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DOE OSTI2025

A Finite Element Method for Compressible and Turbulent Multiphase Flow Instabilities with Heat Transfer

We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Ensemble average and nearest particle statistics in disperse multiphase flows

A relation between the ensemble average and the nearest particle statistics is derived. The relation accounts for interactions among all the particles, not only the nearest one, and can be used to study long-range particle interactions without the difficulty of a divergent integral. As an example, this relation is applied to calculate the particle sedimentation velocity to the first order of the particle volume fraction. Using the relation, an important particle–fluid–particle stress is introduced for general multiphase flows.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Data-Driven Model Reduction of Multiphase Flow in a Single-Hole Automotive Injector

Fuel injector design has a substantial influence on the performance and emissions of direct injection engines. To date, large eddy simulations coupled with a single-fluidmixture modeling approach have shown great success in evaluating the complex interplay among injector design, fuel properties, and operating conditions on the injector performance. However, this simulation approach is too computationally expensive to be used by industry routinely for injector design due to the fine temporal and spatial resolution required to resolve wall-bounded flow within the injector. The work presented in this paper highlights a potential pathway to addressing this issue. To study the influence of injector design, fuel properties, and operating conditions on injector performance, large eddy simulations were performed to model the turbulent multiphase flow development through a side-oriented singlehole diesel injector. Using Latin hypercube sampling, the design space spanning a range of fuel properties, operating conditions, and needle lifts were explored. Two techniques for dimensionality reduction, namely proper orthogonal decomposition and autoencoders, were compared to evaluate their accuracy in representing the flow in a reduced dimensional space. Finally, based on the findings from this work, recommendations are provided in using machine learning approaches within the context of emulation to construct reduced-ordermodels for internal flow development relevant to automotive applications.

42 ENGINEERING↗

DOE OSTI2022

A physics-constrained neural network for multiphase flows

The present study develops a physics-constrained neural network (PCNN) to predict sequential patterns and motions of multiphase flows (MPFs), which includes strong interactions among various fluid phases. To predict the order parameters, which locate individual phases in the future time, a neural network (NN) is applied to quickly infer the dynamics of the phases by encoding observations. The multiphase consistent and conservative boundedness mapping algorithm (MCBOM) is next implemented to correct the predicted order parameters. This enforces the predicted order parameters to strictly satisfy the mass conservation, the summation of the volume fractions of the phases to be unity, the consistency of reduction, and the boundedness of the order parameters. Then, the density of the fluid mixture is updated from the corrected order parameters. Finally, the velocity in the future time is predicted by another NN with the same network structure, but the conservation of momentum is included in the loss function to shrink the parameter space. The proposed PCNN for MPFs sequentially performs (NN)-(MCBOM)-(NN), which avoids nonphysical behaviors of the order parameters, accelerates the convergence, and requires fewer data to make predictions. Numerical experiments demonstrate that the proposed PCNN is capable of predicting MPFs effectively.

Mechanics↗

DOE OSTI2021

Data supporting the article titled "Heterogeneous Multiphase Flow Properties of Volcanic Rocks and Implications for Noble Gas Transport from Underground Nuclear Explosions"

The submission is a Reproducible Research (RR) data archive that contains the supporting multiphase fluid flow and curve fitting results of the Vadose Zone Journal article titled: "Heterogeneous Multiphase Flow Properties of Volcanic Rocks and Implications for Noble Gas Transport from Underground Nuclear Explosions." The article's DOI number is the following: https://doi.org/10.1002/vzj2.20123. Please see the "Methods and Materials" section of the journal article and the ReadMe.txt in the RR_ARCHIVE folder for further details. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND Number: SAND2021-3407 O.

mercury injection capillary pressure↗

DOE OSTI2021

A new coupled multiphase flow–finite strain deformation–fault slip framework for induced seismicity

Production of hydrocarbons and water from subsurface reservoirs are known to cause permanent deformation of the reservoir and seismicity along faults both of which are detrimental to sustainable development of natural resources. Most of the prior studies on understanding fluid flow-induced plasticity and seismicity have focused on one or the other phenomenon due to the numerical difficulty associated with simultaneous modeling of the two failure phenomena because stress and deformation evolve non-linearly in both plasticity and seismicity. However, in reservoirs undergoing long-term production, plastic failure can alter the stress paths of points on a fault such that the onset, location, and magnitude of actual seismic events can no longer be predicted by a poroelastic simulation due to inaccurate stress and deformation history. We present a computational framework for coupled multiphase flow, finite strain poroplastic deformation, and dynamic fault slip and use it to understand the impact of plastic deformation on the onset, location, and magnitude of induced fault slip events. We evaluate the impact of plasticity on reservoir pressure, deformation, induced stress, and fault slip by comparing infinitesimal strain elastic and finite strain poro-elastoplastic models. For real-world applications, we consider different scenarios where the reservoir is either mechanically weaker or stronger than the caprock. We analyze the stress evolution as a function of the change in reservoir pressure to understand the role of contrast in reservoir and caprock elastic moduli on geomechanical stability. The results show that the poroplastic reservoir exhibits larger vertical deformation and delayed slip than the poroelastic reservoir after the same amount of oil production. For the same amount of pressure drop, a reservoir with a smaller modulus than the caprock displays a larger vertical displacement and an earlier onset of both plastic failure and fault slip. For a reservoir with a larger modulus than the caprock, vertical displacement is larger on the reservoir top boundary and smaller on the ground surface, and a higher pressure drop is needed to induce plastic failure and fault slip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Multiscale Experiments and Multiphysics Simulation of Multiphase Flow for Transportable Small Modular Reactors

A new type of safe, small, transportable nuclear reactor would address the intense and ever-growing global demand for energy produced via a resilient, carbon-free energy source. In this regard, transportable small modular reactors (SMRs) are being designed and developed for electricity generation within small/micro-grid/off-grid isolated systems, as well as for heat generation in industrial/residential applications. These reactors feature the capability to be fully factory fabricated and then directly transported to utilities’ sites as “plug-and-play” systems. Research and development (R&D) programs are underway at Idaho National Laboratory (INL) to successfully design, develop, and demonstrate such safe-by-design mobile reactor technologies, in collaboration with partner organizations. Multiscale experimental facilities and multiphysics simulation tools are required for reactor design verification and validation (V&V), and licensing. These advanced reactors are intended to feature passive safety systems such as passive containment cooling systems (PCCS), which consist of multiphase flows and multispecies distributions. This seminar talk will focus on designing and analyzing transportable SMR PCCS by using multiscale experiments and multiphysics computational fluid dynamics (CFD) simulations to support reactor licensing and safety. The corresponding research challenges are addressed via supportive verification and validation results generated by the models and simulation tools in combination with selective parametric and uncertainty analysis. This solution approach could blaze the trail for commercial adoption of such technologies. The facilities, simulation capabilities, and research opportunities available at INL in regard to such reactors and the integrated energy systems with which they go hand in hand are also discussed briefly, and may spark interest in deeper research as well as new collaborative projects.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

OpenACC offloading of the MFC compressible multiphase flow solver on AMD and NVIDIA GPUs

GPUs are the heart of the latest generations of supercomputers. We efficiently accelerate a compressible multiphase flow solver via OpenACC on NVIDIA and AMD Instinct GPUs. Optimization is accomplished by specifying the directive clauses gang vector and collapse. Further speedups of six and ten times are achieved by packing user-defined types into coalesced multidimensional arrays and manual inlining via metaprogramming. Additional optimizations yield seven-times speedup of array packing and thirty-times speedup of select kernels on Frontier. Weak scaling efficiencies of 97% and 95% are observed when scaling to 50% of Summit and 87% of Frontier. Strong scaling efficiencies of 84% and 81% are observed when increasing the device count by a factor of 8 and 16 on V100 and MI250X hardware. The strong scaling efficiency of AMD’s MI250X increases to 92% when increasing the device count by a factor of 16 when GPU-aware MPI is used for communication.

Wilfong, Benjamin↗

NASA NTRS1988

The application of single particle hydrodynamics in continuum models of multiphase flow

A review of the application of single particle hydrodynamics in models for the exchange of interphase momentum in continuum models of multiphase flow is presented. Considered are the equations of motion for a laminar, mechanical two phase flow. Inherent to this theory is a model for the interphase exchange of momentum due to drag between the dispersed particulate and continuous fluid phases. In addition, applications of two phase flow theory to de-mixing flows require the modeling of interphase momentum exchange due to lift forces. The applications of single particle analysis in deriving models for drag and lift are examined.

Decker, Rand↗

DOE OSTI2020

Multiphase flow and granular mechanics

In this perspective we provide a brief overview of the state of knowledge and recent progress in the area of multiphase flow through deformable granular media. We show, with many examples, that the interplay between viscous, capillary, and frictional forces at the pore scale determines the mode of fluid invasion. We pay particular attention to the central role of wettability on the morphology of granular-pack deformation and failure. Beyond their intrinsic interest as processes that give rise to spectacular pattern formation, these coupled phenomena in granular media can control continental-scale fluxes like methane venting from the seafloor and geohazards like earthquakes and landslides. Finally, we conclude this perspective by pointing to fundamental knowledge gaps and exciting avenues of research.

42 ENGINEERING↗

DOE OSTI2021

Polysiloxane coatings on microspheres based on Multiphase Flow with Interface Exchange-Discrete Element Modelling

Polysiloxane coatings on yttria stabilized zirconia (YSZ) microspheres of 500 μm were simulated in a spout fluidized bed coater using Multiphase Flow with Interface Exchange-Discrete Element Modelling (MFiX-DEM). In this work, two different coater configurations were developed to study the influence of gas velocity and its distribution on particle dynamics. The presence of the Wurster tube not only enhances the distribution but also increases the overall residence time of the particles. Investigations were also carried out with different Wurster tube positions (normal, 10% and 20% lowered from its initial position). Among these, 20% lowered Wurster tube position demonstrated the most effective coating process. The effects of gas inlet pressure on the average gas velocity and the distribution of particles were analyzed. More than 97% of the particles can be retained. The derived results, including average gas velocity, particle retention percentage, and distribution of particles with gas velocity, are being used to guide the experimental work in obtaining defect-free coatings for YSZ microspheres.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Wettability control on multiphase flow in patterned microfluidics

Significance The simultaneous flow of multiple fluid phases through a porous solid occurs in many natural and industrial processes—for example, rainwater infiltrates into soil by displacing air, and carbon dioxide is stored in deep saline aquifers by displacing brine. It has been known for decades that wetting—the affinity of the solid to one of the fluids—can have a strong impact on the flow, but the microscale physics and macroscopic consequences remain poorly understood. Here, we study this in detail by systematically varying the wetting properties of a microfluidic porous medium. Our high-resolution images reveal the fundamental control of wetting on multiphase flow, elucidate the inherently 3D pore-scale mechanisms, and help explain the striking macroscopic displacement patterns that emerge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Mimicking Geologic Depositional Fabrics for Multiphase Flow Experiments

A novel laboratory technique is presented for generating two-dimensional beadpacks with reproducible natural geologic sedimentary bedforms. The heterogeneous beadpacks are deposited in a 0.6 m × 0.6 m × 0.02 m glass slab chamber using a programmable two-axis linear actuator. The method takes advantage of natural mechanical sorting processes, along with the ability to program the motion of the arm, to efficiently build cross-beds and ripple laminae similar to those seen in natural water-lain clastic deposits. By using a mixture of grain sizes (200 to 800 μm diameter), depositional fabrics with multiscale heterogeneity (mm to dm) are generated. Reproducibility tests show very high correlation among multiple fabric realizations produced with similar inputs. After introducing this first-of-a-kind capability to produce depositionally realistic fabrics at scales larger than that of rock cores, a demonstrative study is presented that illustrates gravity unstable multiphase flow which is relevant in the context of CO 2 sequestration. Preliminary results highlight the dramatic impact small scale capillary heterogeneities have on multiphase immiscible displacement and can help bridge understanding between core scale experiments and reservoir scale observations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Mechanisms for Microseismicity Occurrence Due to CO 2 Injection at Decatur, Illinois: A Coupled Multiphase Flow and Geomechanics Perspective

Here, we numerically investigate the mechanisms that resulted in induced seismicity occurrence associated with CO 2 injection at the Illinois Basin–Decatur Project (IBDP). We build a geologically consistent model that honors key stratigraphic horizons and 3D fault surfaces interpreted using surface seismic data and microseismicity locations. We populate our model with reservoir and geomechanical properties estimated using well-log and core data. We then performed coupled multiphase flow and geomechanics modeling to investigate the impact of CO 2 injection on fault stability using the Coulomb failure criteria. We calibrate our flow model using measured reservoir pressure during the CO 2 injection phase. Our model results show that pore-pressure diffusion along faults connecting the injection interval to the basement is essential to explain the destabilization of the regions where microseismicity occurred, and that poroelastic stresses alone would result in stabilization of those regions. Slip tendency analysis indicates that, due to their orientations with respect to the maximum horizontal stress direction, the faults where the microseismicity occurred were very close to failure prior to injection. These model results highlight the importance of accurate subsurface fault characterization for CO 2 sequestration operations.

58 GEOSCIENCES↗

DOE OSTI2020

Optimization of a Cyclone Using Multiphase Flow Computational Fluid Dynamics

The U.S. Department of Energy National Energy Technology Laboratory's (NETL) 50 kW th chemical looping reactor (CLR) has an underperforming cyclone, which was designed using empirical correlations. To improve the performance of this cyclone using computational fluid dynamics (CFD)-based modeling simulations, four critical design parameters including the vortex tube radius and length, barrel radius, and the inlet width and height were optimized. Here, NETL's open source multiphase flow with interphase exchange (MFiX) CFD code has been used to model a series of cyclones by systematically varying the geometric design parameters. To perform the optimization process, the surrogate modeling and sensitivity analysis followed by the optimization capability in nodeworks was used. The basic methodology for the process is to employ a statistical design of experiments (DOE) method to generate sampling simulations that fill the design space. Corresponding CFD models are then created, executed, and postprocessed. A response surface is created to characterize the relationship between input parameters and the quantities of interest (QoI). Finally, the CFD-surrogate is used by an optimization method to find the optimal design condition based on the objective and constraints prescribed. The resulting optimal cyclone has a larger diameter and longer vortex tube, a larger diameter barrel, and a taller and narrower solids inlet. The improved design has a predicted pressure drop 11 times lower than the original design while reducing the mass loss by a factor of 2.3.

42 ENGINEERING↗

DOE OSTI2019

Comprehensive comparison of pore-scale models for multiphase flow in porous media

Significance The simultaneous flow of multiple fluid phases through a porous solid occurs in many natural and industrial processes. Microscale physical mechanisms such as the relative affinity of the solid for the fluids (i.e., wettability), capillarity, and viscosity combine with pore geometry to produce a wide variety of macroscopic flow patterns. Pore-scale modeling is an essential tool to connect microscale mechanisms with macroscopic patterns, but quantitative comparisons between different models, and with experimental data, are lacking. Here, we perform an unprecedented comparison of state-of-the-art models from 14 leading groups with a recent experimental dataset. The results underscore the challenges of simulating multiphase flows through porous media, highlighting specific areas for further effort in what is already a flourishing field of research.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Multiphase flow studies for microscale hydrodynamics in the structured packed column

Post combustion carbon capture by solvent absorption in a structured packed column is a promising technology for mitigating greenhouse gas emissions. Computational fluid dynamic (CFD) modelling of such a column is a challenging multiscale problem due to the range in length and time scales. The microscale hydrodynamics play a key role in the overall column efficiency with the interfacial area significantly influencing the mass transfer between the gas and liquid phases. In this context, multiphase flow simulations using the volume of fluid (VOF) method in a representative elementary unit (REU) of the packed column can provide fundamental insights into the microscale hydrodynamics, such as, interfacial area and liquid holdup. The present paper systematically examines the impact of various factors (e.g., physical properties and contact angle) on the interfacial area. The results are compared with existing correlations and a scaling analysis is also performed. The solvent physical properties are characterized by the Kapitza number (Ka), a dimensionless number that depends only on fluid properties. So that the Ka number decreases with increasing viscosity. At a fixed liquid load, the interfacial area and liquid holdup are observed to increase with decreasing Ka number. The impact of contact angle (i.e., solid surface characteristics) is effectively investigated by modifying the wall boundary conditions. The interfacial area and liquid holdup are found to decrease with increasing contact angle. Subsequently, a phenomenological correlation for interfacial area is proposed that includes the impact of these parameters. Finally, this correlation may be used to predict the interfacial area for gas-liquid flow in a structured packing for rivulet to fully wetted flow regimes.

42 ENGINEERING↗

DOE OSTI2020

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

58 GEOSCIENCES↗