Application of Power Time-Projection on the Operator-Splitting Coupling Scheme of the TRACE/S3K Coupled Code

Application of Power Time-Projection on the Operator-Splitting Coupling Scheme of the TRACE/S3K Coupled Code

(Presented at the International Conference on Mathematics and Computational Methods applied to Nuclear Science and Engineering M&C 2013, Sun Valley, Idaho, 2013)

An analysis based on a coupling between the currently available thermal-hydraulics and neutronics codes is an attractive option for dynamic simulation of nuclear power plant transients in terms of developmental cost. The currently adopted temporal coupling scheme is a simple operator-splitting with synchronous time step where the splitting is based on the physics solved by each code. This scheme is known to degrade the overall temporal convergence of the coupled solution. That is, a very small time step size is required to reach an acceptable solution. In this presentation, a simple modification on the temporal coupling scheme based on a time-projection scheme of a solution (i.e., power) is proposed and tested on two different nuclear power plant transients. It is shown that the modification is able to improve the convergence of the coupled calculation.

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Damar Wicaksono

May 08, 2013
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  1. Wir schaffen Wissen – heute für morgen May 7th, 2013

    Sun Valley, Damar Wicaksono Omar Zerkak, Konstantin Nikitin, Hakim Ferroukhi, and Rakesh Chawla M&C 2013 Sun Valley, Idaho, May 5-9, 2013 Application of Power Time-Projection on the Operator-Splitting Coupling Scheme of the TRACE/S3K Coupled Code
  2. stars.web.psi.ch Slide 2 Outline 1. Introduction 2. Improvements of the

    Temporal Coupling 3. Results: PWR Rod-Ejection-Accident (REA) 4. Results: Peach Bottom 2 Turbine Trip (PBTT) 5. Conclusions May 7th, 2013 Sun Valley,
  3. stars.web.psi.ch Slide 3 An important part of reactor safety analysis

    is to evaluate under wide variety of postulated scenarios: • The time-dependent thermal-hydraulic state of the plant • The power response of the core These problems are multi-physics and multi-scale by nature. The evaluation is achieved by means of computer simulation. Codes have been developed for both purposes, and in (in later years) best-estimate manners. The incentive of having best-estimate solution is to remove excessive conservatism in the analysis method. May 7th, 2013 Sun Valley, Introduction
  4. stars.web.psi.ch Slide 4 Two-Phase Hydraulics Heat Conduction Neutron Kinetics q’’’

    q’’ α,ρm ,Tm DMH TFU Tl ,Tg Two-way Coupled phenomena The problems in Nuclear Reactor Analysis are multi-physics in many different aspects and levels. Multiphysics in NRA May 7th, 2013 Sun Valley,
  5. stars.web.psi.ch Slide 5 Two-Phase Hydraulic Heat Conduction Neutron Kinetics q’’’

    q’’ α,ρm ,Tm DMH TFU Tl ,Tg XS Library TRACE Thermal-Hydraulic System Code Simulate-3K Transient Analysis Nodal Code The problems in Nuclear Reactor Analysis are multi-physics in many different aspects and levels. Multiphysics in NRA May 7th, 2013 Sun Valley,
  6. stars.web.psi.ch Point Reactor Kinetics Model (with 1D workaround) Both codes

    are basically multi-physics, but some limitations still exist… In TRACE for instance, This excludes transients that exhibit asymmetrical coupled phenomena in the core. Slide 6 Motivation May 7th, 2013 Sun Valley,
  7. stars.web.psi.ch In S3K for instance, No treatment of boron transport

    (taken as core-averaged). These exclude transients such as (best-estimate) MSLB, boron dilution or transients that have the BOP and the core strongly coupled. Limited balance of plant models Limited control system models Slide 7 Motivation May 7th, 2013 Sun Valley,
  8. stars.web.psi.ch In S3K for instance, No treatment of boron transport

    (taken as core-averaged). These exclude transients such as (best-estimate) MSLB, boron dilution or transients that have the BOP and the core strongly coupled. Limited balance of plant models Limited control system models Slide 8 Motivation May 7th, 2013 Sun Valley,
  9. stars.web.psi.ch TRACE/S3K Coupling Swiss Reactor static analysis using C4/S3 based

    methodology and a database of TRACE model in STARS Slide 9 Motivation May 7th, 2013 Sun Valley,
  10. stars.web.psi.ch Slide 10 Code Coupling Aspects: Spatial vs. Temporal TM-41-11-11

    V.0 CONFIDENTIAL - NOT FOR PUBLIC USE Page 10 (46) Figure 2: Illustration of the TRACE/S3K coupling 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 3 3 3 2 2 2 2 3 3 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 2 2 2 2 2 2 2 2 2 2 3 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 3 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 0 0 0 0 0 0 0 5 0 0 0 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 0 0 0 6 0 0 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 0 0 7 0 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 0 8 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 9 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 Spatial Coupling: Determines how the spatially distributed data are exchanged between the spatial meshing schemes of both codes (their nodalization). May 7th, 2013 Sun Valley, J. Peltonen and T. Kozlowski. Development of effective algorithm for coupled thermal-hydraulic - neutron-kinetics analysis of reactivity transient. Nuclear Technology, 176, 2011.
  11. stars.web.psi.ch Slide 11 Code Coupling Aspects: Spatial vs. Temporal TM-41-11-11

    V.0 CONFIDENTIAL - NOT FOR PUBLIC USE Page 10 (46) Figure 2: Illustration of the TRACE/S3K coupling 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 3 3 3 2 2 2 2 3 3 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 2 2 2 2 2 2 2 2 2 2 3 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 3 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 0 0 0 0 0 0 0 5 0 0 0 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 0 0 0 6 0 0 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 0 0 7 0 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 0 8 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 9 0 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 0 0 0 Spatial Coupling: Determines how the spatially distributed data are exchanged between the spatial meshing schemes of both codes (their nodalization). Temporal Coupling: Determines the time-integration aspects of the coupled physics. Specifically, the time level control and the time-step control (TSC). This work focuses on the TLC. May 7th, 2013 Sun Valley,
  12. stars.web.psi.ch Slide 12 TS3K: Time Level Control Explicit coupling (Operator-Splitting)

    A very small time- step size is needed to achieve adequate accuracy the coupled solution Degrades the convergence of the time-integration May 7th, 2013 Sun Valley,
  13. stars.web.psi.ch Slide 13 TS3K: Time Level Control Explicit coupling (Operator-Splitting)

    A very small time- step size is needed to achieve adequate accuracy the coupled solution Degrades the convergence of the time-integration Conventional OS May 7th, 2013 Sun Valley, J. Judd and G. Grandi. Simulate-3K linkage with reactor system codes. In The 14th International Top- ical Meeting on Nuclear Reactor Thermalhydraulics (NURETH-14), Toronto, September 25-30 2011. Canadian Nuclear Society.
  14. stars.web.psi.ch Slide 14 Stems from solution extrapolation. Nodal power is

    linearly extrapolated before it’s transferred to a new-time TRACE calculation. Resembles a P-E-C (Predict-Evaluate- Correct) variant of Predictor-Corrector on Power = 0.0 (fully-explicit) = 0.5 (half-step) = 1.0 (full-step) Time-Projected Power Scheme May 7th, 2013 Sun Valley,
  15. stars.web.psi.ch Slide 15 Stems from solution extrapolation. Nodal power is

    linearly extrapolated before it’s transferred to a new-time TRACE calculation. Resembles a P-E-C (Predict-Evaluate- Correct) variant of Predictor-Corrector on Power Time-Projected Power Scheme May 7th, 2013 Sun Valley, Jean C. Ragusa and Vijay S. Mahadevan. “Consistent and Accurate Schemes for Coupled Neutronics Thermal-hydraulics Reactor Analysis.” Nuclear Engineering and Design 239, no. 3 (March 2009): 566– 579.
  16. stars.web.psi.ch Slide 16 Verification: Time-Step Refinement An error by time-discretization

    is defined by: is a variable of interest such as power peak, fuel temperature, void fraction, integrated power, etc. “ref” is the reference solution, which is defined as a solution obtained by using smallest time-step size (=10-4 s) allowed by S3K. May 7th, 2013 Sun Valley,
  17. stars.web.psi.ch Slide 17 Outline 1. Introduction 2. Improvements of the

    Temporal Coupling 3. Results: PWR Rod-Ejection-Accident (REA) 4. Results: Peach Bottom 2 Turbine Trip (PBTT) 5. Conclusions May 7th, 2013 Sun Valley,
  18. stars.web.psi.ch Slide 18 A single heated channel model in TRACE

    Strong deformation of the power distribution within a short period of time. Initiated by ejection of highest rod-worth control rod. Transient Cases: Rod Ejection Accident May 7th, 2013 Sun Valley,
  19. stars.web.psi.ch Slide 19 A single heated channel model in TRACE

    A single heated channel is dedicated to each fuel assembly in the S3K model. An S3K model of a PWR core (developed at PSI) is connected to this TRACE model. Transient Cases: Rod Ejection Accident May 7th, 2013 Sun Valley,
  20. stars.web.psi.ch Slide 20 Results: REA – Transient Evolution Power excursion

    is due to rapid control rod- ejection (reactivity insertion) Limited by Doppler reactivity feedback. Reactivity insertion as a boundary condition, independent of TH solution (NRW = 1.66 $) Starts Rod Withdrawal Rod Fully Withdrawn May 7th, 2013 Sun Valley,
  21. stars.web.psi.ch Slide 21 Results: REA – Schemes Comparison Decreasing Δt

    Decreasing Δt Ref. Ref. Conventional OS Time-Projected Power, γ = 1.0 May 7th, 2013 Sun Valley,
  22. stars.web.psi.ch Slide 22 Results: REA – Schemes Comparison (Zoomed) Decreasing

    Δt Decreasing Δt May 7th, 2013 Sun Valley,
  23. stars.web.psi.ch Slide 23 Results: REA – Schemes Comparison (Zoomed) Decreasing

    Δt Decreasing Δt Both schemes converge to the solution with smallest Δt with decreasing Δt Time-Projected Power scheme shows less variation in the power peak prediction May 7th, 2013 Sun Valley,
  24. stars.web.psi.ch Slide 24 Results: REA – Schemes Convergence 1% error

    line May 7th, 2013 Sun Valley,
  25. stars.web.psi.ch Slide 25 Results: REA – Schemes Convergence Using double

    the reference time-step size, the conventional OS yields more than 1 % error in power peak prediction The improved schemes show better convergence result on the power peak prediction. Larger time-step size can be used to achieve a prescribed accuracy 1% error line May 7th, 2013 Sun Valley,
  26. stars.web.psi.ch Max. Fuel Temperature Integrated Power Slide 26 Results: REA

    – Schemes Convergence Larger time-step size can be used to achieve a prescribed accuracy in the time-projected scheme Similar observations on other solutions… Using a larger time-step size, the conventional OS yields more error in both solutions May 7th, 2013 Sun Valley,
  27. stars.web.psi.ch Slide 27 Outline 1. Introduction 2. Improvements of the

    Temporal Coupling 3. Results: PWR Rod-Ejection-Accident (REA) 4. Results: Peach Bottom 2 Turbine Trip (PBTT) 5. Conclusions May 7th, 2013 Sun Valley,
  28. stars.web.psi.ch Slide 28 Transient Cases: Peach Bottom 2 Turbine Trip

    Tightly coupled phenomena with spatial variation in the core power response. Initiated by void collapse in the core due to pressure wave May 7th, 2013 Sun Valley,
  29. stars.web.psi.ch Slide 29 Transient Cases: Peach Bottom 2 Turbine Trip

    Both TRACE model and S3K core model were previously developed at PSI. May 7th, 2013 Sun Valley, K. Nikitin, J. Judd, G. M. Grandi, A. Manera, and H. Ferroukhi. Peach Bottom 2 Turbine Trip 2 Simulation by TRACE/S3K Coupled Code. In PHYSOR 2010 - Advances in Reactor Physics to Power the Nuclear Renaissance. American Nuclear Society, May 2010.
  30. stars.web.psi.ch Slide 30 Results: PBTT – Transient Evolution Pressure peak

    in the RPV initiates void collapse Void collapse initiates power increase Power increase will increase the core voidage again This in turn will cause power reversal May 7th, 2013 Sun Valley, TSV Closure SCRAM Signal SCRAM TSV Closure SCRAM Signal SCRAM
  31. stars.web.psi.ch Slide 31 Results: PBTT – Transient Evolution Thermal-hydraulic feedback

    initiates and limits the power peak (although complete shutdown can only be achieved with SCRAM). May 7th, 2013 Sun Valley, TSV Closure SCRAM Signal SCRAM TSV Closure SCRAM Signal SCRAM
  32. stars.web.psi.ch Slide 32 Results: PBTT – Comparison of Schemes Decreasing

    Δt Decreasing Δt Conventional OS Time-Projected Power May 7th, 2013 Sun Valley,
  33. stars.web.psi.ch Slide 33 Results: PBTT – Comparison of Schemes Decreasing

    Δt Decreasing Δt Conventional OS Time-Projected Power May 7th, 2013 Sun Valley,
  34. stars.web.psi.ch Decreasing Δt Conventional OS Time-Projected Power Slide 34 The

    projected power using very large Δt further under-predict the power peak than the conventional OS Results: PBTT – Schemes Comparison (Zoomed) May 7th, 2013 Sun Valley,
  35. stars.web.psi.ch Decreasing Δt Decreasing Δt Conventional OS Time-Projected Power Slide

    35 Results: PBTT – Schemes Comparison (Zoomed) Very large Δt gives worse estimation of peak than the conventional OS but Better overall convergence behavior (no overshoot, less sensitive to Δt especially in low values) May 7th, 2013 Sun Valley,
  36. stars.web.psi.ch Slide 36 Results: PBTT – Schemes Convergence Peak prediction

    passes below the 1% error, only to rise again afterward. Power Peak May 7th, 2013 Sun Valley, From the convergence plot.
  37. stars.web.psi.ch Slide 37 Results: PBTT – Schemes Convergence May 7th,

    2013 Sun Valley, Integrated Power Energy release error for improved schemes consistently worse than conventional OS
  38. stars.web.psi.ch Slide 38 Results: PBTT – Schemes Convergence May 7th,

    2013 Sun Valley, 0.7 s – 0.85 s 0.5 s – 0.7 s
  39. stars.web.psi.ch Slide 39 Results: PBTT – Schemes Convergence Using larger

    Δt shifts the peaks for all schemes. Schemes which yield worse peak prediction benefit from an error compensation effect May 7th, 2013 Sun Valley, 0.7 s – 0.85 s 0.5 s – 0.7 s
  40. stars.web.psi.ch Slide 40 Outline 1. Introduction 2. Improvements of the

    Temporal Coupling 3. Results: PWR Rod-Ejection-Accident (REA) 4. Results: Peach Bottom 2 Turbine Trip (PBTT) 5. Conclusions May 7th, 2013 Sun Valley,
  41. stars.web.psi.ch Slide 41 Conclusions and Outlook 1. For short and

    fast transients, the proposed improved temporal coupling schemes are enough to obtain accuracy below 1% with reasonably large Δt. 2. There are limits on how accurate coupling schemes can be for a larger Δt, especially for the part of the transient that is strongly dependent on one code. For example, the onset of power peak in REA. Sub-cycling and dynamical adaptive time-stepping might be beneficial in these cases. 3. Time-projected power scheme (with = 1.0) yields the best compromise between a better convergence and the ease of implementation (least footprint) for these two transients. Other similar extrapolation schemes are possible, e.g., exponential. May 7th, 2013 Sun Valley,
  42. This work was partly funded by Eidgenössisches Nuklearsicherheitsinspektorat (ENSI) Bundesamt

    für Energie May 7th, 2013 Sun Valley, Acknowledgements
  43. Thank you very much for your time and attention May

    7th, 2013 Sun Valley,