULATED-EXPERIMENTALI/ EXPERIMENTAL The relationships for the properties used here are given in the next section in detail. The constants and units used are given in the program listing.

(4a)

CP2 = E HEi × TRBi

i = 0 -- 3

(4b)

C P L = CP1 + 12 x CP 2

P V t = A t + A 2 / T R + A 3 x In(TR) + A 4 x T R 6 (la) P V 2 = B 1 + B 2 / T R + B 3 x ln(TR) + B 4 × T R 6 (lb)

(lc)

P V R = EXP(PV1 + W x PV2)

T R is the reduced temperature ( T / T C R ) and P V R is the reduced vapour pressure (PV/PCR), where T C R and P C R are the critical temperature and pressure. The above equations are used for reduced temperatures greater than 0.3 having an average error of 3.5%. Equations (la-c) have been taken from Ref. 17.

Latent heat of vapourization H V = M × ( T C R - T) °'38 for T R < 0.4

i=0-7forTR>0.4

H V = ~ K~ x T R i

(5b)

i=0-5

i=0+4

(2a)

DI = ~ Ei x PR i

i=0+4

(2b)

D2 = E F i x P R i

i= 0- 4 i=0+4

(2c) (2d)

D E N S L = ~ D~ x T R ~ i = 0 + 3

(2e)

PR is the reduced pressure (P/PCR). The average error occured is 1%. For reduced temperatures above 0.95, errors of up to 8 % are to be expected. Equations (2a-e) have been taken from Ref. 17. Liquid specific enthalpy EN1 = ~ Hll x TRBi/(i + 1)

i=0-3

(3a)

T R B i / ( i + 1)

i=0÷3

(3b) (3c)

forP= lbar

(6a)

log (D VISC/D V I S C A ) = P x (NI + N2 × D V I S C A °'27s) for P > l b a r (6b)

The relationships are to be used for reduced temperatures less than 0.75 having an average error of less than 5 %. Eq (6a) has been developed in the present work by least square fitting to the experimental data available from Ref. 17. Liquid thermal conductivity

CD 1 = R 1 +

Do = ~ Ci x P R i

E N T H = (EN1 + 12 × EN2) × T

(5a)

The average error occured is less than 2 % but for reduced temperatures above 0.97 errors may increase to 10%. Equation (5a)has been taken from Ref. 17. Equation (5b) has been developed in the present work by least square fitting to the experimental data available from Ref. 17.

for T R < 1.894

COND = Q1 + Q2 x T

Liquid density

i x PR i

(4c)

The average error is 2 ~. Equations (4a-c) should be used outside the critical region for best accuracy, but the predicted values are identical to saturated liquid specific heat capacities within the limits required for engineering purposes. Equations (4a-c) have been taken from Ref. 17.

D V I S C A = ~ . L i x Ti

Vapour pressure

ENE=~HEiX

i= 0+ 3

Liquid absolute viscosity

PROPERTIES SUBROUTINES

Da=~G

CP 1 = ~, Hli x T R B i

R2 x

TR +

CD 2 = S 1 q- S 2 x P R + + $4 x T R 2 / E X P ( P R / 5 )

(7b)

R 3 x TR 2

S3 x

(7a)

TR

COND = (Q1 + Q2 x T) x CDE/CD1

(7c) forTR

> 1.894

(7d)

The average error is less than 12~. Equations (7a-d) have been taken from Ref. 17. Liquid surface tension S U R T = Z × (1 - T R ) 1'232

(8)

The average error is less than 11%. Equation (8) has been taken from Ref. 17. During the development of the program PROPERTIES, the correlations used compared favourably with estimating methods presented in Ref. 13.

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CASE STUDY A l t h o u g h the s t r u c t u r e a n d a p p l i c a t i o n of t h e p r o g r a m has b e e n d e s c r i b e d , a n e x a m p l e is g i v e n in A p p e n d i x A a n d listed in A p p e n d i x B. T h e t h e r m o d y n a m i c a n d t r a n s p o r t p r o p e r t i e s of N - D o d e c a n e , in the l i q u i d phase, are c a l c u l a t e d for T e m p e r a t u r e = 100 ° C a n d P r e s s u r e = 5 bar. REFERENCES 1 Gordon, S. and McBride, B. J. Computer Programfor the Calculation of Complex Chemical Equilibrium Composition Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations, NASA publication SP-273, 1971 (NTIS number N7137775) 2 Svehla, R. A. and McBride, B. J. FORTRAN IV Computer Program for Calculation of Thermodynamic and Transport Properties of Complex Chemical Systems, NASA technical note TND-7056, 1973 (NTIS number N73-15954) 3 Olikara, C. and Borman, G. L. A computer Program for Calculating Properties of Equilibrium Combustion Products with Some Applications to L C. Enoines, SAE Paper 750468, 1975 4 Krieger, R. B. and Borman, G. L. The computation of apparent heat release for internal combustion engines, Proc. Diesel Gas Power Conf., 1966, ASME paper 66-WA/DGP-4 5 JANAF Thermochemical Tables, 2nd ed., NSRDS-NB537, U.S. National Bureau of Standards, 1971 6 Hires, S. D., Ekchian, A., Heywood, J. B., Tabaczynski, R. J. and Wall, J. C. Performance and NOx Emissions Modelling of a Jet Ignition Prechamber Stratified Charge Engine, SAE paper 760161, 1976 7 By, A., Kempinski, B. and Rife, J. M. Knock in Spark Ionition Engines, SAE paper 810147, 1981 8 Rossini, F. D., Pitzer, K. S., Arnett, R. L, Braun, R. M. and Primentel, G. C. Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds, Carnegie Press, Pittsburgh PA., 1953

9 Benson, R. S. and Whitehouse, N. D. Internal Combustion Engines, Pergamon Press, Oxford, 1979 10 Heywood, J. B. Internal Combustion Engine Fundamentals, McGraw-Hill Book Co., New York, 1988 I I Chapman, S. and Cowling, T. G. The Mathematical Theory ~" Non-Un!form Gases, Cambridge University Press, Cambridge, 1955 12 Hirschfelder, J. O., Curtiss, C. F. and Bird, R. B. Molecular Theory of Gases and Liquids, John Wiley, New York, 1954 13 Reid, R. C. and Sherwood, T. K. The Properties of Gases and Liquids, McGraw-Hill Book Co., New York, 1966 14 Borman, G. L. and Johnson, J. H. Unsteady vaporization histories and trajectories of fuel drop injected into swirling air, Paper 598C, SAE National Powerplant Meeting, Philadelphia, 1962 15 Maxwell, J. B. Data Book on Hydrocarbons, Van Nostrand, Amsterdam, 1950 16 Priem, R. J. Vaporization of Fuel Drops Including the Heating-Up Period, Ph.D. Thesis, Univ. of Wisc., 1955 17 American Petroleum Institute Technical Data Book, 1979 18 Kouremenos, D. A. and Rakopoulos, C. D. The operation of a turbulence chamber diesel engine, with LPG fumigation, for exhaust emissions control, VDI Forshung im lngenieurwesen, 1986, 52(6), 185 190 19 Kouremenos, D. A., Rakopoulos, C. D. and Karvounis, E. Thermodynamic analysis of direct injection diesel engines by Multi-Zone Modelling, ASME-WA Meeting, Boston, 1987 and AES 3(3), 67 77 20 Kouremenos, D. A., Rakopoulos, C. D. and Hountalas, D. T. Thermodynamic analysis of indirect injection diesel engines by two-zone modelling of combustion, Trans. of the ASME and 1990, Journal of Engineering for Gas Turbines and Power, 112(1), 138-149 21 Kouremenos, D. A., Rakopoulos, C. D. and Hountalas, D. T. Computer simulation with experimental validation of the exhaust nitric oxide and soot emissions in divided chamber diesel engines, ASME-WA Meeting, San Francisco, 1989, and AES 10(1), 15 28 22 Kouremenos, D. A., Rakopoulos, C. D. and Kotsiopoulos, P. Performance and emissions characteristics of a diesel engine using supplementary diesel fuel fumigated to the intake air, Heat Recovery Systems & CHP, 1989, 9(5), 457 465

APPENDIX A: PROGRAM LISTING

1 2

3

4 5

192

PROGRAM PROPERTIES OPEN ( 4 , F I L E = ' C R . R E S ' , S T A T U S = ' N E W ' ) WRITE (*,I) FORMAT ( I X , ' T e m p e r a t u r e [C] = ') READ (*,*) TEMPC WRITE (*,2) FORMAT (iX,'Pressure [bar]= ') READ (*,*) PRES P R E S = P R E S * I .E5 CALL LHVAP(TEMPC, HV) CALL V A P R E S ( T E M P C , P V ) CALL D E N S L I Q ( T E M P C , P R E S , D E N S L ) CALL SURTEN(TEMPC, SURT) CALL VI SC (TEMPC, PRES, DVI SC) CALL C O N D U C ( T E M P C , P R E S , COND) CALL CPLIQ (TEMPC, CPL) CALL E N T H A L ( T E M P C , E N T H ) WRITE (4,3) T E M P C , P R E S / I . E 5 FORMAT (iX,'Temperature [C]=',F6.2,3X,'Pressure WRITE (4,14) WRITE (4,4) P V / I . E 5 FORMAT (iX,'Vapour Pressure [bar]=',Fl2.8) WRITE (4,5) DENSL FORMAT (iX,'Liquid D e n s i t y [kg/m3]=',FS.3) WRITE (4,7) ENTH/1000.

Adv. En 9. Software, 1990, Vol. 12, No. 4

[bar]='

F6

2)

7 8 9 10 ii 12 13 14 16 17

FORMAT WRITE FORMAT WRITE FORMAT WRITE FORMAT WRITE FORMAT WRITE FORMAT WRITE FORMAT WRITE FORMAT WRITE FORMAT WRITE FORMAT WRITE CLOSE STOP END

(iX,'Liquid Specific E n t h a l p y [kJ/kg]=',Fl2.5) (4,8) CPL/1000. (iX,'Liquid Specific Heat C a p a c i t y [ k J / k g / K ] = ' , F S . 3 ) (4,9) HV/1000. (iX,'Latent Heat of V a p o u r i z a t i o n [kJ/kg]=',FS.3) (4,10) DVISC*I000. (iX,'Liquid Dynamic V i s c o s i t y [cP]=',Fl2.8) (4,11) ( D V I S C / D E N S L ) * I . E 6 (IX,'Liquid K i n e m a t i c V i s c o s i t y [cSt]=',Fl2.8) (4,12) SURT (iX,'Surface Tension [N/m]=',FI2.8) (4,13) COND (iX,'Liquid Thermal C o n d u c t i v i t y [W/m/K]=',F8.4) (4,14) ******************************************************* (4,16) (IX,'WHEN A VALUE OF A P R O P E R T Y IS SET UP TO 0.0 THE') (4,17) ( I X , ' E Q U A T I O N S USED ARE OUT OF R E L I A B I L I T Y REGION') (4,14) (4)

C

C* FUEL P R O P E R T I E S C*

NAME

: N-DODECANE

C* C* C* C*

FORMULA MOLECULAR WEIGHT F R E E Z I N G P O I N T (at 1 arm) B O I L I N G P O I N T (at 1 atm) CRITICAL TEMPERATURE CRITICAL PRESSURE CRITICAL VOLUME C R I T I C A L C O M P R E S S I B I L I T Y FACTOR S P E C I F I C G R A V I T Y 60F/60F ACENTRIC FACTOR W A T S O N C H A R A C T E R I Z A T I O N FACTOR

: : : : : : : : : : :

C*

C* C* C* C* C* C*

C12H26 MW=170.33 TF=474.44 R=263.56 K=-9.59 C TB=881.00 R=489.43 K=216.28C TCR=II84.gR=658.26 K=385.11C PCR=264. psia=lS.2E5 N/m2 V C R = 0 . 0 6 6 9 f t 3 / I b = 4 . 1 7 6 5 E - 3 m3/k ZCR=0.237 SGR=0.7526 W=0.5622 K=12.74

C C

BLOCK

DATA

COMMON/CRIT/PCR,TCR,VCR,ZCR,TB COMMON/BBBI/BOO,BOI,BO2,BO3,BIO,BII,BI2,BI3,B20,B21 COMMON/BBB2/B22,B23,B30,B3!,B32,B33,B40,B41,B42,B43 C O M M O N / C O N S / A , B , C , D , A A , B B , C C , DD DATA PCR,TCR,VCR,ZCR,TB/264.0,1184.9,0.0669,0.237,881.O/ DATA B 0 0 , B 0 1 , B 0 2 , B 0 3 , B I 0 , B I I , B I 2 , B I 3 , B 2 0 , B 2 1 /

+1.6368,-1.9693,2.4638,-1.5841,-0.04615,0.21874,-0.36461, ÷0.25136,2.1138E-3,-8.0028E-3/ DATA B 2 2 , B 2 3 , B 3 0 , B 3 1 , B 3 2 , B 3 3 , B 4 0 , B 4 1 , B 4 2 , B 4 3 /

÷I2.8763E-3,-II.3805E-3,-O.7845E-5,-8.2328E-5,14.8059E-5, ÷9.5672E-5,-0.6923E-6,5.2604E-6,-8.6895E-6,2.1812E-6/ DATA A,B,C,D,AA,BB,CC,DD/0.84167,-I.4704,1.67165,-0.59198, ÷-0.003826,-0.000747,0.041126,-0.01395/ END C Adv. Eng. Software, 1990, Vol. 12, No. 4

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C S U B R O U T I N E LHVAP(TEMPC,HV) C * * S u b r o u t i n e L H V A P estimates the latent h e a t of v a p o r i z a t i o n * * * * * * * * C * * T E M P C [C], HV [ J / k g ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C * * E r r o r <2% ; for reduced t e m p e r a t u r e s a b o v e 0.97 : error < i 0 % * * ~ * * *

COMMON/CRIT/PCR,TCR,VCR,ZCR,TB IF

(TEMPC.GT.385.)

GOTO 65

TEMPF=9.*TEMPC/5.+32.

50

65 60

TR=(TEMPF÷459.7)/TCR I F ( T R . G E . 0 . 4 ) GOTO 50 TRA=(725.2-TEMPF)/303.9 HV=366095.*TRA**0.38 G O T O 60 POLYI=666.511-7457.69*TR÷35956.7*TR**2. POLY2=-95009.2*TR**3.÷I48446.*TR**4. POLY3=-I37210.*TR**5.469506.4*TR**6.-14897.7*TR**7. HVRED=POLYI+POLY2+POLY3 HV=32113.6*HVRED GOTO 60 HV=0.0 RETURN END

C C SUBROUTINE VAPRES(TEMPC,PV) C * * S u b r o u t i n e VAPRES e s t i m a t e s the vapor * * * * * * * * * * * * * * * * * * * * * * * * * * * * C * * T E M P C [C], PV [ N / m 2 ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C**For reduced t e m p e r a t u r e s above 0.3 : error * * * * * * * * * * * * * * * * * * * * * * * C O M M O N / C R I T / P C R , T C R , V C R , ZCR,TB

TT=(TEMPC*9./5.+491.7)/TCR PRLN0=5.92714-6.09648/TT-I.28862*ALOG(TT)+0.169347*TT**6. PRLNI=IS.2518-15.6875/TT-13.4721*ALOG(TT)+0.43577*TT**6. PRLN=PRLN0+0.5622*PRLN1 PVR=EXP(PRLN) PV=6894.7591*PVR*PCR RETURN END C C SUBROUTINE DENSLIQ(TEMPC,PRES,DENSL) C * * S u b r o u t i n e DENSLIQ e s t i m a t e s the liquid d e n s i t y * * * * * * * * * * * * * * * * * * * C * * T E M P C [C], PRES IN/m2], DENSL [ k g / m 3 ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C**Error <1% ; for reduced t e m p e r a t u r e s above 0.95 : error <8%*******

COMMON/CRIT/PCR,TCR,VCR,ZCR,TB COMMON/BBBI/B00,B01,B02,B03,BI0,BII,BI2,BI3,B20,B21

COMMON/BBB2/B22,B23,B30,B31,B32,B33,B40,B41,B42,B43 TT=(TEMPC*9./5.+491.7)/TCR PP=PRES/6894.7591/PCR A02=B00+BI0*PP+B20*PP**2.+B30*PP**3.+B40*PP**4. AI2=B01+BII*PP+B21*PP**2.+B31*PP**3.+B41*PP**4. A22=B02+BI2*PP+B22*PP**2.+B32*PP**3.+B42*PP**4. A32=B03+BI3*PP+B23*PP**2.+B33*PP**3.+B43*PP**4. CC2=A02+AI2*TT+A22*TT**2.+A32*TT**3. DENSL=675.27569*CC2 RETURN END C 194

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C SUBROUTINE CPLIQ(TEMPC,CPL) C**Subroutine CPLIQ estimates the liquid heat capacity*************** C**TEMPC [C], CPL [J/kg/K]******************************************* C**Error ************************************************************ COMMON/CRIT/PCR,TCR,VCR,ZCR,TB COMMON/CONS/A,B,C,D,AA,BB,CC,DD TT=TEMPC*9./5.+491.7 TT=TT/TB CPI=A+B*TT+C*TT**2.+D*TT**3. CP2=AA+BB*TT+CC*TT**2.+DD*TT**3. CPL=4186.7*(CPI+I2.*CP2) RETURN END C C SUBROUTINE ENTHAL(TEMPC,ENTH) C**Subroutine ENTHAL estimates the liquid enthalpy******************* C**TEMPC [C], ENTH [J/kg] ; ENTH0(0 K)=0.0 ************************** C**Error ************************************************************

COMMON/CRIT/PCR,TCR,VCR,ZCR,TB COMMON/CONS/A,B,C,D,AA, BB,CC,DD TT=TEMPC*9./5.+491.7 TR=TT/TB

ENTHI=A+B*TR/2.+C*TR**2./3.+D*TR**3./4. ENTH2=AA+BB*TR/2.+CC*TR**2./3.+DD*TR**3./4. ENTH=2326.*(ENTHI+I2.*ENTH2)*TT RETURN END C SUBROUTINE VISC(TEMPC,PRES,DVISC) C**Subroutine VISC estimates the absolute viscosity of liquid******** C**TEMPC [C], PRES [N/m2], DVISC [Ns/m2]***************************** C**Error ************************************************************ IF(TEMPC.GT.245.) GOTO i00 TT=9.*TEMPC/5.+32. PP=PRES/6894.7591 DV01=3.21248-3.81521E-2*TT+2.40018E-4*TT**2. DV02=-8.33717E-7*TT**3.~I.4875E-9*TT**4. DV03=-l.05978E-12*TT**5. DV0=DV01+DV02+DV03 DVOE=0.0239+0.01638*DV0**0.278 ALOGV=PP*DVOE/1000. DVRED=10.**ALOGV DVISC=DVRED*DV0/1000. GOTO ii0 100 DVISC=0. ii0 RETURN END C

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195

C SUBROUTINE CONDUC(TEMPC,PRES,COND) C * * S u b r o u t i n e C O N D U C e s t i m a t e s the liquid thermal c o n d u c t i v i t y * * * * * * * C * * T E M P C [C], PRES [N/m2], C O N D [ W / m / K ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C**Error ************************************************************

COMMON/CRIT/PCR,TCR,VCR,ZCR,TB

20 30

TT=TEMPC*9./5.+32. TR=(TT~459.7)/TCR PR=PRES/6894.7591/PCR I F ( P R . L E . I . 8 9 4 ) GOTO 20 CI=I8.42-7.764*TR-I.681673*TR**2. C2=I7.77÷0.65*PR-7.764*TR-2.054*TR**2./EXP(0.2*PR) CONDI=0.07727-4.558E-5*TT COND=I.729578*CONDI*C2/C1 G O T O 30 COND=I.729578*(0.07727-4.558E-5*TT) RETURN END

C C S U B R O U T I N E S U R T E N ( T E M P C , SURT) C * * S u b r o u t i n e SURTEN e s t i m a t e s the s u r f a c e t e n s i o n * * * * * * * * * * * * * * * * * * * C * * T E M P C [C], SURT * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C**Error ************************************************************

COMMON/CRIT/PCR,TCR,VCR,ZCR,TB IF

(TEMPC.GT.385.)

GOTO

45

TR=(TEMPC*9./5.+491.7)/TCR 45 55

SURT=0.0528806*(I.-TR)**I.232 G O T O 55 SURT=0.0 RETURN END

C

A P P E N D I X B: O U T P U T L I S T I N G

Temperature [C]=I00.00 P r e s s u r e [bar]= 5.00 ************************************************ V a p o u r P r e s s u r e [bar]= 0.02096625 L i q u i d D e n s i t y [kg/m3]= 692.406 L i q u i d S p e c i f i c E n t h a l p y [kJ/kg]= 886.17670 L i q u i d S p e c i f i c Heat C a p a c i t y [kJ/kg/K]= 2.470 L a t e n t Heat of V a p o u r i z a t i o n [kJ/kg]= 3 1 1 . 0 6 1 L i q u i d D y n a m i c V i s c o s i t y [cP]= 0.32196700 L i q u i d K i n e m a t i c V i s c o s i t y [cSt]= 0.73384540 S u r f a c e T e n s i o n [N/m]= 0.01886226 L i q u i d T h e r m a l C o n d u c t i v i t y [W/m/K]= 0.1169 ************************************************ WHEN A V A L U E OF A P R O P E R T Y IS SET UP TO 0.0 THE E Q U A T I O N S USED ARE OUT OF R E L I A B I L I T Y R E G I O N ************************************************

196

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