SEARCH · Search NASA

Results for “TWO EQUATION MODEL”

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 127 records · Page 7

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Validating corrosion models: A comparison of governing equations

Experimental validation of Finite Element Method (FEM) models varying electrochemical governing equations, inclusion of chemical reactions, and time on the resultant damage profile for two galvanic couples is explored. Two anode materials (Magnesium AZ31 and Carbon Steel) in contact with a cathode (Stainless Steel 304 L) were modeled in/exposed to NaCl (1 and 0.1 M respectively for the anode materials) for up to one week. The physics approach, inclusion of chemical reactions, and the boundary conditions required to accurately represent the damage profile in FEM models depended on the galvanic couple materials and, ultimately, the corrosion rate. For high rates of corrosion (i.e., magnesium anode), the Nernst-Planck equation with Electroneutrality was sufficient to describe the damage, while, for low rates of corrosion (i.e., carbon steel anode), the Laplace equation was sufficient. In all cases, the most complete governing equation (Nernst-Planck-Poisson Equation) was not necessary to accurately describe the damage. Precipitation reactions in solution also played a critical role in the predicted damage profile, especially for high corrosion rate systems. Finally, for short time periods (< 6 h), the choice of governing equations does not significantly influence damage profile results. Overall, the choice of physics to reduce error in simulations relies on the boundary conditions, geometry, conductivity of the solution, electrochemical potential differences, and time of exposure. The above results are discussed with regard to accuracy and computational savings.

Carbon steel↗

DOE OSTI2021

Numerical investigation of a fueled pre-chamber spark-ignition natural gas engine

Pre-chamber spark-ignition (PCSI) is a leading advanced ignition concept for internal combustion engines with the potential to enable diesel-like efficiency in medium-duty/heavy-duty (MD/HD) natural gas (NG) engines. By leveraging distributed ignition sources from multiple turbulent jets, the PCSI technology can deliver extremely short combustion duration in ultra-lean mixtures and significantly improve the engine thermal efficiency. However, in the automotive industry there is a lack of adequate science base and predictive simulation tools required for commercial development of PCSI engines. Here, in this study, Reynolds-Average Navier-Stokes simulations are carried out to describe the combustion process in lean-burn NG engines, focusing on the combustion modeling approach. Two combustion models, multi-zone well-stirred reactor (MZ-WSR) and G-equation, are used to simulate the combustion process in an MD NG engine equipped with a fueled-PCSI system for four operating conditions close to the lean operating limit. A skeletal chemical mechanism and a laminar flame speed tabulation are used to compute the combustion accurately. Simulation results are compared with experimental data regarding measured cylinder pressure, heat release rate, and combustion duration. By dividing the PCSI combustion process into four distinct phases, the difference between the two models’ results for each phase is analyzed in detail. The MZ-WSR model overestimates the combustion duration for early flame kernel growth in the pre-chamber due to the lack of a specific formulation to take turbulence-chemistry interaction into account. Despite the prolonged combustion duration and low pressure built-up inside the pre-chamber, the model matches the combustion rate in the main-chamber. In contrast, the G-equation model delivers good agreements for the pre-chamber combustion and turbulent jet-driven combustion processes. However, the model starts to underestimate the combustion rate in the main-chamber, especially under ultra-lean mixture conditions. Finally, improvements are needed for both models to simulate the later combustion stage that occurred in the near-wall regions.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

FECM/NETL CO 2 Transport Cost Model (2022): Description and User’s Manual

The FECM/NETL CO 2 Transport Cost Model (CO 2 _T_COM) is an Excel spreadsheet model that calculates the cost of transporting CO 2 from the beginning to the end of a pipeline. This document provides two main functions. First, the document describes the equations and algorithms that are used by the model to calculate technical quantities (such as the minimum inner pipe diameter needed to transport a user-specified CO 2 mass flow rate a specified distance) and engineering-economic quantities (such as capital costs, operating costs and cash flows). Second, the document is a user’s manual for the model that describes the procedures the user must follow to run the model. The document also describes input variables and output variables (i.e., results) for the model.

42 ENGINEERING↗

DOE OSTI2023

FECM/NETL CO 2 Transport Cost Model (2023): Description and User’s Manual

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2026

Validating corrosion models: Influence of physical properties

In chloride containing environments, two metals in physical contact can undergo galvanic corrosion limiting the lifetime of components. Being able to accurately predict galvanic corrosion damage distributions over time has not been widely presented in literature. Therefore, Finite Element Method (FEM) corrosion models were experimentally validated for two galvanic couples as a function of governing equations, environment, anode material, anode:cathode ratio, and time. Carbon steel/stainless steel (CS/SS) and zinc/stainless steel (Zn/SS) galvanic couples were exposed to NaCl solutions at room temperatures for up to 14 days. For the galvanic couples and environments, the Laplace equation with variable conductivity and reactions was sufficient to model the experimental corrosion damage. Increasing the chloride concentration for the CS/SS galvanic couple, regardless of the anode:cathode ratio, decreased the observed and modeled corrosion damage. Decreasing the anode:cathode ratio (i.e., increasing the cathode length), increased the experimentally observed and modeled corrosion damage. For small anode:cathode ratios, the governing equations deviate over long time periods with the Nernst-Plank equation being conservative. For the Zn/SS galvanic couple, the cathode length controls the dominant cathodic reduction reaction. For small cathode lengths, the hydrogen evolution reaction is dominant. For larger cathode lengths, the oxygen reduction reaction is dominant. The results are discussed with regard to the influence of solution chemistry, ohmic drop, and governing reactions. Overall, validated FEM models were presented, and the resultant models, physics, and mechanisms can be applied to other corrosion scenarios with confidence.

Carbon steel↗

DOE OSTI2022

Parameter study of a Kinetic Phase Transition model

We investigate the ability of the two model parameters in the Kinetic Phase Transition (KPT) model of Carl Greeff to describe phase transitions of various types when combined with the tin Equation of states for the phases, SESAME 2162. While the two parameters are correlated, one combination can be associated with the nucleation process giving rise to the hysteresis seen in phase transition paths in pressure-temperature space and another can be associated with the overall timescale of the transition. We acknowledge the desire to have a model where the parameters are more independent of each other for easier model parameter determination.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Physics-informed machine learning of redox flow battery based on a two-dimensional unit cell model

In this paper, we present a physics-informed neural network (PINN) approach for predicting the performance of an all-vanadium redox flow battery, with its physics constraints enforced by a two-dimensional (2D) mathematical model. The 2D model, which includes 6 governing equations and 24 boundary conditions, provides a detailed representation of the electrochemical reactions, mass transport and hydrodynamics occurring inside the redox flow battery. To solve the 2D model with the PINN approach, a composite neural network is employed to approximate species concentration and potentials; the input and output are normalized according to prior knowledge of the battery system; the governing equations and boundary conditions are first scaled to an order of magnitude around 1, and then further balanced with a self-weighting method. Our numerical results show that the PINN is able to predict cell voltage correctly, but the prediction of potentials shows a constant-like shift. To fix the shift, the PINN is enhanced by further constrains derived from the current collector boundary. Finally, we show that the enhanced PINN can be even further improved if a small number of labeled data is available.

25 ENERGY STORAGE↗

DOE OSTI2021

Onset of Plasmoid Reconnection during Magnetorotational Instability

The evolution of current sheets in accretion flows undergoing magnetorotational instability (MRI) is examined through two- and three-dimensional numerical modeling of the resistive MHD equations in global cylindrical geometry. With an initial uniform magnetic field aligned in the vertical (z) direction, MRI produces radially extended toroidal (azimuthal) current sheets. In both 2D and 3D when axisymmetric modes dominate, these current sheets attract each other and merge in the poloidal (rz) plane, driving magnetic reconnection when the Lundquist number S > 3 × 10 2 , making it a possible source of plasmoids (closed magnetic loops) in accretion disks. At high Lundquist numbers in the 2D regime, starting at S = 5 × 10 3 , self-consistent MRI-generated current sheets become thin and subject to plasmoid instability, and therefore spontaneous magnetic reconnection. When nonaxisymmetric 3D modes dominate, turbulence makes the azimuthal current sheets more unstable and stretch vertically. Toroidally extended vertical current sheets in the inner region, as well as larger 3D magnetic islands in the outer regions of the disks are also formed. These findings have strong ramifications for astrophysical disks as potential sources of plasmoids that could cause local heating, particle acceleration, and high energy EM radiation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

A Massively Parallel Implementation of the CCSD(T) Method Using the Resolution-of-the-Identity Approximation and a Hybrid Distributed/Shared Memory Parallelization Model

In this work, a parallel algorithm is described for the coupled-cluster singles and doubles method augmented with a perturbative correction for triple excitations [CCSD(T)] using the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs). The algorithm bypasses the storage of four-center ERIs by adopting an integral-direct strategy. The CCSD amplitude equations are given in a compact quasi-linear form by factorizing them in terms of amplitude-dressed three-center intermediates. A hybrid MPI/OpenMP parallelization scheme is employed, which uses the OpenMP-based shared memory model for intranode parallelization and the MPI-based distributed memory model for internode parallelization. Parallel efficiency has been optimized for all terms in the CCSD amplitude equations. Two different algorithms have been implemented for the rate-limiting terms in the CCSD amplitude equations that entail and -scaling computational costs, where N O and N V denote the number of correlated occupied and virtual orbitals, respectively. One of the algorithms assembles the four-center ERIs requiring N V 4 and N O 2 N V 2 -scaling memory costs in a distributed manner on a number of MPI ranks, while the other algorithm completely bypasses the assembling of quartic memory-scaling ERIs and thus largely reduces the memory demand. It is demonstrated that the former memory-expensive algorithm is faster on a few hundred cores, while the latter memory-economic algorithm shows a better strong scaling in the limit of a few thousand cores. The program is shown to exhibit a near-linear scaling, in particular for the compute-intensive triples correction step, on up to 8000 cores. The performance of the program is demonstrated via calculations involving molecules with 24–51 atoms and up to 1624 atomic basis functions. As the first application, the complete basis set (CBS) limit for the interaction energy of the π-stacked uracil dimer from the S66 data set has been investigated. This work reports the first calculation of the interaction energy at the CCSD(T)/aug-cc-pVQZ level without local orbital approximation. The CBS limit for the CCSD correlation contribution to the interaction energy was found to be -8.01 kcal/mol, which agrees very well with the value -7.99 kcal/mol reported by Schmitz, Hättig, and Tew [ Phys. Chem. Chem. Phys. 2014 , 16 , 22167-22178]. The CBS limit for the total interaction energy was estimated to be -9.64 kcal/mol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Quantum Ornstein-Zernike theory for two-temperature two-component plasmas

Laboratory plasma production almost always preferentially heats either the ions or electrons, leading to a two-temperature state. In this state, density functional theory molecular dynamic simulation is the state of the art for modeling bulk material properties. We construct a statistical mechanics model for the two temperature limit that is theoretically consistent with the molecular dynamics method. We proceed to derive the electron-ion multi-temperature quantum Ornstein-Zernike equations for the first time. This allows the construction of a two-temperature two-component plasma model using the average atom from which we can compute bulk material properties at a fraction of the computation time of the two-temperature density functional theory simulation. The accuracy of the model is benchmarked against ion pair correlation and self-diffusion results from ab initio simulation. Here, we proceed to compute the viscosity and ion thermal conductivity as a function of both ion and electron temperature.

Ab initio molecular dynamics↗

DOE OSTI2021

Mixing Cell Model: A One-Dimensional Numerical Model for Assessment of Water Flow and Contaminant Transport in the Unsaturated Zone

This report describes the Mixing Cell Model code, a one dimensional model for water flow and solute transport in the unsaturated zone under steady state or transient flow conditions. The model is based on the principles and assumptions underlying mixing-cell model formulations. The unsaturated zone is discretized into a series of independent mixing cells. Each cell may have unique hydrologic, lithologic, and sorptive properties. Ordinary differential equations describe the material (water and solute) balance within each cell. Water-flow equations are derived from the continuity equation, assuming that unit gradient conditions exist at all times in each cell. Pressure gradients are considered implicitly through model discretization. Unsaturated hydraulic conductivity and moisture contents are determined by the material specific moisture-characteristic curves. Solute-transport processes include explicit treatment of advective processes, first order chain decay, and linear sorption reactions. Dispersion is addressed through implicit and explicit dispersion. Implicit dispersion is an inherent feature of all mixing-cell models and originates from the formulation of the problem in terms of mass balance around fully mixed volume elements. Expressions are provided that relate implicit dispersion to the physical dispersion of the system. Two FORTRAN codes were developed to solve the water flow and solute-transport equations: (1) the Mixing Cell Model for Flow (MCMF) solves transient water-flow problems and (2) the Mixing Cell Model for Transport (MCMT) solves the solute-transport problem. The transient water-flow problem is typically solved first by estimating the water flux through each cell in the model domain as a function of time using the MCMF code. These data are stored in either ASCII or binary files that are later read by the solute transport code (MCMT). Code output includes solute pore water concentrations, water and solute inventories in each cell and at each specified output time, and water and solute fluxes through each cell and specified output time. Computer run times for coupled transient water flow and solute transport were typically several seconds on a 2 GHz Intel Pentium IV desktop computer. The model was benchmarked against analytical solutions and finite element approximations to the partial differential equations (PDE) describing unsaturated flow and transport. Differences between the maximum solute flux estimated by the mixing cell model and the PDE models were typically less than two percent. This revision includes an option for a fixed concentration lower boundary condition for diffusive fluxes for versions 020321 and later.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Phase-field simulations of fission gas bubble growth and interconnection in U-(Pu)-Zr nuclear fuel

Abstract The growth and interconnection of fission gas bubbles in the hotter central regions of U-(Pu)-Zr nuclear fuel has been simulated with a phase-field model. The Cahn-Hilliard equation was used to represent the two-phase microstructure, with a single defect species. The volume fraction of the bubble phase and surface area of the bubble-matrix interface were determined during growth and interconnection. Surface area increased rapidly during the initial stages of growth, then slowed and finally decreased as bubble interconnection began and coarsening acted to reduce surface area. The fraction of the bubbles vented to a simulation domain boundary, f V , was quantified as a measure of the microstructure’s interconnectivity and plotted as a function of porosity p . The defect species diffusivity was varied; although changes in diffusivity significantly affected the microstructure, the plots of f V vs. p did not change significantly. The percolation threshold p c was calculated to be approximately 0.26, depending on the assumed diffusivity and using an initial bubble number density based on experimental observations. This is slightly smaller than the percolation threshold for continuum percolation of overlapping 3D spheres. The simulation results were used to parameterize two different engineering-scale swelling models for U-(Pu)-Zr in the nuclear fuel performance code BISON.

Aagesen, Larry K. (ORCID:000000034936676X)↗

DOE OSTI2021

Thermodynamic modeling of calcium carbonate scale precipitation: aqueous Na + -Ca 2+ -Cl – -HCO 3 – -CO 3 2– -CO 2 system

To allow for accurate calculations of calcium carbonate scaling in highly saline produced waters, we present a comprehensive thermodynamic model based on the electrolyte nonrandom two-liquid (eNRTL) activity coefficient equation for the aqueous Na ⁺ -Ca ²⁺ -Cl – -HCO 3 – -CO 3 ²– -CO 2 system. The eNRTL binary interaction parameters for the H 2 O:(Na ⁺ -CO 3 2– ) pair, the H 2 O:(Na ⁺ -HCO 3 – ) pair, the (Na⁺-Cl–):(Na ⁺ -CO 3 2– ) pair, and the (Na ⁺ -Cl – ):(Na ⁺ -HCO 3 – ) pair are identified in this work via the regression of thermodynamic, calorimetric, and phase equilibria experimental data. The binary interaction parameters associated with the H 2 O:(Na ⁺ -Cl – ) pair, the CO 2 :(Na ⁺ -Cl – ) pair, the H 2 O:(Ca ²⁺ -Cl – ) pair, and the (Na ⁺ -Cl – ):(Ca ²⁺ -Cl – ) pair are retrieved from the literature. The remaining binary interaction parameters are retrieved from Aspen Plus or set to zero. In addition, the solubility product constants are identified for Na 2 CO 3 ·10H 2 O (s) , Na 2 CO 3 · 7H 2 O (s) , Na 2 CO 3 ·H 2 O (s) , Na 2 CO 3 ·NaHCO 3 2H 2 O (s) , Na 2 CO 3 ·3NaHCO 3 (s) , and CaCO 3(s) via regression of solubility data. Here, the model is capable of accurately calculating all phase equilibria and calorimetric properties at temperatures up to 473.15 K and salt concentrations up to saturation.

42 ENGINEERING↗

DOE OSTI2020

Comprehensive Studies on Hot Compaction and Vibration-Assisted Compaction Tests of Aluminum Powder

Abstract Aluminum powder compaction was studied using both test and simulation. Cold compaction, hot compaction, and vibration-assisted (cold) compaction tests were conducted to achieve different density ratios. First, the hot compaction test (at 300 °C, compression pressure 140 MPa) improved about 6% compared with cold compaction under the same compression pressure. Second, although the relative density ratio does not obviously improve at a vibration-assisted (cold) compaction, the strength of the specimens made under vibration loading is much better than those of cold compaction. Additionally, finite element models with well-calibrated Drucker–Prager Cap (DPC) material constitutive model were built in abaqus/standard to simulate the powder compaction process. The results of the finite element model have very good correlations with test results up to the tested range, and this finite element model further predicts the loading conditions needed to achieve the higher density ratios. Two exponential equations of the predicted density ratio were obtained by combining the test data and the simulation results. A new analytical solution was developed to predict the axial pressure versus the density ratio for the powder compaction according to DPC material model. The results between the analytical solution and the simulation model have a very good match.

Engineering↗

DOE OSTI2024

Model-based optimization strategies for direct hydrogenation of carbon dioxide to dimethyl ether

Here, this study discusses model-based optimization strategies for CO 2 hydrogenation to dimethyl ether (DME) over aCuZnZr (CZZ) and ferrite (FER) mixed catalyst system in a packed-bed reactor configuration. A two-dimensional axisymmetric, nonisothermal packed-bed reactor model was developed using COMSOL Multiphysics 6.2 software. The model solves two-dimensional (radial and axial) heat and mass transport equations in the packed-bed and integrates intraparticle diffusion and heat transfer in a 1D approach. This powerful feature differs from a traditional porous media approach and takes into account any heat and mass transfer limitations that may exist. Analysis shows that the heat transfer limitations are negligible, but strong internal mass transfer limitations were observed at 10 ≤ WHSV ≤ 90 h -1 on the FER catalyst and at 240 °C. The optimum catalyst composition (i.e., mixing ratio) varies depending on the operating regime. The FER catalyst weight in the mixture can be as low as 5 wt.%, but the ideal composition de-pends on the internal mass transfer limitation and its relationship with the operating regime (i.e., weight hourly space velocity, temperature). A catalyst composition of 80 wt.% CZZ and 20 wt.% FER was suggested; this composition can provide high CO 2 conversion and DME production rates at a wide range of temperatures and flow rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

A Transported Livengood–Wu Integral Model for Knock Prediction in Computational Fluid Dynamics Simulation

This work describes the development of a transported Livengood–Wu (L–W) integral model for computational fluid dynamics (CFD) simulation to predict autoignition and engine knock tendency. The currently employed L–W integral model considers both single-stage and two-stage ignition processes, thus can be generally applied to different fuels such as paraffin, olefin, aromatics, and alcohol. The model implementation is first validated in simulations of homogeneous charge compression ignition (HCCI) combustion for three different fuels, showing good accuracy in prediction of autoignition timing for fuels with either single-stage or two-stage ignition characteristics. Then, the L–W integral model is coupled with G-equation model to indicate end-gas autoignition and knock tendency in CFD simulations of a direct-injection spark-ignition engine. This modeling approach is about 10 times more efficient than the ones that based on detailed chemistry calculation and pressure oscillation analysis. Two fuels with same Research Octane Number (RON) but different octane sensitivity are studied, namely, Co-Optima alkylate and Co-Optima E30. Feed-forward neural network model in conjunction with multivariable minimization technique is used to generate fuel surrogates with targets of matched RON, octane sensitivity, and ethanol content. The CFD model is validated against experimental data in terms of pressure traces and heat release rate for both fuels under a wide range of operating conditions. The knock tendency—indicated by the fuel energy contained in the autoignited region—of the two fuels at different load conditions correlates well with the experimental results and the fuel octane sensitivity, implying the current knock modeling approach can capture the octane sensitivity effect and can be applied to further investigation on composition of octane sensitivity.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

On Two-Phase Pressure and Temperature Equilibration with Mie-Grüneisen Equations of State

In the course of reactive flow modeling, the phases of high explosive (HE) reactants and products introduce additional degrees of freedom to the underlying hydrodynamic equations of compressible reactive fluid mechanics. Hydrodynamic simulations track the bulk (mixture) conservation properties of mass, momentum and energy. When multiple phases are introduced, one must decide on appropriate closure rules to determine the relative phase volumes and energy distribution between the phases. One typical closure is to assume that the phases are in pressure and temperature equilibrium. Here, the requisite equations of p-T equilibration are explored for Mie-Grüneisen Equations of State (EOS). Examples with Davis reactants and Davis products EOSs will be given. The Davis forms are used in both the WSD and AWSD reactive flow models.

42 ENGINEERING↗

DOE OSTI2021

Hamiltonian kinetic-Hall magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes

We present two generalized hybrid kinetic-Hall magnetohydrodynamics (MHD) models describing the interaction of a two-fluid bulk plasma, which consists of thermal ions and electrons, with energetic, suprathermal ion populations described by Vlasov dynamics. The dynamics of the thermal components are governed by standard fluid equations in the Hall MHD limit with the electron momentum equation providing an Ohm's law with Hall and electron pressure terms involving a gyrotropic electron pressure tensor. The coupling of the bulk, low-energy plasma with the energetic particle dynamics is accomplished through the current density (current coupling scheme; CCS) and the ion pressure tensor appearing in the momentum equation (pressure coupling scheme; PCS) in the first and the second model, respectively. The CCS is a generalization of two well-known models, because in the limit of vanishing energetic and thermal ion densities, we recover the standard Hall MHD and the hybrid kinetic-ions/fluid-electron model, respectively. This provides us with the capability to study in a continuous manner, the global impact of the energetic particles in a regime extending from vanishing to dominant energetic particle densities. The noncanonical Hamiltonian structures of the CCS and PCS, which can be exploited to study equilibrium and stability properties through the energy-Casimir variational principle, are identified. As a first application here, we derive a generalized Hall MHD Grad–Shafranov–Bernoulli system for translationally symmetric equilibria with anisotropic electron pressure and kinetic effects owing to the presence of energetic particles using the PCS.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗