Measurement of liquid film thickness by optical fluorescence and its application to an oscillating piston positive displacement flowmeter

The movement of the circular piston in an oscillating piston positive displacement flowmeter is important in understanding the operation of the flowmeter, and the leakage of liquid past the piston plays a key role in the performance of the meter. The clearances between the piston and the chamber are small, typically less than 60 νm. In order to measure this film thickness a fluorescent dye was added to the water passing through the meter, which was illuminated with UV light. Visible light images were captured with a digital camera and analysed to give a measure of the film thickness with an uncertainty of less than 7%. It is known that this method lacks precision unless careful calibration is undertaken. Methods to achieve this are discussed in the paper. The grey level values for a range of film thicknesses were calibrated in situ with six dye concentrations to select the most appropriate one for the range of liquid film thickness. Data obtained for the oscillating piston flowmeter demonstrate the value of the fluorescence technique. The method is useful, inexpensive and straightforward and can be extended to other applications where measurement of liquid film thickness is required. © 2011 IOP Publishing Ltd.

Near-complete transuranic waste incineration in a thorium fuelled pressurised water reactor

The production of long-lived transuranic (TRU) waste is a major disadvantage of fission-based nuclear power. Incineration, and virtual elimination, of waste stockpiles is possible in a thorium (Th) fuelled critical or subcritical fast reactor. Fuel cycles producing a net decrease in TRUs are possible in conventional pressurised water reactors (PWRs). However, minor actinides (MAs) have a detrimental effect on reactivity and stability, ultimately limiting the quality and quantity of waste that can be incinerated. In this paper, we propose using a thorium-retained-actinides fuel cycle in PWRs, where the reactor is fuelled with a mixture of thorium and TRU waste, and after discharge all actinides are reprocessed and returned to the reactor. To investigate the feasibility and performance of this fuel cycle an assembly-level analysis for a one-batch reloading strategy was completed over 125 years of operation using WIMS 9. This one-batch analysis was performed for simplicity, but allowed an indicative assessment of the performance of a four-batch fuel management strategy. The build-up of 233U in the reactor allowed continued reactive and stable operation, until all significant actinide populations had reached pseudo-equilibrium in the reactor. It was therefore possible to achieve near-complete transuranic waste incineration, even for fuels with significant MA content. The average incineration rate was initially around 330 kg per GW th year and tended towards 250 kg per GW th year over several decades: a performance comparable to that achieved in a fast reactor. Using multiple batch fuel management, competitive or improved end-of-cycle burn-up appears achievable. The void coefficient (VC), moderator temperature coefficient (MTC) and Doppler coefficient remained negative. The quantity of soluble boron required for a fixed fuel cycle length was comparable to that for enriched uranium fuel, and acceptable amounts can be added without causing a positive VC or MTC. This analysis is limited by the consideration of a single fuel assembly, and it will be necessary to perform a full core coupled neutronic-thermal-hydraulic analysis to determine if the design in its current form is feasible. In particular, the potential for positive VCs if the core is highly or locally voided is a cause for concern. However, these results provide a compelling case for further work on concept feasibility and fuel management, which is in progress. © 2011 Elsevier Ltd. All rights reserved.

Permeability and stiffness of sands at very low effective stresses

Loose saturated sandy soils may undergo liquefaction under cyclic loading, generating positive excess pore pressures due to their contractile nature and inability to dissipate pore pressures rapidly during earthquake loading. These liquefied soils have a near-zero effective stress state, and hence have very low strength and stiffness, causing severe damage to structures founded upon them. The duration for which this near-zero effective stress state persists is a function of the rate of reconsolidation of the liquefied soil, which in turn is a function of the permeability and stiffness of the soil at this very low effective stress. Existing literature based on observation of physical model tests suggests that the consolidation coefficient C v associated with this reconsolidation of liquefied sand is significantly lower than that of the same soil at moderate stress levels. In this paper, the results of a series of novel fluidisation tests in which permeability k and coefficient of consolidation C v were independently measured will be presented. These results allow calculation of the variation of stiffness E 0 and permeability k with effective stress. It is shown that while permeability increases markedly at very low effective stresses, the simultaneous drop in stiffness measured results in a decrease in consolidation coefficient and hence an increase in the duration for which the soil remains liquefied.

Re-examination of the coefficient of determination (r2) using road materials engineering case studies

The analysis of scientific data is integral to materials engineering and science. The correlation between measured variables is often quantified by estimating the coefficient of determination or the r2 value. This is the recognised procedure for determining linear relationships. The authors review the derivation of the r2 value and derive an associated quantity, termed the relative deviation (RD), which is the ratio of the root mean square of the deviations about the fitted line to the root mean square of the deviations about the y bar line expressed as a percentage. The relative deviation has an advantage over the coefficient of determination in that it has greater numerical sensitivity to changes in the spread of data about the fitted line, especially when the scatter is small. In addition, the relative deviation is able to define, in percentage terms, the reduction in scatter when different independent variables are correlated with a common dependent variable. Four case studies in the materials field (aggregate crushing value, Atterberg limits, permeability and creep of asphalt) from work carried out at the Queensland Main Roads Department are presented to show the use of the new parameter RD.

Light absorption and electrical transport in Si:O alloys for photovoltaics

Thin films (100-500 nm) of the Si:O alloy have been systematically characterized in the optical absorption and electrical transport behavior, by varying the Si content from 43 up to 100 at. %. Magnetron sputtering or plasma enhanced chemical vapor deposition have been used for the Si:O alloy deposition, followed by annealing up to 1250 °C. Boron implantation (30 keV, 3-30× 1014 B/cm2) on selected samples was performed to vary the electrical sheet resistance measured by the four-point collinear probe method. Transmittance and reflectance spectra have been extracted and combined to estimate the absorption spectra and the optical band gap, by means of the Tauc analysis. Raman spectroscopy was also employed to follow the amorphous-crystalline (a-c) transition of the Si domains contained in the Si:O films. The optical absorption and the electrical transport of Si:O films can be continuously and independently modulated by acting on different parameters. The light absorption increases (by one decade) with the Si content in the 43-100 at. % range, determining an optical band gap which can be continuously modulated into the 2.6-1.6 eV range, respectively. The a-c phase transition in Si:O films, causing a significant reduction in the absorption coefficient, occurs at increasing temperatures (from 600 to 1100 °C) as the Si content decreases. The electrical resistivity of Si:O films can be varied among five decades, being essentially dominated by the number of Si grains and by the doping. Si:O alloys with Si content in the 60-90 at. % range (named oxygen rich silicon films), are proved to join an appealing optical gap with a viable conductivity, being a good candidate for increasing the conversion efficiency of thin-film photovoltaic cell. © 2010 American Institute of Physics.

Positive Correlations in Tunneling through coupled Quantum Dots

Due to the Fermi-Dirac statistics of electrons the temporal correlations of tunneling events in a double barrier setup are typically negative. Here, we investigate the shot noise behavior of a system of two capacitively coupled quantum dot states by means of a Master equation model. In an asymmetric setup positive correlations in the tunneling current can arise due to the bunching of tunneling events. The underlying mechanism will be discussed in detail in terms of the current-current correlation function and the frequency-dependent Fano factor.

Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

Regression on fixed-rank positive semidefinite matrices: A Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixedrank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks. © 2011 Gilles Meyer, Silvere Bonnabel and Rodolphe Sepulchre.

Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.

Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

Flexible conversion ratio fast reactors: Overview

Conceptual designs of lead-cooled and liquid salt-cooled fast flexible conversion ratio reactors were developed. The performance achievable by the unity conversion ratio cores of these reactors was compared to an existing supercritical carbon dioxide-cooled (S-CO2) fast reactor design and an uprated version of an existing sodium-cooled fast reactor. All concepts have cores rated at 2400 MWt. The cores of the liquid-cooled reactors are placed in a large-pool-type vessel with dual-free level, which also contains four intermediate heat exchangers (IHXs) coupling a primary coolant to a compact and efficient supercritical CO2 Brayton cycle power conversion system. The S-CO2 reactor is directly coupled to the S-CO2 Brayton cycle power conversion system. Decay heat is removed passively using an enhanced reactor vessel auxiliary cooling system (RVACS) and a passive secondary auxiliary cooling system (PSACS). The selection of the water-cooled versus air-cooled heat sink for the PSACS as well as the analysis of the probability that the PSACS may fail to complete its mission was performed using risk-informed methodology. In addition to these features, all reactors were designed to be self-controllable. Further, the liquid-cooled reactors utilized common passive decay heat removal systems whereas the S-CO2 uses reliable battery powered blowers for post-LOCA decay heat removal to provide flow in well defined regimes and to accommodate inadvertent bypass flows. The multiple design limits and challenges which constrained the execution of the four fast reactor concepts are elaborated. These include principally neutronics and materials challenges. The neutronic challenges are the large positive coolant reactivity feedback, small fuel temperature coefficient, small effective delayed neutron fraction, large reactivity swing and the transition between different conversion ratio cores. The burnup, temperature and fluence constraints on fuels, cladding and vessel materials are elaborated for three categories of material - materials currently available, available on a relatively short time scale and available only with significant development effort. The selected fuels are the metallic U-TRU-Zr (10% Zr) for unity conversion ratio and TRU-Zr (75% Zr) for zero conversion ratio. The principal selected cladding and vessel materials are HT-9 and A533 or A508, respectively, for current availability, T-91 and 9Cr-1Mo steel for relatively short-term availability and oxide dispersion strengthened ferritic steel (ODS) available only with significant development. © 2009 Elsevier B.V. All rights reserved.

Cross-comparison of fast reactor concepts with various coolants

Four fast reactor concepts using lead (LFR), liquid salt, NaCl-KCl-MgCl2 (LSFR), sodium (SFR), and supercritical CO2 (GFR) coolants are compared. Since economy of scale and power conversion system compactness are the same by virtue of the consistent 2400 MWt rating and use of the S-CO2 power conversion system, the achievable plant thermal efficiency, core power density and core specific powers become the dominant factors. The potential to achieve the highest efficiency among the four reactor concepts can be ranked from highest to lowest as follows: (1) GFR, (2) LFR and LSFR, and (3) SFR. Both the lead- and salt-cooled designs achieve about 30% higher power density than the gas-cooled reactor, but attain power density 3 times smaller than that of the sodium-cooled reactor. Fuel cycle costs are favored for the sodium reactor by virtue of its high specific power of 65 kW/kgHM compared to the lead, salt and gas reactor values of 45, 35, and 21 kW/kgHM, respectively. In terms of safety, all concepts can be designed to accommodate the unprotected limiting accidents through passive means in a self-controllable manner. However, it does not seem to be a preferable option for the GFR where the active or semi-passive approach will likely result in a more economic and reliable plant. Lead coolant with its superior neutronic characteristics and the smallest coolant temperature reactivity coefficient is easiest to design for self-controllability, while the LSFR requires special reactivity devices to overcome its large positive coolant temperature coefficient. The GFR required a special core design using BeO diluent and a supercritical CO2 reflector to achieve negative coolant void worth-one of the conditions necessary for inherent shutdown following large LOCA. Protected accidents need to be given special attention in the LSFR and LFR due to the small margin to freezing of their coolants, and to a lesser extent in the SFR. © 2009 Elsevier B.V. All rights reserved.

Fertile-free annular fuel for plutonium recycling

Up to 50% increase in the power density of the existing pressurized water reactor (PWR)-type reactors can be achieved by the use of internally and externally cooled annular fuel geometry. As a result, the accumulated stock-piles of Pu, especially if incorporated infertile-free inert matrix, can be burnt at a substantially higher rate as compared with the conventional mixed oxide-fueled reactors operating at standard power density. In this work, we explore the basic feasibility of a PWR core fully loaded with Pu incorporated infertile-free fuel of annular internally and externally cooled geometry and operating at 150% of nominal power density. We evaluate basic burnable poison designs, fuel management strategies, and reactivity feedback coefficients. The three-dimensional full core neutronic analysis performed with Studsvik Core Management System showed that the design of such a Pu-loaded annular fuel core is feasible but significantly more challenging than the Pu fertile-free core with solid fuel pins operating at nominal power density. The main difficulty arises from the fact that the annular fuel core requires at least 50% higher initial Pu loading in order to maintain the standard fuel cycle length of 18 months. Such a high Pu loading results in hardening of the neutron spectrum and consequent reduction in reactivity worth of all reactivity control mechanisms and, in some cases, positive moderator temperature coefficient (MTC). The use of isotopically enriched Gd and Er burnable poisons was found to be beneficial with respect to maximizing Pu burnup and reducing power peaking factors. Overall, the annular fertile-free Pu-loaded high-power-density core appears to be feasible, although it still has relatively high power peaking and potential for slightly positive MTC at beginning of cycle. However, we estimate that limiting the power density to 140% of the nominal case would assure acceptable core power peaking and negative MTC at all times during the cycle.

Liquid salt cooled flexible conversion ratio fast reactor: Neutronic design

This paper presents the neutronic design of a liquid salt cooled fast reactor with flexible conversion ratio. The main objective of the design is to accommodate interchangeably within the same reactor core alternative transuranic actinides management strategies ranging from pure burning to self-sustainable breeding. Two, the most limiting, core design options with unity and zero conversion ratios are described. Ternary, NaCl-KCl-MgCl2 salt was chosen as a coolant after a rigorous screening process, due to a combination of favourable neutronic and heat transport properties. Large positive coolant temperature reactivity coefficient was identified as the most significant design challenge. A wide range of strategies aiming at the reduction of the coolant temperature coefficient to assure self-controllability of the core in the most limiting unprotected accidents were explored. However, none of the strategies resulted in sufficient reduction of the coolant temperature coefficient without significantly compromising the core performance characteristics such as power density or cycle length. Therefore, reactivity control devices known as lithium thermal expansion modules were employed instead. This allowed achieving all the design goals for both zero and unity conversion ratio cores. The neutronic feasibility of both designs was demonstrated through calculation of reactivity control and fuel loading requirements, fluence limits, power peaking factors, and reactivity feedback coefficients. © 2009 Elsevier B.V. All rights reserved.