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DOE OSTI2024

Testing- and Model- Based Optimization of Coal-fired Primary Heater Design for Indirect Supercritical CO 2 Power Cycles (Final Scientific and Technical Report)

The overall objective of this project was to perform the R&D necessary to mitigate the risk associated with the design of a primary heat exchanger for a solid-fired combustion system coupled with an indirect-fired closed-loop Brayton Cycle utilizing supercritical CO 2 . The key technological hurdle was the coupling of a solid-fuel firing system with the primary heater, which poses a singular challenge, which is the management of burner performance and operational conditions in a way to manage heat exchanger tube metal temperatures and temperature ramp rates in the absence of fluid phase change on the inside of the tubes. We designed and built the first ever pseudo power system employing a simple recuperated supercritical CO 2 closed-loop Brayton Cycle coupled to a solid-fuel fired system. Advanced coupled CFD and process modeling were used to design the primary heat exchanger (PHX), which consisted of both radiative and convective sections, to limit tube metal temperatures resulting from the heat release profile of the solid fuel flame near the radiative tubes. The heat exchanger was designed to produce finished CO 2 temperatures of 600 °C a pressure of 20.7 MPa and CO 2 flow of 5.5 kg/s. The constructed PHX was capable of 1.2 MWth heat uptake. During design of the PHX, the modeling showed that most variables influencing flame shape (burner stoichiometric ratio and register velocities and swirl) were not suitable to manage heat flux to the metal surfaces. This is because they substantially increased adiabatic flame temperature through the influence of localized stoichiometric ratio. Excess air and firing rate were the two most powerful variables that could be used to control tube surface temperatures. The coupled system was operated for a total of 407 hours, with the longest continuous run of 248 hours. For 62% of the operational time, the unit was unmanned and in automatic control. The fuels used for the testing included natural gas, two Utah Bituminous coals, woody biomass, and bagasse. During the testing we were able to verify the 1.2 MWth heat uptake and we operated at a finished CO 2 temperature of 607 °C and a pressure of 20.3 MPa simultaneously. The real-time corrosion rate of the Super 304H tube CO 2 surface in the region of the radiative section of the PHX were measured, at an approximate temperature of 550 °C. The two key variables related to corrosion rate are the pressure and flow rate of the CO 2 . A technoeconomic analysis was performed at a scale of 120 MWE. The updated analysis showed that the efficiency of an sCO 2 power producing plant will be related to the pressure drop of the PHX.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2024

Development of Steady-State and Dynamic Mass and Energy Constrained Neural Networks for Distributed Chemical Systems Using Noisy Transient Data

The paper presents the development of algorithms for mass and energy constrained neural network models that can exactly conserve the overall mass and energy of distributed chemical process systems, even though the noisy transient data used for optimal model training violate the same. In contrast to approximately satisfying mass and energy balance constraints of a system by soft penalization of objective function, algorithms have been developed for solving equality-constrained nonlinear optimization problems, thus providing the guarantee of exactly satisfying the system mass and energy conservation laws. For developing dynamic mass-energy constrained network models for distributed systems, hybrid series and parallel dynamic-static neural networks have been leveraged. The developed algorithms for solving both the training and forward problems are validated using both steady-state and dynamic data in the presence of various noise characteristics. The developed data-driven algorithms are flexible to exactly satisfy mass and energy balance constraints for dynamic chemical processes if the system holdup information is available. The proposed network structures and algorithms are applied to the development of data-driven lumped and distributed models of an adiabatic superheater/reheater system, a nonisothermal continuous stirred tank reactor, as well as an electrically heated plug-flow reactor system where one form of energy gets transformed to another. It has been observed that the mass-energy constrained neural networks yield a root mean squared error of <1% with respect to the system truth for the case studies evaluated in this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Photon-recoil and laser-focusing limits to Rydberg gate fidelity

Limits to Rydberg gate fidelity that arise from the entanglement of internal states of neutral atoms with the motional degrees of freedom due to the momentum kick from photon absorption and re-emission is quantified. This occurs when the atom is in a superposition of internal states but only one of these states is manipulated by visible or UV photons. The Schrödinger equation that describes this situation is presented and two cases are explored. In the first case, the entanglement arises because the spatial wave function shifts due to the separation in time between excitation and stimulated emission. For neutral atoms in a harmonic trap, the decoherence can be expressed within a sudden approximation when the duration of the laser pulses are shorter than the harmonic oscillator period. In this limit, the decoherence is given by simple analytic formulas that account for the momentum of the photon, the temperature of the atoms, the harmonic oscillator frequency, and atomic mass. In the second case, there is a reduction in gate fidelity because the photons causing absorption and stimulated emission are in focused beam modes. This leads to a dependence of the optically induced changes in the internal states on the center of mass atomic position. In the limit where the time between pulses is short, the decoherence can be expressed as a simple analytic formula involving the laser waist, temperature of the atoms, the trap frequency, and the atomic mass. These limits on gate fidelity are studied for the standard π-2π-π Rydberg gate and a protocol based on a single adiabatic pulse with a Gaussian envelope.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

The Kelvin–Helmholtz Instability at the Boundary of Relativistic Magnetized Jets

We study the linear stability of a planar interface separating two fluids in relative motion, focusing on conditions appropriate for the boundaries of relativistic jets. The jet is magnetically dominated, whereas the ambient wind is gas-pressure-dominated. We derive the most general form of the dispersion relation and provide an analytical approximation of its solution for an ambient sound speed much smaller than the jet Alfvén speed v A , as appropriate for realistic systems. The stability properties are chiefly determined by the angle ψ between the wavevector and the jet magnetic field. For ψ = π/2, magnetic tension plays no role, and our solution resembles the one of a gas-pressure-dominated jet. Here, only sub-Alfvénic jets are unstable ($0\lt {M}_{e}\equiv (v/{v}_{{\rm{A}}})\cos \theta \lt 1$ , where v is the shear velocity and θ the angle between the velocity and the wavevector). For ψ = 0, the free energy in the velocity shear needs to overcome the magnetic tension, and only super-Alfvénic jets are unstable ($1\lt {M}_{e}\lt \sqrt{{(1+{{\rm{\Gamma }}}_{w}^{2})/[1+({v}_{{\rm{A}}}/c)}^{2}{{\rm{\Gamma }}}_{w}^{2}]}$, with Γ w the wind adiabatic index). Our results have important implications for the propagation and emission of relativistic magnetized jets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Liquid Piston with Spray Cooling Near-Isothermal Compressor

The goal of this project was to prototype and characterize the performance of a liquid-piston spray-cooled gas compressor. The working principle of the compressor enables optimized high-efficiency operation over a very wide range of operating conditions, unlike conventional compressors that are optimized for a narrow range of operating conditions. The compressor technology is suitable for many applications, such as gas pipeline transport, gas storage, and commercial and residential heat pumps. Both physical testing and computational fluid dynamics (CFD) modeling of the processes using the Oak Ridge National Laboratory high-performance computing center were completed. The experimental and CFD studies focused on a near-isothermal liquid-piston compressor (LPC) that uses propylene glycol to compress CO 2 . The first prototype demonstrated isothermal operation during several sequentially executed cycles of CO 2 compression and raised the temperature of the compressed CO 2 by only 2 K, compared with approximately 6 K when the gas was compressed non-isothermally. Isothermal operation was demonstrated at CO 2 flow rates of up to 2 L/min. The second prototype was designed with two compression chambers to allow continuous flow of high-pressure CO 2 . However, the design of the valve train to direct flow between the compression chambers was not sufficient to allow demonstration of CO 2 compression. Numerical simulations of the LPC in which the compression chamber was filled with propylene glycol injected from the bottom inlet were performed using large eddy simulation (LES) with the wall-adapting local eddy-viscosity subgrid-scale model coupled with the multiphase volume of fluid (VOF) model to simulate the transient interface between gas and liquid and to capture the heat and mass transfers within the compression chamber. In this effort, the effects of boundary conditions applied to the LES-VOF calculations (i.e., no wall, an adiabatic wall, and a wall with a heat flux subscribed) on the overall pressure and temperature of the CO 2 gas as well as the transient evolution of flow and heat transfer within the compression chamber were investigated and are discussed in this report. The LES calculation with no wall showed no dynamical flow patterns, and the volume-averaged temperature of CO 2 increased from 305 to 392.7 K, whereas LES calculations with a constant wall temperature or a wall heat flux had similar increases of CO 2 temperatures. The results of the LES simulation using a wall heat flux showed different stages in the compression process and revealed dynamical formation and interaction of CO 2 gas layers and circulation flow patterns within the chamber that contributed to the overall heat transfer between the solid wall, gas, and liquid surface in the compressor. Though an industrial partnership for commercializing the compressor was not secured, the technology was attractive for an industrial partner to use in two research proposals in response to US Department of Energy funding opportunity announcements.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2023

Ultrafast lattice disordering can be accelerated by electronic collisional forces

In the prevalent picture of ultrafast structural phase transitions, the atomic motion occurs in a slowly varying potential energy surface determined adiabatically by the fast electrons. However, this ignores non-conservative forces caused by electron-lattice collisions, which can significantly influence atomic motion. Most ultrafast techniques only probe the average structure and are less sensitive to random displacements, and therefore do not detect the role played by non-conservative forces in phase transitions. Here we show that the lattice dynamics of the prototypical insulator-to-metal transition of VO 2 cannot be described by a potential energy alone. We use the sample temperature to control the preexisting lattice disorder before ultrafast photoexcitation across the phase transition and our ultrafast diffuse scattering experiments show that the fluctuations characteristic of the rutile metal develop equally fast (120 fs) at initial temperatures of 100 K and 300 K. This indicates that additional non-conservative forces are responsible for the increased lattice disorder. In conclusion, these results highlight the need for more sophisticated descriptions of ultrafast phenomena beyond the Born-Oppenheimer approximation as well as ultrafast probes of spatial fluctuations beyond the average unit cell measured by diffraction.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Development of a new quantum trajectory molecular dynamics framework

An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Theory and Simulation of Ultrafast Multidimensional Nonlinear X-ray Spectroscopy of Molecules (Final Report)

Emerging X-ray free electron laser (XFEL) beam sources offer new types of probes of matter with unprecedented spatial and temporal resolutions. These experimental advances must be met by robust theoretical and computational tools that provide predictive modeling capacity of the underlining electronic and structural dynamics. The latter will be essential for the design of sophisticated multi-pulse experiments and for their interpretation. The proposed research effort will focus on developing cutting- edge simulation tools for nonlinear multidimensional X-ray/optical spectroscopies and aims to address key questions in Priority Research Opportunities 1 (Probing and controlling electron motion within a molecule) and 3 (Capturing rare events and intermediate states in the transformation of matter) as mentioned in the BES Roundtable Report “Opportunities for Basic Research at the Frontiers of XFEL Ultrafast Science”. XFEL multidimensional nonlinear techniques, which combine sequences of X-ray and possibly optical pulses, provide a unique experimental toolbox for probing the dynamics of core and valence electronic excitations, as well as material structure. Predictive modeling of these dynamical processes requires the combination of analytical theory for nonlinear interactions of light and matter, robust quantum-chemical methodologies for the accurate description of electronic structure of various materials, and multiscale ab initio electron and nuclear dynamics techniques operating beyond Born-Oppenheimer approximation. These challenges will be addressed with three research thrusts (i) Develop and implement theoretical apparatus for modeling a broad range of multidimensional spectroscopic techniques enabled by present and upcoming XFEL facilities. This thrust also includes the incorporation of a computational module in the DOE supported open-source NWChem computational chemistry package as well as the development of other open-source codes ready for dissemination across a broad user base; (ii) Propose and design new multi-pulse experiments that make use of the capabilities of the incoming LCLS-II facility; (iii) Perform selected applications to specific molecular systems that can be carried out at LCLS-II and demonstrate how these X-ray sources may be used to study nonadiabatic dynamics through conical interactions, electronic correlations in multi-core excitons, and charge transfer/energy transfer processes. The proposed research will be carried out by a multi-disciplinary four-institution research team which combines academia and national laboratories and spans the broad and necessary expertise in theoretical spectroscopy, nonlinear optics, quantum chemistry, molecular non-adiabatic dynamics and code development. The work will be performed in a highly interactive team environment with junior researchers shared between institutions thus cementing cross- disciplinary interactions. The developed simulation tools will be immediately deployed for XFEL facility users, both experimentalists and theorists, via freely distributed codes and databases. Altogether, this project will facilitate establishing XFEL-based multidimensional spectroscopies as a novel diagnostic tool for monitoring electronic and structural dynamics in molecular materials.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory

Migdal-Eliashberg theory describes the properties of the normal and superconducting states of electron-phonon-mediated superconductors based on a perturbative treatment of the electron-phonon interactions. It is necessary to include both electron and phonon self-energies self-consistently in Migdal-Eliashberg theory in order to match numerically exact results from determinantal quantum Monte Carlo in the adiabatic limit. Here in this work we provide a method to obtain the real-axis solutions of the Migdal-Eliashberg equations with electron and phonon self-energies calculated self-consistently. Our method avoids the typical challenge of computing cumbersome singular integrals on the real axis and is numerically stable and exhibits fast convergence. Analyzing the resulting real-frequency spectra and self-energies of the two-dimensional Holstein model, we find that self-consistently including the lowest-order correction to the phonon self-energy significantly affects the solution of the Migdal-Eliashberg equations. The calculation captures the broadness of the spectral function, renormalization of the phonon dispersion, enhanced effective electron-phonon coupling strength, minimal increase in the electron effective mass, and the enhancement of superconductivity which manifests as a superconducting ground state despite strong competition with charge-density-wave order. We discuss surprising differences in two common definitions of the electron-phonon coupling strength derived from the electron mass and the density of states, quantities which are accessible through experiments such as angle-resolved photoemission spectroscopy and electron tunneling. An approximate upper bound on 2Δ/T c for conventional superconductors mediated by retarded electron-phonon interactions is proposed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states

Advances in coherent light sources and development of pump–probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron–nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. Furthermore, this work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Short-Depth QAOA circuits and Quantum Annealing on Higher-Order Ising Models (Rev.2)

The Quantum Alternating Operator Ansatz (QAOA) and Quantum Annealing (QA) are quantum algorithms that are both based on the adiabatic theorem and both have the goal of sampling the optimal solution(s) of combinatorial optimization problems. Quantum annealing has been physically instantiated on D-Wave devices using superconducting flux qubits, and QAOA can be programmed on digital gate-model quantum computers such as the programmable superconducting transmon qubits devices of the IBMQ series, for instance ibm washington. QAOA and QA address the same types of problems, but it is unclear how they will scale to large problem sizes and to larger and higher-fidelity quantum computers. In this article, we present a direct comparison between QAOA, one and two rounds, run on all 127 qubits of ibm washington and QA run on D-Wave Advantage system4.1 and Advantage system6.1. The problems which allow for this comparison are random Ising model problems whose connectivity matches the heavy hexagonal lattice topology of ibm washington and the Pegasus graph connectivity of the two D-Wave devices. We create two classes of problem instances for this comparison: one with higher order terms (ZZZ variable interactions), linear terms, and quadratic terms, and a separate problem type with only linear and quadratic terms. Our QAOA circuits are novel and extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of ibm washington’s heavy hexagonal lattice and can be applied to future heavy-hex chips. We also test the effectiveness of the error suppression technique digital dynamical decoupling on the QAOA circuits. The QAOA circuits compiled to ibm washington are composed of several thousand circuit instructions, approximately 3, 000 depending on the details of the circuit, making these some the largest quantum circuits ever executed on a digital quantum processor. QAOA and QA are compared against the classical heuristic algorithm of simulated annealing and all problem instances are exactly solved using CPLEX in order to evaluate which samplers, if any, correctly found the ground state solution(s) of the problem instances. We find that (i) QA outperforms QAOA on all problem instances, (ii) QAOA samples the problems better than random sampling, and (iii) QAOA angle computation exhibits clear parameter concentration across the ensemble of Ising models.

127 Qubits↗

DOE OSTI2022

Potassium carbonate decomposition modeling within rotating detonation engines for direct power extraction applications

We report that recently, there has been a significant interest in detonation-based combustion systems, such as rotating detonation engines (RDE), due to potential performance advantages in propulsion and energy applications. This includes improvements in thermodynamic efficiency, inherently high gas velocities, and the possibility of achieving an increase in total pressure (i.e. pressure gain) through the combustion process. Due to approximating a constant volume combustion process, these devices also tend to exhibit extremely high local gas temperatures relative to a comparable constant pressure combustor. These advantages overlap well with desirable performance characteristics of direct power extraction (DPE) technologies, such as a magnetohydrodynamic (MHD) generator. Typically, in DPE systems hot combustion products are seeded with an easily ionizable material such as potassium carbonate (K 2 CO 3 ) in order to boost the electrical conductivity. However, due to the short gas residence times within an RDE, it was unclear whether forming an electrically conductive combustion plasma would be feasible for integration with a downstream MHD generator. A model is presented which describes the heating, decomposition, and ionization of solid K 2 CO 3 particles and aqueous solutions of K 2 CO 3 in water, for a given initial particle diameter. This model was combined with available computational fluid dynamics (CFD) data for an oxygen-methane RDE in a one-way coupled Eulerian-Lagrangian framework to predict particle trajectories and the corresponding heating, decomposition, and ionization histories. Electrical conductivities were computed using a previously developed model, and a method was proposed to determine an equivalent average electrical conductivity. Results show that particle sizes below ~30 µm are able to fully decompose before reaching the exit of the RDE. While the one-way coupled nature of the simulations precluded rigorous evaluation of the effects of seed material on detonability, a substantial temperature reduction is expected at the detonation wave front due to heating and decomposition. A preliminary comparison is presented between the RDE and an equivalent constant pressure adiabatic combustor, showing a potential performance advantage for the RDE.

42 ENGINEERING↗

DOE OSTI2022

Entanglement perspective on the quantum approximate optimization algorithm

Many quantum algorithms seek to output a specific bitstring solving the problem of interest—or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial N -qubit product state | 0 〉 ⊗ N and the final one regarding entanglement? Here, we consider the QAOA algorithm for solving the paradigmatic MaxCut problem on different types of graphs. We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits and find that there is a volume-law entanglement barrier between the initial and final states. We also investigate the entanglement spectrum in connection with random matrix theory. In addition, we compare the entanglement production with a quantum annealing protocol aiming to solve the same MaxCut problems. Finally, we discuss the implications of our results for the simulation of QAOA circuits with tensor network-based methods relying on low-entanglement for efficiency, such as matrix product states.

Dupont, Maxime↗

DOE OSTI2021

Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field $\boldsymbol {B}$ inclined at a small angle, $\alpha \ll 1$ (in radians), to the target. Adiabatic electrons are assumed, requiring $\alpha \gg \sqrt {Zm_{e}/m_{i}}$ , where $m_{e}$ and $m_{i}$ are the electron and ion mass, respectively, and $Z$ is the charge state of the ion. An electric field $\boldsymbol {E}$ is present to repel electrons, and so the characteristic size of the electrostatic potential $\phi$ is set by the electron temperature $T_{e}$ , $e\phi \sim T_{e}$ , where $e$ is the proton charge. An asymptotic scale separation between the Debye length $\lambda _{D} = \sqrt {\epsilon _0 T_{{e}} / e^{2} n_{{e}} }$ , the ion sound gyro-radius $\rho _{s} = \sqrt { m_{i} ( ZT_{e} + T_{i} ) } / (ZeB)$ and the size of the collisional region $d_{c} = \alpha \lambda _{\textrm {mfp}}$ is assumed, $\lambda _{D} \ll \rho _{s} \ll d_{c}$ . Here $\epsilon _0$ is the permittivity of free space, $n_{e}$ is the electron density, $T_{i}$ is the ion temperature, $B= |\boldsymbol {B}|$ and $\lambda _{\textrm {mfp}}$ is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances $x$ from the wall such that $\rho _{s} \ll x \ll d_{c}$ , that is, collisions are not treated. A self-consistent solution of the electrostatic potential for $x \sim \rho _{s}$ is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of $\phi (x)$ and results in an analytical expression for the ion distribution function at the target. It assumes that $\tau =T_{i}/(ZT_{e})\gg 1$ , and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For $\tau \gtrsim 1$ , the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.

Physics↗

DOE OSTI2025

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

The Uranium-Containing and Thorium-Containing Anions Studied by Photoelectron Spectroscopy

An in-depth knowledge of actinide chemistry is fundamental to many aspects of nuclear science and technology, including the synthesis and processing of materials and the remediation of waste disposal sites. Among the actinides, the chemical bonding behaviors of actinium and thorium resemble those of the transition metals; the 5f-electrons of protactinium, uranium, neptunium, and plutonium often play important roles in their bonding; and among the still heavier elements, their bonding tends to mimic the lanthanide elements in terms of electron shielding and their f-electron contributions. Bonding that involves 5f-electrons, however, is especially important, in part because of the significance of uranium and plutonium, but also because these elements are among the few where f-electron participation in bonding is relatively common. This work focused on studying uranium-containing and thorium-containing anions in the gas phase using negative ion photoelectron spectroscopy. Since this technique directly probed valence electrons, it was uniquely positioned to address open questions regarding molecular bonding and electron configurations. A particularly important issue concerned how bonding in actinide-containing molecules was affected by modifications to their actinide atoms’ environment, i.e., due to their interaction with ligands. A closely related question was how actinide atoms’ suborbitals were qualitatively reordered and their energies quantitatively shifted as a result of their ligated environments. These were especially relevant issues in regard to uranium due to it having multiple possible oxidation states (OS) and the potential for 5f electron participation in bonding. The effects of ligands on oxidation states and 5f-orbital energies in uranium bonding was expected to be pronounced. Both ligands and excess electrons were seen as probes of actinide atoms within actinide-containing molecules. Our strategy for advancing knowledge of chemical bonding in the actinide-containing species utilized the synergy between experiments and theory, where in some cases experimental results validated theory and where in others computational results assisted in interpreting experiments. Calculations on actinide systems are terrifically challenging due to large spin-orbit interactions, relativistic effects, and just the sheer number of electrons involved. Even in the simplest species, e.g., U and U2, the most sophisticated, modern calculations carried out by the most experienced theorists often only approximate experimentally-measured values, such as electron affinities. For theory to provide confident predictions that can be used to solve real problems it needed an iterative and ultimately corrective mechanism by which its methods can develop further. Experiments can be used to identify when theory has failed; whereupon the subsequent process of using the experiment-theory interplay can be used to find the cause of the failure. Upon fixing it in one case, different test species can be proposed and studied by the experiment-theory combination to determine whether the problem has been corrected. Thus, experiments not only measure the values of molecular properties, they also provide navigational 3 beacons that keep computations off the reefs in an otherwise dark sea with few reference points. Experimental measurements in the actinide field are not only important, they are in actuality essential to computational progress. While it was not always possible to compare the theoreticallydetermined quantity of interest directly with the same experimentally-measured observable, it was usually possible to compare consequential properties that are both calculable and measurable. In the work completed here electron affinities and electronic state spacings were often sensitive consequential parameters. Reasonable agreement between measured and computational values signaled that a calculation that was very likely to be on-track. We had established collaborative relationships with five computational groups, all of which have expertise in computational actinide chemistry. Their PI’s are L. Cheng, D. Dixon, L. Gagliardi, K. Peterson, and B. Vlaisavljevich. Our close interaction with our theory partners led to us suggesting systems to them and them to us. This reciprocal interaction between our experimental and their computational results was among the most important strengths of this work and was a thread woven throughout. Even though anion photoelectron spectroscopic studies are conducted on anions, much of the information that they provide, pertains to the electronic structure of the neutral counterparts of those anions; among these are electron affinities and electronically excited state spacings. Our experimental tools included several specialized ion sources for forming the anionic species of interest, a mass spectrometer for identifying and mass-selecting them, and an anion photoelectron spectrometer for determining their electron affinities (EA) and characterizing the electronic states of the selected anions’ neutral counterparts. Anion photoelectron spectroscopy is conducted by crossing a mass-selected beam of anions with a fixed-frequency laser beam and energy-analyzing the resultant photodetached electrons. The photodetachment process is governed by the energyconserving relationship: hν = EBE + EKE, where hν is the photon’s energy, EBE is the electron binding (photodetachment transition) energy, and EKE is the electron’s kinetic energy. In our apparatus mass-selection is accomplished via time-of-flight mass spectrometry (TOF-MS), electron energy analysis is achieved with either a magnetic bottle or by velocity mapped imaging. Photodetachment of electrons from anions is implemented via either Nd:YAG or excimer lasers. The photodetachment transition energy, i.e., the EBE, between the ground vibrational and electronic state of an anion and the ground vibrational and electronic state of that anion’s neutral counterpart is the adiabatic electron affinity (EA) of that neutral molecule. Likewise, photodetachment transitions between the ground vibrational and electronic state of an anion and the various electronically-excited states of that anion’s corresponding neutral map the electronic spectrum of that neutral species, i.e., the spectral spacings in the photoelectron spectrum are a mirror image of the neutral’s electronic spectrum. It was, of course, crucial to be able to form the anionic species of interest. There, we had a particularly broad field of anion sources from which to choose. These included several variants of pulsed laser vaporization (LV), laser photoemission, infrared desorption plus photoemission, pulsed arc discharge (PACIS), electrospray ionization (ESI), and Rydberg electron transfer (RET). Each of these anion sources were readily combined with, i.e., connected to, the anion photoelectron spectroscopic portion of our apparatus as described above. Among the sources that utilize lasers, visible light for LV sources as well as IR for desorption sources are provided by Nd:YAG lasers. Ultraviolet photons are provided by both Nd:YAG and excimer lasers, whereas the excitation wavelengths for RET experiments come from two Nd:YAG-pumped dye lasers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗