INTRODUCTION TO INSTABILITIES IN NATURAL CIRCULATION SYSTEMS

INTRODUCTION TO INSTABILITIES IN NATURAL CIRCULATION SYSTEMS

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-6)

- INTRODUCTION

- STABILITY OF SINGLE-PHASE NC

- CLASSIFICATION OF INSTABILITIES

- INSTABILITY DUE TO BOILING INCEPTION

- TWO-PHASE NC INSTABILITY

- CONCLUDING REMARKS

OUTLINE OF THE LECTURE T#6

INTRODUCTION

Instabilities are common to both FC and NC systems

NCSs are more unstable. A regenerative feedback is inherent in the mechanism causing NC

Both single-phase and two-phase NCSs exhibit instability whereas only two-phase FCSs are known to exhibit instability

Even two-phase NCSs are more unstable than two-phase FCSs

Any change in the driving force will affect the flow which in turn modifies the driving force leading to a transient oscillatory state even in cases which results in an eventual steady state

stable

Neutrally stable

unstable

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- Following a perturbation if a thermal-hydraulic system returns to its original steady state, then the system is considered to be stable

What is instability?

- If the system continues to oscillate with the same amplitude, then it is considered as neutrally stable

-If the system oscillates with increasing amplitude or shift to a new steady state, then it is considered as unstable

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Limit Cycle OscillationsIn all practical systems oscillation growth cannot continue indefinitely. Instead, oscillation growth is terminated by system nonlinearities leading to limit cycle oscillations

Time seriesLimit Cycle,Phase space (plot ortrajectory), orbit

System nonlinearities

- System temperature cannot be lower than the sink temperature

- Void fraction can only vary between zero and unity

- Neutron flux cannot be negative

DISADVANTAGES OF INSTABILITY

- Premature CHF occurrence can be induced by flow oscillations

- Instability can disturb control systems and pause operational problems in nuclear reactors.

- Sustained flow oscillations may cause forced mechanical vibration of components

- Induce undesirable secondary effects like power oscillations in a BWR

Classification of instabilities

Several kinds of instabilities are observed in NCSs excited by different mechanisms

A fundamental cause of all instabilities is due to the existence of competing multiple solutions so that the system is unable to settle down to any of them permanently

However, differences exist in the transport mechanism, oscillatory mode, phase shift, the nature of the unstable threshold, and its prediction methods

Loop geometry and induced secondary phenomena also affect the instability

Instabilities are classified according to various bases

- analysis method

- propagation method

- nature of the oscillations

- loop geometry,

- disturbances or perturbations

Classification of instabilities – Contd.

Analysis method (or Governing equations used)

Pure static instabilityThe occurrence of multiple solutions and the instability threshold itself can be predicted from the steady state equations governing the process

Examples are Ledinegg instability and the instability induced by the occurrence of CHF

(a) Pure (or fundamental) static instability(b) Compound static instability(c) Pure dynamic instability(d) Compound dynamic instability


Compound static instability

In some cases of multiple steady state solutions, the instability threshold cannot be predicted from the steady state laws alone or the predicted threshold is modified by other effects.

In this case, the cause of the instability lies in the steady state laws, but feedback effects are important in predicting the threshold

Typical examples are the instability due to flow pattern transition, flashing and geysering


Pure Dynamic instability

For many NCSs neither the cause nor the threshold of instability can be predicted from the steady state laws as inertia and feedback effects are important

In this case, there are no multiple steady states, but the multiple solutions appear during the transient

The full transient governing equations are required for explaining the cause and predicting the threshold of instability

Typical example is the density wave oscillations commonly observed in NCSs


Compound dynamic instability

In many oscillatory conditions, secondary phenomena gets excited and it modifies significantly the characteristics and the threshold of pure dynamic instability

In such cases even the prediction of the instability threshold requires consideration of the secondary effect

Typical examples are

- neutronics responding to the void fluctuations

- primary fluid dynamics affecting the SG instability


Propagation method

This classification is restricted to only dynamic instabilities. Dynamic instabilities involve propagation or transport of disturbances. The disturbances can be transported by two kinds of waves

- Pressure or acoustic waves

- Density waves (Stenning and Veziroglu)

In two-phase flow, both waves are present, however, their velocities differ by one or two orders of magnitude allowing us to distinguish between the two

DWI is the most commonly observed instability. The frequency of DWI is of the order of 1 Hz in 2- flow


Based on the nature of oscillations - Flow excursions, - Pressure drop oscillations, - Power oscillations, - Temperature excursions

Based on the periodicity - Periodic oscillations- chaotic oscillations

Based on the oscillatory mode – Fundamental mode

- Higher harmonics

Based on the phase lag - in-phase oscillations, - out-of-phase oscillations- dual oscillations

Based on flow direction - Unidirectional oscillations- Bi-directional oscillations- Chaotic switching


Based on the loop geometry

- Open U-tube oscillations

- Pressure drop oscillations

- Parallel channel oscillations

Based on the disturbances

Certain two-phase flow phenomena cause a major disturbance and induce or modify the instability in NCSs

- Boiling inception- Flashing and geysering- Flow pattern transition- Occurrence of CHF

H

CC

F 0

Time


Closure

The classification based on the analysis method is the most widely accepted one and covers all observed instabilities

All other classifications addresses only a subset of the instabilities

It does not differentiate between NC and FC systems

Most instabilities observed in FC systems are observed in NCSs

However, certain instabilities associated with NCSs are not observed in FCSs – Single-phase instability and the instability associated with flow direction

Hence a specific discussion of instabilities for single-phase and two-phase NCSs is considered useful


STABILITY OF SINGLE-PHASE NCSs

Single-phase NC instabilities can be characterised into three different types

- Static instabilities associated with multiple steady states- Dynamic instabilities- Compound dynamic instabilities

Pure Static instability

Traditionally pure static instability is associated with multiple steady states in the same flow direction

Theoretically certain single-phase NCSs show multiple steady states in the same flow direction. So far no experimental confirmation exists

Multiple steady states in the same flow direction

Multiple steady states with differing flow directions

coolant

Q1

Q2=0

Q1

Q2>Qc

Steady Clockwise flow (Q2=0)

Anticlockwise flow with Q2>Qc

STABILITY OF SINGLE-PHASE NCSs – Contd.

Multiple Steady states with differing flow direction

- Instability with oscillation growth will set in as Q2 nears Qc

- The instability will be terminated by flow reversal- Subsequently even if we reduce power below Qc, instability will not be observed. Also flow will continue in the reverse direction

- The instability cannot be predicted from steady state laws alone

Unlike FC, certain NC systems can exhibit steady flow in both clockwise and anticlockwise directions

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Multiple steady states with differing flow directionsInstability associated with flow reversal in single phase NCS

Similar behaviour is observed in a NCS with throughflow

Even though the flow initiates in the anticlockwise direction, steady flow was never obtained

Stability analysis showed that no steady flow exists with upward flow in the cooler for this loop geometry

Upward flow in the cooler or downward flow in the heater can lead to similar behaviour

Multiple steady states with differing flow directions

Figure-of-eight loop with throughflow

Multiple steady states with feed in header 2 and bleed from header 3 compared with test data

Multiple steady states with differing flow directionsInstability near the flow reversal threshold: With small throughflow, the initial NC flow direction is preserved. As the throughflow is large enough, it reverses the NC flow. Near the flow reversal threshold an instability is observed

F F F F

W+F

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Typical unstable behaviour near the flow reversal threshold.

The oscillation amplitude is larger in the low flow branch

Experiments showed that the flow reversal threshold depends on the operating procedure (hysteresis)

The amplitude of the oscillations increase as the flow reversal threshold approaches

Parallel channel NC systems

Qb

Qm

Qt

cooler

ht

hm

hb

Unequally heated parallel horizontal channels having unequal elevations relevant to PHWRs

Existence of multiple steady states was first explored by Chato (1963)

heat

er

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hm

hl

Parallel vertical inverted U-tubes relevant to

SGs

dow

ncom

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Wn

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W1

Vertical parallel channel system relevant to the RPV of BWRs, PWRs, etc.

Inlet header

Outlet header

Q

Unequally heated parallel channel NC systems exhibit an instability associated with flow reversal due to the existence of mutually competing driving forces

coolant

Vertical parallel channel systeminlet header

outlet header

Q2

W2

Q1

W1 H

W

DowncomerW

Parallel Channel Systems

There is a driving force between thedowncomer and each heated channel promoting upward flow through the heated channels

There is another driving force betweentwo unequally heated channels (due to the difference in densities) favouring downward flow in the low power channel

The actual flow direction is decided by the greater of the two driving forces


coolant

(a) Vertical parallel channel system

inlet header

outlet header

Q2

W2

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H

W

Dow

nco

mer

W

For an unheated channel, upward flow is unstable and stable downward flow can prevail.Keeping Q2 constant, if we increase Q1 then flow reversal in channel 1 occurs if Q1 > Qc (Chato (1963))

Keeping Q2 constant, if we reduce Q1, then the upward flowing channel 1 flow will reverse if Q1<Qc

(Linzer and Walter (2003))

The flow reversal threshold is a function of the power of channel 2.

Channel flow reversal is undesirable as it can lead to instabilities in two-phase systems


It appears that channel flow reversal can be avoided in a system of vertical parallel channels if all the channels are equally powered

However, with vertical inverted U-tubes (as in SGs) and horizontal channels as in PHWRs, mutually competing driving forces exist even if all the channels are equally powered due to the differences in elevation.

Single-phase NC with reverse flow in some of the longest U-tubes are observed in several integral test loops

Steady state with one of the channels flowing in the reverse direction was observed during thermosyphon tests in NAPS

BOTTOM HEADER

TOP HEADER

COOLANT INLET COOLANT OUTLET

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BOTTOM HEADER

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COOLANT INLET COOLANT OUTLET

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Initial steady state was achieved with equal power to Ch-1,2 & 3 and Ch-4 unheated. Ch- 1, 2 & 3 are with upflow and Ch-4 with downflow. Power in Ch-1 was decreased keeping other channels’ power constant. The BLACK curve starts at A. After reaching a power ratio corresponds to B, the flow in Ch-1 reverses from upflow (+ve) to downflow (-ve) and the curve jumps from state B to state C. For the second case, initial steady state was achieved with equal power to Ch-2 & 3 and Ch-1 & 4 unheated. i.e. Ch-2 & 3 with upflow and Ch-1 & 4 with downflow. The BLUE curve starts at D. Power in Ch-1 was increased. After reaching a power ratio corresponds to E, the flow in Ch-1 reverses from downflow (-ve) to upflow (+ve) and the curve jumps from state E to state F.

A

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Dynamic Instability in single-phase NCSs

Essentially the dynamic instability in single-phase systems is also DWI although it was referred to as DWI only recently (Lahey, Jr)

The frequency of DWI in single phase NC (0.0015 – 0.005 Hz) is significantly lower than that in two-phase systems (1-10Hz) due to the low velocities in single-phase NC

Two types of dynamic instabilities are observed in single-phase NCSs- Single channel system instabilities- Parallel channel instabilities

System Instabilities


Flo

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Keller (1966)

All these oscillatory modes can be observed in rectangular loops for different ranges of power

Expansion tank

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Oscillation growth as a mechanism of single-phase instability proposed by Welander (1967)

- Oscillation growth is the usual route to instability from steady state - Compound static instability also shows oscillation growth, but the instability is terminated by flow reversal

Parallel Channel Instability

Parallel channels also exhibit a dynamic instability mode in single-phase conditions

The instability occurs due to the redistribution of flow

Both in-phase and out-of-phase oscillations are predicted

Two-phase NC instabilityPure static instabilityCompound static instabilityDynamic instabilityCompound Dynamic instability

Pure static instability

Flow excursion or excursive (Ledinegg) instabilityBoiling Crisis

Ledinegg instability

Involves sudden change of flow rate to a lower valueThe new flow rate may induce CHFOccurrence of multiple steady states is the fundamental cause of the instability

Ledinegg instability – Contd.

Driving pressure differential

Two-phase system characteristic

a b c

Flow rate

Head

dow

ncom

er

Feed

Steam

heat

er

riser

It occurs during the negative sloping region of the p – W characteristic; d(p)/dW < 0 is the criterion for the Ledinegg instability

Point ‘b’ satisfies this criterion and is therefore unstableThe instability can be avoided by inlet throttling in FCSsInlet throttling may not work as effectively as in FCSs due to the reduction in flow caused by it

Boiling Crisis

Following the occurrence of critical heat flux, a regime of transition boiling may be observed as in pool boiling

Transitionboiling

Filmboiling

Hea

t fl

ux

Ts - Tsat

Nucleate boiling

Natural convection

During transition boiling a film of vapour prevents the liquid from coming in direct contact with the heating surface resulting in a steep rise in temperature

The film itself is not stable causing repetitive wetting and dewetting of the heating surface resulting in an oscillatory surface temperatureThe instability is characterized by sudden rise in wall temperature followed by an almost simultaneous occurrence of flow oscillations

Compound Dynamic Instability

Two-phase NCSs also show an instability associated with flow direction as in single-phase NC

All instabilities associated with boiling inception, flashing and geysering, etc. can also be considered as part of two-phase NC instability.

Flow pattern transition instability also belong to this category

Two-phase parallel channel systems exhibit - Multiple steady states in the same flow direction

- An instability associated with flow reversal as in single-phase flow

Flow Pattern Transition InstabilityTwo-phase systems exhibit different flow patterns with differences in pressure drop characteristics which is the fundamental cause of the instability

Bubbly-slug flow has a higher pressure drop compared to annular flow

A system operating near the slug to annular transition boundary is susceptible to this instability

Theoretical analysis of the phenomena is hampered by the unavailability of validated flow pattern transition criteria and flow pattern specific pressure drop correlations

The instability is found to be similar to Ledinegg instability, but occurs at higher power

Fukuda-Kobori

Type-I instability

Type-II instability

Stable two-phase NC

Fig. 1a: Typical low power and high power unstable zones for two-phase NC flow

Single-phase region

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The low power unstable regionis called the type I instability

In view of the occurrence of islands of instability, the unstable zones can be more than 2.

Generally two unstable regionsare observed for DWI

The number of unstable or stable zones depends on the shape of the stability map

The high power instability iscalled the type II instability

Dynamic instabilities in Two-phase NCSs

Boiling inception during stable single-phase flow

Stable single-phase flow can become unstable with the inception of boiling

The instability due to boiling inception disappears at high pressure

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Large variation of void fraction with small changes in quality at low pressures is the main cause for the instability

Flashing and Geysering are also boiling inception instability

This is essentially the Type-I instability discussed by Fukuda and Kobori.

Flashing Induced InstabilityOccurs in NCSs with tall risers. The rising hot liquid experiences static pressure decrease and may reach its saturation value leading to flashing in low pressure systems

The increased buoyancy force increases the flow which in turn reduces exit enthalpy and may even suppress flashing causing reduction in buoyancy force and flow. Reduced flow leads to larger exit enthalpy leading to the repetition of the process.

The necessary condition for flashing is that the fluid temperature at the riser inlet is greater than the saturation temperature at the exit

The instability is observed only in low pressure systems

Thermodynamic equilibrium conditions prevail during flashing

Geysering Instability

Generally observed in systems with tall risers. Geysering is expected during subcooled boiling taking place at the exit of the heater

As the bubbles move up the riser, bubble growth (due to static pressure decrease) as well as condensation can take place.

Sudden condensation results in depressurisation causing the liquid water to rush to the space vacated by the slug bubble leading to a large increase in the flow rate reducing the driving force

Geysering is a nonequilibrium phenomenon unlike flashing

Both Geysering and flashing instabilities are observed in low pressure systems only

Dynamic Instability in Two-phase NCSsRegenerative feedback and time delay are important for dynamic instability

DWI is the most commonly observed dynamic instability in NCSs and the mechanism causing the instability has already been discussed earlier

A number of geometric and operating parameters affect the instability in addition to certain boundary conditions

Riser height, orificing, length and diameter of source, sink and connecting pipes are the important geometric parameters

Pressure, inlet subcooling, power and its distribution are the important operating parameters

Boundary conditions of interest are wall heat transfer coefficient,heat storage in walls, wall heat losses, constant pressure drop, etc.

Compound Dynamic Instability in two-phase NCSs

If only one instability mechanism is at work, it is said to be fundamental or pure instability. Instability is compound if more than one mechanisms interact in the process and cannot be studied separately

-Thermal oscillations-Parallel channel instability-Pressure drop oscillations-BWR instability-SG instability

The steep variation in heat transfer coefficient gets coupled with DWO

The dryout or CHF point shift upstream of or downstream during thermal oscillations

The large variation in heat transfer coefficient results in significant variation in heat transfer rate even if the wall heat generation is constant

Thermal oscillations are a regular feature of post dry out heat transferheat transfer in steam-water mixtures at high pressures

The variable heat transfer coefficient leads to a variable thermal response of the heated wall that gets coupled with the DWO

Thermal Oscillations

Parallel Channel InstabilityInteraction of parallel channels with DWO can give rise to interesting behaviours as in single-phase NCS

-In-phase oscillations (system instability)- Out-of-phase oscillations-Dual oscillations (overlapping region of IPO and OPO)

In-phase oscillation is a system characteristic and parallel channels may not play a role in this

Out-of-phase oscillation is characteristic of parallel channels. Thephase shift depends on the number of channels

- 2 channels : 1800 ; 3 channels : 1200 ; n-channels :2/nHowever, in a system of n-channels, all parallel channels need not take part in the instability. Depending on the number of channels taking part the phase shift can be anywhere between 2/n to

Mechanism of PCI is similar in single-phase and two-phase systems

Pressure drop oscillationsThis is associated with operation in the negative sloping region of p-w curve.

Caused by the interaction of a compressible volume at the inlet of the heated section with the pump characteristics

Usually observed in FCSs. DWO oscillation occurs at flow rates lower than the flow rate at which PDO is observed

The frequency of PDO is much smaller than DWO.

Very long test sections may have sufficient internal compressibility to cause PDO

Like Ledinegg instability there is a danger of CHF occurrence during PDO

Inlet throttling can stabilize PDO as in the case of Ledinegg instability

Instability in NBWRs

The flow velocity in NBWRs is usually much smaller than FC BWRs

The presence of tall risers causes the oscillation frequency to be much smaller

The only NCR whose stability has been extensively studied is the Dodewaard reactor.

The negative void reactivity stabilizes type I instability. But it may stabilize or destabilize type II instability

Pump trip transients in FC BWRs lead to type II instability

Various bases used for classification of instabilities have been reviewed. The most widely accepted classification is based on the method of analysis used in identifying the stability threshold.

While classifying NC instabilities, it was convenient to consider the instabilities associated with single-phase and two-phase NC separately Natural circulation systems are more unstable due to the regenerative feedback inherent in the mechanism causing the flow.

Besides the instability in single-phase systems, natural circulation loops also exhibit an instability associated with flow reversal in contrast to forced circulation systems.

CONCLUDING REMARKS

Thank you

Density wave instability

Due to the importance of void fraction and its effect on flow, the instability is often referred to as ‘flow-void feedback instability’ in two-phase NCSs

Since transportation time delays are crucial to the instability, it is also known as ‘time delay oscillations’

In single-phase, near critical and supercritical fluids, the instability is also known as ‘thermally induced oscillations’


DWI is most commonly observed in NCSs. The frequency of DWI is of the order of 1 Hz in 2- flow

Instabilities Associated with Boiling Inception

Boiling inception modifies single-phase instability

Boiling inception can induce instabilities in a stable single-phase NCS

Occurrence of single-phase conditions during part of the oscillation cycle is a characteristic feature of this instability

Effect of Boiling inception on single-phase instability

With power increase boiling inception occurs during the low flow part of the oscillation cycle. Instability continues with flow switching between single-phase and two-phase regimes.

Several flow regimes are observed as shown. The change in power required for attaining the condition with two-phase flow for the entire oscillation cycle can be very significant

c) Instability with boiling once in every cycle

(d) Instability with boiling twice in every cycle

(b) Instability with sporadic boiling (a) Single-phase instability

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INTRODUCTION TO INSTABILITIES IN NATURAL CIRCULATION SYSTEMS

Documents

instabilities instability

instability threshold

flow oscillations instability

ledinegg instability

steady state equations

thermalhydraulic system

original steady state

eventual steady state