Some new viewpoints in reactor noise analysis

It is propsed that the linearity criterion and order criterion via frequency spectrum features without any limitation of the model‘s phase can be used in reactor noise analysis.The time constant,natural frequency as well as the recovered transfer function of reactors can bhe obtained via the analyzable model based on reactor noise.     

Numerical tools applied to power reactor noise analysis

In order to be able to calculate the space- and frequency-dependent neutron noise in real inhomogeneous systems in two-group theory, a code was developed for the calculation of the Green's function (dynamic transfer function) of such systems. This paper reports on the development as well as the test and application of the numerical tools employed. The code that was developed yields the space-dependence of the fluctuations of the neutron flux induced by fluctuating properties of the medium in the two-group diffusion approximation and in a two-dimensional representation of heterogeneous systems, for both critical systems and non-critical systems with an external source. Some applications of these tools to power reactor noise analysis are then described, including the unfolding of the parameters of the noise source from the induced neutron noise, measured at a few discrete locations throughout the core. Other concrete applications concern the study of the space-dependence of the Decay Ratio in Boiling Water Reactors, the noise-based estimation of the Moderator Temperature Coefficient of reactivity in Pressurized Water Reactors, the modeling of the beam- and shell-mode core-barrel vibrations in Pressurized Water Reactors, and the investigation of the validity of the point-kinetic approximation in subcritical systems driven by an external source. In most of these applications, calculations performed using the code are compared with at-power plant measurements. Power reactor noise analysis applications of the above type, i.e. core monitoring without disturbing plant operation, is of particular interest in the framework of the extensive program of power uprates worldwide.     

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.     

Application of autoregressive moving average model in reactor noise analysis

In this paper the system of the generalized Yule-Walker equations is derived from the equation of an ARMA model, then a method for its solution is given. Numerical results show the applications of the method proposed.     

Adjoint sensitivity analysis in nuclear reactor fuel behavior modeling

A computer program, SCODE, has been developed for calculating sensitivities for EPRI's SPEAR-ALPHA nuclear fuel performance code FCODE-ALPHA. Eleven critical parameters are assessed for the effects of their independent variations on 33 basic variables in the FCODE-ALPHA model. The enormous wealth of sensitivities that result, consisting of 363 quantities per axial node per time step, are calculated following FCODE-ALPHA computations on each time step. SCODE is based on adjoint sensitivity analysis, which is an analytic technique, obviating the need for numerical differentiation via repeated code runs at varied parameter values. Evaluation of sensitivities is reduced to a problem in linear algebra and is handled by standard matrix manipulations. Compared with the customary numerical differentiation approach, SCODE offers advantages of significant runtime reduction, exactitude of results, and on-line computation of sensitivities.     

Source papers in reactor noise

Reactor noise analysis is of practical importance in securing the safety and availability of nuclear power plants. Recognition of this importance is well disseminated among personnel engaged in research and development as well as supply and management of nuclear energy. Many more people will become concerned with and disciplined in reactor noise signature analysis in the future in order to further develop the technique for its application in balance-of-plant surveillance and diagnostics.

Newcomers to any well matured research field are, however, often perplexed by the quantity of relevant scientific papers; the fruits of creative and earnest research work. Noise analysis research originated as early as the 1940s. This presentation of fundamental and initial breakthrough papers will be useful for newcomers, as well as graduate students of nuclear engineering, who will be, hereupon, informed of the most important developments which have led to our present understanding of the subject.

The author sincerely welcomes any specialist of noise analysis to criticize and supplement this article.     

Analysis of pool-type reactor noise

A theoretical and experimental analysis is presented of pool-type reactor noise caused by thermal hydraulic and mechanical phenomena. The thermal hydraulic model is based on fluctuations of coolant inlet temperature and coolant velocity as noise sources. Resonance peaks in the reactor noise spectrum are explained by simple mechanical models of the reactor structure and the instrument tubes.     

A method for statistical steady state thermal analysis of reactor cores

This paper presents a method for performing a statistical steady state thermal analysis of a reactor core. The technique is only outlined here since detailed thermal equations are dependent on the core geometry. The method has been applied to a pressurised water reactor core and the results are presented for illustration purposes.Random hypothetical cores are generated using the Monte-Carlo method. The technique shows that by splitting the parameters into two types, denoted core-wise and in-core, the Monte Carlo method may be used inexpensively. The idea of using extremal statistics to characterise the low probability events (i.e. the tails of a distribution) is introduced together with a method of forming the final probability distribution. After establishing an acceptable probability of exceeding a thermal design criterion, the final probability distribution may be used to determine the corresponding thermal response value. If statistical and deterministic (i.e. conservative) thermal response values are compared, information on the degree of pessimism in the deterministic method of analysis may be inferred and the restrictive performance limitations imposed by this method relieved.     

A seismic analysis method for a block column gas-cooled reactor core

An analytical method for predicting the behavior of a prismatic high-temperature gas-cooled reactor (HTGR) core under seismic excitation has been developed. In this analytical method, blocks are treated as rigid bodies, are constrained by dowel pins which restrict relative horizontal movement but allow vertical and rocking motions. Coulomb friction between blocks and between dowel holes and pins is also considered. A spring dashpot model is used for the collision process between adjacent blocks and between blocks and boundary walls.Analytical results are compared with experimental results and are found to be in good agreement. The analytical method can be used to predict the behavior of the HTGR core under seismic excitation.     

A probabilistic method for leak-before-break analysis of CANDU reactor pressure tubes

In modern CANDU nuclear generating stations, pressure tubes of cold-worked Zr-2.5Nb material are used in the reactor core to contain the fuel bundles and the heavy water (D₂O) coolant. The pressure tubes operate at an internal pressure of 10 MPa and temperatures ranging from 250°C at the inlet to 310°C at the outlet. Over the expected 30 year lifetime of these tubes, they would be subjected to a total fluence of 3×10²⁶ n m⁻². In addition, these tubes gradually pick up deuterium as a result of a slow corrosion process. When the hydrogen plus deuterium concentration in the tubes exceeds the hydrogen/deuterium solvus, the tubes are susceptible to a crack initiation and propagation process called delayed hydride cracking (DHC). If undetected, such a cracking mechanism could lead to unstable rupture of the pressure tube. The service life of the pressure tubes is determined, in part, by changes in the probability for the rupture of a tube. This probability is made up of the probability for crack initiation by DHC multiplied by the sum of the probabilities of break-before-leak and leak-before-break (LBB). A probabilistic model, BLOOM, is described which makes it possible to estimate the cumulative probabilities of break-before-leak and LBB. The probability of break-before-leak depends on the crack length at first leak detection and the critical crack length. The probability of a LBB depends on the shut-down scenario used. The probabilistic approach is described in relation to an example of a possible shut-down scenario. Key physical input parameters into this analysis are pressure tube mechanical properties, such as the crack length at first coolant leakage, the DHC velocity and the critical crack length. Since none of these parameters are known precisely, either because they depend on material properties, which vary within and between pressure tubes, and/or because of measurement errors, they are given in terms of their means and standard deviations at the different temperatures and pressures defined by the shut-down scenario.     

Application of reactor noise analysis in the candu reactors of Ontario hydro

Reactor noise analysis techniques are being applied in Ontario Hydro's CANDU nuclear generating stations to monitor the dynamic characteristics of critical plant components and processes. A comprehensive analysis of stationary signal fluctuations (noise) of the standard instrumentation of Pickering-B, Bruce-B and Darlington units has been carried out in the past two years. In these measurements the feasibility of applying noise analysis techniques to actual operating data has been demonstrated. The results indicated that the detection and characterization of instrument and process failures, and validation of process signals and instrument functionality can be based on the existence of certain statistical signatures derived from the measured reactor noise signals.     

基于参数的可视化裂变堆芯蒙特卡罗自动建模方法

蒙特卡罗程序已经广泛应用在裂变反应堆设计和验证过程中,快速获得高效的计算模型可以有效缩短反应堆的设计周期。本研究提出并实现了一种裂变堆芯快速蒙特卡罗建模的方法,该方法基于参数可视化和层次化两种建模思想快速构建出精细裂变堆芯计算机辅助设计(Computer Aided Design,CAD)模型且将其快速转换成蒙特卡罗计算模型,同时采用一种新的堆芯分段管理方法实现了大规模裂变堆模型流畅交互。基于此方法快速构建了加速器驱动次临界反应堆(Accelerator Driven Sub-critical System,ADS)的精细堆芯模型,通过与蒙特卡罗程序计算的参考结果进行对比,证明了此建模方法的高效性和可靠性。     

Steam separator modeling for various nuclear reactor transients

Experiments were performed using air and water on three types of centrifugal separators plus gravity and secondary separators. Experiments were also done in the MIT blowdown rig, with and without a centrifugal separator, using steam and water. Appreciable carry-over from the steam generator occurs when the drain lines from the three stages of separation (centrifugal, gravity, and secondary) are unable to carry-off the liquid flow due to the high downcomer water level. Failure scenarios of the separator for conditions ranging from quasi-steady state to fast transients are presented. Separators, in general, in fast (blowdown) transients were found to increase the carry-over slightly. A module showing the general separator model structure is provided and recommendations are made for modeling the separator.     

Dynamics modeling and stability analysis of a fluidized bed nuclear reactor

A theoretical model describing the coupling of neutronics, thermohydraulics and fluidization in a fluidized bed nuclear reactor is presented. The stability of the system is investigated by linearizing and perturbing the system around its equilibrium points and identifying the root loci of the sytem. It is found that within the operational range, the eigenvalues are located in the negative part of the phase plane, implying linear stability. Simulations of transient conditions are performed, viz. a hypothetical startup transient and a quasistatic transient related to noise resulting from stochastic movements of the fuel particles. These simulations show that although the total power of the reactor may reach high values, the fuel temperature is well below safety limits at all times.     

A systematic method to identify nonlinear dynamics of BWR by using the reactor noise

For the identification of the dynamics of the Vermont Yankee BWR with the reactor noise, different parametric models have been tested. The widely used ARMA model is unable to identify the nonlinearity in the noise data. A systematic method by using the NARMA model, which takes advantage of both the ANN and ARMA, is developed. Comparisons are made between the identification results with ARMA and NARMA model. The advantages of identification with NARMA model over ARMA model are demonstrated. The linear-kernels of the identified NARMA models are extracted so that the natural frequency, damping ratio and time constants of the BWR are obtained. The values of those characteristics are well corresponded with the eigenvalues calculated by the differential equations of the Vermont Yankee BWR. The damping ratio with negative value is found to be a criterion for the existence of limit-cycle, which can be seen from the impulse response on the (X_t, X_t−1) plane, in stable nonlinear system.     

A computerized method for flow-induced random vibration analysis of nuclear reactor internals

The general analytical, numberical, and programming techniques of a computerized method for flow-induced random vibration analysis of nuclear reactor internal components is discussed. The statistical approach used is similar to that originally introduced by Powell and subsequently applied to predict the response of flat plates to homogeneous turbulent air flow. The input damping ratios and parameters related to the flow field are assumed to be known from experimental data, while the virtual mass and natural frequency shift effects due to hydraulic loading of the structure are included in the analysis. The latest numerical techniques developed for use with modern, high-speed digital computers are employed to evaluate the acceptance integrals, thus permitting the basic method to be applied to the vibration analysis of complex structures excited by inhomogeneous turbulent flow — a situation that is commonly encountered inside a nuclear reactor. The importance of computer program modulization and its relationship to overlays are discussed. Some representative predicted vibration amplitudes based on a typical pressurized water reactor design are given.     

A fluid-structure finite element method for the analysis of reactor safety problems

A method is presented for the safety analysis of reactor containment structures by means of finite elements. The finite element equations of both fluid and structural elements for arbitrarily large, non-linear response are developed and the way in which they are combined is indicated. Both explicit and implicit integration of the equations in time is considered. Three examples of the application of these methods to the analyses of reactor safety problems are described.     

A hybrid method to generate few-group cross sections for fast reactor analysis

The accuracy of fast reactor core calculation is usually determined by the accuracy of self-shielded few-group cross sections. To further improve the accuracy of cross section generation, a hybrid method is proposed. In the hybrid method, the Monte-Carlo method is used to deal with the resonance effect in both the resolved and unresolved resonance range. The self-shielded ultrafine-group total, fission and elastic scattering cross sections are tallied by the Monte-Carlo method. The scattering transfer matrices are then generated in a synthesis way by using the tallied elastic scattering cross sections and a problem-independent elastic scattering function. The angular flux moments for the group condensation are calculated in an explicit deterministic way. Several tests are done to verify the hybrid method. The results show that the hybrid method avoids the disadvantages of both the traditional deterministic method and the pure Monte-Carlo method. It is a more accurate method to generate the few-group cross sections for fast reactor cores.