Text

Nonproprietary Version of H20DA:Improved Water Properties Package
	ML20037D035
Person / Time
Site:	Seabrook, Vermont Yankee, Yankee Rowe, Maine Yankee
Issue date:	03/24/1981
From:	Albright D, Stephen Schultz, Slifer B; YANKEE ATOMIC ELECTRIC CO.
To:	;
Shared Package
ML19260H917	List: ML20037D034; ML20037D035;
References
	YAEC-1237, NUDOCS 8105210221
	Download: ML20037D035 (86)
	v • d • e

..

I I

n I

9 e a

2

.I

~

H29DA:

/.N IMPROVED WATER PROPERTIES PACKAGE By Dennis Albright I

A I

Frepared By e-4 C.

[$

3/I8/33 D. C. Albrfght (Date)

Nuclear EngineGring Reviewed By f G [..h.

3 /N)d/

t K. E. VSt. John (D'a te )

Nuclear Engineering 3 lI4 l%%

Approved By IMA;:er (Date)

'S. P. Scliultz,

I Fuel..nd Materials Behavior Group Nuclect Engineering I

Approved By I.,.

B. C. Slifer Director

" (Date)

Nuclear E ineering Yankee Atomic Electric Company Nuclear Services Division 1671 Worcester Road Framingham, Massachusetts 01701 I

I

%la 62IOMI

J l

\\

l g

pISCuAMER OF RESPONSIBILITY l

This document was prepared by Yankee Atomic Electric Company for ig its own use.

It is being made available to others as a public service l5 without monetary or other compensatf.on to Yankea, upon the express l

understanding that neither Yankee Atomic Electric Company nor any of its la officers, directors, agents or employees assumes any obligation, 5

r*8Ponsibility or liability, or makes any warranty or representation, with respect to the contents of this document or its accuracy or completeness.

I lI l

lI I

I I

lI II I

I I

I

I I

ABSTRACT This report is being issued as documentation for the H29DA Water

,I Properties Package developed at Yankee Atomic Electric Company.

l The H29DA Water Properties Package can be ured to calculate the thermodynamic properties of water for a wide range of pressures and enthalpics.

lW The code package design is intended to simplify the task of l

properties derivation in new code development. The bulk of water properties are calculated via access to the STH29 subroutines; however, such access is performed internally by the code package thus simplifying input, output, and units conversion tasks. Additionally, useful derivativea of thermodynamic properties and thermal hydraulic conditions for a two phase state mixture are calculated.

An extensive comparison is made between results obtained ueing H20DA I

and data from the ASME Steam Tables. Satisfactory agreement is observed l

I for all properties examined.

The input requirements and output variables are described in detail.

I

'I I

I

-lii-I I

i I

I ACKNOWLEDGEMENTS

(

The author expresses appreciation to the Fuels and Materials Behavior Group for the help they have given me while developing the H29DA Wate.r Properties

(

Package.

The author would like to thank the Word Processing Department and the iI which was a secretaries of the NED group for the typing of this report, difficult task due to the subject matter and notation.

I I

I

'I

'I I

I I

-i -

'I I

I lI TABLE OF CONTENTS I

m l

l ABSTRACT..................................................

iii 1

)

l ACKN0WLEDGEMENTS..........................................

iv LIST OF TABLES............................................

vi LIST OF FIGURES...........................................

vii I.

INTRODUCTION..............................................

1 II.

PROGRAM DESCRIPTION.......................................

1

,I 1

III.

AVAILABILITY OF ADDITIONAL PROPERTIES.....................

8 l

IV.

VERIFICATION OF THE WATER PROPERTIES PACKACE..............

22 V.

DESCRIPTION OF PROGRAM UTILIZATION........................

49 Variable Dictionary for WATER.............................

52 Appendix A - Listing of H29DA....................................

60 Appendix B - Necessary Job Control Cards.........................

75 lg ze App..e1. C - S_ g.

r.b1_......................................

i REFERENCES................................................

77 l

l I

I I

j

-v-l'I

I I

I LIST OF TIBLES Number Title Pag 1

Comparison of Predicted Saturation Temperatures........

25 2A Comparison of Saturated Water Properties Between H2@DA and the ASME Stga.n Tables at a Given Constant p = 25.0 lb /in a......................................

27 g

2B Comparison of Saturdated Water Properties Between H20Da and the ASME Steam Tables at a Given Constant I

2 p = 2200.0 lb /in a....................................

2P f

l 2C Comparison of Saturated Water Properties Between H2 DA and the ASME Steam Tables at a Given Cor.9 tant 2

l p = 1000.0 lb /in a....................................

29 f

I 3A Comparison of Liquid Water Properties Between H20DA 2

and the ASME Steam Tables (p = 2200.0 lb /in 3, f

h = 550.0 BTU /1bm).....................................

36 1

3B Comparison of Liquid Water Properties Between H20DA 2

and the ASME Steam Tables (p = 1000.0 lb /in,,

h = 500.0 BTU /1bm)......................f 37 4A Comparison of Superheated Steam Properties Between H2@DA and the ASME Steam Tables........................

42 l

4B Comparison of Superheated Steam Properties Between H29DA and the ASME Steam Tables.......................,

43 5

Pressure Data Points Used in the Present YAEC Water Property File..........................................

47 lI lI

'I

'I I

-vi-

i I

I LIST OF FIGURES Number Title Page Two-PhaseParametegsCalculatedbyH20DAataPressure 111-1 of p = 1000 lb /in a...................................

16 f

III-2 A DynamicEnthalpyCgiculatedbyH20DAataPressure of p = 1000 lb /in a...................................

17 g

III-2 B The Derivative of the Dynamic Enthilpy with Respect to the Enthalpy Calculated by H20DA at a Pressure of p = 10 0 0 lb / in a.....................................

18 f

TheSlipRatiogalculatedbyH20DAataPressureof III-3A g

p = 1000 1b fin a...........................

20 f

III-3B TheDerivativeoftheSlipRatiowithRespcttotheVoid Fraction at a Pressure of p = 1000 lb /in a............

21 f

IV-1A Saturation Temperature as a Function of Pressure Calculated by H20DA for Low Pressures (less than 2

400 lb /in a)..........................................

23 f

IV-1B Saturation Temperature as a Function of Pressure Calculated by H20DA....................................

24 IV-2A Comparison of Results: The Derivative of the Saturated Vapor Density with Respect to the Pressure.............

31 lI IV-2B Comparisor of Results: The Derivative of the Saturated l

Liquid Der sity with Respect to the Pressure............

32 IV-3A Comparison of Results: The Temperature of Subcooled Liquid as c Function of Enthalpy at a Pressure of I

2 2200 lb /in a......................................

34 p

f l

IV-3B Comparison of Results: The Temperature of Subcooled Liquid as a Fungtion of Enthalpy at a Pressure of p = 10 00 l b / in a......................................

35 f

IV-4A Comparison of Resulta: The Temperature of Superheated

'I Vapor as a Function of Enthalpy at a Pressure of 2

39 p = 10 0 0 lb / i n a......................................

g IV-4B Comparison of Results: The Temperature of Superheated 8

Vapor as a Fugetion of Enthalpy at a Pressure of 40 p=25lbg/ina........................................

-vii-I

I 7.IST OF FIGURES (Cont'd)

E IV-5A Comparison of Results: Temperature of Water in the I

SupercriticalRegimeasaFgnetionofEr.thalpyata Pressure of p = 3500 lb /in a..........................

44 g

IV-5B Comparison of Results: Density of Water in the I

Supercritical Regime as a Fgnetion of Enthalpy at a j

Pressure of p = 3500 lb /in a......................'....

45 f

I I

I Lg l

I 9

-111-lg I

I

lI 18 I.

INTRODUCTION In order to implement certain necessary modifications to FRAPT4 and to prepare a STATE subroutine for the proposed heat-up code WNEDEE, a suitable water properties package must be selected with the potential i

of being of modified to fit the needs of GNEDEE or the necessary FRAPT4 modifications. This report describes an improved water properties package developed to meet these objectives.

An attempt was made to utilize subroutines from the computer code TH0R(1) ir. the water properties package. The advantages thought to be gained from the use of these subroutines were:

.: I 1)

Shorter computer running time, and 2)

The availability of the derivatives of the physical and thermodynamic properties of water, 3) the potential of a smaller computer storage requirement.

There was, however, poor agreement between the steam tables (2) and the results of the TH$R subroutines at lower pressures (of the order of I bar, roughly 14.5 psia). Although attempts were made to modify the THGR water properties subroutis.es, the agreement with the steam tables remained poor.

The STH20(3) water properties subroutines were also examined for 1

use in a water properties package. The STH2O water properties subroutines have these distinct advantages:

1 i

.I

E 1)

They are commonly used in other computer codes such as C9NTEMPT, RELAP, etc.

2)

They have been featured within systems codes which have been approved for licensing by the NRC.

it A comparison of the computer running time was made with the result that the STH29 water property subroutines used slightly less computer time l

than the TH9R subroutines. "owever, the STH29 subroutines require six times as much small core memory as do the TH9R subroutines and roughly twice as l

much large core memory.

I It was decided that the STH29 wa.er property subroutines should be used as a basis for a water properties package because of their accuracy.

The TH9R subroutines do not improve computer utilization sufficiently to j

justify the usage of these subroutines as the water property subroutines 1

needed for transient fuel behavior modeling development work.

The H29DA water properties package was developed as a method of accessing the STH29 subroutines because these subroutines lack the ease of utilitation desired in code development work. Three major drawbacks prevent the STH29 subroutines from being easily utilized:

j I

1)

The STH29 subroutines use SI units. Most codes being used or developed at Yankee Atomic Electric Company use engineering (English) units.

Therefore, the STH29 subroutines require the conversion of the units of input quantities and output (calculated) quantities.

I 2

I

'I 2)

In the STH29 subroutines, the state of the water; that is subcooled liquid, saturated two phase mixture or superheated vapor, must be l

specified. Such selection is required to determine the proper STH29 l

l subroutine and the values of its input parameters. Therefore, before the STH29 subroutines can be utilized, a method of determining the state of the water must be devised and implemented.

l 3)

These subroutines do not calculate all quantities necessary for some applications. These quantities include:

(a) some important derivatives of thermodynamic quantities, and I

(b) two phase thermal hydraulic conditions.

I The H29DA water properties package corrects these drawbacks. The required input to, and the output from, the package are in engineering (English) units. The H29DA package determines the state of the water and uses the appropriate STH2@ suoroutines and input parameters for these subroutines. The scope of the calculation performed by che STH29 rubroutines is increased to provide additional derivatives of thermodynamic quantities and to calculate two phase thermal hydraulic conditions.

A brief description of each section of this report is now presented.

Section II presents a general description of the elements comprising the H29DA water properties package.Section III explains the additional calculational features which expand upon the output of the STH29 package to provide a larger spectrum of water property variables which may be useful for future code development. In Section IV, r?sults obtained using the H29DA water pioperties package are compured with data from the ASME Steam I

3 I

I I

Tables in order to document the ac curacy of the package.Section V describes the input format and output structure of the code. Specific details on code package operation and utilization are provided in the appendices.

,I lI l

I I

IlI 1'I

!I I

I I

,I

I I

I 4

I

\\E I

PROGRAM DESCRIPTION II.

In order to make detailed calculations of water properties, the ibed below.

program is broken down into a number of subroutines descr Subroutine Description Converts the input parameters from English units to SI units.

WATER:

It also calls any following subroutines -:hich are required and converts their output from SI units to English units.

h Converts input parameters fron, English units to SI units whi.c WATERS:

It calls the subroutine are used by the STH26 subroutines.

SAT and converts the output of SAT from SI units to English WATERS should be called only to calculate saturation units.

properties as a function of pressure.

t Converts input parameters from English units to SI and converts WATERT:

degrees Kelvin.

the input temperature from degrees Fahrenheit to It calls the subroutine HCALCl and converts the output to This subroutine should only be called to English units.

l d liquid calculate enthalpy for a single phase, either subcoo e or superheated steam.

Civen the pressure, ti.is subroutine calculates the properties SAT:

of saturated water using the subroutine STH292.

i From the enthalpy and pressure states this subrcutine determ nee QUAL:

t d two-whether the coolant is subcooled liquid (IW=3), satura e s

I C~

^ " ~ " - - - - - - _. _

I phase mixture (IW-2), or superheated vapor (IW=4). The quality, void fraction and " dynamic" enthalpy are calculated here.

E SLIP:

Calculates the slip ratio using a modified Bankoff(4) correlation from the pressure and void fraction input from the subroutine QUAL.

SUB:

Calculates the properties of subcooled liquid from the pressure and enthalpy using the subroutine STH205.

VAP:

Calculates the properties of superheated steam from the pressure and enthalpy using the subroutine STH205.

HCALCl:

Calculates enthalpy of single phase water from pressure and temperature using the subroutine STH203.

G$dF:

Writes out an error message if an error occurs in the input of the STH202, STH203 or STH205 subroutines.

I INITC:

Calls STH20I to read the water properties written in TAPE 15.

In order to put the water property data into the common block

/APRdP/, this subroutine must be called before any other subroutines in this package are called.

The C0MM N blocks used in the H2@DA water properties package are l

i listed below. A brief description of the functirn of these CdMM0N blocks I

is also included.

I I

E s

I

l E

I C6M16N Block Description

/H26/

Used to transfer and output thermodynamic properties.

/DH26/

Used to transfer and output the derivatives of thermodynamic properties.

I

/DH201/

Used to transfer and output some additional derivatives of thermodynamic properties.

/QUALl/

Used to transfer and output two phase thermal hydraulic conditions.

I

/APR@P/

Transfers the array containing the water properties table throughout H20DA to wherever the STH2O subroutines are called.

I

/PMAXDA/

Transfers the maximum values of the cressure in the water I

properties table within H2$DA.

I

/ UNITS /

Transfers the numbers of the input and output devices. The arguments of this CdMM6N block must be specified before any of the subroutines in this package can be called.

I The listing of H20DA provided in Appendix A may help to clarify and illustrate the descriptions of the subroutines and CdMM6N blocks given in this section. A further explanation of the arguments of the CdMMdN blocks

/H26/, /DH20/, /DH201/ and / QUAL 1/ is provided by the variable dictionary in s. mion.

I 7

I

E I

III. AVAILABILITY OF ADDITIONAL PROPERTIES Although the output of the STH2O routines gives an excellent selection of water properties, additional properties are available from the output of this improved water properties package (H20DA). The output of H20DA is described in Section V.

The calculation of these additional water properties in the improved water properties package is described in this section.

I It was thought that the lack of availability of the derivatives of physical and thermodynamic properties of water would hinder the usage of the STH2O routines in the application to transient fuel rod modeling and general systems code development. However, the following physical properties are available as the output of STH2O for a single phase:

S S(6)

(la)

=

K

= -S(7)

(lb)

,I S(8)

(Ic)

C

=

p S(3)

(1d)

V

=

I 1/V (le) o

=

where:

6 1 bY (coefficient of thermal expansic")

(2a)

=

i BT/p V

I 1!

(-1 x the isothermal compressibility)

(2b)

K

=

V'g3p T i

I e

.I

E D

(specific heat)

(2c)

C

=

p BTe p

The following notation has been used:

J l

specific volume (3a)

V

=

density (3b) l 0

=

enthalpy/ unit mass (3c) h

=

p pressure (3d)

I

=

temperature (3e)

T

=

The properties given in (1) can be combined to produce the desired derivatives for single phase (liquid or vapor):

'3b

_ PS (4a)

C p

p BT '-

1 (4b)

P I

3,

_ KC,, _ 8 T - 1 (4c)

BP S'

p I

[h)h KP - 6 T-S (4d)

(3P p

C 1

For water at saturation, 2 phase, the needed derivatives are calculated along the saturatio7 curve:

I N

Ts(p + ap) - Ts(p _ A )

(Sa) p dp sat 2 Ap I

9 I

E l

gx p ' (p + Ap) - p* (p - Ap)

(5b) dh sat hs (p + Ap) - hs (p _ ap)

E dT (Sc)

. o.o dh sat I

dhlX h (p + Ap) - h* (p - Ap)

(5d) 5] sat 2Ap dol

p s (p + 3p) _ ps (p - ap)

(Se) d sat 2Ap th where the superscript s denotes a property of the x phase (x = L, liquid; x = v, vapor) of saturated water. These properties are calculated by calling STH202 twice, at pressures p + 6p and p - Ap.

The subroutine QUAL calculates a number of interesting 2 phase parameters such as the static (X) and dynamic (flow) (X') quality, the void fraction (a), the 2 phase (nodal) density (0 ), the dynamic (flow) enthalpy 3

(h') and the derivative of the dynamic enthalpf with respect to the enthalpy I'

dh' dh

The subroutine SLIP calculates the slip ratio K and its derivative b.

s 33 p l

l The static quality and void fraction are calculated.

h - hs (6a)

X

=

l l

p x (6h) a a

=

ps + (ps _ ps)X hs - h with hty L

(6c)

=

I.

10 I

I

I The two phase (nodal) density pn, is calculated from a and the s

densities of the liquid and vapor phase p[, p,

E (6d)

D =P[(1-G)+ PG n

I The slip ratio K is calculated by the su'iroutine SLIP using a s

modified Bankoff(4) correlation. This correlation has the form:

I (7a) 1-3 K (G.P) -

r(P) s c(r) - a + (1 - c(p))a I

(7b) where c(P) = c1 +

(p/1000.)

3 I

ri - r2 (P/1000.) + r3 (P/1000.)2 (7c) r(P) =

I 2

with p in Ib /in a and f

E (7d)

.71 r1 = 3.53125 c1

=

E

.29 r2 =.1875

=

c2 I

c3

= 3.2062 r3 =.58594 I

This correlation is only used for pressures such that:

llI (7e)

(1 - c(p))r(p) < 1 11 8

8

I otherwise K,

1.0

=

(7f)

The derivative [3K\\ s given by s

i r(p) - (1 a (P))r(p) a (p)-1 (7g)

N,(1 - c(p))(1 - a r

r 5

[c(p) a + 1 - c(p) ar(P)]2 I

I If these calculations are bypassed by setting I,1g = 0, then no slip is p

assumed and the following results are obtained:

K, 1

=

(8a)

I-

.h = 0

'Ba.

(8b) p e

The dynamic quality X' is calculated using the slip ratio:

s X'

aK

=

p7 s

(9a) sp, 3gs+ p[ (1-a)

I From this the dynamic enthalpy can be calculated:

(1-X')h[+X'hs=hh(X' (9b) h'

=

its derivative is q

K O-a g'.

s s p p s+

a p

.g (9c) dh ps + (p ps)(1-X) p s

s dh aK,+p[(1-a) o i

I 12 I

l 1

~

iI If the water is not saturated, then we assign the appropriate values j

to the two phase quantities.

it Liquid Vapor -

K,

=1 1

(10a)

=0 0

(10b) oQ P

X

=0 1

(10c) iIg X'

=0 1

(10d)

3 Q

=0 1

(10e) il h'

=h h

(10f) ll b

=1 1

(10g) i dh It was found, however, that the dynamic enthalpy h' and its l

derivative $ did not approach the proper values as the water went from i

dh a saturated state to a single phase state.

It is necessary to smooth the 1

i results for h' and 8 such that:

I lim h' (h[ + 6h) = h (lla) i 6h->0 i l lim h' (hs - 6h) = h (11b) a-> 0 1

!I l

13

t dh' I

lie (lic) dh 6h+0 h' +6h E

dh' lim

-1 (lld) dh hs - 6h 6h.0

(

t l

E This was accomplished by using a linear approximation over a small range of enthalpies Ah within the saturated region:

.01(hs-h[)

(lle)

.01 Ah where Ah

=

ty Near the liquid phase:

hs i h i h[ + Ab (llf) s s

p i

h-h) h + (h - h ) hj(X')

(llg)

Ah Ah E

dh' (i _ h - hs.) + (h - hs)

(llh) dh' dn Ah Ah dh o

E are defined in the previous equations, (9b) and (9c).

dh wherehj(X')and Near the vapor phase:

I h - Ah i h I hs (111) 8 7

I I

E 14

E E

E (1

h - h) h + (h* - h)h' (X')

(11j) 8 h'

=

r 7

Ah Ah I

dh' (1

h - h) + (hs,- h)

(11k) v

'a dh Ah Ah dh l

J E

For two phase flow farther from the single phase regions, the equations are identical to those given previously in (9b) and (9c).

In order to illustrate the results of the calculations done by the l

subroutine QUAL (equations 6a through lik), calculations were performed 2

using H26DA. These calculations were done at a pressure of p = 1000.0 lb /in,,

f which is near the steady-state operating pressure of a BWR. An enthalpy range including the saturated region, hs = 542.62 BTU /lb, < h < 1192.8 BTU /lb, = hs, was selected for the calculation. The Bankof f slip correlation 7

was selected by setting the input parameter Islip " 1*

I The results of these calculations are shown in Figures 111-1 through III-3.

Figure 111-1 shows the static (X) and dynamic (X') quality and the void fraction (a ) as functions of the fluid enthalpy h.

All three quantities have approached 1 as h goes to hs, although o increases the 7

most rapidly initially. The dif ference between the static quality (X) which is linear with respect to h and the dynamic quality (X') which is non-linear

= 1).

with respect to h results from the slip ratio K, being unequal to 1, (since I,ygp Figures III-2A and III-2B show the relationship between the dynamic 15

1 Figura III-l l

l B

Two Phase Parameters Calculated by H20DA 2

E at a Pressure of p = 1000 lbr/in a 1

. E I

I FIGURE III-1 I(QURLITY), I'(DYNAMIC QUALITY), a(VOID FRRCTION)

VS h(ENTHRLPY) 1.00 iiii e i l

.90

,i l

l

/

\\

.80 e'

l

/

l'

~

l

/

~

l

/

l

/

70 l

l

?'

/

)

/

l

/

.60 I

/

I

/

l

/

e I

/

g

.50

~

I of J

/

I' y

I

/

.40 I

/

I

/

l j

/

i

/

.30 I

/

l 1

l l

h I

I I

20 i

)

.10 i

/

I l

/

I l

li l

0.00

,v,

l SC'O 6C O DCIO 8C'O 9C 0 1030 1130,,,,

0 123 h(BTU /LBM)

I 16 80/08/13

Figura III-2A Dynamic Enthalpy Calculated by H20DA 2

at a Pressure of p = 1000 lbr/in a.

E I

I I

I FIGURE III-2R h' (0YNAMIC ENTHALPY) VS h(ENTHALPY) 1200 i...

I

/_

~

1100

/

1000

[

I r

900 I

i

/

~

800

,e 700

/

l

/

~

600 ~

l 500 ~

~

I SC'O' ' ' '6C O' ' ' '7C'O' ' ' '8C'O' ' ' '9C O' ' ' iO ]d ' ' $ 1 ]d ' ' $ 2 30 h( BTU /LBM )

I 17 80/08/13.

Figura III-2B Th2 Derivativa of tha Dynanic Enthrlpy with Respect to the Enthalpy I

calculated by H20DA at a Pressure of 2

p = 1000 lbr/in a.

I E

E E

FIGURE III-28 dh (0YNAMIC ENTHALPY DERIVATIVE) VS h(ENTHALPY) 2.50 I

2.00

\\

l 1 50 l

a e

\\

1.00 i

. I

.50 s

g N

1 0 00 50 0' ' ' '60 0' ' ' '70 0' ' ' '8C'0' ' ' '90 0' ' ' iO ]d ' ' $ 13d ' ' 12 30 h(BTU /LBM) t 18 80/08/13

!E

+I enthalpy h' and its derivative and the fluid enthalpy, h.

The inequality between h and h' results from the fact that the slip ratio K, is unequal to 1.

! E The slip ratio, K, and its derivative K,h are shown in Figures 4W P

i' III-3A and III-38.

In these calculations bot and BK,} have values WP It is also ap)pa snt from these above 1.0 over much of the enthalpy range.

twofiguresthatalthough[8K,}

increases monotonically broughout the il saturated range for the entha/Plpy h, the slope of the K,(h) curve is

\\aa jg i

i decreasing. This resolts from a increasing very rapidly initially (Figure III-1) where the value of BK,}

is relatively small and then a increases 3a / P much more slowly where BK, is relatively large.

I WP Further clarifications of equations 4a through lik may are provided by the listing included in Appendix A.

4 I I

I I

I i

19 I

1 Figuro III-3A The Slip ratio calculated by H20DA 2

at a Pressure of p = 1000 lbr/in a.

E I

I I

FIOURE III-3R K,(SLIP RRTIO) VS h (ENTHRLPY) l 5.00

'ii' l,-

/

4.00 I-

/

3.00 l

u 2.00

/

'l

/

!I 1.00 6

0.00 SC'0' ' ' '60 0' ' ' '7C:0' ' ' '80'0' ' ' '90'0' ' ' iO 3d ' ' (13d ' ' i2 30 h(BTU /LBM)

.I 20

'E 80/08/13.

Figure III-3B The Derivative of the Slip ratio with I

respect to the void fraction at a 2

Pressure of p = 1000 lbr/in a.

1 I

I e

FIGURE III-38 aa)'(SLIP RATIO DERIVRTIVE)

VS h(ENTHRLPY) 25.00 l'

>i

g 20.00 15.00 l

44

~

% A

~

v 10.00 I

5.00 0 00 50'0' ' ' '60 0' ' ' ' C O' ' ' '80 0' ' ' '9C O' ' ' IO )d ' ' I13d ' ' (2 50 7

h(BTU /LBt:)

1 21 i

80/08/13

l IV.

VERIFICATION OF THE WATER PROPERTIES PACKAGE Before the water properties package described in this report can be used with confidence in the development of fuel behavior modeling or reactor systems codes it must be verified. In order to facilitate the verification of this water properties package, H29DA, a comparison of its

' ~

output with the data from the ASME Steam Tables (5) is provided in this section of this report. The comparison presented here is neither as extensive nor as comprehensive as were the comparisons performed while developing the package, however, it will serve to illustrate the type of I

comparison done and to indicate the errors and accuracies of H29DA.

In order to simplify the presentation, a comparison between the saturated properties of water presented in the ASME Steam Tables (5) and those calculated by H20DA is presented first in this section. To facilitate understanding of this section, Figures IV-1A and IV-1B show the saturation temperature of water, as a function of the pressure,p. The data for these figures were taken from the ASME Steam Tables. The disagreement between lI l-H29DA and the ASME Steam Tables is so small that it cannot be shown on these figures. Instead a tabulation of the data from the Steam Tables and the results from H29DA at a number of pressures will be used to illustrate the results. For ease in comparison, Table 1 uses the variable defined by the equation:

I ATsat(p) " Tf,fA(p)-T (p)

From this table it is very apparent that the agreement between H29DA and the ASME Steam Tables is excellent with regards to the calculation of the l"

saturation temperature, Tsat(p)*

22 I

Figure IV-1A Saturation Temperature as a E

Function of Pressure Calculated by H20DA for Low Pressures 2

(less than 400 lbr/in a).

I FIGURE IV-1R T.,e(p)(SRTURRTION TEMPERATURE) VS.p(PRESSURE)

I 750 700 I

600 550 500 450

/

o 400 f

3

/

u 350 E

/

30C f

250 l

200 l

100 50 O

Cl 5)

' 1C 0 150 20 0

' 250 3C 0 350 4Ct0 l

p(LBf/IN R) 23 I

80/08/13

Figure IV-1B Saturation Temperature as a Function of Pressure Calculated by H20DA I

I FIGURE IV-1B T,,t(p)(SRTURATION TEMPERATURE) VS P(PRESSURE) 750

'E 700 7

g

/

650

/

I 600 m

f SCO

/

f 500

/

[

i 450

/

l

~

400

/

I

- /

g 350 sE l

300 I

250 200 I

150 100 I

50

,I O

Cl 4C 0

' 8C'O

' 12]O 1630 2030 ' 24.:0 ' 2600 ' 3230 p(LBF/IN R) 24 80/08/13.

I TABLE 1 I

Comparison of Predicted Saturation Temperatures ASME I

2 Steam Tables H26DA P(lbs/in a)

T,,g(p) op T,,g(p) og sat (p) 0F AT 15.0 213.03 213.02

.01 25.0 240.07 240.05

.02 50.0 281.02 280.98

.04 100.0 327.82 327.79

.03 200.0 381.80 381.77

.03 400.0 444.60 444.57

.03 800.0 518.21 518.22

+.01 1200.0 567.19 567.16

.03 1600.0 604.87 604.83

.04 2000.0 635.80 635.78

.02

!g

!W 2400.0 662.11 662.10

.01 i

I I

I g

2e I

I In order to verify the accuracy of the calculation of saturated water properties performed by the new water properties package, H29DA, Tables 2A, 2B and 2C were prepared. Each table compares saturated water properties calculated at a given fixed pressure using H29DA with the same properties obtained from the ASME Steam Tables at these pressures. The three values of the pressures used in these three tables have a moderate amount oi significance in the field of reactor safety in that the pressure used in 2

i Table 2A, p = 25 lb /in a occurs during the i flooding of a PWR after a f

2 loss of coolant accident. The pressure used in Table 2B, p = 2200 lb /in,

f is very near the steady-state operating point of most PWR's.

The pressure 2

used in Table 2C, p = 1000 lb /in a is also near the operating point of f

l; -

a BWR.

r In all three tables the agreement between the ASME Steam Tables and the H20DA calculation are excellent for the saturation temperature, g

enthalpies and specific volumes. The pressure derivative of the saturation temperature is also in excellent agreement with the data from the ASME Steam Tables.

i There is some disagreement in the results for the pressure j=

derivatives of the saturation enthalpy and of the saturation densities.

The error in some instances was as great as 9.6%.

This could partly result t

from the finite difference scheme used to calculate the derivatives at the pressure, pf:

l

\\E I

26

I

tl i

TABLE 2A Comparison of Saturated Water Properties Between H2WDA and the ASME Steam Tables At a Given Constant p = 25.0 lb,/in's ASME R29DA Difference f

Property Symbol Units Value Value in Value 2 i

Satsretion Temperature T, g

'F 240.07 24d.05

.001 j

Specific Volume l

3 l

Liquid V

ft /lb,

.01693

.0 g

V ft /lb, 16.301 16.301

.0 3

f Vapor y

1

,l Saturation Enthalpy Liquid

(

BTU /lb, 208.52 208.52

.0 Vapor Q

BTU /lb, 1160.60 1160.60

.0 t

Freemure Derivatives 2

2.22 2.21

.5 l

Ssturation Teeperature dT

F/lb /in g

PJsat l

2 Saturation Enthalpy d h' 3 (BTU /lb,)/(1b /in )

g 7p, sat 2.25 2.24

.5 i

Liquid ( cL)

.8

.0 Vepor (cV) 3 2

d o' '

(Ib,/ft )/(Ib /in )

Szturation Density g

7p sat 5

.064

.061 5.0 Liquid (cL) l 1

.0023

.0 I

Vapor (eV)

Enthalpy Derivatives

(

Saturation Density

]I (1b,/ft3)/(BTU /lb,)

j est

.0284

.0273 3.9 l

Liquid (cL)

I

.0297

.00295

.6 l

Vapor.(cV) l I

I 27 I

I I

TABLE 23 I

Comparison of Saturated Water Properties Between R290A and the ASME Steae Tables At a Given Constant p = 2200.0 lbr/in'a ASME X200A Difterence I

Property Symbol Units Value Value in value 1 Saturation Temperature T,,g

'F 649.45 644.43

.003 Specific volume 3

Liquid V,

f t /lb,

.02669

.02668

.04 g

3 Vapor V

ft /lb,

.1627

.00 y

Saturation Enthalpy Liquid h[

BTU /lb, 695.46 695.51

+.007 vapor hi BTU /lb, 1122.20 1122.05

.013 Pressure Derivatives I

2 Saturation Temperature g

F/(1b /in )

.06550

.06569

.3 f

dp, sat 2

Saturation Enthalpy dj *

(BTU /lb,)/(1b /in )

g dpj aat Liquid (x=L)

.1175

.1174

.1 Vapor (x=V)

.0875

.0877

.2 3

2 Saturation Density

,d_o] E (1b,/ft )/(1b /in )

g dpj aat I

Liquid (x=L)

.00770

.00769

.1 Vapor (x=V)

.00446

.00448

.4 I

Enthalpy Derivatives Saturation Density yx (1b,/ft)/(BTU /lb,)

dh, sa t Liquid (x=L)

.06553

.06549

.1 Vapor (x=V)

.05097

.05107 I

I I

I 28 I

I TABLE 2C Comparison of Saturated Water Properties Between K29DA and the ASME Steam Tables At a Civen Constant p = 1000.0 lb,/in's I

ASME H29DA Dif fe rence Property Symbol Units Value Value in Value 1 Saturation Temperature T

F 544.58 544.58 0.0 sat Specific Volume 3

Liquid V,

ft /lb,

.02159

.02159 0.0 g

3 Vapoe V

ft /lb,

.4460

.4459

.02 y

Saturation Enthalpy I

Liquid h[

BTU /lb, 542.55 542.62

.01 Vapor Q

BTU /lb, 1192.9 1192.8

.01 I

Pressure Derivatives 2

Saturation Temperature g

F/(1b /in a)

.1213

.1212

.1 g

I dp sat 2

[j* sat (BTU /lb)/(Ib /in )

Saturation Enthalpy g

dp

.1525

.1527

+.2 Liquid (x=L)

.0375

.0340

-9.3 Vapor (x=V) 2 Saturation Density ME (1b,/ft3)/(1b /in )

f dpJ sst

.00750

.00802

+6.9 Liquid (x=L)

Vapor (x=V)

.C0250

.00249

.4 Enthalpy Derivatives Saturation Density I*

(1b,/f t)/(BTV/lb,)

dh, sat

.0492

.05252

+6.7 Liquid (x=L)

I

.0667

.07311

+9.6 Vapor (x=V)

I I

I

=

I I

. xA A

A Vxi+1 - Vxt_1 dp 1

I (y i)2 dp sat P +1 P -1 i

i P"Pi I

hsAxi+1 - hsA

- xA xi-1 dh I

dp, sat pf+1 p _3 g

P"Pi I

where the superscript x denotes the x'th phase, (x = L, Liquid; x = V, Vapor) and the superscrtpt A denotes that the ASME Steam Tables are the source of this data. To further explore this discrepancy, Figure IV-2A shows the variacion of the pressure derivative of the saturation density of the vapor 2

2 phase calculated by H29DA in the range 25 lb /in a < p < 3000.0 lb /in,,

f f

This figure illustrates the excellent agreement between the H29DA I

calculations (solid line) and results taken from the ASME Steam Tables E

l (crosses). A comparison of the results from the H29DA calculation (solid line) and those from th1 ASME Steam Tables (crosses) for the ;,ressure derivative of the saturation density of the liquid phase is made in Figure IV-2B.

Although there is some disagreer+nt between ae H29DA results and the ASME results, the H29DA calculations appear to follow the general trend of the ASME data and to be reasonably accurate for use in most calculatiot.s and codes.

t l

Although during certain transients, for example a LOCA, the coolant of a PWR is in a saturated condition, during normal operation and shutdown, the water in the reactor coolant system of a PWR is in a subcooled liquid In this subsection the properties of subcooled liquid water state.

calculard by H29DA will be compared with data from the ASME Steam Tables.

1 ilI 30 lI

Figura IV-2A Comparison of Ragulto:

Th2 Derivative of the Saturated Vapor Density with Respect to the Pressure.

I I

!I

'E FIGURE IV-2R 6V' (PRESSURE DERIVATIVE OF DENSITY)'

VS piPRESSURE) iE E sat FOR SRTURATEG VRPOR 50 l

t l

l 40 0o I

G 9

I C

30 z

u.

as J

I q

J 0

I 20__

rj H2$DAResults

,I

>2 l

W ASME Data

+

l

/

-W 0

(i 4C 0 80 0 1230 1630 ' 2030 ' 2430 ' 2830 ' 3230 P(LBF/IN2 R) l 31 80/08/13 g

l

+w-m--~

w-~

y g,

m.e-,,,e

-,-,e-n,-w-,,w

-,,.,,m,-,,w,-,,,ee,,.v,.

,,,,...,w,y-,,n--,,w,,,-w,-,.,-..n,.,.-,-e,,,,,,,

.,,,---e

Figura IV-2B Comparison of Results:

The Derivative of the Saturated Liquid I

Density with Respect to the Pressure.

I

!I

'I I

FIGURE IV-28 g (PRESSURE DERIVATIVE OF DENSITY)

VS p(PRESSURE) 50 t

, sac FOR SATURRTED LIQUID dp l

I

~

40

'a N

I C

30 I

~

N I

5

(

20-l g

r H2pDA Results

,I g

I'5

~

ASMF Data

+

4

)

V I

,j e

10 A %

> F'-

y N

o

' 40 0

' 8C'O 1230 1630 ' 20]O ' 2430 ' 2830 ' 3230 p(LBF/IN2 R)

I 32 80/08/15.

I I

The relationship between the enthalpy per unit mass h, and the 2

temperature T at a constant pressure p = 2200.0 lb /in a is shown in Figure f

IV-3A.

This figure shows excellent agreement between the ASME data (crosses) and H29DA results (solid line). In Figure IV-3B the seme relationship, 2

T vs h, is shown at p r 1000.0 lb /in a.

The agreement between the ASME f

data (crosses) and the H29DA results (solid line) is again excellent.

In Table 3A, a detailed comparison of the output of H29DA is made with data obtain d from the ASME Steam Tables at an enthalpy of h = 550.0 2

BTU /lb,and p = 2200.0 lb /in a.

From '.:his table it ir apparent that there is f

excellent agreement between the H20DA results and the ASME results in the calculation of the temperatures and specific volumes. The agreement between the H29DA results and the ASME Steam Tables results is also very good for the specific heat, C, the coefficient of thermal expansion, 8, and the p

isothermal compressibility, K.

The calculation of the derivative

, !.S.

.S.

using the ASME Steam Tables was not

'q P, h and(Oh quantities (B P/p 3

p easily done, it involved tedious interpolations before proper finite

,I differencing could be used to approximate the derivatives. Therefore, the maximum error of 9.1% is considered reasonably small and the results of H20DA should be adequate for most uses.

I In Table 3B a comparison of liquid water properties calculated by H20DA

. sgain made with data obtained from the ASME Steam Tables, this 2

time at an enthalpy of h = 500.0 BTU /lb,and at a pressure of p = 1000.0 lb /in,,

f The H20DA results are in excellent agreement with ASME results for all of theoutputvariablesexceptthepressurederivativeofthedensity,[0P).

I (BP/h The disagreement between H29DA and the Steam Tables for this parameter is I

33 I

Figure IV-3A Comparison of Results:

I The Temperature of Subcooled Liquid as a Function of Enthalpy at a Pressure of p = 2200 lbr/in2a I

I I

T FIGURE IV-3A L ( TEMPERRTURE ) VS h(ENTHALPY)

FOR LIQUID STATE WITH p=2200 LBF/IN2 A g-700 e i..

l 600' l

500'

~

g 400'

/

~

I

[

)

~

i 300

/

I 200'

/

H2fDAResults lI

~

ASME Data

+

100'

/

'I lI O

1CO' ' ' '2CO' ' ' '3CO' ' ' '4CO' ' ' '5CO' ' ' '6C'0' ' ' VC0 h(BTU /LBM)

I 34 1I l

80/08/13.

Figura IV-3B Comparison of Results:

I The Temperature of Subcooled Liquid as a Function of Enthalpy at g Pressure of p = 1000 lbr/in a.

e I

lI I

I I

T (TEMPERATURE) VS h(ENTHALPY)

FIGURE IV-3B L

FOR LIQUID STRTE WITH p=1000 LBF/IN2 R I

700 e...

i=

i i i..

I 600

/

500 I

400'

/

I a

300'

/

I 200' l

H2dDAResults ASME Data

+

I O'

1CO' ' ' '2CO' ' ' '3CO' ' ' '4CO' ' ' '5CO' ' ' '6C'O' ' ' YC0 h(BTU /LBM)

I 35 80/08/13.

I TABLE 3A I

Comparison of Liquid Water Properties Between H29DA and the ASME Steam Tables ASME H290A Difference I

Property Symbol Units Value Value in Value !

Inputs:

2 lb /in a 2200.0 2200.0 f

Frsecure p

Eithalpy h

BTU /lb, 550.0 550.0 Outputs:

T:cperature T

F 552.16 552.145

.003 O

Syscific volume V

ft /1b,

.02142

.02141

.05 3

Spscific Heat C

BTU /lb,'F 1.258 1.251

.6 p

Coeff. of Thermal 8 =jl 3 1/'F

.00138

.00140

+1.4 IEspansion v\\

p

.0000151

.7 2

(-11) Isothermal E=1]

1/lb /in

.0000152 g

Compressibility V \\a y Pratsure Derivatives Esthalpy (BTU /lb,)/(11,/in )

.01305

.01186

-9.1 2

.2

-,.0 1,.,,t> m 1,,,i.2) g,

.... t, I..th1p...rt..t...

ub.ut m.TUnb.>

.0519.

.05233 a

g, l

De. m,

I lI 1

1!I l3 I

I 1I 36

.I

,wvw ur-"WyT

-*w g-rmwv-?7 P-d 8-"-**

-+----N'+++w=%wgw-m

^-'-----=7

I I

TABLE 3B Comparison of Liquid Water Properties I

Between H20DA and the ASME Steam Tables ASME M20DA Dif fe rence i

Property Symbol Units Value Value la Value 1 Inputs:

2 l

Pressure p

lb /in a 1000.

1000.0 g

En thalpy h

BTU /lb, 500.0 500.0 Outputs:

Tempe rature T

F 510.26 510.22

.007 I

3 5pecific Volume V

ft /lb,

.02061

.000 Specific Best C

BTU /lb,'F 1.200 1.200

.000 I

p Coeff. of Thermal

$=1 W 1/'F

.001214

.001121

.6 Espa nsion V BT p I

2

(-11) Isothermal E=1[,3V 1/(1b /in )

.0000121

.0000122

.8 f

Compressibility V(ap/ T Pressure Derivatives 2

Enthalpy

[g (BTU /lb,)/(1b /in )

.01110

.01126 1.4 g

\\* p)o 2

2 Denr3ty (1b,/f t )/(1b /in )

.00059

.00056 5.0 g

Enthalpy Derivatives l

Density (1b,/ft )/(BTU /lb,)

.04909

.04937

.6

.I I

I I

I

!I

-w-m

.,n,._,.m-

I only 5.0% of which 2.0% could be attributed to the round-off error caused by having only four significant digits in the ASME Steam Tables, when adequate accuracy for this calculation requires five digits.

I In short, the properties of liquid water as calculated by the H29DA package which uses the STH29(3) subroutines gives a very adequate calculation of subcooled liquid water propcrties.

In order to perform a detailed analysis upon the hot channel of the core of a PWR during a very severe transient such as a LOCA (loss of coolant accident), an adequate knowledge of the properties of superheated steam is necessary. For example, in a recent(6) analysis of a LOCA for the Maine Yankee reactor, the water in the upper nodes of the hot channel of the core is in a superheated state for two time periods. The first time period occurs early in the blowdown segment of the transient, while the 2

2 core pressure was roughly in the range 1200 lb /in a > p > 900 lb /in,,

f f

The second time period occurs later in the blowdown segment of the transient lasting a few seconds until the initiation of refill. During this second 2

time period the pressure is very low, roughly in the range: 50 lb /in,

f 2

> p > 14.7 lb /in a.

For this reason and for ease of comparison with the f

other subsections, a detailed comparison of the properties of superheated steam calculated by the H20DA water properties package and obtained from data from the ASME Steam Tables will be made at pressures of:

p = 1000.0 2

2 lb /in a and p = 25.0 lb /in 3,

f f

In Figures IV-4A and IV-4B, the relationship between enthalpy (h) 2 and temperature T is shown for pressures of p = 1000.0 lb /in a and f

2 p = 25.0 lb /in a respectively. In both figures the agreement between the f

I I

~

Figure IV-4A Comparison of Results:

I The Temperature of Superheated Vapor as a Function of Enthalpy at a Pressure of p = 1000 lbr/in2a.

!I l1-E I

I FIGURE IV-4A T t TEMPERATURE) VS h(ENTHALPY) y FOR VAPOR WITH p=1000 LBF/IN2 A

,I 1700 ii>>

ii E

~

1500 I

~

I 1100'

/

~

900 ~

I 700' H2fDA Results ASME Data

+

500 I

300' 12 3d ' ' i3 )d ' ' i4 )d ' ' iS 3d * ' i6 )d ' ' i7 )d ' ' is)d ' ' ig yg h(BTU /LBM) e 3

3, 80/08/15.

Figura IV 14B 1

I Comparison of Results:

1 The Temperature of Superheated Vapor as a Function of Enthalpy at a 2

' Pressure of p = 25. Ibr/in a.

I E

E I

I FIGURE IV-4B TvfTEMPERATURE) VS h(ENTHALPY)

I FOR VAPOR WITH p=25 LBF/IN2 R 1700

- i..

1500

~

I i

i 1300 ~

~

lE I

1100

/

I 900'

/

700.

/

H2dDAResults

~

ASME Data 4

[

500

/

I

' ?2,e is,e 1,e i8,e ie,e i,,e ie,a ie,0 hlBTU/LBM)

I v

40 i

8 80/08/13.

I ASME Steam Table data and the results from H29DA is excellent although H29DA 0

overpredicts the steam temperature by roughly 2 F for enthalples near 2

saturation at p = 1000.0 lb /in,,

f A detailed comparison of the results from H29DA with data derived 2

from the ASME Steam Table at a pressere of p = 1000.0 lb /in a and an f

enthalpy of h = 1500.0 BTU /lb, is provided by Table 4A.

There is extremely good agreement between the H29DA results and the ASME Steam Table data for all the parameters calculated with a maximum error of 3.3%.

The only flaw in the comparison is a 1.37 F error by H29DA in the calculation of the temperature.

The accuracy of H29DA for low pressure superheated steam is shown in Table 4B.

The properties of superheated steam shown in Table 4B were 2

determined at a pressure of p = 25.0 lb /in a and an enthalpy of h = 1500.0 f

BTU /lb,.

Again, there is excellent agreement between the data from the l

ASME Steam Tables and the results calculated by H29DA. There is a maximum disagreement between these two sources of 2.1% although there is a disagreement between H29DA and the ASME Steam Tables for the steam 0

temperature of AT =.46 F.

l In order to model a reactor during an anticipated transiant without scram, it is necessary to know the properties of water in the supercritical regime, that is for pressures above the critical pressure, perit. A comparison iI of data from the supercritical regime is provided by Figure IV-5A, which shows the relationship between enthalpy (h) and temperature (T), at a 2

pressure of p = 3500.00 lb /in a.

The agreement between the ASME Steam f

Table data (crosses) and the results obtained from H29DA ( olid line) is g

e I

\\E l

l l

TABLE 4A l

l Compariton of Superheated Steam Properties Between R29DA and the ASME Steam Tables E

ASME K200A Dif fe rence Property Symbol Units Value Value in Value 1 Input s 2

Pressure p

lb /in a 1000.0 1000.c g

Enthalpy b

BTU /lb, 1500.0 1500.0 Outputs:

Tempe rature T

F 990.36 991.73

+.14 3

Specific volume V

ft /lb,

.8229

.8225

.05 Specific Heat C

BTU /lb, 4

.565

.569

+.7 p

I Coef f. of Thermal 8=1 BV 1/*F

.0008265

.0008342

+.9 Expansion V af,

(-II) Isothermal KQ 1/lb /in2

.0010526

.0010815

+2.7 g

Compressibility V

/T Pressure Derivatives 2

Enthalpy

(&

(BTU /lb,)/(1b /in )

.7000

.7055

+.8 g

(3P/p 3

2 Density (1b,/f t )/(1b /in )

.00122

.00126

+3.3 g

Enthalpy Derivatives l

Density (Ib,/ft )/(BTU /lb,)

.00178

.0

\\

P 1

I I

I E

I 42 I

L_

TABLE 4B I

Comparison of Superheated Steae Properties Between H290A and the ASPE Steam Tables

.e ASME N20DA Difference I

Ixputs:.Froperty Symbol Units Value value in Value 1 2

Pressure p

'wg/in a 25.0 25.0 Enthalpy b

318"*1b, 1500.0 1500.0 Outputs:

Temperature T

'F 933.33 932.87

.05 3

Specific volume V

ft /1b, 33.146 33.133

.04 Specific Rest C

BTU /lb,'F

.510

.510 p

Coeff. of Thermal 8=1 /3 V'.

1/'F

.0007228

.0007221

.01 Expansion Y Tf),

s I

Compressibility 2

(-11) Isothermal Kal 'N 1/(1bg/in )

.040132

.040881 1.9 p/T l

Pressure Derivatives 2

Enthalpy

[

(BTU /lb;)/(Ibg/in )

28.25 28.85 2.1 3

2 Density (1b,/f t )/(Ib /in )

.00121

.00123 1.7 g

Enthalpy Derivatives Density (1b,/ft3)/(BTU /1b,)

.00004

'I l'I I

I

,;I I

I 43 I

Figuro IV-5A Comparison of Results: Temperature I

of Water in the Supercritical Regime as a Function of Enthalpy at az Pressure of p = 3500 lb /in a.

f I

I I

I FIGURE IV-5A TL(TEMPERATURE) VS h(ENTHALPY)

FOR HRTER WITH P=3500 LBF/IN2 R 2000

~

/

1600_

/

1200 C

I 800 M

H2pDA Results -

ASME Data

+

I 400.

/

j 0

l C) 40 0

, 8C O 1230 1630

,2030 h(BTU /LBM) 1 44 1I 81/02/1:

Figura IV-5B Comparison of Results: Density of Water in the Supercritical Regime as a Function of Enthalpy at a Pressure of p = 3500 lb /in2a.

I f

I I

FIGURE IV-58 p(OENSITY) VS htENTHALPY)

I FOR WATER WITH P=3500 LBF/IN2 R 70 60

\\

g g

~

50

~

2 40

[

H2$DA Results ASME Data

+

[

l Z

30 10 N-I O

Cl

' 4C 0 '

' 800

'1230 '

'1630 '

'2030 h(BTU /LBM)

I 81/02/12

I excellent. Another comparison of H29DA results (solid line) with ASME data is provided by Figure IV-58, which shows the relationship between enthalpy (h) and density (D) at the same pressure. Again, the agreement is excelle it.

The calculation of the properties of water in the supercritical regime is limited to pressures below the maximum pressure data point on the water property data file used by STH29, p,,x.

In the water property data file used by YAEC, this pressure is:

2 pmax = 3624.16 lb /in,

f For pressures above this, that is:

P > Pmax I

The properties are calculated by H20DA using pm,x as the pressure input s

such that the system or fuel model calculation of which H20DA is a part is not terminated, however, an error message is written.

'E This limitation may be partially alleviated by using the STH20G program to generate a water property file to be used specifically for transients which result in very high coolant pressures. The pressure data l

points of the present YAEC water property file are shown in Table 5.

From 1

this table the limitations of the present YAEC water properties file for the calculations of the properties of water at high pressures are obvious.

2 l

Firstly, there are only five pressure data points above p = 2200 lb /in 3, f

l which approximates the operatf ag pressure of a typical PWR.

Secondly, the critical pressure is not included in the data points. Finally, the maximum pressure in this data set may be prohibitively low for some applications.

The ability of H29DA to calculate the high pressure properties of water 46

TABLE 5 Pressure Data Points Used in the Present YAEC Water Property File YAEC Water Other Important Property Fgle Pressurgs

/g (lb /in a)

P (Ib /in a)

Description i

g f

1

.290 2

.725 3

1.450 I

4 2.901 5

7.252 I

6 14.504 14.670 Atmospheric 7

21.755 8

29.008 9

43.511 I

10 58.015 11 87.023 12 116.030 13 145.038 14 217.557 15 290.075 16 362.594 17 435.113 I

18 507.632 19 580.151 20 725.188 21 1087.783 1000.000 BWR operating 22 1450.377 pressure I

23 1812.971 24 2175.565 2200.000 PWR operating 25 2538.159 pressure 26 2900.753 27 3190.829 3208.233 Critical pressure 28 3335.867 29 3625.942 lI I

47

,I

'I

l I may be substantially enhanced by increasing the number of high pressure data points in the water property file, including the data for the critical j

point and increasing the maximum pressure in the data set.

1 Another limitation of the H29DA calculation in the supercritical regime is that H29DA assumes that the cater is a liquid, even though the l

temperature of the water exceeds the critical temperature, Terit, and is considered a vapor in this case.

l When the subroutine WATERT is used to calculate fluid enthalpy, h, for water in the subcooled liquid r superheated steam states from the fluid temperature, tin, there is almost exact agreement with the results obtained from the subroutine WATER which uses the fluid enthalpy, h, to calculate the fluid temperature. Since there are small disagreements between the results of the subroutine WATER and the ASME Steam Tables, there will be similar discrepancies between the results calculated using WATERT and the ASME Steam Table data.

I In conclusion, althor.gh there are some disagreements between H2@DA I

results and the data in the ASME Steam Tables, the water properties package l

H20DA, is generally a very reliable predictor of water properties over the wide range of conditions predicted in reactor analysis and is suitable to be used in fuel behavior performance and reactor systems code applications for both transient and steady-state modeling.

I I

I

.I

I V.

DESCRIPTION OF PROGRAM UTILIZATION In this section a description of the utilization of the H20DA water properties rackage is provided.

I Before any of the subroutines in the water properties package can be called, the values of the variables in the C6MM6N block / UNITS / must be specified. The C6MM6N block / UNITS / supplies the tape number from which the code reads (NINP) or restarts (NRES) or to which the code writes (NOUT) or dumps (NDUMP). This C6MM N block allows the user to assign the tape numbers of the desired input and output devices and communicate this to the water properties package.

Before the H20DA water properties package can be used in a computer code the tapes containing the water properties must be read. This is accomplished by calling the subroutine INITC in this manner:

CALL INITC(N17) where N17 indicates the tape number of the file in which the STH2O water property tables are stored.

i If the properties of water as functions of pressure and enthalpy i

are desired, the subroutine WATER should be called. This is done in the following manner:

,I

[

CALL WATER (P,H,ISLIP,ICF) l l

lg The input arguments of the subroutine WATER are:

P, the pressure in 2

lb /in a; H, the enthalpy in BTU /lb,; and ISLIP, which determines the slip f

l correlation, if any, used in the calculation. The argument IGF is outputed 49 I

I I

to provide an error flag. These arguments are further explained in the variable dictionary provided in this section.

The output of this subroutine except for the error flag, IGF, is through four blocks of labeled C6MM6N. The variables stored in these four C6MM6N blocks (/H26/, /DH26/, /DH261/ and / QUAL 1/) are described in detail in the variable dictionary provided in this section. These C6MM6N blocks are shown in the listing of the subroutine WATER shown in Appendix A.

If the user desires the properties of saturated water, the subroutine WATERS should be called. This subroutine is called in this manner:

CALL WATERS (P,IGF)

I 2

The arguments of the subroutine WATERS are:

P, the pressure in Ib /in a, f

and IGF which is outputed to provide an error flag. The output of this subroutine is through the C6MM6N blocks /H26/, /DH26/ and /DH261/. The variables in these three C0MMeN blocks are described in detail in the l

variable dictionary included in this section. It is important to note that the derivative properties for saturated water are calculated along the saturation line.

If it is desirable to calculate the enthalpy of single phase water, either liquid or vapor, f rom the temperature of this single phase, the subroutine WATERT should be used. This subroutine should be called in the following manner:

CALL WATERT(P, TIN,H6UT.IGF)

I 2

The input arguments of this subroutine are:

P, the pressure in Ib /in,,

f I

50

I and TIN, the temperature in degrees Fahrenheit. The output arguments of WATERT are H6UT, the enthalpy of the water in STU/lb,, and IGF which serves as an error flag. The variable dictionary which follows, further describes these variables.

I I

i

'I 4,

I

!I i

1 lI I

l I

~

!jW 51

I I

Variable Dictionary: WATER I

F6RTRAN Variable Symbol Description Units INPUT I

P p

pressure Ib /in2, f

'I H

h enthalpy/onit mass BTU /lbm g

t 5

ISLIP I,yg

=0 no slip calculation p

=1 slip calculation I

OUTPUT IGF I

error flag Igy M error gy l

/H29/

I TS(l), TS(2)

T,T temperature of liquid, F

t y

vapor at p, h l

l h,h enthalpy/ unit mass of the BTU /lb, HS(l), HS(2) t y

liquid, vapor at p, h 3

RS(1), RS(2)

Ot, P density of liquid, vapor Ib,/ft y

at p, h 3

VS(1), VS(2)

V, V, specific volume of liquid, ft /lb, t

vapor at p, h

'I I

'I

I Variable Symbol Description Units

/DB29/

3 DRH(1), DRH(2)

L, V;

the derivative of the (lb,/ft )/(BTU /lb,)

P P

density with respect to the L

V do

, do enthalpy either with dh sat dh sat pressure constant or along the saturation line 3

2 DRP(1), DRP(2) g L,[ g V; the derivative of the Ib / /(Ib /in )

f 3P h (3Ph

/

j density with respect to the L

do' V pressure with either do dp sat dp sat

~

constant enthalpy or along the saturation line specific heat of the BTU /(lb F)

CP(l), CP(2)

Cpt, Cpy liquid, vapor with constant pressure I

2 L

nV ; the derivative of the (BTU /lb,)/(lb /in )

DHP(l), DHP(2) gl,,

\\3P p 3PJp I

j enthalpy with respect to

[L g

the pressure for the liquid, Y

dp sat dp sat vapor with the density held cons, tant or along the saturation line

'I lI l

I 53 I

~ _, _ _ -. _ _ _ _.... _ _ - _ _ _.

I I

Variable Symbol Description Units I

h 2

d[j sat, g' Y t

the derivative of the

'F/(lb /in )

DTPS(l), DTPS(2) f dp dp sat saturation temperature with respect to the pressure DTDH jd the derivative of the F/(BTU /lb,)

'g g

(3h p temperature with respect to the enthalpy at constant pressure lI l

I I

I lI l

1 l

l I

I g

S.

l

I I

Variable Symbol Description Units I

/QUALl/

HL, HV hs(p), hs(p) saturation enthalpy of BTU /lb liquid, vapor at pressure p I

X X

" static" quality XP X'

" dynamic" quality

!I A

a void fraction 3

RN p,

" nodal" density lb,/ft l

l l

SW K,

slip ratio (Bankoff Correlation)

g W

i DSW K\\

derivative of the slip s

P ratio with respect to the void fraction l

It I

indicates states y

=2 saturated two phase

=3 subcooled liquid

=4 superheated vapor DHPDH dh' derivative of " dynamic" dh g

l enth8l y of the water with

'E P

respect to stetic enthalpy I

(Section [E9) All L. Schor

$NEDEE report) lI I

I Variable Symbol Description Units HP h'

dynamic enthalpy of water BTU /lb, TSAT Tsat(P) saturation temperature of

'F H O as a function of 2

preasure I

I I

II I

I I

lI 56 I

I Variable Symbol Description Units

/DH291/

2 g = 1 '3d minus one times the 1/(lb /in )

AK(1), AK(2)

K g

P T j

isothermal compressibility for the liquid, vapor K

=

y B(1), B(2)

Sg,B the coefficient of thermal 1/ F y

expansion for the liquid, vapor I

/S23/

SPNT(1) single phase pointer used to decrease running time used in SUB, VAP in calling STH295 SPNT(2) 2 phase pointer used in SAT to decrease running time in calling STH292 I

I I

I

1

I i

i I

Variable Symbol Description Units System Input i

/ UNITS /

NINP reading unit number

)

I 3 NOUT printar unit number sl l

HDUMP dump unit mimber i

NRES restart unit number 4I l

Variable Dictionary: WATERS

'I INPtTI P

p pressure Ib /in2, f

OUIPITI I

IGF I

error flag, Igp >0 error gp I

Other outputs are through the common blocks /H20/, /DH20/ /DH201/ with the same definitions as given previously except that all the output pa rame ters are evaluated for saturation at pressure p or along the saturation line at pressure p.

I I

I 58 I

!I l

Variable Dictionary: WATERT s'.

Variable Symbol Description Units INPUT i,n P

p pressure Ib /in2, f

f

I j

T, water temperature "F

TIN g

l OUIPUI

!I I

H6UT h

water enthalpy BTU /lb, out 4

!I IGF I

error flag, Igp>0 gp I

I I

~

I I

I 59 I

I I

)

Appendix A Listing of H29DA This appendix provides a listing of the subroutines in the H29DA water properties package.

I I

I

'I I

I lI l

1'I I

'I I

60 I

lI

I I

t ht MATER fa/Ts OPTSO TRACE FYu 4.t*433F 81/0s/20 la.b6 I

Sutt00 TINE wtTER(P,M,IBLIP,1GF) nattawa C0am0=Fw20/ Ts(2), Matt), este), ~vegg) maTEwpa 3

EUP"UN/Dw30/ D8"If3, DEPT 23, CPtf), DMP(FJ, UTPg(2), DTDM maitwwa e

C0==0N70w2ct/ an(2), s(2) mate =wa 5

I Comm0N7evattywt, Hv, y, 3P, ALP, eN, So, D$ne Iw, DMPDM, MP, TSAT mattawa e

cuamunist3r sP=ItsJ mavg=as T

00mw0N/ UNIT 87 w1NP,NOUT,NDUMP,Ngge maitaba e

CCNVERSION FACTOst FROm ENGL!sM TO 3 I maitwva w

Data agg,anPa,ame aT/16.0145,e594.ft,5326.0,1.57 esitwpa g '.

I DATA PCm!T /22:20000.0/

asitwh80 1

Defa TCRIT/ 687.307 paltwpaL 2

mauttUs 33 5 as 1 Lasu!D C I 0 2 VAPOR n11Enoa n2 I

C INPUT OF STATE IB IN EhGLISM UNITS e BTU, FT, 3EC mattuva 33 esitava 36 6 wwurvi Is aLsv = gabLamm umart C la e 2 gafusaTED maltwua 35 C != a 3 subC00LF0 LTWUID mattwua se 6 aa = a surt=Maavau varva seitava 37 I

C In a 5 LIGute aSovE CRITICAL PREggt.eE wafthuaL 3

saitwua se

IGF e Emeum

=ast=va is it-rsii e v.veisesis.naars.o *Jr.o C CONVEnf thel!su Ihput INTO SI 37m20 Impot mattaus 20 I

PE e AKrasp walgwpa 23 IGF e e saltkwa il na e sn=P

=IL-w

c2 IF(PE.GE. PCRIT) GO Tb s00 matteust I

CsLL seisfu,ise-sit-6e cs IF(IGF

.NE. 0) GD 10 100 ma1Ehua 25 Tsat s TB(t) usitwwa 2

Ceit Gw.g in a, F r e is wir..

- s att-w e cf M8(t) e ML esit=ba 2e I

maTEdua 2w M8(2) S HV sik Je 30 iTii-.Ew. Ei uTCn e u.v mattapa 3:

IF(In.NE. 33 cv TU 2000 CALL sugge,wL,TS(t),as(t),CP(t),esett), hew (t),omp(t),IGF) paltwba 37 r

=rts-w.

23 iFisei.gt ei i,w iv inv RN 3 R$(1) maltqua 3

.Waltwpa 35 DTOM S 1.0/CP(t) j 6vaia,ws

==i6=v.

at svuu IF(!*.hE. 4) Gu Tu 1000 maitmwa 37 I

CALL vaPter,ev,ft(2),es(2),C8(2),88P(2),0 a(2),0w'(2),1GF) mattwwa 3r R

= sit-w.

is iFiasF.=i; v) Gu iu avu t

maltwua es Ofow a t.0/CP(2) maltava 3

RN e Rg(g)

I

--199s CGhii4wi stt*se 2

maltaw&C 5

GO TO 201 maltwuat e

200 CONTIhWE C att--97t t f rrter779ttti ts tt7, C F i n i, o R e s i ), o#wi t17tpr* i i i, i s ; ;

_ e f t$rtt*i.

?

I IF(IGF.NE

0) GU TD 100 maitupat b

maitw940 T8af s TCRIT

=ett=we6 at i.gfC&iti UTCn e maTLhbat 3g 1

0783(1) 3 0.0 malt =wab 12 l

MS(t) e 1.0te>g

=sitwc8L i3 Cart w ttw1rFFIr!1t'I*i matteual tw es(t) e un

aftNFAL 15 201 CONTINUE

-C-ttinyEaT 3tt 67 5Yw2n-tfUtttTT-!MTtMNCtT1= g Ei

=siters a3-I 61 I

MR(RRAL

I I

E MATER 74/7s Opfs0 TeaCE F7N S.6*433P 81/02/20 14.54 I

DO 80 ! stet malERua se I

i 78t!) e TEmPF(TB(!))

maitkva eb esLI: s Metaira-

==is-wa 3

R8t!) e 88(!)/ASE mattNua e7 ORM(I) e ORM(IleaM/aBE haftwba se I

UNP 7 M aeWWFla)/ast mait pa sg 6

DNP(!) 9 AEPae0MP(I)/AH haftWQs 59 CP(!) 6 Ep(I))(aTeaH) maitwua 51 amiga e sNw1.anilj paisuu.

37 I

B(I) e s(!)/af maltwua 53 DTPg(!) e aEpaeaf.DTP3(!)

maltava g.

aFinsiis

.si, c.sj 60 iu se naic-um 35 VS(I) s00 maitupa go I

_ _ GG_TO 20 malthua 57

.. sv.1a,u.

...s.w.

VO(!) s 3 0/R8(!)

mattwva gs to C0hTINUE malt =pa no vium e aTFTwnwTun u sh = w.

et I

MP e MP7aN maTheva e7 NL e ML7AM mafE=u=1 3

nv~~

nv7ar

-ali4waj 2

s RN e RhPast maiLWua e3 T8af a TE"#F(Tsaf) maTkapa em I

iFii=.iv. ii r.U ib si

-etidue

.3 C IERO PROPERTIES OF UNUSED PMasE maitwpa se IP(In.to. 3) fu e 2 mafEWua e7 ITii

.Es. ei is i

-efttta se I

IF(th.Eo. 5) fu a 2 mattwvac 3,

Tat!O) e e,'o mattuva-ee

- ftsrr ic e

68iiUi e v,v V8(10) s 6,0 wattkua 71 I

CP(IO) e e.0 ma1Ehua 7d

iiDi. s,s a+Emba 73 B(10) s 0.0 aaltWDa fu MB(IO) e 0.0 aaltaba 7%

I.

LEniaGi e o.v

-attwv*

in DeP(10) s00

- ftRWA 77 DhP(20) s 0.0 maltwua fe

= sit-we io LirsiiG) = v.v l

25 C0%11NU[

maitava

$0 GO to los saftwpa) isv Ev it*vi

-sttyps ei CALL GCOF(IGF,P,M) maltabab 17 101 COATINUE

=aithba3 3

l Rete;N sYtwve 62 END

.altwua e3

, REFERENCE map (as3)

DEF LINE REFERENCES j

i 102

' I

?00R M ol I

I

'I i

sE MATERS TS/Ts OPfa0 Yaact FTh s. tea 33F 81/02/20 te,5=

SUSSOUT!wE mBTFR8(Pe!GF) maltwtua

/

W Coa >0N7uror TS(2), M8(2), a8(t), v8(3) maTEkbus 3

6urauarDMfor Deatsje DNPt27, EP(tb DaP(P3, uTP8fz), DTDM maitatea e

C0pm0h7Dwicl7 aK(fle B(2) aaftubba 5

I

, EUNvtWsION PaCTURs FRum ENGLgsM Tu 8 I nastetDa T

ComM0h/ UNIT 87 NINe houf,hDump,h8E8 maltabus e

e DATA ASE,AuPa,AM,AT/36.0185e6894,rs.f326.8,1.8/

=aTLW6Da e

C !s 1 LItutB walta5Da e

6 ings sussuuTINE CAL 6uLsIES THE BATURATEu PRnPE41IES UF asTEM aaltanGa I s' C 1 e 2 VAPUR male 45Da 11 1

C Ihput OF STATE IS TN ENGLISM UNITS a RTu, FT, SEC maitwbba 12 6 vuTrui rs arto x= EmbLI5 N B asitunDa 33 C !* a 2 S&icaATED mate 45Da ou

I C I.s e 3 SubC00 LED LgGufD matt 46pa t-6 an a a su-tuwtaTtD vapuu maitwnwa 3

C IGFagas04 i

maltNbua 17 TEMPF(T) a 9.0eff=273.161/5 0 +3P'0 malthbua te s sunwini t mL!sw INPus amTu sa simsu ghPut

=situsv.

30 IBF e0 malth5pa 29 j

Py a aRPaer naftatua

/t s.6L seir*,,4m-)

..ic

.w.-

22 IF(IGF

.ht. 03 GO TU 100 maitw3Da 23 C CONVERT 81(8) 87kfo OUTPuf.hTC ENGL!$w(E) matt = sus 2e Du as issei a m ittstra g3 TS(!) e TEuPF(78(I))

maftasus 2n M8(t) e M8(1)2aN malEN8ka 27 Etili = wetli7siE

==fi-hwe ce 4

DRh(!) e nkat;) ear /a8E maltwbua au j

Dep(!) e anpaepep(!)/ast mattG6us se Lnfiii

.an F e ntrarti);.n wrfswspa 33 CP(!) e Cet!)/(AfeaM) maitwbua 37 Auf!) e arpaeaw(1) ma1Ewspa 33 Biii s mili ei siistv-as t

DTP8(!) e ALPasafeDTSS(1) maitWbua 35 VS(!) e 3.0/93r!)

maltdboa 3e I

su ssnii vi

- ftw3ca 27 i

GO 70 ing maTL= spa)

I j

180 CONTIhut mate =6La 3*

i seiL GEOFi E;,b,ni

-.ttestrar t 101 C0hTINUE maltWava3 3

RETURN malt =5Da 39 i

iwL

- irwtv-

=U 1,

u aEFERENCE MAP (8s3)

Ot" i. I ni

Eftetwrts 1

41 infi wiLLCitaun RLaL REFS 26 28 30 33 ULFI A8

. I REaL aReav DHf01 REFS a

32 DEFINLD 32 Fi so s,

iv 32 35 j

OtFINED t

!E I

e

)

P00ft DHNAl.

1 I

. ~..................................................

I at OUAL 78/Ts 08Ts0 TPaCE PTh a.t+e38F 81/02/20 14 i

l SUSROUTINE suaL(MS,Ps,tSLfP) 5 CDmMCN7Mp0/ 78(2), M8(2), R8(P), v8(8) guaLua i

i guaLua 6u su=revatiinL, Mv, g, ma, age, aw. *=, 38a, Im, paruM, nP, Tsai wungua

?

Data 48E,aupa,am,AT/tt.0tstett04.96.2336.0,1.8/

f OATA PC#1T /fft20000.0/

WuaLua I

I6 ae3 Lauvru GOALuaC 5

C 3 e a vap0R uuskua f

IP(Mt.Lt. M5(g)) GO 70 t evaLua i

OvaLDa APLME.EE. P5ftJ. amp, Ma,61 M4(2)J su 10 i I

IP(MI e87. M8(t)) GO 70 3 huaLua 1

1 CUhTINuE GuaLua 6 suo6uukau L sugu QuaLua hL e Ma wuaLua NW 9 9.9 GUALDa WR e 3.0 WuaLos j

D8h 8 0.0

~wyngwa l

X e 0.0 ObaLua mr e ves WL AL D A i

NP S ML wu.i um 6

ALP s 0,8 GUALua warun = x.n uvagua g

!= a 3 wu=6us IP(ps.gg. PCagT) IM s5 kuALua i

I hiiuea wuaLuaC I CONTINUE e

ww 6va e

C SATURATED 2 PMA8E GuaLua 2

c6 s batij WuALuA 2

I kW e M8(2) wwe6w=

s In a 2 QuaLua p

insensLiiipireisieraisii GuaLua 2

a e ALP s 88(1)*z)(R&(2)*(e8(1)=R8(f))er) vuekv-7 I

PE e 8EFAkPa GuaLuA 3

Ceii eLieseE,4

?,i eve-,IiLIPi GuaLua 3

6 XP ew-Lue 3,

e NS(pleatpe8m/(R8(2384L'*8=*pS(t')*(1.0. ALP))

hP e (1.o=rPle>6(t)

IPEM8(r)

WuaLua 3'

4 e4 Eminimis.o-eLei e kesii==6e cu tua 3

a I

OAw e (a8(t)esstr)/(a8(2)*(kS(l) 48(t))*x))**R ww 6v-

)?

RZ s R8(ple4Le 8= + s8(t)*(1,0. alp) kuaLua 3e e

P L-. O e. -iimvtntru e L7 3 = Li-i ? i e. ei; QuaLDa 37 z

C FOR 2 PMalE FLO= hFAR EITHER OF T*E SINGLE Pua8E REGIONS L;is; 3*

I C Smu01ns TRahS17!048 UET=Et% 2 PM48E

t PMASE Qu Lua 36 a

Jwini. 6 = ins ii-Hsiiii uuaLDa su s

NLI 8 M8(1) + DM8af wwe6v-

=1 Mv1 e M8(2)

Om847 GuaLoa m/

I b?D & We Quakua 43 i

DMDMD e OMoDM eise

==

.w IF(MX.LY. MLt) Gn TO 30 GuaLua 45 ifici.si. Wri) ww 70 =v GuaLDS GO TO 20 wweive

=7 I

30 CohTINuE Wuagua Gb

-C-tit-it3 1s t WuaLua 69 FLB e (MrewStt))/DMSAT w'Uttte 5"

1 NP s (i.e=PLS)eMX + FLS*MPO QVaLua

$1 j

ines-s7.g GuaLua S2 e

r6i - r t1-UnDbU

=

GO TD po wweLva 33 40 CONT! hug suALua Su t Sai TU ysF a

Gu tua SS

..L..

.....e

. e..

p..........................................

1 s

P00R OR Ed.

I

ll l

E GUAL f4/74 OPTse TRACE PYh 4.6+433F 41/02/20 I

...O

.A, ouALDa HP e it.b.F8vleMX

FavaNDO GuaLDA unrua a 10

Fev 9 Pgveunk-u 20 C0hf!NUE wuakua RETURN Guatoa I

I

. C vApuR guaLua GuaLDa s bu=Tipvs wua6ws ML 4 0.0 Guatoa av s na hva.Sa R e 1.0 GUALbe IP 5 1.8 bhaLDa

== a ny uu=Lua ALP e 1.0 SunLba I

Sw y 1.0 bu8Lua van a v.c I

ww-6u=

DNPDM s 1.0 byaLua IW e4 buaLUa l

hiivi-w w = L w = --

END buagua I

REFERENCE MAP (Rei)

DEF LIht REFERENCES 1

2a 62 F5 I

e TYPE REL0 CAT!uN REAL DEFINFD a

EEAL aiFi sz sisi iD REAL guALI REF8 3

35 383e 2e36

,!E DEFINED 2e 51 70 g

2;L ocri,es REAL DEF]hFD a

REAL NEFS So DEFINED 37 I

NiaL

-ifs se wiFisiL e.

REAL QUALI NEFS I

et DEF1hkD 21 73 AE;L WEf3 3

e.

52 i

REAL ouALI REF5 3

35 3'

UEF1hto I

REAL HEF5 2egl 2*54 DEFIht0 52

--Rt

6

^EFi s.5G sees siri-is L.

REak OUALI REFS 3

19 DEFINED 13 REAL REES 47 DEFINED e3 I

?-9E at sv;Li

%Efi 3

e5 DEFINEC 14 69 REAL REFS 51 59 DEF!hED e5

-PE*t AAtao niv Eife r

e iei Ak I

2e35 2es2 43 se 52 REAk GUAll REFS 3

69 DEFINED 18

--RE *t

%2fs e,

DErtht; ee REAL F.P.

REF5 a

2e9 to 13 SP 53 58 59 D

I

--1* f Est a

".?.

Affi 53 uiF!AEG i

IhfEGEk cuALI REFS 3

DEFINED 22 23 I

I 65 ll

I lI

,I l

E SLIP 7a/14 OPfs0 78 ACE FTh e.6*a35F 81/u2/20 to.5*

1 S0800U71=E SLIP (P,4L*,ES,0KB,ISLIP)

SLIPua

.EaL..

.LI..a ca65v6=its int star maisu usaww a auvarrto sa wan' r' 60 mat 6miao=

s6arva

=

C As PauPosED PT 4

3. JUNEs IN napt. pgyg(3,63)

SLIPoa t

I cata CE81, Cast,Cag3/s.7 tee.29,5sta6P/

SL1 pus vaia wastemass,=Esa/3.yallTTETN76,0.55548/

BLAPu*

IFi!8 LIP.EG. 9) 80 TO 20 SLIPDA PC a P71000.0 SLippa I

6 s 6mul*tCutz/655H er6 skaPu*

I e o RngtarCa(Rm8f.PCepn83)

SLA'Da 1

C1 e 1.0 = C 6L196a-I nt-s a siew e64rus

,I a u-o.1

.6arw-at 1F(REP 5.GT. 1.03 GO TO Fe SLIP 9a 1

Anum 5 Ce ALP e Cle(alp 5eR)

SLIPDA l'

sav-s e M5 s (t.g. Alp)/aNuw stipua a

DK5 s (Cl*(l&0.taLP**R)=(1.06 ALP).netaLp.e(p.g.o})/Ahuw2 Stipua 3 I iv CD vinut e61rw= at IF(!&Ll*.EG. 33 60 70 40 SL1pua g 20 C0hflhut 8L1'0a e i.v esit0= ci ai = I 40 COht! HUE SLIPus r) RETuwh SLipua 2 ihO iwiFUa zh I mEFEdEhLE wap (es3) OE7 LINE GiPEttuttG 1 23

9F "

eliGE;71LW REaL F.p. REF3 2ete 16 3*17 DEFIhEu REAL REr3 15 16 DEFIhED le eiei LEF. iv GEFINEG ik REaL NEF3 13 14 DEF! BED 9 I REAL AkF5 e DEFINED 5 l Wt-Nisa w DETThiw i REat aEts e DEF1hED 5 REAL NEFE 13 le IT DEFINED l' -1tt

6

".F. LEriniG g av INTEGER F.W. HEFS T 19 DEFINED 1 ,I REAL F.P. REFs y DEPINED 1 to 2 -*fal ".P.

Eri n

Girt *fD i HEAL NEF3 4 2810 DEFINED e REaL NEF3 33 la 3et? DEF1hEu la -*t*t XiFi is GEF!*t0 is I REaL REFS to DEFINED 6 REAL REFs to DEFINED 4 -# Eat Rifs in GEF1*EO I DEF LINE REFERENCES 1*aCffvt F to 7 13 I l E00R OR M L I ---,.____._--,.,m.,, .---,_._,....--,.,._-.-,,-7,

i I l lI I

E Sud 14/14 OPTS 0 TRACE FTh a.6+a55F 81/02/29 le.Sc I

tu8e0UTINE SUS (P,M,78L,R8L,CPSL,SepteDRMLe0MPLe!GF) Susua i CO*=0h7aPeoPF A(1628) 8 veda 3 su-ev=irmarvai E-ma, r aus ev=wa6 lI C0*>0h7833/ 5pwitt) 8vous s C0= MON 70wirst / an1(2), 81(2) 8voua S 6u-=uaruw1Ter Namremouvensvar nwas euswa e e DIPEh810N 8(23) 8veva 7 LOGICAL tes suoDa e i sunwa E waia 76=]1 pgg[gDOUU.0# C LIuu!D PROPERTIES Sueua 3 Sueva si IT s 0 ai.. eu va iz 4 ir.... P6 av, 8(2) e# 8u004 I IFtr.GT eMan) $(2) e PMax SueuaC i sw s=E ? .u. w6=IT eiga y r, mas iFtr .mi. -ans.anu. E Sueua' 16 8(5) eM Sueua 19 'I _ o 88NT(1) _ susUn se 8(23) 6=66 evaPu5saes,atetwas Sueua 17 IF(Esk) GO To 100 i SphT(l) e 8(23) Sueua la isii sw L. as ia6 I 88L s 1.0/8(3) Sueua 29 l Susun 23 CPSL e 8(8) I l i e eies ow w-42 Sumpa 23 Am se8(1) Ant (t) e au Sueut gu I GuGU; st Gi'il -r Sueua 2e La>L e.R8LeB7tpSL DHkL 8.(ag.tpSL/s).ggeT8L.t.o}/g8L Sueua g7 'L & -beni-D ;6 suGus de I IF(*.GT. PMaN) GO 70 100 Gueual Sunua 29 60 70 103 Gw;ge ir Iww CG,71^,ug SubpaL 5 IG5 e3 Sueva6 e I IF(P.GE. pCp!?) IGF e6 i; W .-ti, wuean is e i idspot i Bueval 8 hRITE(40uf,Il0) 150 F0EmaT(tex, Itw ERROR IN thPuf 0F Sus ) Bueua 33 itzetts 3a is CO,iiavi I Sueus 36 NEluRN Sueua 3e END I

f st*Entf-*A*--(tet!

DEF LINE REFERENCES i e v TYPE aELOCATION 16 ME *t t.f t s f a*GG7 OEfi e NEaL WEF8 36 24 DEFINED 25 l WEAL ARRAY DMIDI REF8 g DEF1hED 26 -,eaL au, s, 2. re r*--ot* t*to e l REAL ARRAY DHf01 REF8 g DEFINED 27 I ,I I

E I E SAT 78/74 OPTS 0 TeaCE Pth a.60a38F 81/02/20 te.5o, I SUsa007th8 sat (PetGF) SaTDa 2 Cumm0h7apBOP/ a(Foaa) Salua 3 6urmunirmagumi rnas, ymaz8 saiva6 ,3 C0=woh7kPD/ T8(2), "S(2), R8(8), v8(t) Satua~ a I C0=m0N/DM80/ Deaff), DRP(2)e CP(a), DNP(p), DTP8(2), DTDn SaTDa 5 su=puM7DMIO / satrJ, strJ saium o Cu=*0=F8es/ SohT(p) Safua 7 C0=m0N7UN!f 8/ NIhreN0uf ehDuwP, wag 8 SafDs a i partNulch asztpJ, acataJ unawa DI"ENSION E81(P), M8t(2) Saipa e LOGICAL ras Safwa to utataslow Biga) saiva is C Ie 1 LIGu!D 8AIDA 17 I C I s_2_ VAPOR _ _.. v. .a,ua i. 6 ,,ucat. 63.uiu, a., Saipa 33 8(2) eP Saipa 15 IF(a.GT. PMaz8) 8(7) e pgans SaTuaL 2 .ivJ s v.o aniva a6 I 8(23) 8 89hT(f) Saipa 37 CALL STM20pta,8, ERR) Salua = IFiieEi wU is isv isise i+ SPNTf2) e 8(73) SalDa 20 I 78(t) s 8(g) Saipa 21 iiiii siti isty. gr = DO 20 Ist,P Salua 23 H8t!) e 8(ta+I) Salpa as t aisi) e i.pisis sei) 3*ipo 25 l C#(!) e 8(20+1) Saipa de an(I) s 8(st+I) 881La 47 bili s Eijevii Gelu; ie 20 C0htINUE Salua kw I C CALCULafluk 0F PRESSU8E DERIVATIVES 8AIva 3r 3 02 7 3*tv11 i IFfp.EE. puaz8) GU 7010 Batuat 3 P2 s P + De Saipat e I IFifi

62. F#e iiDF w 5Gv{"eski..)

EsiW*t S m P2 a *

DP 841LaL e

P1 t P

DP Saipak 7

GG iD ai istp*L e 16 CuNTINUE Estbac w I P2 s PMag8 SalpAL 30 et s 74tstutan Gatpat it DP e.50e(92.pt) 881 pal 1/ 11 00htIhut Safuat 3 I i t t1-e-py--- Gafvet is 8(9) e 8;0 Saipa 3a CALL STM70pta,8,(se) Safua 35 If tt#kF-30-10 IGG E*fve 3e !I 781 e 8(t) Saiua si 00 ft Ist,p 84Tca se R$1f13 i.s/Sittelt inf0* M81(!) e 8(14*I) Saipa 81 2: CDATINug Salpa e5 I Efft-e-ti Eate*t it 8193 s 8.0' Satpa CALL 87ppepta,8, ERR) Salpat 5 1Ptikki nc-tf TDC SaiU*1 .s.. I gg $3R 11

I E I 4E 84T Tapts 0* Tot TRACE PTA e.tes33F 81/02/2u. 14,5' I TS2 8 B(1) Saipat ? 00 22 Inge2 Salvat e M5dfl3 9 1.0/5f30+1J 3aipan 6 M82(!) e 8(lee!) Saipa: 36 I 22 CONTINUE SaTDal 11 vu 33 asser saiuma 32 DTPa(!) e (T31 7823/(2.050P) Salcal 1) DeP(!) 6 (sS1(!!*pS2(I))F(2.teDP) saivat ts I wartaJ s EMUI J 8M5f(I J J /(d.DaDP) sasung it LRat!) e (sBl(I)ee82(I))1(>51(I).ws2(I)) satuat je 23 CONTINUE salus 37 wu Tu as: saium se 100 CONTINUE sa1Da at I rummaitica, ad> tumui am Iarvi ur sai a saiwa =9 no!TE(Nouf,150) aiu Satua er IGF e2 Salpa bu los CONTINUE Salua 56 I 4Eiu== esiv. 37 Ehu salua 53 aEFLWENCE =aP (as3) DE' LINE REFFRENCES 1 15 TT8E RELOCa11DN REAL assay aph0* REFE y to a7 Se Fiei sEkau u-kui kiis a Lira =tw s+ I REAL aReav DH201 mEFS 6 DEFINED 30 REaL &# bay DM20 NEFs g DEFINED 28 W *6 s*Rav uniD Niis 5 sieists se NE*L REF8 55 37 38 48 o' DEFINED 33 36 a3 I Niew s**av u-du etFe 5 strians ei REAL apaay Dh20 REEs g DEFIhEW tl REAL DH2O RE55 5 --ft-* L etwas u-iu NEFe 5 Liri=Ew es Lub! cal REFS 13 20 21 87 8' REAL ARRAY k20 REFS a DEFINED at -steL essaw hiv e ac .e si ud iaiw in WEAL AR4tY REPS 4 46 67 OtFINED 6' i l INTEGER REFs 2*26 2e27 2e28 2829 2a. 3*83 3*B8 ist Eelv iwea

== DEFINED 25 50 59 63 IhTEGEW F.P. DEFINED t 73 P tttia v' tie "ifa e I INTEbEh UNITS REra s INTE4ER UNITE REFS 8 I/O REF8 fl --Tw i tCt n u tti Niis e a meat F,p, REFS 16 SF 33 38 3' I 58 DEFINED I Gi;L ,*aups hEte 3 REAL paaNDA Rett 3 2*17 In 2*36 as E ...............,... ~... -........... -....-......-....... I ?001 IJid8!M. I

I 9E VAP 7a/7e Opts 0 TRACE FTA a.6+s33F 81/02/29 14.56 3 SUteDUT!wt vap(p, METS RvV, CPG,DRps, Dams,eHPG,1GF) vaPua 2 Cr>M04/apscP/ A(7626) tappa 3 62.= mum /Pmaguas raan, pmang varwa6 1 ComuuN7Dutti/ Ant (2), Di(2) vaPua' e COMwDh/873/ 8'hf(f) vakua 5 I suruuh7 UNIT 5/ NIMF,NDUT,4Duny,hugg varua e l DIMENSION 3(23) VaPua 7 LOGICAL tem vaPoa e + uaTa FcRIT /221/0000.0/ varua 4 I IT e 3 vapua to IF(P.GE. PCRIT) !T e a vapua 33 sta) sp varus 12 IF(P.GT. P> Art.AND. P.LT. PCBIT) 8(C) e PMAIS va*0aL 2 8(5) eM vakua 13 I sLd3J e 58NT(l) varya 3e CALL STwf05(a,3,IT,ERs) vaPoa 15 IF(ERk) GD 10 300 vawua le ar=Tsis e str3) varwa 17 I TG e 8(t) vapua se Rvv s 3.3/g(3) vapua no 6FW W a(PJ varws g T. O s Ste) vawba g1 j au sA8(f) vakua 22 l

==3sse e am varw. c3 8t(2) ea vaPua 24 DRMG e.evveB/ CPG vaPDa 25 ws .:an=6s ibi-ic.is...wiruvy v.*ve go w a s lI GD Tu 133 vaPua 2e DRPG e =DWwGeDNPG vakua 27 ave 6vaia,uc va-w. c9 WRITEthouf,150) vakua 3u I 150 FORwaT(tos, 22M ERRUR IN thPUT OF WAP ) vaPua 31 iGF

a va*s

il 101 CONTINUE vakua 33 RETURN varva 36 Amu va*wa 45 REFERENCE map (Re}} 7EE a. i i utfratarts 1 35 r-TTPi niicc iiU, I e REaL ARRAT APROP NEF8 2 14 REAL REF8 Is 27 DEFINED 23 -#f L ^#4.V besui WiF. Giftary c. REaL REFS 25 to 2e27 DEF1htu dr I REaL ARRAY DMf01 REPS a DEFIhED 25 ' # tat e.E. Riis is si stfixt0 a c1 NEaL F.P. HEss fa DEFINED 1 27 ,.EaL ...EF3 R F.P. R is DEF]hEu I 2e E F... ,w. 2. LUGICAL REss a 16 17 .om*.....=e , e em ..o .,e+

==..e e f e 9 **

l 70

'I ?DDROfBiNAL g

.............................................. ~.. I .E INITC 78/Ta Opfte TRACE FTN a.6,allF 81/07/20 la.5s I SuteDUTINE INITC(Nif) Ih!TCua 2 Cor=0N?pwarDa7 emas, Pmax8 Ih11Cual I 60*m0NiUNIT5/ h3hr houT,hou=p, huts a=416ua e C THESE STATEMEhTS DFPEND UPON TML MATER PROP FILE Ih11CuaL y I C VALID FOR RELape.mnDS FILE IhlTCuaL 3 6 er Tg=7tuayunt PUIN15 49414Ws6 C 29 PRL88uRE POIhts th!TCUAL 5 C0"*0N7aPRc9/A(7638) Ih1TCuat e waTa mWBE/ 76E8s shalbwab 7 I DATA NT, Nee Ns, N87/ a7, 29, se, RTF Ih1TChat e CALL STMPO!(a,wif,huSE) Ih!TCua e mW4TttMQUI,171) hUDL 4h41bVs 7 171 FOR=aT(tes, 7M NUBE e, Ill 1h11094 e I NPT s NT

hP Ih!TCuaC 9

r=as = almuni ensi6us6 30 NPT5 s NT, hsp It.11LuaL 33 PaaN$ 5 A(NPTS) 141TCual It I n t illu m 4h416ua 9 END Im1TCua fu EEFENENCE waP (as3) I DEF LIhE aEFERENCES I 1A 4 TTPE sELOCATIuN REAL aReaf aph0P MEF$ a 33 35 17 --twt tSE - u-iis asia 3 INTtGEe UNIT 6 REFS 3 I INTELEW UNIT 6 REF8 3 1/n REFS 12 -initti; WiF6 is Lisi'is is INTkGEN REFs Ig DEFINEb is INitGEk NLF3 !? DEFINED 16 I .-1*dt#E ualib Wifs 3 INTEGER DEFIhED 10 IhttGER NEFS 16 DEFINED to -T*T ttt ; Ni o da se viFi'is iv I I P.T E G E h REPS 13 12 DEFINLD 9 l INTEGEk F.P. NEFs 13 DEFINED 1 l -Stai r ae e WiFi i virinsv ni uv REAL P"ANDa REFs y DEFINED 17 l 6 U8ED AS FILE NAMES, AEE ABOVE g TYPL ARGS SEFERENCES 3 11 DEF LINE REFEsENCES l NY 13 12 I LENGTH MEMBERS

RIAS ha>E(LENGTM) 2 0 PMAX (1) 1 Paart (1)

I e 6 afw' iii i huui sii i~"V""" 3 hkES (1) 71 i l

i I et GOOP Te/Ta OPTSO TeaCE FTN 4,6es33P 81/02/20 14.Sa e i l Sute00T!ast GOOF (IGF,P,M) GDOP uaC I Comm0N70NITB7 w!NP Nr.JTehDump, wets Guup Da 3 4 i 6u=mumpymanuar rnam, ^rmans tuurva6 r O!aENSION aEpst5) GOutua e j Data (atteg!), 1st,5); 6w nafge, au gaf, em gut, as wap, 5M GuaL/ Guut ua g lI paTa aurai4598.76/ mutausc 3 IP(fGP ;ES. e) GO 70 2000 GuuPDa e 2 WRI?t(N0uf,990) P GOUPDaC e seg runwaT(163, aM P 5, F10,3, 30M LBF/INd a) buutuaL 5 I IF(M.LT. 0.g) GU 10 8000 GUuFuaC 6 MRITE(N0uf,fot) M GuusuaC 1 geg rummarglas, an a se Fig.3, WM BTupLRm 3 wuurva6 e GO TO 3001 GubspaC 9 a 3000 CUhTINut GuuFust l i. I Tam a e M wuvewas 33 WRITE (NOUT,202) TIN GUupuaC ( 202 FURwaT(163, 6M TIN s, Pte.3e 6N Dfg F ) GUut0AC 13 wu vu solo muurva6 I 3001 CONTINut EcutuaC 15 IP(IGP.SE* 61 GO TO 1000 buuPwaL to ww vu save www v. e 1 CONTINut Guutua e m8ITE(Nouf,103) aENRtrGF) 60usua t r. i swa rv===ssion, r+n s**sw in si=ia muuizni in==e asa swwe wa at GO TO 2000 GOtJ7DaC 17 late C0=TINut 60upunt te =eiiEi uni,ivii =i ni3) swwew=L 19 I >RITEfhouf,102) GuutuaC du i ~ 102 FORwaT(16E, 23w maTEp af P GT PCaff *=) GuutuaL di iFis=F .wi. p =v iu svuu wwwr v as r7 [ PaaE2 e amazianda Guuppat g3 m#ITEthouT,300) Pmaxt GuutDaC eu 3GG Fwd **i^iuk, is F.Gi. Phak u, Fig.3, ivw LiFiiNe =i EUweJ-E st 2000 CONT!huf buuP ua It RETUNN GuuPua 13 ins avurva ik

EFENENCE map (as3) sif 6ini AgigNingii 1

35 I t-TY?E .EtttttiiG, REAL array REFS a 23 27 DLF1hEU ? REAL REFs 3g DEFINED 6 --*t ' L ---f. F. KEfe is ii ii eifPid INTER.ER F.P. REFB t 20 23 30 UhF IN I INTEGER UNITS REFS P ' M MTtCt; u-TTE REF3 y INTEGER UNITS HEFS P I/O REF8 8 11 18 28 37 I -itvTtitte u=178 NEFe r REAL F.P. REF5 a DEFINED I l l g m P00R ggy g

l I I g DE MCALC1 . e F T r. 0#Ts0 TRACE FTN e.t*433F 81/02/26 14.54. I $ des 0uTINE MCALCl(P,T,If,M,ISF) MCaLC1 i CommONFApN08/ A(76tB) MLaL(1 ) l 6urmuh/uw3Tsi wahpehouTeEM =P,hnEs M6abba 6 DIPEh8!ON g(#3) MLaLLI 5 I LOGICAL gas MLaLCg e sta) y F n6=663 i 8(13 e f MCaLC1 e CALL gTMposta,gr!T, ERR) MCALC1 9 arta==J su ic suo n6=66:

D M s 8(33 MLaLCl il 60 TO tes MLaLCl IP see bu=Tamut P6aL63 13 ISF s 3 MCaLual j

I hAITE(=007,tle) MLALL1 16 aiv ruarait en, rsw truvu an ankui ur Mc=L61 s n6=6La 35 101 C0hTINUE MLaLL: 3e RETuaw NLaLC1 17 z=u n6a66: th REFERENCE map (ass) sEF 6ind utstnancis i 17 1 ives wi6v6-ilb, i REaL ARRAV aPWOP REFS 3 8 LOGICAL ret 3 3 s 9 si&L F.r. vi'iniu 3 as Is!T E G ER F.P. DEFINED g 13 I INTEGER F.P. REFs a OEFIhED 1 MtetE13E; uniis Naia z INTEGER tiNITS kEF5 5 INTEGEh UNITE REFS 3 1/0 kEF5 14 I anises-u ave asus 3 REaL F.P. REF8 6 DEFINED 1 REAL ARRav RLF8 a 8 to OtF1htb e -*E '. i. F.e. AEF. y Li,imiL a ~ I USEU A3 FILE NAugs, 3EE abovE I iiFi auss pEftstacts a 3 I .i CEF 6 WE eEft#ENCii g 12 9 }6 )1 a, a. LENGTM >EPdERS

Bla8 NA>E(LFhGTM)

' --7s te g e (73763 4 0 NINP (1) I hDuf (3) 2 huump i I 3 hPE8 (1) t E .....................---.~.--..-........................... 73 I P00R OfKiiis g

11 i ll l iE NATENT TapT4 OPTS 0 TRACE FTN a 6*a53F 41/ud/20 la.5= Suse0UTINE mATERTtP, TIN,NDUT,tGs) mATEN1ba 2 l Cor=0h7M30/ Ts(2), M8(2), h8(2), vett) ma1E=tus 3 GUMM0h/UNIf5F WINP,40uT,hDb"P,hWEg mantNIba e B Data asE,suPA,am, aft:6.01:5,oses.76,t3ae.e,s.e/ = ATE-ica 5 g Data EPSDT/.00017 maitwtus e ILPPALT3 s LT, a5T.6553/l.sg maitwiwa 1 g C0hvERT INPUT FROM ENbLI5a uh!T3 70.8! F0p SYN 20 RuufthE maltatua e PN 8 A N P e o p' maitW10a e i In e It=PE(TIh) maituiva 31 l CALL Safte,1GF) maTERica 1 r IF(IGF.NE

6) bu 10 100 maitdlua 12 UTm s Tu o Tst J amituiva 33 I

ADTR E ASS (DTu) maitwtya 3 IF(aDYK ;LT. EPSDT) GO TO 200 maikkiua IS av eo naitwiks se IF(Tm.GT. TB(133 IT e 3 maltalka 17 CALL MCALCs(Ps,Tne!T,w,1GF) maitalpa

=

I artger .=t. g3 av iu IVo wait-sua iG CONTERT SI UNITS TO EhELitM FDs uufput malt =1ba e, N0uf a h/AN maltktva c3 wu nu act maitwivak i 200 CONTIhuE naltwipa r3 mRITEthout,150) maltwlba ia 439 Fum-miinsa, sin twh0p izm s Tsay. v=t rMasi Ga66 u=6T )

==isniva s3 e GO TD 101 haiEktbs3 1 100 C0hTINUE maikutua go I esi s.ijn =mitaiwas 2 CALL GOOF (IGF,p,MGF) maltw1 pac 3 101 CONT!*bE hattwiva3 3 kiius

==Ttwtva ,7 END =althTDa /r-I REFERENCE MAP (es3) DEF L!ht REFERENCES 1 30 i w TTPE mELCCaffuN REAL NEF8 la DEFINED 13 --St e L atFs up LiFints = REaL REF8 a UEFINED e I e REaL DEFINED a r-et *t gifi,iv REaL NEFS 13 DEFIhED 12 REaL NfFS la DEFINED 5

Zei AtF.

iy E6 i . REaL F.8 DEFINED 1 20 REaL REF8 3R DEFINED J1 --RE st ettAi rig ' Wit s e INTEGER F.P. REF6 to il if 18 it I DEFINt0 t 'EF8 er Di r7"t#~ ii i8 --t* T Ett e W INTEGER teNITS REF$ 3 ll g pgB3 N KIN A

1'I Appendix B Necessary Job Control Cards This appendix describes in detail the NO3 job control necessary for usage of the H29DA water properties package. Only those job control W i. statements necessary for the usage of the water properties package will be described in this section and the function of these statements in the job stream will be described with respect to the H29DA water properties package only. Statement Function GET,SCLFILE/UN=SCLIBYA. Attaches YAEC software control library I file containing procedure to attach qualified code copies from library. BEGIN,SCLPR C,SCLFILE,STHLLIB. Attach library containing STH29 I subroutines. BEGIN,SCLPR$C,SCLFILE.*eiSV05 Attach data file used by STH29 subroutines. g RENAME, TAPE 15=TP15V05. Renames water tape such that it is compatible with input index in STH29 g I routines. 1 BEGIN,SCLPR$C,SCLFILE,H29DA. Attaches water properties package library containing subroutines described in this report. [This statement inserted into the loader search] LDSET, LIB =STHLLIB/H29DA. Insert the library into the loader 'I search. m l lI E 75 I

I Appendix C I Sample Problem E A sample problem has been provided in the enclosed fiche which are labeled "H20DA VERIFICATION F.UN". This samp>e prob 1em i>1ustrates the use of the H20DA water properties package. Tne driver subroutine for this problem, FRITZ, initially reads the limits to the pressure and entha>py variations. Then FRITZ varies the enthalpy and pressure within these limits while calling the subroutine WATER .d - t. t c. th. r.. 1 t s. f th.....>... c-.. ,h. 11.it.. th.,r.s s.r. -d..th 1.,, v.r 1. c f.r th 1. s.m 1. problem were: E 1000.0 lb /in a i p 11200.0 lb /in a f g 300.0 BTU /lb 1 h 1 1600.0 BTU /lb, l The results were written in a format which is self-explanatory. 'I I E 3 ze I

l E I References l 1) " Development of a Computer Code for the Thermal Hydraulics of Reactors f (TH$R), Third Quarterly Progress Report", W. Wulff, Principal Investigator, BNL 50458, June 1975. 2) Steam Tables, J. N. Keenan, F. C. Keyes, P. G. Hill and J. C. Moore. 3) RELAP4/ MOD 5 - User's Manual, Idaho National Engineering Laboratory, ANCR - NUREG - 1335 (Vol. II). 4) Hydronamic Stability of a Boiling Channel, A. B. Jones, KAPL-2170, (1961). I i l t 5) ASME Steam Tables, Third edition, C. A. Meyer, R. B. McClintook, G. l J. Silvestri, R. C. Spencer, Jr. 6) " Maine Yankee Cycle 5 Core Performance Analysis", P. A. Bergeron, M. I R. Castonguay, P. J. Guimond, J. A. Handschuh, R. C. Harvey, J. W. Heard, A. Husain, M. P. LeFrancois, R. A. Rothrock, L. Schor, S. P. Schultz, G. M. Solan, W. J. Szymczak, YAEC-1202, 1979. l'I E I E g 77 I -}}

ML20037D035

Text

=IL-w

a va*s

Navigation menu

Search