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DOE OSTI2024

A large deformation multiphase continuum mechanics model for shock loading of soft porous materials

A large deformation, coupled finite-element (FE) model is developed to simulate the multiphase response of soft porous materials subjected to high strain-rate loading. The approach is based on the theory of porous media (TPM) at large deformations. Simplifications to the one-dimensional regime studied in the numerical simulations follow. An overview of several different time integration schemes is presented for the purpose of solving the nonlinear dynamic coupled balance of momenta (mixture and fluid) and balance of mass of the mixture equations. Numerical examples are presented for (i) verification against closed-form analytical solutions assuming small loads, (ii) demonstrating large deformation effects at high strain-rate, and (iii) showing differences in deformations between a single-phase elastodynamics model with occluded compressible pore fluid and a multiphase poroelastodynamics model at high strain-rate. The multiphase model shows that the relative motion of the pore fluid significantly dampens the deformation response of the solid skeleton as compared to the single-phase model, and makes it possible to extract quantitative values for the stresses of the different constituents, thereby allowing one to form preliminary conclusions about the onset of damage in the solid skeleton. The novelty of the current work is developing a multiphase, large deformation, mixture theory numerical model for high strain-rate loading of soft porous materials. It was discovered that explicit, adaptive time-stepping Runge–Kutta schemes offer high accuracy at relatively low cost when compared to traditional implicit or explicit central difference time-stepping schemes for shock-like loadings. Here, shock viscosity is added to the mixture momentum balance equation to regularize the shock front, and a stabilization term is added to the mixture mass balance equation to stabilize equal order interpolation finite elements for the coupled finite element solution of multiphase materials.

Engineering↗

DOE OSTI2024

Asymmetric oligomerization state and sequence patterning can tune multiphase condensate miscibility

Endogenous biomolecular condensates, composed of a multitude of proteins and RNAs, can organize into multiphasic structures with compositionally distinct phases. This multiphasic organization is generally understood to be critical for facilitating their proper biological function. However, the biophysical principles driving multiphase formation are not completely understood. Here we use in vivo condensate reconstitution experiments and coarse-grained molecular simulations to investigate how oligomerization and sequence interactions modulate multiphase organization in biomolecular condensates. We demonstrate that increasing the oligomerization state of an intrinsically disordered protein results in enhanced immiscibility and multiphase formation. Interestingly, we find that oligomerization tunes the miscibility of intrinsically disordered proteins in an asymmetric manner, with the effect being more pronounced when the intrinsically disordered protein, exhibiting stronger homotypic interactions, is oligomerized. Our findings suggest that oligomerization is a flexible biophysical mechanism that cells can exploit to tune the internal organization of biomolecular condensates and their associated biological functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Differentiable multiphase flow model for physics-informed machine learning in reservoir pressure management

Accurate subsurface reservoir pressure control is extremely challenging due to geological heterogeneity and multiphase fluid-flow dynamics. Predicting behavior in this setting relies on high-fidelity physics-based simulations that are computationally expensive. Yet, the uncertain, heterogeneous properties that control these flows make it necessary to perform many of these expensive simulations, which is often prohibitive. To address these challenges, we introduce a physics-informed machine learning workflow that couples a fully differentiable multiphase flow simulator, which is implemented in the DPFEHM framework with a convolutional neural network (CNN). The CNN learns to predict fluid extraction rates from heterogeneous permeability fields to enforce pressure limits at critical reservoir locations. By incorporating transient multiphase flow physics into the training process, our method enables more practical and accurate predictions for realistic injection-extraction scenarios compared to previous works. To speed up training, we pretrain the model on single-phase, steady-state simulations and then finetune it on full multiphase scenarios, which dramatically reduces the computational cost. We demonstrate that high-accuracy training can be achieved with fewer than three thousand full-physics multiphase flow simulations – compared to previous estimates requiring up to ten million. This drastic reduction in the number of simulations is achieved by leveraging transfer learning from much less expensive single phase simulations.

25 ENERGY STORAGE↗

DOE OSTI2020

Toward Water Volume Fraction Calculation in Multiphase Flows Using Electrical Capacitance Tomography Sensors

Real-time monitoring of water volume fraction in multiphase flows is an important problem for a number of industrial applications. The water phase in the multiphase flows may correspond to either the dispersed phase or the continuous phase. In the past, several lowcost and nonintrusive techniques based on the electrical capacitance tomography (ECT) has been developed to image and monitor in real-time multiphase flows containing water. Furthermore, such monitoring becomes increasingly challenging for high salinity levels, and no reliable ECTbased method is presently available which could work for obtaining water volume fraction in multiphase flows for all water salinity levels. In this paper, we propose a new approach based on the Hanai’s formula for complex dielectric constant and taking advantage of the Maxwell- Wagner-Sillars effect to obtain, to a good approximation, water volume fractions in multiphase flows containing water as either dispersed or continuous phase.

02 PETROLEUM↗

DOE OSTI2017

Development of a Multiphase Adjoint Capability in OpenFOAM

Thermal hydraulic predictions of flow regimes within nuclear reactor cores require significant computational resources and accuracy to ensure that the core design does not violate the thermal limits of materials. Multiphase computational fluid dynamics (CFD) has become a valuable computational capability for predicting flow characteristics as they relate to applications such as nuclear reactor safety and mixing phenomena around spacer grids within fuel assemblies. Multiphase CFD requires closure relationships for both the effects of turbulence as well as the transfer of mass, momentum, and energy between phases. Understanding the sensitivity of the parameters used in closure relationships is important for improving accuracy, but performing rigorous sensitivity analysis is computationally expensive. Adjoint mathematics have been utilized for reactor physics and fluid dynamics applications with respect to verification, sensitivity analysis, adaptive mesh refinement, and optimization. The usage of adjoint methods to predict the sensitivities of a variety of closure relationship parameters within a given problem has been shown to return sensitivity responses with significantly fewer computations than normal 'large-scale' methods. As the complexity of multiphase CFD methods increases, the demand for accurate verification tools and improvements in computational efficiency also increases, making the development of adjoint capabilities an attractive option. Closure relationships that describe interphase momentum physics in multiphase CFD modelling rely heavily on prescribed constants determined from experimental data. Due to the computational efficiency of an adjoint approach, the time to derive these closure relationships could be dramatically reduced, and data assimilation techniques could be used to return probability density functions of closure models derived using experimental data. This work develops a multiphase adjoint capability for the Eulerian-Eulerian two field, two phase equations. Specifically, the adjoint capability has been developed for the sub-cooled nucleate boiling solver boilEulerFoam developed by Dr. Nam Dinh of NC State University within the open-source CFD library OpenFOAM.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

NETL Crosscutting Research Video Series: Multiphase Flow (Short Version)

For over 30 years, NETL’s work in multiphase flow science has served as one of the cornerstones of the lab’s research portfolio. Multiphase flow refers to the simultaneous flow of gases, liquids and/or solid materials. The goal of the multiphase flow science team is to provide computational modeling tools to help offset the risk and cost of multiphase reactor development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

NETL Crosscutting Research Video Series: Multiphase Flow

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Multiscale modeling of microwave-heated multiphase systems

Modeling of microwave heating of multiphase systems requires resolving the electromagnetic field from the single particle to the entire cavity. We introduce a multiscale methodology for computationally affordable simulations of microwave heating of multiphase systems consisting of one phase dispersed in a continuum phase. The methodology homogenizes the original multiphase system, by taking advantage of the large separation of length scales, to calculate the effective permittivity, effective thermal conductivity, and volumetric power absorbed in each phase. The methodology is rigorously assessed against particle-resolved detailed numerical simulations of model systems. We demonstrate a significant reduction in computational cost while retaining the accuracy of detailed simulations. Lastly, the present methodology enables high throughput exploration of novel multiphase system designs utilizing microwave heating.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

A review of microwave-assisted process intensified multiphase reactors

Microwaves provide alternative heating and allow process intensification due to their rapid, volumetric, and selective nature. Recognizing the central role of multiphase reactors in chemical industry, a recent surge in employing microwaves is observed. We review the recent experimental and modeling investigations of microwave heating of multiphase reactors with emphasis on chemical engineering applications. Here we demonstrate that there is accumulated evidence for improved performance via microwave heating and a clear opportunity for further process intensification. In most of the cases, this improved performance stems from a temperature gradient between two phases. We discuss the ongoing debate on the mechanism by which microwaves affect chemical processes exacerbated by the inability of measuring the temperature distribution in a microwave cavity. We outline recent progress in this direction in monolith reactors and needs for future work. We underscore the lack of detailed modeling and simulation tools even for single-phase systems and emphasize the imperative for multiscale predictive modeling to bridge the experimental-modeling gap. Promising results are shown by a few recently published modeling studies that can predict the experimental measurements in complex multiphase reactors. A combination of experimental and modeling tools can provide a comprehensive picture of the microwave multiphase reactors as well as a means toward scale-up and optimization.

42 ENGINEERING↗

DOE OSTI2024

Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration

Geologic carbon sequestration (GCS) is a safety-critical technology that aims to reduce the amount of carbon dioxide in the atmosphere, which also places high demands on reliability. Multiphase flow in porous media is essential to understand CO 2 migration and pressure fields in the subsurface associated with GCS. However, numerical simulation for such problems in 4D is computationally challenging and expensive, due to the multiphysics and multiscale nature of the highly nonlinear governing partial differential equations (PDEs). It prevents us from considering multiple subsurface scenarios and conducting real-time optimization. Here, we develop a Fourier-enhanced multiple-input neural operator (Fourier-MIONet) to learn the solution operator of the problem of multiphase flow in porous media. Fourier-MIONet utilizes the recently developed framework of the multiple-input deep neural operators (MIONet) and incorporates the Fourier neural operator (FNO) in the network architecture. Once Fourier-MIONet is trained, it can predict the evolution of saturation and pressure of the multiphase flow under various reservoir conditions, such as permeability and porosity heterogeneity, anisotropy, injection configurations, and multiphase flow properties. Compared to the enhanced FNO (U-FNO), the proposed Fourier-MIONet has 90% fewer unknown parameters, and it can be trained in significantly less time (about 3.5 times faster) with much lower CPU memory (<15%) and GPU memory (<35%) requirements, to achieve similar prediction accuracy. In addition to the lower computational cost, Fourier-MIONet can be trained with only 6 snapshots of time to predict the PDE solutions for 30 years. Furthermore, we observed that Fourier-MIONet can maintain good accuracy when predicting out-of-distribution (OOD) data. The excellent generalizability of Fourier-MIONet is enabled by its adherence to the physical principle that the solution to a PDE is continuous over time. Furthermore, the developed Fourier-MIONet makes it possible to solve the long-time evolution of geological carbon sequestration in a large-scale three-dimensional space accurately and efficiently.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Transforming layered 2D mats into multiphasic 3D nanofiber scaffolds with tailored gradient features for tissue regeneration

Abstract Multiphasic scaffolds with tailored gradient features hold significant promise for tissue regeneration applications. Herein, this work reports the transformation of two‐dimensional (2D) layered fiber mats into three‐dimensional (3D) multiphasic scaffolds using a ‘solids‐of‐revolution’ inspired gas‐foaming expansion technology. These scaffolds feature precise control over fiber alignment, pore size, and regional structure. Manipulating nanofiber mat layers and Pluronic F127 concentrations allows further customization of pore size and fiber alignment within different scaffold regions. The cellular response to multiphasic scaffolds demonstrates that the number of cells migrated and proliferated onto the scaffolds is mainly dependent on the pore size rather than fiber alignment. In vivo subcutaneous implantation of multiphasic scaffolds to rats reveals substantial cell infiltration, neo tissue formation, collagen deposition, and new vessel formation within scaffolds, greatly surpassing the capabilities of traditional nanofiber mats. Histological examination indicates the importance of optimizing pore size and fiber alignment for the promotion of cell infiltration and tissue regeneration. Overall, these scaffolds have potential applications in tissue modeling, studying tissue‐tissue interactions, interface tissue engineering, and high‐throughput screening for optimized tissue regeneration.

Shahriar, S. M. Shatil↗

DOE OSTI2019

Liver metastases of neuroendocrine tumors: is it possible to diagnose different histologic subtypes depending on multiphasic CT features?

Purpose: To assess and compare the multiphasic computed tomography (CT) features of neuroendocrine tumor (NET) liver metastases and to investigate the possibility to predict the histologic subtype of the primary tumor. Materials and methods: Between January 2013 and December 2017 patients with biopsy proven NET with at least one liver metastasis who underwent multiphasic CT were enrolled in this study. All cases were acquired using a standardized multiphasic liver CT protocol, arterial, portal, and hepatic venous phases were obtained. Images were retrospectively analyzed in consensus by two abdominal radiologists blinded to clinical data and histologic subtype. The size, number, and location of lesions were noted. Enhancement patterns of each lesion on arterial, portal, and hepatic venous phases were assessed. For quantitative analysis, CT attenuation of tumors, liver parenchyma, and aorta were measured using a circular region of interest (ROI) on arterial, portal, and hepatic venous phases for reflecting the blood supply of the tumor. Tumor-to-aorta and tumor-to-liver ratio were calculated in all three phases. Differences between subtypes of NET liver metastases were studied using ROC analysis of clustered data. Results: A total of 255 neuroendocrine tumor liver metastases divided into 101 (39.6%) pancreatic, 60 (23.5%) gastroenteric and 94 (36.8%) lung NET liver metastases were analyzed. Contrast enhancement of lesions was homogeneous in 78% of patients (n = 199), which was significantly more frequent in patients with pancreatic group than in those with gastroenteric origin (n = 90, 89.1% vs. n = 28, 46.7%; p < 0.001). Gastroenteric NET metastases frequently showed heterogeneous enhancement, which was significantly higher than in the other two groups (50% vs. 3% and 2%). With respect to the location of the primary tumor, the difference in enhancement patterns of the liver lesions was statistically significant (p < 0.001). Pancreatic NET metastases were mostly hyperdense on arterial images and isodense on portal and hepatic venous phase images (79.2%, n = 80). Gastroenteric NET metastases were mostly hyperdense on arterial phase images and hypodense on portal and hepatic venous phase images (n = 28, 46.7%). The most frequent pattern for lung NET metastases was hypoattenuation on all three phase images (n = 44, 46.8%). ROC analysis of clustered data revealed statistically significant differences between pancreatic NET liver metastases, gastroenteric NET liver metastases, and lung NET liver metastases in terms of tumor-to-aorta (T–A) ratio and tumor-to-liver (T–L) ratio (p < 0.001). Conclusion: We observed statistically significant differences in multiphasic CT features (enhancement pattern, T–A ratio, and T–L ratio) between histologic subtypes of NET liver metastases. As the difference in histological subtypes of NET liver metastases results in a different prognosis and different management strategy, these CT features might help to identify the primary tumor when it is not known to ensure accurate tumor staging and to provide optimal treatment.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2021

Preparation and characterization of multiphase ceramic designer waste forms

Abstract The long-term performance, or resistance to elemental release, is the defining characteristic of a nuclear waste form. In the case of multiphase ceramic waste forms, correlating the long-term performance of multiphase ceramic waste forms in the environment to accelerated chemical durability testing in the laboratory is non-trivial owing to their complex microstructures. The fabrication method, which in turn affects the microstructure, is further compounding when comparing multiphase ceramic waste forms. In this work, we propose a “designer waste form” prepared via spark plasma sintering to limit interaction between phases and grain growth during consolidation, leading to monolithic high-density waste forms, which can be used as reference materials for comparing the chemical durability of multiphase waste forms. Designer waste forms containing varying amounts of hollandite in the presence of zirconolite and pyrochlore in a fixed ratio were synthesized. The product consistency test (PCT) and vapor hydration test (VHT) were used to assess the leaching behavior. Samples were unaffected by the VHT after 1500 h. As measured by the PCT, the fractional Cs release decreased as the amount of hollandite increased. Elemental release from the zirconolite and pyrochlore phases did not appear to significantly contribute to the elemental release from the hollandite phase in the designer waste forms.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Hydrodynamical Coupling of Mass and Momentum in Multiphase Galactic Winds

Using a set of high-resolution hydrodynamical simulations run with the Cholla code, we investigate how mass and momentum couple to the multiphase components of galactic winds. The simulations model the interaction between a hot wind driven by supernova explosions and a cooler, denser cloud of interstellar or circumgalactic media. By resolving scales of ${\rm{\Delta }}x\lt 0.1$ pc over $\gt 100$ pc distances, our calculations capture how the cloud disruption leads to a distribution of densities and temperatures in the resulting multiphase outflow and quantify the mass and momentum associated with each phase. We find that the multiphase wind contains comparable mass and momenta in phases over a wide range of densities and temperatures extending from the hot wind ($n\approx {10}^{-2.5}$ ${\mathrm{cm}}^{-3}$, $T\approx {10}^{6.5}$ K) to the coldest components ($n\approx {10}^{2}$ ${\mathrm{cm}}^{-3}$, $T\approx {10}^{2}$ K). We further find that the momentum distributes roughly in proportion to the mass in each phase, and the mass loading of the hot phase by the destruction of cold, dense material is an efficient process. These results provide new insight into the physical origin of observed multiphase galactic outflows and inform galaxy formation models that include coarser treatments of galactic winds. Our results confirm that cool gas observed in outflows at large distances from the galaxy ($\gtrsim 1$ kpc) likely does not originate through the entrainment of cold material near the central starburst.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Synthesis of multiphase self-healing polymers from commodity monomers

A self-healing polymer material that includes a multiphase copolymer, and a method of making the copolymer, are provided. The multiphase copolymer includes one or more hydrogen bond-forming copolymer segments, each segment including a polymerized acrylamide monomer and a polymerized acrylic monomer. The polymerized acrylamide monomer includes functional groups that form hydrogen bonds in the multiphase copolymer, and is present in the one or more copolymer segments in an amount sufficient for self-healing of the multiphase copolymer.

Guan, Zhibin↗

DOE OSTI2022

In situ feature analysis for large-scale multiphase flow simulations

The study of multiphase flow is essential for designing chemical reactors such as fluidized bed reactors (FBR), as a detailed understanding of hydrodynamics is critical for optimizing reactor performance and stability. An FBR allows scientists to conduct different types of chemical reactions involving multiphase materials, especially interaction between gas and solids. During such complex chemical processes, the formation of void regions in the reactor, generally termed as bubbles, is an important phenomenon. The study of these bubbles has a deep implication in predicting the reactor’s overall efficiency. But physical experiments needed to understand bubble dynamics are costly and non-trivial due to the technical difficulties involved and harsh working conditions of the reactors. Therefore, to study such chemical processes and bubble dynamics, a state-of-the-art computational simulation MFIX-Exa is being developed. Despite the proven accuracy of MFIX-Exa in modeling bubbling phenomena, the large-scale output data prohibits the use of traditional post hoc analysis capabilities in both storage and I/O time. Herein, to address these issues and allow the application scientists to explore the bubble dynamics in an efficient and timely manner, we have developed an end-to-end analytics pipeline that enables in situ detection of bubbles, followed by a flexible post hoc visual exploration methodology of bubble dynamics. The proposed method enables interactive analysis of bubbles, along with quantification of several bubble characteristics, enabling experts to understand the bubble interactions in detail. Positive feedback from the experts has indicated the efficacy of the proposed approach for exploring bubble dynamics in very-large-scale multiphase flow simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Pore scale study of multiphase multicomponent reactive transport during CO 2 dissolution trapping

Solubility trapping is crucial for permanent CO 2 sequestration in deep saline aquifers. For the first time, a pore-scale numerical method is developed to investigate coupled scCO 2 -water two-phase flow, multicomponent (CO 2 (aq), H + , HCO 3 – , CO 3 2 – and OH – ) mass transport, heterogeneous interfacial dissolution reaction, and homogeneous dissociation reactions. Pore-scale details of evolutions of multiphase distributions and concentration fields are presented and discussed. Time evolutions of several variables including averaged CO 2 (aq) concentration, scCO 2 saturation, and pH value are analyzed. Specific interfacial length, an important variable which cannot be determined but is required by continuum models, is investigated in detail. Mass transport coefficient or efficient dissolution rate is also evaluated. The pore-scale results show strong non-equilibrium characteristics during solubility trapping due to non-uniform distributions of multiphase as well as slow mass transport process. Complicated coupling mechanisms between multiphase flow, mass transport and chemical reactions are also revealed. Lastly, effects of wettability are also studied. The pore-scale studies provide deep understanding of non-linear non-equilibrium multiple physicochemical processes during CO 2 solubility trapping processes, and also allow to quantitatively predict some important empirical relationships, such as saturation-interfacial surface area, for continuum models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

An immersed boundary method for fluid–structure interaction with compressible multiphase flows

This paper presents a two-dimensional immersed boundary method for fluid–structure interaction with compressible multiphase flows involving large structure deformations. This method involves three important parts: flow solver, structure solver and fluid–structure interaction coupling. In the flow solver, the compressible multiphase Navier–Stokes equations for ideal gases are solved by a finite difference method based on a staggered Cartesian mesh, where a fifth-order accuracy Weighted Essentially Non-Oscillation (WENO) scheme is used to handle spatial discretization of the convective term, a fourth-order central difference scheme is employed to discretize the viscous term, the third-order TVD Runge–Kutta scheme is used to discretize the temporal term, and the level-set method is adopted to capture the multi-material interface. In this work, the structure considered is a geometrically non-linear beam which is solved by using a finite element method based on the absolute nodal coordinate formulation (ANCF). The fluid dynamics and the structure motion are coupled in a partitioned iterative manner with a feedback penalty immersed boundary method where the flow dynamics is defined on a fixed Lagrangian grid and the structure dynamics is described on a global coordinate. We perform several validation cases (including fluid over a cylinder, structure dynamics, flow induced vibration of a flexible plate, deformation of a flexible panel induced by shock waves in a shock tube, an inclined flexible plate in a hypersonic flow, and shock-induced collapse of a cylindrical helium cavity in the air), and compare the results with experimental and other numerical data. The present results agree well with the published data and the current experiment. Finally, we further demonstrate the versatility of the present method by applying it to a flexible plate interacting with multiphase flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗