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INSIGHTS INTO NATURAL CIRCULATION STABILITY

DIPARTIMENTO DI INGEGNERIA MECCANICA, NUCLEARE E DELLA PRODUZIONE UNIVERSITA' DI PISA 56100 PISA - ITALY. INSIGHTS INTO NATURAL CIRCULATION STABILITY. F. D’Auria , A. Del Nevo, N. Muellner – Lecture T7. IAEA & ICTP Course on NATURAL CIRCULATION IN WATER-COOLED NUCLEAR POWER PLANTS

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INSIGHTS INTO NATURAL CIRCULATION STABILITY

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  1. DIPARTIMENTO DI INGEGNERIA MECCANICA, NUCLEARE E DELLA PRODUZIONE UNIVERSITA' DI PISA 56100 PISA - ITALY INSIGHTS INTO NATURAL CIRCULATION STABILITY F. D’Auria, A. Del Nevo, N. Muellner – Lecture T7 IAEA & ICTP Course on NATURAL CIRCULATION IN WATER-COOLED NUCLEAR POWER PLANTS Trieste, Italy, June 25-29 2007

  2. CONTENT 2/48 • FOREWORD • NOMENCLATURE - The fundamental scenario for DWO • SELECTED EXPERIMENTAL FINDINGS - Characterization of DWO, PDO, THO - Kakac & Liu et al. - Subcooling, exit quality and oscillation amplitude – Wu et al., Canti et al. - Pressure and test section length - Jain & Bankoff et al. - Thermal margins and flow oscillations – Kitayama et al., Kasai et al. - Predictive capabilities and use of results – Cheung & Klebanov • SIMPLE LOOP OSCILLATIONS - The loop and the experimental database - System TH code qualification and capabilities - The simulation of microgravity • THE INSTABILITIES IN PWR NC - Background: the LOBI facility and the NC scenario - The siphon condensation • THE NUMERICAL MODEL - The equations and the model structure - Results: the stability maps & physical parameters effects - Results: numerical parameters effects • CONCLUSIONS • APPENDIX 1 : Points of View • APPENDIX 2 : References to Experimental Programs

  3. 3/48 Roadmap for the Training Course on NC in Water-Cooled Reactors

  4. FOREWORD 4/48 • Misale, 1999: • <<If the flow of the system in question is stationary in respect to the temperature, and the velocity, it can be called “stable”. If the flow and the temperature show some oscillations, but the amplitude of the oscillations and the sign of the velocity stay constant in time, the system can be called “neutral”. If finally the system shows oscillations which grow in time and lead to flow reversal, the system can be called “unstable”.>> • However, • Steady-state noise, • Damped system, DR < 1, • Limit cycle, DR = 1, • Unstable system performance, DR > 1, • Bifurcation caused by oscillation, • exist and are used to characterize detected hydraulic scenarios or conditions

  5. NOMENCLATURE 5/48 Acoustic instability: This occurs when standing waves are excited in a single or two-phase system with a frequency in the acoustic range: steam line resonance and acoustic instabilities in the steam dome and upper plenum regions of BWR have been observed Density wave: A density wave is a perturbation in the density of the fluid mixture, which travels along the heated channel with a characteristic speed depending on local conditions. Density wave oscillations (DWO) are the basic mechanism credited for triggering and sustaining the relevant oscillation phenomena in boiling water reactor cores. In other words, the observed instability phenomena have been explained making reference to the delays involved in density wave propagation. Dynamic instabilities: These terms characterize the wider class of instabilities that can be studied only through the use of time-dependent balance equations. Flow regime induced instability: The periodicity of some flow regime (e.g. slug flow) excite this instability mode.  Flow regime "relaxation" instability: This is a static instability due to flow regime changes.

  6. NOMENCLATURE 6/48 Harmonic modes:Harmonic modes are represented by the eigen-functions in which the general solution of the partial differential neutron diffusion equation, applied in a given domain (e.g., the reactor core) with appropriate boundary conditions (e.g., zero neutron flux at the extrapolated boundary), can be decomposed. In this respect, the transient evolution of neutron flux in the core can be viewed as the superposition of harmonic modes, weighted by appropriate functions representing their relative importance at each time. In steady-state conditions, only the fundamental mode is "critical" (i.e., its weight is constant and equal to 1), the higher order ones being decayed during previous transients. During reactor core instability events, harmonic modes may be differently excited giving rise to the observed variety of oscillation patterns (core-wide or regional). Hopf bifurcation: While changing one or more system parameters, a Hopf bifurcation occurs when a stable fixed point becomes unstable and limit cycles appears. In particular, supercritical Hopf bifurcations lead to the appearance of a stable limit cycle, which works as an attractor of trajectories spiralling out from the previously stable fixed point; on the other hand, subcritical Hopf bifurcations involve the appearance of stable and unstable limit cycles, which respectively attract and repel trajectories. In the latter case, in a limited parameter range, the fixed point may be stable for small perturbations and unstable for large ones. Kinematic wave: A wave that progresses with the speed of the fluid, either steam or liquid or two-phase mixture.

  7. NOMENCLATURE 7/48 Limit cycle: A limit cycle is a particular long term periodic solution of the differential equations describing a non-linear system, which is encountered studying the system behaviour beyond the linear stability threshold. Limit cycles are named "stable", if they attract system trajectories starting from nearby states, or "unstable", if they repel them. Stable limit cycles have been observed in BWR and other boiling systems during instabilities and are ideally characterized by a periodic oscillatory behaviour with constant amplitude and frequency. As a matter of fact, limit cycles observed in BWR during tests or inadvertent occurrences are not so ideal, showing gradual changes in amplitude and frequency of oscillations as a result of drift in system parameters. NPCH/NSUB: These are non dimensional quantities whose physical meaning is (Mass flux due to phase change/inlet mass flux) and (boiling channel entrance sub-cooling/latent heat), respectively.

  8. NOMENCLATURE 8/48 Out of phase: Synonymous of regional (oscillations). Parallel channels: Different fuel elements up to including the entire core are reported as parallel channels. Parallel channel oscillations may be either "core wide" either "regional". These terms (i.e. parallel channel) are mostly appropriate for out of core test loops. Phase delay: This is the phase shift between the phase of the oscillations of generic signal and the phase of a reference signal. Pressure drop oscillations (PDO): In this case a Ledinegg type instability and a compressible volume in the boiling system interact. It might be noted that PDO is a dynamic type of oscillations and Ledinegg is a static one. Regional: As opposite to core-wide, the term regional identifies phenomena occurring in different ways in the various regions within a radial core plane. In particular, "regional (or out-of-phase) oscillations" are commonly referred to those instabilities in which different core zones (generally two halves separated by a diameter) show a considerable phase shift in neutron flux oscillations (generally around 180°).

  9. NOMENCLATURE 9/48 Stability boundary: A stability boundary is represented by a relationship between the parameters describing a system status which defines the conditions in which the system shows marginal (or neutral) stability, i.e. in which perturbations are neither amplified nor damped. In a two-dimensional parameter space, this relationship can be represented as a curve separating areas of stable and unstable behaviour. Hyper-surfaces separating stable and unstable multidimensional domains are obtained in the case of systems described by several parameters. Stability margin: A stability margin is a properly defined measure of the distance of a system status from the stability boundary. For instance, control theory suggests the use of "gain" and "phase" margins as a measure of the stability of a linear system. Static instability: These terms identify a class of instabilities that can be theoretically explained without the use of time-dependent conservation equations. Thermal oscillations (THO): Are oscillations heavily involving the heater dynamics in a boiling channel. Cyclic dry-out and rewet phenomena may be involved at a frequency lower than DWO

  10. NOMENCLATURE– THE DWO SCENARIO 2/48 Assumptions: P1, Pe, and Heater Power = const. At t=0, the exit restriction undergoes a sudden small area increase: then a low density two-phase mixture may pass through the exit restriction. The pressure drop through the exit restriction will decrease and this decrease in the exit pressure drop (po - pe) is propagated to the inlet at the speed of sound; therefore, po will decrease and (pl - po) will increase. As a result, inlet velocity is increased. The enthalpy wave with a higher density fluid originated at t=0 at the inlet, reaches the boiling boundary in the time period t1. In the time period t2, the density wave reaches the heater exit. In the time period t3, the density wave reaches the exit restriction. The sum Dt = t1 + t2 + t3, constitutes the transit time of a fluid particle through the system. When the higher density wave reaches the exit after Dt, the exit pressure drop increases and (p1 – po = the driving force) decreases. Thus, inlet velocity decreases and a lower density fluid is set to travel along the heater. But it takes another time interval of Dt, for this adjustment to be felt at the exit restriction. When the new density wave (lower density) arrives at the exit restriction, the pressure drop is given a negative perturbation and practically at the same time the inlet velocity increases accordingly. It takes one high and one low wave to make one cycle, so it can be concluded that the periods of the density-wave oscillations are roughly equal to twice the transit time of a fluid particle through the system.

  11. SELECTED EXPERIMENTAL FINDINGS (DWO, PDO, THO - Kakac & Liu) 1 of 2 11/48 PDO, DWO and THO have been experimentally characterized by Kakac and Liu (1967 – 1990). By using a freon loop having the basic features as those in the figure in the previous slide, but with a vertical heater, DWO, PDO and THO have been characterized as in the following three figures. The range of parameters should be noted and the frequencies. THO manifest with relatively large temperature excursions of the heater DWO DWO THO PDO PDO Characterization of DWO, PDO, THO - Kakac & Liu, 1 of 3

  12. SELECTED EXPERIMENTAL FINDINGS 12/48 PDO, DWO and THO have been experimentally characterized by Kakac and Liu (1967 – 1990). By using a freon loop having the basic features as those in the figure in the previous slide, but with a vertical heater, DWO, PDO and THO have been characterized as in the following three figures. The range of parameters should be noted and the frequencies. THO manifest with relatively large temperature excursions of the heater DWO THO THO PDO PDO & THO Characterization of DWO, PDO, THO - Kakac & Liu, 2 of 3

  13. SELECTED EXPERIMENTAL FINDINGS 13/48 PDO DWO Characterization of DWO, PDO, THO - Kakac & Liu, 3 of 3

  14. SELECTED EXPERIMENTAL FINDINGS 14/48 2 1 3 • Influence of sub-cooling • Influence of exit quality • Relationship between period • of oscillations and transit time Subcooling, exit quality and oscillation amplitude – Wu et al., Canti et al.

  15. SELECTED EXPERIMENTAL FINDINGS 15/48 2 p p p p Pressure influence – Jain & Bankoff et al.

  16. SELECTED EXPERIMENTAL FINDINGS 16/48 Larger ‘L’ should imply larger ‘Q’ Lmax L Lmax Lmax Influence of test section length – Jain & Bankoff et al.

  17. SELECTED EXPERIMENTAL FINDINGS 17/48 1 • Ratio of Q at OSBT over Q at • Onset of Oscillation versus • Mass Flux • 2) Flow and heater rod temperature • recording at OSBT Oscillation is limiting Difficult to detect & suppress 2 Thermal margins and flow oscillations – Kitayama et al., Kasai et al.

  18. SELECTED EXPERIMENTAL FINDINGS 18/48 • Experiment – various sub-cooling • Calculation – same conditions, by • TRACG • 3) Experiment and calculation 1 3 2 Predictive capabilities and use of results – Cheung & Klebanov, 1 of 2

  19. SELECTED EXPERIMENTAL FINDINGS 19/48 EXPERIMENTAL DATA EXPECTED FOR NPP (ESBWR) Predictive capabilities and use of results – Cheung & Klebanov, 2 of 2

  20. SIMPLE LOOP OSCILLATIONS 20/48 The operating conditions and the qualification of steady-state conditions The loop and the experimental database – 1 of 2

  21. SIMPLE LOOP OSCILLATIONS 21/48 • TYPICAL RECORDING • Stable • Unstable – low power • Unstable – high power • The stability map 1 2 4 3 The loop and the experimental database – 2 of 2

  22. SIMPLE LOOP OSCILLATIONS 22/48 • The SYS TH • codes (Relap) • are capable of • reproducing • the main • features of the • oscillations. • However, • systematic • prediction of the • oscilations • was not achieved. • In addition: • Difficulty to • simulate all loop • BIC data, • b) Code allowed • to understand the • role of parameters • like thermal • capacity & heat • losses. Exp & calc 100 w Exp & calc 200 w 2 Exp & calc 900 w Exp & calc 400 w System TH code qualification and capabilities

  23. SIMPLE LOOP OSCILLATIONS 23/48 A reconstructed loop was put on a ‘mobile’ flat plane and connected with a flexible pipe to the PRZ (not shown in the figure). 60°inclination shown in the figure. 90° = horizontal plane  almost no gravity influence on NC. THE LOOP THE TEST MATRIX power angle The simulation of microgravity – 1 of 2

  24. SIMPLE LOOP OSCILLATIONS 24/48 power angle 1 2 • DT across heater vs time for different angles at P = 2000 w • 2. Loop flowrate vs angle for different power Loop flowrate does not achieve the zero value for the horizontal loop (CFD capabilities needed to understand the system performance specificlly at low angles). The loop is ‘more stable’ than its predecessor (previous slides) owing to construction material of the vertical legs (metal instead of plexiglas) that induces higher friction and causes larger thermal capacity, both stabilizing parameters. Where are oscillations? Oscillations occur at 60° angle with power of 1500 and 1000 w as it can be seen in the table on the previous slide. The simulation of microgravity – 2 of 2

  25. THE INSTABILITIES IN PWR NC 25/48 ZONE OF INTEREST The LOBI ITF simulates a PWR with 1/700 volume scale. NC experiment A2-77 was conducted at constant core power, with diffferent values of PS coolant inventory. The NC flow regimes map was derived (fig. on the right, see also lect T20) where 5 Main regimes are distinguished. The 2 instabilities (circled area) is of interest here. Background: the LOBI facility and the NC scenario – 1 of 2

  26. THE INSTABILITIES IN PWR NC 26/48 ZONE OF INTEREST When primary coolant inventory reached about 70% of its initial value wide oscillations were measured all over the loop in DP, velocities (figure above), fluid density and temperature signals. Background: the LOBI facility and the NC scenario – 2 of 2

  27. THE INSTABILITIES IN PWR NC 27/48 t* = generic time within the zone of interest The siphon condensation - 1 of 6, what was measured

  28. THE INSTABILITIES IN PWR NC 28/48 t* = generic time within the zone of interest The siphon condensation - 2 of 6, the code was capable in reproducing the measured scenario

  29. THE INSTABILITIES IN PWR NC 29/48 t* = generic time within the zone of interest The siphon condensation - 3 of 6, the code calculation supplied useful information to understand the measured transient scenario

  30. THE INSTABILITIES IN PWR NC 30/48 GENERIC SG MODEL DERIVED SIPHON CONDENSATION SCENARIO SINGLE U-TUBE MODELLED t1 t2 t3 CONDEN SATION CONDEN SATION & FLOODING SIPHON EFFECT The siphon condensation - 4 of 6, the code calculation results allowed the characterization of the siphon condensation - 1 U-tube

  31. THE INSTABILITIES IN PWR NC 31/48 THE PRESSURE IN SG INLET & OUTLET CHAMBERS IS ALMOST CONSTANT t1 • At the same time [3] groups • of U-tubes exist that are in • Stalled conditions • Flow reversal condition • Undergoing the siphon- • condensation cycle t2 t3 The possible scenario, closer to some exp evidence, is given in the figure, as derived from noding 3 parallel U-tubes. The siphon condensation - 5 of 6, the code calculation results allowed the characterization of the siphon condensation - 3 U-tubes

  32. THE INSTABILITIES IN PWR NC 32/48 A stability map for the siphon-condensation oscillations could be derived related to the considered system. Performed calculations provide system performance when core power and thermal load of individual U-Tubes is varied. The siphon condensation - 6 of 6, additional (by-product) results from the performed study

  33. THE NUMERICAL MODEL 33/48 HEM for a boiling channel (W. Ambrosini et. al) Dimensionless mass, momentum, energy and heater equations (Nn = Number of nodes) The model can be used for linear (by perturbing and studying the stability of the Jacobian matrix) and non-linear stability analysis (time-dependent solution) Relevant parameter for stability analysis and connection with DR The equations and the model structure – W. Ambrosini et al.

  34. THE NUMERICAL MODEL 2/48 34/48 2D • THE 2D & THE 3D STABILITY MAPS • linear stability analysis – • <48 Nodes> 3D 1-stable Results: the stability maps – W. Ambrosini et al.

  35. THE NUMERICAL MODEL 35/48 LINEAR STABILITY ANALYSIS Inlet pressure drop Exit pressure drop Distributed friction Heater mass Froude number Axial power profile Results: physical parameters effects – 1 of 2, W. Ambrosini et al.

  36. THE NUMERICAL MODEL 36/48 NON-LINEAR STABILITY ANALYSIS Limit cycle NPCH = 8; NSUB=12 Limit cycle NPCH = 19; NSUB=12 Limit cycle NPCH = 9; NSUB=3 Results: physical parameters effects – 2 of 2, W. Ambrosini et al.

  37. THE NUMERICAL MODEL 37/48 LINEAR STABILITY ANALYSIS 96 N 24 N 12 N • The influence of number of nodes. • The parameter that affec stability: • the model structure (e.g. HEM or UVUT), • the constitutive equations (e.g. ‘f’’, ‘K’), • the numerical solution method, • the number of nodes. • other than the hardware and the BIC. Results: numerical parameters effects, W. Ambrosini et al.

  38. CONCLUSIONS – 1 OF 2 2/48 • OSCILLATIONS CONSTITUTE A CHALLENGING FIELD FOR EXPERIMENTALISTS AND THEORETICIANS. A MYRIAD RESEARCHERS IS ATTRACTED. • HUNDREDS EXPERIMENTAL PROGRAMS HAVE BEEN CONDUCTED AND DEVOTED TO STABILITY IN HYDRAULIC SYSTEMS. • EXPERIMENTAL DATA ARE MANDATORY TO INTERPRET INSTABILITIES. HOWEVER, PREDICTIVE CAPABILITIES EXIST, BUT STROBGLY AFFECTED BY ADOPTED MODELING ASSUMPTIONS (previous slide). • A VARIETY OF INSTABILITY SITUATIONS ARE RELEVANT TO THE NPP DESIGN AND SAFETY TECHNOLOGY, MOSTLY UNDER NC CONDITIONS (next slide). • CAREFUL EVALUATION OF EXPERIENCE GAINED IS RECOMMENDED BEFORE STARTING NEW ACTIVITIES.

  39. CONCLUSIONS - 2 OF 2 39/48 LIST (NOT EXHAUSTIVE) OF INSTABILITY SITUATIONS RELEVANT IN REACTOR TECHNOLOGY (references in SOAR on BWRS) 1) Oscillations in PWR power (12% nominal) possibly induced by core inlet T caused by oscillations In HTC across SG tubes 2) Time varying mismatches between power generated in different core quadrants (QPTR = Quadrant Power Tilt Ratio) 3) Geysering 4) stability of two-phase natural circulation, 5) siphon condensation in PWR systems, 6) instability in horizontal systems, ; 7) boiling instabilities in narrow channels,; 8) instabilities in RBMK channels; 9) instabilities in single phase natural circulation, (simple & complex circuits) 10) instabilities characterized by very long oscillation periods, with dry-out and rewet cycles in PWR conditions,

  40. APPENDIX 1: Points of View 40/48 The explanation "initiated" by Stenning and Veziroglu, in 1964, is utilized by K. Svanholm (’80s). A very simple system, consisting of a horizontal evaporator and a downstream adiabatic pipe, with inlet and outlet orifices, is considered. The total pressure drop is imposed constant in locations upstream and downstream the inlet and outlet orifices. A disturbance in the system may occur in the term of a slug of liquid reaching the outlet orifice. The pressure drop over the outlet restriction increases proportionally to the density. Keeping in mind that the vapour generation rate and the pressure downstream the outlet orifice are constant, the pressure in the evaporator will increase. Since also the pressure upstream of the inlet is constant the pressure drop over the inlet orifice will diminish and consequently the inlet velocity will be reduced. A two phase mixture of a density smaller than the steady state value will be produced in the evaporator. This perturbation in the density will be transported through the system with the velocity of the two phase mixture. After some period, a mixture of density lower than the steady state value will appear at the outlet orifice. As a consequence the pressure drop across the inlet orifice increases and the two phase mixture produced in the evaporator is of a density above the steady state value. When this high density material reaches the outlet restriction the whole cycle starts over again.

  41. APPENDIX 1: Points of View 41/48 • The essential aspects of this interpretation appear to be: • a perturbation in the pressure drop at the system outlet may give rise to a travelling density wave; • evaporator and downstream pipe may have generic lengths and inclinations; • feedback with power production, e.g. heat exchange in the evaporator, is not necessary to explain instabilities. The only feature necessary to explain the oscillations in their most elementary form is that two components with different densities are present, and may be mixed in different proportions, and that two-phase pressure losses increase with the density. The production of gas phase may be constant. Aspects as sub-cooling, heater dynamics and void reactivity certainly influence the oscillations, and when all these are present, one ends up in extremely complicated systems.

  42. APPENDIX 1: Points of View 42/48 • Rizwan-uddin (90’s)on the basis of numerical experiments, achieves the conclusion that periodic density variations might be not the fundamental mechanism of what is called density wave instability in a classic boiling channel. This is valid at least in the limited range of parameters that he considers. He found that variations in mixture velocity affect the pressure drop characteristics (detected effect) of the channel during the oscillation, more than the variations in mixture density. In certain regions of the parameter space, during the oscillation, pressure drop at the exit does not decrease when a wave of lower density reaches the channel exit; it actually increases due to the simultaneous increase in mixture velocity at the exit, which increases faster than the decrease in mixture density. He also found that oscillation period for the considered range of parameter values is between three and four times the average channel transit times. The conclusion from this analysis is: • parameter ranges (geometrical and thermal-hydraulic) are important in the phenomenology (for DWO); • the travelling of density wave is not necessary to explain the oscillations phenomenology: i.e. 'density wave' oscillations may occur without mixture density oscillations; • fluid velocity oscillations may be more decisive than density oscillations in producing periodic pressure drops.

  43. APPENDIX 2: References to Experimental Programs 43/48

  44. APPENDIX 2: References to Experimental Programs 44/48

  45. APPENDIX 2: References to Experimental Programs 45/48

  46. APPENDIX 2: References to Experimental Programs 46/48

  47. APPENDIX 2: References to Experimental Programs 47/48

  48. APPENDIX 2: References to Experimental Programs 48/48

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