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CONDENSATION-EVAPORATION MODELING OF DRIFT FROM A MECHANICAL COOLING TOWER
Numerical studyfor investigatingthe phase change behavior of a drift from a mechanical draft cooling tower is presented. A k-ε turbulence model, discrete phase model, species transport equations, and a heat-mass exchange model are solved simultaneouslyto capture the heat and mass transfer effects of a drift condensing and evaporatingeffects. The simulation result is compared to an available real scale test data and its limitation is also discussed. A parametric study is carried out by varying the ambient dry bulb temperature, ambient relative humidity, wind speed, liquid droplet diameter, and the drift amount. It is found that by combining the evaporation and condensation models, a drift phase change phenomena is accurately depicted. A parametric study reveals that wind speed impact is affected by the ambient temperature and the number of liquid droplets and their size play a critical role in the phase change phen
Development and Validation of Dense Discrete Phase Flow Models for Concentrating Solar Power Particle Receivers
This report summarizes a recent project aimed at developing and validating the necessary tools to enable more accurate modeling of denser and more complex particle flows in next-generation particle receivers used in concentrating solar power towers. A newly developed CFD/DEM simulation capability was created by coupling existing the modeling and simulation tools Sierra and LAMMPS. This new capability permitted the inclusion of additional physics for particle drag and particle collisions to model
Numerical study on aerosol sampling in a nuclear facility duct with a 90-degree elbow
Due to the challenging design requirements, elbows are often unavoidable in duct configuration, and these 90-degree bends introduce swirl, velocity variations, recirculation, and secondary flow. These disturbances make it difficult for nuclear facilities to meet particle sampling standards. A series of numerical analyses are conducted to track aerosols in a nuclear facility duct having a 90-degree elbow with the assistance of computational fluid dynamics (CFD). A turbulence model, a continuity, and a momentum, a discrete phase model, and species transport equations are solved simultaneously to track aerosols in the duct. The effect of turbulence models, turbulent dispersion models, droplet drag model, aerosol amount, aerosol spray configuration, guide vanes, and mixers are investigated. Simulation results are analyzed per relevant testing codes such as DOE-HDBK-1169, ASME AG1, ISO 14644-3, ACGIH, and ANSI/HPS N13.1.
An end-to-end deep learning method for solving nonlocal Allen–Cahn and Cahn–Hilliard phase-field models
Here, we propose an efficient end-to-end deep learning method for solving nonlocal Allen–Cahn (AC) and Cahn–Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential equation-based AC or CH phase-field models result in diffuse interfaces between phases, with the only recourse for remediation is to severely refine the spatial grids in the vicinity of the true moving sharp interface whose width is determined by a grid-independent parameter that is substantially larger than the local grid size. In this work, we introduce non-mass conserving nonlocal AC or CH phase-field models with regular, logarithmic, or obstacle double-well potentials. Because of non-locality, some of these models feature totally sharp interfaces separating phases. The discretization of such models can lead to a transition between phases whose width is only a single grid cell wide. Another motivation is to use deep learning approaches to ameliorate the otherwise high cost of solving discretized nonlocal phase-field models. To this end, loss functions of the customized neural networks are defined using the residual of the fully discrete approximations of the AC or CH models, which results from applying a Fourier collocation method and a temporal semi-implicit approximation. To address the long-range interactions in the models, we tailor the architecture of the neural network by incorporating a nonlocal kernel as an input channel to the neural network model. We then provide the results of extensive computational experiments to illustrate the accuracy, predictive capabilities, and cost reductions of the proposed method.
Computational model development and validation of fuel dispersal phenomena
As the US nuclear industry is renewing efforts to extend the rod average burnup limits in existing pressurized water reactors, it becomes imperative to investigate the safety implications associated with high burnup fuel fragmentation and the potential dispersal of fragmented fuel into the reactor coolant system. Additionally, as there is a growing interest in transitioning to new nuclear fuel designs to accommodate higher fuel burnup levels, it becomes essential to conduct studies on fuel behavior during design basis accident scenarios, particularly during a postulated loss-of-coolant accident, in order to ensure the safe operation of light-water reactors. The present study develops a computational model to simulate the complex three-phase flow of the fuel dispersal phenomena that occur following a breach in the cladding, when the stream of solid fuel particles and carrier fission gas stream may interact with the surrounding liquid medium. Furthermore, the proposed framework considers the solid phase as discrete Lagrangian particles while the interpenetrating gas–liquid continuum is modeled using a Eulerian framework. The developed simulation framework is validated with experimental results performed in a separate-effect test facility by comparing predicted particle settlement locations with the experimental observations reported in the literature. Key highlights of this study include the interpretation of the high-pressure boundary conditions and the three-phase flow coupling strategy. Also discussed are the gas–liquid hydrodynamics and the behavior of particles as they are transported through the gas and liquid phases.
CFD unified approach under Eulerian–Lagrangian framework for methanol and gasoline direct injection sprays in evaporative and flash boiling conditions
Innovative synthetic fuels for advanced propulsion systems, such as methanol and ammonia, and synthetic blended fuels (E00, E10, and E30), known for their high volatility, are often injected directly into combustion chambers. It follows that Eulerian–Lagrangian spray models need to accurately capture the spray collapse as a consequence of flash boiling onset and be capable of proficiently handling the preferential evaporation of multi-component fuels in evaporative scenarios. So, we performed the assessment of an Eulerian–Lagrangian CFD code for simulating methanol and E00 gasoline blend sprays in both early and late injection conditions involving flash boiling conditions and preferential evaporation. The adoption of an effervescent breakup model and of a non-equilibrium phase transition model for the discrete phase allows the adoption of a setup that is almost completely free from specific constant tuning, especially for what concerns the breakup model. We validated the simulations using experimental PLV maps of methanol and E00 sprays issued from the ECN Spray M injector. The results highlight a significantly different morphology of the methanol spray compared to the E00 one under late injection conditions. Under stratified combustion, low-volatile fuels are likely to be ignited first, and the flame propagates toward the high-volatile fuels. In conclusion, the spray collapse was also correctly reproduced, inducing the presence of a low-pressure zone and modifying the spray morphology.
Membrane Degradation in PEM Fuel Cells: Part I. Modeling Gas Crossover and the Pt Band
Understanding chemical degradation of the proton-exchange membrane in fuel cells is crucial for extending their lifetimes. Herein, various degradation reactions reported in literature are organized and analyzed, including direct radical generation and an indirect (Fenton) pathway. To understand the transport of dissolved H 2 and O 2 crossover gases as they relate to membrane degradation, an agglomerate-scale model is introduced, treating gas, ionomer, and catalyst as discrete phases. The model reveals a key phenomenon: at working potentials, dissolved gases are mostly consumed at the interface between the catalyst layer and the membrane, leaving little gas to cross the membrane. Under open-circuit conditions, dissolved gases are not consumed and can then cross the membrane. This explains high H 2 O 2 concentrations and degradation rates seen in experiments but not captured in previous models. Following mixed-potential theory, crossover gases supply the hydrogen-oxidation and oxygen-reduction reactions, which occur simultaneously on individual Pt particles comprising the Pt band in the membrane, forming reactive species (H 2 O 2 , OH·). Results show crossover gas almost entirely reacts on the Pt band, allowing little to reach the opposite electrode. Furthermore, the micro-scale geometry of the catalyst-layer/membrane interface impacts the gas crossover at working potentials, indicating that cell construction affects membrane durability.
Assessing Critical Conditions for Scour Near Obstructions using Bed Shear, Particle Onset of Motion Balances, and CFD-DEM Modeling of Granular Beds
Computational Fluid Dynamics combined with a Discrete Element Method is one of the computational methods that can be used to model multiphase flows. In this method various phases, gas and liquid or solid, are present in the same computational domain. The local averaged Navier–Stokes equations determine the flow of the continuous phase fluid and are solved using the traditional CFD finite volume approach. DEM is based on a Lagrangian formulation, which solves the equations of motion, expressed in ordinary differential equations, for representative particles as they move in space and time. The interactions between the continuous fluid phase and discrete solid phase are modeled with the use of Newton’s laws of motion via drag force. The particles interact with each other and with the boundaries of the fluid continuum, and the resulting contact forces are included in the equations of motion. The properties of solid particles and boundaries are treated as elastic bodies, with specified density, elastic modulus, and Poisson’s ratio. Particle shapes may vary from single spherical particles to more complex-shaped composite particles. The particles may be introduced into the domain by random or structured injection at a point, surface, or volume, depending on the application. More details on the formulation can be found in the Simcenter STAR-CCM+ User’s Manual and OpenFOAM website.
Natural fracture mapping and discrete fracture network modeling of Wolfcamp formation in hydraulic fracturing test site phase 1 area, Midland Basin: Fractures from 3D seismic data, image log, and core
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Assessment of model parameters in MFiX particle-in-cell approach
The limitations in numerical treatment of solids-phase in conventional methods like Discrete Element Model and Two-Fluid Model have facilitated the development of alternative techniques such as Particle-In-Cell (PIC). However, a number of parameters are involved in PIC due to its empiricism. In this work, global sensitivity analysis of PIC model parameters is performed under three distinct operating regimes common in chemical engineering applications, viz. settling bed, bubbling fluidized bed and circulating fluidized bed. Simulations were performed using the PIC method in Multiphase Flow with Interphase eXchanges (MFiX) developed by National Energy Technology Laboratory (NETL). A non-intrusive uncertainty quantification (UQ) based approach is applied using Nodeworks to first construct an adequate surrogate model and then identify the most influential parameters in each case. This knowledge will aid in developing an effective design of experiments and determine optimal parameters through techniques such as deterministic or statistical calibration.
Mesoscale Modeling of the Effects of Accelerated Burnup on UO2 Microstructural Evolution
Accelerating the nuclear fuel qualification process will rely on some combination of advanced modeling and simulation techniques with accelerated irradiation testing and separate effects experiments to enable the development of new fuel concepts in a shorter time frame. One of the key challenges to successfully leveraging accelerated irradiation tests will be understanding the artifacts that may be introduced with accelerated accumulation of dose and/or burnup. This work presents phase field (MARMOT) simulations of the evolution of representative 2D UO2 microstructures up to 40 MWd/kgU. Simulations were performed under both commercial light water reactor fuel conditions as well as those that would be expected for highly accelerated (~10x) burnup conditions similar to those used in the MiniFuel irradiations in Oak Ridge National Laboratory’s High Flux Isotope Reactor. The phase field model was coupled with a discrete nucleation algorithm to model re- structuring at high burnup. The effect of the different fission rates in both microstructures was investigated at two temperatures: 650?C and 800?C. The lower temperature simulations both showed an onset of restructuring at nearly 60 MWd/kgU. More extensive restructuring was obtained in the MiniFuel microstructure compared with that of the PWR fuel. At 800?C, no restructuring was obtained as a result of the thermally activated diffusion of Xe atoms and U vacancies to fission gas bubbles, which reduces the nucleation driving force. These results highlight the importance of using modeling and simulation tools to inform the environmental conditions during targeted accelerated irradiation tests to extract the most useful fuel performance data.
A phase-field model for void and gas bubble superlattice formation in irradiated solids
A phase-field model to simulate the formation of both void and gas bubble superlattices is derived from a grand potential functional, assuming 1D diffusion of self-interstitial atoms. The model is capable of accounting for superlattice formation by either a nucleation and growth or spinodal decomposition mechanism; in this work, we focus on the nucleation and growth mechanism, using a discrete nucleation approach in the phase-field model. In simulations of void formation, short aligned rows of voids were initially formed, followed by growth in the size of the aligned rows, and finally leading to superlattice formation, consistent with experimental observations. Void superlattice spacing as a function of model parameters was quantified. Increased nucleation rates led to smaller superlattice spacing, while increased vacancy diffusivity led to larger superlattice spacing. In simulations of gas bubble superlattice formation, superlattice spacing decreased with increasing gas atom flux, consistent with experimental observations. Here, simulations with increasing ratio of gas atom flux to vacancy-interstitial pair production led to increased superlattice spacing, which is inconsistent with experimental observations at high gas atom flux rates; this discrepancy is attributed to the fact that the model does not account for bound gas atom-vacancy pairs that may dominate at high gas flux rates.
Modeling Dense Particle Flow in Multistage and Obstructed Flow Receivers Using High Fidelity Simulations
Particles are a leading contender for next-generation, concentrating solar power technologies, and the design of the particle receiver is critical to minimize the levelized cost of electricity. Falling particle receivers (FPRs) are a viable receiver concept, but many new designs feature complex particle obstructions that include dense discrete phase flows. This creates additional challenges for modeling as particle-to-particle interactions (i.e., collisions) and particle drag become more complex. To improve upon existing modeling strategies, a CFD-DEM simulation capability was created by coupling two independent codes: Sierra/Fuego and LAMMPS. A suitable receiver model was then defined using a traditional continuum-based model for the air and a granular model for the particle curtain. A sensitivity study was executed using this model to determine the relevance of different granular model inputs on important quantities of interest in obstructed flow FPRs: the particle velocity and curtain opacity. The study showed that the granular model inputs had little effect on the particle velocity magnitude and curtain opacity after an obstruction.
Efficient Reformulation of Linear and Nonlinear Solid-Phase Diffusion in Lithium-ion Battery Models using Symmetric Polynomials: Mass Conservation and Computational Efficiency
Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms, along with suitable discretization or approximations for the solid-phase diffusion equation. The solid-phase diffusion equation represents the main computational burden for typical pseudo-2-dimensional (p2D) models since these equations in the pseudo r -dimension must be solved at each point in the computational grid. This substantially increases the complexity of the model as well as the computational time. Traditional approaches towards simplifying solid-phase diffusion possess certain significant limitations, especially in modeling emerging electrode materials which involve phase changes and variable diffusivities. A computationally efficient representation for solid-phase diffusion is discussed in this paper based on symmetric polynomials using Orthogonal Collocation and Galerkin formulation (weak form). A systematic approach is provided to increase the accuracy of the approximation (p form in finite element methods) to enable efficient simulation with a minimal number of semi-discretized equations, ensuring mass conservation even for non-linear diffusion problems involving variable diffusivities. These methods are then demonstrated by incorporation into the full p2D model, illustrating their advantages in simulating high C-rates and short-time dynamic operation of Lithium-ion batteries.
Theoretical Review of the MFIX Fluid and Two-Fluid Models
MFIX (Multiphase Flow with Interphase eXchanges) is a general purpose code that can be used for describing the hydrodynamics, chemical reactions, and heat transfer of dense or dilute multiphase fluid flows. MFIX calculations give detailed information on pressure, temperature, composition, and velocity distributions in the defined system. This report provides an overview of MFIX’s expressions for single phase flow and continuous dispersed multiphase flow (i.e., the two-fluid model). In addition to the two fluid model (MFIX-TFM), MFIX contains a discrete element model (MFIX-DEM) and a multi-phase particle in cell model (MFIX-PIC) that are not reviewed within this document.
A consistent and conservative Phase-Field method for multiphase incompressible flows
In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.
On High-Order/Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model
In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar–Gross–Krook (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. Furthermore, the accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.