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Transport Modeling of Kinetically Limited Microscale Extraction Systems: Droplet and Supported Liquid Membrane Separations
Microfluidic droplet extraction devices can be used to efficiently measure solute phase transfer kinetics in liquid–liquid extraction systems. In this work, a droplet extraction apparatus was constructed using off-the-shelf and custom 3D printed parts for less than 110 USD. The interfacial kinetics of the transfer of Pu(IV) between an aqueous nitric acid phase and a 5 v/v% tridodecylamine (TDA) in toluene phase were characterized by determining the extent of Pu(IV) transfer between phases at different flow rates. Forward interfacial rate constants calculated from this data using an analytical model are 5.6 × 10 –3 mm s –1 under extraction (aqueous-to-organic solute transfer) conditions and 3.3 × 10 –3 mm s –1 under stripping (organic-to-aqueous solute transfer) conditions. The analytical model is valid when the rate of solute transfer across the interface between the two liquid phases has pseudo-first-order reversible reaction kinetics and is slow relative to the rate of solute transport to the interface. The change in the outlet concentration with residence time determined using the analytical model was compared with the results of a numerical model accounting for advection/diffusion to the interface in addition to kinetically limited interfacial solute transfer. These calculations revealed that for systems with forward interfacial rate constants greater than approximately 10 –2 mm s –1 , the analytical model must be supplemented with a numerical transport model accounting for an additional advection/diffusion mass transfer resistance. This threshold corresponds to a Damköhler number of one. The measured interfacial kinetic rate constants for Pu(IV)/TDA were used in a supported liquid membrane (SLM) numerical model, which showed that the Pu(IV) phase transfer kinetics are fast enough for use in a practical separation.
A New Model for Simulating the Imbibition of a Wetting-Phase Fluid in a Matrix-Fracture Dual Connectivity System
The imbibition experiment is an effective approach for measuring petrophysical properties of porous media, with many such experiments performed over the past decade. Quite some empirical, analytical, and numerical models have been developed to simulate spontaneous imbibition of the wetting phase fluid into porous media, but limitations still exist. In previous studies, the imbibition process has been considered to give a piston-like displacement or the porous medium modeled as multiply-sized pores linked with bonds; both approaches fail to yield comprehensive results due to their neglect of the presence of irregular fractures or nonuniform flow paths through the matrix. By building a numerical model for simulating laboratory-scale experimental data, we performed imbibition tests on several fractured Barnett Shale samples having fractures either parallel ( P ) or transverse ( T ) to the bedding plane and used MATLAB to build a new numerical model by combining the imbibition process in fractures and the matrix using concepts from percolation theory. The experimental data show that the rocks with P -direction fractures have a more steady increase of imbibition rates than the case of T -direction one. As the shale matrix with low pore connectivity hampers the upward water movement, the imbibition rate of shales with T -direction fractures will decrease suddenly after the bottom layer in contact with water is saturated during the initial period. This wetting phase movement (WPM) model can simulate 3D porous media with 2D fractures. The rate of imbibition by fractured porous media is associated with physical parameters such as porosity and fracture distribution (e.g., the number and angle of fractures). Using Monte Carlo methods, we examined fracture parameters and predicted elapsed time and cumulative water imbibition, for the Barnett Shale samples. The results show that the rate of imbibed water mass is sensitive to the number of fractures directly connected to water source, and the connectivity between two neighboring grid cells is a key parameter for the wetting-front progression. The findings of this study can help to better understand the imbibition process with multiple influencing processes and factors in fractured-matrix rocks. Although the experiments, data simulation, and prediction results are based only on Barnett Shale samples, the model is readily applicable to imbibition tests of other fractured rocks to show the spatial and temporal behavior during a dynamic imbibition process that are not easily captured experimentally.
Quantifying Groundwater Response and Uncertainty in Beaver‐Influenced Mountainous Floodplains Using Machine Learning‐Based Model Calibration
Abstract Beavers ( Castor canadensis ) alter river corridor hydrology by creating ponds and inundating floodplains, and thereby improving surface water storage. However, the impact of inundation on groundwater, particularly in mountainous alluvial floodplains with permeable gravel/cobble layers overlain by a soil layer, remains uncertain. Numerical modeling across various floodplain structures considers topographic and sediment complexity and multidirectional flow, linking inundation to groundwater response. This study develops a model‐data integration workflow to address uncertainty in groundwater response to beaver‐induced inundations in a mountainous alluvial floodplain in the Upper Colorado River Basin. Uncertain factors include seasonal hydrologic dynamics, hydraulic conductivities, floodplain structures, and meteorological forcings. We employed an ensemble of groundwater models, based on geophysical and hydrologic data, with machine learning‐based calibration using a neural density estimator. This allowed us to quantify the vertical flux from the soil layer to the permeable gravel bed, the down‐valley underflow within the gravel bed, and their ratios. Results show a significant increase in the vertical flux relative to down‐valley underflow, from 2 during dry pond periods to 20 during wet periods, serving as an analogy for conditions without and with beaver ponds. The study highlights the influence of floodplain structure on groundwater storage, water balance, and water quality impacted by beaver ponds. A thick gravel bed layer, with a large down‐valley underflow, minimizes the effect of beaver‐induced inundation on water quality. We emphasize the need for field‐scale measurements of floodplain structure and improved characterization of evapotranspiration changes to reduce uncertainty in groundwater response. Plain Language Summary Beavers change the flow of water in river corridors by creating ponds, expanding wetlands, and flooding floodplains. This increases surface water area, promotes plant growth, and enhances biodiversity. However, the impact of this flooding on groundwater flow is not well understood, especially in mountainous areas with gravel layers where water moves easily beneath soil. In this study, we used numerical modeling to investigate how beaver ponds influence groundwater in a mountainous floodplain of the Upper Colorado River Basin. We adapted a machine learning method to validate our numerical models using multiple field data sets. Our findings show that beaver ponds significantly increase vertical water flow from the soil to the gravel during wet periods, compared to when the ponds are fully drained. The study also highlights the importance of floodplain structure in controlling both water flow in gravel layers along the river direction and vertical flow from the soil to the gravel with the presence of beavers. To reduce uncertainty in groundwater response, we emphasize the need for more field‐scale measurements of floodplain structure, hydraulic properties, and evapotranspiration changes. Key Points Floodplain structures and hydraulic conductivities are important for groundwater response with beaver ponds in mountainous floodplains Large down‐valley underflow in permeability‐stratified floodplains reduces beaver‐induced impacts on groundwater storage and water quality Machine learning‐based model calibration methods are effective for estimating posterior distributions of groundwater model parameters
Theoretical estimates of flammability bounds for thin condensed fuel diffusion flames in microgravity using detailed models of chemistry and radiation
Recently, U-shape flammability maps have been constructed showing minimal oxygen vs. flame strain for opposed flame spread in micro-gravity by Olson and Ferkul. The U-shape defines the limiting flammability bounds from radiative extinction and flame blow-off. Here, the minimum of the U corresponds to the minimum possible oxidizer concentration where burning can occur, and is an important quantity of interest for fire safety. While high strain extinction bounds have been well analyzed, low strain radiative extinction has not. To estimate low strain extinction, in this study an analytical theory is developed based on thin flame theory coupled with a heat and mass transfer model for solid fuels. A reaction progress variable based on the Damköhler number is adapted in the theory to account for incomplete combustion at high strain rates and enable the capturing of the full flammability map. The analytical model is compared to a one dimensional numerical model w/ detailed chemical kinetics and coupled radiation heat transfer in planar and spherical geometries. The flammability maps are then qualitatively compared to experimental extinguishment data compiled by Olson and Ferkul for cylindrical rods of PMMA showing similar trends. The results show the newly developed analytics capture the radiative extinction bound compared to the numerical model and qualitatively agrees with microgravity data.
Analyzing the Validity of Brazilian Testing Using Digital Image Correlation and Numerical Simulation Techniques
Characterizing the mechanical behavior of rocks plays a crucial role to optimize the fracturing process in unconventional reservoirs. However, due to the intrinsic anisotropy and heterogeneity in unconventional resources, fracture process prediction remains the most significant challenge for sustainable and economic hydrocarbon production. During the deformation tracking under compression, deploying conventional methods (strain gauge, extensometer, etc.) is insufficient to measure the deformation since the physical attachment of the device is restricted to the size of the sample, monitoring limited point-wise deformation, producing difficulties in data retrieval, and a tendency to lose track in failure points, etc. Where conventional methods are limited, the application of digital image correlation (DIC) provides detailed and additional information of strain evolution and fracture patterns under loading. DIC is an image-based optical method that records an object with a camera and monitors the random contrast speckle pattern painted on the facing surface of the specimen. To overcome the existing limitations, this paper presents numerical modeling of Brazilian disc tests under quasi-static conditions to understand the full-field deformation behaviors and finally, it is validated by DIC. As the direct tensile test has limitations in sample preparation and test execution, the Brazilian testing principle is commonly used to evaluate indirectly the tensile strength of rocks. The two-dimensional numerical model was built to predict the stress distribution and full-field deformation on Brazilian disc under compression based on the assumptions of a homogenous, isotropic and linear elastic material. The uniaxial compression test was conducted using the DIC technique to determine the elastic properties of Spider Berea sandstone, which were used as inputs for the simulation model. The model was verified by the analytical solution and compared with the digital image correlation. The numerical simulation results showed that the solutions matched reasonably with the analytical solutions where the maximum deviation of stress distribution was obtained as 14.59%. The strain evolution (normal and shear strains) and displacements along the central horizontal and vertical planes were investigated in three distinguishable percentages of peak loads (20%, 40%, and 90%) to understand the deformation behaviors in rock. The simulation results demonstrated that the strain evolution contours consistently matched with DIC generated contours with a reasonable agreement. The changes in displacement along the central horizontal and vertical planes showed that numerical simulation and DIC generated experimental results were repeatable and matched closely. In terms of validation, Brazilian testing to measure the indirect tensile strength of rocks is still an issue of debate. The numerical model of fracture propagation supported by digital image correlation from this study can be used to explain the fracturing process in the homogeneous material and can be extended to non-homogeneous cases by incorporating heterogeneity, which is essential for rock mechanics field applications.
Summary of CTF Modeling and Numerical Improvements for Boiling Water Reactor Simulation
This report documents geometry and numerical improvements made to CTF for the modeling of boiling water reactor (BWR) geometry and operating conditions. These activities are part of a larger program to extend the Virtual Environment for Reactor Applications (VERA) to better support BWR modeling and simulation. The activities documented in this report added features to CTF, including support for mixed-fuel cores, modeling of the upper plenum, and modeling of the lower tie plate form losses. A review of the spacer grid modeling approach was also performed, and a plan was discussed for future improvement. The parallelization of the model was improved, leading to a roughly 2× improvement in CTF runtime and a 1.6× improvement in total VERA runtime. An in-depth review of the governing equations and their linearization was performed and is documented in this report. Once implemented, this new linearization will allow CTF to take much larger timesteps, leading to more significant reductions in CTF and VERA runtimes.
Modeling Assessment of Tidal Energy Extraction in the Western Passage
Numerical models have been widely used for the resource characterization and assessment of tidal instream energy. The accurate assessment of tidal stream energy resources at a feasibility or project-design scale requires detailed hydrodynamic model simulations or high-quality field measurements. This study applied a three-dimensional finite-volume community ocean model (FVCOM) to simulate the tidal hydrodynamics in the Passamaquoddy–Cobscook Bay archipelago, with a focus on the Western Passage, to assist tidal energy resource assessment. IEC Technical specifications were considered in the model configurations and simulations. The model was calibrated and validated with field measurements. Energy fluxes and power densities along selected cross sections were calculated to evaluate the feasibility of the tidal energy development at several hotspots that feature strong currents. When taking both the high current speed and water depth into account, the model results showed that the Western Passage has great potential for the deployment of tidal energy farms. The maximum extractable power in the Western Passage was estimated using the Garrett and Cummins method. Different criteria and methods recommended by the IEC for resource characterization were evaluated and discussed using a sensitivity analysis of energy extraction for a hypothetical tidal turbine farm in the Western Passage.
Highly Accurate Experimental Heave Decay Tests with a Floating Sphere: A Public Benchmark Dataset for Model Validation of Fluid–Structure Interaction
Highly accurate and precise heave decay tests on a sphere with a diameter of 300 mm were completed in a meticulously designed test setup in the wave basin in the Ocean and Coastal Engineering Laboratory at Aalborg University, Denmark. The tests were dedicated to providing a rigorous benchmark dataset for numerical model validation. The sphere was ballasted to half submergence, thereby floating with the waterline at the equator when at rest in calm water. Heave decay tests were conducted, wherein the sphere was held stationary and dropped from three drop heights: a small drop height, which can be considered a linear case, a moderately nonlinear case, and a highly nonlinear case with a drop height from a position where the whole sphere was initially above the water. The precision of the heave decay time series was calculated from random and systematic standard uncertainties. At a 95% confidence level, uncertainties were found to be very low—on average only about 0.3% of the respective drop heights. Physical parameters of the test setup and associated uncertainties were quantified. A test case was formulated that closely represents the physical tests, enabling the reader to do his/her own numerical tests. The paper includes a comparison of the physical test results to the results from several independent numerical models based on linear potential flow, fully nonlinear potential flow, and the Reynolds-averaged Navier–Stokes (RANS) equations. A high correlation between physical and numerical test results is shown. The physical test results are very suitable for numerical model validation and are public as a benchmark dataset.
Modeling of Supercritical CO2 Shell-and-Tube Heat Exchangers Under Extreme Conditions: Part II: Heat Exchanger Model
Abstract Heat exchangers play a critical role in supercritical CO2 Brayton cycles by providing necessary waste heat recovery. Supercritical CO2 thermal cycles potentially achieve higher energy density and thermal efficiency operating at elevated temperatures and pressures. Accurate and computationally efficient estimation of heat exchanger performance metrics at these conditions is important for the design and optimization of sCO2 systems and thermal cycles. In this paper (Part II), a computationally efficient and accurate numerical model is developed to predict the performance of shell-and-tube heat exchangers (STHXs). Highly accurate correlations reported in Part I of this study are utilized to improve the accuracy of performance predictions, and the concept of volume averaging is used to abstract the geometry and reduce computation time. The numerical model is validated by comparison with computational fluid dynamics (CFD) simulations and provides high accuracy and significantly lower computation time compared to existing numerical models. A preliminary optimization study is conducted and the advantage of using supercritical CO2 as a working fluid for energy systems is demonstrated.
High-Fidelity Numerical Wave Tank Verification & Validation Study: Wave Generation Through Paddle Motion: Preprint
This paper presents a numerical benchmark study of wave propagation due to a paddle motion using different high-fidelity numerical models, which are capable of replicating the nearly actual physical wave tank testing. A full time series of the measured wave generation paddle motion which was used to generate wave propagation in the physical wave tank will be utilized in each of the models contributed by IEA OES Task 10's participants, which includes both computational fluid dynamics (CFD) and smooth hydrodynamic particle (SPH). The high-fidelity simulations of the physical wave testcase will allow for the evaluation of the initial transient effects from wave ramp-up and its evolution in the wave tank over time for two representative regular waves with varying levels of nonlinearity. A couple of interesting metrics like the predicted wave surface elevation at select wave probes, wave period, and phase-shift in time will be assessed to evaluate the relative accuracy of numerical models versus experimental data within specified time intervals. These models will serve as a guide for modelers in the wave energy community and provide a base case to allow further and more detailed numerical modeling of the fixed Kramer Sphere Cases under wave excitation force wave tank testing.
Community Geothermal: Borefield Design, Thermal Conductivity, and Subsurface Modeling Data - Chicago, IL
This dataset encompasses the development of a geothermal energy system for the West Woodlawn neighborhood in Chicago, Illinois. This project is part of a broader initiative to design and deploy geothermal heating and cooling systems at a community scale. The dataset includes thermal conductivity test results, calculations for borehole sizing based on the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) method, as well as simulated thermal loads based on actual energy usage from individual buildings. Also provided here are files used for numerical modeling via COMSOL Multiphysics to simulate borefield design and subsurface thermal behavior. Two manuscripts are attached, which outline the broad objectives of the project and a description of the numerical modeling methodology and results.
Modeling Induction Stirring and Particle Tracking in Molten Uranium
Two independent numerical models have been developed to simulate the behavior of carbon impurities in molten uranium metal. Informed by experimental parameters, one model was created using the commercial software Star-CCM+ and compared with another developed using open-source codes, including OpenFOAM, Finite Element Method Magnetics (FEMM) and a First Passage Kinetic Monte Carlo (FPKMC) approach. The target experimental system features a 404g uranium metal charge containing an average carbon concentration of 139 ppm which was melted in a vacuum induction furnace at 1400° C then resolidified. The microstructures of the uranium and its impurities before and after melting have been characterized and reported separately. Prior to simulating the uranium-carbon system described, the numerical models were validated using a previously published nonradioactive experimental system to ensure agreement with expected output values. Focus has been placed on modeling velocity fields under induction stirring and impurity particle trajectories.
Computational capacity in hydrodynamic real-time hybrid simulation applied to simulate the dynamic response of floating offshore wind turbines
Real-time hybrid simulation (RTHS) mitigates similitude distortions in model-scale tests of floating offshore wind turbines (FOWTs) by coupling physical experiments with numerical models in real time. The coupling requires faster-than-real-time numerical computations to satisfy temporal similitude with the physical experiment, presenting a bottleneck for using more complex numerical models in RTHS. This paper presents a hydrodynamic-RTHS (hydro-RTHS) framework for FOWTs that simulates the hydrodynamics physically and the aerodynamics numerically with sensor feedback from the physical testing. The framework adapts the three-loop hardware architecture to leverage greater computational resources and mitigate strict temporal requirements, enabling more computationally demanding numerical analyses in hydro-RTHS. The three-loop hardware architecture integrates multiple machines, each dedicated to either numerical analysis or RTHS controls, with a rate-transition algorithm to synchronize the tasks executed across the different machine processors. Virtual and physical tests verified and validated the hydro-RTHS framework, respectively. The ”virtual” tests, which approximates the physical domain numerically, verified the RTHS framework with respect to a numerical full-scale complete FOWT model simulated in the open-source software, OpenFAST. The virtual tests were able to maintain comparable control signals while enabling greater computational resources for the numerical calculations. Real-world physical tests demonstrated that the hydro-RTHS framework computes aerodynamic forces similar to the complete OpenFAST model, validating the hydro-RTHS framework using the three-loop hardware architecture. Findings show that the hydro-RTHS framework with the three-loop hardware architecture is computationally efficient, with reserve capacity to simulate more complex problems due to the customized software, hardware, and rate-transition algorithm.
TEAMER Technical Support for Aquantis (Modeling): Cooperative Research and Development Final Report, CRADA Number CRD-21-17763
NREL will provide numerical modelling support to Requestor by completing four successive stages of numerical modeling effort which are capable of accurate predicting the performance of the Aquantis turbine. NREL will develop a baseline OpenFAST model (a couple model of AeroDyn and ElastoDyn solver) of the Aquantis turbine, subsequently couples this model to OrcaFlex or within OpenFAST framework to preliminarily design and explore a full floating tidal turbine system in a control co-design process.
Sensitivity Analysis and Effective Parametrization of PEM Fuel Cell Models
The cost of proton-exchange-membrane fuel cells (PEMFCs) remains a major hurdle in large-scale commercialization of this technology. To improve their performance and reduce cost, novel materials and electrode designs are continuously envisioned, e.g., non-PGM catalyst layers, ultra-thin Pt/Pt-Ni based catalyst layers, structured ionomer arrays or NSTF catalyst layers.1 Understanding the impact of these improvement strategies can be extremely time and cost intensive due to complex physical phenomena and large design space. We have previously developed a PEMFC modeling framework2 which has been a time and cost effective tool for understanding and optimizing the complex multi-physics phenomena within PEMFCs; however, several of the cell parameters used in the modeling have large spread in measured data.3 Furthermore, several transport parameters such as water adsorption kinetics have not been accurately measured and the approximations are spread over several orders of magnitude. These uncertainties cause problems in ascertaining accuracy of the modeling approach and they reduce the predictive power of the numerical models. The aim of this work is to identify the sensitivity of PEFC numerical model outputs to various input parameters. The previously in-house developed MEA modeling framework2 is used for PEMFC modeling. The sensitivity of the model outputs with respect to inputs parameters is obtained by analyzing the condition numbers for different output-input pairs at varying operating conditions. An example of the sensitivity analysis is shown in Figure 1. The condition numbers are obtained for the entire possible range of input parameters at varying operating conditions to identify the most crucial parameters of the PEMFC model. Based on our preliminary analysis, parameters related to kinetics (exchange current density and ECSA) and heat/water management in electrodes and ionomer (ionomer fraction, thermal conductivity) are most crucial. One of the major goals of this work is to identify the most crucial set of parameters towards which the model shows maximum sensitivity. This will guide future experimentalists to measure these properties with higher accuracy. Furthermore, the sensitivity analysis will also enable us to optimize the PEMFC performance by selectively targeting the most sensitive parameters and thereby making the largest impact. Acknowledgements The work is funded under the Fuel Cell Performance and Durability Consortium (FC-PAD), by the Fuel Cell Technologies Office (FCTO), Office of Energy Efficiency and Renewable Energy (EERE), of the U.S. Department of Energy under contract number DE-AC02-05CH11231. The authors would like to thank Nathan Craig at Robert Bosch LLC for his valuable input in designing the sensitivity analysis. The authors would also like to thank Giovanna Bucci and Matthias Hanauer at Robert Bosch for their valuable inputs and discussion. References P. K. Sinha, W. Gu, A. Kongkanand and E. Thompson, J. Electrochem. Soc., 158, B831 (2011). L. M. Pant, M. R. Gerhardt, N. Macauley, R. Mukundan, R. L. Borup and A. Z. Weber, Electrochim. Acta, 326, 134963 (2019). R. Vetter and J. O. Schumacher, ArXiv181110091 Phys. (2018). Figure 1
Propagation of Input Uncertainties in Numerical Simulations of Laser Powder Bed Fusion
Laser powder bed fusion has the potential of redefining state-of-the-art processing and production methods, but defect formation and inconsistent build quality have limited the implementation of this process. Numerical models are widely used to study this process and predict the formation of these defects. Presently, the uncertainties of model input parameters and thermophysical properties used by these numerical simulations have not been investigated. In the present study, the uncertainty in these input parameters and material properties are quantified for laser powder bed fusion, with and without a simulated powder bed, to determine their influence on the predictive accuracy of an experimentally validated numerical model. Accounting for all possible sources of uncertainty quickly becomes computationally expensive on account of the curse of dimensionality. Uncertainty in laser absorption, solid, and liquid specific heat of the metal were found to have the largest effect on model prediction reliability with or without the use of a powder bed. Results also illustrate that accounting for these three uncertain parameters still captures the majority of model prediction uncertainty. Furthermore, the methodology of this study may be used to understand the uncertainty in as-built microstructure through propagation to microstructure prediction models, or applied under processing conditions where high Péclet numbers are observed and the thermal convection and fluid flow within the molten pool are substantial.
Toward integrating high-fidelity CFD approaches in the thermal-hydraulic analysis of turbulent dry cask systems
Nuclear power plants have been supplying resilient and reliable electricity for decades, contributing to energy independence of the U.S.. However, nuclear waste management remains one of the most significant challenges in the industry. The safety of dry cask storage systems relies heavily on their thermal-hydraulic performance. Computational Fluid Dynamics (CFD) simulations are often used to demonstrate this performance and ensure that the system design meets safety standards. This study presents reduced numerical models for various types of dry cask systems. These numerical models can produce efficient and fast results based on the employed modeling strategies. Additionally, the study uses a novel approach to high-fidelity simulations to evaluate modeling assumptions in dry cask modeling. Large Eddy Simulations (LES) are used for this purpose, particularly in regions where fluid velocity is relatively high and the turbulence characteristics become important. Furthermore, the results of these high-fidelity simulations will enhance the interpretation of outcomes produced from a lower-fidelity CFD model.