Fortran Program for Thermodynamics

7/21/2019 Fortran Program for Thermodynamics

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Technical ote

A F O R T R A N p r o g r a m f o r c a l c u l a t i n g t h e

thermodynamic and transport propert ies o f d iese l fue l

D . A . K O U R E M E N O S C . D . R A K O P O U L O S A N D E . A . Y F A N T I S

Nat iona l Techn ica l Univers i ty o f A thens Mech an ica l Eng ineer in9 Depar tmen t Therm al

Engineerin9 Sect ion 42 Pat iss ion Street Ath ens 10682 Greece

A d v a n c e d m o d e l s o f t h e t h e r m o d y n a m i c p r oc e s s e s in

i n t e rn a l c o m b u s t i o n e n g i n e s r e q u ir e t he e x a c t e s t i m a -

t i o n o f 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 pe r t ie s

o f c o m b u s t i o n r e a c t a n t s a n d p r o d u c t s . A l t h o u g h

m a n y w o r k s h a v e b e e n r e p or t e d o n t h e p r o p e r ti e s o f

a i r fu e l v ap ou r an d com bu s t i on p rod u cts a s tu d y on

th e p rop ert i e s o f th e fu e l l i qu i d p h as e s eems to be

l ack i n g i n th e op en l i t era tu re . T h es e p rop ert i e s are

v ery i mp o rtan t for s i mu l a t i n g th e fu e l d rop l e t ev ap or-

a t i on p roces s wh i ch p l ays an i mp o rtan t ro l e on d i es e l

e n g i n e c o m b u s t i o n a n d e m i t t e d p o l l u ta n t m o d e l l in g .

I n t h e p r es e n t w o r k t h e v a l u e s o f t h e t h e r m o d y n a m i c

an d tran s p ort p rop ert i e s o f l i qu i d d i es e l fu e l are

com p u ted as a fu n ct i on o f p res s u re an d temp e ra tu re

b y p o l y n o m i a l f i t t in g a g a i n s t a v a i l a b l e e x p e r i m e n t a l

d a ta . T h i s i s accomp l i s h ed i n a f rac t i on o f a s econ d

w h e n u s i n g a p e r s o n a l c o m p u t e r w i t h a v e r y s m a l l

error . N- Dod ecan e i s t rea ted i n th e p res en t s tu d y

wh i ch forms a rep res en ta t i v e fu e l o f th e d i es e l fu e l in

mos t d i es e l en g i n e cyc l e s i mu l a t i on s . T h e re l ev an t

c o m p u t e r p r o g r a m s u b r o u t i ne s a r e g i v e n i n an e d u c a -

t io n a l f o r m i n F O R T R A N - 7 7 l a ng u a g e.

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 calcula-

tions are carried out on a computer. Relationships which

model the composition and/or thermodynamic proper-

ties 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

Pap er acce pted July 1990. Discu ssion closes April 1991.

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 form6'7, giving the isobaric

specific heat capacity and enthalpy in terms of tempera-

ture. Especially for pure hydrocarbon compounds, rela-

tionships 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 com-

puted 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 proper-

ties of the diesel fuel in the liquid phase. N-Dodecane is

treated in the present study, since it forms a representa-

tive of the diesel fuel in most diesel engine cycle simula-

tions. The relationships used here have been taken from

Ref. 17 in the case of vapour pressure, liquid densi ty,

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 f rom 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

190 Adv. Eng. Sof tw are 1990 Vol . 12 No. 4 ~

ComputationalMechanics Publications


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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 import-

ant and useful tool as a part of a general package

program which simulates the in-cylinder processes in a

diesel engine cycle simulation.

D E S C R I P T I O N O F T H E M A I N P R O G R A M

The FORTRAN-77 program called properties is listed in

Appendix A. Program PROPERTIES includes the

subroutines needed for the calculation of the thermo-

dynamic 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 proper-

ties 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.

P R O P E R T I E S S U B R O U T I N E S

Vapour pressure

PV = A t + A2 /T R + A 3 x In( TR) + A 4 x TR 6 (la)

P V2 = B 1 + B 2/ TR + B 3 x ln (TR) + B 4 T R 6

(lb)

V R

= EXP(PV1 + W x PV2) (lc)

TR

is the reduced temperature

( T / TCR )

and

P V R

is the

reduced vapour pressure (PV/PCR), where TCR and

PCR 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 . Equa-

tions (la-c) have been taken from Ref. 17.

Liquid density

Do = ~ Ci x PR i

i=0+4 (2a)

DI = ~ Ei x PR i

i=0+4 (2b)

D2 = E F ix PR i i = 0 - 4 (2c)

D a=~ G ix PR i

i=0+4 (2d)

DE NS L = ~ D~ x TR ~ 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)

E NE = ~ HE i X TR B i / ( i +

1) i = 0 3 (3b)

ENTH = (EN1 +

12

EN2) T

(3c)

TR B

is the reduced temperature

(T/TB),

were

TB

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/o are 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

CP 1 = ~, Hli x TR B i i = 0 + 3 (4a)

CP2 = E HEi TRBi

i = 0 -- 3 (4b)

CPL = CP1 +

12 x

CP 2

(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.

Latent heat of vapourization

HV = M (T CR -

T) '38 for

TR 0.4 (5b)

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. Equa-

tion (5b) has been developed in the present work by least

square fitting to the experimental data available from

Ref. 17.

Liquid absolute viscosity

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

T i i= 0- 5 fo rP = lbar (6a)

log (D VISC/D VISC A) =

P x (NI + N2 DV IS CA '27s) for P >

lbar (6b)

The relationships are to be used for reduced tempera-

tures 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

CO ND = Q1 + Q2 x T

for

TR 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 - TR ) 1'232 (8)

The average error is less than 11 . Equation (8) has been

taken from Ref. 17.

During the development of the program PROPER-

TIES, the correlations used compared favourably with

estimating methods presented in Ref. 13.

Adv. Eng. Sof tware, 1990, Vol. 12, No. 4 191


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C A S E S T U D Y

A l t h o u g h t h e s t r u c tu r e a n d a p p l i c a t i o n o f t h e p r o g r a m

h a s b e e n d e s c r i b ed , a n e x a m p l e i s g i v e n in A p p e n d i x A

a n d l i s t ed i n 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 o f N - D o d e c a n e , i n t h e l i q u id p h a se ,

a r e c a l c u l a t e d f o r T e m p e r a t u r e = 1 00 C a n d P r e s s u r e =

5 b a r .

R E F E R E N C E S

1 Go rdon , S. and M cBride , B . J . Computer Program or the Calcula-

tion of Complex Chemical Equilibrium Composition Rocket Perfor-

mance, Incident and Reflected Shocks, and Chapman-Jouguet

Detonations, NA SA pub l ica t ion SP-273 , 1971 NT IS num ber N71-

37775)

2 Svehla, R. A. and M cBride , B. J . FOR TRA N IV Computer Pro-

gram for Calculation of Thermodynamic and Transport Properties

of Complex Chemical Systems, N A S A t e c h n i c al n o t e T N D - 7 0 5 6 ,

1973 N TIS numb er N73-15954)

3 Ol ika ra , C . and Borman , G. L. A computer Program or Calculat-

ing Properties of Equilibrium Combustion Products wi th Some

Applications to L C. Enoines, SAE Pa per 750468 , 1975

4 Kr ieger, R . B . and Borm an , G. L . The com puta t ion o f apparen t

hea t re lease fo r in te rna l combus t ion eng ines , Proc. Diesel Gas

Power Conf., 1 9 6 6 , A S M E p a p e r 6 6 - W A / D G P - 4

5 JANA F Thermochemical Tables,

2nd ed . , NSRDS-NB537 , U.S .

Na t ion a l Bureau o f S tandards , 1971

6 Hires, S . D. , Ekch ian, A. , He yw ood , J . B. , Taba czyns ki, R. J . and

Wall, J . C. Performance and NOx Emissions Modelling of a Jet

Ignition Prechamber Stratified Charge Engine,

SAE p aper 760161 ,

1976

7 By, A. , Kem pinski, B. and Rife, J . M.

Knock in Spark Ionition

Engines,

SAE paper 810147, 1981

8 Rossini, F . D. , Pitzer, K. S., Arn ett , R. L , Brau n, R. M. and

Pr imen te l , G. C . Selected Values of Physical and Thermodynamic

Properties of Hydrocarbons and Related Compounds, Carneg ie

Press, Pit tsburgh PA., 1953

9 Benson, R. S. and Wh itehouse , N. D. Internal Combustion Engines,

Pergamon Press, Oxford, 1979

10 Heywood, J . B. Internal Combustion Engine Fundamentals,

M c G r a w - H i l l B o o k C o . , N e w Y o r k , 1 9 88

I I Chapm an , S . and Cowling , T . G. The Mathematical Theory ~"

Non-Un form Gases, Cambr idge Univers i ty P ress , Cambr idge ,

1955

12 Hirschfelder, J. O., Curtiss, C. F. and B ird, R. B. Molecular Theory

of Gases and Liquids,

John Wiley , New York , 1954

13 Reid, R. C. and Sh erwo od, T. K. The Properties of Gases and

Liquids,

M c G r a w - H i l l B o o k C o . , N e w Y o r k , 1 9 66

14 Borman , G. L . and Johnson , J . H. Uns teady vapor iza t ion h is to r ies

and trajectories of fuel dro p injecte d into swirling air , Pape r 598C,

SAE National Powerplant Meeting, Phi lade lph ia , 1962

15 Ma xwe ll , J . B.

Data Book on Hydrocarbons,

V a n N o s t r a n d , A m -

sterdam, 1950

16 Prie m, 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 Kou remen os , D. A. and R akopou los , C . D. The opera t ion o f a

tu rbu lence chamber d iese l eng ine , wi th LPG fumiga t ion , fo r

exhaus t em iss ions con t ro l ,

VDI Forshung im lngenieurwesen,

1986,

52 6), 185 190

19 Kourem enos , D. A. , Rakopou los , C . D. and K arvoun is , E .

Therm odyna mic ana lys is o f d i rec t in jec tion d iese l eng ines by

M u l t i - Z o n e M o d e l l in g ,

ASME-WA Meeting,

Boston , 1987 and

AES 3 3), 67 77

20 Kourem enos , D. A., Rakopo u los , C . D. and Houn ta las , D. T .

Therm odyna mic ana lys is o f ind i rec t in jec tion d iese l eng ines by

two-zone m ode l l ing o f comb us t ion , Trans. of the ASME and 1990,

Journal of Engineering for Gas Turbines and Power,

112 1),

138-149

21 Kou remen os , D. A. , Rakopou los , C . D. and Houn ta las , D. T .

Compute r s imula t ion wi th exper imen ta l va l ida t ion o f the exhaus t

nitr ic oxide and soot emissions in divided chamber diesel engines,

ASME-WA Meeting, San F ranc isco , 1989 , and AES 10 1), 15 28

22 Kou remen os , D. A. , Rakop ou los , C . D. and Kots iopou los , P .

Per fo rmance and emiss ions charac te r is t ic s o f a d iese l eng ine us ing

supplementary diesel fuel fumigated to the intake air , Heat Reco-

very Systems & CHP, 1989, 9 5 ), 457 465

A P P E N D I X A : P R O G R A M L I S T IN G

P R O G R A M P R O P E R T I E S

O P E N ( 4 , F I L E = C R . R E S , S T A T U S = N E W )

W R I T E ( * , I )

1 F O R M A T ( I X , T e m p e r a t u r e [C] = )

R E A D ( *, *) T E M P C

W R I T E ( * , 2 )

2 F O R M A T ( i X , P r e s s u r e [ b a r ] = )

R E A D ( * ,* ) P R E S

P R E S = P R E S * I . E5

C A L L L H V A P ( T E M P C , H V )

C A L L V A P R E S ( T E M P C , P V )

C A L L D E N S L I Q ( T E M P C , P R E S , D E N S L )

C A L L S U R T E N ( T E M P C , S U RT )

C A L L V I S C ( T E M P C , P R E S , D V I S C )

C A L L C O N D U C ( T E M P C , P R E S , C O ND )

C A L L C P L I Q ( T E M P C , C P L )

C A L L E N T H A L ( T E M P C , E N T H )

W R I T E ( 4 ,3 ) T E M P C , P R E S / I . E 5

3 F O R M A T ( i X , T e m p e r a t u r e [ C ] = , F 6 . 2 , 3 X , P r e s s u r e

W R I T E ( 4 , 1 4 )

W R I T E ( 4, 4) P V / I . E 5

4 F O R M A T ( i X , V a p o u r P r e s s u r e [ b a r ] = , F l 2 . 8 )

W R I T E ( 4 ,5 ) D E N S L

5 F O R M A T ( i X , L i q u i d D e n s i t y [ k g / m 3 ] = , F S . 3 )

W R I T E ( 4 , 7) E N T H / 1 0 0 0 .

[ b a r ] = F 6 2 )

1 9 2

Adv. En 9. Softwar e, 1990, Vol. 12, No. 4


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7 F O R M A T ( i X , ' L i qu i d S p e c i f i c E n t h a l p y [ k J / k g ] = ' , Fl 2 . 5 )

W R I T E ( 4 , 8) C P L / 1 0 0 0 .

8 F O R M A T ( i X , ' L i qu i d S p e c i f i c H e at C a p a c i t y [ k J / k g / K ] = ' , F S . 3 )

W R I T E ( 4 , 9) H V / 1 0 0 0 .

9 F O R M A T ( i X , ' L a t e n t H e a t o f V a p o u r i z a t i o n [ k J / k g ] = ' , F S . 3 )

W R I T E ( 4 ,1 0 ) D V I S C * I 0 0 0 .

1 0 F O R M A T ( i X , ' L i q u i d D y n a m i c V i s c o s i t y [ c P ] = ' , F l 2 . 8 )

W R I T E ( 4, 11 ) ( D V I S C / D E N S L ) * I . E 6

i i F O R M A T ( I X , ' L iq u i d K i n e m a t i c V i s c o s i t y [ c S t ] =' , F l 2 .8 )

W R I T E ( 4 ,1 2 ) S U R T

1 2 F O R M A T ( i X , ' S u r f a c e T e n s i o n [ N / m ] = ' , F I 2 . 8 )

W R I T E ( 4 , 1 3 ) C O N D

1 3 F O R M A T ( i X , ' L i q ui d T h e r ma l C o n d u c t i v i t y [W/m/K]= ,F8.4)

W R I T E ( 4 , 1 4 )

14 F O R M AT * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

W R I T E ( 4 , 1 6 )

1 6 F O R M A T ( I X , ' W H E N A V A L U E O F A P R O P E R T Y I S S E T U P T O 0 . 0 T H E ' )

W R I T E ( 4 , 1 7 )

1 7 F O R M A T ( I X , ' E Q U A T I O N S U S E D A R E O U T O F R E L I A B I L I T Y R E G I O N ' )

W R I T E ( 4 , 1 4 )

C L O S E ( 4 )

S T O P

E N D

C

C * F U E L P R O P E R T I E S

C N A M E : N - D O D E C A N E

C * F O R M U L A : C 1 2 H 2 6

C * M O L E C U L A R W E I G H T : M W = 1 7 0 . 3 3

C * F R E E Z I N G P O I N T (at 1 a r m) : T F = 4 7 4 . 4 4 R = 2 6 3 . 5 6 K = - 9 . 5 9 C

C * B O I L I N G P O I N T ( at 1 a tm ) : T B = 8 8 1 . 0 0 R = 4 8 9 . 4 3 K = 2 1 6 . 2 8 C

C C R I T I C A L T E M P E R A T U R E : T C R = I I 8 4 . g R = 6 5 8 . 2 6 K = 3 8 5 . 1 1 C

C * C R I T I C A L P R E S S U R E : P C R = 2 6 4 . p s i a = l S . 2 E 5 N / m 2

C * C R I T I C A L V O L U M E : V C R = 0 . 0 6 6 9 f t 3 / I b = 4 . 1 7 6 5 E - 3

C * C R I T I C A L C O M P R E S S I B I L I T Y F A C T O R : Z C R = 0 . 2 3 7

C * S P E C I F I C G R A V I T Y 6 0 F / 6 0 F : S G R = 0 . 7 5 2 6

C* A C E N T R I C F A C T O R : W = 0 . 5 6 2 2

C* W A T S O N C H A R A C T E R I Z A T I O N F A C T O R : K = 1 2 . 7 4

m 3 / k

C

C

B L O C K D A T A

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

COMMON/BBBI/BOO,BOI,BO2,BO3,BIO,BII,BI2,BI3,B20,B21

C O M M O N / B B B 2 / B 2 2 , B 2 3 , B 3 0 , B 3 , B 3 2 , B 3 3 , B 4 0 , B 4 1 , B 4 2 , B 4 3

C O M M O N / C O N S / A , B , C , D , A A , B B , C C , D D

D A T A

PCR,TCR,VCR,ZCR,TB/264.0,1184.9,0.0669,0.237,881.O/

D A T A 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 . 2 5 1 3 6 , 2 . 1 1 3 8 E - 3 , - 8 . 0 0 2 8 E - 3 /

D A T A 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 . 5 6 7 2 E - 5 , - 0 . 6 9 2 3 E - 6 , 5 . 2 6 0 4 E - 6 , - 8 . 6 8 9 5 E - 6 , 2 . 1 8 1 2 E - 6 /

D A T A

A,B,C,D,AA,BB,CC,DD/0.84167,-I.4704,1.67165,-0.59198,

- 0 . 0 0 3 8 2 6 , - 0 . 0 0 0 7 4 7 , 0 . 0 4 1 1 2 6 , - 0 . 0 1 3 9 5 /

E N D

C

Adv. Eng. Sof tw are 1990 Vol . 12 N o. 4

1 9 3


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C

S U B R O U T I N E L H V A P ( T E M P C , HV )

C * * S u b r o u t i n e L H V A P e s t im a t e s t he l at e n t h e a t o f v a p o r i z a t i o n * * * * * * * *

C * * T E M P C [C], H V [ J / k g ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C * * E r r o r < 2 ; f or r e d u c e d t e m p e r a t u r e s a b o v e 0 . 97 : e r r o r < i 0 * * ~ * * *

5

65

6

C


I F ( T E M P C . G T . 3 8 5 . ) G O T O 6 5

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

T R = ( T E M P F 4 5 9 . 7 ) / T C R

I F ( T R . G E . 0 . 4 ) G O T O 50

T R A = ( 7 2 5 . 2 - T E M P F ) / 3 0 3 . 9

H V = 3 6 6 0 9 5 . * T R A * * 0 . 3 8

G O T O 6 0

P O L Y I = 6 6 6 . 5 1 1 - 7 4 5 7 . 6 9 * T R 3 5 9 5 6 . 7 * T R * * 2 .

P O L Y 2 = - 9 5 0 0 9 . 2 * T R * * 3 . I 4 8 4 4 6 . * T R * * 4 .

P O L Y 3 = - I 3 7 2 1 0 . * T R * * 5 . 4 6 9 5 0 6 . 4 * T R * * 6 . - 1 4 8 9 7 . 7 * T R * * 7 .

H V R E D = P O L Y I + P O L Y 2 + P O L Y 3

H V = 3 2 1 1 3 . 6 * H V R E D

G O T O 6 0

H V = 0 . 0

R E T U R N

E N D

C

S U B R O U T I N E V A P R E S ( T E M P C , P V )

C * * S u b r o u t i n e V A P R ES e s t i m a t es t h e v a p or * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C * * T E M P C [C], P V [ N / m 2 ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C * * F o r r e d u c e d t e m p e r a t u r e s a b o v e 0 . 3 : e r r o r * * * * * * * * * * * * * * * * * * * * * * *

C O M M O N / C R I T / P C R , T C R , V C R , Z C R , T B

TT= TEMPC*9./5.+491.7)/TCR

P R L N 0 = 5 . 9 2 7 1 4 - 6 . 0 9 6 4 8 / T T - I . 2 8 8 6 2 * A L O G ( T T ) + 0 . 1 6 9 3 4 7 * T T * * 6 .

P R L N I = I S . 2 5 1 8 - 1 5 . 6 8 7 5 / T T - 1 3 . 4 7 2 1 * A L O G ( T T ) + 0 . 4 3 5 7 7 * T T * * 6 .

P R L N = P R L N 0 + 0 . 5 6 2 2 * P R L N 1

P V R = E X P ( P R L N )

P V = 6 8 9 4 . 7 5 9 1 * P V R * P C R

R E T U R N

E N D

C

C

S U B R O U T I N E D E N S L I Q ( T E M P C , P R E S , D E N S L )

C * * S u b r o u t i n e D E N S L IQ e st i m a t e s t h e l i q ui d d e n s i t y * * * * * * * * * * * * * * * * * * *

C * * T E M P C [C], P R E S I N/ m 2] , D E N S L [ k g / m 3 ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C * * E r r o r < 1 ; f or r e d u c e d t e m p e r a t u r e s a b o v e 0 . 9 5 : e r r o r < 8 * * * * * * *


C O M M O N / B B B I / 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

COMMON/BBB2/B22,B23,B30,B31,B32,B33,B40,B41,B42,B43

TT= TEMPC*9./5.+491.7)/TCR

PP=PRES/6894.7591/PCR

A 0 2 = B 0 0 + B I 0 * P P + B 2 0 * P P * * 2 . + B 3 0 * P P * * 3 . + B 4 0 * P P * * 4 .

A I 2 = B 0 1 + B I I * P P + B 2 1 * P P * * 2 . + B 3 1 * P P * * 3 . + B 4 1 * P P * * 4 .



C C 2 = A 0 2 + A I 2 * T T + A 2 2 * T T * * 2 . + A 3 2 * T T * * 3 .

D E N S L = 6 7 5 . 2 7 5 6 9 * C C 2

R E T U R N

E N D

C

1 9 4

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6/7

C

S U B R O U T I N E C P L I Q T E M P C , C P L)

C * * S u b r o u t i n e C P L I Q e s t i m a te s t he l i q u id h e a t c a p a c i t y * * * * * * * * * * * * * * *

C * * T E M P C [C], C P L [ J / k g / K ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C * * E r r or * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


C O M M O N / C O N S / A , B , C , D , A A , B B , C C , D D

T T = T E M P C * 9 . / 5 . + 4 9 1 . 7

T T = T T / T B

C P I = A + B * T T + C * T T * * 2 . + D * T T * * 3 .

C P 2 = A A + B B * T T + C C * T T * * 2 . + D D * T T * * 3 .

C P L = 4 1 8 6 . 7 * C P I + I 2 . * C P 2 )

R E T U R N

E N D

C

C

S U B R O U T I N E E N T H A L T E M P C , E N T H )

C * * S u b r o u t i n e E N T H A L e s t i m a t es t he l i q ui d e n t h a l p y * * * * * * * * * * * * * * * * * * *

C * * T E M P C [C ], E N T H [ J/ kg ] ; E N T H 0 0 K ) = 0 . 0 * * * * * * * * * * * * * * * * * * * * * * * * * *

C * * E r r or * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


C O M M O N / C O N S / A , B , C, D , A A , B B , C C , D D

T T = T E M P C * 9 . / 5 . + 4 9 1 . 7

T R = T T / T B

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.

E N T H = 2 3 2 6 . * E N T H I + I 2 . * E N TH 2 ) * T T

R E T U R N

E N D

C

S U B R O U T I N E V I S C T E M P C , P R E S , D V I S C )

C * * S u b r o u t i n e V I S C e s t i m a t e s t h e a b s o l u t e v i s c o s i t y o f l i q u i d * * * * * * **

C * * T E M P C [ C], P R E S [N / m2 ] , D V I S C [ N s / m 2 ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C * * E rr o r * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

I F T E M P C . G T . 2 4 5 . ) G O T O i 0 0

T T = 9 . * T E M P C / 5 . + 3 2 .

P P = P R E S / 6 8 9 4 . 7 5 9 1

D V 0 1 = 3 . 2 1 2 4 8 - 3 . 8 1 5 2 1 E - 2 * T T + 2 . 4 0 0 1 8 E - 4 * T T * * 2 .

D V 0 2 = - 8 . 3 3 7 1 7 E - 7 * T T * * 3 . ~ I . 4 8 7 5 E - 9 * T T * * 4 .

D V 0 3 = - l . 0 5 9 7 8 E - 1 2 * T T * * 5 .

D V 0 = D V 0 1 + D V 0 2 + D V 0 3

D V O E = 0 . 0 2 3 9 + 0 . 0 1 6 3 8 * D V 0 * * 0 . 2 7 8

A L O G V = P P * D V O E / 1 0 0 0 .

D V R E D = 1 0 . * * A L O G V

D V I S C = D V R E D * D V 0 / 1 0 0 0 .

G O T O i i 0

1 0 0 D V I S C = 0 .

i i 0 R E T U R N

E N D

C

Adv. En9. Sof tw are 1990 Iiol . 12 N o. 4

195


7/7

C

S U B R O U T I N E C O N D U C T E M P C , P R E S , C O N D )

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 t h e l i qu i d t h er m a l c o n d u c t i v i t y * * * * * * *

C * * T E M P C [C], P R E S [ N /m 2] , C O N D [ W / m / K ] * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C * * E r r o r * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


T T = T E M P C * 9 . / 5 . + 3 2 .

T R = T T ~ 4 5 9 . 7 ) / T C R

P R = P R E S / 6 8 9 4 . 7 5 9 1 / P C R

I F P R . L E . I . 8 9 4 ) G O T O 2 0

C I = I 8 . 4 2 - 7 . 7 6 4 * T R - I . 6 8 1 6 7 3 * T R * * 2 .

C 2 = I 7 . 7 7 0 . 6 5 * P R - 7 . 7 6 4 * T R - 2 . 0 5 4 * T R * * 2 . / E X P 0 . 2 * P R )

C O N D I = 0 . 0 7 7 2 7 - 4 . 5 5 8 E - 5 * T T

C O N D = I . 7 2 9 5 7 8 * C O N D I * C 2 / C 1

G O T O 3 0

2 0 C O N D = I . 7 2 9 5 7 8 * 0 . 0 7 7 2 7 - 4 . 5 5 8 E - 5 * T T )

3 0 R E T U R N

E N D

C

C

S U B R O U T I N E S U R T E N T E M P C , S U RT )

C * * S u b r o u t i n e S U R T EN e s t i m a t e s t he

C * * T E M P C

C * * E r r o r

45

55

C

s u r fa c e t e n s i o n * * * * * * * * * * * * * * * * * * *

[C], S U R T * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


I F T E M P C . G T . 3 8 5 . ) G O T O 4 5

T R = T E M P C * 9 . / 5 . + 4 9 1. 7 ) / T C R

S U R T = 0 . 0 5 2 8 8 0 6 * I . - T R ) * * I . 2 3 2

G O T O 5 5

S U R T = 0 . 0

R E T U R N

E N D

APPENDIX B: OUTPUT LISTING

T e m p e r a t u r e [ C ] = I 0 0 . 0 0 P r e s s u r e [ b a r] = 5 . 0 0

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

V a p o u r P r e s s u r e [ ba r ] = 0 . 0 2 0 9 6 6 2 5

L i q u i d D e n s i t y [ k g / m 3 ]= 6 9 2 . 4 0 6

L i q u i d S p e c i f i c E n t h a l p y [ k J /k g ]= 8 8 6 . 1 7 6 7 0

L i q u i d S p e c i f i c H e a t C a p a c i t y [kJ/kg/K]= 2 . 4 7 0

L a t e n t H e a t of V a p o u r i z a t i o n [ k J / 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 [ c P] = 0 . 3 2 1 9 6 7 0 0

L i q u i d K i n e m a t i c V i s c o s i t y [ c St ]= 0 . 7 3 3 8 4 5 4 0

S u r f a c e T e n s i o n [ N / m] = 0 . 0 1 8 8 6 2 2 6

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 . 1 1 6 9

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

W H E N A V A L U E O F A P R O P E R T Y I S S E T UP T O 0 . 0 T H E

E Q U A T I O N S U S E D AR E O U T O F R E L I A B I L I T Y R E G I O N

196 Adv. Eng. Sof tw are 1990 Vol . 12 No. 4

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