Calculation of the ex-core neutron noise induced by individual fuel assembly vibrations in two PWR cores

Calculation of the neutron noise induced by fuel assembly vibrations in two pressurized water reactor(PWR) cores has been conducted to investigate the effect of cycle burnup on the properties of the ex-core detector noise. An extension of the method and the computational models of a previous work have been applied to two different PWR cores to examine a hypothesis that fuel assembly vibrations cause the corresponding peak in the auto power spectral density(APSD) increase during the cycle. Stochastic vibrations along a random two-dimensional trajectory of individual fuel assemblies were assumed to occur at different locations in the cores. Two models regarding the displacement amplitude of the vibrating assembly have been considered to determine the noise source. Then, the APSD of the ex-core detector noise was evaluated at three burnup steps. The results show that there is no monotonic tendency of the change in the APSD of ex-core detector; however, the increase in APSD occurs predominantly for peripheral assemblies. When assuming simultaneous vibrations of a number of fuel assemblies uniformly distributed over the core, the effect of the peripheral assemblies dominates the ex-core neutron noise.This behaviour was found similar in both cores.     

Reactor noise measurements in the safety and regulating systems of CANDU stations

Reactor noise measurements of safety and regulating system intrumentation are performed in the CANDU nuclear power stations of Ontario Power Generation (OPG) and Bruce Power. Station signals included in the noise measurements are in-core flux detectors (ICFD), ion chambers (I/C), flow transmitters, pressure transmitters, and resistance temperature detectors (RTD). Their frequency dependent noise signatures are regularly measured during steady-state operation, and are used for parameter estimation and anomaly detection.

The specific applications include the following areas:

Flux noise measurements to detect and characterize (a) anomalies of in-core flux detectors, ion chambers and their electronics, (b) mechanical vibration of fuel channels and in-core detector tubes induced by coolant/moderator flow.

Pressure and flow noise measurements to estimate the in-situ response times of flow/pressure transmitters and their sensing lines installed in the reactor's coolant loops.

Temperature noise measurements to estimate the in-situ response times of thermal-well or strap-on type RTDs installed in the reactor's coolant and moderator loops.

Borssele PWR noise: Measurements, analysis and interpretation

In the Borssele reactor — a 450 MWe PWR — reactor noise measurements have been performed during four fuel cycles. Measurements were made with a set of ex-core neutron detectors, on one occasion an in-core displacement transducer, and with primary coolant pressure sensors. Digital analysis was applied, where the most powerful tool was the computer programme FAST, which computes auto and cross power spectra for all combinations from a set of many simultaneously recorded signals.

Analyses of neutronic signals show a reactivity noise peak at 9.2 Hz, core barrel motion peaks at about 12 and 15 Hz, a damped oscillation at about 2 Hz. Results are given for begin and end of each fuel cycle. The r.m.s. value of the low frequency noise appears to depend linearly on the boron concentration over a wide range.

Also some results of primary coolant pressure noise are presented, with coherent peaks below 15 Hz and incoherent peaks above.

The second part of the paper describes an alternative way of analyzing and interpreting noise spectra, namely attempts to decompose the neutronic power spectra into physical components, using the information present in the CPSD's of all detector combinations. The components are characterized by their detector position dependency. Effects considered are: uncorrelated noise, global reactivity noise, core motion attenuation noise, and a possible coupling between reactivity and core motion. Results show excellent separation into reactivity and core motion components with possibilities to separate overlapping peaks. Weak peaks become more easily detectable. At low frequencies the decomposition of the spectra is not yet complete, however.     

Vibration measurements in PWR obrigheim by use of in-core accelerometers

Two accelerometers were inserted into the reactor of the NPP Obrigheim (Germany), one into the core and the other above the core. The amplitude of different components vibrations (fuel element (FE), reactor pressure vessel-core barrel (RPV/CB) and the instrument string-instrument tube (IS/IT) system) were measured. Neutron-mechanical scale factors (SFs) were calculated for the in-core detectors.     

Analysis of an MTC noise measurement performed in ringhals-2 using gamma-thermometers and in-core neutron detectors

A noise measurement in the Swedish Ringhals-2 PWR was performed in January 2002 by using twelve gamma-thermometers and two in-core neutron detectors, all located on the same axial level in the reactor. The gamma-thermometers are very versatile tools since they allow estimating the core-averaged moderator temperature noise throughout the core. This core-averaged temperature noise was then used to estimate the MTC by noise analysis, via a new MTC noise estimator. It was shown that whatever the location of the neutron detector might be, the MTC is always correctly estimated by this new MTC noise estimator, without any calibration to a known value of the MTC prior to the noise measurement. For the purpose of comparisons, the MTC was also estimated by using a single gamma-thermomemeter and a single core-exit thermocouple, together with an in-core neutron detector. In such cases, the MTC was systematically underestimated, with a stronger bias for the core-exit thermocouple than for the gamma-thermometer. This shows that the main reason of the MTC underestimation by noise analysis in all the experimental work until now was due to the radially non-homogeneous temperature noise throughout the core. The resulting deviation from point-kinetics of the reactor response has a negligible effect.     

Two-group theory of noise in reflected reactors with application to vibrating absorbers

A one-dimensional semi-analytic method, based on the adjoint technique, has been developed for two-group treatment of noise in reflected reactors. The adjoint for a symmetric system is given and examined in detail. The local and global characters of noise are investigated for in-core and ex-core perturbations. Finally, the noise induced by a vibrating absorber is determined.     

Identification of reactor internals'' vibration modes of a Korean standard PWR using structural modeling and neutron noise analysis

The vibration characteristics of a Korean standard PWR reactor internals have been estimated through a three-dimensional finite element analyses and verified by using the mode separated power spectral density functions obtained from the ex-core neutron noise signals. Also the natural vibration modes of the fuel assembly have been identified measuring both the ex-core and the in-core neutron noise signals which are close to each other. As a result, the fundamental bending mode frequency of the reactor internal structure is found to be around 8 Hz and the fundamental shell mode frequency 14.5 Hz, respectively. It is also shown that the fundamental bending mode frequency of the fuel assembly is 2.3 Hz and the 2^nd bending mode frequency 5.8 Hz, respectively. These results can be used for the supplements of the Korean standard PWR's CVAP (Comprehensive Vibration Assessment Program) data.     

Noise analysis performed at the sodium cooled power reactor KNK I for malfunction diagnosis and plant surveillance

In order to use neutron noise analysis as an effective tool for early malfunction detection it is necessary to identify the driving forces and to calculate their contributions to the power fluctuations. In this paper the influence of a considerable number of measured noise sources on neutron noise within a large frequency range (10⁻³ Hz to 10³ Hz) is investigated for the sodium cooled power reactor KNK I (thermal core, 58 MW_th).

The experimental basis for the analysis is numerous records of the following signals at various power levels: neutron noise which has been measured with an in-core fission chamber and 3 ex-core ionisation chambers; the sodium inlet temperature and the coolant flow in both primary coolant loops and the movement of the control rods. In addition signals from acoustic-, seismic- and pressure transducers and the coolant outlet temperature were collected.

The influence of the thermohydraulic- and of the control system on neutron noise has also been calculated by means of the relations for linear and multiple-input systems. Important for this analysis is the reactivity-power transfer function. Calculations of this function could be confirmed by measurements using a pseudo-random binary signal as reactivity input.

The following results were obtained from the analysis of the auto-power spectral densities of the neutron flux: Fluctuations of the coolant inlet temperature and the coolant flow are relatively small sources for neutron noise. However, reactivity adjustments resulting from the automatic control system because of the inherent instability of the reactor turned out to be an important driving force.

The influence of still unknown driving forces increased considerably with the reactor power. Since the coolant flow was proportional to the reactor power in order to keep the coolant temperature constant, this result indicates that turbulent flow must have induced stochastical movements of core components. These movements are considered to have mainly caused the unknown reactivity driving forces. Their magnitude could be determined reliably only in the frequency range, in which external feedback mechanisms through the primary coolant system were negligible. For 30 to 50 % reactor power the contribution was about 30 % (for f > 5·10⁻³ Hz) and for full power it increased to about 80 % (for f > 5·10⁻² Hz) of the measured neutron noise. For frequencies > 5 Hz the white detection noise prevails. Single peaks in this frequency region could be explained by coherence function investigations between in-core and ex-core neutron detector signals and by correlation of these signals with displacement- and pressure fluctuations.

Though the measured neutron noise could not be unambiguously related to driving forces, the combination of analytical and empirical methods makes the results also applicable for the design of surveillance techniques for other sodium cooled reactors (e.g. LMFBRs). Examples for possible applications are given.     

堆外探测器读数与堆内功率分布的关系研究

通常认为堆外探测器读数与反应堆总功率之间存在正比关系,这其实很不合理,在实际运行过程中会出现很大的偏差。堆芯功率分布和堆外探测器读数的映射关系可以通过空间响应函数来更好地表达。论文介绍了空间响应函数的计算方法,压水堆的堆外探测器空间响应函数的特点、影响因素,以及其在反应堆功率重构中作用。     

Actinide destruction and power peaking analysis in a 1000 MWt advanced burner reactor using moderated heterogeneous target assemblies

The purpose of this research was to determine the effect of moderated heterogeneous subassemblies located in the core of a sodium-cooled fast reactor on minor actinide (MA) destruction rates over the lifecycle of the core. Additionally, particular emphasis was placed on the power peaking of the pins and the assemblies with the moderated targets as compared to standard unmoderated heterogeneous targets and a core without MA targets present. Power peaking analysis was performed on the target assemblies and on the fuel assemblies adjacent to the targets. The moderated subassemblies had a marked improvement in the overall destruction of heavy metals in the targets. The design with acceptable power peaking results had a 12.25% greater destruction of heavy metals than a similar ex-core unmoderated assembly. The increase in minor actinide destruction was most evident with americium where the moderated assemblies reduced the initial amount to less than 3% of the initial loading over a period of five years core residency. In order to take advantage of the high minor actinide destruction and minimize the power peaking effects, a hybrid scenario was devised where the targets resided ex-core in a moderated assembly for the first 506.9 effective full power days (EFPDs) and were moved to an in-core arrangement with the moderated targets removed for the remainder of the lifecycle. The hybrid model had an assembly and pin power peaking of less than 2.0 and a higher heavy metal and minor actinide destruction rate than the standard unmoderated heterogeneous targets either in-core or ex-core. The hybrid model has a 54.5% greater Am reduction over the standard ex-core model. It also had a 27.8% greater production of Cm and a 41.5% greater production of Pu than the standard ex-core model. The radiotoxicity of the targets in the hybrid design was 20% less than the discharged standard ex-core targets.     

In-core coolant flow monitoring of pressurized water reactors using temperature and neutron noise

Noise measurements were performed at the Loss-of-Fluid-Test (LOFT) and Sequoyah-1 pressurized water reactors (PWRs) in order to investigate the possibility of inferring in-core coolant velocities from cross-power spectral density (CPSD) phases of core-exit thermocouple and in-core neutron detector signals. These noise measurements were used to investigate the effects of inlet coolant temperature, core flow, reactor power, and random heat transfer fluctuations on the noise-inferred coolant velocities. The effect on the inferred velocities of varying in-core neutron detector and core-exit thermocouple locations was also investigated. Theoretical models of temperature noise were developed, and the results were used to interpret the experimental measurements.Results of these studies indicate that the neutron detector/thermocouple phase is useful for monitoring core flow in PWRs. Our results show that the interpretation of the phase between these signals depends on the source of temperature noise, the response times and locations of the sensors, and the neutron dynamics of the reactor. At Sequoyah-1 we found that the in-core neutron detector/core-exit thermocouple phase can be used to infer in-core coolant velocities, provided that the measurements are corrected for the thermocouple response time.     

A methodology for benefit assessment of using in-core neutron detector signals in core protection calculator system (CPCS) for Korea standard nuclear power plants (KSNPP)

Core Protection Calculator System (CPCS) is a digital computer based safety system generating trip signals based on the calculation of departure from nucleate boiling ratio (DNBR) and local power density (LPD). Currently, CPCS uses ex-core detector signals for core power calculation and it has some uncertainties. In this work, a quantitative economic benefit assessment of using in-core neutron detector signals is carried out. In-core detector signals which directly measure the inside neutron flux of core are applied to CPCS to obtain more accurate power distribution profile, DNBR and LPD to reduce the calculation uncertainties. In order to improve axial power distribution calculation, piecewise cubic spline method is applied. Simulation is also carried out to verify its applicability to power distribution calculation in this work. Simulation result shows that the improved method reduces the calculational uncertainties significantly and it allows larger operational margin. It is also assured that no power reduction is required while Core Operating Limit Supervisory System (COLSS) is out-of-service when the improved method is applied.     

Numerical simulator for noise diagnostic investigations in NPPs

A coupled thermohydraulics and neutron model is used to simulate signals of thermocouples, ex-core and in-core neutron detectors of nuclear power plants (NPP). Noise sources are generated as time functions and the dynamic behavior of the reactor core is modeled by one-dimensional two-group diffusion equations coupled with an axial thermohydraulics model. These equations are solved by numerical methods and the resulting time series are considered as virtual measurements. We show that one can model only a finite set of noise sources with high accuracy by this approach because of the finite nature of numerical methods. The selection of length of space segments is presented and the effect of space aliasing is briefly discussed. An automatic stepsize selection algortihm is introduced which was applied successfully in the simulator. Simulation results are analyzed and compared with real measurements by studying disturbance propagation in the coolant.     

Applicability of neutron noise technique for diagnostics of in-core components for heavy water reactors

Neutron flux signal is composed of a steady or mean component resulting from the flux produced by power operation of the reactor and a very small fluctuating component called ‘noise’ component. Analysis of neutron noise from suitably located sensors is a proven technique to monitor the in-core components of light water reactors (LWRs). However, the use of neutron noise has been rare, if any, for heavy water reactors (HWRs) as it was generally felt that the unfavourable transfer function characteristics of the reactors would limit its applicability. To assess the applicability of technique in pressurised heavy water reactors (PHWRs), experiments were carried out using in-core and out-of-core neutron sensors in a research reactor. This paper discusses the measurement details and results of the experiment. This paper concludes that the neutron noise technique can be effectively utilised for diagnostics/characterisation of the in-core components of heavy water reactors.     

In-Core SCC Growth Behavior of Type 304 Stainless Steel in BWR Simulated High-Temperature Water at JMTR

Irradiation-assisted stress corrosion cracking (IASCC) is one of the critical concerns when stainless steel components have been in service in light water reactors for a long period. In-core IASCC growth tests have been carried out using the compact tension-type specimens of type 304 stainless steel that had been pre-irradiated up to a neutron fluence level around 1 × 10²⁵ n/m² under a pure water simulated boiling water reactor (BWR) coolant condition at the Japan Materials Testing Reactor (JMTR). In order to investigate the effect of synergy of neutron/gamma radiation and stress/water environment on SCC growth rate, we performed ex-core IASCC tests on irradiated specimens at several dissolved oxygen contents under the same electrochemical potential condition. In this paper, results of the in-core SCC growth tests are discussed and compared with the results obtained by ex-core tests from a viewpoint of the synergistic effects on IASCC. From results of in-core and ex-core tests using pre-irradiated specimens, the effect of synergy of neutron/gamma radiation and stress/water environment on SCC growth rate was considered to be small, because the in-core data under the same ECP condition were similar to the ex-core data under the DO = 32 ppm condition.     

Kalman Filter Applied to Estimation of Neutron Flux Distribution and Optimum Allocation of In-Core Detectors

Estimation of the spatial distributions of prompt neutrons and delayed neutron precursors has been studied by analyzing the output signals of in-core neutron detectors. In this paper, application of distributed Kaiman filter is attempted for a one-dimensional core model having statistical fluctuations. Assuming that their statistics are determined by Schottky formula, the error covariance matrix of estimation is computed in order to evaluate the filter performance. In the computation of this matrix, the algebraic Riccati equation is solved by generalized Newton-Raphson method.

From the viewpoint of estimation accuracy, it is also an important problem to optimize the detector locations. Considering the cases where estimation is focussed on a specified quantity related to prompt and delayed neutrons, the optimum allocations of two detectors are searched numerically. It is inferred that the optimized allocation has a considerable effect on estimating the shapes of the distributions where higher terms of spatial harmonics cannot be neglected.     

去射线效应堆外探测器响应函数计算研究

堆外探测器响应函数表征了堆芯活性区各位置处的裂变中子对堆外探测器响应的贡献,通过共轭S_N输运计算可快速得到堆外探测器的响应函数。然而,堆外探测器远离堆芯且相对于堆芯体积很小,S_N方法的计算结果会受到射线效应的影响。为解决堆外探测器响应函数计算中的射线效应问题,研究了共轭首次碰撞源射线效应消除方法。此外,为克服共轭首次碰撞源方法在三维堆芯计算中面临的计算量大、内存需求高等问题,研究了共轭首次碰撞源的并行化计算方法和动态内存管理方法。基于韩国Kori-1压水堆的计算结果表明：共轭首次碰撞源S_N方法和多群蒙特卡罗方法具有相当的计算精度,但计算效率高1个量级。     

基于BP神经网络的堆芯三维功率重构方法研究

堆芯功率分布包含了堆芯内的大量信息,由于在反应堆运行过程中无法直接测量堆芯内所有位置的功率,因此需通过其他方法得到堆芯三维功率分布的情况。本文以秦山一期工程为对象,利用堆外中子探测器在不同棒位和不同功率下的计数及BP神经网络对堆芯三维功率分布进行重构计算,并利用REMARK程序对该计算结果进行验证。结果表明,该功率重构方法能在反应堆运行的50%～100%功率范围内,较好地呈现堆芯三维功率分布。     

Investigation of the two-phase flow in a boiling water reactor using neutron-noise technique

In this paper, the fluctuations of the neutron flux (“neutron noise”) of the Mühleberg BWR are investigated. Above 2 Hz, the noise measured by the in-core neutron detectors is driven exclusively by local fluctuations of the void fraction. Characteristic changes of the neutron-noise signature along the axis can be attributed to changes of flow pattern. By measuring the phase lag between pairs of axially placed neutron detectors, the transit time of the steam between the detectors can be evaluated. The measured transit times are applied to the study of two-phase flow in the core. The neutron-noise method has the advantage of providing in-core information under operational conditions.