Two-point Model Research Articles

Reactivity Effects of Concrete Slabs in Single and Coupled Cores of Rectangular Parallelpiped Geometry

Abstract The concrete is an important material to examine the calculation model employed in the evaluation of criticality safety for nuclear fuel cycle facility. Therefore, the data of the reflection and the isolation effects on reactivity were experimentally obtained using the Tank- type Critical Assembly (TCA). Critical experiments were performed for both the single and coupled cores where low-enriched-uranium fuel rods were arranged in a rectangular parallel- piped geometry. For the single core, the concrete slabs were positioned at one side of the core, whereas they were positioned between two cores for the coupled core to measure the reactivity interaction characteristics. Main parameters were selected as the thickness and the boron content of concrete, and the water-level worth method was applied to measure the reflection effect on the single core and the reactivity interaction effect from one core to the other core on the coupled system including symmetric and asymmetric arrangements. Some benchmark calculations were also executed using the SRAC code system to assess the accuracy of this code system. Moreover, the dependency of the reactivity interaction effect on the concrete thickness and the core geometry was examined on the basis of the Avery's two-point model.

NEAR-INFRARED MEASUREMENT OF SURFACE MOISTURE ON POROUS MATERIALS

An instrument using the near-infrared reflectance technique was designed to measure surface moisture on porous materials. The basic instrument design consists of a radiation source, a lens system, narrow-band interference filters, a detector, and a data acquisition system. The instrument function, operation, and calibration are discussed in detail. The modified Kubelka-Munk function is used for the data transformation. The experimental data from glass beads of 65, 120, and 450 μm in diameter show that a two-point linear model can be utilized for calibration. The instrument uncertainty is estimated to be less than ±6.2%.

Reactivity Effects of Concrete Slabs in Single and Coupled Cores of Rectangular Parallelpiped Geometry.

Abstract The concrete is an important material to examine the calculation model employed in the evaluation of criticality safety for nuclear fuel cycle facility. Therefore, the data of the reflection and the isolation effects on reactivity were experimentally obtained using the Tank- type Critical Assembly (TCA). Critical experiments were performed for both the single and coupled cores where low-enriched-uranium fuel rods were arranged in a rectangular parallel- piped geometry. For the single core, the concrete slabs were positioned at one side of the core, whereas they were positioned between two cores for the coupled core to measure the reactivity interaction characteristics. Main parameters were selected as the thickness and the boron content of concrete, and the water-level worth method was applied to measure the reflection effect on the single core and the reactivity interaction effect from one core to the other core on the coupled system including symmetric and asymmetric arrangements. Some benchmark calculations were also executed using the SRAC code system to assess the accuracy of this code system. Moreover, the dependency of the reactivity interaction effect on the concrete thickness and the core geometry was examined on the basis of the Avery's two-point model.

Spatial relationships of multivariate data

Spatial factor analysis (SFA) is a multivariate method that determines linear combinations of variables with maximum autocorrelation at a given lag. This is achieved by deriving estimates of auto-/cross-correlations of the variables and calculating the corresponding eigenvectors of the covariance quotient matrix. A two-point spatial factor analysis model derives factors by the formation of transition matrixU comparing auto-/cross-correlations at lag “0,”R 0, with those at a specified lag “d,”R d, expressed asU d=R 0 −1 Rd. The matrixU d can be decomposed into its spectral components which represent the spatial factors. The technique has been extended to include three points of reference. Spatial factors can be derived from the relationship: $$\left[ {\begin{array}{*{20}c} {U_{d1} } \\ {} \\ {\begin{array}{*{20}c} {} \\ {} \\ \end{array} } \\ {U_{d2} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {R_0 R_{d3} } \\ {} \\ {\begin{array}{*{20}c} {} \\ {} \\ \end{array} } \\ {R_{d3} R_0 } \\ \end{array} } \right]^{ - 1} \left[ {\begin{array}{*{20}c} {R_{d1} } \\ {} \\ {\begin{array}{*{20}c} {} \\ {} \\ \end{array} } \\ {R_{d2} } \\ \end{array} } \right]$$ where the factors ofU d1 andU d2 predict the relationships of the variables over three lag distances and orientations from matricesR d1,R d2, andR d3. Estimates of auto-/cross-correlation can be achieved using irregularly spaced or gridded data from experimental correlograms or function estimates determined from the experimental correlograms. The technique has applications in studies where several variables have different spatial ranges or zones of influence.

The conductivity of aluminum nitride ceramics

Based on the analysis of the experimental behavior of the conductivity of highly dispersed aluminum nitride ceramics on temperature and frequency, conclusions are drawn about the existence in polycrystalline AIN of electromigration hopping mechanisms. At low temperatures and for high frequencies, the conductivity can be described within the framework of a two-point model, but as the temperature increases, or as the frequency decreases, a transition is observed through multiple jumps. The electromigration activation mechanisms dominate at temperatures higher than 370 K.

Identification of the transfer function between turbulence and aircraft

As the procedure to measure wind in flight is fairly well developed, it becomes possible to identify the transfer function between turbulence and an aircraft. In the view of system theory and the inherent nature of an aircraft, the approach to identificatio n is divided into two steps: first, to estimate steady aerodynamic derivatives by flight in smooth air; second, to identify the higher frequency aerodynamic transfer function by flying in a turbulent atmosphere. The latter is mainly studied here. The airplane is considered as a two-point model to describe more physically the dynamic response of an aircraft due to turbulence and the complex interaction among different parts of the airplane. The relevant effects, as far as possible, have been taken into account for simulating the complete aircraft model, which includes a model for the rigid aircraft motion and a model corresponding to the effect of turbulence. The latter unknown model is established on the analysis of its physical background. An example is demonstrated by flight test data of the research aircraft Dornier DO 128 of the Technical University of Braunschweig. This aircraft has an additional time lag of 0.1 s that will include primarily the effects of unsteady aerodynamics.

On Modeling of Plasma Edge Conditions at Divertors with Solid Metal Neutralizers

AbstractIt is widely recognized that results from divertor models can be quite sensitive to the boundary conditions that are assumed at the divertor neutralizer plate. However, some past models assumed electron and ion heat transmission coefficients with little justification. In fact, energy and momentum fluxes from backscattered neutral deuterium and tritium atoms can significantly contribute to the energy and momentum balance of the divertor plasma and consequently affect the estimates of steady-state plasma conditions. In illustration of this point, a two-point model similar to that of Galambos and Peng is rederived, including momentum and energy sources from charge-exchange and a self-consistent fluid treatment of the sheath heat transmission coefficients. Divertor conditions associated with the International Tokamak Reactor (INTOR) and International Thermonuclear Experimental Reactor (ITER)-like fusion reactors are estimated, and the effects of including the backscattered fluxes are discussed.

Some new smoother implementations for discrete-time gaussian reciprocal processes

Abstract The smoothing problem for discrete-time gaussian reciprocal processes is examined. For this class of process, the smoother takes the form of a second-order two-point boundary-value nearest-neighbour model. This smoother is non-causal, but admits causal implementations which extend the two-filter and Rauch-Tung-Striebel smoothing formulae of Gauss-Markov processes. A multi-rate implementation based on a block cyclic reduction method is also described.

An efficient deterministic‐probabilistic approach to modeling regional groundwater flow: 2. Application to Owens Valley, California

The applicability of a deterministic‐probabilistic model for predicting water tables in southern Owens Valley, California, is evaluated. The model is based on a two‐layer deterministic model that is cascaded with a two‐point probability model. To reduce the potentially large number of uncertain variables in the deterministic model, lumping of uncertain variables was evaluated by sensitivity analysis to reduce the total number of uncertain variables to three variables: hydraulic conductivity, storage coefficient or specific yield, and source‐sink function. Results demonstrate that lumping of uncertain parameters reduces computational effort while providing sufficient precision for the case studied. Simulated spatial coefficients of variation for water table temporal position in most of the basin is small, which suggests that deterministic models can predict water tables in these areas with good precision. However, in several important areas where pumping occurs or the geology is complex, the simulated spatial coefficients of variation are over estimated by the two‐point probability method.

The bias in Monte Carlo eigenvalue calculations

We study the Monte Carlo estimation of eigenvalues of the stationary transport equation by source iterations with a fixed sample size. The sample-size-dependent eigenvalue bias, characteristic of the simplistic application of this kind of calculation, is analyzed and explained, and ways to control it are suggested. A two-point reactor model, the analysis of which is very simple, is qualitatively discussed to introduce the subject. A mathematical analysis of the model follows, and is then generalized to the application of the Monte Carlo procedure to realistic neutronic assemblies. Finally, algorithms which remove the bias are considered, and their respective effectiveness discussed.

Modeling and estimation of discrete-time Gaussian reciprocal processes

Discrete-time Gaussian reciprocal processes are characterized in terms of a second-order two-point boundary-value nearest-neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics. This second-order model is the analog for reciprocal processes of the standard first-order state-space models for Markov processes. The model is used to obtain a solution to the smoothing problem for reciprocal processes. The resulting smoother obeys second-order equations whose structure is similar to that of the Kalman filter for Gauss-Markov processes. It is shown that the smoothing error is itself a reciprocal process. >

Two-point transport model for cold divertor plasmas

A two-point model for plasma transport along divertor field lines is presented here. Solutions for the steady-state plasma temperature, density, and flow speed at the divertor throat and plate are found for a given throat heat flux, divertor field line length, neutral recycling coefficient, and throat density. Because of the simplicity of the model, it is useful for parameter surveys and indications of general trends. Results from the model show that more than one steady-state solution can exist for a particular throat density and that the range of throat densities for which solutions exist is limited. Also, for a constant plasma flux at the divertor throat, as neutral recycling increases, the throat density must also increase to compensate for a large decrease in plasma flow speed at the throat.

Influence of internal degrees of freedom on flow of a rarefied gas over a flat plate

Flow of a rarefied gas over a flat plate has been investigated numerically by a number of authors, using both the kinetic model equations (e.g., 1, 2]) and the Boltzmann equation [3, 6], In most cases a solution was found for a monatomic gas. The appreciable influence of the molecule structure on local and total aerodynamic characteristics and on the flow field over a flat plate at small angles of attack was noted in [1, 5, 7], where the authors examined various models for the rotational molecular degrees of freedom. In the present paper a two-point repulsion center model with constant collision cross section is used to investigate the influence of internal degrees of freedom of the molecule in flow over a plate, positioned parallel to (angle of attack α = 0), and transverse to (α = 90 °) a rarefied gas stream. The data are compared with those calculated for a monatomic gas and from experimental results.

Effects of erythromycin on membrane-bound chloroplast ribosomes from wild-type Chlamydomonas reinhardi and erythromycin-resistant mutants

1. 1. Treatment of wild-type cells of Chlamydomonas reinhardi with high concentrations of erythromycin results in increased recovery of membrane-bound chloroplast ribosomes, presumably by preventing polysomal runoff during harvesting of cells. No such membrane-retention effect is detected if erythromycin is added after harvesting of cultures, before cell breakage. 2. 2. Growth of wild-type cells is inhibited by 10 μg/ml erythromycin, but a concentration twice as high is required to increase recovery of membrane-bound wild-type ribosomes. On the other hand, the concentrations of erythromycin which inhibit growth of mutant ery-M1b produce a membrane-retention effect. Mutant ery-U1a is resistant to high concentrations of erythromycin and no membrane-retention effect is detectable at concentrations which produce one in wild type and ery-M1b. 3. 3. These results can be reconciled by a two-point model of the mechanism of erythromycin action on chloroplast ribosomes in Chlamydomonas.

Thermodynamic properties of a two-point doubly-degenerate Hubbard model

The static susceptibility and specific heat as a function of temperature are calculated for a two-point doubly-degenerate Hubbard model. The results are compared with the nondegenerate case.

Studies of neutronic coupling by reactor noise analysis in the time domain for facilities of RCN, Petten

After a review of existing literature on determination of neutronic coupling from reactor noise, the paper gives a survey of the work on this subject done from 1966 at RCN, Petten, using noise analysis in the time domain. A summary is given of the formulas used for the analysis of the noise. In particular a matrix inversion method is described, by which a matrix of kinetic parameters (“reactor matrix”) and decay constants of the prompt modes can be found from the set of correlation functions. The experimental set-ups are shortly described. Signals from ionisation chambers and from neutron counters have been processed with digital computers. Auto- and corss-correlation functions were determined by direct calculation or by a multi-detector Rossi-α algorithm. Coupling measurements have been performed in the LFR with two-slab core and annular core, in the STEK-Argonaut with two to four coupled thermal cores, and with the various fast-thermal coupled systems STEK-4000, -3000, -2000 and -1000 with a detector in each zone. Experimental results are shown, namely an early determination of coupling reactivity for two weakly coupled cores, the application of the matrix inversion method for various thermal cores, and the attempts to determine the reactor matrix in fast-thermal cores. It was found that the methods of analysis worked well for the various weakly coupled thermal cores. The measurements in the failry strongly coupled core STEK-4000 could be interpreted by a two-point model. The matrix inversion method could be used for the other STEK cores with more pronounced higher mode effects. The two-point analysis did not lead to consistent results, however. Also Avery model calculations have been applied for these cores, but led to results different from the experimental data. It is concluded that the straightforward two-zone Avery model does not apply here and that a two-mode analysis is not sufficient to describe a system like STEK. An extension of the present theory to enable analysis for more nodes (or modes) than detectors is needed.

Investigations of the influence of feedback and coupling effects on neutron noise in a nuclear reactor

The neutron power spectral density of power reactors is influenced by many parameters. These can be summarized into two groups. The first being reactivity perturbations whose statistical characteristics are unknown in most cases, and the second being various feedback and spatially dependent transfer functions. In the case of all effects being simultaneously present, which is the case for power reactors, it is extremely difficult to understand the spectra in detail. However some of the reactivity perturbations and their influence on the neutron noise in large power reactors can be simulated in a zero power reactor. In this way the effects can be studied more flexibly without the interference of other effects. This paper describes investigations of the influence of a known feedback—namely a control loop with known transfer function—on the spectra of neutron chamber signals. Theoretical formulas for the spectra are derived using the point reactor model. These formulas were verified by noise measurements in a zero power reactor. In addition, special attention is given to the noise generated by the control loop. The influence of this feedback noise on the spectra is verified experimentally. In large reactors space dependent transfer functions must be taken into account. As a first approximation to handle the spatial dependence, the afore-mentioned investigations were extended to the two-point reactor model. Corresponding experimental work was done for the Argonaut Reactor Karlsruhe (ARK) with a symmetrical two-slab core loading. As an application to a more realistic situation coolant boiling in a BWR has been investigated. The boiling must be considered as a feedback mechanism as well as an external reactivity perturbation. In order to simulate the steam bubble content, nitrogen gas was injected into the water moderator of the ARK. By modulating the total gas flow according to the instantaneous reactor power the feedback effect was simulated. The gas flow produced a bandlimited, white reactivity noise. The upper break frequency could be used to determine the travelling time of the bubbles through the core.

Investigations of the two-detector covariance method for the measurement of coupled reactor kinetics parameters

For the measurement of point kinetics parameters of zero power reactors many different methods have been widely used and described in the literature. These include Rossi-α, probability distribution, variance-over-mean, frequency analysis, and polarity correlation of neutron detector signals. Up to now kinetics parameters of a coupled two-point reactor model have been measured only by two noise analysis techniques: Rossi-α (correlation functions) and frequency analysis (power spectral density, coherence functions) using two detectors to obtain space-dependent neutron signals. This paper describes for the first time investigations of two-detector covariance measurements and their application to the determination of coupled kinetics parameters. This technique is compared with the Rossi-α method by theoretical considerations and measurements using identical detector signals in both analysis techniques. Results were also compared to those measured previously at the same reactor by frequency analysis. Theoretical formulas for the Rossi-α experiment and variance and covariance measurements in a symmetrical two-point reactor model were derived. The material properties and neutron lifetimes for each reactor zone were assumed equivalent. The transport time of neutrons from one zone to the other was neglected. The parameters of the model include the decay constant of prompt neutrons and the coupling reactivity of the two core zones. These parameters were determined by least-squares fitting the theoretical curves to the experimental data. The measurements have been performed at the Argonaut Reactor Karlsruhe (ARK) with a symmetrical two-slab core loading for different subcritical levels. Variances and covariances of neutron counts from detectors placed in both core regions were measured in two different ways. In the first method the two-dimensional probability distribution of the number of counts from the detectors was measured using a small digital computer. The computer was used to control the gating times of two specially designed counting registers and to calculate the first and second moments. From that the covariances were calculated in real time and displayed on a CRT as a function of the counting time interval. In the second method the variance and the covariance of the detector pulses were directly measured without using the probability distributions. For this purpose a new analyser based on a special calculational algorithm was developed. This analyser can be built easily with low hardware expense. The results obtained by the Rossi-α and variance method agreed quite well. In contrast to point reactor parameter determination, where Rossi-α and variance techniques are equivalent, the variance and covariance method appear superior to the Rossi-α method in applications to coupled reactors. Kinetics parameters of a two-node reactor model can be determined more accurately by the variance technique. The effect of dead-time losses in the signal channels or in the analyser on the measured variances was also studied. The variance technique was found to be more sensitive to dead-time than the Rossi-α technique. Therefore variance measurements at fast reactors yield incorrect results except special fast electronics is used in the pulse channels.

Two-point correlation model and the redistribution of Reynolds stresses

A quasi-isotropic locally homogeneous model for the two-point double-velocity correlation tensor is developed by the application of a plausible set of symmetry restrictions to this tensor. The two-point correlation is related to the single-point correlation by three independent functions, and reduces to the nonisotropic single-point correlation and the isotropic two-point correlation in the limiting cases. It is shown that the model implies that by the use of three independent microscales (and macroscales) it is possible to describe a matrix of 27 elements of microscales (and macroscales) which describe the nonisotropic field. The model is also used to calculate the dissipation rate of the components of the Reynolds stresses. Finally, a formula which expresses the redistribution of the velocity fluctuations due to pressure fluctuations is developed.

Self-Limiting Power Excursion Characteristics of Light Water Reactor, (VI)

The theoretical analysis code named REACT, devised for covering pulsed operation of the HTR, is based on a two-point kinetic model, one point representing the average of the core, while the other is optional (e.g. hottest spot). The behavior of reactor power and other parameters are calculated by the average point, and the temperature of the hottest spot by the other point at same time. Improvements were brought to the code based on experimental data, and good agreement was found between calculation and experimental results obtained for pulsed operation. The feedback reactivity due to the Doppler effect was comprehensively evaluated by recalculation of experimental data; the void behavior was also investigated.