\ U J

^'"'CAU Of "^ NBS TECHNICAL NOTE 1 025

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Interactive Fortran IV

Computer Programs

for the Thermodynamic

and Transport Properties

of Selected Cryogens

(Fluids Pack)

30

5753

0. 1021

980

. 2
NATIONAL BUREAU OF STANDARDS

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the institute for Computer Sciences and Technology.

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^Sonie divisions within the center are located at Boulder, CO 80303.
Interactive Fortran IV

Computer Programs

for the Thermodynamic

and Transport Properties

of Selected Cryogens

(Fluids Pack)

R. D. McCarty

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder. Colorado 80303

Ol^riI-! CJ

llMteeat Burtw ot Stwtvis

Ubnry. C-01 Admin. M|.

DEC 4 1980

- U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology and Innovation

I, S NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued October 1980
National Bureau of Standards Technical Note 1025

Nat Bur. Stand. (U.S.). Tech. Note 1025. 112 pages (October 1980]

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1980

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington. D.C. 20402

Price $4.50 (Add 25 percent additional for other than U.S. mailing)
Contents

Page

Abstract 1 1. Introduction 1 2. Uncertainty of the Calculated Properties 2

3. Computer Routines 3

4. Conclusions 4

5. Properties of Hydrogen 15

6. Properties of Helium 19

7. Properties of Neon 23

8. Properties of Nitrogen 27

9. Properties of Oxygen 31

10. Properties of Argon 35

11. Properties of Methane 39

12. References 43

Appendix 1: Example of the Use of the Program 44

Appendix 2: Program Listings 47

m
List of Tables

Page

Table 1. List of Subprograms .«»,,. 5 Table 2. Properties and Associated Estimated Uncertainties for

Hydrogen « <, . » , « . , » . , . 16

Table 3. Pressure and Temperature Range for Hydrogen 17

Table 4. Properties for Computer Program Performance Test for

Hydrogen 18

Table 5. Properties and Associated Estimated Uncertainties for

Helium , . . » = , . « 20

Table 6. Pressure and Temperature Range for Helium 21

Table 7. Properties for Computer Program Performance Test for

Helium » 22

Table 8. Properties and Associated Estimated Uncertainties for Neon . 24

Table 9. Pressure and Temperature Range for Neon 25

Table 10. Properties for Computer Program Performance Test for Neon. . 26

Table 11. Properties and Associated Estimated Uncertainties for

Nitrogen 28

Table 12. Pressure and Temperature Range for Nitrogen 29

Table 13. Properties for Computer Program Performance Test for

Nitrogen 30

Table 14. Properties and Associated Estimated Uncertainties for

Oxygen ........ ...... 32

Table 15. Pressure and Temperature Range for Oxygen .... 33

Table 16. Properties for Computer Program Performance Test for

Oxygen 34

Table 17. Properties and Associated Estimated Uncertainties for

r\iM\Jll e « • • « « • « • e • • a « 6 • • • • 9 » • • • • • • \J\J Table 18. Pressure and Temperature Range for Argon 37

Table 19. Properties for Computer Program Performance Test for

Argon . 38

Table 20. Properties and Associated Estimated Uncertainties for

Methane 40

Table 21. Pressure and Temperature Range for Methane 41

Table 22. Properties for Computer Program Performance Test for

Methane 42

IV
INTERACTIVE FORTRAN IV COMPUTER PROGRAMS FOR THE THERMODYNAMIC

AND TRANSPORT PROPERTIES OF SELECTED CRYOGENS [FLUIDS PACK]*

R. D. McCarty

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

The thermodynamic and transport properties of selected cryogens have been

programmed into a series of computer routines. Input variables are any two of P,

p or T in the single phase regions and either P or T for the saturated liquid or vapor state. The output is pressure, density, temperature, entropy, enthalpy for

all of the fluids and in most cases specific heat capacity and speed of sound.

Viscosity and thermal conductivity are also given for most of the fluids. The

programs are designed for access by remote terminal; however, they have been

written in a modular form to allow the user to select either specific fluids or specific properties for particular needs.

The program includes properties for hydrogen, helium, neon, nitrogen,

oxygen, argon, and methane. The programs include properties for gaseous and

liquid states usually from the triple point to some upper limit of pressure and

temperature which varies from fluid to fluid. Computer listings of the

FORTRAN IV codings are presented. Copies of the programs may be obtained from

either the Thermophysical Properties Division of the National Bureau of Standards

at Boulder, Colorado, or from Walter Scott at the NASA-Johnson Space Center in

Houston, Texas.

Key Words: Argon; computer programs; density; enthalpy; entropy; equation of

state; heat capacity at constant pressure; heat capacity at constant

volume; helium; hydrogen; methane; neon; nitrogen; oxygen; thermal

conductivity; velocity of sound; viscosity.

1. Introduction

Recent technological developments which made possible personal interaction

with large computer systems by remote terminal has proved to be a real advantage

in situations where immediate response to requests for data are important. This

computer program was developed in response to a need for thermodynamic and

transport property data in an interactive mode. The program makes possible the

Work sponsored by NASA- Johnson Space Center on Contract No. PO T-6570C.
acquisition of thermodynamic and in some cases the transport properties of seven different cryogenic fluids. Those fluids are: hydrogen, helium, neon, nitrogen,

oxygen, argon, and methane. All of the properties are calculated from empirical

equations which are derived from the existing experimental data via weighted

least squares fit of mathematical models to those data. The reader who is

interested in the details of the correlations is referred to the sources cited

for each fluid in the sections to follow.

Five of the fluids (hydrogen, nitrogen, oxygen, argon and methane) utilize

the same mathematical model of the equation of state, and four of the fluids

(nitrogen, oxygen, argon and methane) utilize the same correlating function for

the transport properties. No transport properties for hydrogen, or neon, are given. Using the same functional form for the properties of several different

fluids greatly simplifies the computer programs, since all that is needed to

switch from one fluid to another is a different set of coefficients to the

equations.

The properties of helium and neon are calculated from empirical functions

which are different than those of the other five as well as each other. The

addition of these two fluids represents approximately half of the total length

(core storage) of the entire program.

The programs have been written with a dual purpose in mind. As has already

been mentioned the primary purpose is to make available to the user in an interactive mode, the thermodynamic and transport properties of selected fluids.

The second purpose is to provide the necessary subroutines to the user who has a very specialized need. Therefore the program has been written in a modular form

which allows the user to extract almost any combination of fluids and

properties.

The remainder of this report includes a section devoted to each fluid and an additional section describing the general part of the program.

2. Uncertainty of the Calculated Properties

When calculating thermodynamic properties from an empirical equation of

state, one should be aware of certain problem areas where it is difficult to

estimate realistically what the uncertainties really are in a given property. In

the critical region (p +_ 0.2 p and T +_ 0.05 T ), the calculated density may

be in error by several percent, while the calculated pressure or temperature will

not be as inaccurate. Specific heat capacities and the thermal conductivity in
the critical region become very large values and no realistic estimate of the

uncertainty may be made. Saturation boundaries, gas, liquid and solid are potential areas of large uncertainties for derived thermodynamic properties,

especially heat capacities. In the compressed liquid, calculated pressures will

have an uncertainty of several percent. This is a consequence of the nature of

the surface and is in no way the fault of the equation of state.

In each of the following sections on the individual fluids, uncertainty

estimates will be given for that particular fluid. These estimates have been

obtained from the source documents and do not reflect the potential large

uncertainties of the problem areas outlined above.

3. Computer Routines

The thermodynamic properties produced by the computer program listed in

Appendix A are all calculated using a mathematical model of the equation of state

of the fluid and classical thermodynamic relationships. The reader who is

interested in the thermodynamics and mathematics of the problem is referred to

McCarty (1975). Table 1 lists all of the subprograms with pertinent information

for each.

In general eleven or twelve significant figures need to be carried in the

property calculations to insure no round off errors in the result, and sample

values for checking performance are included in each of the sections on the

properties of a particular fluid. Performance should be checked periodically

when running on a time-share system.

The program, once executed, leads the user through a series of input

requests and the use of the program should be self-explanatory after the

particular system requirements for access and execution are satisfied.

Upper and lower pressure and temperature limits have been imposed on each

fluid according to the range of validity as claimed by the original source document. The lower pressure limit is an indication of where the program fails

due to the limitations of the computer calculations. All of the functions reduce

to the ideal gas in the limit of zero pressure but because of some terms in the

equation which have very large exponents, the iterative solution for density

fails at very low pressures. Because these models are empirical and cannot be

trusted to give even reasonable results outside their ranges of pressure and

temperature, the user is cautioned not to change the pressure and temperature

limits originally set in the program.
4. Conclusions

The preparation of this program has demonstrated the utility of maintaining

functional form when modeling properties of several different fluids. With a single functional form, the change from one fluid to another becomes a matter of

switching constants and even more important the addition of more fluids to the

scope of the program becomes very simple.

The author wishes to acknowledge the support of NASA, without which this

work would not have been possible, and in particular the support and

encouragement of Walter Scott at the Johnson Space Center.
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14
5. Properties of Hydrogen

The thermodynamic properties of hydrogen are calculated from a 32 term

empirical equation of state. The source of the equation of state is NBSIR 75-814

(Roder and McCarty, 1975). The program allows the option of ortho, para, and

normal hydrogen modifications. The properties for normal and ortho hydrogen are obtained by changing the ideal gas thermodynamic properties from parahydrogen to

ortho or normal hydrogen. This changes the derived thermodynamic properties but

does nothing to the PVT surface. Therefore the PVT for all of the hydrogen

options are the same.

15
Table 2. Properties and Associated Estimated Uncertainties for Hydrogen

Property All Uncertainties in Percent (Except Enthalpy)

Liquid (below T ) Gas (below T^)

c Fluid (above T„)

c

pressure 5.0 0.25 0.20

density 0.1 0.25 0.2

temperature 0.1 0.25 0.2

enthal py 1 J/rrlOl 3 J/mol 5.10 J/mol

entropy 1.0 1.0 1 Cp 3.0 2.0 3.0

Cv 3.0 2.0 3.0

speed of sou nd 2.0 1.0 1.0

The above are based on the estimated average difference between calculated

and true value, including problem areas as described in section 2.

16
Table 3. Pressure and Temperature Range for Hydrogen

Temperature range 13.8 to 400 K -434.83 to 260.43°F

Pressure range to 1200 bar

to 17404.5 psia

Fixed Points

Triple Point Temperature 13.8 K*

-434.83°F

Triple Point Pressure 0.07043101 bar

1.0215154 psia

Triple Point Density-Vapor 0.0632229 moles/liter

0.007956667 Ib/cu ft

Liquid 38.21429 moles/liter

4.809273 Ib/cu ft

Critical Point Temperature 32.938 K*

-459.67°F

Critical Point Pressure 12.83768 bar

186.19481 psia

Critical Point Density 15.556 moles/liter

1.95774 Ib/cu ft

*

This particular value is used to define the point in the sense that it was used as input into the program.

•kic See Section 3 for more detailed explanation of the lower limits of

pressure.

17
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18
6. Properties of Helium

The tliermodynamic properties of helium are calculated from a 32 term

modified Benedict-Webb-Rubin equation of state. The source of the equation of

state is a paper by McCarty (1973). The transport properties for helium are from

NBS Technical Note 631 (McCarty, 1972). Tabular values of the thermodynamic and

transport properties of helium are given in Technical Note 631 and are identical

to those produced by this computer program.

19
Table 5. Properties and Associated Estimated Uncertainties for Helium

Property

pressure

density

temperature

enthal py

entropy

Cp

Cu

All Uncertainties in Percent (Except Enthalpy)

speed of sound

thermal conductivity

viscosity

Liquid (below T )

10.0

0.5

.5 2.0

2.0

2.0

2.0

2.0

10.0

8.0

Gas (below T^)

c

0.2

0.2

0.2

1.0

1.0

2.0

1.5

1.0

10.0

8.0

Fluid (above T ) c'

0.2

0.2

0.2

1.0

1.0

.5

.5

.5

10.0

10.0

The above are based on the estimated average difference between calculated

and true value, including problem areas as described in section 2.

20
Table 6. Pressure and Temperature Range for Helium

Temperature range

Pressure range

Fixed Points

Lambda Temperature

Lambda Pressure

Lambda Density-Vapor

Liquid

Critical Point Temperature

Critical Point Pressure

Critical Point Density

2 to 1500 K -456.07 to 2240. 33°F

to 1000 bar

to 14504. psia

2.1720 K*

-455.760°F

.04963285 bar**

.71986364 psia

.2904484 moles/liter

.72575547 Ib/cu ft

36.53426 moles/liter

9.1289672 Ib/cu ft

5.2014 K*

450.307°F

2.274640 bar

32.990864 psia

17.3987 moles/liter*

4.347485 Ib/cu ft

This particular value is used to define the point in the sense that it was

used as input into the program, the program does not reproduce this number

exactly.

See Section 3 for more detailed explanation of the lower limits of

pressure.

21
<A E O o U *".^ 00 cr> I— a.

LO

<^

CVJ

CTi o

to

ro o•

CVi

03

cu

O)

uo 1 E

00

CTi OCO

CO

CDOCVJ o

+-> CO

(JE

s-o

MS_

OJ D_E

fO

SC7) O

s_ Q_

SO)

+->IDQ.Eoo

S-o

CO

<u

S-O)a.o

s_

0)

+-> -a -r- c o

13O

O r—

OO OJ E o oE

c_> I oE

<5:f Lf)

t£>

1—1• o

r-H

s_fO ^

Ln

C\J ro ^ t—

CM o r—

• O t—

^• 4-> CO

n3 1—1

S-o

Q. UD

(O r^ > p^

CVJ TD .—

O) • -M CTi ro CO

s_3

+-> fO V£) OO LO

cr>

(£)

i-H• COCO

CO

CM

cr> LO• o

CM

CM

00

S-03 J3

LO

CM

OO UD

i—i r^ O I-H • r^

1—1 i^

«*

4-> • 03 o^

-o

•r—Z5cr o •r— .—

_J r--. CO

•o CT. OJ • 4-> CT> fO r—

S-13

+-> fO r^

OO o^CM

00

00

•=:f CT>

<X> 00• COCO

1^

CO^• to

LDCO

S- I-H 03 J3OOO<—

CM

•o 00 c <X) 03 CO

LD

i^ • CO o r-H oCO

+-> CM

fO COCO

OJ cn

CO 00

03 • .^ o

Q- CM

<u r^

en CTi c: UD

*r- CM

00 CM

CO• CO

yD

cr>•

LO

p-«.

Q.E

cn

CM

CM

CT)

CM

CM

OJ Q

OCMOcr>

I-H CM

CM

CTi CO

CM

CM

CO

00

COo

00

CM

22
7. Properties of Neon

The thermodynamic properties of neon are calculated from an 18 term

empirical equation of state by McCarty and Stewart (1965). No specific heat

capacities are calculated for neon because the accuracy of the model of the

equation of state does not warrant the calculation. Transport properties for neon are not available in the form of a mathematical model as is the case for some of the other fluids.

23
Table 8. Properties and Associated Estimated Uncertainties for Neon

Property All Uncertainties in Percent (Except Enthalpy)

Liquid (below T ) Gas (below T ) Fluid (above T )

pressure

' 10.0 0.5 0.5

density 2.0 1.0 1.0

temperature 2.0 1.0 1.0

enthalpy 20.0 1.0 10.0

entropy 20.0 1.0 10.0

The above are based on the estimated average difference between calculated

and true value, including problem areas as described in section 2.

24
Table 9. Pressure and Temperature Range for Neon

Temperature range

Pressure range

Fixed Points

Triple Point Temperature

Triple Point Pressure

Triple Point Density-Vapor

Liquid

Critical Point Temperature

Critical Point Pressure

Critical Point Density

25 to 300 K -414.67 to 80.33°F

.1** to 200 bar

1.450 to 2901. psia

25 K*

-414.67°F

.5102339 bar**

7.4003172 psia

.2528246 moles/liter

.31855482 Ib/cu ft

61.45071 moles/liter

77.42688 Ib/cu ft

44.40 K*

•379.75°F

26.57086 bar

385.37775 psia

23.93 moles/liter*

30.151 Ib/cu ft

This particular value is used to define the point in the sense that it was used as input into the program.

See Section 3 for more detailed explanation of the lower limits of

pressure.

25
>i M CO • rTM 1 CO E—

CO CD • I— a. >

•t-> r— >

fO • I— i^ E -(-> I 5- E

a; :3 c .^ T3 3 o 1— C E

OJ 2:

S- M-

+-> >,

CO -l-> <U -a

1— c u 00

13

cu , E

00 O) c >•

(T3 E

s_

<+-s_O) D_E

fO

S- >

C7) C_3

s_ ^ D.

S- '0

CU E +J

13 -3

Q.E Q.

(_)

s_

14-

00

(U :^

•r-

(-> , S- LO

0) E Q. ^"D

J- Q_

1-

LO

+-> re

s-o

CL

cu

+-> CM

LDCDO

00

S-03

LO

csj ro3

CT

-a

OJ

+->

S-

+-> ro 00

r-H

IT) COCO

S-

<T3 JDO

CM

•o

to ooCO

+-> fa

O)to

n3

<U

CJ)

oo

cr>

(JD o

0) jQ

re oE

CO

CO

en00

CO

CO

CTi CO o• CO E

CU

CX3

cr> o

CM

00O

CM

>>

10

(U Q

CM

I—

O

CO

CMCO

CT>• in

0000oenCO

CO

26
8. Properties of Nitrogen

The thermodynamic properties are calculated from a 32 term modified equation

of state taken from Jacobsen, et al . (1973). The same functional form of the

equation of state used for nitrogen has also been used here for hydrogen, oxygen,

argon and methane. The transport properties are from Hanley, et al . (1974).

27
Table 11. Properties and Associated Estimated Uncertainties for Nitrogen

Property All Uncertainties in Percent (Except Enthalpy)

" ) Fluid (above T )

0.3

0.2

0.2

1.0

1.0

5.0

5.0

1.0

6.0

2.0

Liquid (below T ) Gas (belo

pressure 5.0 0.3

density 0.5 0.3

temperature 0.5 0.3

enthal py 3.0 1.0

entropy 2.0 1.0

^p 5.0 5.0

Cv 5.0 5.0

speed of sound 2.0 0.25

thermal conduct ivity 4.0 4.0

viscosity 2.0 2.0

The above are based on the estimated average difference between calculated

and true value, including problem areas as described in section 2.

28
Table 12. Pressure and Temperature Range for Nitrogen

Temperature range

Pressure range

Fixed Points

Triple Point Temperature

Triple Point Pressure

Triple Point Density-Vapor

Liquid

Critical Point Temperature

Critical Point Pressure

Critical Point Density

63.15 to 1900 K 346 to 2960. 33°F

0** to 1000 bar

to 145040. psia

63.15 K*

346 °F

.1246399 bar**

1.807749 psia

.2396164 moles/liter

.04190847 Ib/cu ft

30.97717 moles/liter

54.178504 Ib/cu ft

126.26 K*

232.402°F

34.10034 bar

484.5836 psia

11.21 moles/liter*

19.606 Ib/cu ft

This particular value is used to define the point in the sense that it was used as input into the program.

•k-k See Section 3 for more detailed explanation of the lower limits of

pressure.

29
+-> •r—

(/) OO

CO

r Eu

CD

a.

CM

VD

t-^ I—

00• CVJ

I—

in

t—

LO

CvJ «^

.—I• CO

CM

LO

cno

SfO

1-

+-> >

•-- ^ +-> I u E

Z3 --^ -O 3 c E o

CVJ CM

cn

LO

CM

CO

CO oI

00

Ln

CO• LOCO o

CO

O)oc

fOE

s_o

If-s-O) Q.Em

s_O

s_ Q_

S-<u

ClEoo

S-o

4-

in

o;

•r— -M

i.CDQ.O

SCO

Q)

03

ac:o

5^

+->

•I

oo oo

00

cn "vf CTl CO ^ LO

CO 00 00

00 "e • • 00 • o

r^ CO i~ ^ t-H S- en 00

i~ fO

to X)

O

jd LO

LO CM I-H CM CO

CO o I—CO -o <£)

i-H <o o LO c I-H o LO • o (O O • 00 I-H CM CO

I-H LO 00 i^ cyi • +-> • • iZ +-> <—

fO r-~ o CO

(O CM -o

CM oCO

CM o S- • 1— e o ^ +J

Q. CM cr o (tJ CO

-D to ^ •I— 00 o > O _i VO O) o LO cr> CO LO

-a CTi o r-- (O 00

<u • o • -C • +-> .—1 +-> r-- D_ r~- fO CO fO LO CO

s- S- cu 3 r3 1

4-> +-> en

fO (T3 CO c

i>^ OO OO r^ •1— LO 1 r^ r--. oo 00 ^— "^r CO r~- o -si- LO CO E • LO • • 00

CM oE

vooLOCO

r-i CM

CM

I-H CO• o

COI

00

LO

CO•

00

CLE

cu

<£> CM

CO

<£> CM

vo

CO

1^

+-> rCOC

OJ Q

OE

CO

I-H CO

CO<*

CM

COCO• CO

CM

CO

I-H OCO

o^

COCM

30
9. Properties of Oxygen

The thermodynamic properties of oxygen are calculated from a 32 term

empirical equation of state given in NBSIR 78-882 by Weber (1978). The

functional form of the oxygen equation of state is the same as was used for

hydrogen, nitrogen, oxygen and methane. The transport properties are from Hanley

et al. (1974).

31
Table 14. Properties and Associated Estimated Uncertainties for Oxygen

Property All Uncertainties in Percent (Except Enthalpy)

Liquid (below T )

pressure 5.0

density 0.1

temperature 0.1

enthal py 0.5

entropy 0.5

Cp 3.0

Cv 3.0

speed of sou nd 2.0

thermal conductivi ty 4.0

viscosity 2.0

Gas (below T )

0.25

0.25

0.2

0.25

0.25

5.0

5.0

0.5

4.0

2.0

Fluid (above T^)

c

0.15

0.15

0.1

0.5

0.5

3.0

3.0

0.5

6.0

2.0

The above are based on the estimated average difference between calculated

and true value, including problem areas as described in section 2.

32
Table 15. Pressure and Temperature Range for Oxygen

Temperature range

Pressure range

Fixed Points

Triple Point Temperature

Triple Point Pressure

Triple Point Density-Vapor

Liquid

Critical Point Temperature

Critical Point Pressure

Critical Point Density

54.359 to 400 K

-361.8238 to 260.33°F

0** to 1200 bar

to 17404. psia

54.359 K 361.8238°F

.001490085 bar

.021611856 psia

**

.0003275488 moles/liter

6.5431796 x 10"^ Ib/cu ft

40.81997 moles/liter

81.542780 Ib/cu ft

154.481 K*

181.4242°F

50.42218 bar

731.31190 psia

13.63 moles/liter

27.228 Ib/cu ft

This particular value is used to define the point in the sense that it was used as input into the program.

k-k See Section 3 for more detailed explanation of the lower limits of

pressure.

33
>1

+-> o

CO

00I

CD

a. I

co

en

COro

CTi O• O

un

CDCD

>^Xo

03

4-> O

c:oo I

inoo• CO

CT> 1—

oLO

00 oLO o

+-> tooc

03E

i_o

Ms_<u D.E

s_CDO

s- D_

S_

+-> Q.Eoo

s-o

4-

to

cu

•r-

+-> s-O)CLo

s-- Qc:

13o

4-> Uo

'cij

<_i

oo

VO VO *£>

CVJ

O CSJ CO «3 ^ CT> "e^ • • LO

00• OJ

r-.

O s_ CO r—

scr> 03 r~. S- fO -Q

(0 ^ o

LO

O

LO

O CVi 1—

C\J ro

CO IJD I—

CO -o <^

O

r-H r-» o o c CO

CT> • • LO 03 CO

t—

t—

ro r>» .—

r~-. LO i^ vo • ^ +-> • • +-> I—

03 O^ o r:)- 1 03 OJ CM o CM 'o S_ o ro e o 3 4_) ^^- "D

Q.

03 ro

00

•1—CT ro 03 ^ >

<^ 00 ^

ro _l r-H OJ CO

OJ CO «^ "O

OJ CO• DOJ

C\J• 03 ^ x: • +-> ro

1—1 +-> 03 ^ Q_ o LO

QJ ^ 3 13

-(-> -l-> C71 ^

03 03 LO

C t/^ "^ OO CT> •r— l£> 1 rf ^ U~) O OE

00

LO• cr> •

cr>

CM• o

vo

O)

03

OE

CO

ro

LO• ro

LOOJ

CMCOo

CM

00

•^

CM• oro

cr> E

CL)

LOro

<y> o

LOCO

cnoCTi

•->

COc

<u Q oE

LOOJ

cr> CDro

en

00

LO• LOCO

ro

CM

CM

34
10. Properties of Argon

The thermodynamic properties of argon have been calculated from a 32 term

empirical equation of state from Hanley, et al . (1974). The functional form of

the argon equation of state is the same as was used for hydrogen, nitrogen,

oxygen and methane. The transport properties for argon were also taken from

Hanley, et al . (1974).

35
Table 17. Properties and Associated Estimated Uncertainties for Argon

Property All Uncertainties in Percent (Except Enthalpy)

T ) Fluid (above T ) c ^ c

0.3

0.3

0.3

1.5

1.0

5.0

5.0

5.0

6.0

2.0

Li qu id (below T ) Gas (bel

pressure 10.0 0.3

density 0.25 0.3

temperature 0.25 0.3

enthal py 2.0 1.0

entropy 1.0 1.0

Cp 5.0 5.0

Cv 5.0 5.0

speed of sou nd 5.0 5.0

thermal conductivi ty 4.0 4.0

viscosity 2.0 2.0

The above are based on the estimated average difference between calculated

and true value, including problem areas as described in section 2.

36
Table 18. Pressure and Temperature Range for Argon

Temperature range 83.80 to 400 K -308.83 to 260.33°F

Pressure range 0** to 1000 bar

to 14504. psia

Fixed Points

Triple Point Temperature 83.80 K*

-308.83°F

Triple Point Pressure .6890708 bar**

9.9941271 psia

Triple Point Density-Vapor .1015395 moles/liter

.25322653 Ib/cu ft

Liquid 35.40018 moles/liter

88.283522 Ib/cu ft

Critical Point Temperature 150.86 K*

-188.122°F

Critical Point Pressure 48.98050 bar

710.40210 psia

Critical Point Density 13.41 moles/liter

33.443 Ib/cu ft

•

This particular value is used to define the point in the sense that it was used as input into the program.

•k-k See Section 3 for more detailed explanation of the lower limits of

pressure.

37
O

to

00I Eo

a.

CM

CM o

CO

CTi in

CM

CO

I—

LT) O

(O co

S- <c

s_o

4-

4-> U)

O)

cuoc

fOE

s-o

Hs_(U a.

{-eno

s- G.

t-(U

4-> 13Q.Eoo

s-o

a;

•r-

«-> s_Q.O

s- a.

-M

•r—> E 4-> I S- CJ E

CD :3 ^

— c E oo

CJO

CM

en

<^in

00•

CT^ 00O• 00

CM 3O

00 CD Oo

CM o o .—

CM o 00

VI 00 LO

CO ~E • o • CO • U3 r^ o J- 1—1

i-H 5- vo fO r-^

S- fO

fO J2 o JD

LO

LD CM I—

CM ro

CO ro 1—1 vo o r~- 1—

CM o CO E CM o O • 1—1 fC OO • <3^ I—

r—

o I—

LO 1—

i<i r-- • -!-> • • i^ +J CO (O "^ o LO

fO t—

-a CO oCO

r-H 'o s- • r— E o 3 4J

a. LO cr CM 03 CO -3 fO CO •1— <^ CM > <X5 _j CM OJ LO

CTl

O 00O T3 CM -o O fO OO

CU • cu • JZ. • +-> OO +-> r—

a. <—

03 CM fO LO OO

S- S- CD =5 =3

+-> +-> en

to fO UD c LO

:i^ 00 ^ oo

O •1

LO

1—

00 oo 00 1

<^ r-^ LO o LO CO LO E

•-0 • 00

CM • LO • oen

cr>

CU J3

03 oE

CM• LOCM

cn

CTi 5J-• CM

LT) CTi CM

LOOO

CM

Q.E

(U

OO

LO

1—1 00

CM• 00

oo

LO

CO

CM

00

•r— 00

(U o oE

CM

LO ooor-. 00

oo

LO

00o• CM

38
11. Properties of Methane

The thermodynamic properties of methane are calculated from a 32 term

empirical equation of state by McCarty (1974). The functional form of the

methane equation of state is the same as was used for hydrogen, nitrogen, oxygen,

and argon. The transport properties are from Hanley, et al . (1977).

39
Table 20. Properties and Associated Estimated Uncertainties for Methane

Property

pressure

density

temperature

enthalpy

entropy

Cp

Cv

speed of sound

thermal conductivity

viscosity

All Uncertainties in Percent (Except Enthalpy)

Liquid (below T )

5.0

0.1

0.1

1.0

0.5

2.0

2.0

1.0

5.0

3.0

Gas (below T )

0.25

0.25

0.25

0.5

0.5

5.0

5.0

0.3

5.0

3.0

Fluid (above T^)

c'

0.25

0.25

0.25

0.5

0.5

2.0

2.0

0.3

4.0

2.0

The above are based on the estimated average difference between calculated

and true value, including problem areas as described in section 2.

40
Table 21. Pressure and Temperature Range for Methane

Temperature range

Pressure range

Fixed Points

Triple Point Temperature

Triple Point Pressure

Triple Point Density-Vapor

Liquid

Critical Point Temperature

Critical Point Pressure

Critical Point Density

90.68 to 500 K -296.446 to 440.33°F

0** to 350 bar

to 5076. psia

90.68 K*

296.446°F

.1174350 bar**

1.7032507 psia

.01569094 moles/liter

.015713995 Ib/cu ft

28.15114 moles/liter

28.192503 Ib/cu ft

190.555 K*

116.671°F

45.98838 bar

667.00507 psia

10.23 moles/liter*

10.245 Ib/cu ft

This particular value is used to define the point in the sense that it was used as input into the program.

k-k See Section 3 for more detailed explanation of the lower limits of

pressure.

41
>>

4-> 1/1

•1

1 CO E o u O ~~^

lO en

•I— a. >

>>

4-> 'r— ,

>

(T3 • r— iii: E 4-> 1 O) S- O E c <v ZS ^^-.^ fO x: -a 3 x: h- c: E

+-> o ^

O) o ^

s_o

<+- 5^

+-> -M

00 o • 1— QJ d U C/l 1— 3 O ^.^ O E

O) oo 'oJ u > c

fOE

i-o

<4-S-O) a.E

fO >

s_ (_) CTO ^ s- 1 a. 'o

s_ E

OJ 4J -D 3

Q. Q. E O O

(_J

S-o

4-

co i^

<U 1 •^ ^»

+-> 00

O

S- E

a>Q. -D o

S- Q_• ^ CM

O

CM rc E

CD "-3 r-~ jQ

fO

CO

Lf> o•

00

LO

<—

CM• CO

CO

LO

LO

LO• .—

Px

CM

1-fO J3

IT) CMCO 00

1—

<^ o I—

• en

I—

r^• -M LO

fO CM

S_O

Q. •^

fO cr. > CM00 D CM

<U • 4-3 LO

fC ro

i~. 3

+J

fO oo r^o

r-. LO• CM

UO

00

CMO• 00

CMo• 00o

cr> LO• ,—

LOCO

s- 1—1 fO JDLO

CM

ro

r-H CO o o • r-^ 1—

<^

r--

-(-> •

(T3 CMn -o• ^

13cr CO

•f— CO

_j oI—

-a 00

O) • +j LO

n3 LO

s_

13

+-> 03 CTi oo CM

CM

r~-

.—)• CT>

r>- o

CO

00

CM

00o• CO

CO

LO oCMO• CMCM

CMCO

00OLO

00

00LO

P-^• ^o s- I

(O jQOLOCOD CM c LO

fO "5J- CT<

::^ I—

• o .—

o CO

+-> fO CM

LO

OJ LO

to CM

fO «*

.^ • Q_ LO

LO

O) 'ct c

•1— <^

oo CT> LO

<T>• 00

CM

COCO

LO

LO

a.E

<U

<Ti ro

LO

cri CO

LO

>>

•r-

«/l

CL) Q

CM

LOCO

r-4 CO

LO

CT> CM

co• LOCM

OLO

LO

LOCO

42
12. References

[1] Roder, H. M. and McCarty, R. D., A Modified Benedict-Webb-Rubin Equation of

State for Parahydrogen-II , Nat. Bur. Stand. (U.S.), Interagency Report

NBSIR 75-814 (1975).

[2] McCarty, R. D., Thermodynamic Properties of Helium 4 From 2 to 1500 K at

Pressures to 10^ Pa, j. Phys. Chen. Ref. Data 2, No. 4, 923-1042 (1973).

[3] McCarty, R. D., Thermophysical Properties of Helium-4 From 2 to 1500 K with

Pressures to 1000 Atmospheres, Nat. Bur. Stand. (U.S.), Tech. Note 631

(1972).

[4] McCarty, R. D. and Stewart, R. B., Thermodynamic Properties of Neon from 25

to 300 K Between 0.1 and 200 Atmospheres, Advances in Thermophysical

Properties at Extreme Temperatures and Pressures . The American Society of

Mechanical Engineers (1965).

[5] Jacobsen, R. T., Stewart, R. B., McCarty, R. D. and Hanley, H. J. M.,

Thermophysical Properties of Nitrogen from the Fusion Line to 3500 R [1944 K] for Pressures to 150,000 PSIA [10342 x 10^ N/m^], Nat. Bur.

Stand. (U.S.), Tech. Note 648 (Dec 1973).

[6] Hanley, H. J. M., McCarty, R. D. and Haynes, W. M., The Viscosity and

Thermal Conductivity for Dense Gaseous and Liquid Argon, Krypton, Xenon,

Nitrogen and Oxygen, J. Phys. Chem. Ref. Data 3, No. 4, 979-1017 (1974).

[7] Weber, L. A., A Modified Benedict-Webb-Rubin Equation of State for Gaseous

and Liquid Oxygen, Nat. Bur. Stand. (U.S.), Interagency Report NBSIR 78-882

(1978).

[8] McCarty, R. D., A Modified Benedict-Webb-Rubin Equation of State for

Methane Using Recent Experimental Data, Cryogenics !£, No. 5, 276-80 (May

1974).

[9] Hanley, H. J. M., Haynes, W. M. and McCarty, R. D., The Viscosity and

Thermal Conductivity Coefficients for Dense Gaseous and Liquid Methane, J.

Phys. Chem. Ref. Data 6, No. 2, 597-609 (1977).

43
Appendix 1

Example of the Use of the Program

44
LALL y rPRGPS

HI y WELCOME IG THE UIGRED OF FEU ID FRGPERlIE3» IF YGU ARE NG I FAMIEIAR WITH THE

PRGGKAh FEEASE ENTER A

! WHEN IHE PROGRAM ASKS FOR A FI...UID SEEECTIONy ENTER WM, APPRGPRIAn- Nl iMBFR

AN INAPPROPRIATE NUMBER WIFE TERMINATE THE PROGRAM

WHEN THE PROGRAM ASKS FOR A PRESSUREy DENSIIYy AND

TEMPERA I iJREy ENTER ANY 2 OF THE THREE AND A FOR IHE THIRD.

IHE ORDER MUSi DE Py DyTy AND ONE OF IHE THREE MUSI BE 0.

IF AEE THREE ARE IHE PROGRAM ASKS FOR A NEW FEU ID

IF YOU ARE INTERESTED IM A DEI- INI T ION OF THE VARIOUS

MODIFICATIONS OF HYDROGEN ENTER A ly IF NOT ENTER A

? IF YOU ARE INTERESTED IN THE SOURCES OF THESE PROGRAMS

ENTER A 1 IF NOT ENTER A 0,

? SELECT A FLUID FROM THE FOLLOWING LIST

PARA HYDROGEN^^^I

NORMAL HYDROGEN- 10

ORTHO HYDROGEN^^^t. I HELIUM^=:2

NEGN^^:^3 NITR0GEN:^^:4

OXYGEN^: :^/ ARGON --6 ME THANE7

TERMINATION-8

? 4 THE RANGE OF TEMPERATURE FOR NITROGEN IS 63.15 TO I900K

WITH PRESSURES TO 10000 BAR

DO YOU PREFER ENGINEERING UNITS OR METRIC UNITS ? ENTER A FOR ENGINEERING UNITS OR A I FOR METRIC

? I DO YOU WANT SATURATION PROPER 1 1 ES ? ENTER FOR YES OR 1 FOR NO

"i- 1 DO YOU WANT A SINGLE POINT OR A TABLE OF PROPERTIES ? ENTER A FOR A SINGLE POINT OR A 1 FOR A TABLE

? I ENTER A PRESSUREy A STARTING TEMPERATURE v A FINAL

TEMPERATURE AND A TEMPERATURE INCREMENT y IN BARSy DEGREES

Kv AND IN THAT ORDER

? lOy 100y200yl0

PRESSURE DENSITY TEMP H S CP VX' S SOUND COND MISC

BAR MOL/L K J/MOL J/MOL-K J/MOL-K M/S MW/M -K MI F -m-S

10.00 24.6342 100.00 --2032.40 94.64 64.36 26.23 616.75 98,53 73:i. .3

10.00 1.3169 110.00 2731.63 140,55 40.17 23.18 194.20 12.77 79./

10.00 1.1452 120.00 3111.38 143.85 36.25 22.33 208.92 13.35 85.5

10.00 1.0226 130.00 3462.67 146.67 34.19 21.85 221.53 14.02 91.5

10.00 .9282 140.00 3797.88 149.15 32.94 21.56 232.83 14.73 97.5

10.00 .8523 150.00 4122.94 151.39 32.12 21.36 243.20 15.47 103.4

10.00 .7894 160.00 4441.10 153.45 31.55 21.23 252.87 16.23 109.2

10.00 .7360 170.00 4754.35 155.35 31.13 21.14 261.98 17.00 114.9

10.00 .6901 180.00 5063.95 157.12 30.81 21.07 270.64 17.76 120.6

10.00 .6499 190.00 5370.75 158.78 30.56 21.02 2 78.93 18.53 126.1

10.00 .6145 200.00 5675.36 160.34 30.37 20.98 286.88 19.29 131.5

ENTER A PRESSUREy A STARTING TEMPERATURE y A FINAL

TEMPERATURE AND A TEMPERATURE INCREMENT y IN BARSy DEGREES

Kv AND IN THAT ORDER

? y y y

45
SELECT A FLUID FROM THE FOLLOWING LIST

FAR A HYDROGEN^:::!

NORMAL HYDRUGEN^^^^I.0

ORTHO HYDROGEN- II HELIUM:=2

NE0N:^-3

NITROGEN-4

GXYGEN~5

ARG0N^=^6

METHANE:^^/

TERMINATION^^^^e

' 8

;xii

46
Appendix 2

Program Listings

47
• UP y DTP 9 PCC y PIP y ICC y TIP y TUL y ILL ? PUL y DC

100

:i.0l ?9

102

104

y TCyDCy XyPCySIG

TO IHE WORLD Or- PROGRAM PLEASEFLUID \- ENTER A ^OPERTIESy

*)

10

11

13

105

106

.07

r-' R G R A M F I... U I D S ( 1 H P LJ I' --

8 y U F F-' LJ T ) DIMENSION 0(32) yVP';9)

C M M ij N / D A r A / G y F< y A M M A COMMON /CONT/IF

CGMMON/CRI T/EM y EOK y RM

FORMAT (* Hly WELCOME

INOT FAMILIAR WITH THE

PRINT 100

READ 101 y

if<ij;;;q«o)call info

FORMAT(Il)

PRINT 102

PRINT 104

FORMAT (* SELECT A FLUID FROM THE FOLLOWING LIST*)

FORMAT (* PARA HYDROOEN^^^l*/* NORMAL HYDROGEN^^^^IO*/*

1 Y D R G E N 1 1 * / * H E L I U M - 2 * / * N E. N 3 * / * N I T F< Q G E. N = 4 * / *

2 E N ^= 5 * / * A 1^' G N 6 * / * M E T H A N E; 7 * / *

4 TERM I NATION--^ 8*)

READ *yIF

GO TO ( 1 y 2 y 3 y 4 y 5 y 6 y 7 y 999 y 999 y 1 y 1 1 ) y I F CALL DATA PH2

GO TO 13

CALL DATA HE

GO TO 99

CALL DATA NE

GO TO 99

CALL DATA N2

GO TO 13

CALL DATA 02

GO TO 13

CALL DATA AR

GO TO 13

CALL DATA CH4

GO TO 13

CALL NH2

GO TO 13

CALL 0H2

GO TO 13

PRINT 105

FORMAT (* DO YOU PREFER ENGINEERING

1/* ENTER A FOR ENGINEERING UNITS

READ 101 ylU

PRINT 106

FORMAT (>K DO YOU

1/t ENTER FOR YES OR 1 FOR NO*)

READ 101 ylC

PRINT 107

FORMAT (* DO YOU

IF YOU ARE NO I

ORTHO H OXYG

UNITS

OR A : OR METRIC UNIT:FOR METRIC*)

?*

WANT- S A r U R A T 1 N F' R F' E R T 1 E S ? * YES OR

WAN(

FOR A ;; AINC

19

108

1/* ENTER A READ 101 ylU

IF(IC.EQ»0)GO TO 30

IFdV^EQ.DGO TO 40

iF<iu j:-;;q,o)go to 19

PRINT 103

READ *yPyDyT

P^^-P/ 1.0 1325

GO TO 20

PRINT 108

F R M A T ( * E N T F R I-' R Hi: S S U R E 1/* TEMPERATURE IN DEGREI

READ *yPyDyT

P==P/ 14. 695949

D -•= D * 1 6.01 8 4 6 3 7 :!. / E M

SINGLE POINT OR A TABLE OF PR 01' iLE POINT OR A 1 FOR A TABLE*)

ERTIES ?*

:n LB/SQ

; F*)

INy DENSITY IN LB/CU FTy AND*

48
IF( I . ECnO.OGO TO 20

T=(T-32. )/:l. .8 + 27:5.15

20 IF(P.LE.O.O)GO TO 14

103 FORMA T(* ENTER PRESSURE IN BAR? DENSITY IN MOLES/LITER i- AND TEMP

lATURE IN KELVINS*)

IF(D*LE.O.O)GO TO 17

IF(T.LE*0.0)GG TO 12

GO TO 22

12 IF(P J_E.0.0R.D.LE.0.0)G0 TO 99

T--=:FIND T(pyD)

CALL LIMITS ( p..Ty ID

IF(IL.LE,0)GO TO 22

GO TO 16

17 IF(T.LE.0.GR.P,LE.0)G0 TO 99

CALL LIMITS (Pi.T, ID

IF(IL.LE.O)GO TO 22

D^FIND D(P.T)

GO TO 16

14 IF(D J_E.O.O.GR.T,LE,0)GO TO 99

P-FIND PCDs-T)

CALL LIMITS(PyTjID

IF(IL.LE.O)GO TO 22

16 C A I.. L R E P !• (

I-' , D ? T ? l' U y i: V ? I C , I !- y T F f D E L 1 ) GO TO 22

30 PRINT 109

109 FORMAT (* DO YOU WANT SATURATED LIQUID OR SATURATED VAPOR*

1/* ENTER A FOR LIQUID OR 1 FOR VAPOR*)

READ 101 » IP

IF(IV»E0.1)G0 TO 40

PRINT 111

111 FORMAT (* DO YOU UANT TO ENTER WITH TEMPERATURE OR PRESSURE * 1/* ENTER FOR TEMPERATURE OR 1 FOR PRESSURE*)

READ 101 y II IFdI.EQ.DGO TO 35

211 IFdU.EQ.DGO TO 31

112 FORMAT (* ENTER A TEMPERATURE IN DEGREES F*)

PRINT 112

READ *yTI

T=(TI-32. )/ 1.3+273. 15

IF(T.LE.0.0)G0 TO 99

GO TO 33

31 PRINT 113

113 FORMAT (* ENTER A TEMPERATURE IN DEGREES K*)

READ *yT

33 IF(T.LE.0.0)G0 TO 99

I

F'

( I . G T , T C C . R ., T . L \ . f 7 F' ) G 1 3 4

P=VPN(T)

I F ( I P . EQ . ) P-P+ . 0000

1

D=FIND D(PyT)

C A L I.. RE P R ( P-' y D y \ y I U y I V y I C y 1

1"' y T

F'

y D E I... T ) GO TO 211

34 PRINT 114yTCCy TTP

114 FORMAT (* YOUR INPUT TEMPERATURE IS OUTSIDE THE RANGE OF THE*

1/* SATURATION TEMPERATURES FOR THIS FLUID.*

2/* TC:=*yF6.2»* TTP=:*yF6.2y* TRY AGAIN*)

GO TO 211

35 IFdU.EQ. DGO TO 36

PRINT 115

115 FORMAT (* ENTER A PRESSURE IN LB/SQ IN*)

READ *yPI

IF(PI.LE.O.O)GO TO 99

P==PI/14.695949

GO TO 37

49
36 PRINT l:I.A

:l. 16 FGRMATOK ENTER A PRESSURE IN BAR*)

READ *yPI

:i;i- (p:[.>EE.o.o)i;jO to 99

p:::^pj:/:l. .0:1.32^ 37 ;[F(P,GT.PCC.0R.P J...T.PTP)G(J TO 38

T--=^FIND TV(P)

p::.UP|M(T)

IF( :i:p*EQ.0)p:-T"'i.0001

D^^H-IND D(P?T)

t; A I... L 1^ E p R ( F ^ 1.1 c r y [ u y :i: V V i c; y :i: ! y r i-- y d e. i... t ; GO TO 35

38 PRINT lI7yPCCyPTP

117 FORMAT <:K YOUR INPUT PRESSURE IS OUTSIDE THE RANGE OF SATURATION*

1/>K PRESSURES FOR THIS FEU ID.*

2/* PC"^*yF6,3y* PTP^^=*yF6.5y* TRY AGAIN*)

GO TO 35

40 IFdC.EQ.DGO TO 50

IF(IU,Ea,l)GO 7 41

PRINT lie

118 FORMAT (* ENTER A STARTING TEMPERATURE v A FINAE TEMPERATURE*

1/* AND A TEMPERATURE INCREMENT y IN DEGREES F AND IN THAT ORDER*)

READ *yTSyTFyDEET

IF(DEET,EE.O.O)GO TO 99

TS^(TS-32. )/l .8+273,15

TF:^(TF-32. )/l .8 + 273.15

DELT^^^DELT/1.8

I F ( r s . I... T . T (

I-' , R . r s . G r . T c; c; ) g o r' o 4 5

1

1-- ( r I" . I.. T . T T

1^' . R . T I- . G T . T C G ) G T 45

GO TO 42

41 PRINT 119

119 FORMAT (* ENTER A STARTING TEMPERATURE y A FINAE TEMPERATURE*

1/* AND A TEMPERATURE INCREMENT IN KEE"vJINS AND IN THAT ORDER*)

READ *yTSvTFyDEET

I F ( D E L, r , L E , . ) G T 9 9

I F- ( r S . I._ I' . T T P „ R . T S . G J . l' C C ) G T 4 5

:i: F' ( r F . l r . t t p . o f< . t f . g t . i c c; ) g o t o 4 5

42 T^^TS

P=::VPN(T)

I F (I P . EQ » . ) P^M"'+ . 000

D==n-"IND D(PyT)

C A I.. I.. R E I • R ( F y D ? J y I U y I U y 1 C y 1

1"' y T I"' y D E L T ) GO TO 40

45 PRINT 120yTCCyTTP

120 FORMAT <* EITHER YOUR STARTING OR FINAL TEMPERATURE IS OUTSIDE*

L/* THE RANGE OF SATURATION TEMPERATURES.*

2/* TC:=^*yF6.2y* TTP^^:^*yF6.2y* TRY AGAIN*)

GO TO 40

50 IFdU.EQ.l )G0 TO 51

PRINT 121

121 FORMAT (* ENTER PRESSURE v STARTING TEMPERATURE y FINAL TEMPERATURE*

1/* AND A TEMPERATURE INCREMENT y IN LB/CU FTy DEGREES Fv AND IN*

2/* THE ABOUE ORDER*)

READ *yPIyTSyTFyDELT

IF(DELT J_.E.O.O)GO TO 99

P^M=M/ 14. 695949

T-(TS-32. )/ 1.8+273. 15

TF::=(TF-32. )/ 1,8 + 273. 15

DE-:LT==D£LT/1.8

CALL LIMITS(P,TyIL)

if(il.le.o)go to 50

CALL LIMITS(pyTFylL)

IF(IL.LE.0)G0 to 50

50
60 TO 52

51 F'RINT 122

;l.22 FDF^MATOk ENTFR A PRESSURE!- A SrARTING TEMPERATURE k A FlrifiA...*- J./* rEMPERATURE AND A lEMPERATURE INCREMENTS' IN BARSy DEGREES*

2/* Ky AND IN THAT ORDER*)

READ *yPIvTSvTFvDEET

IF(DEET,EE.O.O)GU TO 99

J:::: IS

P^^^^Pl/ I. 0:1.325 CALL LIMITS(PyTvIL)

iF(iL j...e.gm:)o to 50

CALL LIMirS(Pi'TFylL)

IF(IL.LE*0)GO TO 50

52 D^==M-IND D(PyT)

C A L L R E !"• R ( P i- D v T y I U ? I V - I C v :i: F s- T F y D E: I... T ) GO TO 50

999 CONTINUE

STOP

END

SUDROUTINE DATA ET

PRINT :loo 100 FORMAT (* ETHANE IS SCHEDULED TO BE ADDED TO THE FLUIDS*

1/* PACK IN THE NEXT FISCAL YEAR*)

RETURN

ENTRY DATA PR

PRINr 101

101 FORM Arc* PROPANE IS SCHEDULED TO BE ADDED TO THE FLUIDS*

1/* PACK AFTER FY 78*)

RETURN

ENTRY DATA NH3

PRINI 102

102 FORMAT (* AMMONIA IS SCHEDULED TO BE ADDED TO THE FLUIDS*

1/* PACK DURING FY 78*)

RETURN

ENTRY DATA SH

ENTRY DATA SO

PRINT 103

103 FORMAT (* THE SLUSH PROGRAMS WILL BE ADDED TO THE FLUIDS*

1/* PACK IN FY78*)

RETURN

END

S U B R U T I N E R E I-' R ( F' y D ^ l > I U > I ^> v 1 v 1

1-'

i- T f v D E L l"

)

D I M E N S 1 N G ( 3 2 ) y V F' ( 9 ) COMMON/ D AT A/G •> R y GAMMA y Up y DIP y PCC y FTP y TCC > ITP y TUL ; TLL y PUL

COMMON/CONT/IC

COMMON/CRI T/EM y EOK y RM y TC y DC y X y PC y SI

G

N::^-500 IF(iy»EQ.0)TF:=T- !

PRINT 100

IF(IU.EQ.O)GG TO 1 PRINT 102

GO TO 2

1 PRINT 103

PRINT 104

2 CONTINUE

DO 10 I^^^lyN

IFd.EQ.DGG TO 3

D^^FIND D(PyT)

3 H:^ENTHAL(PV

s^M:;:NTROP(DyT)

U^SOUND(Dy I CPP^CP(DyT)

51
].o*of;;.:i;i:m;-q.:i. :i)GO to 20

JfH9S9CPFfCK>^9i,hJ\UK>

20

101

100

102

103

104

21

Ti'Hi'SvCPPi'Ck^^.^vW

MP

105

9

10

11

a:=P*l» 01325

IF(lU.Ea«0)60 TO 21

if(];c.eq,i«of;;»ic.eq.

1f"(ic«eq.9)g0 to 20

TH==THERM(Di'T)

U-=VISC(D.T)

PF<INT lOlvayD

GO TO 9

PRINT lOlvQ^DiGO TO 9

FORMAT ( F8 . 2 s- F8 . 4 , F9 . 2 i- F9 . 2 ^ F8 .

FORMAT (* PRESSURE DENSITY TF

1 SOUND COND yiSC*)

FORMAT (* BAR MOL/l. K IM/S MW/M-K MiG/CM-b*)

FORMAT (* LB/SO IN LB/CU FT DEG F

1 F/S BTU LB/FT-S*)

FORMAT (*

1 FT--HR-F E + 7*)

H=H/(2.324445*EM)

S^S/(4«ie4001*EM)

CPP=::CPP/ ( 4 . 184001*EM ) CV"v'=:C'v'V/(4»184001*EM)

U-U*3» 280840

P0==P*14» 695949

D0-D*EM/16* 01 846371

TO=^T>K 1.8-459. 67

I F ( :i: C . E Q . 1 . R . I C . G T . 8 ) G T 2 2

TH^^^THERM ( D ? T ) * , 0005781 76

<v'='v'ISC ( D !- T ) * . 00671 96897

PR INT 105 9 PO s- DO y TO 9 H y S y CPF

FORMAT < F8 . 1 y F8 . 3 y 2F9 . 2 y F8

GO TO 9

PRINT 1 1 y PO y DO y TO y H y S y CF-'F T=T+DELT

IF(T.GT.TFf ,01)G0 TO 11

IF(I«.E«.0)P==VPN(T)

IF(IP.E0.0)P-P+.0001

CONTINUE

CONTINUE

RETURN

END

'F8.

H

F7.2yF 1)

CP CM

J/MOL J/MOL-K J/MOL-K

BTU/LB BTU/LB-F

CVVyWyTHyU

1 9 2F7 . 3 '> F8 . y F7 . 4 y f? . 3 ) CVVyW

52
BUBRGUTINE DATA CH4

DIMENSION G(32) !.MP<9) yGKll)

DIMENSION G>^(9;' i-GK?) !'F'v'(4) ? F T ( 4 ) »EV(8) >ET(3)

DIMENSION A(20)

COMMON/SEN/BETA ?X0» DELTA V El 7 E2? AGAM

COMMON/CPID/GI

COMMON/CRIT/ EM> EOK? RM» TCy DC > X , PC> SIG

COMMON/DATA/ G i- R r GAMMA y UP t DTP » PCC 7 FTP v TCG 7 TTP , 1 UL v TLL v PUL y DCC

COMMON/DATA 1/GU r GT ? FV y FT » EV y ET

COMMGN/ISP/NyNldrNWW

COMMON/SATC/A ? DTPV

NUU^O

PRINT 100

100 FORMAT <* THE RANGE OF TEMPERATURE FOR METHANE IS 90.68 TO 500 K*

1/* WITH PRESSURES TO 350 BAR*)

N==0 $ NU^O

EM:==16.042 $ E0K==168, $ RM:=4 . lOlE -03 * TC = 190.555

DC = 0.1627 $ X=1.7124 $ PC=^45.95 $ SIG = 3.68

X0=0.164 $ BETA-0.355 * DELTA-4.352 $ El-2.03 $ E2==0,287

AGAM^l.190

C PARAMETERS FOR TRANSPORT

C PROPERTIES - HANLEY ET . AL. JOURNAL

C OF PHY. CHEM. REF. DATA VOL 6 NO 2

C; 1977

C DATA SUBROUTINE FOR METHANE

Gy ( 1 ) == -2 . 0909747942Ef2

GV( 2 )=2. 64726921 81 E+2

G"v'(3)=-1. 47281 756 13E + 2

G'J(4)=4.7167401921EH

GV ( 5 ) =~9 . 491 8721 789E+0

GV(6)=1 .2199792872E+0

GV ( 7 ) = -9 . 62799355746E--2

GV ( 8 ) =4 . 274 151 6570E-3

GV ( 9 ) =-8 . 1 415307247E-05

GT(l)=:--2. 147621 3 125E + 5

GT(2)==2.1904610575Ei5

GT(3)=-8.6180973719E+4

GT(4)==1 .49609e6936E+ 4

GT( 5 )=-4. 7306603 177Ei2

GT ( 6 ) =-2 .3311 779643E+2

GT(7)==3.7784390759EH

GT ( 8 ) =-2 . 3204806092E+0

GT ( 9 ) -5 . 31 17637687E-2

EV(1)==-1 .0350606586E+1

EV ( 2 ) =4 . 2903609488E-2

EV(3)-1.7571599671Efl

EV(4)=6.1276818706E+3

EV ( 5 ) =-3 . 19391 8656E f

3

EV (6) =1.88730 11594Ei2

EV(7)=1.4529023444E+2

EV(8)=0.162

FV(1)==1. 6969859271

FV ( 2 ) = - . 13337234608

FV(3)=1.4

FV(4)=168.

FV(4)=168.

FT(1)=-.252762921

FT (2)= .3343285931

FT(3)=1.12

FT(4)=16S.

ET(1) -^-7.0403639907

ET(2)^-=.7442 1462902

ETC 3 )-12. 3 19512908

53
ET(4)^=2,220973B50:I.Ef3

ET ( 5 ) ^=-8 . S525979933E+2

ET<6)=72.83'5897919

ET<7)=--2. 97069 14540

ET(8)=^0.1628

C PARAMETERS FOR THERMODYNAMIC

C PROPERTIES •• MCCARTY y CRYOGENICS

C VOL 14 NO S MAY 1974 AND tvOODWIN

C NBS TECH NOTE 653 APRIL 74

R=^» 08205616

GAMMA^---,0096

GI ( 1 ) ==-1 . 8044750507Ef6

A ( 1 ) = .1 83603246 1 36Ef02

A( 2)=- -,182553840603E-01

A( 3)= , 5866238071 78E+00

A( 4)^ -.1060058946B3E-I02

A( 5)- »167157622432E+03

A( 6):= -.155569173217E+03

A( 7)=^ .106609415022E+03

A( 8)-= --,341087933790Ef02

A( 9)^^ .973203073452Ei01

A ( 10 ) = - , 38841001 838eEi02

A(ll)^= .529573454771Ei02

A (12)^ -.29107530473BE-i02

A (13)^= ,585307647478Ef01

A ( 14 ) = . 6372765321 86Ef00

A (15)^= 994444109622E-03

A(16)=== •-392314821657E -01 A (17)=^ 728820880748Ef00

A(18)n:: -.625821815315Ef01

A(19)=- 295561390641E+01

A ( 20 ) = - ; 763972649504Ef00

GI ( 2 ) ===7 * 7426666393Ef 4

GI(3) = ~l,3241658754EJ-3

GI(4)-1»5438149595E+1

GI( 5 ) =^-5 . 1479005257E-2

01(6)^=1*08091 72 196E-4

GI(7)--6.5501783437E-8

GI(8)=-- -6, 7490056 171E-fO

GI(9)- ,3Ei4

01(10)^4:7l( 11)^^0

TO ^=2 9 8 15

HO-19196.1

GI(IO)-==HO-HI(TO)

T0=300

S0=0.86 ,4854941

GKID---SO-SI(TO)

G( l)-= -.1870279976B5E-01

G( 2)=^ .1 03387 108009Ef01

G( 3)== -.155387625619Ef02

G(4)- 77231 1478564Ef03

G< 5):== -•.377103300895E+05

G( 6)== .846818843475E-03

G( 7)^ - 496415884529E+00

G< 8)== , 8699093524 14Ef02

G( 9)^ -•322821592493E+05

G(10)- • . 3 9 5 8 4 3 026 3 1

E - 4

G ( 1 1 ) - .266772318035E-01

G(12)^ -»304010057839Ef01

G(13)^ 191584507536E-03

G ( 1 4 )

--^-^ •.195587933458E-03

0(15):= .607479967879Ef01

0(16)=^ -»529609525984E-03

54
G (1. 7 )

^^^ , :I.S22642B<f>004E •• O''? G(18)^ -.:L 09952 182842E- 01. G( 19 /-^ . :I.91.395549929E:-03

G (20)^-: . 3 8 6 4 7 O 7> 7 4 6 E f O 5

G ( 2 1 )

^:-- - , 1 5 7 9 3 ;;Tf1 2 6 :i. 2 e + 7

G(22)::- .19l527014440:LEf03

G(23)==-- . :l6599608;l.629E + 07

G ( 24 ) - . 603051 14671 IE f 00

G ( 25 )

••::: . 3764851 62e08E + 02

G(26)=: .1255936e0622E-02

G ( 27 ) ^^ - . 3435700325 1 3E + 02

G < 28 ) = - . 5409450941 39E-05

G(29):^ .185622284663E-02

G ( 30 )

^=^ . 770786979245E -Oa G(31)= •- 2868683 18650E -OS

G ( 32 ) ^ . 372376961 647E-04

D T P== . 28 151 1438 1 423E + 02

DTPV:=. 1590041 545 160E~01

VP( 1):==4. 77748580

0P(2)^=1. 76065363

iv^PC 3)=: -.56788894

OP (4):= 1.32786231

0P(5)=1.5

OP (6)^:::. 1158993

0P(7)::^-90.68

VP(8)==190.555

OP (9)^^-0.0

TCC-0P(8)

PC(>=OPN ( TCC ) *1 .01325

PTP==0P(6))K1.01325

TTP^0P(7)

rUL=500.

TLL^TTP

PUL=350.

IiCC=:10.23

RETURN

END

SUBROUTINE DATA N2

DIMENSION G(32) !.0P(9) i-GKll ) DIMENSION 00(9) »GT(9) yF0(4) »FT(4) yE0(8) »ET(8)

DIMENSION A (20)

COMMON/CRIT/ EM» EOK » RM» TC i- DC> X -i PCir SIG

COMMON/SATC/A»DTPV

COMMON/DATAl /GO •, GT i FO , FT , EO s- ET

COMMON/SEN/BETA i-XOy DELTA V El » E2.' AGAM

COMMON/DA lA/G y R v GAMMA , OP y DTP y PCC y FTP y TCC y TTP y TUL y TLL y PUL y DCC

common/cpid/g:i:

COMMON/ ISP/NyNWyNUW

NWU=0

PRINT 100

100 FORMAT (* THE RANGE OF TEMPERATURE FOR NITROGEN IS 63.15 TO 1900K*

1/* WITH PRESSURES TO 10000 BAR*)

N=:0 * NW^^l

EM = 28.016 $ E0K^=118. $ RM=3.933E-08 $ TC^126.24

DC==.3139 $ X^^l. 67108 $ PC^33.98 $ SIG-<J.54

XO-0.164 * BETA-0.355 $ DELTA-4.352 % £1^-=2.17 * E2 = 0.287

AGAM- 1.1 90

c PARAMETERS FOR TRANSPORT

c PROPERTIES FROM HANLEY ET. AL

.

c JOUR. PHY. CHEM. REF DATA 00L3y NO

c 1974

G0(l)--1.81224240000E+2 % G0(2)-l.

G0(3)=-9.1^j42324494E+1 % G0(4):=---2.

9915327374Ef2

3255484059E+1

55
Gy(5)===-3.630721422B $ GV ( 6 ) -3, 645750681 IE J. GV ( 7 ) --2 . 226:1. 8808 1.7E-2 f GV ( 8 ) ^7 B053904895E -4

eg (9)=~ 1.1 894029 :l.04E-5

GT ( 1 ) =-2 , 0029573972E + 4 $ GT ( 2 )

••^=-4 9765746684E+3

GT ( 3 ) ==8 . 018B959378E+3 * GT ( 4 ) ==-5 . 502271 6888Ef3

GT(5)==1.5363738965Ef3 $ G T ( 6 ) --2 * 2974737257E + 2

GT(7)^=^1.9360547346Efl * GT ( 8 ) --8 . 5677385768E~1

GT < 9 ) ^=1 . 5564670935E-2

EV(l)==-9. 8255690362 $ Ek^ ( 2 ) ^-5 . 7156092139E •••001

E^/* ( 3 ) ^1 . 609461 1 148E+001 * EV ( 4 ) -3 . 69540861 58E f 003

EV ( 5 ) ==-8 . 088980 11 80E^i-002 $ Ei^ ( 6 ) ^-^6 . 8464435640E^f001

EV(7)^==-2, 1241135912 $ EU ( 8 ) ^^^0 . 315

F(J ( 1 ) :=- 1 .121 7739623 * F V ( 2 ) ^-^0 . 3291 23 1 7244

FV(3)^=1.4 $ Fiv'(4)-118.

FT ( 1 )

:==: . 53875666637 $ FT ( 2 ) - . 06102791 1 104

FT<3) = 1.2 $ FT(4)^-^118.

ET(l)=~2.9402951255E-fl $ ET ( 2 ) ::::3 . 7201743333E-tl

ET(3)=-3.9013509079Efl $ ET ( 4 ) ^::^-3 . 18261094B5E-f 1 C THERMODYNAMIC PROPERTIES FROM

C NBS TECH NOTE 648 - DEC 77

C JACOBSEN ET. AL.

R=8.20539E-2

GAMMA—-.0056

GI(1)= -0.735210401157252E 03

GI(2):= 0. 34223998041 1978E 02

GI<3)^= --0.557648284567620E 00

GI(4)= 0.350404228308756E 01

GI(5)=^ -0.1 733901 8508 1005E~04

GI ( 6 ) = 0.1 74650849766463E^07

GI<7)= -0.356892033544348E-11

01(8)^=== 0.100538722808834E 01

GI(9)= 0. 3353406 lOOOOOOOE 04

T0==298.15 $ 30-191.502 f H0:=^8669.0

GI(10)-=GI<11):=0

GI(10) = H0--HI(T0)

GI(11)^--SG-SI(T0)

G ( 1 )

:^ 0.1 36224769272827E-02

G( 2)- 0.1 703246990859 IE 00

G( 3)=^^ -0.24390072 1871 41 3E 01

G( 4):--= 0.341007449376470E 02

G( 5)^=^ -0. 422374309466 167E 04

G( 6):^:^ 0.105098600246494E-03

G( 7)== -0.11 259482652208 lE-01

G( 8)=^ 0.142600789270907E-03

G( 9)=^ 0.1 8469850 1609007E 05

G(10)= 0.811140082588776E-07

G(ll)^-= 0. 23301 1645038006E~02

G(12)- -0.507752586350986E 00

G ( 1 3 )

--= . 48502788193 1 2 1 4E-04

G(14)- -0.11 3656764 115364E-02

G(15):= -0.707430273540575E 00

0(16)=== 0.751706648852680E-04

0(17)==== •O, 111614119537424E-05

G(18)= 0.368796562233495E-03

G(19)= --0.201317691347729E-05

G ( 20 ) == -0 . 169717444755949E 05

0(21)== -0. 11 971 9240044 192E 06

0(22)= -0.975218272038281E 02

0(23)== 0.554639713151823E 05

0(24)== -0.179920450443470E 00

0(25)== -0.256582926077184E 01

0(26)== -0.41370 7 7 1 5 9 7 8 9 1.": - 3

G(27)= -0.256245415300293E 00

56
G ( 28 ) - -0 . 124222373740063E-()6

G(29)= 0, 1 03556^358401 6SE-04

G ( 30 ) == -O 5386991 66558303E.-09

G(31)- -0,757415412839596E-08

A( 1)- -. 158453465507E:i02

A( 2)=^^ . 41913691 1423E 01

A( 3)= -.101965371660^+01

A( 4):^- .134763743799E+ 02

A( 5)== -.109930399087E+03

A( 6)= .925518835497Ef02

A( 7)-^ -.956233831320E}02

A( 8)=:: .100104366710E+ 03

A( 9)::= ~.701857937398E+ 02

A (10)=^ 900076998647E + 01

A(ll)= . 286981 120347Ef02

A ( 12 ) == - . 21 676760 1780Ef02

A( 13)^- . 49655822647 lE + 01

A (14)== .218307928477E-f02

A ( 1 5 ) =^ •- . 126493309807E + 00

A(16)= .241544188633E+01

A( 17):= -.245256a71794Ef02

A ( 18 ) •=

. 9359252071 24E + 02

A ( 19 )

=-- - . 36093825 1632E+02

A (20)== . 75745327 1989E + 01

G ( 32 ) = . 5853671 7206952 1E--07

VF(1):=:5. 1113192094 % VP ( 2)=6 . 482667539E-1

VP(3)=-1 . 510873091 6E-1 % "^P ( 4 )=-7 . 4028493342E -1 'v'P(5) = 1.5 % VP(6)==.123 $ VP(7)==63.15 * VP ( 8 ) =126 . 26

VP(9)=0.0

D r P == .309 7 7 1 7 7414 7 7 E \ 2

D I PV:=:. 2428220857 lOE-1

TCC=^:VP(8)

PCC-iv'PN(rCC))i< 1.0 1325

PTP==^^P(6)*1.01325

TTP-lv'P(7)

TLL=riP

IUL=:1900.

PUL=: 10000.

DCC==11.21

RETURN $ END

SUBROUTINE DATA AR

D I MENS ION G ( 32 ) ? ^P ( 9 ) c G 1 (11)

DIMENSION 0^(9) !.GT(9) >F>J(4) yFT(4) tE«v'(8) ?ET(8)

DIMENSION A (20)

COMMON/SEN/BETA !.X0> DELTAS El V E2y AGAM

COMMON/SATC/AyDTPV

COMMON/CRIT/ EM» EOKv RMi- TC> DC » X x PC » SIG

COMMON/DATA/G » R r GAMMA » VP ? DTP » PCC i PTP » TCC » TTP ? TUL , TLL i PUL » DCC

COMMON/DATAl /GU » GT » FU ? FT i EU » ET

COMMON/CPID/GI

COMMON/ 1 SP/N ). NW i- NWU

NWUI=0

N: = $ NW==1

EM==39.948 * E0K:=152,8 % RM = 3.669E-08 % TC=::150.725

DC=::0 , 533 $ X== 1 . 7 1 24 * PC:=-47 . 983 % S I G = 3 . 297

X0-:0.183 % BETA=-0.355 % DELTA:-4.352 $ £1=^:2.27 *E2^0.287

AGAM=1 .190

C TRANSPORT PROPERTIES

C FROM l-IANLEY ET. AL

,

C J, PHY. CHEM, REF DATA ^Q\- 3

C NO 4 1974

GV ( 1 ) ==6 . 1 1 45472787E + 1

Gk,' ( 2 ) ==-- 1 . 039439031 2E + 2

57
G *^ ( 3 )

^- 6 . 7 5 9 4 6 1 4 6 :l. 9 1: }• 1 6^(4) =^-2 » 2;\)36S09380E f 1. GV(5)-4. 2593950138

GV ( 6 ) ::^-4 , 725267 1 ()93E- • 1. Gk^(7)-3,1795275425E-2

G'v' ( 9 ) ^- :l. . 16290B3780E -3 0^(9) -.-

:|. . 80430 1 0592E --S GT ( :l. ) ^-^^6 , 2777703742E+ 3 * C) T ( 2 )

^^ -9 6096376637E + 3

GT ( 3 ) -5 . 8887549 1 9:I.Ef3 % GT ( 4 ) -- J. . 8920926320E+3

GT(5)-3»4e86571437E{-2 $ GT ( 6 ) ^=^--3 . 801.678A:I.93EH

GT( 7 )-^2» 52072831.67 $ GT ( 8 )

^= -9 , ;1.098744478E-2

GT ( 9 )

---^1 3990842942E -3 EV( J. )-- 1.0010993993E + :l % E^v* ( 2 ) -2 » 0694685712E- J. Ek;(3)^:^:l.* 6029 :L 451. 22Ef:l. $ EV ( 4 ) =^1. , 1.71.7461.351E}-3

\z.y} ( 5 ) ^-5 * 6995898780E + 2 $ Ef ( 6 ) ^=^4 , 0136071.933E+1.

E^'(7)^3.98701.22403E + J. $ E^>( 8 )

^^-^ . 537

F>v'( 1)^=1. 4653652433 $ FV ( 2 ) ^^--0 . 77487424965

F'J(3)==^^1.4 $ F'^(4)=^::L52»8

FT (!)== 24142:10327 $ FT ( 2 )-. 075696234255

FT(3)^:^a* * FT (4)^152.8

ET<1)--2.4116686960E+1

ET(2):=^ 3. 069485997 lE + l ET ( 3 ) ^=2 . 2956551 674E + 3

ET(4)=^: --3«5559415848Ei2

C TRANSPOFv'T PROPERTIES FROM

C HANLEY ET, AL . J. PHY» CHEM REF

C DATA yOL 3 NO 4 1974 AND

C GOSMAN ET. AL. . NSRDS MON 27 1964

R^^-. 08205616

GAMMA— » 0055

g;i:( 1)^=01 (2 )==Gj(3)-o

GJ:(4)^^njI<9)===2.5

GI(5) =:G1(6)=-G1(7):::^0

Gl (8)^=0

G.I(10)^--G:[(11)=^0

T0=^87.28 $ S0-=129.1786 $ H0::=9504 . 8916

GI(10)^=H0-HI(T0)

GI(11)^-=S0-S1(T0)

G( 1 ) =^3. 434265724235 lE-3

G(2)=5.7857036681387E-2

G( 3 )=-2» 69824708 12264E+0

G( 4)^=1. 6481 655285291 E + 2

G ( 5 ) ^- 1 . 28494724204 16E+4

G ( 6 )

^:= -3 . 2636490894686E-4

G(7)=--:2.4629470190841E-1

G ( 8 ) ^-6 . 9585445697842Efl

G ( 9 ) = 1 . 9 1 96 1 56939788E+4

G(10)^1.6603909805594E-5

G( 11)=- 1.08603 16345366E -2

G (12 ) ::^=3 . 323 1 759004885E + G( 13)^2. 177636 1947053E-5

G(14)==5.16150B5812771E--3

G( 15):=---! . 1366705407293E+0

G(16)^^^-2.9018517618859E-4

G ( 17 ) =3 . 7898289698060E -6 G( 18)^-=1 . 1030489790987E-3

G(19)-=-1.4674092942955E -5 G ( 20 ) =- 1 , 14796 1 07161 79E+4

G(21 )==-3.9393312963830E+5

G ( 22 ) =:-9 . 9620084307336E+

G ( 23 ) --- 1 . 857534704601 lE+4

G ( 24 ) --=-2 . 939348387 1 1 36E -

G ( 25 ) = 1 6408588086762E f

58
G ( 26 ) ^ -4 . 04471 7422935;^E:-4

G ( 27 )

^^ - 2 . 08200071 65976Ef

G ( 28 ) :^:-5 > 496V320649612E-7

G ( 29

)

=7 * 51 37405277667E-5

G ( 30 ) = -2. 86674255 18207E- 10

G ( 31 ) ^-6 . 3003722866B34E--8

G (32) - 2 * 5 2 8 7 4 1 34409 3 6 E -

6

A( 1)= -.270262923777Ef02

A( 2)^:- . 131 040241 B66E-I00

A( 3)^^^ -26748<S^3B128E + 01

A( 4)==== .300176804406E + 02

A( 5)^==^ -, 875899 149326E + 02

A( 6)-^- -

. 408267436456E + 02

A( 7)^ .1 0426806645 lE+03

A( 8):::: •»671278555379EI-02

A( 9)::^: , 151002935701Ei02

A< 10)::^ «331243536637E-f02

A ( 1 1 ) ^-

: 63314621 258 1 Ef02

A( 12^^^^ •.427149706899E-i-02

A (13)^^ 100599900030Ef02

A (14)=:=^ . 137682084900Ef02

A( 15)^^ -.664630363191E-01

A (16)^ .13336B782730Ei01

A (17)=^ -. 144371463244E-I02

A ( 18 )

^^- . 601938472000E}02

A ( 1 9 )

^-^ - . 23088B463B87Ef02

A (20)=: .465318358887E+01

yp( 1 )::-3. 4151115519 $ UP(2):=::1 . 1910812519

VP(3):^-3.407632334E-1 * MP ( 4 ) -M:}. 9555855251E - 1 yp(5)^=l»5 % VP(6)::=»68005 * VP ( 7 ) ^^=83 < 80 % VP ( 8 ) ^^^150 , 86

VP(9)=0.0

DTP==. 3540027619 188Ef02

DTPV- . 1029227022329

PFv-INT 100

100 PORMAK* THE TEMPERATURE RANGE EOR ARGON .IS 83.8 TO 400 K*

1/* WITH PRESSURES TO 1000 BAR*)

TCC=:'v'P(8)

PCC::^UPN(TCC)*1 .01325

PTP=VP(6)*1. 01325

TTP-^^P(7)

TUL:--:400. TLL-=TTP

pui...=aooo.

DCC^13.41

RETURN * END

SUBROUTINE DATA 02

D I MENS I ON G ( 32 ) s- VF' (9)1- G 1 (11)

D 1 MENS 1 ON G V ( 9 ) > GT ( 9 ) ? F'J ( 4 ) . FT ( 4 ) 7 EM ( 8 ) » ET ( 8 ) DIMENSION A (20)

COMMON/SATC/A»DTPV

COMMON/DATA 1 /G>J , GT » PV i FT i EV ? ET

COMMON/SEN/BETA i-XO 7 DELTA* Ely E2!' AGAM

COMMON/CRIT/ EMr EOK » RMv TC* DCs- X y PC y SIG

COMMON/DATA/G y R y GAMMA y UP y DTP y PCC y FTP y TCC y TTP y TUL y Tl. L y PUI... y DCC

COMMON/ ISP/NyNWyNWU

COMMON/CPID/GI

NWW^O

N==0 $ NW--=1 X0=0.183 % BETA:=0v355 % DELTA:=4.352 $ El -2. 21 * E2:=0.287

EM = 31.9988 $ E0K:^113.0 $ RM::=3 . a896E -08$ TC==154,575

DC-=0.4362 * X:=:2.210636 $ PC^-:49.770 * 810 = 3.437

AGAM = 1.190

TRANSPORT PROPERTIES

59
FROM HANLEY ET. AL

VOL. 3f NO 4f 1974

GV ( 1 ) ^=-9 . 7076378'593Ef:l.

GV(3)=-2.4668758B()3E + 1 $

GV(5)-^3»78S1049522E 1 $

6>v'(7)=-1.1134441304E-2 $

Gy < 9 ) = 1 . 027937964 lE-5

GT (1 ) :==-2 . 0395052:1. 93Ef^

GT(3)=-- 1.20141 751 83Ef5

GT ( 5 ) = -5 * 4244239598E+3

GT ( 7 ) =-3 . 285482 1539E+

GT(9)=~1 .46109B6820E~2

EV< 1)=~ 1.21 523870 17E-H

Ey(3)=1.82011614A8E+l

E'v'<5) = -2.7498956948E + 3

£V(7)==1.1911504104Ef2 $

FV<1)=4. 3526515153 $ FVC

F>v'(3) = 1.4 $ FV(4)^=100.

FT(l)-=.3060 $FT(2) = ,: FT(3) = 1.12 $ FT (4) ==100,

ET(1):^-1.2310400765E + 1 * ET(3)=-2.9944878721E+3 $

% GV ( 2 ) -8 . 280 1254201 Ef

GU(4)==2. 1324360243

GV(6)-=-l .0487216090E-1

Gk; ( a ) =-5 . 3676093757E -4

$ i:

GT ( 2 ) -2 . 4088 1 4 1 709E+5

GT ( 4 ) -3 . 2954949 19E+4

GT (

) ^5 . 4734865540E+2

GT(8)-= 1.0753572 103

EV(2)=:-3.1421728994E-:

:V(4):^2.7390429525Ef2

EV ( 6 ) =--2 . 4340689667E + 2

EV(8)-.435

)= -2.0361263878

785

ET(2)=: 1.679950426 lE + 1 ET ( 4 ) =4 . 7350508788E+2

c THERMODYNAMIC PROPERTIES

c FROM WEBER - TO BE PUBLISHEB

R=8.20L 39E-2

GAMMA— .0056

GI(l)-- -0.498199853711943E 04

Gl(2)= 0.23024777999521 BE 03

GI(3)= -0.345565323510732E 01

GI(4)"- 0.3521876773671 16E 01

GI(5)= ~0.435420216024420E 04

GI(6)= 0. 134635345013 162E--07

GI(7)= 0.162059825959105E -10

Gl(8)= 0.1 031 4685 1572565E 01

GI(9)= 0.223918105000000E 04

GI(10)==GI(11)=0

TO-298. 15 $ H0=8682. $ S0=-205.037

GI(10)=^HO-HI(TO)

G ( 1 ) = -.4308768468E-03

G ( 2 ) = .1979591095Ef00

G(3) = -.4143014968Ef01

0(4)-^ .1853654396E+03

G(5) = -.1270637452E+05

G(6) = .1536388737E-04

G ( 7 ) = .1326068945E-02

(3(8) - -.21 99275 123E+01

G(9) = .4705445127Ef04

G(10)= .47281 980 17E-06

G ( 1 1 ) = . 24304081 98E-02

G(12)= -.1896759615E+00

G<13)= -.6887067207E-05

G ( 1 4 ) = -.61 32885 180E-03

G(15)= -.1836518694Ef00

G(16)= .2575663871E-04

G ( 1 7 ) = -.2415604646E-06

G(18)- .1438680B31E-03

G(19)= -.1703915986E-05

G(20)= ~.2353705917E+04

G(21>= -.2271707669Ef06

0(22)^:=^ -.275381 547 lE+02

G(23)= .9277648729E+05

G(24)= -.4114926856E-01

G(25)= .1982233262E+01

60
G ( 26 ) = ~ . 1239651 1 42E-03

G(27)= -.6322588664Ef00

G(28)= -.2443207666E-07

G(29)= .1328704370E -04

G(30)== -.1146313812E-09

G(31)= -.1021169305E-07

0(32)=:^ .2334998237E-06

GI(11)-B0-SI(T0)

A( 1)==^ .581394753076Ef02

A( 2)= -. 490241 196133E-01

A( 3)^^ 168328893252Ef01

A( 4)=-- ~.325161223398E+02

A( 5)= .55()300989872E + 03

A( 6)= ~.510968506115Ei03

A( 7)= .315091559049E+03

A( 8)- •-232566659258E + 02

A( 9)== -,488425479359E + 02

A(10)= ~.150624217523Ef03

A(ll)= .280441 60385 lE+03

A(12)-^= -.1 76693896861 E+03

A(13)== ,403247747449E + 02

A( 14):^^^ .252198688365E + 01

A (15)= -.136098316472E-01

A (16):= .28231 61 59403E+ 00

A(17)=^ -.286645905341E + 01

A (18):= .617024212284E+ 01

A(19)= -810220795462Ei00

A(20)= ~.279601068969E+00

ypd) =7. 568956 $ VP ( 2 ) =^5 . 004836 $ VP ( 3 )::=-2 . 137460

VP(4)=3. 454481 $ VP ( 5 ) = 1 . 514 * <JP ( 6 )

^^^^ . 0014606

yp(7)=54.359 * 'v'P(8)-154.581

yp(9):=0.0

DTP:=.4081997364372E + 02

DTPV=.3318894767078E-03

PRINT 100

100 FORMAT (* THE TEMPERATURE RANGE FOR OXYGEN IS 54.359 TO 400 K*

1/* WITH PRESSURES TO 1200 BAR*)

TCC-yp(8)

PCC--^VPN(TCC)*1 .01325

PTP = ^;P(6)*1.01325

TTP=VP(7)

TUL=400.

TLL=TTP

PUL:=1200.

DCC=:13.63

RETURN $ END

SUBROUTINE DATA P H2

D I MENS I ON G ( 32 ) ? VP ( 9 ) y 1 ( 1 1

)

DIMENSION GV(9)»GT(9) ,Fy(4) .FT (4) »EU(8) »ET(8)

DIMENSION A (20)

COMMON/SATC/A»DTPy

COMMON/CPID/GI

COMMON/GRIT/ EMv EOKi- RM y TCr DC t X , PCs- SIG

COMMON/DATA/G r R f GAMMA , WF y DTP ? PCC y FTP y TCC y TTP y TUI... v TLL y PUL y DCC

COMMON/DATAl /Gk/* y GT y FV » FT y E'J y ET

COMMGN/PARA/PERCEN

COMMON/ISP/N

N=l

GO TO 1 ENTRY N H2

N=2

GO TO 1 ENTRY H2

61
N-3

GO TO 1 ENIRY E H2

N=:4 GO TO 1 ENTRY F H2

N-~-^5 1 CONTINUE

c NO TRANSPORT PROPERTIES FOR HYD

c THERMODYNAMIC PROPERTIES FROM

c RODER AND MCCARTY IR 7S-814 AND

c IR 74--3S7

R=.081>05616

GAMMA=^-»0041

G( 1) - 4.614387755654E-4

G( 2) --- 4.2331845S6086E-2

G( 3) =-5,096556226503E-l

G( 4) - 2.923059738269E+0

G( 5) —2. 98760914721 IE fl

G( 6) = 1.883148601410E-5

G( 7) =-1 .322256954639E-3

G( 8) = 3.016504431701E-1

G( 9) = 5.093705560851E-I1

G(10) = 1.973828324919E-7

G(ll) ^ 2»858492039828E--4

G ( 1 2 ) ="-2. 228279239 123E-2

G(13) —2»257481136764E-6

G(14) = 2.414272369746E-5

G(15) =:-1.6957133985a8E-3

G(16) =-5. 39367639 1275E-7

6(17) - 3»998955244328E-9

G(18) -- 1.142457561274E-6

G ( 1 9 ) —1 »25256622S896E-8

0(20) =-4.917861934882£H

G(21) =-1 .585666017368E+2

G(22) =-1 .901602946272E-1

G(23) - 9.198020862500E-f0

0(24) =-3.180455518810E--4

0(25) - l»191057791926E-3

6(26) =-3»7913!52773225£-7

G(27) =-3,983377699095E-5

G(28) -=-1.234510854688E-10

G(29) - 1.950266293499E-9

0(30) :=-2. 38034391 7 109E-13

6(31) =-4 073576608 192E~1

A( 1) = .9166177201B7E+02

A( 2) =^ -.179492524446E+00

A( 3)^ .454671158395E+01

A( 4) == -»658499589788Ei02

A( 5) = .734466804535E-f03

A( 6) == -.682501045175Ei03

A( ?) .631783674710E+03

A( 8)^= -»539408B73282E+03

A( 9)^ .430923811783E+03

A(10)^= -. 30029573881 lE+03

A ( 1 1 ) .156567165346Ef03

A(12) =•=^ -.504103608225E + 02

A(13) = .720706926514E+01

A(14)-= -.1 239444403 18E+03

A(15) .1 40334800 142E+01

A(16)-•= -.211 0238043 13E + 02

A(17): .173254622817Ef03

.A(.1f!)-= -. 44429458087 lEf 03

;OGEN

62
A(19)^-: .1386?936S355Ei03

A (20)^^: -. 231^774 J. 6101 5E:f 02

G(32) ^^ 8.801354930777E-12

UP( 1)^-3.05300134164

VP( 2)^^=2. 808 109258 13

VP(3)=-0. 655461 2 16567

MP(4)=:1. 59514439374

VPC 5):=^ 1.58 14454428

VP(7)-13.a

yp(6)=^0.0695

'v'P<8)==^32.938

Vp(9)::.0

DTP^,3821428945438E+02

i:iTPV=:^*6322296353698E 01

EM=^2. 01594

PRINT 100

100 FORMAT (* THE TEMPERATURE RANGE FOR HYDROGEN IS 13.8 TO 400 K*

1/* WITH PRESSURES TO 1200 BAR*)

TCC::::VP(8)

PCOVPN ( TCC ) * 1 . 1 325

PTP^::VP(6)>K1.01325

TTP^-^^VP(7)

TUL^:=400. TLI.J-TTP PUL=^1200.

DCC=^=15.556

RETURN

END

S U B R U ) I N E. P R P S ( F P y D D j- r T ) C THE 32 TERM EQUATION OF STATE » INPUT IS DENSITY ( MOLES /L ) i- C TEMPERATURE(K) !- OUTPUT (PP) IS PRESSURE IN ATM i- OR DP/DD IN

C; LITER -ATM/MOLE OR DP/DT ATM/K OR SHHjOR C^^ AT ONE LIMIT OF

C INTEGRATION

DIMENSION X(33)

D I MENS I ON B ( 33 ) !> G ( 32 ) EQUIt^ALENCE ( B -- X ) COMMON/DATA/G , R ? GAMMA

COMMON/ 1/B

DATA(ID:^::1 ) DATA(IZ-^l)

1 CONTINUE

IF(IZ.LE.0)G0 TO 2

IZ==0

2 CONTINUE

D=DD

p=::pp GM^GAMMA

D2=D*D

D3=a.i2*D

D4-D3*D

D5:^=D4>KD D6^D5*D

D7 = D6)KD

D8^^^ai7*D

D9=:D8*D

D10=D9*D

D11^^D10*D

D12^=:D11*D

D13^:^D12*D

TS:^=:SQRT (T)

T2==T)KT

T3=^=^T2*T 63
T4==r3*T

T5=^T4*T

F^^-^EXP (GM*ri2)

GO 1(3 (^00»200^.30()!'400»500v600r700) vK

ENTRY PRESS

C ENTRY FOfOR F'RESSUREs. INPUT

C AND TEMP. IN MOI.../I... AND K?

GO TO 1 :100 CONTINUE

B( :L)==D2>KT

B( 2)-^D2*TS

B( 3)^^D2

B( 4)^-D2/T

B( 5)^=D2/T2

B( 6)=D3*T

B( 7)=a:i3

B( B)==D3/T

B( 9)-D3/T2

B(10)-=D4)KT

B(l:l. )-^^a;i4 B(12)==D4/T

B(.13)=:D5

B(14):^=D6/T

B(1!5)=^^'D6/T2

B(16)==D7/T

B(17)=D8/T

B(18)='D8/T2

B(19)^-:D9/T2

B(20):=D3*F/T2

B(21)^=D3*F/T3

B(22)==D5*F/T2

B(23) =D!5*F/T4

B(24)=--^D7*F/T2

B<25)=D7*F/T3

B(26)=-D9*F/T2

B(27)==D9>KF/T4

B(2a)=Dll*F/T2

B(29)=D.1.1*F/T3

B(30)^^D13)KF/T2

B(31)^=D13*F/T3

B(32)=:D13*F/T4

IF (ID. GT. 0)00 TO 102

IS DENi

OUTPUT

ITY

IS IN ATM,

B(33)-P-R*D*T

RETURN

102 P=0

DO 101 I:^::1?M 101 P^-P+B(I)*G(I)

P-=PfR)!<D*T

pp:.:p RETURN

ENTRY DPDD

c PARTIAL OF PRESSURE WIT

c DENSITY -- SEE PRESSURE

c ENTRY FOR UNITS

K=^2 GO TO 1 200 CONTINUE

Fl-2,.00*F>i<GM*D

r- 2 1 =^ 3 . * F * D 2 + 1- J. * D 3

F22-S.000*F*D4 iFl*D5

f 2 3 - 7 . * F * D 6 + 1 1 * D 7

•I RESPECT TO

64
F24-=-=9 .000*1- )KD8 +F1*D9

I" 2 5 ^- 1 1 .00* I" * D 1 f I- 1. * D 1

1

F26===13.00*F*D12 + Fl>KD:l.3 B( 1)-=:2.00*D*T

B( 2):==2.00*i:i*TB

B( 3)----2,00^l\

hi 4) :==2.00*D/T

B( 5)=--^2<,00*li/T2

B( 6):=3.00*D2*T

B( 7)-3.00*D2

B( 8)===3.00*D2/T

B( 9)=--3.00*i:i2/T2

B(10)-=4.00*D3*T

B(11)-4.00*D3

B(12)^4.00*D3/T

B (13) -5. 00*04

B(14)---6,00*05/T

B(15)--==6.00*0'5/T2

B(16)=--7.00*06/T

B(17)=8.00*07/T

B(:l8)=::=8.00*07/T2

B( :19)=:^9.00*DS/T2

B(20):==F2:L/T2

B(2:L)^=F21./T3

B(22)=F22/T2

B(23)-F22/T4

B(24)-F23/T2

B<25)==F23/T3

B(26)^F24/T2

B(27)-F24/T4

B(28)-F25/T2

B(29)=t.F25/T3

B(30)-==F26./T2

B(31):==F26/T3

B(32)==T-26/T4

M-32

IF(:i:O.GT.O)GO TO 202

B( 33 )=:p-R*T

RETURN

202 F-^0 00 20.1. I^-^ls-M 201 p:=-P + B(I)*G(;i:)

p==pfR*r

pp=p

RETURN

ENTRY OPOr

c PARTIAL OF PRESSURE UII TH RESPECT

c TO TEMPERATURE - SEE F RESSURE

c ENTRY FOR UNITS

K<i

GO TO 1 300 CONTINUE

X( l>-02

X( 2)-==D2/(2.00*TS)

X( 3)^=^0

X( 4)^-02/T2

X( 5) —2.00*02/T3

X( 6) -03

X( 7):^-=0 X( 8)===-D3/T2

X< 9)^-2.00*03/T3

X(10)=04

X(11)==0

65
X( 1.2)— 1:14/12 X< 13)^=0

X(1.4)—-D6/T2

X (15) --2. 00*1.16/13

X(16)^^=-D7/T2

X(17)^^=-DB/T2

X<18)^^^-2»00*DB/T3

X(19)=^-2.00>KD9/T3

X(20)^=-2.00>KD3>KF/T3

X<2:l)^^^--3.00*D3)KF/T4

X(22)^^:^-2.00*DS*F/T3

X ( 23 ) =^-4 . 00)f<D5)KF/T5

X ( 2 4 ) ^^ 2 ,00* B 7 * F / T 3

X(25)::^>-3»00*i:i7*F/y4

X ( 26 ) "—2 * 00*D9*F/T3

X ( 27 )

^^-^ --4 00)KD9>KF/T5

X ( 2 8 ) ^ - 2 * D 1 1 * I-- / T 3

X ( 2 9 ) - ••• 3 * .D 1 1 * I" / r 4

X ( 30 ) ^^-2 . 00*1:1:1. 3*F/T3

X ( 3 1 ) ^ 3 . * n :L 3 * F / T 4 X (32)—4.00*0 :l.3*F/T5

:i:f(]:lugt.o)go to 302

X(33)^F-'P-R*D

RETURN

302 P==^0 DO 301 1^1 v32

301 P=-PfG(I)*X( 1)

PP=^^PiR*D

RETURN

ENTRY DS:ON c part:i:al. of entropy with

C RESPECT TO THE G CaEFF:i:(nENTS

!<.•:= 4

GO TO 1 400 cont:[nue

c s=so-r*logf ( d*r*t/p0 ) f ( i1s.dn ( d ) -dsdn ( 0) ) *101 32s +cp0s ( t ) G1=:F/(2,00*GM)

02- ( F*D2-2 <, 00*G1 ) / ( 2 , 00*GM ) 03=^ ( F*D4~4 . 00*02 ) / ( 2 . 00*GM ) G4=== ( F*D6 -6 * 00*G3 ) / ( 2 . 00*GM ) G5= ( F*D8 -8 . 00*04) /( 2 » 00*GM

)

06== ( F*D 10-10, 00*05 ) / ( 2 . 00*GM ) X( I)::-—

X( 2)=^:=-D/(2,00*TS)

X( 3)=0,D0

X( 4)=fD/T2

X( 5)::^:2,00*i:i/T3

X( 6):==-i:i2/2.00

X( 7)===0.D0

X( 8)=^i:i2/(2.00*T2)

X( 9)::=D2/T3

X(10)=--=-D3/3.00

X(ll)=^-=0,ri0

X(12)==D3/(3.00*T2)

X(13):=0.ri0

X(14):==D5/(5.00*T2)

X ( 1 5 ) == 2 . 00*115/ ( 5 . 00*T3 ) X(16)===D6/(6.00*T2)

X(17)==D7/(7.00*T2)

X ( 18 ) -2 . 00*ri7/ ( 7 . 00*T3 ) X(19)-=DB/(4.00*T3)

X(20):=2,00*61/T3

X(21)==3.00*G1/T4
402

401

500

X(22)

X(23)

X(24)

X(25)

X ( 26

)

X(27)

X ( 28

)

X(29>

X(30)

X(31)

X(32)

IF (ID

RETIJR

DO 40

P = P + G PP = F- RE- TUR

ENTRY

TERMS

GO TO

CONTI

H==^H0f + (P/D

G2=(F

G3==(F

G4^(F

G5^=(F

06=^ (

F

X( 1)

:::^2,00*G2/T3

^=4.00*G2/T5

^-^2.00*G3/T3

••:^3. 00*03/ 7 4

==2.00*04/7 3

^:^4,00*G4/T5

=^2.00*G5/T3

=:=3.00*b5/T4

^2.00*G6/T3

^^•=3.00«06/T4

=:4.00*06/T5

,GT«0)GO TO 40: N

1 1^1. y 32

( I)*X( I )

DUDN

NEEDED FOR ENTHALPY CALCOLATION

1 NUE

< r *DSDN ( D ) --DSDN ( ) ) * 1 1 -•R*T)* 1.0 1.325

(2.00*GM)

*D2- •2 . 00*01 ) / ( 2 . 00*0M ) *D4-4 . 00*02 ) / ( 2 . 00*GM

)

*D6-6 . 00*03 ) / ( 2 , 00*GM ) *D8 -a . 00*04 ) / ( 2 . 00*0M

)

3251 ( DUDN ( D- DUDN ( ) ) * 1 1 . 325 + CPOH ( T

)

*D10-10 . 00*05 ) / ( 2 . 00*0M

)

=--D*T X( 2)^-D*TS

X< 3)^-::D X( 4)-D/T

X( 5)=::D/T2

X( 6)-=D2*T/2.00

X( 7)=D2/2.00

X( 8)-=D2/(2.00*T)

X( 9)=D2/(2.00*T2)

X(10)-=D3*T/3.00

X(ll)==D3/3.00

X(12)==D3/(3,00*T)

X(13)=D4/4.00

X(14)==D5/(5.00*T)

X(15)=D5/(5.00*T2)

X(16)::=D6/(6.00*T)

X(17)=-==D7/(7.00*T)

X<1B)^-=D7/(7.00*T2)

X(1V)=D8/(B.00*T2)

X(20)=G1/T2

X(21)=G1/T3

X(22)-:G2/T2

X(23)==G2/T4

X(24)^03/T2

X(25)=G3/T3

X(26) =^G4/T2

X<27)=^G4/T4

X(28)=G5/T2

X(29):=G5/T3

X(30)=G6/T2

X(31)==G6/T3

X(32)===G6/T4

67
IF(ID.GT.O)GO TO 50 '!> RETURN

502 P=0

DO 501. :i:-i>32

501 P=P+G(I)*X(I)

PF-P

RETURN

ENTRY TDSDT

C TEMP. TIMES THE PARTIAL OF

C ENTROPY WITH RESPECT TO TEMP.

K=:6 GO TO 1 600 CONTINUE

C CV=^CVO+(Ti:iSDN(/)-Ti:iSDN(D) )*10

G1=F/(2.00*GM)

G2-(F*D2-2.00*Gl)/( 2.00*GM)

G3=(F*D4-4.00*G2)/( 2.00*GM)

G4=(F*D6-6.00*G:5)/( 2.00*GM)

G5=<F*D8-8.00*G4)/( 2.00*GM)

G6= < F*D1 0-.1.0 . 00*G5 ) / ( 2 . 00*GM ) X(1):=0

X< 2)=~D/(4.00*TS)

X<3)=0

X( 4)=:2.00*Li/T2

X< 5)=6.00*D/T3

X(6)=0

X(7)=0

X< 8)=D2/T2

X( ?)-3.00*D2/T3

X(10)==0

X(ll)-:=0

X(12)=^ (2.00*r.i3)/(3. 00*T2)

X(13)=0

X(14):==(2.00>KD5)/(5. 00*T2)

X<15)==(6.00*D5)/<5. 00*T3)

X(16)=D6/<3.00)KT2)

X(17)=(2.00*D7)/(7. 00*T2)

X(18)-=(6.00*D7)/(7. 00*T3)

X(19) = (3.00*ri8)/(4. 00*T3)

325

602

601

X<20)=6.000*G1/T3

X(21)=-12.00*G1/T4

X(22)=6.000*G2/T3

X(23)==20.00*G2/T5

X(24)=6.000*G3/T3

X(25)=12.00*G3/T4

X(26)=6.000*G4/T3

X(27)=20.00*G4/T5

X(28)=6.000*G5/T3

X(29)=12.00*G5/T4

X(30)=6.000*G6/T3

X(31)=12.00*G6/T4

X(32)=--20.00*G6/T5

IF(IIi.GT.0)G0 TO

RETURN

P=0

DO 601 1=^1 >. 32

P=P+G(I)*X(I)

PP=P

RETURN

ENTRY DP2D2

SECOND PARTIAL OF

RESPECT TO DENS IT

K=7

602

PRESSURE WITH

Y SQUARED

68
GO TO 1 700 CONTINUE

F1-=2.*F*GM*D

F12=:2.*F1*GM*D + 2.*F*GM

F212= ;j.*Fl*D2f;i.*2.*D*F + F12*D3 + Fl*3.*D2

F222 = 5 *F1*D4 +5 . *4 . *D3*F f 5 . >KD4*FlfF12*D5

F232=7 . *F 1 *D6 + 7 . *6 . *Ei5*F + 7 . *D6*F 1+F 1 2*07

F242=9.*F1*D8+9.*8.*D7*F+9.*D8*F1+F12*D9

F252=11.*F1>KI:i10+:L0,*11.*D9*F+11.*D10*F1+F12*D11

F262=13.*F1*D12+13.*12.*D11*F+13»*D12*F1+F12*D13

B(1)=2,*T $B(2)^2.*TS $ B(3)^-==2.

B(4)=2./T $ B(5)=2./T2 i B(6)-6.*D*T

B(7)=6.*D $ B(8):=:6.*D/T $ B(9)=6.*D/T2

B(10)=^12.*D2*T $ B(ll)=12.*Ii2 $ B( 12 ) = 12 . *D2/T

B(13)=20.*D3 $ B(14)=30»*D4/T * B( 15 ) =30 . *D4/T2

B(16)==42.*D5/T $ B( 17 ) =56 *D6/T $ B ( 18 ) =56 »*ri6/T2

B(19)=72.*D7/T2 $ B ( 20 ) =F212/T2 $ B ( 21 ) =F212/T3

B(22)=F222/T2

B(23)=F222/T4 $ B( 24 )=F232/T2 $ B ( 25 ) =F232/T3

B(26)=F242/T2 $ B ( 27 ) =F242/T4 $ B( 28 )=F252/T2

B(29)=F252/T3 $ B ( 30 ) =F262/T2 * B ( 31 ) =F262/T3

B(32)=F262/T4

M=32

IFdD.GT.OGO TO 702

B(33)=PF

RETURN

702 P=0

DO 701 1=1 »M 701 P = P + B(1)>KG<1)

PP = P RETURN

END

FUNCTION VPN(TT)

C CALCULATES VAPOR PRESSURE IN ATMOSPHERES

C FOR AN INPUT TEMPERATURE IN KEH^IN

DIMENSION G(32) , VP ( 9

)

COMMON/DATA/G ? R f GAMMA r UP

T = TT

X= ( 1 -VP ( 7 ) /T ) / ( 1

. -UP ( 7 ) /UP ( 8 )

)

UPN=UP ( 6 ) *EXP ( UP ( 1) *X+UP ( 2 ) *X*X+UP ( 3 ) *X**3+UP ( 9 ) *X**4+UP ( 4 ) *X*

1<1.-X)**UP(5)

)

RETURN

END

FUNCTION FINDTU(POBS)

C ITTERATES THE UAPOR PRESSURE EQUATION

C FOR A TEMPERATURE ( IN KELUIN)

C GIUEN AN INPUT PRESSURE IN ATMOSPHERES

COMMON/DATA/G » R » GAMMA y UP 7 DTP

DIMENSION G(32)i.UP(9)

T=UP ( 8

)

DO 7 1 = 11-10

P=UPN(T)

IF ( ABS ( P-POBS ) - . 000001 *POBS ) 8 y 8 i- 6

6 CONTINUE

CORR= ( POBS-P ) /DPDTUP ( T

)

7 T=T+CORR

8 CONTINUE

FINDTU=T

RETURN

END

FUNCTION CU(Di'T)

C CALCULATES SPECIFIC HEAT CAPACITY

C AT CONSTANT UOLUME FOR AN INPUT

69
C OF DENSITY AND TEMPERATURE IN MC)I.../L AND K DATA(F^=8.31434)

DD^^^ai

TT::::T CALL TDSDT(CDvDD5.TT)

DD==0

CALL TDSDT(COvDDvTT)

CU^^CF'I ( TT) + < CO-CD ) *101 . 325

CV=-CU-R

RETURN

END

FUNCTION FIND D ( P ? T

)

C ITTERATES EQUATION OF STATE

C FOR DENSITY r Olk^EN PRESSURE

C AND TEMP. IN ATM. AND KEL>^IN, IF

C ITTERATION FAILS TRY USING

C FUNCTION CALLED FIND M

D I MENS I ON G ( 32 ) >. VP < 9 ) COMMON/DAT A/G r R ^ GAMMA y ^^P v DTP y PCC ? PTP r TCC y TTP v TUL ? PUL ? DCC

IF(TT.GT»VP(8))G0 TO 100

I F ( P » G I U P N ( I T ) ) (3 T 1 1 DD=^SATy(TT)

GO TO 102

100 PC^=PCC/ 1.01 325

X" ( 1 , 1 / ( 9 . *PC ) ) *P f .7/9,

DD=:=^P/(R*T*X)

I F ( P/PC . GT . 20 . . AND . T/VP ( 8 ) . LT . 2 . 5 ) DD^=-DTP

GO TO 102

101 DD^^=^SATL(TT)

102 CONTINUE

DO 10 I = -ly50

I F ( DD . LE .0.0. OR . DD . G I . 50 . ) GO 70 1

CALL PRESS (PP^DDvTT)

IF ( PP. LE. 0.0) GO TO 11

P2=PP

IF ( ABS ( P-P2 ) -1 . E -7*P .) 20 v 20 , 1

1 CALL DPDD(PPi.DDyTT)

IiP=.pp

C0RR=(P2-P)/DP ~^^

IF ( ABS ( CORR ) -1 . E -/^DD ) 20 ? 20 v 10

10 DD^aiD-CORR

11 CALL REGULA(P»DD!'T)

20 FIND D=DD

RETURN

END

SUBROUT INE REGULA ( P I y DD ? TT

)

C ITTERATES EQUATION OF STATE FOR DENSITY WHEN FIND D FAILS

DIMENSION G(32)yMP(9)

COMMON/DATA/G > R r GAMMA y VP y DTP y PCC y PTP y TCC y TIP y ) UL y TLL y PUL y DCC

T::::TT P-^PI

D2 = IF(T.LT.TCC)GG TO 10

DO=DCC*TCC/T

GO TO 20

10 PP=k;PN(T)

IF(P.GT.PP)GO TO 15

DO=SAT"v'<T)

DO 11 1=1 y 150

CALL PRESS(POyDOyT)

IF(PO.GE.P)GO TO 12

11 Do^^a:io-i-.oooi*Do

70
GO TO 42

12 D1--^D0 13 CALL PKEH

IF(Pl»LTv

>S<P1

P)Gi)

vDl vT)

14

IF(D1,LE:. 1*P TP)GO TO 42

D0 = D1

Z^(P1-P)/P

IF(Z,LT,

.

l)Z--= .1 IF(Z.GT» 9)Z=^ .9

D1^D1-Z*D1

GO TO 13

14 CALL PRE!: DO 140 ID==i:il P3^P1ii;>(PO

= ly50

• DO ,J)

1F(ABS(P- 1 1 ) . LT. .00001*P)GO TO 40

P2=:p-pi

Dl=ril+<D1 -D0)*P2 /(Pl-PO)

:i:f(abs(d--Dl) . LE. . 00001 )KD) GO ro 40

1F(ABS(P--PI) .> LT. . 005*P)D2 ...p] ND M (

F-' yT.Dl)

1F(D2,GT. 0.0. AND .D2.LT.S0 . )D1:=D2

D2=0

CALL PRESS ( PI yDl

IF(P0.GT.P.AND.F

IF(P0.Lr.P.AND.F

GO TO 140

120 P0^-P3

DO-^D

140 CONTINUE

GO TO 41

15 DO==SATL(T>

DO 16 1=1 y 10

CALL PRESS ( P0» DO yT)

IF(P0.LE.P)G0 TO 17

16 D0^D0-.0001*D0

GO TO 42

17 Dl-DO

18 CALL PRESS(Pl?DlrT)

1F(D1.GE,50. )G0 TO 42

IF(P1.GT.P)G0 TO 14

D0 = D1

Z-(P-P1)/P

Z=Z*10

IF(T/TCC*LT. .6)Z=1.

IFCZ.LT.l. )Z=1.

.IF(Z.GT.9. )Z-9.

D1=D1+.01*D1*Z

GO TO 18

20 CALL PRESS (POyDOrT)

IF(P.LE.PO)GO TO 30

Dl-DO

21 CALL PRESS(PlyDlyT)

IF(P1.GE.P)G0 TO 14

IF(D1.GE,50. )G0 TO 42

D0-=D1

Z:=:(P-pi)/p

Z=^Z*10

.[F(Z.LT,1)Z:=^1

IF(Z.GT.9)Z=--^9

D1^D1+.1*D1*Z

GO TO 21

30 Dl-DO

31 CALL PRESS(PlyDlyT)

yT)

l.GT ,P)GO TO 1 20

l.LT .P)GO ro 1 20

71
IF(P1J_E J-')GO TG ;l.4 I F ( D 1 . L E; w 1 * F-' I1-' ) G 1 4 2

D0=D1

Z==(P1-P)/F'

Z=Z*10

IF(Z J...T.:l. )Z=:^1 IF(Z.GT.9)Z-9

Dl:^-Dl-.i*Dl*Z

GO TO 31

40 DD--^ril RETURN

41 PRINT 101»P»TvD

102 FORMAT (* REGULA FAILED AT P-*i.F7,2!-* AND T=*»F7.2)

101 FORMAT(* DENSITY ITTERATION FAILED AT P^--^* y F7 . 2 ^ * AND J=tfF7,2f

1/* DENSITY RETURNED IS*vE17.8)

RETURN

42 PRINT 102tP»T

RETURN

END

FUNCTION CP(DyT)

C CALCULATES SPECIFIC HEAT CAPACITY

C AT CONSTANT PRESSURE FOR INPUT OF

C DENSITY AND TEMPERATURE IN MOL/L AND K

C CP IS IN JOULES/MOL-K

CVEE=CV(DfT)

CALL DPDT(DPTyDyT)

CALL DPDD(DPDyDyT)

CP=CVEE+ ( T/ ( D**2 ) * ( DPT)K*2 ) /DPD ) * 10 1 , 325

RETURN

END

FUNCTION DPDTVP(TT)

C CALCULATES THE DERIVATIVE OF PRESSURE

C WITH RESPECT TO TEMPERATURE AT

C SATURATION. INPUT IS TEMP. IN Ky OUTPUT IS ATM/K.

COMMON/DATA/G y R y GAMMA y VP

DIMENSION G(32) yVP(9)

IF(TT.GT.VP(8))G0 TO 1

X=-- ( 1 , -VP < 7 ) /T ) / ( 1 ~VP ( 7 ) /VP ( 8 ) ) DXDT== ( VP ( 7 ) /T>K*2 > / ( 1 . VP ( 7 ) /VP ( 8 ) ) DPDT==VP ( 1 ) 5KDXDT + 2 . >KVP ( 2 ) *X*DXDT+VP ( 3 ) *3 . *X**2*DXDT+VP ( 4 ) *

1( (l.-X)**VP(5) )*DXDT + VP(4)*X*( (1. -X)**('v'P(5)-l. ) ) *UP ( 5 ) * ( -DXDT ) DPDT==DPDT*VPN(T)

DPDTVP^^^DPDT

RETURN

1 DPDTVP^^O

RETURN

END

FUNCTION FIND M(PyTyDD)

C ALTERNATIVE FOR FIND Dy INPUT IS

C PRESSURE IN ATM.y T IN KELVIN AND

C DENSITY IN MOL/L. INPUT DENSITY

C IS A STARTING VALUE FOR ITTERATION

C OF EQUATION OF STATE FOR SOLUTION FOR P AND T

Tr::::T DO 10 I-ly50

CALL PRESS (PPyDDyTT)

P2^^^PP IF ( ABS ( P-P2 ) -1 . E -7*P ) 20 y 20 y

1 CALL DPDD( PPyDDyTT)

i;ip:rpp

C0RR::=(P2--P)/DP

D^^-DD 72
;i:f(abs (corr) -i. .E •7)KD)20y20y3.0

I:lD-I:lD-coRR

F]:NI:l M-O

RETURN

F.I:ND M^n=DD Ri;nuRN

END

FUNCTION ENTHALCP . D . T ) CALCULATES ENTHALI^Y FDR INPUT OF

PRESSURE!. DENSITY AND TEMP. IN

ATM.» MOL/L AND K . OUTPUT IS IN

10

20

c

cc

C JOULE S/MOL

R=. 082056 16

DD-D

TT-T

CALL DSDN(SD»DDvTT)

CALL DUDN(UD!-DD»TT)

DD-0

CALL DSDN(SO!.DD!'TT)

CALL DUDN(UO»DDyTT)

ENTHAL- T* ( SD -SO ) *101 . 325f ( UD •UO ) *101 . 325fHI ( T ) + ( P/D -R*T ) *101 . 325

RETURN

END

FUNCTION ENTROP(D!<T)

C CALCULATES ENTROPY

C FOR AN INPUT OF DENSITY AND

C TEMP. IN MOL/L AND K. OUTPUT IS IN

C JOULES/MOL-K

R^=. 082056 16

DD==D

Tr:n:T CALL DSDNCSDvDD^TT)

DD = CALL DSDN(SOyDD»TT)

ENTROP^-^ ( SD-SO ) *101 325-R>KAL0G < D)!<R*T ) *101 . 325 + SI ( T)

RETURN

END

FUNCTION SATL(TT)

C CALCULATES THE DENSITY OF THE

C SATURATED LIQUID AT TEMPw T IN KELUIN.

C OUTPUT IS IN MOL/L.

DIMENSION A (20)

DIMENSION G(32) !.»^P(9)

COMMGN/DATA/G v R f GAMMA , Klf y DTP v PCC > FTP v TCC » TTP 9 TUL y TLL » PUL y DCC

CGMMON/SATC/AyDTPV

K^14

KK=-7

GO TO 10

ENTRY SATV

K=l

KK=--:13 10 IF(T.GE.TCC)GO TO 20

T^TT

ITT^^TCC

IFCITTH-T.LT.l. )T=:0:TT

X:^:(T-TCC)/(TTP-TCC)

D:^-:A(K)*ALOG<X)

DO 11 I-2!.KI\

MM--=I IF(MM.GE.5)MM^=MMfl

1

1

D^^D fA < K ) * ( 1 . -X** ( ( MM-5 ) /3 . ) ) IF(K.LT.14)G0 TO 12

73
D

-- D c c f E X p ( II ) * ( n r I"' - i:i c t;

)

GO TO 13

1

ti -^ ti c; c f E X !- ( ti ) * ( i:i r p ^ d o c; ) 13 SATL^^D

IF ( I T Ti 1 -T r > LT . 1 ) SA I LJ^^J - ( D DCC ) * ( \\-'\ ) RETURN

20 DSATL^^^DCC

RETURN

END

FUNCTION SOUND(DyT)

C CALCULATES THE SPEED OF SOUND

C FOR AN INPUT OF DENSITY AND TEMP*

Q IN HOL/L AND KELVIN. OUTPUT IS IN

C METERS/SECOND.

COiiMON/CRIT/W

CALL DPDD(DPyDyT)

SOUND^^- ( ( CP ( D » T ) /CV ( D v T ) ) *DP*1 01325 . /W ) ** , 5

RETURN

END

FUNCTION VISCCDDvT;-

C RETURNS VISCOSITY IN ( G/CM- S ) )KEf 6 » C T IN K, D IN MOL/L

COMMON/CRIT/EM

D::^DD*EM/1000.

V I s c ^== D 1 1... V ( T ) f I" D c; V ( D V r ) f E X c e: s v ( d » t ) RETURN

END

FUNCTION THERM (DDi-T)

C RETURNS TC IN MW/M-Ky T IN Ky D IN MOL/L

COMMON/HAN/CRyTCI

COMMON/ISP/N:.'NW

COMMON/CRIT/EM

D^^a:iD*EM/I000,

IF(NW.EQ.O ) GO TO 3

CR-CRITC(DvT)

T H E R ^-~ D 1 1... r ( T ) + F D C T' ( D v T ) >i< 1 . f E X C IE S T ( D y r ) f C R TCI=^THER-CR

THERM-THER

RETURN

3 CR:M:;RITC(DyT)

THERM^::T:iILT < T ) + FDCT ( D y T ) f EXCEST ( D r T ) +cr

TCI^^THERM-CR

RETURN

END

FUNCTION EXCESVCDvT)

C CALCULATES EXCESS VISCOSITY

COMMON/DATA 1 /GV y GT y FV y FT y EV y ET

COMMON/ I SP/NyNW

DIMENSION GV ( 9 ) y GT ( 9 ) y FV ( 4 ) y FT ( 4 ) y EV ( 9 ) y ET ( 8

)

R2=^D** ( , 5 ) * ( ( D •••EV ( 8 ) ) /EV ( 8 ) ) R^^^^D** ( . 1

)

X-^^ZV ( 1 ) •f EV ( 2 ) *R2^IEV ( 3 ) *R lEV ( 4 ) )KR2/ ( T*T ) f EV ( 5 ) *R/T** (1.5) -f EV ( 6 ) /T

l^fEV(7)*R2/T

Xl-EV(l)^fEV(6)/T

EXCESV^^MEXP (X)-EXP (XI)

RETURN

ENTRY EXCEST

C CALCULATES EXCESS THERMAL CONDUCTIVITY

IF(NU.EQ.O ) GO TO 3

R^^D>K*( .1 ) X-^HiT ( 1 ) •! ET ( 2 ) *R-f ET ( 3 ) *R/T** (1.5) -f ET ( 4 ) /T

Xl::^ET(l)^fET(4)/T

EXCESV-t^- ( EXP ( X ) -EXP ( X 1 ) ) / 1 RETURN

74
3 R2'D^it ( 5 ) * ( ( D-ET ( 8 ) ) /ET ( 8 ) ) R^D**( .1 ) X=ET ( 1 ) f ET ( 2 ) *R2 + ET ( 3 > >KRf ET ( 4 ) *R2/ ( T*T ) f ET ( S ) *R/T** (1.5) +ET < 6 ) /T

lfET(7)*R2/T

Xl^==ET(l)iET(6)/T

EXCEGy-:EXP (X)-EXP (Xl)

RETURN

END

FUNCT.(:ON FDCv^CCiyT)

C FIRST DENSITY CORRECTION

C FOR tilSCOSITY AND THERMAL CONDUCT I'v'ITY COMMON/DATA l/GU > GT . F"-; c FT , EV ? ET

DIMENSION GW ( <? ) . GT ( 9 ) , FV ( 4 ) >- FT ( 4 ) ; EV ( 8 ) > ET ( 8 ) FDCV- ( FV ( 1 ) f FV ( 2 ) * ( Fiv" ( 3 ) -ALOG ( T/FV ( 4 ) ) ) **2 ) )KD RETURN

ENTRY FDCT

F DCV- ( FT ( 1 ) +FT ( 2 ) * ( FT < 3 ) -ALOG ( T/FT ( 4 ) ) ) trZ ) *D

RETURN

END

FUNCTION CRITC(D»T)

C CALCULATES CRITICAL ENHANCEMENT

C FOR THERMAL CONDUCTHJITY

COMMGN/CRIT/ EM? EOK? Ri-i, TC y DCy X y PCy SIG

COMMON/CHECK/DELD s- DELT f DSTAR , TSTAR

COMMON/H JM/EPSI , CPCV , RRR , AKT

L; M M N / 1 S P / N y N W y N W W

C D IN G/CM3 y f IN K

C OUTPUT UNITS ARE MU/M,K

AV = 6.0225E:-23 * BK==1 . 38054E-16

DELD;=-ABS (D--DC)/DC $ DELT^^^^ABS (T-TO/TC

C CALCULATE DISTANCE PARAMETER

R^-- ( RM*>K2 . 5 ) * ( D**0 , S ) * ( AU/EM ) *)i<0 . 5

R=-R* ( EOK**0 . 5 ) *X/ ( T>K*0 * 5 ) RRR^R

C GENERAL EQUATION

DX:--^D*1000.0/EM

CALL DPDT(DPTyDXyT)

C DPDT IN ATS PER DEG.

D !"• r

:•:: ri P T * 1 . ]. 3 2 5 E + 6

C DPDT NOU IN DYNES PRR DEG

CALL DPDD(DPDyDXyT)

C DPDD UN ATSy MOL/L

DPD^^DPD* ( I * 1325E + 6 ) * ( 1 000 . 0/EM ) CDPDD NOW IN DYNES y GM/CM3

I F ( DPD . LT . . ) DPD== 1 . 94 VIS=:VISC(DXyT)*<l,0E-06)

C VISCOSITY IN GM/CM,S

IF ( DEED »EQ. 0.25. OR. DELD.LT. 0.25) 8yI0

8 IF ( DELT. EQ. 0.025. OR. DELT . LT . . 025 ) 9y 10

9 COMPRES=SENG(DyT)

GO TO 12

10 COMPRES=:: 1 . 0/ ( D>KDPD ) **0 . 5

12 EX=--^T^K*T>K*2* ( DPT**2 ) *COMPRES

EXB:^R* ( ( BIOKT ) **0 . 5 ) * < D**0 . 5 ) * ( ( AV/EM ) **0 . 5 ) CRIT:^EX/(EXB*6.0*3.14159*VIS)

C PUT IN DAMPING FACTOR

BDD^-< (D-DC)./DC)**4

BTT=^( (T-TC)/TC)**2

FACT=EXP (-18.66*BTT - 4.25*BDD)

DELC=^CRIT*FACT/100.0

CRITC=--DELC

AKT=---COMPRES*COMPRES

EPSI^-=R*R*BK*T* ( A»v'*D/EM ) >!<AKT EPSI=:EPSI**0.5

75
C CALC CP-C>v' CPCV-T* ( DFT**2 ) *AK T/D

RETURN

END

funct:i:on sen(3(DtT)

c scaled equation of state for critical region

COMMON/CRIT/ EM^ EOKr RM» TCi- DC» X f F'C » SIG

COMMON/SEN/BETA !.XOy DELTA vEIf E2y AGAM

CGMMON/CHECK/DELD y DELT y DSTAR » TSTAR

DSTAR- D/DC $ TSTAR^^T/TC

BETO^^l./BETA

XX-DELT/DELD*)f<BETO

AG==^AGAM--1»0

BET2^=- 2»0)XBETA

AGB--^AG/BET2

DELl^^-DELTA-l.O

AGBB= (AG-BET2)/BET2

XXO=(XX+ XO)/XO

XXB==XX0**BET2

BRAK=^1.0 f E2)KXXB

BRAK1^=BRAK**AGB

H = E1*XX0*BRAKJ.

HPRI«^^=(E:l./XO)*BRAI\l + ( AG/XO ) *E1*E2* ( XXB ) * ( BRAK**AGBB ) RC0M=^(DELD**DEL1)*(DELTA*H - ( XX/BETA ) *HPRIM ) RC0MP=: 1 . 0/ ( RC0M*DSTAR**2 ) RCM:^:^RCOMP/(PC>K:l. 01325E+ 06)

C RCM IN DYNES

RCM^==RCM**0«'5

C

SENG^^RCM

RETURN

END

FUNCTION DILV(T)

C GIVES DILUTE GAS >v'ISCOSITY AND THERMAL

C CONDUCTIVITY FOR AN INPUT TEMP. IN

C KELVIN. OUTPUT UNITS ARE SAME AS

C THOSE IN Vise AND THERM

COMMON/ ISP/N 9 NW y NWW

COMMON/DATA 1/GV » GT y FV y FT y EV y ET

DIMENSION GV(9) yGT(9) yFV(4) yFT(4) yEV(8) vET(S)

SUM=--=0 TF^-^a**(l./3. ) TFF=--=T**(-4./3.)

DO 10 I-ly?

TFF=TFF*TF

10 SUM-SUMfGV(I)*TFF

IF(NWW.EQ.7) GO TO 9

DILV=SUM*1000.

GO TO 11

9 DILV==SUM

11 RETURN

ENTRY DILT

TF-T)K>K(l./;3. ) TFF^T**<-4./3.

)

SUM-=0

DO 20 I-ly9

rFF::-TFF*TF

20 SUM^SUMfGT(I)*TFF

DILV-SUM

RETURN

END

FUNCTION CPI(T)

C CALCULATES IDEAL GAS THERMO PROPERTIES

76
C F-OR ALL FLUIDS EXCEPT H2 INPUT IS IN

C KELVIN y OUTPUT IS IN JOULES p MOL/L AND K C0MM0N/CPID/G(11)

COMMON/ISP/N

IF(N.NE.O)GO TO 5

1 U=G(9)/T

EU-EXP (U)

TS=1./T*>K4

GO TO (2»;3!-4),K

2 CPI=:G(8)*U*U*EU/(EU-1. )**2

DO 10 1^1 5-7 TS-TS*T

10 CPI=CPI+G(I)*TS

CPI=CPI*8.314;34

RETUF^N

•5 CPI-^CPO(T»N)

RETURN

ENTRY SI

IF" (N.NE.O)GO TO 6 K = 2

GO TO 1 3 CPI-G(8)*(U/(EU-1.)~AL0G(1.-1./EU))

1 -G ( 1 ) *TS*T/3 . -G ( 2 ) *TS*T*T/2 . -G ( 3 ) /T + G ( 4 ) *AL0G ( T ) +G < 5 ) *T tG ( 6 ) *T*T/2

2.+G(7)*T**3/3.

CP I -CP 1*8.31434+0 (11)

RETURN

6 CPI=CPOS(T»N)

RETURN

ENTRY FH

IF(N.NE.O)GO TO 7

K-3

GO TO 1 4 CPI=G(8)*U*T/(EU-1.)-G(1)/(2.*T*T)-G(2)/T+G(3)*AL0G(T)+G(4)*T

l+G(5)*T*T/2.+G(6)*T**3/3,fG(7)*T**4/4.

CPI=CPI*8.31434fG(10)

RETURN

7 CPI-=:CP0F1(Ti-N)

RETURN

END

FUNCTION CPO(TI»N)

DIMENSION T(58) yCPP(58) !.CPN(58) K;P0(58) i'CPE(58)

CGMMON/PARA/PERCEN

C CALCULATES IDESL GAS SPECIFIC HEAT FOR H2 BY INTERPOLATING

C DATA TAKEN FROM RP 1932!- UNITS OF THE TABLES ARE CAL/MOL DEG 5,

C UNITS OF OUTPUT ARE JOULES/MOL DEG K. THE INDEX N DETERMINES THE

C SPECIESj-FOR N:^-lfPARAHYDR0GEN>N^:^2 NORMALr N=3 ORTHO? N:-^-4 EQUILIB

C N=5yS0ME ORTHO-PARA MIXTURE SPECIFIED BY COMMON /PARA/ .PERCENT

C RANGE OF TEMP IS FROM 10 TO SOOOK.

DATA(T^

1 10. Or 12.0). 14.0)' 16.0? 18. Ot 20. Oy 25. Or 30. 0» 35. Or 40. Or 45. Or

2 50, Or 55. Or 60. Or 65. Or 70, Or 75. Or 80, Or 85, Or 90, Or 95, Or 100. Or

3105. 0» 110, Or 115. Or 120. Or 125. Or 130. Or 135. Or 140. Or 145. Or 150. Or 160. Or

4 170. Or 180. Or 190. Or 200. Or 210. Or 220. Or 230. Or 240. Or 250. Or 260. Or 270. Or

5280. Or 290. Or 300. Or 350. Or 400. Or 500. Or 600, r700, rlOOO, r 1500, r2000, r 63000, r4000, r5000.

)

DATA ( ( CPE ( I ) r 1 = 1 r 58 ) =4 , 968 r 4 , 96884 r 4 , 97647 r 5 , 01 153 r 5 .07451 ? 5 . 208

1 1 r 5 . 83508 r 6 . 81 282 r 7 . 87989 r 8 . 6061 3 r 9 . 0023 1 r 9 . 08005 r 8 . 93278 r 8 . 65894 r 28 . 33603 y 8 ,01207 , 7 .71009 r 7 . 4416 r 7 , 21 109 r 7 .01858 r 6 . 85857 r 6 . 72557 r 6 .

6

32055 r 6 , 53555 r 6 . 46904 r 6 . 42003 r 6 , 38403 r 6 , 36151 r 6 , 34602 r 6 , 33753 r 6 , 340

401 r 6 , 34577 r 6 . 37276 r 6 . 4 1 3 r 6 45925 , 6 . 50975 r 6 . 5605 r 6 , 6095 r 6 , 65724 r 7 6 , 692 r 6 , 734 r 6 , 771 r 6 , 804 r 6 , 832 r 56 . 856 r 6 . 877 r 6 , 395 y 6 , 950 r 6 . 974 r 6 , 993 r 7 . 009 r 7 , 036 r 7 , 219 r 7 , 720 r 8 , 195 r 77
969 !> 4. 972 1-4. 983 y 036^6. 245 1-6. 454!'

753)- 7. 807^7. 8701-

68.859? 9, 342?9«748)

1 4 . 968 9 A „ 968 f 4 . 968 v 4 . 968 ? 4 . 968 9 4 . 968 y 4 . 968 i- 4 . 968 v 4 . 968 y 4 , 968 » 4 968 v 24 . 968 V 4 . 968 , 4 . 968 v 4 . 969 v 4 . 972 1-4.975^4. 981 v 4 . 990 » 5 . 002 ? 5 . 018 y 5 039 ? 35.064 v5. 094 p5. 129 y 5. 169y 5.213^5*261!- 5. 313y 5. 369 y 5. 427y 5. 487»5.612y

45 . 741 y 5 . 868 .» 5 . 992 y 6 . 109 y 6 . 219 ? 6 . 320 y 6 . 41 1 » 6 . 493 y 6 . 566 y 6 . 629 y 6 . 684 y 56 . 732 y 6 . 773 y 6 . 808 y 6 .917 y 6 . 962 y 6 . 993 y 7 . 009 y 7 . 036 y 7 . 219 y 7 . 720 y 8 . 195 » 68. 859 y 9. 342 y 9. 748)

1 4 . 968 y 4 . 968 ? 4 . 968 y 4 . 968 y 4 . 968 y 4 . 968 y 4 . 968 y 4 . 968 y 4

25 . 006 y 5 . 048 y 5 . 1 1 4 y 5 . 207 y 5 . 328 y 5 . 475 y 5 . 646 y 5 . 835 y 6

36 . 659 y 6 . 854 y 7 . 037 y 7 . 203 y 7 . 35 1 y 7 . 480 y 7 . 590 y 7 . 68 1 y 7

47 . 883 y 7 . 858 y 7 . 808 y 7 . 742 y 7 . 667 y 7 . 59 1 y 7 . 5 1 6 y 7 . 445 y 7 . 380 y 7 . 322 y 7 . 270 > 57 . 225 y 7 . 186 y 7 . 152 y 7 . 050 y 7 . 010 y 6 . 998 y 7 . 010 y 7 . 037 y 7 . 219 y 7 . 720 y 8 . 159y

68. 859 y 9. 342 y 9. 748)

DATA (CRN:-

14 . 968 y 4 . 968 y 4 . 968 y 4 . 968 y 4 . 968 y 4 . 968 y 4 . 968 y 4 . 968 y 4 . 968 y 4 . 969 y 4 . 972 y 24 . 977 y 4 . 983 y 5 . 005 y 5 . 029 y 5 . 06 1 y 5 . 1 00 y 5 . 1 47 y 5 . 20 1 y 5 . 26 1 y 5 . 325 y 5 . 393 y 35 . 463 y 5 . 534 y 5 . 606 y 5 . 677 y 5 . 748 y 5 . 8 1 6 y 5 . 882 y 5 . 947 ,

. 008 y 6 . 067 y 6 . 1 77

46 . 276 y 6 . 366 y 6 . 446 y 6 . 5 1 7 y 6 . 58 1 y 6 . 638 y 6 . 687 y 6 . 73 1 y 6 . 769 y 6 . 802 y 6 . 831

y

56 855 y 6 . 876 y 6 . 894 y 6 . 950 y 6 . 974 y 6 . 993 y 7 . 009 y 7 . 036 y 7 . 2 1 9 y 7 . 720 y 8 . 1 95 y 68. 859 y 9. 342 y 9. 748)

GO TG(ly2y3y4y5) yN

1 C P ^- A T K J: N T ( T 1 y C P P y I y 5 8 y retui';:n 2 C; r-' 8 A T K I N T ( T 1 y t) F' N y T y 5 8 y RETURN

3 C P ^- A r K 1 N T ( T 1 y C) F" y T y 5 8 y RETURN

4 C P -- A T K 1 N T ( T :i: y C P E y T y 5 8 y RETURN

5 TUP- T I +.5

tdn^^t:i;-.5

HUP==CP0H(TUPy5)

HDN:--=C;pOH(TDNy5)

CPO^^-^CHUP-HDN)

RETURN

END

PUNCTION CPGH<T1 yN)

D 1 MENS I ON T ( 58 ) y HP ( 58 ) y HN ( 58 ) y HO ( 58 ) y HE ( 58

)

COMMON/PARA/PERCEN

C CALCULATES THE ENTHALPY OF THE IDEAL GAS FOR H2 BY INTERPOLATION

C DATA TAKEN FROM RP 1932 y UNITS OF TABLES ARE CAL/MOL

C UNITS OF OUTPUT ARE JOULE/MOL. THE INDEX N DETERMINES THE SPECIES

C SPECIES y FOR N=:lyPARAHYDR0GENyN^=2 NORMAL y N^i ORTHOy N=^4 EQUILIB

C N=^:5yS0ME ORTHO-PARA MIXTURE SPECIFIED BY COMMON /PARA/ y PERCENT

C RANGE OF TEMP IS FROM 10 TO 5 00 OK.

DATA(T:-::

1 10. Oy 12. Oy 14. Oy 16. Oy 18. Oy 20. Oy 25. Oy 30 . y 35. Oy 40. Oy 45. Oy

2 50. Oy 55. Oy 60. Oy 65. Oy 70. Oy 75. Oy 80. Oy 85. Oy 90. Oy 95.0yl00.0y

3105.0 y 1 10. Oy 1 15. y 120.0y 125. Oy 130. Oy 135. Oy 140. Oy 145. Oy 150. Oy 160.0

y

4170 . y 180 . y 190 . y 200 . y 210 . y 220 . y 230 . y 240 . y 250 . y 260 . y 270 . y 5280. y 290. y 300. y 350. Oy 400. Oy 500. Oy 600. y/OO. y 1000. y 1500. y2000.

y

63000. y4000. y5000.

)

6yNESy .01)*4.184

6yNESy .01)*4.184

6yNESy .01 ))K4.184

6yNESy .01)*4.184

DATA(HN=^

1 303. 67

y

1 427. 86

y

3 628. 02

y

4 841. 40

y

313.60y

452.71

y

653. 64 y 869.61

y

353. 35y

552. 32y

758. 92y

378. 19

y

577. 40

y

786. 06

y

403. 03

y

602. 62

y

813. 55y

985 . 91 y 1015 . 80 y 1045 . 99 y

323. 54 y 333. 48 y 343.41

y

477. 56 y 502. 43 y 527. 34

y

679.51 y 705. 66 y 732. 13

y

898. 17 y 927. 08 y 956. 33

y

51 1 07 . 22 y 1 1 69 . 49 y 1 232 . 7 1 y 1 296 . 78 y 1 36 1 . 60 y 1 427 . 1 y 1 493 . 20 y 1 559 . 84 y 6 1 626 . 93 y 1 694 . 44 y 1 762 . 30 v 1 830 . 48 y 1898 . 9 1 y 1 967 . 57 y 2036 . 43 y 2382 . 74 y 72730 . 94 y 3429 . 46 y 4129 . 51 y 4831 . 66 y 6966 . 23 y 10697 . 2 y 14679 . 2 y 823230. 9 y 32345. y 41895. ) 78
DATA(HP=--=

49 . 68 y 59 .61, 69 , 55 ? 79 . 49 , B9 . 42 k 99.36. 1 24 . 20 r 1 49 . 04 ?

! 173.88? :l.98,737 223. 6li. 248*587 273. 7:L? 299.1:1.? 324.90? 35 ) ')A., r 3 378.22? 406.01? 434.71? 464.38? 495.09? 526.84? 559.62? 593.41?

4 628.14? 663.75? 700.14? 737.23? 774.92? 813.10? 85:1..69? 890.60?

5 969 .04 ? 1047 . 84 ? 1 126 . 58 ? 1204 . 93 ? 1282 . 69 ? 1359 . 74 ? 1436 . 03 ? 151 1 . 56 ? 61586.36? 1660.49? 1733.99? 1806.95? 1879.42? 1951 . 47 ? 2023 . 15? 2377 . 83

?

72729 . 17 ? 3429 . 24 ? 4129 . 48 ? 4831 . 65 ? 6966 . 23 ? 10697 . 2 ? 14679 . 2 ? 823230. 9? 32345. ? 41895.

>

DATACHO1 388.33? 398.27? 408.20? 418.14? 428.07? 438.01? 462.85? 487.69?

2 512.53? 537.37? 562.21? 587,05? 611.89? 636.73? 661.57? 686.42?

3 711.29? 736.18? 761.11? 786.09? 811.14? 836.28? 861.54? 886.93?

4 912.49? 933.23? 964.18? 990 . 37 ? 1016 . 80 ? 1043 .51 ? 1070 .50 ? 1097 . 78?

51153.27? 1210.04? 1268.09? 1327.39? 1387.91 ? 1449 . 56 ? 1512 .26 ? 1575 . 93

?

61640 . 46 ? 1705 . 76 ? 1771 . 74 ? 1338 . 32 ? 1905 .41 ? 1972 . 94 ? 2040 . 86 ? 2384 . 38 ? 72731. 52? 3429. 53? 4129. 52? 4831 . 66 ?6966 . 23 ? 10697 . 2 ? 14679 . 2

?

823230. 9? 32345. ? 41895.

)

DATAd-IE--^

1 49.68? 59.62? 69.57? 79.56? 39.66? 99.96? 127.50? 159.12?

2 195.77? 236.90? 280.97? 326,24? 371.33? 415.35? 457.86? 498.74?

3 538.05? 575.93? 612.56? 648.13? 632.82? 716,78? 750.14? 783.03?

4 815.54? 847.76? 879,77? 911.63? 943.40? 975 . 1 1 ? 1006 . 30 ? 1033 . 52

?

5 1 1 02 . 1 1 ? 1 1 66 , 03 ? 1 230 . 39 ? 1295 . 23 ? 1 360 . 58 ? 1 426 . 43 ? 1492 . 76 ? 1 559 . 55 ? 61626 .75 ? 1694 . 32 ? 1762 . 23 ? 1830 .43 ? 1898 . 38 ? 1967 . 55 ? 2036 . 42 ? 2382 . 74 ? 72730 . 94 ? 3429 . 46 ? 4 1 29 . 5 1 ? 4831 . 66 ? 6966 . 23 ? 10697 . 2 ? 14679 , 2 ? 323230. 9?32345. ?41895.

)

GO T0(l?2?3?4?5) ?N

1 C P H =^ A T K I N T ( T I ? H l"' ? T ? 5 3 ? 6 ? N E S ? , 1 ) * 4 . 1 8 4 RETURN

2 CF'n|-h=:ATKINT(TI ?HN?T?58? 6?NES? .01 )*4.1S4

RETURN

3 CPOhh-ATKlNT ( T.I ? HO ? T ? 53 ? 6 ? NES ? . 01) *4 . 184

RETURN

4 CPOI-T^=ATK 1 NT (

1" I ? HE ? T ? 53 ? 6 ? NES ? . 1 ) *4 . 1 84

RETURN

5 PERCE -^PERCEN /lOO.

CPOH^-^ ( ATK I NT ( T I ? HO ? T ? 58 ? 6 ? NES ? . 1 ) * ( 1 . -PERCE ) +

1 ATK I NT ( T J V HP ? T ? 58 ? 6 ? NES ? . 1 ) *PERCE ) )K4 . 1 84

RETURN

END

EUNCTION CPOS(TI?N)

DIMENSION T ( 60 ) ? SP ( 60 ) ? SN ( 60 ) ? SO ( 60 ) ? SE ( 60

)

COMMON/PAR A/PERCEN

C CALCUIATFS THE ENTROPY OF THE IDEAL GAS FOR H2 BY INTERPOLATING

C DAKFN FROM RP 1932? UNITS OF THE TABLES ARE CAL/MOL DEO K. 1 C UNITS OF OUTPUT ARE JOULES /MOL DEG K. THE INDEX N DETERMINES I HE

I- SPECIFS?FOR N-J ?PARAHYDR0GEN?N=2 NORMAL? N = 3 ORTHO? N-4 EQUILIB

C N-5?S0ME ORTHO-PARA MIXTURE SPECIFIED BY COMMON /PARA/ ? PERCENT

C RANGE OF TEMP IS FROM 10 TO 5000K.

DATA<T::n

1 10.0? 12.0? 14.0? 16.0? 13.0? 20.0? 25.0? 30.0? 35.0? 40.0? 4u.0?

? 50.0? 55.0? 60.0? 65.0? 70.0? 75.0? 80.0? 85.0? 90.0? 95.0? 100.0?

3105 . ? 1 1 . ? 1 15 . ? 120 . ? 125 . ? 130 . ? 135 . ? 140 . ? 145 . ? 150 . ? 160.0 ? 4170 . ? 180 . ? 190 . ? 200 . ? 210 . ? 220 . ? 230 . ? 240 . ? 250 . ? 260 . ? 270 . ? 5280 . ? 290 . ? 300 . ? 350 . ? 400 . ? 450 . ? 500 . ? 550 . ? 600 . ? 700 . ? 1000 .

?

61500 . ? 2000 . ? 3000 . ? 4000 . ? 5000 . ) DATA(SP- ., ^, ,, ,_,^ , _, ...^ Ul 1 . 2 1 4 ? 1 2 . 1 20 ? 1 2 . 836 ? 1 3 . 549 ? 1 4 . 1 35 ? 1 4 . 658 ? 1 b . / 66 ? 1 6 . o72 ? 1 / . 433 ?

I 18, 102? 18. 638? 19. 214? 19. 693? 20. 135? 20. 548? 20. 933? 21. 310? 21. 669?

0-5'' . 01-'' ?

-:'-:' . 356 ? 22 . 688 ? 23 . 014 ? 23 . 334 ? 23 . 648 ? 23 . 957 ? 24 . 260 ? 24 . 557 ? 424. 843? 25. 132? 25. 410? 25. 681? 25. 945? 26. 451? 26. 929? 27. 379? 27. 302?

523 . 201 ? 23 . 577 ? 28 . 932 ? 29 . 268 ? 29 . 586 ? 29 . 889 ? 30 . 1 /7 ? 30 . 452 ? 30 , 716 ? 79
630 , 969 ? 3 1 . 21 2 J 32 . 305 v 33 . 244 v 34 . 069 > 34 . 806 y 35 .473^36. 082 ? 37 , 1. 65 i- 739. 7011- 42* 720. 45, 007 1-5 1.22:1.^53.839!- 55. 969)

1 1 5 . 58 1 i- 1 6 . 486 ^ 1 7 . 252 1-17. 9 1 6 9 1 8.50 1 1-19. 024 y 20 1 35 , 2 1 . 038 ,21. 804 , 222 . 468 !- 23 . 053 ? 23 . 576 K 24 . 050 !- 24 . 482 !/ 24 . 880 1- 25 . 248 y 25 . 591 1- 25 . 9 1 2 y 326 . 2 1

y 26 . 500 y 26 . 77 1 y 27 . 029 y 27 , 275 y 27 . 5 1 2 y 27 , 739 y 27 . 958 y 28 . 1 70 y 423 . 375 y 28 . 575 y 28 . 769 y 28 . 958 y 29 . 143 y 29 . 502 y 29 . 846 y 30 .

77

,

30 . 498 y 530 . 808 y 31 . 109 y 31 . 401 y 31 . 684 y 31 . 958 y 32 . 225 ? 32 . 484 ? 32 . 735 y 32 . 979 y 633 . 2 1

y 33 . 446 y 34 . 505 y 35 . 432 y 36 . 253 y 36 . 989 y 37 . 656 y 38 . 265 y 39 . 348 » 741 . 884 y 44 . 903 y 47 . 190 y 51 . 221 y 53 . 839 y 55 . 969

)

IiATA(SN^=

1 15. 607 y 16. 512 y 17. 278 y 1 7. 941 y 18. 527 y 19. 050 y 20. 159 y 21. 064 y 21. 830

y

222 . 494 y 23 . 079 y 23 . 603 y 24 . 078 y 24 . 5 1 3 y 24 . 9 1 4 y 25 . 288 y 25 . 638 y 25 969 y 326 . 283 y 26 . 582 y 26 . 868 y 27 . 1 43 y 27 . 407 y 27 . 663 y 27 . 9 1 1 y 28 . 1 5 1 y 28 . 384 y 428 . 61 1 y 28 . 832 y 29 . 047 y 29 . 256 y 29 . 461 y 29 . 856 y 30 . 234 y 30 . 595 y 30 . 942 y 531. 274 y 3 1 . 594 y 3 1 90 1 y 32 . 1 97 y 32 . 483 y 32 . 758 y 33 . 025 y 33 . 282 y 33 . 53 1

y

733 . 772 y 34 . 005 y 35 . 073 y 36 . 003 y 36 . 825 y 37 . 561 y 38 . 228 y 38 . 836 y 39 . 920 y 742. 455 y 45. 475 y 47. 762 y 51. 221 y 53. 839 y 55. 969)

DATA(SE1 1 1 . 215 y 12 . 120 y 12 . 887 y 13 . 554 y 14 . 149 y 14 . 692 y 15 , 918 y 17 . 069 y 18 . 196 y 2 1 9. 294 y 20. 331 y 21 285 y 22. 1 45 y 22. 91 ly 23. 592 y 24.1 98 y 24. 740 y 25. 229

y

325. 674 y 26. 080 y 26. 455 y 26, 804 y 27.1 29 y 27. 435 y 27. 724 y 27. 999 y 28. 260

y

428 . 5 1 y 28 . 750 y 28 ., 980 y 29 . 203 y 29 . 4 1 8 y 29 . 828 y 30 . 2 1 6 y 30 . 584 y 30 . 934 y 531 . 269 y 3 1 . 59 1 y 31 . 899 y 32 . 1 96 y 32 . 482 y 32 . 758 y 33 . 024 y 33 . 282 y 33 . 53 1

y

633 . 772 y 34 . 005 y 35 . 073 y 36 . 003 y 36 . 825 y 37 . 561 y 38 . 228 y 38 . 836 y 39 . 920 y 742 . 455 y 45 . 475 y 47 . 762 y 51 . 221 y 53 . 839 y 55 . 969

)

60 T0(ly2y3y4y5) yN

1 CPOS = ATK I NT ( T I y SF-' y T y 60 y 6 y NES y . 1 ) *4 . 1 84

F^ETURN

2 CPOS^:::A TKINT ( TI y SN y T y 60 y 6 y NES y . 01 ) *4 . 184

F^ETUFv'N 3 CPC)S^^=A TK 1 NT ( T I y SO y T y 60 y 6 y NES y . 1 ) >K4 . 1 84

f;;etuf<n 4 CPOS^^^-ATK :I: NT ( T I y SE y T y 60 y 6 y NES y . 1 ) *4 . 1 84

RETURN

5 PERCE -PERCEN /I 00.

(:;POS--= ( ATK I NT ( T I y so y T y 60 y 6 y NES y . 1 ) * ( 1 . -PERCE ) +

1 ATK ;i: NT ( T 1 y SP y T y 60 y 6 y NES y . 1 ) *PERCE ) *4 . 1 84

C TF-IE EXPRESSION FOR THE ENTROPY OF EQUILIBRIUM H2 IS INCORRECT y C THE ENTROPY OF MIXING MUXT BE ADDED TO MAKE IT COMPLETE

RETURN

END

FUNCTI ON ATK INT ( X y YMAT y XMAT y NELMTS y NMAX y NESSY y ACRCY

)

C THIS PROGRAM HAS BEEN CHANGED SO THAT THE OSCILLATING NATURE OF

C THE MATRIX TO BE INTERPOLATED EXISTS ONLY AT THE UPPER END OF THE

C TABLE

C THIS ROUTINE WILL TAKE INPUT MATRICES OF UP TO 999 ELEMENTS EACHy

C ARRANGED SO THAT THE X MATRIX (XMAT) IS IN EITHER ASCENDING OR

C DESCENDING ORDER y SELECT NMAX OF THESE POINTS y CHOSEN SO THAT

C SUCESSIVE X i; A LUES OSCILATE ABOUT THE VALUE OF THE ARGUMENT X C UNLESS THE ENDS OF THE XMATRIX INTERFERE (IN THIS CASE THE

C OSCILATORY NATURE IS LOST BUT THE PROGRAM WILL STILL PERFORM AN

C INTERPOLATION) y INTERPOLATE ON THESE NMAX PAIRS OF DATA BY

C AN OSC I LATINO VARIABLE POINT AITKEN INTERPOLATION ALGORITHM

C EITHER UNTIL THE PERCENTAGE CHANGE IN THE INTERPOLANT IS LESS

C THAN THE ACRCY ARGUMENT (THE ARGUMENT NESSY INDICATES THE

C NUMBER OF THE POINT JUST BEFORE THE LAST ONE CHECKED) OR UNTIL

C THE NMAX POINTS ARE ALL USED. IT IS SUGGESTED THAT NMAX

C BE LESS THAN 10 y AND OF COURSE LESS THAN NELMTS. NELMTS

C INDICATES THE NUMBER OF ELEMENTS IN XMAT OR YMAT.

C IF NESSY IS ZERO IT INDICATES THAT THE INTERPOLATION REQUIREMENT

C HAS NOT BEEN SATISFIED. IF NESSY IS 1 IT MEANS THAT THE VALUE OF

C X LIES OUT SIDE THE RANGE OF XMAT.

80
DIMENSION YMAT(999)» XMAT ( 999 ) , A ( 2:1. y 20 ) 100 F0F<MAT(42HINT£RP0LAT]:0N REQUJ:F;;E;:MENT not satisfied (X-=yE16. 8 »1H)/3:JH

1 LAST 2 AF'PRGX I M AT I ONS OF Y ARE ( Y:--" v E 1 6 , 8 y I H ? r E 1 6 » 8 » 1 H ) ) 200 F0RMAT(55HTHIS REPRESENTS AN EXTRAPOLATION OF THE XHAT MATRIX(X-=»

1E;L6.8s.1H)/33HN0 CALCULATION HAS BEEN PERFORMED)

300 FORMAT (24HNELMTS IS LESS THAN NMAX)

400 FORMAT (22HNMAX IS LAR(3ER THAN 20)

IF(NMAX-20)71y71y69

69 PRINT 400

ATI\INT=--0a)

RETURN

71 IF ( NMAX -NELMTS ) 75 » 75 9 73

73 PRINT 300

ATKINT=0.0

RETURN

75 CONTINUE

C FIRST TWO SUCCESS H^E VALUES OF THE XMATRIX THAT STRADDLE THE

C VALUE X WILL BE SOUGHT

JJl-NELMTS-1

DO 20 I^lrJJl

DIFl-X-XMAT(I)

DIF2==-XMAT(I + 1)-X

IF(DIF1)16»15>16

15 ATKINT=YMAT(I)

NESSY =NMAX

RETURN

16 IF(DIF2)18yl7y 18

17 ATI\INT = YMAT(I + 1)

NESSY =:^NMAX RETURN

18 RATIO^-^DIFl/ DIF2

IF(RATI0)20!;20!'19

19 IMID=I

GO TO 32

20 CONTINUE

C AT THIS POINT ONE COULD PRINT THE FOLLOWING STATEMENT

C WRITE OUTPUT TAPE 6»200i'X

NESSY=^1

ATKINT^^O.O

RETURN

32 CONTINUE

C NOTE THAT RATIO IS POSITIVE IF THE TWO POINTS STRADDLE X C REGARDLESS WHICH IS LARGER

JJJ=IMID

JUP-IMID

JDN=IMID

IF ( JJJ + NMAX-NELMTS+l ) 98 ? 98 t 102

98 DO 201 J=lyNMAX

JJJ-IMID+J-1

A(lyJ)-XMAT(JJJ)

201 A(2y J)==YMAT(JJJ)

GO TO 203

102 DO 41 J-lyNMAX

JJ--J/2

J0E-^J-2*JJ

C JOE IS IF J IS EVEN AND 1 IF J IS ODD

IF( J-1 ) 33 y 40? 33

33 IF(JDN-l)34y36y34

34 IF ( JUP-NELMTS ) 35 y 37 >• 35

35 IF( JOE) 37 y 36 y 37

36 JUP=JUP+1

JJJ=JUP

GO TO 40

81
37 JDN=--0DN-:L

JJJ-JDN

BO TO 40

40 Adi'.D^XMAKJJJ)

A(2i'J)^=^YMAT(JJJ)

4 3. CONTINUE

203 NNN^^^^NMAX+1

DO 6 J:^-=3i.NNN

DO 5 K^^Ls-NMAX

C J IS THE COLUMN NUMBER

C K IS THE ROW NUMBER

OA ( J » K ) = ( A ( J-l - K ) -A ( J- 1 9 J-2 ) ) * < X

:l. +A( J-i)' J-2)

IF(K-L)3!'2y3

2 I F ( ABS ( ( A ( J 1- L ) -A ( J- 1 y I.

3 CONTINUE

5 CONTINUE

6 CONTINUE

NESSY^^=0

C AT THIS POINT ONE COULD

C WRITE OUTPUT TAPE 6yl00

ATKINT--=A(NNNyNMAX)

RETURN

7 NESSY^^^J-l

ATKINT^=^A( JyL)

RETURN

END

SUBROUTINE LIMITS(PvTy I DIMENSION G(32) yi^P(9)

C M M N / D A T A / G v R v G A M M A IE(P.GT*PUP)GO TO 1.0 I f ( J : G T T U I... <. R < J . I... T . r I... I._ ) G r

IL^^^^I REUJRN

10 PRINT II;' PUP

11 FORMAT (* THE INPUT PRIi: I/* THE RANGE FOR THIS

IL^^O

RETURN

12 PRINT 13vTLL!'TUL

13 FORMAT (* THE INPUT TEMPERATURE

1/)K THE RANGE FOR THIS EQUATION

IL^^^O RETURN

END

SUBROUTINE DATA NE

PRINT 105

105 FORMAT (* THE TEMPERATURE RANGE

1/* WITH PRESSURES TO 200 BAR*

YOU MAY ENTER THIS R PvD OR Jf AND FOR

EITHER P OR Ty AND

TO CHANGE FLUIDS ENT

::44»4 PC^^:26.54

TTP::::25,

PUL^^200.

TUL^^^^300.

TLL=^^^25* EM:-20,183

PRINT 104

-Ads- J-2 ) ) / < A ( 1 y K ) -A ( 1 y J-2 ) )

.n /A ( J y L ) ) -ACRC Y/ 1 00 ) 7 y 7 y 3

PRINT OUT THE FOLLOWING STATEMENT

X y A ( NNN y NMAX ) y A ( NNN- 1 y NMAX~1

)

UPyDTPyPCCyPTPyTCCy TULyTL h-UP

SSURE

EQUAT

Ul.Jl :ONS

THE

^OM

RANGE

TO *y

THIS EQUATION

Oy* BAR*)

our OF

FROM *. RANGE*F6»2y* TO *yF6»0y* K*)

OF NEON 5 TO 300 KELUIN*

2/*

1/*

4./*

5/*

TC^

UTiNE w;i IH ANY TWO OF IHE k^ARIA BLES*

HE THIRi; y FOR SATURAI ION ENTER WITH*

l-OR THE OTHER "WO ylF YOU WANT *

R l-OR ALI . T HI-;EE INPUT VARIABL ES*)

82
104 FUKriAlC* DO YOU WANT ENGINEERING UNITS OR METRIC UNITS ?*

I/* ENTER A EOR ENGINEERING UNITS OR A I FOR METRIC*)

CALL DAI A N READ 102? lU

102 FORMAT(II)

17 IF*;IU*EQ.>0M3U TO 18

PRINT 103

103 l-ORMATOK ENTER PRESSURE IN BAR? DENSITY IN MOLES/I. T TER ? AND TEMPER

lAIURE IN KELUINSJK)

24 READ *jpyDyT

P=:p/ 1.0 1325

GO 10 19

18 PRINT 106

106 rORMATOK ENTER PRESSURE IN LB/SQ IN? DENSITY IN LB/CU HT AND*

1/* fEMPERATURE IN DEGREES F*)

READ *yp7D?T

P=P/14.6y'5<^49

D

--= D* 1 6 . ]. 8 4 6 3 7 :l. / E M IF(T,EQ.O»0>GO TO 19

r==(T-32, )/l .8 + 273.15

19 CONTINUE

IF<Pa..E.O.O)GO TO 14

IF(D.LE,0*0)GO TO 13

IF<T.LE.O.O)GO TO 12

GO TO 21

1

2

I

F'

( !-

. L E . , . R <. D . I... E .0.0) G T 1

5

T==FNDTNE''. P»D)

IF ( P . GT . PUL . OR . T . 6T . TUL . OR . T . L f . TLL ) GO TO 25

GO TO 16

13 IF(T .LE.0.0.0R.P.LE.0.0)G0 TO 15

I F ( P . GT . PUL . OR . T . GT . TUL . OR . T . LT . TLL ) GO TO 25

131 D=FNDDNE(P?T)

GO TO 16

14 IF(D<.LE.0.0.0R.T.LE.0.0)G0 TO 15

P^-FNDPNE(DyT)

I F ( P . GT . PUL . OR . T . GT . TUL . OR . T . LT . TLL ) GO TO 25

16 H^ENTHNE(PyDjT)

S:^ENTRNE(Di-T)

PP==P* 1.0 1325

IF(IU.Ea.O)GO TO 23

PRINT 100?PPyD?TH-l>S

100 FORMAT (* PRESSURE::::* !.F7.2y* BAR r DENSITY^:* » F7 . 4 y * MOLES/LITER > TE*

1 *MPERATURE::=* y F6 . 2 ? * KEL^viIN*

2/* ENTHALPY=:*?F9.2?* JOULES/MOL? ENTROPY::::* ? F6 . 2 ? * JOULES/MOL-K* ) GO TO 17

23 P0::::P* 14. 695949

T0::::T*l,8-459.67

DO-:::D*EM/ 16. 01 846371

H0:=H/(2.324445*EM)

SO::::S/ < 4.1 8400 1*EM)

P R I N r 1 1 yP0 9 D - T ? H v S

101 FORMAT (* PRESSURE:--=*vF10.3).* LB/SQ IN» DENSITY=* ? FIO . 4 » * LB/CU FT*

1/* TEMPERATURE:=:*!-F8.2y* Fv ENTHALPY^::* ? F9 . 2 ? * BTU/LB*

2/* ENTROPY-:*? F6, 2?* BTU/LB-F*)

GO TO 18

15 1F(P.LE.0.0.AND.TJ..E.0.0)G0 TO 21

IF(P.GT.0.0)G0 TO 20

I F ; r . G T . T C . R . T . L f . T f F' ) G T 2 2

p:--'v'PNNE(T)

109 FORMAT (* DO YOU UANT SATURATED LIQUID OR VAPOR*

1/* ENTER A 1 FOR UAPOR OR A FOR LIQUID*)

PRINT 109

83
READ *yIP

:i,F (:i:p.gt.o)f-'^^^p~»oooi.

:i;F(:i;p.EQ.o)p^=M-'f.()oo():i.

GO TO .131. 20 ;i:r(p,GT*PC)GQ to 22

T:^=*;pti:;:ne(P)

PRINT 1.09 READ >Ky:i;P ]:f(:i:p,gt.o)P^-^p-.oooi.

j;F(IP.EQ.0)p::^=P+.00001

GO TO 1.31. 22 PRINT 1.07 .07 FORMAT (* YOUR INPUT PRESSURE 01- 1./* OF THE SATURATION CURUEi- TC^^ 2/* TRY AGAIN*)

GO TO 17

21 RETURN

PRINT 108

!•• y< M A I ( * Y U R' I N I-' U T T E ii I-' E R A T' U R' li 1/* TEMP MUST BE BETWEEN 25 AND

2/* AND 200BAR» TRY AGAIN*)

GO TO 17

END

SUBROUTINE DATA HE

PRINT 105

105 FORMAT (* THE TEMPERATURE RANGE

TEMPI

44 .4 V :rature isPC-2A.89»

OU

T

T OF RANGE*

TRIPLE ^=25.*

.08 OR PRESSURE IS OUT OF RANGE*

300K AND PRESSURE BETWEEN*

1/*

2/*

3/*

4/*

5/*

TC

PC

TTP.

PUL^^ TUL =

TLL.^^

WITH iESSURES TO

YOU MAY ENTER

P»D OR Jv AND

OF HELIUM IS 2. 177

000 BAR*

THIS ROUTINE WITH ANY TWO OF THE

FOR THE THIRD? FOR SATURATION

TO 1500 KELVIN*

OR Jv AND A

:: FLUIDS ENTIi FORA THEFOR

or HER TWO

ALL THREE

y IF

INPUT

VARIABLES*

ENTER WITH*

YOU WANT * VARIABLES*)

INEEP: RINGING UNITJ

UNITS OR

; OR

A 1 METRIC UNITSFOR METRIC*)

?*

EITHER P TO CHANGIi

5.201

2.245

^2.17

1000.

1500.

2.177

EM-4.0026

PRINT 104

104 FORMAT (* DO

1/* ENTER A READ 1021-10

FORMAT(Il)

IF(IU.EQ.O)GO

PRINT 103

103 FORMAT (* ENTER PRESSURE IN BARy DENSITY IN MOLES/LITERv AND TEMPER

lATURE IN KELVINS*)

24 READ *i'pyDi.T

P^=^P/ 1.0 1325

GO TO 19

PRINT 106

FORMAT (* ENTER

1/* TEMPERATURE

READ *yPyDyT

P^::^P/ 14, 695949

D^^D*16.0ie4637:

1F(T.EQ,0.0)G0

102

17

YOU WANT ENG

FOR ENG I NEE

TO 18

18

06 PRESSURE

IN DEGREE

LB/SQ INy DENSITY IN LB/CU FT AND*

*)

./EM

TO 19

T-(T-32. ) /I. 8+273. 15

19 CONTINUE

IF(P.LE.O.O)GO TO 14

IF(D.LE.O.O)GO TO 13

IF(T.LE.O.O)GO TO 12

84
GO TO 2.1. 12 :[F" (P.I...E,0<.O.0R.UJ_E»O.O)GO TO 1.5 T^^FNDTHE(I->D)

I F (

I"- . G T V !• U L. . R . T . G T . T U I... . R . T 1.. r . 7 L.. I... ) G 1 C) 2 5

GO TO 16

1

3

j: f (I . l e , . . r . F' . i... e: . o . o ) g o r o i ir; 1 F ( P . GT <, PUL . OR . T » G I . TUL . OR . r . I... T' , TLL ) GO 70 25

131 D=:FNDDHE(P?T.>

GO TO 16

14 IF(D,LE.O.O.OR.T.LE,().0)GO TO 15

P^:4"N.DPHE(D»T)

:i: F (

r-' , g r . p u l . o r . r Cv r t u l . o r . r . i... t . r i... i... ) g (3 r o 2 5

16 H-Hi;;NTHHE(DyT)

B^=ENTRHE(Di>T)

W^^^^SOUNHECDyT)

CPP^^CPHEdJsrT)

TH^:^^THERHE(.0!'T)*100.

y^^-^yiSCHEdii'T)

PP=-P)K1 .01325

IF(HJ.EQ.O)GO TO 23

PR I NT 1 00 f PR f D 9 T y H i- S c GPP ,CK>K}>li, IW y K> 100 FORMAT(* PRESSURE= *yFa»2T* BARi> DENS:i:TY==* » F7 . 4 i- * MOLES/LITER. TE*

l*MPERATURE^-=* y \-7 . 2 v * KELVIN*

2 / * t: N T H A L., P Y ^-^^ * !. F 9.2!.* J (J U I... hi S / M 1.. ^ E: N T \< E' Y = * y I 6 . 2 y * ..) 1.) L E: S ./ M L. - K *

3 / * t; E'

-^ * y E 7 . 2 y * J L E: S / M 1.. - K y G V == * y F' 7 . 2 y * J U 1... I.-: S / M L - K * 4/* SPEED OF S0UNEM^^*vFe.2y* METERS/SEC*

5/* THERMAL CONDUCTIVITY:^^* y F7 . 2 ? * M WATS/M-K*

6/* VISC0SlTY^-:*yF7.2y* MICRO G/CM-SK

)

GO TO 17

23 PO::=H='* 14. 695949

TO-T* 1.8-459. 67

D ^- D * E M / 1 6 . 1 B 4637

1

HO:::0-I/(2.324445*EM)

SO=--S/< 4.1 8400 1*EM)

CPPO^-^CPP/ ( 4 . IB4001*EM.)

0^0:^:0^^/(4. 18400 1*EM)

W0=:W*3. 280840

TH0:=TH*. 000578176

V0==U*.00671'i'6897

P R 1 N I' 1 1 y E' y n y 7 y H y S y C F' P y C V V y W y 7H y V 101 FORMAT(* PRESSURE::--*yF10.3y* LB/SQ INf DENSITy?*y FIO. 4 y * LB/CU FT*

1/* TEMPERATURE-* •F8.2y* Fy ENTHALPY^::* y F9 . 2 y * BTU/LB*

2/* ENTR0PY:::*7F6.2y* BTU/LB-F*

3/* Cp:=*yF7.3y* AND CV^-:* y F7 . 3 y * BTU/LB-F*

4 /

S E'

E

E: D OF 8 U N

D

-^ * y E 8 . 1 y * E I' /

S

E:

C

* 5/* THERMAL CONDUCTIVITY::::* y F7 . 2 y * BTU/FT-HR-F*

6/* VlSC0SITY::::*yF7.2y* LB/FT-S X Ei7*)

GO TO IS

15 :i:f(p<.lE:.o.o.and.t.le.o.o)GO to 21

1F(P.GT.0.0)G0 TO 20

I F ( T . G T . T C . \< . I . I._ 7 . 7 T P ) G T 2 2

P::=VPNHE(T)

PRINT 109

READ *yIP

IF(]:P.GT.0)P=:p-.0001

J: E ( I

E'

. G E . 1 ) F' ::: E' f . 1 109 FORMAT (* DO YOU WANT SATURATED LIQUID OR VAPOR*

1/* ENTER A 1 FOR VAPOR OR A FOR LIQUID*)

GO TO 131

20 IF(P.GT.PC)GO TO 22

T::::VPTEHE(P)

85
PR IN I 109

F<EAD >Kv;i:p IF"(1P.GT\0)P^:=P--.000:I.

IF ( 1 P. GE.1)P-Pf .0000:1

GO TO 131

PRINT 107

FORMAT (>K YOUR INPUT PRESSUR •;: OR TEMF ERATURE IS OUT OF RANGE*

1/* OF THE SATURATION CURVETC^:^: 5,201 V PC:::: 2..; '75 V T TRII-LE:=:2.177*

2/* TRY AGAIN*)

107

GO TO 17

21 RETURN

25 PRINT 108

108 FORMAT (* YOUR INPUT TEMPERATURE OR PRESSURE IS OUT OF RANGE*

1/* TEMP MUST BE BETWEEN 2.177 AND 1500K AND PRESSURE BETWEEN*

2/* AND lOOOBARf TRY AGAIN*)

GO TO 17

END

SUBROUTINE INFO

PRINT 2

2 FORMAT (* WHEN THE PROGRAM ASKS FOR A FLUID SELECTION y ENTER THE AP

IPROPRIATE NUMBER*

2/* AN INAPPROPRIATE NUMBER WILL TERMINATE THE PROGRAM*)

PRINT 1

1 FORMAT (* WHEN THE PROGRAM ASKS FOR A PRESSURE. DENSITY). AND*/* T lEMPERATUREy ENTER ANY 2 OF THE THREE AND A FOR THE THIRD »*/* TH

2E ORDER MUST BE Py D^Tv AND ONE OF THE THREE MUST BE 0. * 3/* IF ALL THREE ARE THE PROGRAM ASKS FOR A NEW FLUID*)

PRINT 110

110 FORMAT (* IF YOU ARE INTERESTED IN A DEFINITION OF THE VARIOUS*

1/* MODIFICATIONS OF HYDROGEN ENTER A 1? IF NOT ENTER A 0*)

READ *i.IC

IFdC.NE.DGO TO 111

CALL H2 INFO

111 PRINT 112

112 FORMAT (* IF YOU ARE INTERESTED IN THE SOURCES OF THESE PROGRAMS*

1/* ENTER A 1 IF NOT ENTER A 0*)

READ *)'IS

I F ( :i: S , E Q . 1 ) C A L. I... S U R' C E RE) URN

END

SUBROUTINE H2 INFO

PRINT 100

100 FORMAT (* THE HYDROGEN MOLECULE IS MADE Up' OF TWO HYDROGEN ATOMS*

1/* THERE ARE TWO POSSIBLE RELATIVE ORIENTATIONS OF THE NUCLEAR*

2/* SPIN OF THE ATOMS IN A MOLECULE OF HYDROGEN. I.E. THE SPINS*

3/* MAY BE IN THE SAME DIRECTION (ORTHO) OR IN OPPOSITE DIRECTIONS*

4/* (PARA). THE RELATIVE AMOUNTS OF ORTHO AND PARA HYDROGEN IN*

5/* A SAMPLE OF EQUILIBRIUM HYDROGEN IS TEMPERATURE DEPENDANT*)

PRINT 101

101 FORMAT (* AT ROOM TEMPERATURE EQUILIBRIUM HYDROGEN IS 75 PERCENT*

1/* ORTHO AND 25 PERCENT PARA AND IS CALLED NORMAL HYDROGEN*

2/* AT 20 KELVIN EQUILIBRIUM HYDROGEN IS 99,8 PERCENT PARA.*)

RETURN

END

SUBROUTINE SOURCE

PRINT 100

100 FORMAT (* THIS PROGRAM WAS WRITTEN BY R.D. MCCARTY AT THE NATIONAL*

1/* BUREAU OF STANDARDS IN BOULDER COLORADO UNDER A CONTRACT WITH*

27* THE JOHNSON SPACE CENTER IN HOUSTON TEXAS. THE NASA CONTRACT*

:i/t MONITOR AT JSC IS WALTER SCOTT. THE DOCUMENTATION OF THE*

4/* PROGRAM IS IN PREPARATION AND IS PLANNED AS A JOINT*

5 / * N A S A - N B S' F' U B l_ :i: C A 1 I ON*)

86
RETURN

END

I-' L) N C T 1 iNi f M El D H E ( F' :i: . T I

)

C SOLVES THE HELJUH EQUATION OF STATE FOR DENSIfY IN MOI/I ITER

C GIUEN A PRESSURE IN ATMOSPHERES AND A TEMPFRATURE IN IiFGRFFS K T-TI • " ""

F-4'I IF a\LT.5.2)Ga TO 6

IF(T.LT.I5, )PM-PMELT(T)

IF(PM*LT.P)00 fO 30

IF(T*GT.IOO. )L;0 TO 1 PC~2 . 2449+ ( T-5 , 201 4 ) * 1.76

IF(PJ_T.PC)GO TO 1 PM-200 , + ( T-5 . 2 > * 12 . 3

1

D=17 . 399+ ( ( PM-PC ) / ( PM- PC+1 . ) ) *2 , 33*17 . 399

GO TO 7 2 D:-=»0001

IF(T.LT.4.2)G0 TO 7

1 yB^^VIRB(T)

RT=0.0820558*T

P1=-^RT/P

ri=l,/(Pl+VB)

60 TO 7 6 IFCP.LT.VPNHECT) )G0 TO 2

DS=46.18+(T-2. )*4.02

DL=DSATL ( T ) *1000 . /4 . 0026

DEL=DS-DL

Ph=PMELTCT)

IF(P»GT.PM)GO TO 30

D=^DL + DEL*P/PM

7 DO 10 I:=l»50

P2==FNDPHE(D>T)

IF ( ABS ( P -P2 ) -1 , £-7*P ) 20 » 20 y 8

3 DP=DPDDHE(D»T)

C0RR^(P2-P)/DP

I F ( ABS ( CORR ) - 1 . E-7*D ) 20 > 20 v 1 10 D^=D-CORR

FNDDH£=:0

RETURN

20 FNDDHE:==D RETURN

30 FNDDHE^O

RETURN

END

FUNCTION FNDPHE ( DD . TT

)

C THE MAIN EQUATION OF STATE ROUTINE FOR HELIUM:

C THE INPUT IS DENSITY IN MOLES/LITER AND TEMPERATURE

C IN DEGREES K x THE OUTPUT IS PRESSURE r DP/DD ? DP/DT y ENTHALPY >• C ENTROPY AND C^^ IN ATMOSPHERES AND JOULES

DIMENSION A(26) yB(27y4)

COMMON/ I DEX/ ID

DATA(ID-=0)

DATA( (BCD ? I =^82 s- 108) =

1 5.988310109E-9y-4»9653052187E-7»-3.8116033499E-6!'3.68116713

13E-S !- -1 . 483069 1 828E-4 , 3 . 05961 74335E -4 » -3 39081 90224E -4 ? 1 . 962408024

22E-4» 1 5527899712E-5 7 -3.61 10403503E-5»~1 .0a39788073E -5^4. 972810121

37E-5 , 1 .9381 451 09E-5 ? -4 . 149640S96E~4 f -5 . 7465772899E -4 9 -4 . 3470945634

4E-3 9 "6 . 8383888924E -2 ? -2 . 1 382474225E-2 9 2 , 7106954908E-2 9 -1 . 262796778

58E-2 9 2 . 587575338E-3 , 7 . 904 1608815E--2 y -1 . 402472431 8E-4 9 -2 . 8278987249

6E-7 r 1 . 73364 10358E--6 ? -2 . 54541 87855E -6 9 -0 . 0005 ) DATA ( ( B ( I ) 7 1^^:55 y 81 ) =-1 . 4802195348E-8 9 4 .1721791 1 19E-7 9 -2 . 3326553271

87
yj^

1 E-~7 , 4 0855 1 1. 088E -7 v 1 . 09()0567964E-5 v -5 . 0()60952775E-5 » :l. 1. 312765043

2E--4v •i »2539843287E-4!' 1. , 966J.3806a8E-6 y 1. . 7:l.22932666E-4 y 2 . 305:1000563

3E" 4 V -9 . 6564739 1 E- -4 » -3 . 6027 735292E--5 » 1. . 6079946555E -3 » -2 . 744 1.7636 :l. 5

4E--2 ? . 14739506957 , - . 43559344838 v 1 . 3447956078 » -1 7040375125 y . 9026267

5404075.6875644111E-3y -l »4438146625E- 1 y3.3768874851E--3y 1 ,0754201218

6E-6 V -4 . 5264622308E-5 » 3 . a597388864E--5 , - . 0005 ) DATA( (B( I ) y :i>^^28y54)^--4»2287454626E -8y4.4529354413E-7y-l »0246150954

1E--5 y 8 5254608956E -5 y -2 .51 63069255E •4 y 3 . 2877709285E-4 y

- 1 . 0601 95758

2 E - 4 y - 1 » 6 8 7 7 3 8074 E - 4 y - 3 . 2 1 2 095063 2 E - 5 y 1 . 4 1 5 9 0189 7 E - 4 y 1 . 4 7 2 5 6 3 7 1 4E -3 y -2 . 618354941 E-3 y 2 . 0461 50 1 1 1 7E -5 1

. 2746996288E-3 y -2 , 0272929583

5E-2y7.4648036615E--2y~, 17217966521 y , 51053439738 y -. 4017B202697 y 6 . 26829864632 y 7 . 906601204E -3 y -8 . 9393485656E -2 y - . 15076580053 y 72 . 6882494327E-6 y -3 . 37943 16835E- 5 y ••2 , 4495951 1 95E-5 y - . 0005 ) DATA< (B(l) yl:=--ly27):^ A -1 509686261 9E-7 y 6 . 4640898904E-7 , 4 . 1362357367E-5 y 1-3 .79101 90353E--4 ? 1 . 3806454049E-3 y -2 . 508541 2058E--3 y 2 . 3697560398E-3

2 y -9 . 572646 1 066E-4 y 3 . 740593 1 823E-5 y -6 , 4 1 03220333E -4 ? 31 . 85793661 77E-3 y 7 . 4007986606E--4 , 1 . 4792568 1 48E -4 y -3 . 2531 355477E-3 y 4 1 . 95 1 8739286E 2 y

- . 1057 1817 1 35 y . 33 1 64944449 y - .511 30022535 y 53.9940004906E-ly -.15555244471 y 4. 906264031 E-3 y -2,61 48004377E-2y

63 . 4221 685545E -2 y 5 . 4 1 59662622E--6 y - 1 . 0687806777E-5 y & . 9484651 869E -6 y 7 -.0025)

KP==:1 GO TO 10

ENTRY DP D THE

l\P-2

GO TO 10

ENTRY DF'DD HE

KP:^^3 GO TO 10

ENTRY ENTRHE

Kp:=4

GO TO 10

ENTRY ENTHHE

KP^^5

GO TO 10

ENTRY CVHE

KP=6

10 K1^^=0

KH-^^^l KK=1

K4-:^l IF(i:i:i.NE.O)GO TO 20

j:f(tt.ge.15. )go to 20

if (tt.gt. 10)00 to 30

if (dd.gt. 17.3987)00 to 40

11 :i::=i T::::rT D=DD

8 GO TO (9yl00y200y300y400y500)KP

9 D2^^D*D

D3:^^-D2)K.D D4==D3>KD

D5^^D4*D

GAfi(iA:^-^B(27y 1)

EX-EXP(Ii2*GAMMA)

EXD3::=EX*D3

EXD5::^^EX>i<D5

N=^l A(N)^^^D5)KD $ N^=N+1

88
A(N)=^A(N-1. )/T $ N^---h\il DO 2 :t-lv6

f:i>=;i; A(N):^a:iS)f<T**( .75-Fi;/4. ) no 3 i = :Lv4

A(N) :^D4*T>K*(1. .5-F:I; ) 3 N^^N + 1 DO :i. .[.^i,8

FI==.l A ( N ) =--^D3* I ** ( 1 » •5-F1/2 . )

1 continue:

DO 4 1-15.3

Fi = :[ A(N)::::EXD3)KT**( 1 -FI ) 4 N=^N + 1 DO 5 1-1 V

3

Fl-I

A(N)-EXD5*T**(1.-F1)

5 N-N+l

N^^^N-l

7 P-0

DO 15 J-lvN

IS P=P+B( J»1)*A(J)

F-==P+ . 0a20'558)XD*T)« ( 1 . +y 1 RB ( T ) )KD ) IF(KHa..T.l)GO TO 413

GO T0(S0i'50)'30y40)K

100 D2-D*D

D3-D**3

D4-D3*D

D'5-D4*D

DA-D5X<D

T2-T)KT

T3-T2>KT

T4-T**4

M-I

GAMMA-B(27yM)

EX-EXP<D2*GAMMA)

N-1

R-, 0820558

A(N)--=0.0 $ N-NM

A(N) = (--1 . )*DA/T2 $ N-Nfl

DO 102 1-1 1.6 Fl = l A(N)-D5)KT**( ,75~FI/4. ••1 . )*( .7S-F1/4. ) 102 N=:N+1

DO 103 I-ls'4

FI = 1 A(N)-D4*T**( 1 S-Fl/l .-1 . )*( 1 ,5-FI

)

103 N-N+1

DO 101 1-1 !-

8

FI-1

A(N)-D3*T**( l»5-FI/2,-l» )*(1 .5-F1/2.

)

101 N-N+1

DO 104 1-17 3

FI-1

A(N)-EX)XD3>KT*>K( 1 . -FI-l . )*( 1 , -FI ) 104 N-N+1

DO 105 I-ly3

89
105

11.5

200

202

103

201

204

205

2i:

300

f 1 -

A ( N ) ^^^^EX*!:!^*!** ( 1 . -F I - 1 . ) * ( 1 < F :i;

)

N^:^:N+l

p::::0 DO 115 J^::^l. i-N P^:^P + A( J)*B(JyM)

!• :=:: 1=' + R * H * ( 1 . { V

R B ( ) ) * D ) f R * 1:1 * I * D B ti r ( I > * Li 1-M

GG T0(50v50v30v40)K

D2^^^D*D

03:^=^1:12*11 D4=D3*D

D5=D4*D

GAMMA^:=B(27.M)

EX^EXP(D2*GAMMA)

DEX==-GAMMA*2,>KD)XEX

N===l

R==::0 0820558

A(N)-:6.*ri5 $ N^^-^N+l A(N)=A(N-1 )/T * N^^^Nfl DO 202 l:::=lv6 F ]:=•= I A ( N ) =5 . *D4*T** ( . 75-F :i:/4 « )

DO 203 1-11-4

F1--I A ( N ) =:::D3*4 « *T** ( 1 . 5--F I ) N = N+1

DO 201 l:::-l!'8 Fl-^1 A ( N ) ^D2*3 . *[** ( 1 . 5-F 1/2 .

)

N^^N+l

DO 204 1-1.3

FI-I

A ( N ) - ( DEX*D3+3 . *D2*EX ) *T** ( 1

. -F 1

)

N=-=N+1 DO 205 1-1 T

FI==-I A ( N ) - ( DEX*DS+5 . >KD4*EX ) *T)K* ( 1 . -F I ) N-Nfl s. N.-;=N-1 P==0 DO 215 J-li-N

P-P+A( J)>KB( JyM)

I-M

P-P+R*T* ( 1 . +2 . *D*V1RB (T )

)

GO T0(50i'50>30!'40)K

D2-D*D

D3==D2*D

D4-D3*D

N-=:l R==. 0820558

M-I

GAMMA-B(27!»H)

EX-EXP(D2*GAMMA)

A(N)==0.0 $ N-N+1

A(N):=(D4*D/5. )*T**(-2, )>K(-1, ) * N-N+1

DO 302 I-lyft

FI-I

A(N)-(D4/4. )*}**( .75--F1/4.--1. )*( , 75-F 1/4. )

90
302 N:^N+:l, DO 303 l-^^lvA

A < N ) ^^ ( D3/3 . > * T** ( 1 5-F I - :l„ ) * ( :l, . 5 -I- I ) 303 N::^N+:l. DO 301 J^:-:li.8

f;[:^::i: A(N) =-(D2/2. )*T*>K(i. . ;^ -F 1/2 . -••J. * )*(:!. .5-f:i:/2. ) 301 N=:^N + 1 DO 304 I -11-3

Fj;^==i A ( N ) ^ (EX/ ( 2 . *GAMMA ) ) XcT** ( 1 , -F 1 - 1 . ) * ( 1 . - F I ) 304 N=N+1

DO 305 ]>li'3

f:l^=^i A ( N ) := ( D2*EX/ ( 2 , 5KGAMMA ) -EX/ ( 2 >KGAMMA**2 ) ) * 1T**( 1 ,-FI-l . )*( 1

. -Fl)

305 N:::N+1 N^=N-1

s I N T ^- D * R * ( V :i: R B ( r ) + r * d b d r ( t )

)

DO 306 I^-^li-N 3 6 s j: n t = s I N r + B ( :i: y M ) * A ( j: ) N:^^^21 EX=:1.

D2=^0

DO 310 1-1 V

3

f:[==i

A(N):^^(EX/(2.*(3AMMA) )*!**( 1 .-Fl- 1 . )*< 1 . -FI

)

310 N^=N+1

DO 311 1=^1 1-3 Fl=:l

<^(N )---( D2*EX/ ( 2 . *GAMMA ) -EX/ ( 2 » *GAMMA**2 ) ) * 1T*)K<1 .~F1-1. )*(1.-F]:)

311 N=^N+1

N = N-1

DO 312 1=^21 yiN 312 SINT = SINT-B ( I y M ) *A ( .[ ) p.::(9.37:l.658 + 5,193043*AL0G(T/4.2144)-25.31469*(SINT + R*AI...0G(R*T*D) ) ) p:-:^P*4.0026

GO T0(50»50»30y40)K

400 KH^^^O GO TO 9

413 PP:^P

KH=1

D2=^D*D

D3=D*D2

D4:--ai3*D

N=l

R=:=. 0820558

GAMMA-B(27yM)

EX=-EXP(D2>KGAMMA)

A(N)=---(D4*D)/5. $ N^^=Nfl A(N):==(D4*D/5. )*(2./r ) $ N---=Nfl DO 402 I-^=ly6 F .[--=]: A(N)::^(D4/4. )*(T**( .75~Fl/4, )-!**( ,75-FI/4. )*( .75-FI/4. ) ) 402 N=^N+1

DO 403 1^1 y

4

FI-I

A ( N > := ( D3/3 . ) * ( T** ( 1 . 5-F 1 )-!**( 1 . 5-F I ) * ( 1 , 5-F I ) )

91
403 N = N + :l. DO 401 J::--^1'/8

A ( N )

^-^ ( D2/2 . ) * ( T** ( :l. . 5-F I /2 > ) -T** ( 1. . ^;J-F 1' /2 » ) * ( 1 » 5 -F :i: /2 . ) ) 401 N=:Nfl

DC) 404 l:=^li.3 Fi=o: A ( N )

^^^ ( EX/ ( 2 *GAMMA ) ) * ( T** ( 1 . -F I ) T** ( 1 » ••F I ) * ( 1 » -F I ) ) 404 N^N+1

DO 40:j I:=^lf3 FI = I A < N )

^=: ( D2*EX/ ( 2 *GAMMA ) -EX/ ( 2 , *GAMMA**2 ) ) * ( T** ( 1 -F I ) -I** ( 1 -F I

)

1*(1.-F1) ; 405 N--^Nfl N=N -1 HINT-^^R*T*T*D*DBDT(T) *( -1» ) DO 406 1=1 iH

406 HINT^^HINT + B (l i- M ) *A ( I ) N^^21

D2^==0 EX::=1. DO 410 ;i>-^i!.3 FI = I (h'M)---i EX/ ( 2 . *(3AMMA ))*(!**( 1 . -FT ) -T** ( 1 . -Fl ) * ( 1 . -F 1 ) ) 410 N--N+1

DO 411 1^=1 »

FI=^I A ( N ) =^ ( D2*EX/ ( 2 . *GAMMA ) -EX/ ( 2 *GAMMA**2 ) ) * ( T** ( 1 . -F I ) -T** ( 1 , --F I

)

l*(l.-F;n)

411 N^NH

N-N-1

DO 412 I==21i'N

412 HINT-HINT-B ( 1 v M ) *A ( I

)

P^--2 1.82282+5,1 93043* (T-4. 2 144) +25. 31 469* (HINTfPP/D-R*r)

P^P*4.0026

I = M GO T0(50r50!.30>-40)K

500 D2-D*D

D3=^^D2*D

D4---D3*D

N^^^^l R-. 0820558

GAMMA^B(27i-M)

EX=:EXP(D2*GAMMA)

SIN T==T*D*R* ( 2 . *DBD T ( T ) +D2DBDT2 ( T ) *T ) A(N):^=0.0 % N-N+1

A(N)-^(D4*D/5. )*T**( -2, )*(-l. )*(--2. ) * N-N+1

DO 502 1=^11-6 FI^^I

A(N)--^(D4/4. )*!**( .75-F1/4.-1. )*( .75~FI/4. )*( .75-FI/4. ~1. ) 502 N^N+1

DO 503 1-1 y

F- I -

A ( N ) ( D3/3 . ) * T** ( 1 . 5-F I - 1 . ) * ( 1 . 5-F 1 ) * ( 1 . 5-F I - 1 . ) 503 N=:^N+1 DO 501 1:^:^1,8

F- 1 - :i: A(N)-(D2/2. )*!**( 1 .5-F1/2. -1 )*( 1 .5~F]:/2. ) * ( 1 .5-FI/2.-1 , ) 501 N---N+1 DO 504 ;i>l!.3

FI = I

92
A(N):^(EX/(2.*GAMMA) )*!**( ! -F-I~l. )* ( 1

. -FI ) * (1. . -FI-1 . ) 504 N^^Nfl

DO "505 I- Is. 3

f:i>i

a(n) = (ei2)kex/(2.*gamma) -ex/(2.*gamma**2) )*

1T**( 1

. -FI-1 . )*( 1 -FI )*( 1 . -Fl-I. . ) 505 n^=n+:l

DO 506 ]>1j.N

506 SINT-SINT + B(Ii'M)*A(I)

EX-1. . D2-0

N==21

DO 510 1-1.3

f;[=i

A(iM) = (EX/(2.*GAMMA) )*T**(1 .-FI-l . )*( 1 .-FI )*<1.~FI-1. ) 510 N=:N+1

DO 511 ]>li>3

FI^l

A ( N ) - ( D2*EX/ ( 2 . *GAMMA ) -EX/ ( 2 . *GAM«A**2 ) )

1T**(1. -FI~1. )*(1.-F]:)*(1,-FI-1. ) 511 N=N+1

N=N-1

DO 512 1=21.

N

512 P=P-B(I.M)*A(1)

P==5 » 1 93043* ( 3 , /5 . ) *4 . 0026 -P*101 3278

1^=M GO T0(50!'50»30.40)K

20 K=2

1:^-3 IFdD.NE 0)1 = 4

T=TT

D=DD

GO TO 8

30 K = 3

GO T0(33.34y35)KK

33 D=DD

T=-rT KK = 2

IF(DD.GT»17,3987)G0 TO 40

1 = 1 GO TO 8

34 PT;t = P

1 = 3

KK = 3

T = TT

D = DD

GO TO 8

35 PTIII=P

38 F=(15.-T)/5,

P = F*PTI+(1. -F)*PTi:i].

1F<I\H»LT,1)G0 TO 413

FNDPHE=P

RETURN

40 :i;F(K,£0.3)K1 = 3

GO TG(41y42y43!-44)K4

41 K = 4

:[-:2 K4=2

D = DD

1F(K1«EQ.0)T=TT

GO TO 8

93
42

11=^^:1.7.398 7 1.5 '

:i. 4 ) ti II s A

) :i:f(t I... ( r ) * :l. O . / 4 . O O 2 6

K4^=^3 GO TG 8

43 PI IDC -P

:i: 1

00 TO 8

44 PIDC^: = P

p=::^piDc;f (p:i::n;i-p:i::i:DC)

K4=l

]:f(ki.eq.3)go to 30

FNDPHE-P

50 l-NDPHE-^P

RETURN

END

rUNCT.TON CPHECDi-T)

CSINH(P)

FOR HELIUM i- INPUT IS DENSITY

OUTPUT IS JOULES/MOL-K

;SEE ALSO NEXT PAGE)

P^:==Ci^HE ( D » T ) + ( T* ( DPDTHE ( D y T ) **2 ) / ( ( D**2 ) *DPDDHE ( D ^ T ) ) ) * :l. 1 CPHE^^P

END

FUNCTION SOUNHE(D!'T)

VELOCITY OF SOUND FOR HELIUMv INPUT IS DENSITY (MOLES/LITER)

( M 1... E S / 1... I T E R ) AN D T E

P E. R A T U R li- ( K )

32

:S/SEC

>5311. ) )**.5

AND TEMPERATURE < KELVIN )>' OUTPUT IS IN METRE

S^- ( ( CPHE ( D , T ) /CVHE ( D ? T ) ) * ( DPDDHE ( D f T ) *i SOUNHE^^^S

END

FUNCTION VIRB(T)

DIMENSION A( 9) 5-^(45)

DATA(A--5.081571004IE -7y-l.II686a()862E~4yl.I652480354E-2y

1 7.44745B7998E-2y-5.3143174768E-ly-9.5759219306E -l!- 2 3 . 9374414843 9 -5 . 1370239224 9 2

,

0804456338

)

COEFFICIENTS FROM PROGRAM 5/28/70--1630

THIS SUB PROGRAM CALCULATES THE SECOND VIRIAL COEFFICIENT

I

FOR

HELIUM. THE RANGE IS INPUT IS TEMPERATURE

NEGATIVE THE ROUTINE

. V FOR OTHER VALUES OF

ROM 2 TO 1500 DEG K.

IN DEGREES KELVIN AND lUSEs- IF I SUE IS OR

CALCULATES B FOR THE EQUATION PV^-^^RT ( 1+ BD+ . . lUSEy THE ROUTINE CALCULATES THE VARIANC OF B AT THE INPUT TEMP

UNITS ARE ATM? DEG KELVINv AND MOLES/LITERi- 4/3/69 -1253 ? R D . MCCARTY

REVISED 2/12/70-925

B=::0 DO 5 I-ly9

FI-I

B=::B+T** ( 1 . 5 -FI/2 . ) )KA ( I ) VIRB-B

RETURN

END

FUNCTION DBDT (T)

DIMENSION A(9) yV(45)

THIS SUB PROGRAM CALCULATES

HELIUM. THE RANGE IS FROM

IN DEGREES KELVIN AND lUSEv

CALCULATE

lUSEs- THE

THE

?. TO

IF :

SECOND VIRIAL COEFFICIENT FOR

1500 DEG K. INPUT IS TEMPERATURE

SUE IS OR NEGATIVE THE ROUTINE

B F R J H E E Q U A r 1 N F' V = R T ( 1 f B D f . . . !- F R T H E R V A L U E S F ROUTINE CALCULATES THE VARIANC OF B AT THE INPUT TEMP

DATA ( A=~5 . 08 157 1004 IE -7 y -1 1 168680862E~4 y 1 . 1652480354E-2 y

. 7 . 4474587998E-2 y -5 . 3143174768E-1 y -9 . 57592 19306E-1

,; 3 . 9374414843 y -5 . 1 370239224 y 2 . 0804456338 ) UNITS ARE ATMy DEG KELVINy AND MOLES/LITER y 5/28/70-1630y R . D . MCCARTY

94
UNITS AR E A Thy DEC KELVIN

y

AND MOL ES

B^Q

no 5 :[ = i v9

FI = I B-B+T**( .5-FI/2 -1 <.)*(! .5-1-"1/2 . )*( »

b

D2DBDT2== B RETURN

END

FUNCTION UPNH£( TT)

GVJES A VAPOR PRESSURE -OR HEL lUM IN

TEMPERATURE IN KELVIN. THi; : FUNCTION

1 B-0

no 5 1-1.9

I" I = I 5 B:-=B + T** ( . 5--FI/2 . ) *A (I ) * ( 1 . 5-FI/2 . ) DBDT:=B

RETURN

END

FUNCTION D2DBDT2(T)

DIMENSION A(9)

DATA ( A-- 5 . 0ai5710041E-7 ,-l> 1 168680862E-4 , 1 . .1.6524803S4E-2 9 1 7.4474587998E-2 7-'5.3143174768E-ls'-9,5759219306E-l!-

2 3 . 9374414843 y -5 . 1370239224 y 2 . 0804456338

)

C THIS SUB PROGRAM CALCULATES THE SECOND VIRIAL COEFFICIENT FOR

C HELIUM. THE RANGE IS FROM 2 TO 1500 DEG K. INPUT IS TEMPERATURE

C IN DEGREES KELVIN AND lUSEy IF ISUE IS OR NEGATIVE THE ROUTINE

C CALCULATES B FOR THE EQUATION PV =RT ( HBD+ . . , ? FOR OTHER VALUES OF

C lUSEy THE ROUTINE CALCULATES THE VARIANC OF B AT THE INPUT TEMP

C UNITS ARE ATMy DEG KELVINy AND MOLES/LITER y 5/28/70-1630y R . D .MCCARTY

FI/2. ))i(A( I

C GIVES A VAPOR PRESSURE FOR HELIUM IN ATMOSPHERES GIVEN A

C TEMPERATURE IN KELVIN. THE FUNCTION REPRODUCES THE 1968 HELIUM

C TEMPERATURE SCALE TO .0001 KELVIN

DIMENSION C(12) yD(14)

DATA (C==-3. 9394635287 y 141. 27497598 y --1640,7741565 y 11974. 557102 y 1-55283. 309818 y 16621 9. 56504 y -325212. 82840 y 398843. 22750

y

2-277718 . 06992 y 83395 . 204 1 83

)

DATA (D:^-49. 510540356 y 651. 923641 7 y -3707, 5430856 y 12880. 67349 ly

1 -30048 . 545554 y 49532 . 267436 y -59337 . 558548 y 52311 , 296025 y 2-33950 , 233134 y 16028 . 674003 y -5354 , 1 038967 y 1 199 . 0301 906 y 3 -161 . 46362959 y 9 . 881 1553386

)

T:=TT T=^T-DELT(T)

p::.() IF(T~2.1720>10i'10yl

1 DO 5 I=--^lyl0

5 P:=-P+C( I)*T**(2~I)

VP =:EXP(P)/.76E + 6

VPNHE-VP

RETURN

10 DO 15 I::^lyl4

15 P = P-KD(I)*T**(2~I)

VP =EXP(P)/.76E+6

VPNHE^VP

RETURN

END

FUNCTION DELT(TT)

C ADJUSTS THE TEMPERATURE TO A NEW SCALE

T==TT DELT=--.001+.002*T

RETURN

END

FUNCTION VPTEHE(PP)

C SOLVES THE VAPOR PRESSURE EQUATION FOR TEMPERATURE GIVEN A PRESSURE

C THE FLUID IS HELIUM AND THE UNITS ARE ATMOSPHERES AND KELVINS

P = PP

95
IF(P*LT. <.842105)(3G TO .1.2 T-5«0

PCAL=='v'PNHE(T)

GO TO 13

12 PCAL~. 049737

I F ( ABS < P •PCAL ) "- , 000000 1 *PP ) 1. 1. > :L J. i

1 T-=2.1720

13 DO 10 I==ly26

DP:=tiVPNHE(T)

DEL=^(PCAL-P)/DP

T==T-DEL

PCAL==VPNHE(T)

I F ( ABS ( P-PCAL ) - » 000000 1 >KP ) 1 1 !- 1 1 , 2

2 I F ( ABS ( DEL ) - * 0000001 * T ) 1 1 r 1 1 y 1 10 CONTINUE

PF;INT 100?T

11 MPTEHE=T

Fv'ETURN 100 FORMAT (* TEMPERATURE ITTERATION FAILED AT T=*..E14.7)

END

FUNCTION DVPNHE(TT)

C GIVES THE DERIVATIVE OF THE VAPOR PRESSURE FOR HELIUM GIVEN A

C TEMPERATURE IN KELVIN9 PRESSURE IS IN ATMOSPHERES

DIMENSION C(12) ?D(14)

DATA (C:^=-3 . 9394635287 , 141 27497598 , --1640 . 7741365 9 11974 . 557102 r 1-55283. 309818 r 16621 9. 56504 f -3252 12. 82840 y 398843. 22750

y

2-277718 . 06992 y 83395 . 204183

)

DATA < D^^~49 .510540356 y 65 1 . 9236417 y -3707 . 5430S56 y 12880 . 67349 1 y 1 -30048 . 545554 v 49532 . 267436 y -59337 . 558548 y 52311 . 296025 y 2-33950. 233134 , 16028 . 674003 y -5354 . 1 038967 y 1 199 . 0301906 y 3 -161. 46362959 y 9. 881 1553386)

pu:r() T^-TT-DELT(TT)

IF(T-2.1720)10yl0yl

1 DO 5 1=1 y 10

5 P^4-'-| C ( I ) XcT** ( 1 - 1 ) * ( 2- 1 ) DVPNHE-^:M"'*VPNHE(T)

RETURN

10 DO 15 I=:lyl4

^-

15 P=P+D(I )*T*>K< l-I )*(2-I ) DVPNH£==P*VPNHE(T)

RETURN

END

FUNCTION TRANSP ( DD y TT

)

C HELIUM

C THIS ROUTINE CALCULTATES THERMAL CONDUCTIVITY AND VISCOSITY

C FOR AN INPUT OF DEGREES KELVIN AND DENSITY IN MOLES PER LITER

C THE RANGE OF TEMPERATURE IS FROM 2 TO 2000 K

C FOR TEMPERATURES BELOW 300 K FORMULAS OFD VINCE ARP AND GE STEWARD

C ARE USEDy FOR TEMPERATURES ABOVE 300 THE DILUTE GAS OF A CRITICAL

C COMPILATION FROM ENGLAND IS USED FOR BOTH VISCOSITY AND

C THERMAL CONDUCTIVITY AND THE EXCESS FUNCTIONS FROM THE ROUTINES BY

C ARP AND STEWART) THE EXCESS FUNCTIONS ARE CALCULATED FOR TEMPS

C ABOVE 300 K WITH THE TEMPERATURE DEPENDENCE HELD AT 300 K

C FOR TEMPS BELOW 300 K TO 100 K THE VISCOSITY EXCESS IS CALC

C FROM STEWARTS ROUTINE BUT THE DILUTE GAS VALUES ARE TAKEN FROM

C THE ENGLISH CORRELATION FOR TEMPS BETWEEN 100 AND 110 T

C DILUTE GAS CALCULATION IS AVARAGED

ENTRY THERHE

1 D-DD

RH0:=^D*4.0026E-3

96
IF(TJ_T.300. )G0 TO 5

TH030-UISCX(300. )*. 00781736

TH0300-C0NZ(30O.

)

DEL300:==EiELC ( 300 . r RHO ) THO=VISCX ( T ) * . 00781736+TH0300-TH030

THE=TH0300*DEL300-TH0300

TF<ANSF'=:THO + THE

RETURN

5 TRANSP=:CC)NZ ( T ) *DELC ( T y RHQ ) +CRIT IC ( T y RHO ) C OUTPUT IN MW/CM.K

RETURN

ENTRY VISCHE

D = DD

T^^TT

II-(T.LT.100. )G0 TO 1.0 IF<T.LT.300. )G0 TO 8

ETAO=yiSCX(T)

ET030=VISCX(300»

)

ET0300-VISCDT(0.0y300»

)

ETE300='v' ISCDT ( D , 300 . ) ~ET0300

TRANSP=ETA0+ETE300

C OUTPUT UNITS ARE MICROPOISE

RETURN

8 IF(T»LT.1.10. )Ga TO 9

ETAO = <v'ISCX(T)

ETEB = y ISCDT ( D y T

) -UISCDT ( . y T

)

TRANSP=ETAO+ETEB

RETURN

9 ETA1:=:^^ISCDT(O.0t100. ) ETA2=:'v'ISCX(110. ) ETA0^ETA1+(ETA2-ETA1)*(T-100. )/10.

TRANSP-=ETAO + 'v'I SCDT ( D y T ) -^ I SCDT ( . y T ) RETURN

10 TRANSP=VISCDT(DyT)

RETURN

END

FUNCTION ^;iSCX( T ) C CALCULATES THE DILUTE GAS VISCOSITY FOR HELIUM

C FOR TEMPERATURES FROM 11 OK TO 300K

k^ISCX --= 196. * T ** 0,71938 * EXP ( 12.451 / T - 295.67 / T / T

A 4.1249 ) RETURN

END

FUNCTION DELC(TEMPy RHO)

C CALCULATE THE EXCESS THERMAL CONDUCTIiv^ITY FOR HELIUM y INPUT IS

C TEMPERATURE(K) AND DENSITY ( MOLES/LITER ) OF HELIUM

C K=^KZ£RO*EXPF(B(T)*RHO + C(T)*RH0**2)

C THIS PROGRAM RETURNS EXPF ( B ( T ) *RHO + C(T)*RH0**2)

1 BB^--ALOG(TEMP) $ CC = 1.0/TEMP

BETTY - 4.7470660612 - 5 . 3641468153*BB + 3 . 4639703698*BB**2

2 -1.0702455443*BB**3 f . 1571349306*BB**4 -0 . 00892140047*BB**5

B=EXP( BETTY)

C = 2.2109006708 + 187 . 74174808*CC - 1281 . 0947055*CC*CC

3 +3645.2393216*CC**3 - 3986.6937948*00**4

DELC==EXP(B*RHO + C*RHO*RHO)

RETURN

END

F U N C; T 1 N C N Z ( T E M I"'

)

C KZERO IN MILLIWATTS/CM-Ky T IN KELVIN9 22 JUNE 71.

1 ANNE==ALOG(TEMP)

PAT = -4.3611622157 + 1 . 9250159286*ANNE - . 52544120165*ANNE**:

1+ 0.090045763885*ANNE**3 - . 0054773874708*ANNE**4

97
CONZ^^EXP(PAT)

F^'ETURN

END

FUNCTION ^^ISCDKDGCjT)

C W.G, STEWARD i-S DATA 2:^ JUNE 71

C INPUT UNITS ARE KELVIN AND MOL/I.ITER

C OUTPUT UNITS ARE MICROPOISE

r L_ --^^ A I... (;; < r > $ r ^ d g g * 4 . o o 2 6 / .1. » A N N E :--^ - .

3 5 3 1 1 743/ T L *• I. , 3 4 7 8 4 1 + I » 2 6 S 4 6 4 9 * r I... 1 ••() > I49564i:i5:l.*TL.*TL + <• 0121:^20841 A*TL**3

DETTY::::R)!<(--47.52952S9/TL + 87.6799309 --42 * 074I^^89*TL

1 i8 . 33128289*TL*TL •••0 . 589252385)KTL**3 )

C; A R L R * R * < r.v 4 7 . 3 9 2 6 7 / T I... - 9 04.8 7 0586 f 4 3 1 . 4 4 9 2 8 * T I... 1 -81 .4504854*TL*TL f 5 . 37008433*TL)K)k3 ) D A G M A R' ^-^ R Xo^ 3 * ( - 1 6 8 4 . 3 9 3 2 4 / T L, f 3 3 3 1 . 8 6 3 -• ,1 6 3 2 . 1 9 1 7 2 * T I... 1+308 . 804413)KTL*TL - 20 . 2936367*TL**3 ) V j; S C D r

^-

E. X F' ( A N N E + B E I T Y + C A R 1... f D A G MAR)

RETURN

END

I u N c r 1 N l; r i t i c ( r e: m !-• > i"< i-i o ) C CRITICAL ANOMALY FOR HE THERM. CON . ^ SCALED FROM H -2 C T IN KELVIN !- REQUIRES DENSITY IN GRAMS/CC AND CP IN JOULES/MOLE

C THIS DECK OF 18 SEPT 70 y I HAVE USED MCCARTY'S HE DECKS OF 7/18/70

4 T^^^^TEMP 5 DML=-RHO/0. 0040026

6 IF<T .GE. 11.83) GO TO 11

IF(RH0.GT.0.12) GO TO 11

7 CPl^=CPHE(DMLvT)

8 CP2:=CPHE(DMLv 11.83)

9 CRITIC^=0 . 0026* ( CPl -CP2 ) /4 . 0026

10 IF(CRITIC)llvl2!'12

11 CRITIC=:^0.0

12 RETURN

END

FUNCTION DSATV(TT)

C CALCULATES THE SATURATED LIQUID AND VAPOR DENSITIES FOR HELIUMv

C INPUT IS TEMPERATURE(K) OUTPUT IS GM/CC (SEE NEXT PAGE)

DIMENSION GV(6) i'GL(6)

DATA < GL^- . 1 2874326484 f - . 43 1 282 1 7346 v 1 . 785 1911 824 y -3 . 3509624489 ? 1 3. 0344215824y-l. 0981289602)

DATA ( GV^^ - . 069267495322 , - . 1292532553 v . 2934747071 2,-, 40806658212 » 1 .358095056241. -.11315580397)

DATA (DC-. 06964)

DATA (TC^-5. 2014)

r=:TT DCAL^=DC

R-(1.-T/TC)

DO 1 1=1 V

FI^=a

1 DCAL-DCAL+GV ( I ) *R** ( FI/3 .

)

DSATV-DCAL

RETURN

ENTRY DSATL

Tr.TT DCAL==DC

R^^d. -T/TC)

DO 2 I:^-=1p6 F I

--^-

2 D C A I... ^-- D C A I... + G L ( I ) * R * * ( F I / 3 . ) DSATV^DCAL

RETURN

END

98
l-UNCl ION

c CAI. CULATE THE

c our PUT IS PRE

DIMEN SIGN

• MEI...T(TT)

MELTING PRESSURE FDR HELIUMv INPUT IS TEMP K» iSURE IN ATMOSPHERES

A ( 5 ) DATA(A-^3;3.2By44. 1;:j6v:v|. ,799 » -4 . 8159 y , 30:5I3 ) T.::TT IF(T.LE.5.2)GG TO 7

PMELT^^ - 1 7 . SOf 17*3 lA'-j/tTtt 1 .. 5554 1

4

PMELT:=:PMEL.T>K. 98066/ 1 .01325

RETURN

7 P^-=0,0

DO 9 I^^l!-5 9 P==:p + A( I )*T>!<*<I-I ) PMELT-P*9. 80665/ 1 0.1325

RETURN

END

FUNCTION FNIiPNEdJyT)

C CALCULATES THE PRESSURE IN ATMOSPHERES FOR NEGN^

C USES DENSITY (MOL /LITER) AND TEMPERATURE OF NEON AS INPUT

1 FNDPNE^^M-'C(D!-T)

RETURN

END

FUNCTION ENTHACPj-DvT)

COMMON A I y A2 i A3 ? A4 ? A5 y A6 » A7 v A8 v A9 y AlO y AI .1. . A12 » A13 y A14 ? A15 , A16 i- AI7

I y A 1 8 y A 1

9

DI^D

D2=^D*>K2

D3^=^D2*D

D4:^::D3*D D5-=D4>i<D

Tl-T

T2-:::T*T T3::^^T2*T

T4:--:T3*T EX=EXP(A19*D2)

EXI1:=(EX-I . )/(2.*AI9)

EXI3^^EX*D*D/ ( 2 *A19 ) - ( EX -I . ) / ( 2 . *AI9)f<*2 ) ENTHA -^P/D-Al*Tf A4*D3/3 . +A5*D4/ ( TI*2 . ) l-A6*D2*T2/2<.{-A9*D2/TI+3.*A10*D2/(T2*2. ) 2-|-A12*Dlf2.*AI3>kDl/Tl + 3.*A14>KDl/T2

3 + 3 . * A 1 5 * E X 1 1 / T 2 f 4 . * A 1 6 * E: X 1. 1 / T 3

4i3.*A17*EXI3/T2 + 4.*A18)KEXI3/T3

6 + A2>KD5/5 . +A8*D2/2

.

C CALCULATES ENTHALPY CHANGE FROM TO FINITE DENSITIES ALONG

C ISOTHERM ACCORDING TO DTRI4

C FOR NEON INPUT IS PRESSURE IN ATMOSPHERES r DENSITY IN MOLES/LITER

C AND TEMPERATURE IN Ky OUTPUT IS JOULES PER MOLE.

RETURN

END

FUNCTION DLiaNE(T)

C FOR NEON

IF(T-44.4)l!-2»2

1 A:=^^ -8. 9200910

B = 35. 44.1.50349

C==:--64. 720906

D=^57.7456I9

E-==-20.259619r2

R= ( 1 . O-T/44 . 4 ) ** ( 1 . 0/3 . ) DENR^^ 1 . + A*R + D*R)l<R + C*R**3fD*R**4+ E*R**5

RSATD-=10.>K*DENR

DLiaNE=:=RSATD*.484*I000.028/20.I83

RETURN

99
2 RSATri=l.

DLIQNE=-RSATD*« 484*1000. 028/20. 1.83 RETURN

C UNITS ARE IN GM -MOLES/LITER

END

FUNCTION IiPDDNE(i:in!.TT)

DIMENSION G(:I.B)

3 COMMON A.lyA2»A3vA4yA5i'A6»A7»A8!'A9»A:L0TAll>A12rAi;^yA14yA.t5i.AlA»A17

lyA18yA19

D1==DD

T1=TT

D2--=D1**2

D;5~D2*D1

D4:=D3*D1

D5-D4*D1

T2:---T1**2 T;^-T2*T1

T4=T3*T1

EX==EXP(A19*D2)

EX1==EX*D1*2.*A1.9

EX3=3.*D2*EX+D3*EX1

EX5=-5 . *D4*EX+D5*EX 1 G(1)=D5*6. *A2

G(2)^-T1*D3*4. *A3

G(3):^-D3*4.*A4

G(4)-D4*5.*A5/T1

G(S)=3.*D2*T2*A6

G(6)-=3.*D2*T:l.*A7

G(7>^3.*D2*A8

G(8)=^3.*D2*A9/T1.

G(9)=^=3.*D2*A10/T2

G(10)=D1*2.*T1*A1J.

G<11)=D1*2.*A12

G(12)==aU*2.*A1.3/T1.

G(:L3)-D1*2,*A.14/T2

G(14)-EX3*A15/T2

G(15)=EX3*A1A/T3

G(16)==EX5*A1.7/T2

G(17)-EX5*A18/T3

P2=A1*T1 ---^ DO 11 K^=lyl7

11 P2=^P2fG(K)

DPDDNE^^^P2

C CALCULATES THE FIRST DERIVATIVE OF PRESSURE WITH RESPECT TO

C DENSITY ACCORDING TO DTP 1

RETURN

END

FUNCTION ENT(D>T)

COMMON Al !> A2 y A3 y A4 y A5 y A6 y A7 y A8 y A9 y AlO y Al 1 y A12 y A13 y A14 y A15 y A16 y A17

lyA18yA19

D1=D

D2-^D**2

D3-=D2*D

D4--nD3>KD D"5=-D4*D

T1==T

T2=--=T*T T3^^^T2*T

T4=:-T3*T

EX-^-^EXP(A19*D2)

EXI1=--=EX/(A19*2. ) EX 1 3^=:EX*D*D/ ( 2 . *A 1 9 ) - ( EX ) / ( 2 . * A 1 9**2 )

100
ENT =A3*D4/(T2*4. ) -A:5*D3/3 . -A6*ri2*Tl

l-A7*D2/2 . +A9)KD2/ ( 12*2 . ) +A1.0*D2/T:'5

2-Al:L*Dl+Ai;5*Dl/T2fA14>K2.*Dl/T3

3 + A15*2 . *EXI 1/T3 f A:I.A*3 . *EXI 1/T4

4+A17*2,*EXI3/r3+A18*3.*EXI3/T4

5-Al*AL.0G(Al*T*D)

C CALCULATES ENTROPY AT ONE LIMIT OF INTEGRATION ? ISOTHERMAL

y

C ACCORDING TO DTRI4

RETURN

END

FUNCTION £NTR(D»T)

C FOR NEON

COMMON A;LyA2i'A3!rA4yA5yA6f Ays' A8fA9>A10 » Ally AI2yA13rA14 TA15!'A16y A17

lyA18yA19

D1 = D D2^^D**2

D3=^D2*D

D4-D3*D

D5-D4*D

Tl^-^T T2-=T*T

T3=T2*T

T4^T3*T

EX:=EXP(A19*D2)

EXI1=(EX-1,)/(2.*A19)

EXI 3=EX*D*D/ ( 2 . *A1 9

) - ( EX-1 , ) / ( 2 *A1 9**2 ) ENTR --A5*D4/(T2*4. ) -A3*D3/3 . -A6*D2*T1

l-A7*D2/2 . +A9*D2/ ( T2*2 . ) +A10*D2/T3

2-All*Dl+A13*Dl/T2fA14*2.*Dl/T3

3+A15*2.*EXIl/T3fA16*3,*EXIl/T4

4+A17*2.*EXI3/T3+A18*3,*EXI3/T4

S-A1*AL0G(A1*T*D)

C CALCULATES ENTROPY ALONG AN ISOTHERM FROM TO A FINITE DENSITY

C ACCORDING TO DTRI4

RETURN

END

C FOR NEON

SUBROUTINE DATA N

C SETS THE CONSTANTS TO THE EQUATION OF STATE FOR NEON

3 COMMON AlyA2!'A3!.A4rA5yA6rA7yA8»A9»A10i.All>A12yA13yA14!'A15?A16>A17

lyA18yA19

Al=, 0820535

A2=,28010178E-07

A3=. 14244722E-03

A4:=-. 14175051E-03

A5==-»28070869E~04

A6:=-» 101851 46E-06

A7=,42496352E-05

A8=:«25826979E-02

A9^. 12417383

A10=^-~.62382566E-01

All=,17237659E-02

A12=-. 16730352

A13=-.61781598E+01

A14=.87257402E+02

A15=.19355993E-f02

A16=- . 84739643E+03

A17=~.6552S926E-01

A 18= . 234531 13E + 01

A19=-.53186241E-02

RETURN

END

101
C FOR

C AND

FUNCTION PC(DD-'TT)

NEONsrp IS IN ATMOSI

TT IS ]:n i\t:L.v:i:N d:i:hens:i:on gcib)

HERI DD :i:n mo LITER

A2 1 A3 1 A4 1. A5 y A6 ? A7 , A8 ? A9 y A J. y A 1 :l. y A :l 2 y A :l. Z y A J. 4 y A 1 '5 y A .1. 6 y A .1.

C SOL

C FOR

COMMON A1. lyAlByAiy

CALCUALTE

Dl-^DD

T:L:^::TT D2=D1**2

Ii3-i;i2>l<D:L D4--^D3*D:l.

D6""D5>KD1.

'\2:^1\%%7..

T3-T2*T:l.

T4""T3*T:I. EX=EXP(A1.9*D2)

GCI. )^^DA*A2

G(2)^:^T:l.*i:i4*A3

(3(3>^^D4>KA4

G(4)^::D5*A!:v/T:l

G(5)-D3*T2*A6

G(6)-^a;i3*T:l.>KA7

G(7)=-D3*A8

G(8)-^D3*A9/T:l.

G(9)=D3*A],()/T2

G(:L0)-D2*T.1.*A:I.1.

G(H)=:D2*A12

G(12)^==D2*a:i.3/t:i.

G<:L3)--D2*A:I.4/T2

G(:L4)=ti3*EX*A1.5/T2

G ( 1 S )

^-^^ D 3 * E X * A :l, 6 / r 3

G(:i.6)^d;!^*ex*a.i.7/T2

G(:L7)-D5*EX>KAie/T3

P2^Z

DO :i. J. K^^i y:i.7 P2^=:p2fG(K)

PC=P2

RETURN

END

FUNCTION FNDTNE(PyD)

VES THE NEON EQUATION

A INPUT OF PRESSURE

DATA ( DTP=^6 J. . 78 ) y ( DC^^=23 PI--P

DD:=D IF(DD.

TT^:=44,

PRESSURE ACCORDING TO DTRI4

OF STATE FOR TEMPERATURE IN KELVIN

IN ATMOSPHERES AND DENSITY IN MOL/L

93)

GO

TT = DO

TO

24

1.0

GT»DC)GO

4

';>

TO

54+<I9.86/(DTF'

I^^lylO

P2^FNDPNE(DDyTT)

IF(A]E(S(PP-P2) -1.

22 DP:^4:iPDTNE(DDyTT)

C0RR^-"(P2-PP)/DP

IF(ABS(CORR)--I,E

10 TT==TT--CORR

20 FNDTNE-TT

RETURN

-DC) )*(DTP-DD)

-7*PP)20y20y22

)20y20yI0

102
. TCOGG TO ;l.() SSCPP^DDi-TT)

100

END

I- UNCI :i: ON FIND F'(DyT)

DIMENSION G(:i2) 7(v>P(9)

t;OMMON/DATA/G y R ; GAMMA

DD^^^D

IF (IT. I... CALL. PR I FIND P^^PP

RETURN

P^^^^VPN'TT)

Oy::::FIND D(p-.000I i-TT)

DL^^^^FIND D(Pf.OOO;l. .TT)

I F ( DD . LE . D'J <, OR » DD . GE . DL

PRINT lOOvDVSDLvDD

CALL PRESSCPPjFDVi-TT)

FIND P^^PP

D-DV

RETURN

FORMAT (* THE STAT

'* DENSITY IN THE

THE DENSITY OF

THE DENSITY OF

AND THE INPUT DENS

SATURATED VAPOR IS

VP p DTP > PCC V P IF' , TCC V TTP , TUI... » 11. 1 , PUL.. , DCC

)G0 TO :l.

POINT

..I QUID

THi;

IHi:

YOU HAVE SPECIFIED CORRESPONDS TO A *

\> A p 1^ c e: X I s r e n c e v< e g :i: o n * SATURATED VAPOR IS %,S-6.A,% MOLES /LIT

SATURATED LIQUID IS *»F8.47* MOLES /LI

TY * 4»* MOLES /LITER*

::d L F8*

ASSUMED*)

OF PRESSURE WITH RESPECT TO

' A7 ir AS V A9 1- A 1 ; A 1 1 y A 1 2 v A :l. 3 y A I 4 y A 1 5 , A 1 6 y A .1 7

12/*

3/*

4/*

5/*

END

FUNCTION DPDTNE(DyT)

GIVES THE FIRST DERIVATIVE

TEMPERA rURE FOR NEON

INPUT PARAMETERS ARE DENSITY ( MOLES/LITER ) AND TEMPERATURE ( K

)

DIMENSION G(18)

3 C M M N A 1 7 A 2 ? A 3 y A 4 ; A '5 > A 6 l»A18yA19

DI^^DD

TI=--TT D2:^:^D1**2 D3=a;i2*DI

D4^^=D3*DI

D5==a.i4*DJ. D6^::D5*D:L

T2=:::T:l.**2 T3==^T2*TI

•I/i.:::T3*ri EX==^^EXP(AI9*D2)

G ( 1 ) =^0 G(2):^:a:i4*A3

0(3)^=0

G(4)=^:-Dl^*A5/T2

G(5)^=-=2.*D3*TI*A6

G(6):^D3*A7

G<7)-=0

G(8)^=-D3*A9/T2

G(9)^=-2.*D3*AI0/T3

G(10)==D2*AII

G( 11)^^-0

G(12)==-D2*A13/T2

ER*

TER*

0(13)^^:^-2

G(14):=:-2

G(15)::^-3

G<16)^::--2

0(17) ^=-3 P2=:D1*A1

*D2*A14/T3

*D3*EX*A115/T3

*D3*EX*A16/T3

*D5*A17*EX/T3

*D5*A18*EX/T4

103
11

C SOL

C F C AND

)STATE FOR HELIUM

KELVIN) GIVEN A PF<ESSURE

LITER

11

10

20

DO 11 K-lyl7

P2==P2fG(l\)

DPDTNE^^^P2

RETURN

END

FUNCTION FNDTHE(PvD

VES THE EQUATION OF

OR A TEMPERATURE (IN

A DENSITY IN MOLES/

DATA(DTP:=<36,514) , (D

DD-D

IF(DD«GT.DC)GO TO 1 TT^^^5<.201 GO TO 2

. 1 77+ ( 3 , 024/ ( DTP -DC ) ) * ( DTP-DD

)

I-li-lO

NDPHE(DDyTT)

IF(ABS<PP -P2)-1.E

DP---=DPDTHE(DD>-TT)

C0RR^^(P2-PP)/DP

IN ATM

TT=^ DO

P2^

7>XPP)20!'20!' 11

C SOL

C IN

C MOL

IF(ABS(CORR)-l,i;:

TT:=-TT-CORR

END THE- IT RETURN

END

FUNCTION FINDT(FVE THE THIRTY TWL

) 20)- 201- 10

D)

TE RM EQUATION OF STATE FOR

URE IN ATMOSPHERES AND

TEMP

A DEN

ERATURI

KELVIN GIVEN A PRE' SITY li ES/LITER

DIMENSION G(32) »VP('

COMMON/DATA/G s- R v GAMMA » VP > DTP v PCC y FTP r TCC , TTP y TUL y TLL y PUL y DCC

pp..p DD-D

IF(P«GE.PCC/1.0132

TSAT:=M-INDTV(PP)

DV=^=FIND D(PP-» 00001

DL=4-IND D(PP-f ,0001

IF(DD,GT*DV,AND»DD.I

TT^^TSAT

GO TO 2

TCC

10 I-lylO

9)

)G0 TO 1

yTSAT)

TSAT)

LT.DDGO TO 30

TT

DO

CALL PRESS (P2yDDyTT) T'-7)f<PP)20y20yll

T)

IF(ABS(PP •P2)-l ,i;i 11 CALL DPDT(DPyDDy-1

C0RR:^^(P2-PP)/DP

IF ( ABS ( CORR ) -1 . E--5 ) 20 y 20 y 10

10 TT=^TT-CORR

20 FINDT=^TT

RE I URN

30 FINDT^^-^TSAT

D^^^aiV PRINT lOOyDVyDLyDD

.00 FORMAT <* THE STATE

1/* A DENSITY IN THIi 2/* DENSITY OF THE S 3/* DENSITY OF THE J 4/* INPUT DENSITY li S/* SATURATED VAPOR

RETURN

END

POINT YOU HAVE SPECIFIED

: LIQUID VAPOR COEXISTENC

i A 1 U R A J E. D V A F^' R J: S * y I" iiJ. 4 y ;ATURATED LIQUID IS*yF8,4

;)KyF8.4y* MOL ES/LITER*

c N D :i: r j o n s a r e a s s u m i:- d * >

CORR

E REG

* MOL

y* MO

ESPONDS TO*

ION*

ES/LIT

LES/LI'

ER*

TER*

104
ES/MOLE -K

e: ( T ) INTIiLGR ^^1... Ol- (CF r- ) i: T vTOy 1 :> 1. 7. 092

T-27.09 2))!' 2. b

funct:i:(:)n cposne(T)

c calculates the iintegral of (cp/t)dt from vtos'to t for neon

c to :i:s 27.092 and cf' is at zero pressure v 5/2r

C F-' = e . 3 1 4 3 4 * A I... G ( T' 727. 9 2 ) * 2 . 5

CP0SNE^:=CP

RETURN

C UNITS ARE JOU

END

FUNCTION CPOHNE

C CALCULATES THE INTEGRAL OF (CPT)DT FROM ?T0yT0 T FOR NEONi-CP AT

C ZERO PRESSURE

CP ^=--8. 31434* ( CPOHNE::^CP

RETURN

C UNITS ARE JOULES/MOLE-K

END

FUNCTION FNDDNE(PPyTT)

C SOL^v^ES THE EQUATION OF STATE FOR NEON FOR DENSITY (MOLES/L)

C GIVEN A PRESSURE IN ATM AND A TEMPERATURE IN K FLU IN

P^H--'P T==TT

D^^20.

IF(TT.GT.44,4)GG TO 2

PSAT^^^^ypNNECTT)

D^^^.OOI IF (PSA I .GE.PP)GO TO 2

D^:^DLIQNE(T)H.

2 CONTINUE

DO 10 1^=1 1-50 P2==PC(D!-T)

IF ( ABS ( P ••P2 ) - 1 . E -6*l-' ) 1 1 9 1 1 V 1 1 DP^DPDDNE(D»T)

I

F'

< A B S ( ( F' ••" F 2 ) / D P ) - 1 , E ~ A * D ) 1 1 y 1 1 ? 1 10 D^:^D-(P2-P)/DP

FNDDNE^^^O

RE (URN

11 FNDDNE^^-^D RETURN

END

FUNCTION ENTH (PyDvT)

COMMON A 1 y A2 y A3 i- A4 v A5 , A6 ? A7 v A8 y A9 v A 1 y A 1 1 y A 1 2 y A 1 3 y A 1 4 y A 1 5 y A 1 6 y A 1

7

lyA18yA19

D1---^D D2^=^T:i*>K2 D3^^D2>XD

D4==D3>KD

D'5""D4*D

Tl=-T

T2^=:=T*T T3::::T2*T

T4:-^T3>K1 ex::h::xp(ai9>kd2>

EXI1-EX/(A19>K2. ) EXI3^^^:EX*D>KD/ ( 2 . >KA19 ) - ( EX ) / ( 2 . )KA19**2 ) E N T H -^ F' / D + A 4 * D 3 / 3 . f A 5 * D 4 / ( T 1 * 2 . ) l"A6*D2*T2/2 , f A9>KD2/T 1 V5 , >KA10*D2/ ( T2*2 . ) 2f A 1 2S<D 1 f2 . * A 1 3*D 1 /T 1 «-3 . >t<A 1 4*D 1 /T2

3f 3 , *A 1 S*EX 1 1 /T2 + 4 . * A 1 6*EX 1 1 /T3

4 + 3,>KA17*EXI3/T2f4.)KA18>KEXI3/T3

6 + A 2 :* D S / 5 * f A 8 * D 2 / 2 . C CALCUALTES ENTHALPY A I ONE LIMIT OF INTEGRA HON ACCORDING

C J D T R 1 4 y :i; S T H E R M A L

105
I

RI::.TURN

I:.:nd function vpti£ne(pp)

soLUEs Till::: uapgr pressure EauAT:i:oN for temperature g:i:ve

THE Fi..u:i:n :i;s neon and the UN:ns are atmospheres and ki:: X::::44, PCAL^^^^VRNNErf

}

N A I- \..V.\.Mi

:l.3

:l.() 11

:l i:

DC 10 I^^^\.'>':'iO DP::^DUPNNE(T)

DEL-^^:(PCAL-P>/DP

t^^-^t-del pcal::^^mpnne<t>

:i: F (ADS ( p'-pc; Ai...

) ••• , ooooo i

*!:• ) 1 1 .' 1 1 >

IF ( ABS ( DEL )

• . 00000 1* T ) 1 'I > 1 1 v 10

CONTINUE

VPIENE^^^T

RE f URN

END

F UNCTION ENTHNECPyD?T)

CALCULATES THE ENTHALPY FOR NEON IN ,JOULES/MUl.. E . OIOFN

IN ATMOSPHERES^ THE DENSITY IN MOLES/LI TFR y AND fHE TEMPI:- KELOINS

D A ( A ( l-l l:i < :i, 8638645 E. -f 4 ) IF(T.LT.44v4:)G0 TO 52

t: N rHNE^^MIOf-CPOHNE ( \ ) iEN I HA ( P v D y 1 ) *101 . 325

RE r URN

'••SAT^^^MPNNE(T)

PSAT^=:PSAT-<.000:I

DyAp:^:M-NDDNE(PHAT'Lr ) IF(D.I..E.DOAP)Gn TO 1 PSAT-T-"'SAT'f .0002

DL IU-FNDDNF':PSAT»T)

111 -n-IO-} CPOHNE ( T > iENTHA ( PS AT y DOAP v T ) *101 , 325

H2::T:iypNNE ( T ) * ( 1 . /DVAP- 1 . /Dl. IQ ) *T>Kl<

H3^==^ ( ENTH ( P , D / T ) -ENTH ( PS AT v Dl. 1 Q y 7 )

"i *

ENTHNE^^:MHl--H2-fH3

RETURN

i::nd FUNCTION EN iRNEcDi-T)

CALCULATES THi:: ENTROPY FOR NEON 0:i:VI::N Di::NSITY JH MOLES

AND "FEMPLRATURE IN KELVINS v OUTPUT IS IN JOULES.' MOLE -K DATA ( S0:-6S . 52101455 ) IF(T.LT > 44. 4) GO TO 52

NTRNE^^^^SOf CPi:)SNE * I" ; f F NTR ( D y T ) * 1 1 .325

REFURN

PSAT^^^^UPNNE(T)

PSAT^^^T^'SAT -^OOOl

DUAP^^::FNDDNE <: PSA F V T ) IF(D,LEvDyAP)GO TO :l PSAF^-^PSA F-f .0002

DLI(:L::M:'NDDNE(PSATyT)

s :i. s -f c ! s N 1:: ( r ) -f i;:: n j R' ( 1:1 a f v t > * 1 1 .

.x 2 5

S2^::a:i'v'PNNE ( T ) * ( 1 . /DVAP- I . /DLIQ ) )l<101 . 325

S3^^^ ( ENT ( D V T ) -ENT ( DL 10 v I ) ) >K 1 1 325

ENTRNE^^^^Sl -S2iS3

REFURN

END

THE I RA )UIRESSURE

it. IN.

I 0:l .325

FUNCTION V GIVES A VA

Q •-- (7.46

BVAp:^:;(10.0?{<*Q/760.0)

•NNE(T>

OR PRFSSURE FOR NEON IN AFMOSPHERES GIVEN A

.16 "106<.090/T --.0356616*T -f . 00041 10V2*T*T )

:.MP IN is

106
F<ETURN

END

FUNCTION nVPNiMEd)

DERIVAflVE OF THE VAPOR PRESSURE CURVE FOR NEON

a:^^::l.06,090/T*>K2--.0356616f-2.*.0004:l 1092*T

DMPNE^^^^VPNNE ( T ) *Q*2 * 302585093

DVPNNE^^^DVPNE

RETURN

EN 1.1

107
NBS-114A (REV. 9-78)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS TM-1025

l,ik>'/v, 'fiW&im^WMimWiiWC''W4. TITLE AND SUBTITLE IflTERACTIVE FORTRAN IV COMPUTER PROGRAMS FOR THE TIlERfiO- DYNAMIC AMD TRANSPORT PROPERTIES OF SELECTED CRYOGENS

[FLUIDS PACK]

5. Publication Date October 1980

•• Perfersring Ofganization Code

7. AUTHOR(S) R. D. McCarty

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

19, Pfe|ftct/Tas*;/Wor)< Unit Ho.

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS rs(ree<. City, state, ZIP) NASA-Johnson Space Center

Houston, Texas

Contract No. PO T-6570C

13. Type of Report & Period Covered

14. tpMNMR^ A«(»cy &Mte

15. SUPPLEMENTARY NOTES

I ] Document describes a computer program; SF-185, FIPS Software Summary, is attached.

1$. ABSTRACT (A 200~word or leaa (actual aummary of most significant information. If document includes a significant bibliography or

literature survey, mention it here,) The thermodynamic and transport properties of selected cryogens have been programmed

into a series of computer routines. Input variables are any two of P, p or T in the

single phase regions and either P or T for the saturated liquid or vapor state. The

output is pressure, density, temperature, entropy, enthalpy for all of the fluids and

in most cases specific heat capacity and speed of sound. Viscosity and thermal

conductivity are also given for most of the fluids. The programs are designed for access by remote terminal; however, they have been written in a modular form to allow

the user to select either specific fluids or specific properties for particular

needs.

The program includes properties for hydrogen, helium, neon, nitrogen, oxygen, argon,

and methane. The programs include properties for gaseous and liquid states usually

from the triple point to some upper limit of pressure and temperature which varies

from fluid to fluid. Computer listings of the FORTRAN four codings are presented.

Copies of the programs may be obtained from either the Thermophysical Properties

Division of the National Bureau of Standards at Boulder, Colorado, or from Walter

Scott at the NASA-Johnson Space Center in Houston, Texas.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons) Argon; computer programs; density; enthalpy; entropy; equation of state; heat

capacity at constant pressure; heat capacity at constant volume; helium; hydrogen;

methane; neon; nitrogen; oxygen; thermal conductivity; velocity of sound; viscosity.

18. AVAILABILITY [X] Unlimited

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