Akitoshi Hotta

Development of BWR regional instability model and verification based on ringhals 1 test

Abstract The mathematical model of LAPUR , the well-known frequency domain stability code, was reviewed and modified from the viewpoint of the pure thermohydraulic and neutronic-thermohydraulic interaction mechanisms. Based on the ex-core loop test data, the original combined friction and local pressure loss model was modified taking account of the different dynamic behavior of these two pressure loss mechanisms. That is, the perturbation terms of the two-phase friction multiplier and mass flux correction factor were adjusted semi-empirically. With reference to the neutronic-thermohydraulic interaction, the new regional instability model was introduced considering not only the sub-criticality but also the shape of the higher neutron flux mode. The efficient three-dimensional modal analysis schemes were studied and realized as the independent two energy-groups diffusion code, ACCORD . The power iteration scheme was applied with Wielandt method. In order to resolve tightly clustered harmonic modes, the proper initial guess was given which was derived by the horizontally two-dimensional calculations taking account of the primary important first azimuthal modal shape. The adequacy of the instability evaluation system was verified based on the Ringhals 1 test data which were supplied to participants of the OECD/NEA BWR stability benchmark project. The predominant first azimuthal oscillating power shape was evaluated based on Local Power Range Monitor (LPRM) signals. The prediction by ACCORD shows an excellent agreement both in the LPRM responses and the angle of the neutral line. The measured core-wide and regional instability decay ratios were compared with the prediction by Modified LAPUR . Both the bias and standard deviation of the decay ratios are about 0.1 for both instability modes, which is acceptable in the practical design. An extensive phenomenological study was performed regarding the regional instability predominance. The dependence of the core-wide and regional decay ratios was investigated for several power shape indices. It was indicated that the newly proposed distance-weighted 2nd order axial power momentum will be a good index.

Development of Parallel Coupling System between Three-Dimensional Nodal Kinetic Code ENTREE and Two-Fluid Plant Simulator TRAC/BF1

The high-speed three-dimensional neutron kinetic code ENTRÉE was developed based on the polynomial and semi-analytical nonlinear iterative nodal methods (PNLM and SANLM) with also introducing the discontinuity factor. In order to enhance the efficiency of transient calculation, the nonlinear correction-coupling coefficients are intermittently updated based on the changing rate of core state variables. By giving the analytical form for two-node problem matrix elements, the additional computing time in SANLM was minimized. A fast algorithm was developed for the multi table macro-cross section rebuilding process. The reactivity component model was implemented based on the variation of the neutron production and destruction terms. The code was coupled with the two-fluid thermal hydraulic plant simulator TRAC/BF1 through PVM or MPI protocols. Two codes are executed in parallel with exchanging the feedback parameters explicitly. Based on the LMW PWR transient benchmark, it was shown that both PNLM and SANLM spend less than 20% excess computing time in comparison with the coarse mesh finite difference method (CFDM). The implementation of the discontinuity factor was verified based on the DVP problem. Adequacy and parallel efficiency of the coupling system TRAC/BF1-ENTREE was demonstrated based on the BWR cold water injection transient proposed by NEA/CRP.

Numerical Study on Observed Decay Ratio of Coupled Neutronic-Thermal Hydraulic Instability in Ringhals Unit 1 under Random Noise Excitation

The core stability in the Ringhals Unit 1 was estimated under the numerical random noise that simulates indefinable two-phase flow noise sources in actual cores. This noise model is expressed as a product of band white amplitude and arbitrary shape functions. In evaluating decay ratios, the conventional free-decaying method based on a clean modal disturbance was replaced with the response analysis method based on a numerical moderator density noise. The stability monitoring procedure was reproduced numerically by giving the spatially random shaped noise disturbance and by linearly varying the moderator density reactivity multiplier. It was confirmed that the observed regional decay ratio based on differential LPRM signals proposed by Hagen sometimes shows a discontinuous jump from the stable to the unstable region as predicted by Pazsit. Nevertheless, the regional decay ratio based on the extracted modal response will show a continuous change under the same condition. It was clarified that this jumping is mainly induced by the local fluctuation of moderator density at the frequency range which overlaps with a predominance range of the fundamental mode. It was demonstrated that this kind of numerical noise analysis is useful in verifying the monitoring algorithm before applying it in actual plants.

BWR Regional Instability Analysis by TRAC/BF1-ENTREE - I: Application to Density-Wave Oscillation

In this study, applicability of the TRAC/BF1-ENTREE code to regional instability was demonstrated in two parts. In Part I, fidelity of numerical models was studied with regard to the density-wave oscillation. Based on the FRIGG-4 loop test, predictability of the code has been demonstrated. An appropriate time integration scheme was explored, and it was found that the numerical viscosity can be minimized by applying the semi-implicit method and specifying the material Courant number close to unity. Applicability of the code was studied for simulating parallel channel configurations. The bypass channel effect was quantified as a function of its flow area and power level. The influence of flow mixing at the upper and lower plena was studied.

BWR Regional Instability Analysis by TRAC/BF1-ENTRÉE - II: Application to Ringhals Unit-1 Stability Test

Based on the Ringhals unit-1 stability test results, the coupling system TRAC/BF1-ENTREE has been bench-marked for predicting decay ratio and limit-cycle amplitude of the regional instability. The core was mapped into fewer CHAN groups based on the first azimuthal mode flux shape and the guidelines to minimize the numerical interregion stabilizing interaction. The system was further applied to detailed phenomenological studies. A symmetric pattern of the first azimuthal mode gave a dynamic boundary condition for ideal out-of-phase flow oscillations and lowers the regional instability threshold. The intermode interaction between the fundamental and first azimuthal modes was demonstrated under postulated large oscillations. Self- and mutual-modal reactivities were evaluated based on the higher modal flux shapes derived by ACCORD-N.

Neutronic model for modal multichannel analysis of out-of-phase instability in boiling water reactor cores

Abstract A neutronic model for linear multichannel analysis of out-of-phase (regional) instability in a BWR core is derived. In this model, the zero-power transfer function of a spatial-harmonic mode, the nodal component of the harmonic amplitude and the node-wise feedback coefficients for the mode appear. Applying the modal expansion technique to a transient flux, we can formulate the above transfer function, nodal component and feedback coefficients. When the λ-mode eigenvalues, eigenfunctions and adjoint-eigenfunctions are numerically obtained by a three-dimensional calculation, these quantities can be evaluated. We derive a lumped neutronic model by the reduction of the present multi-channel model. Consequently, the lumped feedback coefficients for the first-harmonic mode and the nodal component of the harmonic amplitude can be explicitly expressed.

Regional instability evaluation of Ringhals unit 1 based on extended frequency domain model

The frequency domain model has been extended for the regional instability evaluation while retaining its practicality and improving the reliability of major influential numerical models. The unified friction and local pressure loss model of the original LAPUR was modified considering the different dynamic characteristic of two pressure loss mechanisms. The detailed ex-core recirculation loop model was implemented and the neutron point kinetics model was also modified to reflect the inter-mode void reactivity interaction. The neutron flux modal analysis code, ACCORD-N, was developed based on the nonlinear iterative nodal method. Efficient schemes were proposed to give the higher mode initial flux guess. The modified code system was verified based on the Ringhals unit 1 stability test data. Extensive studies were performed to identify influential factors in the regional instability. A dependence of the decay ratio was investigated with regard to the sub-criticality of the first azimuthal mode, Nyquist plots and several power shape indices. It seemed reasonable to conclude that the regional instability was strongly influenced by the thermal hydraulic mechanism. Including the simulation results of other reactors, the distance weighted axial power momentum, named the AS-value, gave a good account of both core-wide and regional instability modes.

Nonlinear iterative nodal method applied to neutron flux modal analysis

The CCCMA (Correction Coupling Coefficient Modal Analysis) method has been proposed to improve the spatial resolution of the neutron flux modal analysis. The improvement has been achieved by including the higher order intra-nodal information through the NLM (Nonlinear Iterative Method)-correction coupling coefficient. The new code system, ENTREE/ACCORD-N, has been developed in which both the polynomial and semi-analytical Legendre flux expansion functions have been implemented. The application to the two-dimensional homogeneous and heterogeneous cores that were created from the stability test point, in Ringhals Unit 1 was demonstrated. The neutral line angle, eigenvalue and power shape obtained by the CCCMA were compared with those by the FDMA (Finite Difference Modal Analysis) of various mesh sizes. The CCCMA was shown to improve the solution accuracy significantly in the heterogeneous core. The ratios of the NLM-correction to FDM. (Finite Difference Method) coupling coefficients in the fuel region gave ...

Proposal of an Effective Initial Guess Scheme for Higher Harmonic Mode Calculation of Boiling Water Reactor Cores

The initial flux guess schemes for improving the numerical convergence were investigated based on the calculation results of the Ringhals-1 test data. Higher harmonic modes can be calculated with ACCORD making use of the power method and substraction method. The predicted higher harmonic mode shape during regional oscillation events was compared with the measurement of LPRM signals

Simulation of boiling water reactor one-pump trip transient by TRAC/BF1-ENTRÉE

Abstract The three-dimensional plant simulator TRAC/BF1-ENTRÉE was validated based on a one-pump trip test. Trends in major plant process parameters and three-dimensional power distributions were studied with regard to in-core flow reduction, insertion of control blades, and neutron spectrum mismatch. An improved moderator direct heating model was proposed by separately modeling the neutron slowing down and the gamma-ray absorption mechanism. The delayed heat conduction caused by the gamma heating in metallic regions was implemented. Sensitivities of water level and three-dimensional power were studied by varying the core power history, the dryer loss coefficient, and the neutron kinetics solution approach.