Shallow water equations: Magic and limitations

D Liang from Cambridge University explains the shallow water equations and their applications to the dam-break and other steep-fronted flow modeling. They assume that the horizontal scale of the flow is much greater than the vertical scale, which means the flow is restricted within a thin layer, thus the vertical momentum is insignificant and the pressure distribution is hydrostatic. The left hand sides of the two momentum equations represent the acceleration of the fluid particle in the horizontal plane. If the fluid acceleration is ignored, then the two momentum equations are simplified into the so-called diffusion wave equations. In contrast to the SWEs approach, it is much less convenient to model floods with the Navier-Stokes equations. In conventional computational fluid dynamics (CFD), cumbersome treatments are needed to accurately capture the shape of the free surface. The SWEs are derived using the assumptions of small vertical velocity component, smooth water surface, gradual variation and hydrostatic pressure distribution.

Tomorrow's cities - a framework for building resilience

Urbanisation is the great driving force of the twenty-first century. Cities are associated with both productivity and creativity, and the benefits offered by closely connected and high density living and working contribute to sustainability. At the same time, cities need extensive infrastructure – like water, power, sanitation and transportation systems – to operate effectively. Cities therefore comprise multiple components, forming both static and dynamic systems that are interconnected directly and indirectly on a number of levels, all forming the backdrop for the interaction of people and processes. Bringing together large numbers of people and complex products in rich interactions can lead to vulnerability from hazards, threats and even trends, whether natural hazards, epidemics, political upheaval, demographic changes, economic instability and/or mechanical failures; The key to countering vulnerability is the identification of critical systems and clear understanding of their interactions and dependencies. Critical systems can be assessed methodically to determine the implications of their failure and their interconnectivities with other systems to identify options. The overriding need is to support resilience – defined here as the degree to which a system or systems can continue to function effectively in a changing environment. Cities need to recognise the significance of devising adaptation strategies and processes to address a multitude of uncertainties relating to climate, economy, growth and demography. In this paper we put forward a framework to support cities in understanding the hazards, threats and trends that can make them vulnerable to unexpected changes and unpredictable shocks. The framework draws on an asset model of the city, in which components that contribute to resilience include social capital, economic assets, manufactured assets, and governance. The paper reviews the field, and draws together an overarching framework intended to help cities plan a robust trajectory towards increased resilience through flexibility, resourcefulness and responsiveness. It presents some brief case studies demonstrating the applicability of the proposed framework to a wide variety of circumstances.

Generating power from waves on a breakwater.

Outlines the possibility for wave power generation at artificial islands by construction of a breakwater. Reviews the development of wave energy systems, and describes several wave generators, e.g. the Mauritius lagoon system, the Nodding Duck, the oscillating cylinder, the oscillating water column and the Lancaster Bag. Applications and costs are outlined. (C.J.U.)

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.

The performance of closed reactor grade plutonium-thorium fuel cycles in reduced-moderation pressurised water reactors

The production of long-lived transuranic (TRU) waste is a major disadvantage of fission-based nuclear power. Previous work has indicated that TRU waste can be virtually eliminated in a pressurised water reactor (PWR) fuelled with a mixture of thorium and TRU waste, when all actinides are returned to the reactor after reprocessing. However, the optimal configuration for a fuel assembly operating this fuel cycle is likely to differ from the current configuration. In this paper, the differences in performance obtained in a reduced-moderation PWR operating this fuel cycle were investigated using WIMS. The chosen configuration allowed an increase of at least 20% in attainable burn-up for a given TRU enrichment. This will be especially important if the practical limit on TRU enrichment is low. The moderator reactivity coefficients limit the enrichment possible in the reactor, and this limit is particularly severe if a negative void coefficient is required for a fully voided core. Several strategies have been identified to mitigate this. Specifically, the control system should be designed to avoid a detrimental effect on moderator reactivity coefficients. The economic viability of this concept is likely to be dependent on the achievable thermal-hydraulic operating conditions. © 2012 Elsevier Ltd. All rights reserved.

First-principles energetics of water: a many-body analysis

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for solid, liquid and cluster forms of water. We use a many-body separation of the total energy into its 1-body, 2-body (2B) and beyond-2-body (B2B) components to analyze the deficiencies of two popular DFT approximations. We show how machine-learning methods make this analysis possible for ice structures as well as for water clusters. We find that the crucial energy balance between compact and extended geometries can be distorted by 2B and B2B errors, and that both types of first-principles error are important.

Use of axially graded burnable boron for hot-spot temperature reduction in a pressurized water reactor core

Shortly after the loading of a pressurized water reactor (PWR) core, the axial power distribution in fresh fuel has already attained the characteristic, almost flat shape, typical of burned fuel. At beginning of cycle (BOC), however, the axial distribution is centrally peaked. In assemblies hosting uniform burnable boron rods, this BOC peaking is even more pronounced. A reduction in the axial peaking is today often achieved by shortening the burnable boron rods by some 30 cm at each edge. It is shown that a two-zone grading of the boron rod leads, in a representative PWR cycle, to a reduction of the hot-spot temperature of approximately 70 °C, compared with the nongraded case. However, with a proper three-zone grading of the boron rod, an additional 20 °C may be cut off the hot-spot temperature. Further, with a slightly skewed application of this three-zone grading, an additional 50 °C may be cut off. The representative PWR cycle studied was cycle 11 of the Indian Point 2 station, with a simplification in the number of fuel types and in the burnup distribution. The analysis was based on a complete three-dimensional burnup calculation. The code system was ELCOS, with BOXER as an assembly code for the generation of burnup-dependent cross sections and SILWER as a three-dimensional core code with thermal-hydraulic feedback.

Microheterogeneous Thoria-Urania Fuels for Pressurized Water Reactors

A thorium-based fuel cycle for light water reactors will reduce the plutonium generation rate and enhance the proliferation resistance of the spent fuel. However, priming the thorium cycle with ²³⁵U is necessary, and the ²³⁵U fraction in the uranium must be limited to below 20% to minimize proliferation concerns. Thus, a once-through thorium-uranium dioxide (ThO2-UO2) fuel cycle of no less than 25% uranium becomes necessary for normal pressurized water reactor (PWR) operating cycle lengths. Spatial separation of the uranium and thorium parts of the fuel can improve the achievable burnup of the thorium-uranium fuel designs through more effective breeding of ²³³U from the ²³²Th. Focus is on microheterogeneous fuel designs for PWRs, where the spatial separation of the uranium and thorium is on the order of a few millimetres to a few centimetres, including duplex pellet, axially microheterogeneous fuel, and a checkerboard of uranium and thorium pins. A special effort was made to understand the underlying reactor physics mechanisms responsible for enhancing the achievable burnup at spatial separation of the two fuels. The neutron spectral shift was identified as the primary reason for the enhancement of burnup capabilities. Mutual resonance shielding of uranium and thorium is also a factor; however, it is small in magnitude. It is shown that the microheterogeneous fuel can achieve higher burnups, by up to 15%, than the reference all-uranium fuel. However, denaturing of the ²³³U in the thorium portion of the fuel with small amounts of uranium significantly impairs this enhancement. The denaturing is also necessary to meet conventional PWR thermal limits by improving the power share of the thorium region at the beginning of fuel irradiation. Meeting thermal-hydraulic design requirements by some of the microheterogeneous fuels while still meeting or exceeding the burnup of the all-uranium case is shown to be potentially feasible. However, the large power imbalance between the uranium and thorium regions creates several design challenges, such as higher fission gas release and cladding temperature gradients. A reduction of plutonium generation by a factor of 3 in comparison with all-uranium PWR fuel using the same initial ²³⁵U content was estimated. In contrast to homogeneously mixed U-Th fuel, microheterogeneous fuel has a potential for economic performance comparable to the all-UO2 fuel provided that the microheterogeneous fuel incremental manufacturing costs are negligibly small.

First-principles energetics of water clusters and ice: a many-body analysis.

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.