SMR/1848-T15 Course on Natural Circulation Phenomena and ...indico.ictp.it/event/a06203/session/36/contribution/24/material/0/0.pdf · SMR/1848-T15 Course on Natural Circulation Phenomena

SMR/1848-T15

Course on Natural Circulation Phenomena and Modelling inWater-Cooled Nuclear Reactors

P.K. Vijayan

25 - 29 June 2007

Bhabha Atomic Research Centre (BARC), Mumbai, India

T15 - Experimental Validation and Data Base of Simple Loop Facilities

EXPERIMENTAL VALIDATION AND

DATABASE OF SIMPLE LOOP

FACILITIES

P.K. VijayanReactor Engineering Division,

Bhabha Atomic Research Centre, Mumbai, India

IAEA Course on Natural Circulation in Water-Cooled Nuclear Power

Plants, ICTP, Trieste, Italy, 25-29 June, 2007 (Lecture : T-15)

OUTLINE OF THE LECTURE T#15

- INTRODUCTION

- STEADY STATE BEHAVIOUR OF 1- LOOPS

- STEADY STATE BEHAVIOUR OF 2- LOOPS

- STABILITY BEHAVIOUR OF 1- LOOPS

- EXPERIMENTAL DATABASE FOR INSTABILITY

OF 2- LOOPS

- STATIC INSTABILITY OF 2- LOOPS

- DYNAMIC INSTABILITY OF 2- LOOPS

- CONCLUDING REMARKS

Advantages of Simple loop Facilities

INTRODUCTION

- Easy to construct and operate

- Minimum of instrumentation

- Large amount of easily reproducible data can be

generated economically in a short time

- Phenomena taking place is easily traceable

- Theoretical and numerical modelling is far more easier

- Data interpretation is easy

INTRODUCTION – Contd.

Contribution of simple loop facilities

- Phenomenological understanding of NC process

- Development of theoretical model and computer codes

- Steady state, transient and stability performance of NCS

- Development and testing of scaling laws

. Hysteresis or conditional stability phenomenon,

. Nature of the unstable flow

- oscillatory modes, phase shift and flow regimes

. Flow redistribution in parallel channels

Topic of this lecture - Contribution of simple loop facilities on the

study of steady state and stability behaviour of single-phase and

two-phase loops

3

2

hh QTor3

1

22

0

2

2 gHCp

RQT hh

Steady state performance of single-phase loops

Lc

Lh

S=0,Lt

S=Lhl S=Lc

L4

L2 COOLER

L1

L3

S=Lh

INLETOUTLET

HEATER

H

2

2

0

RWTdzg

NC in a simple NDL

For an incompressible Boussinesq fluid

3

12

02

RCp

HgQW h

Integrating and rearranging

3

1

hQWor

3

12

02

RCp

ZgQW ch

The core or heater Th can be obtained as

For other orientations of source and sink

Where Zc : C-L elev. diff. betn. sink and source

Generalized Flow CorrelationThe total loop hydraulic resistance

N

i ii AK

D

fLR

12

1

Replace the local loss coefficients Ki with an equivalent length, Lei

i

iii

f

DKLe So that iiieff LeLL

Define reference area and diameter for the NDL as

t

tN

i

ii

t

rL

VLA

LA

1

1N

i

ii

t

r LDL

Dand1

1

If the entire loop follows a friction law of the form bii

pf

Rer

G

m

N

GrCRe

brand

pC

ad

l

D

LNwhere

rN

i i

bb

eff

r

tG

3

12;

121

then

fully laminar loop

Generalized Flow Correlation – Contd.

A Generalized correlation valid for all orientations can be obtained as

before if linear variation of temperature is assumed in the coolerr

G

zm

N

GrC cRe

The error, E, introduced by this

assumption is < 1% if Stm< 1

Stm

Laminar

Turbulent flow

Stm

Laminar flow

Turbulent flow

EE

0.01 0.1 1 10

1.00

1.01

1.02

1.03

1.04

1.05

0.01 0.1 1 10

1.00

1.02

1.04

1.06

1.08

5.0

1768.0ReG

zm

N

Grc

75.2

1

96.1ReG

zm

N

Grc

43.0

3548.0ReG

zm

N

Grc

fully turbulent loop

transition region (empirical)

HHVC VHVC

Steady state performance of single-phase loops

The Generalized flow correlations were found useful to compare the

performance of various loops

Uniform diameter loops (UDLs)

Nonuniform diameter loops (NDLs)

Database for UDLs

Total Number of loops : 14

Loop diameter : 6 to 40 mm

Loop height : 0.38 to 2.3 m

Total circulation length : 1.2 to 7.2 m

Lt/D ratio : 75 to 1100

Fluid used : mostly water and freon in one case

Pressure : near atmospheric to near critical pressure (freon)

Source and sink orientations: all four (HHHC, HHVC,VHHC and VHVC)

Loop types : Open and closed loops

Loop shapes : Rectangular, toroidal, figure-of-eight loops

Steady state performance of UDLs

Comparison of UDL data - Without local losses, NG=Lt/D

- With local losses, NG= (Leff)t/D

102

104

106

108

1010

1012

1014

100

102

104

106

Bernier-Baliga(1992)

Misale et al.(1992)

Vijayan et al.(1994)

Huang-Zelaya(1988)

Holman-Boggs(1960)

Creveling et al. (1975)

Laminar flow correlation

Turbulent flow coppelation

Transition flow correlation

Bau-Torrance(1981)

Haware(1983)

Ho et al. (1997)

Nishihara(1997)

Re

Grm/N

G

102

104

106

108

1010

1012

1014

100

102

104

106

Creveling et al. (1975)

Huang-Zelaya (1988)

Vijayan et al. (1994)

Holman-Boggs (1960)

Ho et al. (1997)

Misale et al. (1992)

Nishihara (1997)


Turbulent flow correlation


Hawre et al. (1983)

Bernier-Baliga (1992)

Bau-Torrance (1981)

Re

GrmD/L

t

Good agreement with laminar flow correlation in the low Re zone

and good agreement in the turbulent flow correlation in the high

Re zone.

Without local losses With local losses

Local losses are significant in the high Reynolds number zone

Steady state performance of NDLs

Most practical applications of NC employ NDLs

NDL database

Total Number of loops : 10

Loop diameter : 3.6 to 97 mm

Loop height : 1 to 26 m

Total circulation length : 10

to 125 m

Fluid used : water

Pressure : up to 90 bar

Source and sink

orientations: HHVC and VHVC

Loop types : closed loops

105

106

107

108

109

1010

1011

1012

101

102

103

104

105




Vijayan et al. (1991)

Hallinan-Viskanta(1988)

Jeuck et al. (1-loop data)




Zvirin et al. (1-loop data)

Zvirin et al. (2-loop data)

John et al.(1991)

FISBE

Re

ss

Grm/N

G

NDL data neglecting local losses

Loop shapes : Rectangular and figure-of-eight loops

Data for low Re agrees with laminar flow correlation and high Re

data agrees with turbulent flow correlation

Steady state performance of Single-phase Loops

102

104

106

108

1010

1012

1014

1016

100

101

102

103

104

105

106




NDL data

UDL data

Re

ss

Grm/N

G

General Remarks


is good for Grm/NG < 106


is good for Grm/NG > 1010

Significant data scatter

exists in 106 < Grm/NG <

1010 as the loop is

neither fully laminar

nor fully turbulent. The

empirical correlation is

good in this region

For specific loops good agreement with laminar flow correlation is

obtained even up to Re of 1200 (Grm/NG< 5x107). Similarly

turbulent flow correlation is found to give good results for Re >

2000 (Grm/NG > 2x108)

UDL and NDL data neglecting local losses

Steady State Performance (1- NC)

The flow rate increases with power as well as with loop

diameter as expected.

Measured and predicted flow

rate for 26.9 mm i.d. loop

0.0 0.5 1.0 1.5 2.0 2.50.000

0.025

0.050

0.075

0.100

Flo

w (

kg

/s)

Power (kW)

Experimental data

Blasius correlation (f = 0.316 Re-0.25

)

f = 0.184 Re-0.2

0.00 0.25 0.50 0.75 1.000.0000

0.0125

0.0250

0.0375

0.0500

6 mm loop

23.2 mm loop

11 mm loop

Flo

w -

kg

/s

Power - kW

Effect of loop diameter on

predicted flow rate

Based on the Homogeneous Equilibrium Model (HEM). The pressure

losses in the system are negligible compared to the static pressure so

that (constant pressure system) the fluid property variation with

pressure is negligible.

The inlet subcooling is negligible so that the density variation in the

single-phase heated section can be neglected.

Complete separation of steam and water is

assumed to occur in the SD so that there is

no liquid carryover with the steam and no

vapor carry-under with water (see Figure)

Lh

Loop relevant to BWRs

S=0,St

S=SSD

S=SSD

Steam

drum

down

comer

Steam Ws, hs

Feed

WF, hF

H

S=SspS=Sh

LB Heater

A constant level is maintained in the SD, so

that the single-phase lines always run full

The heater is supplied with a uniform heat

flux and the SD can be approximated to a

point heat sink. Heat losses are negligible

Steady state Performance of Two-phase Loops

The steady state one-dimensional governing equations for the two-

phase NCS

0ds

dWConservation of mass

pipes

heaterD

q

ds

dh

A

Wh

h

i0

4 "

Conservation of energy

tiiii LA

WK

AD

Wfg

ds

dP

ds

d

A

W2

2

2

2

2

2

22sin

vConservation of momentum

Integrating the momentum equation around the closed loop and

noting that we get vd 0dP

22

2

122

2 RW

A

K

DA

fLWdzg

tN

i i

where dz=ds.sin


Two-phase density in the buoyancy force term can be approximated as

lhr hh1

p

hh

v

v

1where

l

g

lg

x

xwhere

11

1

1

Both the definitions are equivalent for a constant pressure system

in the two-phase regime if HEM is applicable

0.0 0.2 0.4 0.6 0.8 1.00

100

200

300

400

500

600

700

800

Pressure=70 bar

De

nsity

Quality

=l[1-

tp(h-h

l)]

=g+(1- )

l

Fluid: water

Density variation in the two-phase region


2

2RWdzhg hr

If we can approximate h to be a constant over the loop, then

3

1

22

R

HgQW hhrNoting that hss=Qh/W,

tp

B

B

s

sN

Ni i

tp

LO

N

Nii

tpLO

N

i i

sp

A

K

DA

fL

A

K

DA

fL

A

K

DA

fLRwhere

122

2

122

2

122

Replacing the local loss coefficients in terms of an equivalent length

and if a friction factor correlation of the form f=p/Reb is valid

throughout the loop

It may be noted that the above assumption (i.e. f=p/Reb) may not be

valid always for reactor loops.

tp

B

B

s

sN

Ni i

bb

eff

LO

N

Nii

bb

effLON

i i

bb

eff

l

bb

l

rhrAD

L

AD

L

AD

LWpdzhhg

121

2

121

2

121

2

2


tp

B

B

s

sN

Ni i

bb

eff

LO

N

Nii

bb

effLON

i i

bb

eff

l

bb

l

rhrAD

L

AD

L

AD

LWpdzhhg

121

2

121

2

121

2

2

Nondimensionalizing the above with the following substitutions

t

ieff

ieff

t

ii

r

ii

r

ii

ss

r

ss L

Lland

L

Ll

D

Dd

A

Aa

H

sS

H

zZ

h

hh

W

W;;;;;;H

inrinr

N

i

ii

t

r

t

t

N

i

ii

t

r hhandLDL

DL

VLA

LAwhere

tt

;;1

;1

11

r

G

mss

N

GrCRe

brand

pC

A

gQDGr

A

WDWhere

r

lr

hIlrm

lr

ssrss

3

12;;Re

3

23

tp

B

B

s

sN

Ni i

bb

eff

LO

N

Ni i

bb

eff

LO

N

i i

bb

eff

r

tG

ad

l

ad

l

ad

l

D

LN

121

2

121

2

121

looplaminar1768.0Re2

1

G

mss

N

Gr

loopturbulentN

Grand

G

mss

11

4

96.1Re


Special CasesSingle-phase natural circulation

thatsoLO ,12and

ad

l

D

LN

tN

i i

bb

eff

r

tG

121

CpTisCpIf T

p

h

v

Cpv

1 thenconstant, getwethatso

Twhere

p

T

v

v

1

pp

hCpTh

v

v

1v

v

1

Two-phase NCLSingle-phase NCL

3

1

22

R

HgQW hhr

3

1

22

p

hTr

RC

HgQW

tp

B

B

s

sN

Ni i

tp

LO

N

Nii

tpLO

N

i i

sp

A

K

DA

fL

A

K

DA

fL

A

K

DA

fLR

122

2

122

2

122

tN

i i

sp

A

K

DA

fLR

122

r

G

mss

N

GrCRe

r

G

mss

N

GrCRe

tp

B

B

s

sN

Ni i

bb

eff

LO

N

Ni i

bb

eff

LO

N

i i

bb

eff

r

tG

ad

l

ad

l

ad

l

D

LN

121

2

121

2

121

tN

i i

bb

eff

r

tG

ad

l

D

LN

121

3

23

lr

hhlrm

A

gQDGrand3

23

lr

hTlrm

CpA

gQDGrand

Two-Phase Natural Circulation

coolant

Schematic of the different test loops

separator

condenser

heater

Neutron

window 2445

2020

2210

2036

575

(a) 7, 9.1, 15.74 & 19.86 mm loops

heater

850

1180 655

1180

885

condenserseparator

1515

3400

subcooler

(b) 49.3 mm loop

Extensive database exists for the steady state performance of two-phase loops.

However, complete geometric details are not always available

Range of Parameters of Data

Pressure : 0.1-7 MPa Power : 0.3-40 kW Tsub : 0.1-16 K

Quality : 0.4-24% Diameter: 7, 9.1, 15.7, 19.9 & 49.3 mm


Testing of correlation with data

107

108

109

1010

1011

1012

1013

1014

1015

102

103

104

105

106

Power:0.3 - 65 kW

Pressure:0.1-13.8 MPa

Tsub

:0.1-64 0C

quality:0.4-69.3%

0.6C(Grm/N

G)

r

1.4C(Grm/N

G)

r

Re

ss

Grm / N

G

Present Theory

UDL data

NDL data

Effect of pressure on two-phase NC flow

Testing with correlation

Loops considered: 5

Literature data is not utilized as

yet except one NDL data

The experimental data is in

reasonable agreement with

the theoretical correlation

At constant power, the flow rate goes through a peak and then reduces

with increase in pressure

0 20 40 60 800.0

0.5

1.0

1.5

2.0

Equation (7)

Experimental data

Power=30 kW

Loop diameter : 49.3 mm

Mass F

low

Rate

(kg/s

)

Pressure (bar)

theory

Effect of Power on Steady State Flow in 2- NCLs

With increase in power, the steady

state flow may increase, decrease or

remain practically unaffected.

(a) Flow increases with power (b) Flow decreases with power

(c) Flow invariant with power

Different NC flow regimes exist

in two-phase loops

15 30 450.5

1.0

1.5

2.0Pressure: 9.6 bar

Sub-cooling: 1 oK

Ma

ss F

low

Rate

(kg/s

)

Power (kW)

Equation (7)

Experimental data

RELAP5/MOD3.2 (Two-fluid model)

TINFLO-S

theory

1500 2000 2500 3000 3500 40000.01

0.02

0.03

9.1 mm diameter tube

12.6 - 14.6 bar (abs)Mass f

low

rate

(kg

/s)

Power (W)

Experimental data

TINFLO

Equation (7)theory

2000 3000 4000 50000.00

0.01

0.02

0.03

0.04

9.1 mm i.d. loop

Tsub

: 8 - 16K

Pressure: 57+1 bar

Mass F

low

Rate

(kg/s

)

Power (W)

Experiment

RELAP5/Mod 3.2

TINFLO-S

Eq.(7) with h calculated by Eq. (9)theory

NC Flow Regimes in two-phase NCLs

Effect of quality on void fraction Different flow regimes in 9.1 mm loop

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1 bar

220bar

221.2bar

170

bar

70 bar

15 b

ar

Vo

id f

ractio

n

Quality

0 20 40 60 80 1000

1

2

3

4

5

6

Loop Diameter= 9.1 mm

170 bar

70 bar

15 bar

GDR

Compensating Regime

Friction Dominant Region

GDR

Flo

w n

orm

alis

ed

to

100

% F

P

Power (%)

Gravity Dominant Regime: Occurs at low qualities where there is a large

change in void fraction with small change in quality. Characteristic of this regime is

that NC flow increases with power

Friction Dominant Regime: Occurs at high qualities where there is a small

change in void fraction with change in quality. Characteristic of this regime is that flow

decreases with increase in power. Generally observed during low power operation.

Compensating Regime: The increase in buoyancy force is compensated by a

corresponding increase in frictional force resulting in practically constant flow

Effect of Loop Diameter on two-phase NC Flow Regimes

The friction dominant regime shifts to lower pressures with increase in loop

diameter

At high pressures, only the gravity dominant regime may be observed if the

power is low.

Knowledge of the flow regimes helps to understand the stability behaviour of two-

phase loops

0 20 40 60 80 1000.0

0.4

0.8

1.2

1.6

2.0

Loop Diameter: 19.86 mm

GDR: Gravity Dominant Regime

Compensating Regime

170 bar

50 bar

15 bar

GDR

Friction Dominant RegionGDR

Flo

w n

orm

alis

ed t

o 1

00%

pow

er

Power (%)0 20 40 60 80 100

0.0

0.4

0.8

1.2

1.6

2.0

170 bar

8 bar

2 bar

GDR

Compensating Regime

Friction Dominant RegimeGDR

Loop Diameter= 49.3 mm

GDR: Gravity Dominant RegimeFlo

w n

orm

alis

ed t

o 1

00%

pow

er

Power (%)

(a) 19.86 mm loop (b) 49.3 mm loop

Stability Behaviour of Single-phase

Loops

Extensive database exists on single-phase instability and a few of the

general characteristics observed are discussed below

- Hysteresis

- Instability mechanisms and flow regimes

- Flow regime switching and oscillation period

- Limit cycles

- Effect of power

- Prediction of instability threshold

- Prediction of limit cycles

- Techniques for stabilization

Hysteresis Phenomenon

From the linear analysis, it appears that the stability threshold is a

unique value.

A region of hysteresis (conditional stability) exists where the instability

threshold depends on the operating procedure

The phenomenon is observed in simple rectangular loops, figure-of-

eight loops with throughflow, parallel channel systems and two-

phase loops

The effect of the following three operating procedures are investigated

- Start-up from rest (Instability threshold: 105 W)

- Power raised from stable steady state (Threshold : 270 W)

- Power step back from an unstable state (Threshold : 60 W)

The instability thresholds were found to be different for all the

three cases with the coolant secondary conditions maintained constant

Oscillatory flow regimes

Flo

w r

ate –

kg

/s

p – mm of water column

(f) limit cycle for chaotic switching

p -

mm

Time – s

(e) time series for chaotic switching

p -

mm

Time – s (c) time series for bi-directional pulsing (d) limit cycle for bi-directional pulsing

Flo

w r

ate

-k

g/s

p – mm of water column

(b) limit cycle for unidirectional pulsing

p -

mm

Time - s (a) time series for unidirectional pulsing

24000 26000 28000 30000 32000

-3

-2

-1

0

1

2

3

10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000-3

-2

-1

0

1

2

3

10000 12000 14000 16000 18000 20000-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3-0 .2

-0 .1

0 .0

0 .1

0 .2

-3 -2 -1 0 1 2 3-0.2

-0.1

0.0

0.1

0.2

Orientation : HHHC

Plotted from a time series of 21800 seconds after neglecting initial transients

Flo

w r

ate

- k

g / s

P - mm of water column

-3 -2 -1 0 1 2 3-0.2

-0.1

0.0

0.1

0.2

A rich variety of

oscillatory flow

regimes are possible

-unidirectional

-bi-directional

-chaotic switching

The shape of the

limit cycle depends

on the chosen

parameter space

Mechanism causing instability

Welander proposed that oscillation growth as the mechanism

causing instability

0 5000 10000 15000 20000-3

-2

-1

0

1

2

3

Orientation : HHHCP across the bottom horizo

P -

mm

of

wa

ter

co

lum

n

Time - s

270 W

0 5000 10000 15000 20000 25000-3

-2

-1

0

1

2

3

P -

mm

of

wa

ter

co

lum

n

Time - s

10000 15000

Time - s

Period tripling

Period doubling105 W

165 W

0-3

-2

-1

0

1

2

3

P -

mm

of

wa

ter

co

lum

n

(a) Oscillation growth from steady state (b) Start-up from rest at low power c) Start-up from rest at high power

Oscillation growth is the mechanism causing instability. But

differences are visible

Flow regime switching leads to period jump

Experimental 3-D Phase space of 1- NC

-30-20

-100

1020

30

100

200

300

400

-0.1

0.0

0.1

0.2

unconditionallystable

unconditionallyunstable

conditionallystableP

ow

er

-W

Flowrate

- kg/s

P - Pa

The various flow regimes like unconditionally stable, conditionally

stable (hysteresis) and the unconditionally unstable

The amplitude of

oscillation is found to

increase with power.

Effect of power

The phase plots also deform

with increase in power

The oscillations also become

more chaotic with increase

in power

Effect of powerThe frequency of oscillation increases with increase in power

except when period jump occurs

0 100 200 300 400 500 600 700200

300

400

500

600

T=250.6+784.12exp(-Qh/142.81)

T = 427.5-1.0117Qh

unidirectional pulsing

bidirectional pulsing

best fit line for unidirectional pulsing

best fit line for bidirectional pulsing

Pe

rio

d o

f o

scill

atio

n -

s

Power - W

The period of unidirectional oscillation is found to decrease

linearly where as the period of bi-directional oscillation is found

to decrease exponentially

Prediction of Stability Map

The stability map is usually predicted by the linear theory

Often the wall effects and heat losses are neglected

The prediction is significantly affected by the friction factor correlation

Good comparison with experimental data is obtainable with a loop

specific empirical correlation.

The same correlation when used for other loops can show

significantly different results

However, accounting for the wall and heat loss effects good

prediction can be expected for fully laminar and turbulent loops

For certain loop geometry such as the toroidal loop, the adequacy

of 1-D theory is questionable due to the continuous variation of

the gravitational component

Prediction of Limit Cycles1-D theory is expected to give good prediction of the steady state

flow if the local losses are accounted for a fully laminar and fully

turbulent loop.

Good prediction of the stability map is also expected for the fully

laminar and fully turbulent loop if wall thermal effects and heat losses

are accounted

However, prediction of the limit cycle oscillations is a bigger challenge

in single-phase loops as all three (laminar, turbulent and transition

regimes) are encountered in rapid succession especially when periodic

flow reversal takes place.

In such cases, a criterion for laminar to turbulent flow transition is

also required. Different transition criteria also can give interesting results

The predicted limit cycles can be significantly different due to the 3-D

effects caused by the flow which is never fully developed

Techniques for stabilizingIncreasing the Stm and Lt/D are always stabilizing.

Increasing the Lt/D is commonly used in NCSs. Introduction of

orifices is the usual method. The location of the orifice does not

matter in single-phase systems

Instability is observed in loops with Lt/D < 300.

Introduction of orifices reduce the flow and heat transfer

capability significantly.

Use of thick conducting walls are found to stabilize single-phase

systems

In addition process control techniques are being tried out to

stabilize single-phase NCSs

There are techniques which does not affect the flow

Database for instability of two-phase

NC loops

Extensive database from simple loop facilities exist for two-phase

NC instability

Most instabilities such as flashing, geysering, Type I DWI,

Ledinegg type instability and even CHF induced instability are

found to occur during initiation of boiling.

For analysis purposes, it is important to separate them out based

on their mechanism and characteristics as analysis methods are

different

This is often lacking in the database

Experimental Stability Map (2- NC)

Typical low power and high power instability

Two unstable regions are found

for two-phase NCLs.

The first unstable zone in the

two-phase region occurs at a

low power and hence at low

quality and is named as type I

instability by Fukuda and

Kobori (1979). Similarly, the

second unstable zone in the

two-phase region occurs at high

powers and hence at high

qualities and is named as type II

instability.

Type-I instability occurs in the gravity dominant regime whereas

type-II instability occurs in the friction dominant regime. Instability

is not found in the compensating regime during the present tests.

0 5000 10000 150000.0

0.7

1.4

2.1

2.8

3.5

Stable 2- flow

Boiling inception

Stable 1- flow

Type-II instability

Type-I instability

Loop diameter: 9.1 mmPressure: 13.7 bar

P -

Pa*0

.1;

Tsub-

K

Pow

er

-kW

Time - s

Power

0

20

40

60

80

100

Tsub

P across flow meter

Experimental Findings on Type-I Instability

It occurs right from the boiling inception. The amplitude of

oscillations first increases, reaches a peak and then

decreases with increase in power eventually leading to

stable flow.

0

10

20

30

40

1000

1-

p (

mm

of

wc)

Time (s)

(a) Power = 20 kW

0.5 0.6 0.7 0.8 0.90

50

100

150

200

p across 1- region

Power = 14.82 kW

p a

cross

1-

reg

ion (

Pa)

Flow rate (kg/s)

Phase plot at 15 kW and 2.2 bar

-3 -2 -1 0 1 2 3-0.2

-0.1

0.0

0.1

0.2

Flo

w -

kg/s

Generally unidirectional oscillations, but more

chaotic than single-phase NC

4600 4800 5000 5200

0

25

50

Time (s)

P -

mm

13000 13500 14000 14500 15000-500

0

500

1000

P -

Pa

Time (s)

7.4 bar (g) pressure

9.1 mm ID tube

The limit cycle is similar to that found in single-phase

flow except that it is more chaotic. Very few studies on

validation of limit cycles

Limit cycle for UDO in

single-phase loop

1200 2400 36000.0

0.7

1.4

2.1

2.8

3.5

Stable 2- flow

Boiling inception

Stable 1- flow

Type-I instability

Loop diameter: 9.1 mm

Pressure: 13.7 bar

P -

Pa

*0.1

;T

su

b -

K

Po

we

r -

kW

Time - s

Power

0

20

40

60

80

100

Tsub

P across flow meter

Experimental Findings on Type-I Instability

The amplitude of type-I oscillations reduce significantly with increase in pressure. Further, type-

I instability is not observed beyond a critical value of the system pressure.

0 4000 8000 12000 160000

200

400

600

800

1000

0

20

40

60

80

100


Pressure: 18.5 bar

Time - s

P -

Pa

Pre

ssu

re -

ba

r (g

)

Stable 2- flow

stable 1- flow

Type-I

instability

1667 W1660 W

1450 W

1309 W

Pressure

Stable 2- flow

stable 1- flow


Pressure: 25 bar

Time - s

P -

Pa

Pre

ssu

re -

ba

r

0 4000 8000 120000

200

400

600

800

1000

0

20

40

60

80

100

4000 5000 60000

250

500

750

1000

Pressure

P -

Pa

P -

Pa

P

Pressure

-4

-2

0

2

4

Pre

ssure

- b

ar

(g)

Pre

ssu

re -

ba

r (g

)

P

(b) Start-up at 5.4 bar

Time - sTime - s(a) Start-up at 3.1 bar

2000 3000 4000 5000 60000

250

500

750

1000

-2

0

2

4

6

Effect of pressure on the instability due to boiling inception in 19.2 mm

i.d. loop

The critical value of

pressure beyond

which type-I instab-

ility disappears is

found to decrease

with increase in the

loop diameter.

Experimental Findings on Type-II Instability (2- NC)

A general characteristic of the type-II instability is that the

oscillation amplitude keeps increasing with power.

0 2000 4000 6000 8000 10000 12000 14000-20

0

20

40

60

80

100

Pressure: 13.5 bar

- P Across bottom horizontal leg

1385 W

1470 W 1598 W1689 W

2995 W

3969 W

1091 W

Upper threshold

Lower

thrshold

L d U th h ld t bilit

P m

m o

f w

ate

r co

lum

n (

1-

)

Pre

ssu

re (

g)-

bar

Time (s)

18000 20000 22000 24000 260000

20

40

60

80

100

4052 W

3634 W2803 W2225 W

1629 W

1400 W

1400 W

1400 W

P m

m w

ate

r colu

mn

Pre

ssure

(g)-

bar

Time (s)

4000 6000 8000 10000 12000 140000

20

40

60

80

100

5060 W

4611 W

2957 W2680 W

2355 W

2068 W

1105 W

P m

m w

ate

r colu

mn

Pre

ssu

re (

g)-

bar

Time (s)

(a) 13 bar (b) 18 bar (c) 25 bar

The upper threshold of instability at different pressures

Type-II instability is found to occur after the flow starts to decrease with increase in

power in the present experiments. Type-II instability occurs in the friction dominant

regime and it occurs at higher qualities.

Prediction of Stability Map

Linear analysis based on the drift flux model is given by Ishii-Zuber(1970)

Saha and Zuber (1978) modified this model by taking into account the effect of thermal nonequilibrium effect.

Thermal nonequilibrium effect predicts a more stable system at low subcooling compared to thermal equilibrium model

These predictions showed poor agreement at high subcooling conditions when compared to experiments

Furutera (1986) showed that the threshold of instability could be predicted with reasonable accuracy using the homogeneous model. However, the two-phase friction multiplier and the heat capacity in the subcooled boiling region has a significant effect

Since then many others showed that it is possible to predict thethreshold of DWI using HEM

Theoretical Findings on Instability (2- NC)

(a) Effect of drift velocity (b) Effect of subcooling

Comparison of measured and predicted stability maps

0 2 4 6 8 100

20

40

60

80

Stable region for 2.5 deg. C and Unstableregion

for 5 deg. C

Stable

Unstable

Tsub

= 5.0 0C

Tsub

= 2.5 0C

Unstable experimental data

Stable experimental data

TINFLO-s

Pow

er (

kW

)

Pressure (bar)

0 10 20 30 40 50 600

4

8

12

16

Stable

Unstable

Loop diameter 9.1 mm

Martinelli-Nelson model

sub=5 K; C

0=1

Experimental threshold of type-I instability

Experimental threshold of type-II instability

Vgj=0

Vgj=0.1

Vgj=0.2

Po

we

r (k

W)

Pressure (bar)

Unstable

The stability of the test loops were studied with a linear stability code TINFLO-S

based on the drift flux model. The drift flux parameters (Co and Vgj) for slug flow

were used as it was the most frequently observed flow pattern during the tests. The

Martinelli-Nelson two-phase friction multiplier model was used in the computations.

Theoretical Findings on Instability (2- NC)

(a) (b)

Predicted stability map for various loop diameters

6 12 18 24 30

0

50

100

150

200

Unstable

Unstablestable

pressure = 70 bar

Po

we

r (k

W)

subcoolng (K)

7 mm 10 mm

15 mm 20 mm

25 mm

7 14 21 28 35

0

30

60

90

Unstable

Unstable

Stable

loop diameter

Pressure = 70 bar

exit q

ua

lity

subcooling (K)

7 mm

10 mm

15 mm

20 mm

25 mm

40 mm

Effect of loop diameter on stability

The stable zone enhances with increase in loop diameter which is consistent with the

test results.

Type-II instability threshold shifts to higher qualities with increase in loop diameter.

Beyond 40 mm loop diameter, the upper threshold is not found in the two-phase

region (i.e. 0<quality<1).

By appropriate choice of the loop diameter, it is possible to eliminate the type-II

instability in the two-phase loops.

Design Considerations (2- NC)

(a) 7mm loop (b) 10mm loop (c) 15 mm loop

Stability controlled designs and loop diameter

0 7 14 21 28 350

5

10

15

20

25

stability map

CHF

Loop diameter = 10 mm

Pressure = 70 bar

Stable

Pow

er

(kW

)

subcooling (K)

Unstable

0 7 14 21 28 350

5

10

15

stability map

CHF

loop diameter = 7 mm

pressure = 70 bar

Pow

er

(kW

)

subcooling (K)

UnstableStable

0 7 14 21 28 350

20

40

60Loop diameter : 15 mm

Pressure : 70 bar

Stability map

CHF

Stable

Po

wer

(kW

)subcooling (K)

Unstable

Unstable

Since both instability and CHF needs to be avoided in the design of two-phase natural

circulation systems two types of designs are possible depending on which of them is

limiting the maximum power that can be extracted.

Stability-Controlled Designs

The maximum power is limited by the stability, as the threshold of type-II instability is

lower than the CHF threshold. This situation arises in small diameter loops.


CHF-controlled Designs

(a) 15 mm (b) 20 mm loop (c) 25 mm loop

CHF controlled designs and effect of loop diameter

7 14 21 28 350

40

80

120

Loop diameter : 20 mm

Pressure : 70 bar

CHF

Stable

Po

we

r (k

W)

subcooling (K)

stability map

Unstable

Unstable

0 7 14 21 28 350

50

100

150

200

CHF

Loop diameter = 25 mm

Pressure = 70 bar

Stable

Po

we

r (k

W)

subcooling (K)

Stability map

Unstable

Unstable

0 7 14 21 28 350

20

40

60Loop diameter : 15 mm

Pressure : 70 bar

Stability map

CHF

Stable

Pow

er

(kW

)

subcooling (K)

Unstable

Unstable

The CHF threshold is much below the type-II instability threshold and

hence CHF limits the maximum power that can be extracted. This

situation arises in large diameter loops.

Design of forced circulation BWRs is usually CHF controlled.


Operating line for stability controlled designs

0 3 6 9 12 150.00

0.25

0.50

0.75

1.00

Loop diameter = 10 mm; Pressure = 70 bar

De

ca

y R

atio

(-)

Power (kW)

Subcooling

5 K

10 K

15 K

Variation of decay ratio while going from

the lower to the upper threshold

Since two-phase NCSs are not

completely stable over the entire

subcooling-power map an operating

line needs to be specified for ensuring

stability for all anticipated operations

like start-up, power raising, and step

back. The decay ratio goes through a

minimum while moving from the

lower to the upper threshold for a

fixed subcooling. Ideally, the

operating line shall pass through the

minimum decay ratio line (locus of all

minimum decay ratio points) so that

all oscillations will die down in the

quickest possible manner.

For stability-controlled designs, one could choose the operating line as

the minimum decay ratio line

1500 2000 25000

100

200

300

400

pressure drop

p -

Pa

/10

7 mm ID test section

TE-13

Trip occured

Te

mp

era

ture

- 0

C

Time (s)

0

25

50

75

100

Unstable oscillations and CHF

Design Considerations

Premature occurrence of CHF and test

section burnout can be an issue during

oscillatory flows in two-phase loops. In

the present experiments, premature CHF

occurrence was observed only for the test

section diameters of 7 and 9.1 mm. The

occurrence of burnout during instability

was more frequent in 7 mm diameter loop

than in 9.1 mm loop. Inspection of the

burnt out test sections revealed that the

burnout is not restricted to the test section

outlet.

In the larger diameter test sections, the CHF power was significantly

large compared to the available power preventing the burnout during

unstable oscillatory flow.

Typical CHF occurrence during

oscillatory flow

Premature Occurrence of CHF

0.01.5

3.04.5

0

5

10

15

20

25

30

35

0.033

0.034

0.035

0.036

Power = 30 kW, Mass flow rate at CHF = 0.03 kg/s, P = 70 bar

CHF Zone

No CHF Zone

Am

plit

ude

(%)

Mean

flow

rate

(kg/s

)

Frequency (Hz)

0

4.375

8.750

13.13

17.50

21.88

26.25

30.63

35.00

Premature occurrence of

CHF is a problem at low

oscillation frequency. It is

also important at high

frequencies if the oscillation

amplitude is large

Concluding Remarks

Single-phase Loops

Using a generalized dimensionless relationship, it is possible to

compare the steady state performance of different loops

Friction factor correlations, wall thermal capacitance and heat

losses significantly affect the prediction of instability threshold

Reasonable prediction of the threshold is possible for fully

laminar and fully turbulent loops if the wall thermal capacitance

and heat losses are accounted

1-D theory is able to predict the trend of the time series and the

different unstable flow regimes. However, the shape of the limit

cycles are significantly different.

3-D effects are important for unstable oscillatory flows and the

applicability of 1-D theory for the prediction of limit cycles is

debateable

Concluding Remarks

Two-phase loops

Lack of generalized dimensionless groups make it difficult to

compare the steady state performance of different loops

The threshold of instability can be predicted with reasonable

accuracy using the homogeneous model. However, the two-phase

friction multiplier and the heat capacity in the subcooled boiling

region has a significant effect

Although, extensive database exists, often it is not possible to

identify the instability type from the data

Very few studies are reported for the validation of the

observed limit cycles

Thank you

Documents

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