NIOBIUM-1% ZIRCONIUM, NATURAL-CIRCULATION, BOILING-POTASSIUM CORROSION LOOP TEST
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BOILING↗
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Flow of a fluid-solid mixture: Normal stress differences and slip boundary condition
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Mixture theory↗
Inertia-driven particle migration and mixing in a wall-bounded laminar suspension flow
Laminar pressure-driven suspension flows are studied in the situation of neutrally buoyant particles at finite Reynolds number. The numerical method is validated for homogeneous particle distribution (no lateral migration across the channel): the increase of particle slip velocities and particle stress with inertia and concentration is in agreement with former works in the literature. In the case of a two-phase channel flow with freely moving particles, migration towards the channel walls due to the Segré-Silberberg effect is observed, leading to the development of a non-uniform concentration profile in the wall-normal direction (the concentration peaks in the wall region and tends towards zero in the channel core). The particle accumulation in the region of highest shear favors the shear-induced particle interactions and agitation, the profile of which appears to be correlated to the concentration profile. A 1D model predicting particle agitation, based on the kinetic theory of granular flows in the quenched state regime when Stokes number St = O(1) and from numerical simulations when St < 1, fails to reproduce the agitation profile in the wall normal direction. Instead, the existence of secondary flows is clearly evidenced by long time simulations. These are composed of a succession of contra-rotating structures, correlated with the development of concentration waves in the transverse direction. The mechanism proposed to explain the onset of this transverse instability is based on the development of a lift force induced by spanwise gradient of the axial velocity fluctuations. The establishment of the concentration profile in the wall-normal direction therefore results from the combination of the mean flow Segré-Silberberg induced migration, which tends to stratify the suspension and secondary flows which tend to mix the particles over the channel cross section.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Numerical comparison of bubbling in a waste glass melter
Radioactive tank waste is scheduled for vitrification at the Hanford Tank Waste Treatment and Immobilization Plant, also known as the Vit Plant, being constructed at the Hanford Site. Testing of the pilot-scale, joule-heated DuraMelter 1200 at the Vitreous State Laboratory has shown that bubbling increases the melt rate, and as a result, melter throughput. Computational fluid dynamics (CFD) models of this pilot-scale waste glass melter were developed to improve our understanding of the processes that occur within the melter to aid in process optimization and troubleshooting of the Vit Plant melters. Unfortunately, model validation is complicated by the difficulty of obtaining suitable experimental data for operational melters attributed to the large-scale, radioactivity and high temperatures at which these melters are operated. This study focuses on confirming the fidelity of the CFD models to accurately reproduce the bubbling behavior. Because of the paucity of experimental data at the resolution required for CFD validation, a code-to-code comparison was used to evaluate two common approaches for simulating flows of immiscible fluids on numerical grids and resolving multiphase interfaces. Here, the volume of fluid and level set methods are used to track the dynamically evolving interfaces between the molten glass and the air bubbles. To aid in the verification of the results of these codes, a comparison of the bubble behavior, growth, and frequency of bubble generation are presented and a grid convergence study is performed for the two approaches. In addition to comparing the numerical results to available experimental data and observations from pilot-scale testing, the results are evaluated in relation to laboratory experiments with bubbles injected into viscous fluids, empirical correlations obtained from the published literature, and the basic laws of fluid dynamics. Furthermore, the results of this work can assist in validating waste glass melter models and provide a better understanding of the flow patterns within the WTP melters.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
On the role of electron impact in an atmospheric-pressure microwave discharge in liquid n-heptane
The role of electron impact in the dissociation of n-heptane in an atmospheric-pressure microwave discharge in liquid n-heptane was investigated using a self-consistent two-dimensional model. The model includes the Navier–Stokes equations for a two-phase subsonic flow of incompressible liquid and compressible gas, the heat conduction equation, Maxwell’s equations for the microwave field, the Boltzmann equation for plasma electrons, and the balance equations for the electron density and weight fraction of n-heptane in the gaseous and liquid phases. It is shown that the effect of electron impact is negligible at times longer than 10{sup –3} s.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Continuum shock mixture models for Ni+Al multilayers: Individual layers and bulk equations of state
Continuum shock mixture models are reviewed and applied to determine the equations of state for five different compositions of Ni x Al y , as well as bulk Ni+Al reactive multilayers, by combining the fundamental property data for elemental nickel and aluminum. From the literature, we down-select and evaluate two analytical models for the mixture Hugoniot, i.e., the well-known method of kinetic energy averaging (KEA) and a recent model proposed by Jordan and Baer [J. Appl. Phys. 111, 083516 (2012)]. Fundamentally, the former method assumes pressure equilibrium, whereas the latter assumes a common particle velocity and mixture sound speed from compressible two-phase cavitating flows. Additionally, we construct thermodynamically complete equations of state by fitting Einstein oscillator series models for the specific heat at constant volume. Finally, the solid solution approximation is invoked for intermetallic compositions, which are not strictly physical mixtures. Overall, the KEA model provides a better fit to the available Ni x Al y and Ni+Al multilayer shock compression data; however, there are combinations of material properties where the performance of these two models is thought to be reversed. Moreover, the results of this work include the first analytical solution of Jordan–Baer that does not require numerical root finding, as well as proposed modifications to the Einstein oscillator series to incorporate some effects of local pressure–temperature equilibrium and reaction–diffusion. Future work is planned that will use these equations of state in mesoscale simulations to study shock-induced reaction in Ni+Al multilayers, and the intended application is illustrated with a brief 2D hydrocode example.
36 MATERIALS SCIENCE↗
Orificed Flow Results for a Two-Phase Natural Circulation Loop
Researchers at University of Wisconsin - Madison have constructed a 1/4 scaled experimental facility to study the operation of a two-phase natural circulation decay heat removal system. The Reactor Cavity Cooling System (RCCS) is a decay heat removal safety system designed for high temperature generation IV reactors. The system removes decay heat by encircling the outside of the walls of the pressure/containment vessel with cooling channels. These channels are filled with either air in an open loop configuration or water in a closed loop configuration. Radiative and convective heat loads from the pressure vessel induce a buoyancy driven flow in the risers. In accident conditions, the water-based system reaches saturation and the resulting steam is vented off further removing heat until the water inventory is depleted. The water based system has been under investigation at University of Wisconsin - Madison for variations in performance under various flow restriction cases.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
COMPUTATION FLUID DYNAMICS ANALYSIS FOR GENERIC SMALL MODULAR REACTOR CONTAINMENT SEPARATE EFFECTS TEST
It is desirable for fourth-generation Small Modular Reactors to be passively cooled in standard and accident operations. Passive Containment Cooling Systems can reject heat from the containment structure, without using pumps or blowers. The targeted design containment structure is a large, domed, stainless steel, cylindrical vessel. In a postulated Design Basis Accident, steam will flash inside containment. Steam condensation occurs on the inner containment wall and transfers heat through the steel containment into a large body of water known as the annular reservoir (AR) surrounding the vessel serving as the ultimate heat sink. Natural circulation drives the flow in the AR and heat will be released to the environment by evaporation of water. Unique containment geometry requires a separate effects test (SET) facility for the verification and validation of the computer code and evaluation model development and assessment for reactor licensing efforts. In this study, STAR-CCM+, a computational fluid dynamics (CFD) code was used to inform the decision-making process on the design of the SET. The CFD simulation modeled, a two-phase turbulent flow with fluid film development and heat transfer for different containment geometries. The Reactor Excursion and Leak Analysis Program will also be used in a code-to-code verification against the CFD results.
21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
Parametric and Sensitivity Analysis of a Steam Generator Model Using Python and Machine-Learning Tools
For this study, we used Python and machine-learning tools to perform a comprehensive parametric and sensitivity analysis on a steam generator (SG) model. (The Python model was based on a previously completed MATLAB framework for the Holtec SMR-160 SG.) We investigated the influence of various input parameters (e.g., heat transfer coefficient [HTC], Nusselt number, and heat exchanger effectiveness) on the system’s output. With machine-learning tools such as the Risk Analysis Virtual Environment (RAVEN), which was developed at Idaho National Laboratory, we were then able to perform an automated analysis of the SG inputs’ effect on the HTC. The analysis results give valuable insights into the performance and optimization of SG systems. We found the inlet mass flow rate (MFR) to have the greatest impact on the HTC, followed closely by the inlet temperature, and then pressure. Shifting of the input parameters causes the location of the maximum HTC along the SG length to change incrementally. The cold leg (CL) MFR was also found to impact the HTC magnitude as well as the location of the maximum HTC. At between 0.4–0.9 of the total SG length, the input parameters experience maximum impact on the HTC, leading us to suggest that sensors be efficiently placed on the SG so as to closely and effectively monitor thermal-hydraulic properties during reactor operation. We also found that the sensitivity data calculated manually agrees with the RAVEN – based data, confirming the same range of maximum sensitivity. However, the RAVEN-based analysis showed that cold leg pressure and hot leg temperature have a greater impact on the heat transfer coefficient than the mass flow rate, implying that a manual sensitivity study taking only two samples is not accurate.
20 FOSSIL-FUELED POWER PLANTS↗
Thermochemical reduction modeling in a high-temperature moving-bed reactor for energy storage: 1D model
The design of robust and efficient high-temperature thermochemical reactors and determination of operating conditions are critical steps toward enabling high-efficiency long-duration solar energy storage. This work presents a computational model for the thermal reduction of a metal oxide material (Mg-Mn-O) up to 1450 °C and the coupled complex transport phenomena in a novel tubular thermal reactor design that features the capability for a high extent-of-reduction (high energy storage density) and inherent heat recuperation. A one-dimensional model coupling counter-current gas–solid flow, two-phase heat transfer, thermochemical redox reactions, and species transport in a moving-bed reactor is developed. Simplified versions of the model are validated with published results in the literature for packed beds with both inert and reactive particles; the fully coupled model is also validated with experimental measurements of a moving-bed reactor in terms of local temperatures and oxygen release at the exit. Detailed comparisons on the effects of different boundary conditions in the reaction zone (prescribed wall temperature vs. heat flux conditions) and formulations based on a simple uniform flow assumption vs. plug flow using Ergun equation for gas flow are investigated. The results are compared with experimental measurements, and for all cases, the energy flow components in the reactor system and the thermal to chemical conversion efficiency and overall system efficiency are computed. Finally, the predicted high thermal-to-chemical efficiency ~95% and system efficiency ~30% agree with experimental measurements.
25 ENERGY STORAGE↗
FY22 Progress on Multicontinuum Methods in Containment
Estimation of two-phase fluid flow properties is important to understand and predict water and gas movement through the vadose zone for agricultural, hydrogeological, and engineering applications, such as containment transport and/or containment of gases in the subsurface. To estimate rock fluid flow properties and subsequently predict physically realistic processes such as patterns and timing of water, gas, and energy (e.g., heat) movement in the subsurface, laboratory spontaneous water imbibition with simultaneous temperature measurement and numerical modeling methods are presented in the FY22 progress report. A multiple-overlapping-continua conceptual model is used to explain and predict observed complex multi-phenomenological laboratory test behavior during spontaneous imbibition experiments. This report primarily addresses two complexities that arise during the experiments: 1) capturing the late-time behavior of spontaneous imbibition tests with dual porosity; and 2) understanding the thermal perturbation observed at or ahead of the imbibing wetting front, which are associated with adsorption of water in initially dry samples. We use numerical approaches to explore some of these issues, but also lay out a plan for further laboratory experimentation and modeling to best understand and leverage these unique observations.
58 GEOSCIENCES↗
Operando X-ray tomography and sub-second radiography for characterizing transport in polymer electrolyte membrane electrolyzer
Utilizing hydrogen gas as an energy carrier and enabling a hydrogen economy is a promising step towards decarbonization. Water electrolysis is a key process in hydrogen generation, but electrolyzers face a couple technological hurdles before widespread integration could occur. Understanding morphology evolution and transport processes in an operating polymer electrolyte membrane (PEM) electrolyzer is key to reducing cost and increasing efficiency. In this study, combined operando X-ray computed tomography and radiography are used to study transport and degradation in PEM electrolyzers subject to applied current densities. Tomography enables three-dimensional steady-state imaging but does not capture transport subtleties. Radiography is limited to two-dimensions but does capture transient phenomena. The tomography results depict degradation of the catalyst layer on the anode side of the electrolyzer. The rate of degradation was observed to increase as the applied current density increased. The catalyst particle detachment is due to autonomous propulsion during the oxygen evolution reaction. Particles that mechanically rip off the membrane were observed to be redeposited into the porous transport layer. During radiography, sub-second exposure time is required to capture the transient behavior of oxygen evolution, even at the lower current densities (50-200 mAcm -2 ). Various flow regimes were observed in the channel ranging from bubbly to slug flow depending on current density. In conclusion, experimental observations agree with a model that an increase in current density increases oxygen bubble diameter and decreases bubble residence time within the electrolyzer channel.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Experimental study of three-dimensional CO 2 -water drainage and fracture-matrix interactions in fractured porous media
Estimation of CO 2 storage capacity in fractured porous reservoirs requires a better understanding of the CO 2 -water flow fundamentals in fracture-matrix systems. There are few core-flood experiments on three-dimensional CO 2 -water drainage in a fracture-matrix system, yet none have examined the impacts of the capillary continuity of fractures and fracture-matrix interactions. In this study, twelve drainage experiments were conducted in four fracture-matrix columns, each comprising a vertical stack of a cylindrical rock core, a filter paper serving as an analogue to a horizontal fracture, and a ceramic plate. Here, the core sample was surrounded by open space at the top and circumferential sides to model fractures, allowing for 3-D CO 2 -water drainage in the rock core and displaced water draining across the horizontal fracture. X-ray computed tomography was conducted to visualize the dynamic invasion/drainage processes in four rock core samples showing contrasts in anisotropy, permeability, and heterogeneity. Experimental results show (1) the equilibrium CO 2 saturations in the rock matrix vary from 0.10 to 0.60 at controlled capillary pressures up to 200 kPa, (2) the CO 2 saturations in the matrix increase with water saturation in the horizontal fracture resulting in better capillary continuity for water to drain across the fracture, and (3) the fracture water saturation can be enhanced by the non-uniform fracture capillary pressure and countercurrent flow of CO 2 and water across the fracture-matrix interface. In the case of high fracture water saturation, matrix CO 2 saturation largely depends on matrix anisotropy and heterogeneity. The core-scale experimental results contribute to understand the fracture-matrix interactions and CO 2 storage efficiency in fractured porous media.
54 ENVIRONMENTAL SCIENCES↗
Interfacial gauge methods for incompressible fluid dynamics
Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena.
42 ENGINEERING↗
Empirical derivation of a Nusselt number in a thermally stratified enclosure
A hydrophilic gelatin suspension possesses thermal properties that may affect the ratio of convective to conductive heat transfer across a boundary. This ratio, also known as Nusselt's number, can represent laminar or turbulent flow regimes. In this study, thermal transitioning empirical values were determined using a gelatin as a polymer gel surrogate. The crux of this study was to (a) quantify heat transfer properties of the gelatin as a suspended semi-solid and (b) understand thermal profiles with respect to particle size and loading. We can adduce the existence of a thermally induced: lower rise velocity, stratified Nusselt number, and a boundary layer.
42 ENGINEERING↗
The roll-up and merging of coherent structures in shallow mixing layers
The current study seeks a fundamental explanation to the development of two-dimensional coherent structures (2DCSs) in shallow mixing layers. A nonlinear numerical model based on the depth-averaged shallow water equations is used to investigate the temporal evolution of shallow mixing layers, where the mapping from temporal to spatial results is made using the velocity at the center of the mixing layers. The flow is periodic in the streamwise direction. Transmissive boundary conditions are used in the cross-stream boundaries to prevent reflections. Numerical results are compared to linear stability analysis, mean-field theory, and secondary stability analysis. Results suggest that the onset and development of 2DCS in shallow mixing layers are the result of a sequence of instabilities governed by linear theory, mean-field theory, and secondary stability theory. The linear instability of the shearing velocity gradient gives the onset of 2DCS. When the perturbations reach a certain amplitude, the flow field of the perturbations changes from a wavy shape to a vortical (2DCS) structure because of nonlinearity. The development of the vertical 2DCS does not appear to follow weakly nonlinear theory; instead, it follows mean-field theory. After the formation of 2DCS, separate 2DCSs merge to form larger 2DCS. In this way, 2DCSs grow and shallow mixing layers develop and grow in scale. The merging of 2DCS in shallow mixing layers is shown to be caused by the secondary instability of the 2DCS. Eventually 2DCSs are dissipated by bed friction. The sequence of instabilities can cause the upscaling of the turbulent kinetic energy in shallow mixing layers.
42 ENGINEERING↗
Effect of Computational Schemes on Coupled Flow and Geo-Mechanical Modeling of CO 2 Leakage through a Compromised Well
Carbon capture, utilization, and storage (CCUS) describes a set of technically viable processes to separate carbon dioxide (CO 2 ) from industrial byproduct streams and inject it into deep geologic formations for long-term storage. Legacy wells located within the spatial domain of new injection and production activities represent potential pathways for fluids (i.e., CO 2 and aqueous phase) to leak through compromised components (e.g., through fractures or micro-annulus pathways). The finite element (FE) method is a well-established numerical approach to simulate the coupling between multi-phase fluid flow and solid phase deformation interactions that occur in a compromised well system. We assumed the spatial domain consists of a three-phases system: a solid, liquid, and gas phase. For flow in the two fluids phases, we considered two sets of primary variables: the first considering capillary pressure and gas pressure (PP) scheme, and the second considering liquid pressure and gas saturation (PS) scheme. Fluid phases were coupled with the solid phase using the full coupling (i.e., monolithic coupling) and iterative coupling (i.e., sequential coupling) approaches. The challenge of achieving numerical stability in the coupled formulation in heterogeneous media was addressed using the mass lumping and the upwinding techniques. Numerical results were compared with three benchmark problems to assess the performance of coupled FE solutions: 1D Terzaghi’s consolidation, Liakopoulos experiments, and the Kueper and Frind experiments. We found good agreement between our results and the three benchmark problems. For the Kueper and Frind test, the PP scheme successfully captured the observed experimental response of the non-aqueous phase infiltration, in contrast to the PS scheme. These exercises demonstrate the importance of fluid phase primary variable selection for heterogeneous porous media. We then applied the developed model to the hypothetical case of leakage along a compromised well representing a heterogeneous media. Considering the mass lumping and the upwinding techniques, both the monotonic and the sequential coupling provided identical results, but mass lumping was needed to avoid numerical instabilities in the sequential coupling. Additionally, in the monolithic coupling, the magnitude of primary variables in the coupled solution without mass lumping and the upwinding is higher, which is essential for the risk-based analyses.
deformation flow↗
Roles of bulk viscosity on Rayleigh-Taylor instability: Non-equilibrium thermodynamics due to spatio-temporal pressure fronts
Direct numerical simulations of Rayleigh-Taylor instability (RTI) between two air masses with a temperature difference of 70 K is presented using compressible Navier-Stokes formulation in a non-equilibrium thermodynamic framework. The two-dimensional flow is studied in an isolated box with non-periodic walls in both vertical and horizontal directions. The non-conducting interface separating the two air masses is impulsively removed at t = 0 (depicting a heaviside function). No external perturbation has been used at the interface to instigate the instability at the onset. Computations have been carried out for rectangular and square cross sections. The formulation is free of Boussinesq approximation commonly used in many Navier-Stokes formulations for RTI. Effect of Stokes’ hypothesis is quantified, by using models from acoustic attenuation measurement for the second coefficient of viscosity from two experiments. Effects of Stokes’ hypothesis on growth of mixing layer and evolution of total entropy for the Rayleigh-Taylor system are reported. The initial rate of growth is observed to be independent of Stokes’ hypothesis and the geometry of the box. Following this stage, growth rate is dependent on the geometry of the box and is sensitive to the model used. As a consequence of compressible formulation, we capture pressure wave-packets with associated reflection and rarefaction from the non-periodic walls. The pattern and frequency of reflections of pressure waves noted specifically at the initial stages are reflected in entropy variation of the system.
42 ENGINEERING↗