Flux Shape Research Articles

Demonstration of Multigroup Multiband Cross Section Generation in Monte Carlo Simulations

This is the investigation into the generation of high-fidelity multigroup multiband cross sections from Monte Carlo neutron transport simulations. Previous methods for generating multigroup multiband (MGMB) cross sections, and multigroup cross sections, assume an approximate shape for the scalar flux. This approximate flux shape is the product of an energy-dependent spectrum and a cross-section-dependent self-shielding factor for the material of interest. Since, these methods assume a scalar flux a priori, the cross sections generated may not be sufficiently consistent with the actual scalar flux of any particular problem. Instead, in our approach we tally both the reaction rate and the flux for each energy group and cross section magnitude band using the Mercury Monte Carlo particle transport code and compute the group-band cross sections from these tallies. This approach eliminates the need for assuming a flux by using a Monte Carlo simulation to calculate these cross sections. The increased physical fidelity of MGMB also requires more data storage, since more than one cross section value needs to be stored per energy group. However, this storage tradeoff could be mitigated by using less energy groups.

Improved Accuracy in the 2-D/1-D Method with Anisotropic Transverse Leakage and Cross-Section Homogenization

The Two-Dimensional (2-D)/One-Dimensional (1-D) method allows pin-resolved computational transport solutions for large, full-core light water reactor simulations at relatively low computational cost compared to a true three-dimensional (3-D) transport method. The 2-D/1-D method constructs an approximation to the 3-D transport equation with (1) a 2-D transport equation in the radial variables and , discretized on a fine radial spatial grid, and (2) a 1-D transport (or approximate PN) equation in the axial variable , discretized on a radially coarse spatial grid. The 2-D and 1-D equations are coupled through transverse leakage (TL) terms. In this paper, a new 2-D/1-D P3 method with anisotropic transverse leakages and anisotropic homogenized 1-D cross sections (XSs) is proposed to improve the accuracy of conventional 2-D/1-D with pin homogenization. It is shown that only the polar component of the anisotropic homogenized XS has a significant effect on the solution; the azimuthal component is negligible. However, the polar and azimuthal components of the leakage terms are both important. The new method is implemented in the 2-D/1-D code Michigan PArallel Characteristics Transport (MPACT). The method in this paper is shown to achieve nearly 3-D transport accuracy with sufficient refinement in space and angle. The improvement of this new method compared to the previous 2-D/1-D method in MPACT is most notable in problems with strong axial leakage and sharp axial discontinuities, such as control rod tips or part-length rods. The method is computationally more expensive than the existing 2-D/1-D method with isotropic TL and XSs, but this additional cost may be justified when the axial flux shape does not vary smoothly due to axial heterogeneity and needs to be resolved well.

Position-dependent delayed-neutron fractions for IQS calculations and application to PHWR kinetics calculations

Abstract The core of a Pressurized Heavy-Water Reactor (PHWR) contains fuel bundles with burnups varying between zero and the discharge burnup. Because the delayed-neutron fraction varies (decreases) with burnup, the spatial variation of the fuel burnup causes the delayed-neutron fraction to also depend on position. High-fidelity kinetics calculations need to account for such spatial dependence of the delayed-neutron fraction. This work documents the implementation of the capability to model position-dependent delayed-neutron fractions in the multi-group diffusion code DONJON which performs kinetics calculations using the Improved Quasi-Static (IQS) method. Consistent with the IQS method, the effect of the spatial variation of the delayed-neutron fraction is accounted for both in the overall effective delayed neutron fraction and in the spatial dependence of the delayed-neutron source. Consequently, both the amplitude and the shape of the neutron flux are impacted by the position-dependence of the delayed-neutron fraction. The functionality of the newly-implemented capability is tested for a stylized coolant-voiding transient in a PHWR core and differences in reactor power and core neutron flux shape are shown to exist between the results of calculations that use position-dependent delayed-neutron fractions and those that only use spatially uniform ones.

Investigation of antineutrino spectral anomaly with reactor simulation uncertainty

Recently, three successful antineutrino experiments (Daya Bay, Double Chooz, and RENO) measured the neutrino mixing angle θ13; however, significant discrepancies were found, both in the absolute flux and spectral shape. Much effort has been expended investigating the possible reasons for the discrepancies. In this study, Monte Carlo-based sampling was used to evaluate the fission fraction uncertainties. We found that fission cross-section uncertainties are an important source of uncertainty for 235U, 239Pu, and 241Pu, but for 238U, elastic and inelastic cross-sections are more important. Among uncertainty related to manufacturing parameters, fuel density is the main uncertainty; however, the total manufacturing uncertainty was very small. The uncertainties induced by burnup were evaluated through the atomic density uncertainty of the four isotopes. The total fission fraction uncertainties from reactor simulation were 0.83%, 2.24%, 1.79%, and 2.58% for 235U, 238U, 239Pu, and 241Pu, respectively, at the middle of the fuel cycle. The total fission fraction uncertainty was smaller than the previously derived value of 5%. These results are helpful for studying the reactor antineutrino anomaly and precisely measuring the antineutrino spectrum in the Daya Bay antineutrino experiment.

Effect of Aberration on the Estimated Parameters of Relativistic Radio Jets

The influence of aberration on the observational parameters of radio jets and estimates of their physical properties is studied. Aberration distorts the apparent shapes of radio sources. Two identical relativistic jets (whose spectra have maxima) moving approximately along the line of sight could be observed as a compact GPS radio source (jet) and an extended source with a power-law spectrum (counterjet). The apparent flux densities, shapes, and spectra of relativistic radio jets are distorted even when the jets lie in the plane of the sky (across the line of sight). Exact formulas are derived for the estimated physical parameters of relativistic radio jets, taking into account aberration.

The Origins of the Gamma-Ray Flux Variations of NGC 1275 Based on Eight Years of Fermi-LAT Observations

Abstract We present an analysis of eight years of Fermi-LAT (>0.1 GeV) γ-ray data obtained for the radio galaxy NGC 1275. The γ-ray flux from NGC 1275 is highly variable on short (∼days to weeks) timescales, and has steadily increased over this eight year timespan. By examining the changes in its flux and spectral shape in the LAT energy band over the entire data set, we found that its spectral behavior changed around 2011 February (∼MJD 55600). The γ-ray spectra at early times evolved largely at high energies, while the photon indices were unchanged at later times despite rather large flux variations. To explain these observations, we suggest that the flux changes at the early times were caused by injection of high-energy electrons into the jet while, later, the γ-ray flares were caused by a changing Doppler factor owing to variations in the jet Lorentz factor and/or changes in the angle to our line of sight. To demonstrate the viability of these scenarios, we fit the broad band spectral energy distribution data with a one-zone synchrotron self-Compton (SSC) model for flaring and quiescent intervals before and after 2011 February. To explain the γ-ray spectral behavior in the context of the SSC model, the maximum electron Lorentz factor would have changed at the early times, while a modest change in the Doppler factor adequately fits the quiescent and flaring state γ-ray spectra at the later times.

Design concepts of small CANDLE reactor with melt-refining process

The innovative CANDLE (Constant Axial shape of Neutron flux, nuclide densities and power shape During Life of Energy production) burnup strategy has several advantages over conventional fast reactor designs: namely, the reactor characteristics do not change with burnup, it is possible to withdraw the burnup reactivity control mechanism, there is no need for orifice control along with burnup, and it is easy to extend reactor life by increasing the core height and using natural uranium as fresh fuel. Maintaining the fuel cladding integrity of a CANDLE reactor during operation is one of the key technological challenges that still need to be addressed. The introduction of the melt-refining process has shown great potential for solving this challenge in the high-burnup condition of large CANDLE reactors. The purpose of the present study was to design a small CANDLE reactor with the melt-refining process. With metallic fuel of natural uranium (90 wt% U, 10 wt% Zr), ODS cladding material, and lead-bismuth eutectic (44.5 wt% Pb, 55.5 wt% Bi) coolant, a 300-MWt reference core of 1.3-m radius and 2.2-m length can realize CANDLE burning. The results of our analysis demonstrate that it is possible to design a small CANDLE reactor with the melt-refining process. The analysis focused on the impacts of core homogenization, melt-refining, and the cooling and waiting times of the fuel. From the equilibrium analysis, the burning region velocity, neutron flux distribution, power density distribution, and core nuclide number density distribution were obtained. Applying the melt-refining process reduced the burning region velocity from 0.70 cm/year to 0.59 cm/year. Meanwhile, the minimum effective neutron multiplication factor and core averaged discharged fuel burnup were increased from 1.0047 to 1.0235, and from 435.2 GWd/t to 523.7 GWd/t, respectively.

Unsteady MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid with Cattaneo heat flux and different particle shapes

The paper aims to investigate the unsteady natural convection flow and heat transfer of fractional Maxwell viscoelastic nanofluid in magnetic field over a vertical plate. The effect of nanoparticle shape is first introduced to the study of fractional Maxwell viscoelastic nanofluid. Fractional shear stress and Cattaneo heat flux model are applied to construct the governing boundary layer equations of momentum and energy, which are solved numerically. The quantities of physical interest are graphically presented and discussed in detail. It is found that particle shape and fractional derivative parameters have profound influence on the flow and heat transfer.

Enhanced geometric capabilities for the transient analysis code T-ReX and its application to simulating TREAT experiments

Advances in computational architecture have prompted a resurgence in the simulation of reactor transients from first principles. Most codes are unable to simulate transient events with complex models, and require numerous approximations. The code T-ReX (Transient-Reactor eXperiment simulator), an extensive update to TDKENO, has been developed as a transient analysis tool with few geometric limitations, and minimal theoretical approximations. T-ReX achieves this by employing the Improved Quasi-Static (IQS) method to solve the time-dependent Boltzmann transport equation with explicit representation of delayed neutrons. The primary change in T-ReX relative to TDKENO is the incorporation of a modified version of the Monte Carlo code KENO-VI to calculate the flux shape and model the geometry of a problem. Using KENO-VI to model systems allows exact representation of the geometry. The changes to T-ReX are verified by comparison of solutions to computational benchmark problems found with a previous version of TDKENO that made use of KENO V.a, and several other codes with time-dependent capabilities. In addition, a three-dimensional KENO-VI model of the Transient Reactor Test Facility (TREAT) core is used in simulations of several temperature-limited transient experiments from the M8 Calibration series. T-ReX produces results that agree with benchmark problems and are in better agreement with TREAT experimental data than TDKENO.

Neutrino Physics with Nuclear Reactors: An Overview

Nuclear reactors provide an excellent environment for studying neutrinos and continue to play a critical role in unveiling the secrets of these elusive particles. A rich experimental program with reactor antineutrinos is currently ongoing, and leads the way in precision measurements of several oscillation parameters and in searching for new physics, such as the existence of light sterile neutrinos. Ongoing experiments have also been able to measure the flux and spectral shape of reactor antineutrinos with unprecedented statistics and as a function of core fuel evolution, uncovering anomalies that will lead to new physics and/or to an improved understanding of antineutrino emission from nuclear reactors. The future looks bright, with an aggressive program of next generation reactor neutrino experiments that will go after some of the biggest open questions in the field. This includes the JUNO experiment, the largest liquid scintillator detector ever constructed which will push the limits of this detection technology.

Temperature of a sliding contact between wire rope and friction lining

Abstract This paper studies the three-dimensional (3d) transient temperature field of a friction lining and a sliding wire rope. An efficient multigrid solver is developed. The multigrid code is validated by a comparison with a well-known analytical solution. The influence of several parameters on the temperature rise is investigated. Sliding velocity has a great influence: the larger the velocity, the larger the average temperature rise and the temperature fluctuation at a certain time. Two approximate solutions characterized by simple heat flux forms are proposed, using only a limited computational effort. A comparison of the temperature rise by the original and the two simplified schemes is performed. It is found that the heat flux shape influence is limited to the surface temperature and the temperature rise far below the contact surface depends only on the total heat flow.

Going with the Flow: Water Flux and Cell Shape during Cytokinesis

Cell shape changes during cytokinesis in eukaryotic cells have been attributed to contractile forces from the actomyosin ring and the actomyosin cortex. Here we propose an additional mechanism where active pumping of ions and water at the cell poles and the division furrow can also achieve the same type of shape change during cytokinesis without myosin contraction. We develop a general mathematical model to examine shape changes in a permeable object subject to boundary fluxes. We find that hydrodynamic flows in the cytoplasm and the relative drag between the cytoskeleton network phase and the water phase also play a role in determining the cell shape during cytokinesis. Forces from the actomyosin contractile ring and cortex do contribute to the cell shape, and can work together with water permeation to facilitate cytokinesis. To influence water flow, we osmotically shock the cell during cell division, and find that the cell can actively adapt to osmotic changes and complete division. Depolymerizing the actin cytoskeleton during cytokinesis also does not affect the contraction speed. We also explore the role of membrane ion channels and pumps in setting up the spatially varying water flux.

Comparisons of Rare-Earth and Rare-Earth-Free External Rotor Permanent Magnet Assisted Synchronous Reluctance Motors

This paper presents the comparisons of five-phase external rotor permanent magnet assisted synchronous reluctance motors (PMa-SynRMs) with neodymium (Nd) and ferrite (Fe) based PMs. Five-phase PMa-SynRMs, in general, have been proposed as an alternative to conventional three-phase motors utilized in automobile applications. However, with increased attention towards higher torque density and lower torque pulsations in electric motor designs, five-phase external rotor PMa-SynRMs can be highly attractive. In addition to increased fault tolerance and reliability of five-phase PMa-SynRMs, an adaptation of external rotor design can significantly increase the average torque developed with reduced torque pulsations and back-electromotive force (EMF) harmonics. However, with the design complexity involved in such high performance five-phase PMa-SynRM designs, the shape of flux barrier and choice of PMs have been one of the main challenges. In this study, novel five-phase external rotor PMa-SynRM designs with optimal flux barrier number and shape with Nd and Fe PMs are presented. Finite element simulations are conducted on the 2-D designs to compare their performance characteristics such as torque developed, torque pulsations, structural stability, thermal heat flow, demagnetization effects, and back-EMF harmonics. Optimal 3.8 kW Nd-based and 3.7 kW Fe-based five-phase external rotor PMa-SynRM designs are fabricated, and experimental tests are conducted on the prototypes to compare the results with a benchmark internal rotor PMa-SynRM.

A Study on Reconstruction of Intrapin Power Distribution in Pinwise Two-Group Diffusion Analysis

Detailed pin-by-pin core calculations are under development to replace the conventional assembly-based nodal methods. This research investigates a novel intrapin reconstruction procedure coupled with these pinwise calculations to obtain a detailed power profile within a fuel rod. The reconstruction process is based on the well-established form function (FF) method. In this paper, the fuel rod is geometrically divided into 40 equi-volume subsections where the intrapin power is reconstructed with corresponding heterogeneous FF. The intrapin homogeneous flux distributions are approximated by using the analytical solution of the two-group neutron diffusion equation with pinwise boundary constraints. Four types of constraints are considered to determine the flux shapes: surface-average net current, surface-average, corner-point, and volume-average cell fluxes. Therefore, six different combinations of the boundary constraints are separately evaluated for the intrapin power profile. All necessary information, including burnup-dependent FFs, homogenized group constants, reference power distribution, and pinwise boundary constraints, are predetermined from a high-fidelity Monte Carlo calculation. The numerical results demonstrate that the intrapin power can be retrieved for enriched and Gd-loaded fuel pins with reasonable accuracy, even at rodded conditions and in highly burned conditions of 10 and 30 GWd/tonne U. In addition, a sensitivity analysis is also performed to assess the feasibility of the proposed method when it is coupled with a pinwise calculation.

Non-parametric determination of H and He interstellar fluxes from cosmic-ray data (Corrigendum)

Top-of-atmosphere (TOA) cosmic-ray (CR) fluxes from satellites and balloon-borne experiments are snapshots of the solar activity imprinted on the interstellar (IS) fluxes. Given a series of snapshots, the unknown IS flux shape and the level of modulation (for each snapshot) can be recovered. We wish (i) to provide the most accurate determination of the IS H and He fluxes from TOA data alone, (ii) to obtain the associated modulation levels (and uncertainties) while fully accounting for the correlations with the IS flux uncertainties, and (iii) to inspect whether the minimal force-field approximation is sufficient to explain all the data at hand. Using H and He TOA measurements, including the recent high-precision AMS, BESS-Polar, and PAMELA data, we performed a non-parametric fit of the IS fluxes $J^{\rm IS}_{\rm H,~He}$ and modulation level $\phi_i$ for each data-taking period. We relied on a Markov chain Monte Carlo (MCMC) engine to extract the probability density function and correlations (hence the credible intervals) of the sought parameters. Although H and He are the most abundant and best measured CR species, several datasets had to be excluded from the analysis because of inconsistencies with other measurements. From the subset of data passing our consistency cut, we provide ready-to-use best-fit and credible intervals for the H and He IS fluxes from MeV/n to PeV/n energy (with a relative precision in the range [2-10\%] at 1$\sigma$). Given the strong correlation between $J^{\rm IS}$ and $\phi_i$ parameters, the uncertainties on $J^{\rm IS}$ translate into $\Delta\phi\approx \pm 30$~MV (at 1$\sigma$) for all experiments. We also find that the presence of $^3$He in He data biases $\phi$ towards higher $\phi$ values by $\sim 30$~MV. The force-field approximation gives an excellent ($\chi^2/$dof$=1.02$) description of the recent high-precision TOA H and He fluxes.

Dissecting the long-term emission behaviour of the BL Lac object Mrk 421

We report on long-term multi-wavelength monitoring of blazar Mrk 421 by the GASP-WEBT collaboration and Steward Observatory, and by the Swift and Fermi satellites. We study the source behaviour in the period 2007-2015, characterized by several extreme flares. The ratio between the optical, X-ray, and \gamma-ray fluxes is very variable. The \gamma-ray flux variations show fair correlation with the optical ones starting from 2012. We analyse spectropolarimetric data and find wavelength-dependence of the polarisation degree (P), which is compatible with the presence of the host galaxy, and no wavelength-dependence of the electric vector polarisation angle (EVPA). Optical polarimetry shows a lack of simple correlation between P and flux and wide rotations of the EVPA. We build broad-band spectral energy distributions with simultaneous near-infrared and optical data from the GASP-WEBT and UV and X-ray data from the Swift satellite. They show strong variability in both flux and X-ray spectral shape and suggest a shift of the synchrotron peak up to a factor $\sim 50$ in frequency. The interpretation of the flux and spectral variability is compatible with jet models including at least two emitting regions that can change their orientation with respect to the line of sight.

Observations of Sagittarius A* during the pericenter passage of the G2 object with MAGIC

Context. We present the results of a multi-year monitoring campaign of the Galactic Center (GC) with the MAGIC telescopes. These observations were primarily motivated by reports that a putative gas cloud (G2) would be passing in close proximity to the super-massive black hole (SMBH), associated with Sagittarius A*, located at the center of our galaxy. This event was expected to give astronomers a unique chance to study the effect of in-falling matter on the broad-band emission of a SMBH. Aims. We search for potential flaring emission of very-high-energy (VHE; $\geq$100 GeV) gamma rays from the direction of the SMBH at the GC due to the passage of the G2 object. Using these data we also study the morphology of this complex region. Methods. We observed the GC region with the MAGIC Imaging Atmospheric Cherenkov Telescopes during the period 2012-2015, collecting 67 hours of good-quality data. In addition to a search for variability in the flux and spectral shape of the GC gamma-ray source, we use a point-source subtraction technique to remove the known gamma-ray emitters located around the GC in order to reveal the TeV morphology of the extended emission inside that region. Results. No effect of the G2 object on the VHE gamma-ray emission from the GC was detected during the 4 year observation campaign. We confirm previous measurements of the VHE spectrum of Sagittarius A*, and do not detect any significant variability of the emission from the source. Furthermore, the known VHE gamma-ray emitter at the location of the supernova remnant G0.9+0.1 was detected, as well as the recently discovered VHE source close to the GG radio Arc.

Processing the spike- like radon anomaly exhalation from the soil surface by electrical model

A model based on electric circuit theory has been developed to simulate the radon concentration in an accumulator chamber from the soil surface. This model simulates the radon generation on earth as a voltage source, diffusion to the earth's surface as an electrical conductor, the convection flux of radon as an electrical current source and radon concentration in a chamber as a voltage across a capacitor. We use this model for processing the spike like an anomaly of radon. This paper offers a radon anomaly spike like has a duration time less than several hours. It is shown that the time constant of a general setup is very large with compare the duration time of a spike like anomaly. In this condition the actual shape of radon flux in earth is different from radon measuring concentration in the chamber.With regard to this model it is shown that the rise time of measured radon concentration must be equal the duration time of a spike like anomaly and the fall time must have a constant time equal the five times of constant time of our setup and it is independent of the shape of the anomaly.

Studies on neutron spectrum characterization for the Pneumatic Fast Transfer System (PFTS) of KAMINI reactor

Characterization of neutron energy spectrum along with the determination of sub-cadmium to epithermal neutron flux ratio (f) and the epithermal neutron flux shape factor (α) has been carried out at pneumatic fast transfer system (PFTS) of KAMINI reactor. The facility has been extensively used for the neutron activation analysis (NAA) studies using both k0-NAA and relative method. This paper describes the multi-foil activation method to determine the reaction rates followed by the generation of computed guess spectrum to unfold the neutron spectrum using least square minimization approach.

Burning velocities of DME(dimethyl ether)-air premixed flames at elevated temperatures

This paper reports the measurement of laminar burning velocities of DME (dimethyl ether)-air mixtures at higher mixture temperatures using planar flames stabilized in a controlled temperature mesoscale diverging channel. The reliability of this technique for flame speed measurement at high mixture temperatures has been established through various numerical studies using detailed 3-D computational model for DME-air mixtures. The distribution of fuel-air mass flux, reaction zone, and flame shape indicate that a planar flame is indeed formed in both transverse and depth directions of the channel. The stabilized flame is independent of any stretch effects except mild hydrodynamic strain due to channel divergence (30-50 s−1), and measured values of laminar burning velocities are within ±5% of the actual value. The experiments were carried out at various equivalence ratios (ϕ = 0.7–1.4) and elevated mixture temperatures (350–640 K). The burning velocities and temperature exponents were determined using the planar flames stabilized at different mixture inlet velocities and temperatures. Slightly rich mixtures (ϕ = 1.1) point to the maximum burning velocity, in good agreement with recent literature at ambient conditions. Temperature exponents for different equivalence ratios increase to both sides of ϕ = 1.1. Numerically calculated laminar burning velocities with different chemical kinetic schemes compared well with the measured burning velocities at higher mixture temperatures.