2291-16 Joint ICTP-IAEA Course on Science and Technology ...indico.ictp.it/event/a10196/session/26/contribution/19/...two-phase and SC fluid systems Joint ICTP-IAEA Course on Science

2291-16

Joint ICTP-IAEA Course on Science and Technology of Supercritical Water Cooled Reactors

Walter AMBROSINI

27 June - 1 July, 2011

Universita' degli Studi di Pisa Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione

Largo Lucio Lazzarino, 1 56122 Pisa

ITALY

FLOW STABILITY OF HEATED CHANNELS WITH SUPERCRITICAL PRESSURE FLUIDS

Flow stability of heated channels with supercritical pressure fluids

Walter AmbrosiniUniversità di Pisa

Dipartimento di Ingegneria Meccanica Nucleare e del la Produzione

Joint ICTP-IAEA Course on Science and Technology of SCWRs Trieste, Italy, 27 June - 1 July 2011

Objectives

Objectives of this Lecture are:• To review the basic mechanisms of flow instability

• To shortly describe techniques and tools adopted to predict unstable behaviour

• To present a comparison of unstable behaviour in two-phase and SC fluid systems

Joint ICTP-IAEA Course on Science and Technology of SCWRs, Trieste, Italy, 27 June - 1 July 2011 (SC15) Flow stability of heated channels with supercritical pressure fluids

International Atomic Energy Agency

Introduction

• Assuring a stable flow behaviour of industrial equipment is oneof the important design objectives

– instability may perturb operation, challenging control systems– the inadvertent occurrence of oscillations may endanger

sensitive equipment• fatigue• exceeding thermal margins

• Nevertheless, instabilities are often encountered in fluid systemsbecause of

– presence of delays between causes and effects due to transportof perturbations (advection)

– non monotonic trends in pressure drop vs. flow characterist ics– nonlinear behaviour of governing equations (advection terms)– intrinsically unstable flow regimes in multiphase flow



• Classical control theory concepts constitute a useful basi s forunderstanding and modelling linear stability in fluid syst ems

– approach applicable to study the effect of small perturbations , i.e.for linear behaviour

– zeroes and poles of transfer functions define stability conditions– practical stability criteria available (Nyquist, Routh-Hurwitz)

• When nonlinear behaviour is addressed, often transition tochaos by different routes is observed

– generally, periodic behaviour is first observed (limit cycles)– chaos is a deterministic but unpredictable aperiodic behav iour

arising due to sensitivity to initial conditions (SIC ) by differentroutes

Introduction



• In nuclear reactors unstable behaviour may be favoured or af fectedin its nature by the presence of neutronic feedback

– power production is affected by flow oscillations– fluid density variations in moderated systems affect the closed loop

gains (e.g., higher gain --> lower stability)– spatial harmonic modes in nuclear reactor core are affected by the

thermal-hydraulic feedback

• Flow oscillations in nuclear reactors are unwanted because theyperturb the power production and the heat transfer capabili ties

• Unstable behaviour must be therefore prevented or mitigate d inNPPs by different means:

– designing for stable normal operation– avoiding known unstable operating conditions– suppressing instabilities by corrective actions– shutting down the reactor , whenever needed

Introduction



Basic mechanisms of flow instabilitySingle-Phase Natural Circulation

• Even in single-phase natural circulation flow oscillation smay take place as a consequence of delays due to fluidtransit along the loop

• Typical configurations of the more frequently studiedloops are reported hereafter

Heat Exchanger

Electric Heater Warm Wall

Cold Wall

Heating

Cooling

γ



• Unstable behaviour was predicted by Welander in (1967)and then observed in many experimental loops

• An intuitive explanation for this behaviour was alsoprovided in Welander’s paper:– pockets of fluid with perturbed temperature emerging from

the source and the sink result in a perturbation of the flowrate

– this , in turn, affects the residence time of the pockets in thesource and the sink at the subsequent passages;

– thus, for different combinations of physical parameters,temperature perturbations may be damped or amplified .

Basic mechanisms of flow instabilityWelander’s mechanism



-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 2000 4000 6000 8000 10000

Time [s]

Flo

w R

ate

[kg/

s]

Basic mechanisms of flow instabilityFlow rate oscillations


Typical observed or predicted behaviour:the flow oscillates with repeated flow reversals

This mechanism may be possibly active also in supercritical fluid systems


Boiling channel instabilities have a great concern for our discussion, sinceunstable phenomena occurring in them are closer to those env isaged inheated channels with supercritical fluids

Both static and dynamic instabilities are considered:– Static: Ledinegg type , flow regime relaxation, geysering– Dynamic: density-wave , pressure drop, flow regime, acoustic

The pressure drop oscillations occur when a system that woul d be prone tothe static Ledinegg instabilities is coupled with compress ible devicesallowing for dynamic oscillations of the system

We will shortly review only the Ledinegg type and the density waveoscillations

Basic mechanisms of flow instabilityBoiling channels



For a single channel , the Ledinegg instability can be expected when theinternal pressure drop to flow characteristics has a non mon otonous trend

The reference situation is depicted below

Basic mechanisms of flow instabilityStatic Ledinegg type instability


UUppppeerr PPlleennuummwwii tthh iimmppoosseedd

pprr eessssuurr ee

LL oowweerr PPlleennuummwwii tthh iimmppoosseedd

pprr eessssuurr ee

UUUnnniii fff ooorrr mmmHHH eeeaaattt iii nnnggg

Outletorificing

Inletorificing

Distributedfriction

p∆

W

All Vapour

All Liquid

RealCharacteristicswith Negative Slope Region

Monotonous Real

Characteristics

p∆

UUppppeerr PPlleennuummwwii tthh iimmppoosseedd

pprr eessssuurr ee

LL oowweerr PPlleennuummwwii tthh iimmppoosseedd

pprr eessssuurr ee

UUUnnniii fff ooorrr mmmHHH eeeaaattt iii nnnggg

Outletorificing

Inletorificing

Distributedfriction

W

All Vapour

All Liquid

Pressure DropCharacteristicswith Negative Slope Region

Monotonous Presure Drop

Characteristic s

p∆


Depending on the slope of the static external and internal pressure drop-to-flow characteristics, the system can be found stable or unstable in anexcursive way

p∆

W

1extp −∆

2extp −∆intp∆

0W

In fact, representing the systemdynamics by

and linearising by perturbation theequation, it is found

( ) ( )ext int

dWI p W p W

dt= ∆ − ∆

( ) ( ) ( ) ( )

0 0

0 exp ext int

W W W W

d p d p tW t W

dW dW Iδ δ

= =

∆ ∆ = −

The pure exponential trend explains the classification of “excursive”instability. Therefore, the system is stable or unstable if

( ) ( )0 0

ext int

W W W W

d p d p

dW dW= =

∆ ∆< or

( ) ( )0 0

ext int

W W W W

d p d p

dW dW= =

∆ ∆>

Basic mechanisms of flow instabilityStatic Ledinegg-type instability (cont’d)


Different boundary conditions may result in different stab ilitycharacteristics :

– an imposed flow condition (e.g., positive displacement pump) always stabilizesthe system

– an imposed external pressure drop condition (single channel in a bunch ofmany) may make the system unstable

p∆

W

imposed

flow

0W

p∆

W0W

imposed

external p∆

1P 2P0P0P

1W 2W

In the latter case, the system drifts from the unstable P 0 point to either P1 orP2, which are stable

Basic mechanisms of flow instabilityStatic Ledinegg type instability (cont’d)

International Atomic Energy AgencyJoint ICTP-IAEA Course on Science and Technology of SCWRs, Trieste, Italy, 27 June - 1 July 2011 (SC15) Flow stability of heated channels with supercritical pressure fluids

Unlike Ledinegg instability, density-wave oscillations represent a dynamicphenomenon , i.e., their occurrence depends on the dynamic characteristics ofthe systems

Simplified Rational Explanation:If sinusoidal flow perturbationshaving different frequency areapplied to the system, for a givenfrequency the perturbation inpressure drop may be out-of-phase with the flow perturbation�� THE PERTURBATION

IS AMPLIFIED

t

inWδ

( )totpδ ∆

In fact, at that frequency the system reacts as it had a negative hydraulicimpedance

IF A SYSTEM IS UNSTABLE AT SOME SELECTED FREQUENCY IT MUST BE CONSIDERED UNSTABLE

Basic mechanisms of flow instabilityDensity-wave oscillations



Though the static pressure drop vs. flow rate characteristics does not help todecide if a system is stable or not under certain conditions , it identifies theregion where instability may occur ; i.e., for a a constant pressure drop:

p∆

W

extp∆

DWO Ledinegg

Outletorificing

Inletorificing

Upper PlenumUpper Plenumwithwith imposedimposed

pressurepressure

LowerLower PlenumPlenumwithwith imposedimposed

pressurepressure

UniformUniformUniformHeatingHeatingHeating

Distributedfriction

Outletorificing

Inletorificing

Upper PlenumUpper Plenumwithwith imposedimposed

pressurepressure

LowerLower PlenumPlenumwithwith imposedimposed

pressurepressure

UniformUniformUniformHeatingHeatingHeating

Distributedfriction

Basic mechanisms of flow instabilityDensity-wave oscillations



• If properly linearised, the governing equations for two-ph ase flowmay be used to provide stability maps in the Ishii-Zuber plan e, i.e.the plane of the phase change number and the subcoolingnumber, for selected values of the other dimensionlessparameters ( ΛΛΛΛ, Fr, K in, Kout , etc.)

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

Stable

Constant Zr Lines

Unstable for DWOs

Unstable f

or Ledinegg I

nst.

FourSample

OperatingPoints

( )Aρlnt

zR ∆= 1

,

, ,

lv satpch

lv sat l sat

vQN

W h v=

&

, ,

, ,

l sat in lv satsub

lv sat l sat

h h vN

h v

−=

In this figure, ZR is adimensionless amplificationfactor positive for unstableand negative for stableconditions

Basic mechanisms of flow instabilityStable and unstable behaviour in boiling channels


Dimensionless power-to-flow ratio

Dimensionless degree of subcooling


0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

2.000

0 2 4 6 8 10 12

Dimensionless Time

Dim

ensi

onle

ss In

let F

low

Positive PerturbationNegative Perturbation

Npch = 12, Nsub = 3

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

2.000

0 5 10 15 20 25

Dimensionless Time

Dim

ensi

onle

ss In

let F

low


Npch = 12, Nsub = 5

0.985

0.990

0.995

1.000

1.005

1.010

1.015

0 10 20 30 40 50

Dimensionless Time

Dim

ensi

onle

ss In

let F

low


Npch = 12, Nsub = 7

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

0 10 20 30 40 50Dimensionless Time

Dim

ensi

onle

ss In

let F

low


Npch = 12, Nsub = 9

DWO DWO

DWO Ledinegg


Basic mechanisms of flow instabilityStable and unstable behaviour in boiling channels

See the definition of the operating points in the p revious page

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

Kin=1

Kin=12

Kin=6

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

Kex=6

Kex=0

Kex=2

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

Λ=0Λ=5

Λ=2.85

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

bFr=0.333

Fr=0.002

Fr=0.033

Inlet pressure drops increase stability

Outlet pressure drops decrease stability

Distributed friction has a mixed effect

The Froude number also changes the Ledinegg instability region

Basic mechanisms of flow instabilityParametric effects for boiling instabilities


Harmonic modes of neutron distribution in BWR cores

may change their level of subcriticality due to thermal-hydraulic feedback ,resulting in CORE WIDE or OUT-OF-PHASE (regional) power oscillations,triggered by density waves, at relatively high power-to-fl ow ratios

022 =+∇ nnn B ϕϕ

%Power

%Flow

100

50

030

Possible

Instability

Region

Exclusion

Region

Line of Operation

with Pumps

Line of Operation

in Natural Circulation

Core wide

Power Oscillations

−

Regional

Power Oscillations

when the fundamental

mode is the most unstable

when higher order modes are most unstable

Basic mechanisms of flow instabilityCoupled neutronic and thermal-hydraulic effects


Basic mechanisms of flow instabilityCoupled neutronic and thermal-hydraulic effectsA functional sketch of the interaction between thermal-hyd raulic and neutroniceffects in reactor cores is reported hereafter.This is also a sketch of the aspects requiring a proper modell ing


Basic mechanisms of flow instabilitySCWR phenomena

• Stability is addressed as an issue of great importance for SCWR design

• Heated channels with supercritical pressure fluids are ass umed to besusceptible to similar instability phenomena as observed i n boiling channels

• The transition across the pseudocritical temperature can b e considered as asort of “pseudo-boiling” phenomenon, giving rise to denser fluid at channelinlet and lighter one at the outlet

• This is one of the reasons why the basic understanding and the numericaltools developed for two-phase flow instabilities are found immediatelyavailable for being converted into understanding and numer ical tools to beapplied to supercritical pressure instabilities

• The scarcity of relevant experimental data on instabilitie s in supercriticalpressure systems is presently a problem to be coped with in order toascertain that this process of knowledge transfer from one r esearch field toanother is made without forgetting any important differenc e



While two-phase flow models must be used for the thermal-hyd raulic analyses ofBWR stability, single-phase flow governing equations with allowance for s trongproperty changes are sufficient for SCWRs

This remarkable simplification should not mislead:– the heavy (liquid-like) and light (gas-like) fluid may be un evenly distributed in the

channel cross section giving rise to buoyancy phenomena aff ecting transfers in acomplex way

– specific constitutive laws are required (and still under de velopment) to representsupercritical fluid phenomena

So, a complex behaviour is anyway expected even if the govern ing equations aresimpler with respect to the two-phase flow case

Tools for predicting unstable behaviourGoverning equations


“Codes” is the name adopted for complex computer programs adopted innuclear reactor analysis

– Time domain codesThey are based on some kind of numerical discretisation and integration in timeThey are suitable for predicting the transient behaviour in a free or forced evolutionof a system, even beyond the stability limitThey are affected at different extent by truncation error effects

– Frequency domain codesThey are so called because they are based on linearised equations that areconverted to transfer functions by Laplace transformThey are therefore suitable to predict the stability thresholdThe classical control theory principles are therefore used to study stabilityThe algebra they are based on is sometimes very cumbersome

Codes of both categories can be very complex addressing many real plantdetails (see the previous sketch of coupled effects)

Tools for predicting unstable behaviourGeneral classification



Classical two-phase flow system codes can be adopted for sup ercritical fluidanalyses provided their property packages allow for the cal culation atsupercritical pressure; only the single-phase version of g overning equations isobviously necessary

As mentioned, they should be upgraded for application at sup ercritical pressuresby appropriate constitutive laws for heat transfer and fricti on

At the moment, classical transient codes for the safety anal ysis of LWRs(RELAP5, TRACE, etc.) are applied to supercritical pressur es with no majornumerical problem, unless the critical pressure is crossed or the operatingpressure is too close to the critical one

In addition to heat transfer and friction, critical flow from supercritical pressureconditions is another field needing development

Tools for predicting unstable behaviourModels and codes



• As mentioned heated channels with boiling and supercritica l fluidsshare a common basic feature

THE FLUID ENTERS THE CHANNEL AT HIGH DENSITY AND GETS OUT OF IT AT LOW DENSITY BECAUSE OF HEATIN G

• The related instability phenomena can be considered quite s imilarbecause of this basic similarity

• Dimensionless numbers to study stability were proposed by v ariousAuthors in similarity with the classical phase change and su bcoolingnumbers adopted for boiling channels

Two-phase vs. SC flow stability phenomenaBasic reasons for similarity




1 - “Heavy fluid” region

2 - “Heavy and light fluid mixture” region

Two-phase vs. SC flow stability phenomenaDimensionless numbers for SC flow stability

Zhao et al. (2005)


Zhao et al. (2005)

• Feedback loop of the transferfunctions for the pressure drops inthe three regions


•Typical stability map

3 - “Light fluid” region



Ortega Gómez et al. (2006)• These authors propose two dimensionless numbers similar to the ones

adopted for boiling channels



Ortega Gómez et al. (2006)• The balance equations are discretised by FEMLAB

• Typical stability map




Yeylaghi et al. (2011)• The Authors use a very compact and simple dimensionless form alism

derived from balance equations applied in the prediction of staticinstabilities

(e = exit, i = inlet)


• Typical results show a verysuccessful prediction ofstability boundaries, fordifferent fluids and also fordifferent channel orientations

• The outlet temperature at theonset of excursive insta-bilities is also found close tothe pseudocritical value


• In analogy with the case of the boiling channel, the followin gdimensionless parameters were introduced (Ambrosini and S harabi,ICONE14, 2006):

• These definitions do not need introducing any fictitious ps eudo-saturated state and make reference to the single thermodynamic statethat really matters in supercritical fluids: the pseudocri tical point



Ambrosini and Sharabi (2006)


The 1D dimensionless balance equations therefore become

with the inlet boundary condition

* * * * * *

* * * *0 0

w w

L t L z t z

∂ ρ ∂ ρ ∂ ρ ∂ ρ∂ ∂ ∂ ∂

⇒ + =

* * * * ** *

* *( )TPC q

h w hN f z

t z

∂ ρ ∂ ρ∂ ∂

′+ =

* * * *2 *

* * *

w w p

t z z

∂ ρ ∂ ρ ∂∂ ∂ ∂

+ +*

* * * * * *2( ) ( 1)in exK z K z wFr

ρ δ δ ρ = − − Λ + + −

( )*

,

pcin in pc SUBPC

p pc

h h h NC

β= − = −




SPC


One of the useful features of the definition of dim ensionless density isits capability to collapse all the trends as a func tion of dimensionless enthalpy nearly into a single line no matter the pr essure





The trans-pseudocritical number is defined as

having the meaning of a power-to-flow dimensionless ratio; in fact, it is:

Therefore, in similarity with boiling channels for N PCH and NSUB, in the N TPC -

NSPC plane the lines for which NSPC = NTPC + const. represent the loci at

constant exit dimensionless enthalpy

* 0

0 ,

pchTPC TPC in

in p pc

q LN N

w A C

βρ

ρ′′Π′= =

,

pcchannelTPC TPC in

channel p pc

QN N

W C

β= =

&





Comparison betweentransient code behaviourwith stability mapsproduced for an IAEACode ComparisonBenchmark




RELAP5 is used incomparison within house codes

In-house transient code and for vertical and horiz ontal channel

Boiling Channels Heated Channels with Supercritical Fluids

Bearing in mind the boiling channel paradigma,heated channels with supercritical fluids are also predicted to show both density-

wave oscillations and Ledinegg excursive instabilit ies

0 5 10 15 20 25 30

Npch

0

5

10

15

20

Nsu

b

Stable

Unstable for DWOs

Ledinegg

Stable

Nnodes = 48, Kin = 12, Kout = 2, Fr = 0.05, Λ = 3.687

Ledinegg Instability

DWO Instability


Two-phase vs. SC flow stability phenomenaComparison of Stability Maps


Boiling Channel Heated Channels with Supercritical Water

0.120

0.125

0.130

0.135

0.140

0.145

0.150

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Axial Coordinate [m]

Mas

s F

low

Rat

e [k

g/s]

Time = 310.5 sTime = 312.1 s

0.030

0.035

0.040

0.045

0.050

0.055

0.060

0.065

0.070

0.00 1.00 2.00 3.00 4.00 5.00


Mas

s F

low

Rat

e [k

g/s]

Time = 3088.8 sTime = 3090.7 s

0

100

200

300

400

500

600

700

800

900

1000

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00


Mix

ture

Den

sity

[kg/

m3 ] Time = 310.5 s

Time = 312.1 s

0

100

200

300

400

500

600

700

800

900

1000

0.00 1.00 2.00 3.00 4.00 5.00


Flu

id D

ensi

ty [k

g/m

3 ]

Time = 3088.8 sTime = 3090.7 s


Two-phase vs. SC flow stability phenomenaComparison of Transient Behaviour

System codes

Density waves appear as a sort of flow

wave phenomenon in both cases




System codesTo study stability with a system code, time histories of NTPC vs. time areobtained while power is slowly increased and an automatic or visual criterion isused to identify the threshold for unstable behaviour

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 200 400 600 800 1000 1200

Time [s]

Tra

ns-P

seud

ocrit

ical

Num

ber


Both models show swings of flow rate distribution similar to those predicted by 1D codes:

again, the global instability mechanism appears the same

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5


Mas

s F

low

Rat

e [k

g/s]

258.00 s260.00 s

Time [s]

Standard k-e with Wall Functions - Kin = 0, Kout = 0

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5


Mas

s F

low

Rat

e [k

g/s]

49.9051.30

Yang-Shih Model - Kin = 0, Kout = 0

Time [s]

k-εεεε with wall functions low-Re Yan g & Shih model



CFD Codes – Circular Pipes

Also the FLUENT code was applied

to study density wave

oscillation instabilities


A major difference is found in the capability of th e low-Re model to identify heat transfer deterioration during osci llations:

wall functions cannot catch the occurrence of this phenomenonthat resembles Boiling Transition occurring during instabilities in BWRs

250

300

350

400

450

500

550

600

650

700

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5


Wal

l Tem

pera

ture

[°C

]

Time = 258 sTime = 260 s

300

400

500

600

700

800

900

1000

1100

1200

1300

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5


Wal

l Tem

pera

ture

[°C

]

Time = 49.9 sTime = 51.3 s

k-εεεε with wall functions Yang & Shih model



CFD Codes – Circular Pipes


The standard k- εεεε model of FLUENT was used with wallfunctions addressing the following cases

for the triangular pitch subchannel: o rod diameter: 7.6 mm; o pitch: 8.664 mm; o active height: 3 m.

for the square pitch subchannel: o rod diameter : 10.2 mm; o pitch: 11.2 mm; o active height: 4.2 m;


Two-phase vs. SC flow stability phenomenaComparison of Transient BehaviourCFD Codes – Fuel Bundle Slices


By raising the power to appropriate levels , while keepingconstant the pressure drop across the channel, unstablebehaviour is observed in both cases

0 10 20 30 40 50

Time (s)

3880

3920

3960

4000

4040

4080

Po

wer

(W

)

triangular pitch assemblyinlet flow rateoutlet flow rateheating power

-0.002

0

0.002

0.004

0.006

0.008

Mas

s fl

ow

rat

e (k

g/s

)

0 20 40 60

Time (s)

10800

11000

11200

11400

11600

11800

Po

wer

(W

)

-0.01

0

0.01

0.02

0.03

Mas

s fl

ow

rat

e (k

g/s

)

square pitch assemblyinlet flowoutlet flowheating power




The same mechanism of flow oscillations is observed as in thecase of circular pipes

AGAIN, IT SEEMS THAT THE OVERALL INSTABILITY MECHAN ISM IS SIMILAR AS PREDICTED BY 1D MODELS

0 1 2 3

Axial coordinate (m)

0.0012

0.0016

0.002

0.0024

0.0028

Mas

s fl

ow

rat

e (k

g/s

)

Triangular pitch assemblyt = 32.8 st = 33.6 s

0 1 2 3 4 5

Axial coordinate (m)

0

0.002

0.004

0.006

0.008

0.01

0.012

Mas

s fl

ow

rat

e (s

)

square pitch assemblyt = 41.2 st = 42.6 s





Conclusion

Flow instabilities in supercritical pressure fluid system s are predictedin close similarity with those observed in two-phase flow

A plenty of tools and theories developed for boiling channelinstabilities is available to be used with supercritical fl uids

Though this lecture covered only basic aspects , in comparison withthe two-phase flow case, the complexity of these tools can beconsiderable, including the coupling with neutronics and t he differentrelevant reactor systems as reported in some of the works whosereading is suggested in the References

Experimental data are presently needed to confirm the predi ctionsobtained by available tools


Thank you for your attention,

Walter Ambrosini



Description of Basic Phenomena related to Boiling Channel Instabilities

Bourè, J.A., Bergles, A.E., Tong, L.S., 1973"Review of Two-Phase Flow Instability“, Nuclear Engineering and Design,25, (1973), pp.165-192.

D’Auria, F., (Editor) et al., 1997"State-of-the-Art Report on Boiling Water Reactor Stability" , NEA/CSNI/R(96)21,OCDE/GD(97)13, OECD/NEA Paris, 1997.

Lahey, R.T., and Moody, F.J., 1993,“The thermalhydraulics of a boiling water reactor” , American Nuclear Society1993.

March-Leuba, J., and Rey, J.M., 1993"Coupled Thermohydraulic-Neutronic Instabilities in Boiling Wate r NuclearReactors: A Review of The State of the Art", Nuclear Engineering and Design, 145, (1993), pp. 97-111.

Specific works mentioned in the lecture

Ortega Gómez, T., Class, A., Lahey, R.T., Jr., Schulenberg, T., 2006 and 2008,“Stability analysis of a uniformly heatedchannel with supercritical water” , Nuclear Engineering and Design 238 (2008) 1930–1939. Also published in 2006 atICONE-14.

Yeylaghi, S., Chatoorgoon, V., and Leung, L., 2011,“Assessment of non-dimensional parameters for static instabilityin supercritical down-flow channels”, The 5th Int. Sym. SCWR (ISSCWR-5), P69, Vancouver, British Columbia,Canada, March 13-16, 2011

Zhao, J., Saha, P., Kazimi, M.S., 2005.Stability of supercritical water-cooled reactor during steady-state and slidingpressure start-up.The 11th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11), Paper:106, Popes’ Palace Conference Center, Avignon, France, October 2-6, 2005.


References


Works on Supercritical Pressure Instabilities whose reading is particularly suggested

Cai, J., Ishiwatari, Y., Ikejiri, S., Oka, Y., 2009,“Thermal and stability considerations for a supercritical water-cooledfast reactor, with downward-flow channels during power-raising phase of plant startup”, Nuclear Engineering andDesign 239 (2009) 665–679.

Yi, T.T., Koshizuka, S., Oka, Y., 2004. “A linear stability analysis of supercritical water reactors, (I) thermal–hydraulic stability”, Journal of Nuclear Science and Technology 41, 1166–1175.

Yi, T.T., Koshizuka, S., Oka, Y., 2004.“A linear stability analysis of supercritical water reactors, (II) coupledneutronic thermal–hydraulic stability”, Journal of Nuclear Science and Technology 41, 1176–1186.

Zhao, J., Saha, P., Kazimi, M.S., 2008,“Core-wide (in-phase) stability of supercritical water-cooled reactors - I:Sensitivity to design and operating conditions”, Nuclear Technology Volume 161, Issue 2, February 2008, Pages 108-123

Zhao, J., Saha, P., Kazimi, M.S., 2008,“Core-wide (in-phase) stability of supercritical wayer-cooled reactors - II:Comparison with boiling water reactors” , Nuclear Technology, Volume 161, Issue 2, February 2008, Pages 124-139

Zhao, J., Saha, P., Kazimi, M.S., 200c,“Coupled neutronic and thermal-hydraulic out-of-phase stability ofsupercritical water-cooled reactors, Nuclear Technology”, Volume 164, Issue 1, October 2008, Pages 20-33

Zuber, N., 1966,“An analysis of thermally induced flow oscillation in the near-critical and supercritical thermal-dynamic region”, Report no. NASA-CR-80609, General Electric Co., NY, USA.


References


Works by the Lecturer

W. Ambrosini, P. Di Marco and J.C. Ferreri,"Linear and Non-Linear Analysis of Density-Wave InstabilityPhenomena",International Journal of Heat and Technology, Vol. 18, No. 1, 2000, pp. 27-36

W. Ambrosini, M. Sharabi, 2006 and 2008,“Dimensionless parameters in stability analysis of heated channels withfluids at supercritical pressures”, Nuclear Engineering and Design 238, (2008) 1917–1929. Also published in 2006 atICONE-14.

W. Ambrosini“On the analogies in the dynamic behaviour of heated channels with boiling and supercritical fluids” ,Nuclear Engineering and Design, Vol. 237/11 pp 1164-1174, 2007.

W. Ambrosini and M. Sharabi,“Assessment of Stability Maps for Heated Channels with Supercritical Fluids versusthe Predictions of a System Code”, Nuclear Engineering and Technology, Vol. 39, No. 5, October 2007.

M. Sharabi, W. Ambrosini, S. He, J.D. Jackson“Prediction of turbulent convective heat transfer to a fluid atsupercritical pressure in square and triangular channels”, Annals of Nuclear Energy, Volume 35, Issue 6, June 2008,Pages 993-1005.

M. Sharabi, W. Ambrosini, S. He, Pei-xue Jiang, Chen-ru Zhao, “Transient 3D Stability Analysis of SCWR Rod BundleSubchannels by a CFD Code”, ICONE-16, 16th International Conference on Nuclear Engineering, May11-15, 2008,Orlando, Florida USA.

Walter Ambrosini, “Discussion on the stability of heated channels with different fluids at supercritical pressures”,Nuclear Engineering and Design, 239 (2009) 2952–2963.

Walter Ambrosini,“Assessment of flow stability boundaries in a heated channel with different fluids at supercriticalpressure”, Annals of Nuclear Energy 38 (2011) 615–627.


References


Documents

2291-16 Joint ICTP-IAEA Course on Science and Technology ...indico.ictp.it/event/a10196/session/26/contribution/19/...two-phase and SC fluid systems Joint ICTP-IAEA Course on Science