SEARCH · Search NASA

Results for “Two Phase Flow”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Flavor Fragmentation Function Factorization

A definition of partonic jet flavor that is both theoretically well-defined and experimentally robust would have profound implications for measurements and predictions especially for heavy flavor applications. Recently, a definition of jet flavor was introduced as the net flavor flowing along the direction of the Winner-Take-All axis of a jet which is soft safe to all orders, but not collinear safe. Here, we exploit the lack of collinear safety and propose a factorization theorem of perturbative flavor fragmentation functions that resum collinear divergences and describe the evolution of flavor from the short distance of jet production to the long distance at which hadronization occurs. Collinear flavor evolution is governed by a small modification of the DGLAP equations. We present a detailed all-orders analysis and identify exact relations that must hold amongst the various anomalous dimensions by probability conservation and the existence of fixed points of the renormalization group flow. We explicitly validate the factorization theorem at one-loop order, and demonstrate its consistency at two loops in particular flavor channels. Starting at two-loops, constraints on phase space imposed by flavor measurements potentially allow for non-trivial soft contributions, but we demonstrate that they are scaleless and so explicitly vanish, ensuring that soft particles are summed inclusively and all divergences are exclusively collinear in nature. This factorization theorem opens the door to precision calculations with identified flavor in the infrared.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Growing neoclassical tearing modes seeded via transient-induced-multimode interactions

Nonlinear extended magnetohydrodynamics simulations demonstrating seeding of neoclassical tearing modes (NTMs) via magnetohydrodynamics-transient-induced multimode interactions are presented. Simulations of NTMs are enabled by two recent NIMROD code developments: the implementation of heuristic neoclassical stresses and the application of transient magnetic perturbations (MPs) at the boundary. NTMs are driven unstable by the inherently pressure driven kinetic bootstrap current, which arises due to collisional viscosity between passing and trapped electrons. These simulations use heuristic closures that model the neoclassical electron and ion stresses. NTM growth requires a seed island, which is generated by a transiently applied MP in simulations. The capability is demonstrated using kinetic-based reconstructions with flow of a DIII-D ITER Baseline Scenario discharge (La Haye et al., in Proceedings IAEA FEC, 2020). The applied MP seeds a 2/1 NTM that grows in two phases: a slow growth phase followed by a faster robust growth phase. Additionally, an evolving sequence of higher order core modes are excited at first. Power transfer analysis shows that nonlinear interactions between the core modes and the 2/1 helps drive the initial slow growth. Once the induced 2/1 magnetic island reaches a critical width, the NTM transitions to faster robust growth, which is well described by the nonlinear modified Rutherford equation. Furthermore, this work highlights the role of nonlinear mode coupling in seeding NTMs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

High Impedance Fault Detection Through Quasi-Static State Estimation: A Parameter Error Modeling Approach

This paper presents a model for detecting high impedance faults using parameter error modeling and a two step per-phase weighted-least squares state estimation process. The proposed scheme leverages the use of Phasor Measurement Units and synthetic measurements to identify per-phase power flow and injection measurements which indicate a parameter error through ?2 Hypothesis Testing applied to the composed measurement error. Although current and voltage waveforms are commonly analyzed for high-impedance fault detection, wide area power flow and injection measurements, which are already inherent to the state estimation process, also show promise for real-world high-impedance fault detection applications. The error distributions after detection share the measurement function error spread observed in proven parameter error diagnostics and can be applied to high-impedance fault identification. Further, this error spread across measurement functions related to the fault will be clearly discerned from measurement error. Case studies are performed on the IEEE 33-Bus Distribution System along with the proposed model in Simulink.

Cooper, Austin↗

DOE OSTI2023

Crystallographic Study of Product Phases of Carbothermic Reduction and Nitridation of Hafnium Dioxide

Details of the carbothermic reduction/nitridation to synthesize hafnium nitride (HfN) and hafnium carbide (HfC) are scarce in the literature. Therefore, this current study was carried out to evaluate two pathways for synthesizing these two refractory materials: direct nitridation and carbothermic reduction/nitridation. Two mixtures of hafnium dioxide and carbon with C/HfO 2 molar ratios of 2.15 and 3.1 were nitridized directly using flowing nitrogen gas at elevated temperatures (1300–1700 °C). The 3.1 C/HfO 2 molar ratio mixture was also carbothermically reduced under flowing argon gas to synthesize HfC, which was converted into HfN by introducing a nitridation step under both N 2(g ) and N 2(g) -10% H 2(g) . X-ray diffraction results showed the formation of HfN at 1300 and 1400 °C and HfC 1–y N y at ≥1400 °C under direct nitridation of samples using a C/HfO 2 molar ratio of 2.15. These phase analysis data together with lower lattice strain and greater crystallite sizes of HfC 1–y N y that formed at higher temperatures suggested that the HfC 1–y N y phase is preferred over HfN at those temperatures. Carbothermic reduction of 3.1 C/HfO 2 molar ratio samples under an inert atmosphere produced single-phased HfC with no significant levels of dissolved oxygen. In conclusion, carbothermic reduction nitridation made two phases of different carbon levels (HfC 1–y N y and HfC 1–y 'N y ', where y' < y), while direct nitridation produced a single HfC 1–y N y phase under both N 2 and N 2 -10% H 2 cover gas environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Experiments and CFD simulation of mass transfer and hydrodynamics in a cylindrical bubble column

Flow visualization, Particle Image Velocimetry (PIV) and dissolved oxygen charging experiments are carried out in a small-scale cylindrical air-water bubble column at different superficial gas velocities. Void fraction profile, total gas holdup, liquid phase velocity field and volumetric mass transfer coefficient are obtained. Details of each experiment are given, with a new procedure for obtaining a 2D void fraction profile from flow visualization by image processing and time averaging which could provide useful information for CFD model validation. The experimental results are analyzed and compared with simulations where good agreement is found for both local and global flow patterns. The averaged governing equations and constitutive relations used in the simulation are discussed briefly, with emphasis on the proper comparison between simulations and experiments based on the derivation of the two-fluid model. Finally, by conducting three sets of experiments related to phase distribution, velocity field and mass transfer in the same apparatus, a validated CFD model for multiphase mass transfer is established and can be used in the future design of a multi-phase reactor.

42 ENGINEERING↗

DOE OSTI2020

Conservation Voltage Reduction (CVR) via Two-Timescale Control in Unbalanced Power Distribution Systems

Voltage control devices are employed in power distribution systems to reduce the power consumption by operating the system closer to the lower acceptable voltage limits; this technique is called conservation voltage reduction (CVR). The different modes of operation for system’s legacy devices (with binary control) and new devices (e.g. smart inverters with continuous control) coupled with variable photovoltaic (PV) generation results in voltage fluctuations which makes it challenging to achieve CVR objective. This paper presents a two-timescale control of feeder’s voltage control devices to achieve CVR that includes (1)a centralized controller operating in a slower time-scale to coordinate voltage control devices across the feeder and (2) local controllers operating in a faster timescale to mitigate voltage fluctuations due to PV variability. The centralized controller utilizes a three-phase optimal power flow model to obtain the decision variables for both legacy devices and smart inverters. The local controllers operate smart inverters to minimize voltage fluctuations and restore nodal voltages to their reference values by adjusting the reactive power support. The proposed approach is validated using the IEEE-123 bus (medium-size) and R3-12.47-2 (large-size) feeders. It is demonstrated that the proposed approach is effective in achieving the CVR objective for unbalanced distribution systems.

optimal control, distributed generation, fluctuati↗

DOE OSTI2022

Vapor–liquid equilibrium estimation of n-alkane/nitrogen mixtures using neural networks

Understanding fluid phase behavior, like VLE, in high P&T conditions is crucial for developing high-fidelity simulations of chemically reacting flows in liquid-fueled combustion systems and also forms an integral part of the design-modeling of the control processes in chemical industries. Two data-driven models have been proposed here in this study, each of which was competent in estimating VLE for the Type III binary systems of C 10 /N 2 and C 12 /N 2 , at pressures ranging up to 50–60 MPa. Both models showed better performance in predicting equilibrium pressure as compared to VLE modeled using PR-EOS. A modified model has also been proposed, capable of estimating the full phase envelope for the binary systems of C 10 /N 2 and C 12 /N 2 across a wide range of temperatures, and thus exhibit the mixture critical pressure at the concerned temperature. The diverse applicability of the proposed network architecture was further exhibited while estimating the VLE of a ternary system of C 1 /C 10 /N 2 .

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Thermal Gradient Effects on Redox Evolution and Volatility-Driven Fractionation in Ternary U/Ce/Cs Condensates

Understanding how thermal history influences redox evolution and chemical fractionation is essential for characterizing high-temperature condensation in complex materials, including nuclear debris. Here, we tested the hypothesis that distinct thermal regimes in a plasma flow reactor influence redox pathways and elemental partitioning in ternary U/Ce/Cs systems. A configurable plasma flow reactor was modified with an external tube furnace to impose two distinct thermal gradients: continuous ambient cooling and a furnace-assisted thermal hold-up near 1400 K followed by rapid cooling. Transmission electron microscopy characterized phase identity, morphology, and nanoscale element distributions, while inductively coupled plasma-mass spectrometry quantified bulk elemental ratios. Across both thermal regimes, uranium and cerium condensed as UO 2 and CeO 2 as dominant refractory oxide products. Uranium partially oxidized to α-UO 3 during extended ambient cooling, while furnace-assisted hold-up preserved UO 2 and produced partial reduction of cerium to Ce 2 O 3 . Cesium remained volatile upstream and condensed later in the reactor, forming Cs 2 O and Cs-uranate phases with the highest incorporation after thermal hold-up. Bulk ICP-MS measurements supported these observations. U/Ce ratios remained comparatively stable and Cs displayed delayed and apparent transient enrichment that matched the nanoscale measurements. This integrated approach provides a quantitative method for linking thermal gradients to redox evolution and volatility-driven fractionation. These results show how the plasma flow reactor can identify where equilibrium descriptions remain adequate and where kinetic effects from residence time and temperature history must be considered when interpreting condensation behavior in multicomponent systems.

and nuclear chemistry↗

DOE OSTI2020

Mechanistic modeling of CO 2 well leakage in a generic abandoned well through a bridge plug cement-casing gap

Both known and unmapped plugged and abandoned wells are potential leakage pathways for CO 2 from geologic carbon sequestration (GCS) sites. Although many abandoned wells have cement bridge plugs installed to prevent leakage, the seal between the cement and the inner casing wall is subject to failure. In this study, we carried out detailed T2Well simulations of cases of sudden non-Darcy flow of CO 2 and brine leakage up the gap between a cement plug and the inner steel casing wall that becomes a fully connected flow path during the post-injection period. The goal of our study was two-fold: (1) to understand the dynamics, rates, and the characteristic temporal signals associated with the onset of leakage through various gap-aperture sizes, and (2) to suggest potential monitoring strategies based on the findings. Simulation results show that the leakage of CO 2 and brine upward is transient with interesting phase interference behavior. Time-dependent oscillatory flows with varying pressure, temperature, and flow rates of CO 2 and brine show strong dependence on gap aperture. Phase-change and decompression lead to very low temperatures at the top of the well for gap apertures larger than 4 mm suggesting that remote thermal monitoring at the ground surface may be an effective way of monitoring even if well locations are not known a priori. Pressure in the well is also indicative of CO 2 leakage. The temporal patterns of changing temperature and pressure may be useful diagnostic signals for leakage detection. Finally, these transient leakage signals may provide information on the cause of leakage and/or characteristics of the flow path that could inform effective remediation design and execution approaches.

58 GEOSCIENCES↗

DOE OSTI2024

The role of RF-induced E×B flows in the mitigation of scrape-off-layer convective transport during ion cyclotron resonance heating

Abstract While multiple experiments have reported a decrease in intermittent fluctuations in the far Scrape-Off-Layer (SOL) during ion cyclotron resonance heating (Antar et al 2010 Phys. Rev. Lett. 105 165001, Li et al 2022 Nucl. Eng. Technol. 54 207–19, Antar et al 2012 Nucl. Fusion 52 103005), the physical mechanism behind this observation has not been fully established yet. In this work, we demonstrate, for the first time, a direct correlation between the amplitude of RF-induced E×B flows and turbulence suppression in the far SOL. Using the Gas Puff Imaging (GPI) diagnostic on Alcator C-Mod, we show again that Ion Cyclotron Range of Frequencies can significantly alter the flow in the SOL and introduce a shear layer in regions magnetically connected close to the antenna (Cziegler et al 2012 Plasma Phys. Control. Fusion 54 105019). With the 4-strap field-aligned antenna operated in dipole phasing, the ratio of the power coupled by the central two straps to the power coupled by the outer two straps was varied. The resulting RF-induced radial electric field magnitude thus varied, and we show that the impact on the far SOL turbulence correlates with the modified E×B velocity. We then apply a newly-developed blob tracking algorithm (Han et al 2022 Sci. Rep. 12 18142) to higher-resolution GPI videos in order to directly observe the process of blob shearing by RF-induced E×B flows. We show that the radially sheared poloidal flows act as a transport barrier by stretching, stopping, and destroying filaments, which is consistent with the observed difference in turbulence statistics.

Diab, R. (ORCID:0000000342065868)↗

DOE OSTI2023

In-silico quantification of intersubject variability on aerosol deposition in the oral airway

The extrathoracic oral airway I s not only a major mechanical barrier for pharmaceutical aerosols to reach the lung but also a major source of variability in lung deposition. Using computational fluid dynamics, deposition of 1-30 µm particles was predicted in 11 CT-based models of the oral airways of adults (7 healthy subjects and 4 patients with chronic obstructive pulmonary disease). Simulations were performed for mouth breathing during both inspiration and expiration at two steady-state flow rates representative of resting/light activity (18 L/min) and of that typically used during aerosol inhalation from a dry powder inhaler (45 L/min). For each subject, oral deposition increased with increasing particle size and flow rate. When averaged over all subjects, there was no significant difference in oral deposition efficiency between inspiration and expiration, unlike subregional deposition that show significantly different patterns between the two breathing phases. Consistent with previous in-vitro inspiratory studies, our data showed a large intersubject variability in oral deposition. These results highlight the need for incorporating morphological variation of the upper airway in predictive models of aerosol deposition for accurate predictions of particle dosimetry in the intrathoracic region of the lung.

Computational fluid dynamics (CFD), Inertial impac↗

DOE OSTI2022

Large Magnetic Gap in a Designer Ferromagnet–Topological Insulator–Ferromagnet Heterostructure

Abstract Combining magnetism and nontrivial band topology gives rise to quantum anomalous Hall (QAH) insulators and exotic quantum phases such as the QAH effect where current flows without dissipation along quantized edge states. Inducing magnetic order in topological insulators via proximity to a magnetic material offers a promising pathway toward achieving the QAH effect at a high temperature for lossless transport applications. One promising architecture involves a sandwich structure comprising two single‐septuple layers (1SL) of MnBi 2 Te 4 (a 2D ferromagnetic insulator) with ultrathin few quintuple layer (QL) Bi 2 Te 3 in the middle, and it is predicted to yield a robust QAH insulator phase with a large bandgap greater than 50 meV. Here, the growth of a 1SL MnBi 2 Te 4 /4QL Bi 2 Te 3 /1SL MnBi 2 Te 4 heterostructure via molecular beam epitaxy is demonstrated and the electronic structure probed using angle‐resolved photoelectron spectroscopy. Strong hexagonally warped massive Dirac fermions and a bandgap of 75 ± 15 meV are observed. The magnetic origin of the gap is confirmed by the observation of the exchange‐Rashba effect, as well as the vanishing bandgap above the Curie temperature, in agreement with density functional theory calculations. These findings provide insights into magnetic proximity effects in topological insulators and reveal a promising platform for realizing the QAH effect at elevated temperatures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.

42 ENGINEERING↗

DOE OSTI2021

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.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2026

Comparison of URANS and LES predictions for the open phase of the OECD NEA CSNI fluid structure interaction CFD benchmark

The OECD NEA CSNI WGAMA CFD Task Group ran a benchmark in 2020 and 2021 to assess the predictive capabilities of coupled fluid structure interaction (FSI) CFD analysis methods. This paper presents the predictions made for the open phase of the benchmark using URANS and LES turbulence modelling approaches, and a comparison of the results to the experimental data. The benchmark comprised a channel containing two inline cylinders in cross-flow. The cylinders were fixed at one end, free at the other, and had measured resonant frequencies and damping properties. The URANS modelling used ANSYS Fluent 2-way coupled to ANSYS Mechanical. The LES modelling used Nek5000, 1-way coupled to Diablo. Comparisons with cross-channel velocity profiles are presented, both for the mean flow and its RMS. Comparisons are also made to the frequency spectra for point measurements of fluid velocity and pressure, and for the accelerations of the free end of each cylinder. URANS predicts the average velocity profiles relatively well, and is able to predict the velocity and acceleration spectra at the shedding frequency. However, the frequency content at the 4th harmonic of the shedding frequency is low in the URANS flow fields, and so does not excite accelerations at the resonant frequency of the cylinders. LES makes better predictions of the average profiles, and the velocity spectra agree well at both the shedding frequency and at higher frequencies. In conclusion, the 1-way coupled LES results show good agreement for acceleration spectra.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Combining Distributed Electrochemical Measurements with a Semi-Empirical Model to Identify Local Variations in Overpotentials for PEM Water Electrolyzers

Abstract A segmented cell and PCB approach was used to demonstrate an advanced technique for measuring and understanding the electrochemical behavior of PEM water electrolyzers. By employing a semi-empirical model, discrete modes of overpotential and their spatial distributions were identified in an operating cell. Distributed area-specific resistance (DASR measurements indicate that local dehydration of the polymer electrolyte membrane is the primary driver of increased polarization, behaving similarly to mass transport-limited currents at low flow rates due to ineffective gas-phase bubble removal. To improve quantification, the overall ohmic overpotential is divided into background (η Ohm,b ) and mass transport-coupled (η Ohm,mt ) components. Two types of anode diffusion media, a baseline PTL and a thin foil liquid/gas diffusion layer (LGDL), were examined. The results show significant variations in η Ohm,b and highlight that ineffective bubble removal leads to pronounced local dehydration. The effect of cell temperature on various overpotentials was also examined. Negligible differences in diffusion overpotential were observed when comparing PEWE performance using the PTL and LGDL, despite major differences in two-phase fluid transport within each diffusion media. This underscores the critical role of the catalyst layer's micro-porous structure in diffusion processes. The study highlights the complex nature and intricacies of mass transport limitations within PEWEs.

Roy, Anirban (ORCID:0000000163803386)↗

DOE OSTI2021

Characterizing the Effect of Capillary Heterogeneity on Multiphase Flow Pulsation in an Intermediate–Scale Beadpack Experiment using Time Series Clustering and Frequency Analysis

An intermediate-scale beadpack drainage experiment was conducted to investigate how simple layered lamination heterogeneity affects CO 2 flow. Two simple layers of capillary barriers are manually packed in the tank and slow drainage was carried out using analog fluids to mimic the capillary- and gravity-dominated CO 2 upward migration process in deep saline aquifers. Nonwetting phase saturation time series clustering analysis and frequency analysis have been conducted on the experimental data. Additionally, modified invasion percolation numerical simulations were done on a digital model of the beadpack to compare to experimental results. Results show that capillary barriers can lead to strong pulsation behavior, which in turn can cause unexpected early breaching through other barriers. The inlet pressure is found to be able to respond to saturation changes in far regions of the domain, indicating that the wetting phase can transmit pressure changes from the other phase. Although static simulations were not able to capture all the dynamic behavior observed in the experiment, Monte Carlo composite simulation results combining many different realizations can better illustrate how the nonwetting phase will behave in the heterogeneous domain. Furthermore, our results suggest the need for CO 2 storage site selection with preference given to aquifers with more capillary barriers with finer grain sizes to avoid flow pulsation and to retard plume upward migration.

58 GEOSCIENCES↗

DOE OSTI2022

Newton trust-region methods with primary variable switching for simulating high temperature multiphase porous media flow

Coupling multiphase flow with energy transport due to high temperature heat sources introduces significant new challenges since boiling and condensation processes can lead to dry-out conditions with subsequent re-wetting. The transition between two-phase and single-phase behavior can require changes to the primary dependent variables adding discontinuities as well as extending constitutive nonlinear relations to extreme physical conditions. Practical simulations of large-scale engineered domains lead to Jacobian systems with a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. Performance assessment of potential nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainty in material properties, boundary conditions, and failure scenarios. Due to the numerical challenges, standard NR iteration may not converge over the range of required simulations and require more sophisticated optimization method like trust-region. In this study, we use the open-source simulator PFLOTRAN for the important practical problem of the safety assessment of future nuclear waste repositories in the U.S. DOE geologic disposal safety assessment Framework. The simulator applies the PETSc parallel framework and a backward Euler, finite volume discretization. We demonstrate failure of the conventional NR method and the success of trust-region modifications to Newton’s method for a series of test problems of increasing complexity. Trust-region methods essentially modify the Newton step size and direction under some circumstances where the standard NR iteration can cause the solution to diverge or oscillate. Furthermore, we show how the Newton Trust-Region method can be adapted for Primary Variable Switching (PVS) when the multiphase state changes due to boiling or condensation. The simulations with high-temperature heat sources which led to extreme nonlinear processes with many state changes in the domain did not converge with NR, but they do complete successfully with the trust-region methods modified for PVS. This implementation effectively decreased weeks of simulation time needing manual adjustments to complete a simulation down to a day. Finally, we show the strong scalability of the methods on a single node and multiple nodes in an HPC cluster.

54 ENVIRONMENTAL SCIENCES↗