AE-85

CO

w<

An Experimental Study of Pressure

Gradients for Flow of Boiling Water

in Vertical Round Ducts (Part 3)

Kurt M. Becker, Gunnar Hemborg

and Manfred Bode

This reporf is intended for publication in a periodical. Referencesmay not be published prior to such publication without theconsent of the author.

AKTIEBOLAGET ATOMENERGISTOCKHOLM SWEDEN 1962

AE-85

AN EXPERIMENTAL STUDY OF PRESSURE GRADIENTS FOR FLOW

OF BOILING WATER IN VERTICAL ROUND DUCTS (Part 3)

by

Kurt M Becker, Gunnar Hernborg and Manfred Bode

Summary

The present report contains the results of the third phase of an

experimental investigation concerning frictional pressure gradients for

flow of boiling water in vertical channels. The test section for this phase

consisted of an electric heated stainless steel tube of 3120 mm length and

3,94 mm inner diameter.

Data were obtained for pressures between 8 and 41 ata, steam

qualities between 0 and 58 %, flow rates between 0,0075 and 0,048 kg/sec

and surface heat flux between 20 and 83 W/cm .

The results are in excellent agreement with our earlier data for flow

in 9, 93 and 7, 76 mm inner diameter ducts which were presented in AE-69

and AE-70.

The present measurements substantiate our earlier conclusion that

the nondimensional pressure gradient ratio, *f , is, in the range investi-

gated, independent of mass flow rate, inlet subcooling and surface heat flux.

On the basis of the measured pressure gradients, the following

empirical equation has been established for engineering use.

This equation correlates our data (about 800 points) with a discrepancy less

than - 15 per cent and is identical with the c

from measurements with the 7, 76 mm duct.

than - 15 per cent and is identical with the corresponding equation obtained

LIST OF CONTENTS

Page

I. introduction '3

Preliminary Runs .3

3. Range of Variables 4

4. Results and Discussion 5

5. Pressure Drop Correlation 6

6. Conclusions 6

Nomenclature 8

Bibliography 9

This report is intended for publication in a periodical. References may

not be published prior to such publication without the consent of the author

1. Introduction

The purpose of the present report is to summarize the results ob-

tained during the third phase of an experimental study of frictional pressure

gradients for flow of boiling water in vertical round ducts of 3120 mm

heated length.

The first and second phases of the investigation dealt with ducts of

9,93 mm and 7, 76 mm inner diameters. The results from these phases

were presented in AE-69 (1) and AE-70 (2). The data of the present report

have been obtained using a duct of 3, 94 mm inner diameter. The experi-

mental techniques employed for studying the 3,94 mm duct have been identi-

cal with the techniques earlier used for the 7, 76 mm duct. A description

of the apparatus, instrumentation and method of testing is therefore omitted

in the present report, and the readers are referred to AE-69 and AE-70.

The total experimental programme includes also a duct of 12,99 mm

inner diameter^ "When this programme is completed a final report will be

writtens where all the data will be discussed and compared to two phase flow

pressure drop data in the literature.

No detailed discussions will therefore be presented in the present

report. Only brief comments will be given with reference to the figures

showing the experimental results. For better understanding of the data,

the reports AE-69 and AE-70 should therefore be consulted.

2. Preliminary Runs

For checking the accuracy of the experimental techniques the follow-

ing preliminary runs were made

1. One-phase flow friction coefficients

2. One-phase flow heat transfer

3. One-phase flow heat balances

Figure 5 shows the measured friction coefficients which are corre-

lated with an average discrepancy of + 1 % by the equation

f = 0,229 Re~°'2 1 9 (1)

Figure 6 shows the measured Nusselt numbers compared to the well-

known McAdams equation. Our data are on the average about 15 per cent

lower than the equation.

The results from the heat balance measurements are given in the table

below.

Run

1

2

3

4

5 •

mkg/sec

0,0574

0,0360

0,0627

0, 0494

0,0255

Net Heat InputkJ/sec

17,2

10,85

23,13

10,92

8,0

waterkj/sec

17,4

10,8

23,08

10,92

7 , 9

Erro

- 1,2

+ 0,5

+ 0,2

0

+ 1,2

The accuracy of the heat balances are excellent.

3. Range of Variables

Series of runs were made at fixed values of pressure, p, and heat

flux, q/A. For the heat flux, values of approximately 33, 50 and 70 W/cm

were selected. For a heat flux of 33 W/cm the lowest pressure obtainable

at the entrance of the test section was~10 ata. The corresponding pressures

for heat fluxes of 50 and 70 W/cm were 14 respectively 20 ata. The maximum

operating pressure was 40 ata, and the test series were then performed

for the values of q/A and p shown in the table below.

q/A (W/cm2)

20

33

50

70

83

p (ata)

20

10, 20, 30, 40

14, 30, 40

20, 30, 40

30

It should be noted that one test series was also performed at a heat

flux of 20 W/cm'' and a pressure of 20 ata, and one series at a heat flux

of 83 "W/cm and a pressure of 30 ata.

Each series consisted of 4-7 runs with different mass flow rates.

The mass flow rate for all runs was in the range from 0, 0075 kg/sec to

0, 048 kg/sec.

With these values of the mentioned parameters steam qualities between

0 and 0, 58 were obtained in the test section.

The total experimental programme for the two-phase flow measure-

ments consisted of 88 runs.

4. Results and Discussion

In figures 8 to 11 the measured frictional pressure gradient ratio..

*$ , is plotted against the steam quality, x, with the static pressure as

parameter. The relatively large deviations from the mean pressures

given in the diagrams are mainly caused by the axial pressure gradients

in the test section.

Figure 12 shows a summary of the data presented in figures 8 to l lo

j -values at x = 1,0 computed by means of one-phase flow theory are

also given, as well as the results by Martinelli and Nelson (3).

In figures 13 and 24 our results are plotted according to the method

by Lockhart. and Martinelli (4), using ^ ' andX as variables.

Our conclusion in AE-70 that the mass flow rate has no effect on the

j -values is completely verified by examining the data in the figures..

Figures 25, 26 and 27 show data obtained at fixed heat fluxes, but

different pressures. Comparing these figures with figures 30, 31 and 32

of AE-69 and figures 25, 26 and 27 of AE-70, almost identical pressure

relationships are found for all three ducts.

Figures 28 and 29 give results from runs with different heat fluxes,

but with almost constant pressures. As for the 9,93 and 7, 76 mm ducts,

no effect of surface heat flux has been observed in the range investigated.

5. Pressure Drop Correlation

Using the same method as for the 9, 93 and 7, 76 mm ducts, a pressure

drop correlation has also been derived on the basis of the experimental

results obtained with the present duct. From the curve in figure 30 and

figure 39 of AE-69 we arrived after some simplifications at the follow-

ing empirical equation

^ Z = 2400 ( - ) ° ' 9 6 + 1 (2)

This equation is identical with equation 1 of AE-70, valid for the 7, 76 mm

duct.

Figure 31 shows a plot of arbitrarily selected \P -values against the

ratio x/p. The solid line represents equation 2. The equation correlates

the data within an accuracy of + 15 per cent.

A plot of the measured *f -values against the values for f computed

by means of equation 2 is given in figure 32.

Figure 33 shows a comparison between equation 2 and our data ear-

lier presented in figures 8 to 11. The agreement between the equation and

the data is excellent.

A more detailed discussion of the data and the literature on the subject

will be given in the final report concerning all the diameters investigated.

6. Conclusions

Frictional pressure drops for flow of boiling water in a round vertical

duct of 3, 94 mm inner diameter have been measured for a large range of

variables.

In the limiting cases of x = 0 and x = 1,0, our data are in

excellent agreement with one phase flow theory.

In the two phase flow region the present data are in excellent

agreement with our earlier results obtained with 9, 93 mm and 7, 76 mm

ducts, and our conclusions arrived at in AE-69 and AE-70 have been

verified.

We conclude that in the range investigated inlet subcooling, surface

heat flux and mass flow rate have no effect on the frictional pressure

gradient ratio j .

With regard to the diameter effect the difference in results for the

three ducts studied up to now is so small, that we conclude that for

engineering purposes the effects of changing the diameter in the range

investigated is negligible.

Nomenclature

Symbol

f

Nu

m

P

Pr

q/A

Re

x

X t t

Definition

Friction coefficient

Nusselt number

Mass flow rate

Pre s stir e

Prandtl number

Heat flux

Reynolds number

Steam quality

Pressure gradient ratio

Parameter defined by eq. 12ref. (1)

Unit

Dimensionless

Dimensionle s s

kg/

kg/

s e c

c m

Dimensioniess

W/cm2

Dimensionless

kg/kg

Dimensionless

Dimensionless

• Bibliography

1. Becker K M, Hernborg G and Bode M,

An Experimental Study of Pressure Gradients for Flow of Boiling

Water in a Vertical Round Duct (Part 1), Report AE-69, March 1962.

2. Becker K M, Hernborg G and Bode M,

An Experimental Study of Pressure Gradients for Flow of Boiling

Water in a Vertical Round Duct (Part 2), Report AE-70, March 1962.

3. Martinelli R C and Nelson D B,

Prediction of Pressure Drop during Forced Circulation Boiling of

Water, Trans. ASME, vol. 70, 695, 1948.

4. Lockhart R W and Martinelli R C,

Proposed Correlation of Data for Isothermal Two Phase, Two

Component Flow in Pipes, Chem. Eng. Progress, Vol. 45, 39, 1949.

MAKE UPWATER

CONDENSER

TO DRAIN

MANOMETER

T ) OUTLET TEMPERATURE" THERMOCOUPLE

I — - 7 ELECTRODES

FEED PUMP

CIRCULATINGPUMP Ö

3.94 MM |.D. TESTSECTION

^ 2 x 1 2 COPPER-CONSTANTAN/ THERMOCOUPLES

INLET TEMPERATURETHERMOCOUPLE

MANOMETER

TO U-TUBE

WATERCOOLER

PREHEATER

*—\ V^FLOWMETER CERAMIC AMD

MAGNETIC FILTER

RG. t FLOW DIAGRAM.

COORDI-NATE

31903165'30753035299529058815277527352697264525552475242723852295221521892125203519631955189518651855181517751747173516951655I6l51605157515341515147514351395135513451321131512551215117511351107IO85995915

825735655641565k75

43539537430521513545200

ELEC-TRODE TAP

r10

r12

r13

THERMO-COUPLE

121

12121

211

211

21

a12111.

211121

111,112

11111

211

211

2121

2112

MARK

toTA1, TA2,TA3

TA4TS1, TB2,TB3

TB4

TCI, TC2TC3TC4

TD1, TD2,TD3TD4

TE1, TE2,TE3

TE4

TF1, TF2,

TF?

TI21,TI22TF4

TGI, TG2,

TG3

TG4

TH1, TH2,

TH3

TH4

TJI, TJ2,TJ3TJ4

TK1, TK2,TK3TK4

T U , TL2,TL3TI31,TI32TL4

TM1, TM2,TM3TM4TNI, TN2,

SECTION

B

•p ^ ^

o- TA3

- TA4

- TB3

- TB4

p, —

Pi, -

PQ -

TC3

TC4

TD3

TD4

TE3

TE4

TP3

TP4

TG3

TG4

- TH4

TJ3

TJ4

TK3

TK4

- TL3

- TL4

- TM3

- TM4

FI6.2. LOCATION OF ELECTRODES, PRESSURE TAPSAND THERMOCOUPLES ON TEST SECTION.

Fig. 3. Apparatus

130

125

120

115

R= 1.136-10"2 Pi + 1.034-103{t-20)l

50 100TEMPERATURE, t. °C

150

FIG. 4. ELECTRIC RESISTANCE OF 3.9£ MM TESTSECTIONS

5-KT 10" 510*

REYNOLDS NUMBER i V /

FIG. 5. FRICTION COEFFICIENTS FOR ISOTHERMAL FLOW OFWATER IN 3.94 MM DUCT.

500

o

-SL

100

50

20

Nu= 0.023- 15°/o

r » • ' L

5-1Ö4 10S

REYNOLDS NUMBER,

3-105

FIG. 6. HEAT TRANSFER RATES FOR ONE PHASEFLOW OF WATER.

PBAft

21.0-

20.5-

t'C

160

RUN 3MASS FLOW RATE m » 0.0150 kg/sHEAT FLUX, q/A » 33.27 w/cm2

BULK TEMPERATURE. t Q

0.20-

0.10-

0 -

02-0.10-

-0.20-i

vSECTION

14QMAM3

120P13

M M

0

/ LA L3 KA

P12 P11

| L K

,500

K3 JA

P10

| .

J3 HA

P9

1 | H

1000

H3

P

GA

8

G

G3 FA

P7

F3 E

P6

F

1S00

A E3 DA

PS PA

• E D

2000

D3 CA C3

P3

I ',2500

8A

P2

B

B3 AA A3Z-COORDINATE

P1

A(3000

FIG. 7. PRESSURE, TEMPERATURE AND STEAM QUALITY DISTRIBUTIONS ALONG TEST SECTION.

! 1

= 9.75 ± 1

RUN,

o 22a 23v 24o 25x 26

.8

<ij

ata/A(w/cmZ),

34.5434.4134.6534.5734.78

m(kg/s)

0.01870.01520.01330.01190.0110

t t 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

STEAM QUALITY, x

F!6.8. MEASURED PRESSURE GRADIENT RATIOS.

I _

MARTINELLI-NELSON

t 3.0 ata

RUN, q/ACW/cm2),

oAV

9X

o6

t,

1235

525354566768

33.4833.3233.2733.1220.6120.5920.6469.9670.2270.66

0.02420.01990.01500.01090.00980.00880.00750.033?0.02980.0249

t 10.1 02 03 Of, 0.5 0.6 0.7 0.8

STEAM QUALITY, x

FIG. 9. MEASURED PRESSURE GRADIENT RATIOS.

o

o

9-

10,

i—

oth-inZUiQ

CCtaU lCC

COUIaca.

-

-

— i

" Ur~ il

v_ - »

i i i

iy/K MARTINELLI-& NELSON

Y<

i i i

1

o&vQ

X

+6

•o

1

1

28.8 tRUN,

111213373839647374

I

I

4-

2.8 ata

q/A(w/cm2),

32.5732.5732 5050.0350.5750.3482.427 0.486 9.47

1

1

-

—

m{kg/s)

0.01340.01150.00980.01600.0144 _0.01250.0293 ~"0.0201 -0.0177

—

—

1 t

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

STEAM QUALITY, x

FIG. 10. MEASURED PRESSURE GRADIENT RATIOS.

o

sT

\~M—inO

DC

CO

DC

COCO

PRE

-

-

— £- v/'- 4/

- /_ //- c

I

I

1 i

/

1

- * * !

1

MARTINELL1-NELS0N

p =

oA

V

a

i.

66.6

1

40.2 t

RUN,

181920798081868788

1

1.6 ata

q/A(W/cm2)

32.0631.9531.9068.8869.0668.134 8.324 7.854 8.06

1

1 1

—-—

—

_—

m(kg/s) _

0.0131 —0.0106 _0.00960.0202 —0.01850.0161 _0.01570.01310.0123

| I0.1 0.2 0.3 0.4 05 0.6 0.7 0.8

STEAM QUALITY, x

FIG. 11. MEASURED PRESSURE GRADIENT RATIOS.

p = 9.6p = 19.5p = 28.8

GO p = 40.2

PRESENT RESULTSMARTINELU- NELSON

10 20 30 50 60 70 80 90,- STEAM QUALITY, x %

FIG.12. COMPARISON WITH THE MARTINÉLLI AND NELSON METHOD.

100

100 r

cc

zUJ

<cco 10Hi

ccininacQL

5 -

~ \ LOCKHART-I \ MARTINELLI

- #\^

i i i i i • i i I

p —19. 9 t

RUN,

D 51* 52» 53° 54

i i i i i

0.8 ota

q/A(w/cm2}

20.4920.612 0.592 0.64

\*»s ^

. . .1

m{kg/s)

0.01340.0 0980.0 0880.0075

0.1

FIG. 13.

0.5 1 10 30

MEASURED PRESSURE GRADIENT RATIOS.

100

.50

10

5

2

\- \- SL \

- ^M. \ LOCKHART-\ \ MARTINELLI

" Nk

_

i i i i, i t i l .— -

P =

•

A9o

I 1

9.6 • 1.

RUN,

212223242526

8 ata

q/A(w/cm2)

3 5.1634.5434.4134,6534.5734.78

\

I I I I I

m(kg/s

0.02420.01870.01520.01330.01190.0110

0.1 0.5 1

FIG. H.

10 Xtt 30

100

-50o

en

CD

LU

ceCOcnmcea.

10

111

p = 19. 9 t 0.8 ata

RUN, qkw/cm2), m(Ug/s)

o 1 33.4 8 0.02422 33.32 0.01993 33.27 0-01504 33.22 0.01305 33.12 0.01096 3296 0.0097

0.1

FIG. 15.

0.5 10 X 30tt

MEASURED PRESSURE GRADIENT RATIOS.

100

10

50

o

cc

o

10UJ

a.

ina.

32.943 3.0133.01

88

p = 29.91 1.1 ata

RUN, q/Atw/crr2), m(kg/s)

0.02270.02500.01920.01590.01340.01150.0098

i i i i , . . . I0.1 10

* t t30

FIG. 16.

100

50

<ac

t—

<£10WIf)

8! s

LOCKHART-

MARTINELLI

p -

oA

V

9ö

• o

o

39.1 ± 1RUN,

U151617181920

.1 ataq/A(W/cm2),

32.8132.5232.2932.1932.0631.9531.90

m(kg/s

0.02850.02190.01760.0U30.01310.01060.0096

0.1 0.5 10 30

FIG. 17. MEASURED PRESSURE GRADIENT RATIOS.

100

50

o

1—

52 10

U)

a:

a:a.

LOCKHART-MARTINELLI

1 1 1 1 1 1 1

p =

o

6

ov

<?

13.8 tRUN,

404142434445

1.5 ataq/A(w/cm2)

52.4451.8151.7451.6151.5351.22

m(kg/s

0. 03120.02540.02180.02000.01770.0157

1 XJ01 0.5 10 X tt

30

FIG. 18.

100

o<a:

UJQ<

a:

trIDtn01

CL

p=29.0 11.3 ata

RUN, q A{W cm2),

50.6051.0150.0850.0350.5750.34

L0CKHART-MARTfNELLI

_L _L , I I . , , ! , 1 , 1 , 1 JL J I I 1 I

rh(kg s)

0.02850.02290.0191 .0.01600.014 40.0125

J0.1 0.5 1 5 10 ^ 30

FIG.19. MEASURED PRESSURE GRADIENT RATIOS.

100

' ^ 5 0

ö*

on

zLUO

cc° 10tuOf

CO

ut 5

a.

2

\

~ \ LOCKHART-I V MARTINELLI

" ^X \

>*, X** X^\, \

t i l l

p =

oA

V

96o

XX.

r \XXXa

\ 1

39.5 t

RUN,

838485868788

\

\

i i

1.2 ota

q/A(W/cm2),

49.0748.2148.4248.3247.8548.06

\

1 ! 1 1 I

rh(kg/s)

0.02460.02010.01740.01570.01310.0123

i j

0.1

Fl6. 20.

0.5 10*tt 3 0

MEASURED PRESSURE GRADIENT RATIOS.

ioo r

^ 5 0

UJ

o

i ioOJO£

tnoou

5 -

_ \\ LOCKHART-

I V MARTINELLI

wXX

1 I

1

1

1

1

, , 1

p=19.0 t

RUN,

o 65A 66v 67o 68

3.0

q/A{W/cm2}

70.2069.9670.2270.66

\

, , , , I

m{kg/s)

0.04300.03370.02880.0249

i i

0.1 0.5 1

FIG. 21

10Xtt

30

ef

a:

toQ

or

LUOC

CDenIxlcca.

100

50

10

5

2

\ LOCKHART-\ MARTINELLI

^a \

x\N* x- >i,

-

1 1 1 1 t 1 ! 1 1

P =

O

&

V

96o

\

28.5 tRUN

697071727374

\

\

. 1 1

2.0 otoq/A(W/cm2)

71.6571.4970.9870.2570.4869.4 7

\

a \ .

1 1 1 I

m(kg/s)

0.04220.03400.02640.02370.02010.0177

I ,..J0.1 0.5 10 30

FIG. 22. MEASURED PRESSURE GRADIENT RATIOS.

100

50

5-

Qi

1—2UJQ< 10a:oLUaif) 5toLU(X.CL

2

\

~ \ LOCKHART-\ MARTINELLI

"*%«. \

^NA X

---—-

i i i i i i 111

p =39.4 t 1.

A

V

96o

-oo

X\k x.*K \

\

i j_

RUN,

76

777879808175

1 i i

6 ataq /A(W/cm2

68.7 769.0869.0368.8869.0668.1369.21

I °i i i i

), * ( k g / s

0.03120.02660.02260.02020.01850.01610.0340

i i

0.1 0.5 10 V 30

FiG. 23. MEASURED PRESSURE GRADIENT RATIOS.

100

50

<

UJO

2ff.O 12.5 otaRUN, q/Atw/cm2) m(kg/s)

o 61 83.53 0.04760.0i390.03770.0293

626364

8i.l 862.6582.4 2.

10CKHART-MARTINELLI

1 i i t i r i I

0.1 0.5 10 30

FIG. 2A. MEASURED PRESSURE GRADIENT RATIOS.

qk ^ 33 W/cm2

100

EC

h~ZUJoacauiac

uata.

10

• LOCKHART-MARTINELLI

i t i i I

0.1 0.5 1 5 10 30

FIG. 25. PRESSURE GRADIENT RATIOS AT CONSTANTHEAT FLUX

100

50

10

5

2

\

—

_

I [

q/A w/

LOCKHART-MARTINELLI

i i i i i i 1

•13.8 ata

i

cm

0 ata

/39.5

I ;

ata

i i i i 11 i i0.1 0.5 1 10 v 30

"MtFIG. 26. PRESSURE GRADIENT RATIOS AT CONSTANT

HEAT FLUX.

100

50

o

cc

UJQ<

g 10iLlocz>

UJ

a.

q/A-70 w/cm

LOCKHART- MARTINELLI

t 1 1 1 1 1 1 t i t i i i i I0.1 0.5 1 10 30

-tt

FIG. 27. PRESSURE GRADIENT RATIOS AT CONSTANTHEAT FLUX.

OCO

cc

COenUJ

a.

100

50

10

5

2

I 33 W/

/ , 271 W/cm

i t

cm

s•

1

p ~

) W/cm

\>

i i i

30ota

2

V

.1 • . .

/ 8 3 W/cm2

V[ 1 1 1 1 1 1

0.1 0.5'tt

FIG. 28.

100

5 50

QC

I—ZUJQ

ceID

% 10COCOUJ

a:Q_

0.1

ata

0.5

FIG. 29. EFFECT OF HEAT FLUX ON PRESSUREGRADIENT RATIOS.

100

50

o

fl

X

o 10

5

2

—

l t

1 i

t

—

-

i 1 i l i i i

qJAW/crtf)

o 339 50o- 71o 83

PRESENT' RESULTS

[Q_ SHER AND 6REEN

Q

1 l i i i i i i 1 i {

10 50 100 300

PRESSURE, p ata

FIG. 30. EFFECT OF PRESSURE ON PRESSUREGRADIENTS.

100

50

10

5

1

i i i i I i | .i

-

-

1 i i i i i 1 (

i i

O (

Å

^\

1 ' ' ' ' 1 ' ' • ' • ' • '

15 °/o LIMIT , , / / /

I I

I I

ml

2 v 0 96"••• <p = 2400(—) ' + 1

P ~

i i i i i I l i ) i l i i l

0.001 0.01 0.1RATIO OF STEAM QUALITY TO PRESSURE, X / P crrf/kp

FIG. 31. PRESSURE DROP CORRELATION.

100

50

10

5

1

I

yy x i i t i m i

c

15 %

i

LIMIT S//

1 1

1 i

i

—

1 t

i t

i

I 1 1 | 1 1 1 1 15 10 50 100

FIG. 32. MEASURED PRESSURE DROP RATIO VERSUSCOMPUTED PRESSURE DROP RATIO.

9.7S ato

19.5 ata

40.2 oto

137 ata

EXPERIMENTAL RESULTS

EQUATION

1 I0 0.05 0.10 0.15 Q20 02S 0.30 0.35 WO (US 0.50 0.55 0.60 0.65 0.70 0.75

STEAM QUALITY, x

FIG.33. COMPARISON BETWEEN PRESSURE DROP CORRELATION AND EXPERIMENTAL RESULTS.

aso

LIST OF PUBLISHED AE-REPORTS

1—9. (See Ihe back cover of earlier reports.)

10. Equipment for thermal neutron flux measurements in reactor R2. By E.Johansson, T. Nilsson and S. Claeson. 1960. 9 p. Sw. cr. 6:—.

11. Cross sections and neutron yields for U235, Uö s and Pu2* at 2200 m/sec.By N. G. Sjöstrand and J. S. Story. 1960. 34 p. Sw. cr. 4:—.

12. Geometric buckling measurements using the pulsed neutron source me-thod. By N. G. Sjöstrand, M. Mednis and T. Nilsson. 1959. 12 p. Sw. cr.4s—. Out of print. Cf.: (Arkiv för fysik 15 (1959) nr 35 pp 471—82.)

13. Absorption and flux density measurements in an iron plug in Rl. By R.Nilsson and J. Braun. 1958. 24 p. Sw. cr. 4:—.

14. GARLIC, a shielding program for GAtnma Radiation from Line- andCylinder-sources. By M. Roos. 1959. 36 p. Sw. cr. 4:—.

15. On the spherical harmonic expansion of the neutron angular distributionfunction. By S. Depken. 1959. 53 p. Sw. cr. 4:—.

16. The Dancoff correction in various geometries. By I. Carlvik and B. Pers-hagen. 1959. 23 p. Sw. cr. 4:—.

17. Radioactive nuclides formed by irradiation of the natural elements withthermal neutrons. By K. Ekberg. 29 p. Sw. cr. 4:—.

18. The resonance integral of gold. By K. Jirlow and E. Johansson. 1959. 19 p.Sw. cr. 4:—.

19. Sources of gamma radiation in a reactor core. By M. Roos. 1959. 21 p.Sw. cr. A:—.

20. Optimisation of gas-cooled reactors with Ihe aid of mathematical compu-ters. By P. H. Margen. 1959. 33 p. Sw. cr. 4:—.

21. The fast fission effect in a cylindrical fuel element. By I. Carlvik andB. Pershagen. 1959. 25 p. Sw. cr. 4:—.

22. The temperature coefficient of the resonance integral for uranium metaland oxide. By P. Blomberg, E. Hellstrand and S. Homer. I960. 14 p.Sw. cr. 4:—.

23. Definition of the diffusion constant in one-group theory. By N. G. Sjö-strand. 1960. 8 p. Sw. cr. 4:—.

24. Transmission of thermal neutrons through boral. By F. Akerhielm. 2nd rev.ed. 1960. 15 p. Sw. cr. 4s—.

25. A study of some temperature effects on the phonons in aluminium byuse of cold neutrons. By K.-E. Larsson. U. Dahlborg and S. Holmryd.1960. 21 p. Sw. cr. 4:—.

26. The effect of a diagonal control rod in a cylindrical reactor. By T. Nils-son and N. G. Sjöstrand. 1960. 4 p. Sw. cr. A:—.

27. On the calculation of the fast fission factor. By B. Almgren. 1960. 22 p.Sw. cr. 6:—.

28. Research administration. A selected and annotated bibliography ofrecent literature. By E. Rhenman and S. Svensson. 2nd rev. ed. 1961. 57 p.Sw. cr. 6:—.

29. Some general requirements for irradiation experiments. By H. P. Myersand R. Skjöldebrand. 1960. 9 p. Sw. cr. 6:—.

30. Metallographic study of Ihe isothermal transformation of beta phase inzircaloy-2. By G. Östberg. 1960. 47 p. Sw. cr. 6:—.

31. Calculation of the reactivity equivalence of control rods in the secondcharge of HBWR. By P. Weissglas. 1961. 21 p. Sw. cr. 6:—.

32. Structure investigations of some beryllium materials. By I. Fäldt and G.Lagerberg. 1960. 15 p. Sw. cr. 6:—.

33. An emergency dosimeter for neutrons. By J. Braun and R. Nilsson. 1960.32 p. Sw. cr. 6:—.

34. Theoretical calculation of the effect on lattice parameters of emptyirlgthe coolant channels in a DiO-moderaled and cooled natural uraniumreactor. By P. Weissglas. 1960. 20 p. Sw. cr. 6:—.

35. The multigroup neutron diffusion equations/1 space, dimension. By S.Linde. 1960. 41 p. Sw. cr. 6:—.

36. Geochemical prospecting of a uraniferous bog deposit at Masugnsbyn,Northern Sweden. By G. Armands. 1961. 48 p. Sw. cr. 6:—.

37. Spectrophotometric determination of thorium in low grade minerals andores. By A.-L. Arnfelt and I. Edmundsson. 1960. 14 p. Sw. cr. 6 . ~ .

38. Kinetics of pressurized water reactors with hot or cold moderators. ByO. Norinder. 1960. 24 p. Sw. cr. 6 s—.

39. The dependence of the resonance on Ihe Doppler effect. By J. Rosén.1960. 19 p. Sw. cr. 6:—.

40. Measurements of the fast fission factor (£) in UO2-etements. By O. Ny-lund. 1961. Sw.cr. 6:—.

44. Hand monitor for simultaneous measurement of alpha and beta conta-mination. By I. O. Andersson, J. Braun and B. Söderlund. 2nd rev. ed.1961. Sw. cr. 6:—.

45. Measurement of radioactivity in the human body. By I. D. Anderssonand I. Nilsson. 1961. 16 p. Sw. cr. 6:—.

46. The magnetisation of MnB and its variation with temperature. By N.Lundquist and H. P. Myers. 1960. 19 p. Sw. cr. 6:—.

47. An experimental study of the scattering of slow neutrons from H2O andD2O. By K. E. Larsson, S. Holmryd and K. Olnes. 1960. 29 p. Sw. cr. 6:—.

48. The resonance integral of thorium metal rods. By E. Hellstrand and. J.Weitman. 1961. 32 p. Sw. cr. 6:—.

49. Pressure tube and pressure vessels reactors; certain comparisons. By P.H. Margen, P. E. Ahlström and B. Pershagen. 1961. 42 p. Sw. cr. 6:—.

50. Phase transformations in a uranium-zirconium alloy containing 2 weightper cent zirconium. By G. Lagerberg. 1961. 39 p. Sw. cr. 6:—.

51. Activation analysis of aluminium. By D. Brune. 1961. 8 p. Sw. cr. 6:—.

52. Thermo-technical data for DjO. By E. Axblom. 1961. 14 p. Sw. cr. 6:—.

53. Neutron damage in steels containing small amounts of boron. By H. P.Myers. 1961. 23 p. Sw. cr. 6:—.

54. A chemical eight group separation method for routine use in gammaspectrometric analysis. I. Ion exchange experiments. By K. Samsahl.1961. 13 p. Sw. cr. 6:—.

55. The Swedish zero power reactor R0. By Olof Landergärd, Kaj Cavallinand Georg Jonsson. 1961. 31 p. Sw. cr. 6:—.

56. A chemical eight group separation method for routine use in gammaspectrometric l i II D t i l d l t i l h B K S h l18 p. 1961. Sw.

A chemical eight group separation method for routine use in gammaspectrometric analysis. I I . Detailed analytical schema. By K. Samsahl.18 1961 S . cr. 6 : - .

57. Heterogeneous two-group diffusion theory for a finite cylindrical reactor.By Alf Jonsson and Göran Näslund. 1961. 20 p. Sw. cr. 6:—.

58. Q-values for (n, p) and (n, a) reactions. By J. Konijn. 1961. 29 p. Sw. cr.

59. Studies of the effective total and resonance absorption cross sections forzircaloy 2 and zirconium. By E. Hellstrand, G. Lindahl and G. Lundgren.1961. 26 p. Sw. cr. 6:—.

60. Determination of elements in normal and leukemic human whole bloodby neutron activation analysis. By D. Brune, B. Frykberg, K. Samsahl andP. O. Wester. 1961. 16 p. Sw. cr. 6:—•

61. Comparative and absolute measurements of 11 inorganic constituents of38 human tooth samples with gamma-ray speclromeiry. By K. Samsahland R. Söremark. 19 p. 1961. Sw. cr. 6:—.

62. A Monte Carlo sampling technique for multi-phonon processes. By ThureHögberg. 10 p. 1961. Sw. cr. 6:—.

63. Numerical integration of the transport equation for infinite homogeneousmedia. By Rune Håkansson. 1962. 15 p. Sw. cr. 6:—.

64. Modified Sucksmith balances for ferromagnetic and paramagnetic mea-surements. By N. Lundquist and H. P. Myers. 1962. 9 p. Sw. cr. 6:—.

65. Irradiation effects in strain aged pressure vessel steel. By M. Grounesand H. P. Myers. 1962. 8 p. Sw. cr. 6:—.

66. Critical and exponential experiments on 19-rod clusters (R3-fuel) in heavywater. By R. Persson, C-E. Wikdahl and Z. Zadwörski. 1962. 34 p. Sw. cr.6:—.

67. On the calibration and accuracy of the Guinier camera for the deter-mination of interplanar spacing;. By M. Möller. 1962. 2] p. Sw. cr. 6:—.

68. Quantitative determination of pole figures with a texture goniometer bythe reflection method. By M. Möller. 1962. 16 p. Sw. cr. 6:—.

69. An experimental study of pressure gradients for flow of boiling wafer ina vertical round duct. Part I. By K. M. Becker, G. Hernborg and M. Bode.1962. 46 p. Sw. cr. 6:—.

70. An experimental study of pressure gradients for flow of boiling water ina vertical round duct, Part I I . By K. M. Becker, G. Hernborg and M. Bode.1962. 32 p. Sw. cr. 6:—.

71. The space-, time- and energy-distribution of neutrons from a pulsedplane source. By A. Claesson. 1962. 16 p. Sw. cr. 6:—.

72. One-group perturbation theory applied to substitution measurements withvoid. By R. Persson. 1962. 21 p. Sw. cr. 6:—.

73. Conversion factors. By A. Amberntson and S-E. Larsson 1962. 15 p. Sw.cr. 10:—.

74. Burnout conditions for flow of boiling water in vertical rod clusters.By Kurt M. Becker 1962. 44 p. Sw. cr. 6:—.

75. Two-group current-equivalent parameters for control rod cells. Autocodeprogramme CRCC. By O. Norinder and K. Nyman. 1962. 18 p. Sw. cr.6 !**"*•

76. On the electronic structure of MnB. By N. Lundquist. 1962. 16 p. Sw. cr.6:—*

77. The resonance absorption of uranium metal and oxide. By E. Hellstrandand G. Lundgren. 1962. 17 p. Sw. cr. 6s—.

78. Half-life measurements of »He, «N , »O, *>F, 2«AI, "Se™ and ' " Ä g . By J.Konijn and S. Malmskog. 1962. 34 p. Sw. cr. 6:—.

79. Progress report for period ending December 1961. Sw. cr. 6:—.

80. Investigation of the 800 keV peak in the gamma spectrum of SwedishLaplanders. By I. ö . Andersson, I. Nilsson and K. Eckerstig. 1962. 8 p.Sw. cr. 6:—.

81. The resonance integral of niobium. By E. Hellstrand and G. Lundgren.1962. 14 p. Sw. cr. 6—.

82. Some chemical group separations of radioactive trace elements. By K.Samsahl. 1962. 18 p. Sw. cr. 6:—.

83. Void measurement by the (y, n) reaction. By S. Zia Rouhani. 1962. Sw.cr.6:—.

84. Investigation of the pulse height distribution of boron trifluoride pro-portional counters. By I. O. Andersson and S. Malmskog. 1962. Sw. cr.6:~~*.

85. An experimental study of pressure gradients for flow of boiling waterin vertical round ducts. (Part 3). By Kurt M. Becker, Gunnar Hernborgand Manfred Bode. 1962. Sw. cr. 6:—.

Förteckning över publicerade AES-rapporter

1. Analys medelst gamma-spektrometri. Av Dag Brune. 1961. 10 s. Kr 6:—.

Additional copies available at the library of AB Atomenergi, Studsvik, Nykö-ping, Sweden. Transparent microcards of the reports are obtainable throughthe International Documentation Center, Tumba, Sweden.

EOS-tryckerierna, Stockholm 1962