INTRODUCTION TO INSTABILITIES IN NATURAL CIRCULATION SYSTEMS

1. INTRODUCTION TO INSTABILITIES IN NATURAL CIRCULATION SYSTEMS P.K. Vijayan Reactor 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)

2. OUTLINE OF THE LECTURE T#6

3. INTRODUCTION Instabilities are common to both FC and NC systems NCSs are more unstable. A regenerative feedback is inherent in the mechanism causing NC 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 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

4. What is instability? stable Neutrally stable unstable Flow – kg/s Time - s • Following a perturbation if a thermal-hydraulic system returns to its original steady state, then the system is considered to be stable • 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

5. Limit Cycle Oscillations In all practical systems oscillation growth cannot continue indefinitely. Instead, oscillation growth is terminated by system nonlinearities leading to limit cycle oscillations Limit Cycle, Phase space (plot or trajectory), orbit Time series 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

6. DISADVANTAGES OF INSTABILITY • Sustained flow oscillations may cause forced mechanical • vibration of components • Premature CHF occurrence can be induced by flow • oscillations • Induce undesirable secondary effects like power • oscillations in a BWR • Instability can disturb control systems and pause • operational problems in nuclear reactors.

7. 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

8. Classification of instabilities – Contd. Instabilities are classified according to various bases - analysis method - propagation method - nature of the oscillations - loop geometry, - disturbances or perturbations

9. Classification of instabilities – Contd. Analysis method (or Governing equations used) (a) Pure (or fundamental) static instability (b) Compound static instability (c) Pure dynamic instability (d) Compound dynamic instability Pure static instability The 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

10. Classification of instabilities – Contd. 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

11. Classification of instabilities – Contd. 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

12. Classification of instabilities – Contd. 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

13. Classification of instabilities – Contd. 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

14. Classification of instabilities – Contd. 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

15. Classification of instabilities – Contd. C C F 0 Time H 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

16. Classification of instabilities – Contd. 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

17. 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 Multiple steady states in the same flow direction 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 with differing flow directions

18. STABILITY OF SINGLE-PHASE NCSs – Contd. coolant Steady Clockwise flow (Q2=0) Anticlockwise flow with Q2>Qc Q2=0 Q2>Qc Q1 Q1 Multiple Steady states with differing flow direction Unlike FC, certain NC systems can exhibit steady flow in both clockwise and anticlockwise directions • - 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

19. Multiple steady states with differing flow directions stable unstable Grm Clockwise flow Anticlockwise flow Stm 1415 C 800 2100 26.9 1180 H 410 385 620 620 410 Instability associated with flow reversal in single phase NCS 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 Similar behaviour is observed in a NCS with throughflow

20. 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

21. Multiple steady states with differing flow directions F F F F W+F W Instability 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 The amplitude of the oscillations increase as the flow reversal threshold approaches 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)

22. Q Outlet header hl downcomer hm Parallel vertical inverted U-tubes relevant to SGs Q1 W1 Q2 W2 Q3 W3 Qn Wn Qd=0 Wd hs Inlet header heater Vertical parallel channel system relevant to the RPV of BWRs, PWRs, etc. cooler Parallel channel NC systems ht Qt hm hb Qm Qb Unequally heated parallel horizontal channels having unequal elevations relevant to PHWRs Existence of multiple steady states was first explored by Chato (1963)

23. Parallel Channel Systems outlet header W coolant Q1 W1 Downcomer Q2 W2 H W inlet header Vertical parallel channel system Unequally heated parallel channel NC systems exhibit an instability associated with flow reversal due to the existence of mutually competing driving forces There is a driving force between the downcomer and each heated channel promoting upward flow through the heated channels There is another driving force between two 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

24. Parallel Channel Systems outlet header W coolant Q1=0 W1 Q2 W2 Down comer H W inlet header (a) Vertical parallel channel system 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

25. Parallel Channel 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

26. A E F B C D • 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.

27. 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

28. Dynamic Instability in single-phase NCSs 1415 305 Expansion tank cooler 800 2200 Flow C Time Heater Keller (1966) 410 H 385 620 C 620 410 H System Instabilities Flow Time All these oscillatory modes can be observed in rectangular loops for different ranges of power Welander (1967)

29. Dynamic Instability in single-phase NCSs 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

30. Two-phase NC instability Pure static instability Compound static instability Dynamic instability Compound Dynamic instability Pure static instability Flow excursion or excursive (Ledinegg) instability Boiling Crisis Ledinegg instability Involves sudden change of flow rate to a lower value The new flow rate may induce CHF Occurrence of multiple steady states is the fundamental cause of the instability

31. Ledinegg instability – Contd. Steam Two-phase system characteristic b a c Head riser Driving pressure differential Feed Flow rate heater downcomer 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 unstable The instability can be avoided by inlet throttling in FCSs Inlet throttling may not work as effectively as in FCSs due to the reduction in flow caused by it

32. Boiling Crisis Transition boiling Film boiling Natural convection Heat flux Nucleate boiling Ts - Tsat Following the occurrence of critical heat flux, a regime of transition boiling may be observed as in pool boiling 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 temperature The instability is characterized by sudden rise in wall temperature followed by an almost simultaneous occurrence of flow oscillations

33. 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

34. Flow Pattern Transition Instability Two-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

35. Dynamic instabilitiesin Two-phase NCSs Fukuda-Kobori Generally two unstable regions are observed for DWI The low power unstable region is called the type I instability The high power instability is called the type II instability The number of unstable or stable zones depends on the shape of the stability map In view of the occurrence of islands of instability, the unstable zones can be more than 2.

36. 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 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.

37. Flashing Induced Instability Occurs 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

38. 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

39. Dynamic Instability in Two-phase NCSs Regenerative 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.

40. 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

41. Thermal Oscillations The variable heat transfer coefficient leads to a variable thermal response of the heated wall that gets coupled with the DWO Thermal oscillations are a regular feature of post dry out heat transfer heat transfer in steam-water mixtures at high pressures 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

42. Parallel Channel Instability Interaction 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. The phase shift depends on the number of channels - 2 channels : 1800 ; 3 channels : 1200 ; n-channels :2/n However, 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

43. Pressure drop oscillations This 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

44. 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

45. CONCLUDING REMARKS 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.

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47. Classification of instabilities – Contd. Density wave instability DWI is most commonly observed in NCSs.The frequency of DWI is of the order of 1 Hz in 2- flow 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’

48. 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

49. 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