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Quantifying uncertainty in uranium concentration measurements via K-edge densitometry

This study quantifies the uncertainty in uranium concentration predictions of fluoride and chloride-based salts within a steel pipe using K-edge densitometry. Modeling and simulation was conducted with the Monte Carlo N-Particle Transport (MCNP) code. The quality of of this technique’s prediction in a pipe requires proper characterization of the pipe’s thickness, which is dependent on the source size and axial offset from the pipe centerline. The thickness was determined as either the center-line thickness seen by the X-ray source or an average value determined through random sampling. Generally, the predicted concentrations were slightly better at lower offset with the random sampling thickness and using the center-line thickness for the highest offsets. For a line-beam source and varying axial offsets, the relative error of concentration was within 1% of the true value but uncertainty increased by 2 orders of magnitude. Similarly, for no axial offset, the relative error was significantly less than 1% while no trend for uncertainty was found. However, at the largest possible offset for a given source size, the concentrations become erroneous and greater than the allowable 1% relative error. Furthermore, high offsets tended to increase the variance of the transmission spectra by 3 orders of magnitude.

Characterization and Analytical Technique↗

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Materials Design Directions for Solar Thermochemical Water Splitting

The sustainable, economical production of molecular hydrogen is a crucial component of a net zero-greenhouse-gas-emissions future. Solar thermochemical water splitting (STWS) offers a renewable route to hydrogen with the potential to help decarbonize several industries, including transportation, manufacturing, mining, metals processing, and electricity generation, as well as provide sustainable hydrogen as a chemical feedstock. STWS uses high temperatures generated from concentrated sunlight or other sustainable means for high-temperature heat to produce hydrogen and oxygen from steam. For example, in its simplest form of a two-step thermochemical cycle, a redox-active metal oxide is heated to ≈1700-2000 K, driving off molecular oxygen while producing oxygen vacancies in the material. The reduced metal oxide then cools (ideally with the extracted heat recuperated for re-use) and, in a separate step, comes into contact with steam, which reacts with oxygen vacancies to produce molecular hydrogen while recovering the original state of the metal oxide. Despite its promising use of the entire solar spectrum to split water thermochemically, the current estimated cost of hydrogen produced via STWS is ≈4-6× the U.S. Department of Energy (DOE) Hydrogen Shot target value of $1/kg. One contributing approach to bridging this cost gap is the design of new materials with improved thermodynamic properties to enable higher efficiencies. The state-of-the-art (SOA) redox-active metal oxide for STWS is ceria (CeO 2 ), due to its close to optimal, although too high, oxygen vacancy formation enthalpy and large configurational and electronic entropy of reduction. However, ceria requires high operating temperatures and its efficiency is insufficient. Therefore, efforts to increase the efficiency of STWS cycles have focused on further optimizing oxygen vacancy formation enthalpies and augmenting the reduction entropy via substitution or doping and materials discovery schemes. Examples of the latter include the perovskites BaCe 0.25 Mn 0.75 O 3 and (Ca,Ce)(Ti,Mn)O 3 . These efforts and others have revealed intuitive chemical principles for the efficient and systematic design of more effective materials, such as the strong correlation between the enthalpies of crystal bond dissociation and solid-state cation reduction with the enthalpy of oxygen vacancy formation, as well as configurational entropy augmentation via the coexistence of two or more redox-active cation sublattices. The purpose of this chapter is to prepare the reader with an up-to-date account of STWS redox-active materials, both the SOA and promising newcomers, as well as to provide chemically intuitive strategies for improving their cycle efficiencies through materials design – in conjunction with ongoing efforts in reactor engineering and gas separations – to reach the cost points for commercial viability. First, we will introduce the thermodynamics of STWS using a two-step, metal-oxide, thermochemical cycle with economics in mind. We also will compare the pros and cons of processes that do or do not involve phase changes. Second, we will describe the qualities that make ceria the SOA STWS redox-active material, as well as its limitations. Third, we will survey some of the most promising candidates to date in the search for materials to supplant ceria, emphasizing the post-ternary, metal-oxide-perovskite alloys. Lastly, we will enumerate and discuss the following materials design directions for STWS redox-active materials: crystal reduction potentials as a proxy for oxygen vacancy formation enthalpies, engineering the electronic and configurational entropy of reduction via f-shells and simultaneous redox, and vetting materials stability via temperature-dependent phase diagrams and melting-point prediction.

08 HYDROGEN↗