Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “equilibrium modeling”

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.

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

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Modelling Equilibrium and Fractional Crystallization in the System MgO-FeO-CaO-Al2O3-SiO2

A mathematical modelling technique for use in petrogenesis calculations in the system MgO-FeO-CaO-Al2O3-SiO2 is reported. Semiempirical phase boundary and elemental distribution information was combined with mass balance to compute approximate equilibrium crystallization paths for arbitrary system compositions. The calculation is applicable to a range of system compositions and fractionation calculations are possible. The goal of the calculation is the computation of the composition and quantity of each phase present as a function of the degree of solidification. The degree of solidification is parameterized by the heat released by the solidifying phases. The mathematical requirement for the solution of this problem is: (1) An equation constraining the composition of the magma for each solid phase in equilibrium with the liquidus phase, and (2) an equation for each solid phase and each component giving the distribution of that element between that phase and the magma.

Herbert, F.↗
NASA NTRS1981

A variational approach to the question of temporal stability of equilibrium models of solar prominences. I - The formal theory

A Lagrangian approach to the equations describing small amplitude departures from equilibrium of solar prominences is presented. Seven quantities are derived which, by analogy to the concepts of energy, momentum, and angular momentum, are conserved under conditions corresponding to ignorable coordinates of classical mechanics. It is expected that these conservation laws will be useful as criteria of accuracy in obtaining eigenfrequencies for the perturbation equations when numerical techniques are used. The method is capable of handling complicated spatial dependences and has internal criteria for assessing the accuracy of any given numerical convergence scheme.

Lerche, I.↗
NASA NTRSDate not supplied

Aqueous Alteration on the Ryugu Parent Body Constrained by Chemical Equilibrium Models

The composition of solid samples returned from the asteroid 162173 Ryugu byHayabusa2 indicates aqueous alteration of rocks that formed a parent body of Ryugu [1, 2]. As on parent bodies of carbonaceous chondrites [3-5], Ryugu materials could have went through (1) accretion of anhydrous and reduced rocky grains together with water-rich ices, (2) melting of ices in the body’s interior through release of radiogenic heat [6], and (3)aqueous alteration of rocky and organic materials that produced secondary minerals, salt- and organic-bearing water solutions, gases, and altered organic matter. Although the bulk chemical composition and major mineralogy (phyllosilicates, magnetite, pyrrhotite, carbonates, phosphates, etc.) of Ryugu [1,2]are similar to those of CI carbonaceous chondrites [3-5, 7], the lack of sulfates and a deficiency of oxygen in the returned samples suggest a distinct alteration pathway. Chondritic materials [3-5] do not indicate complete chemical equilibration though low-temperature parent body processes. However, calculations of chemical equilibria in modeling rock-water-gas type systems[e.g., 8, 9], could assess deviations of chondritic materials from equilibrium conditions and constrain partitioning of chemical elements between solid, aqueous, and gas phase for different stages of alteration. Here we constrained speciation of solid, aqueous, and gaseous phases during aqueous alteration on the Ryugu parent body through chemical equilibrium calculations.

M Yu Zolotov↗
NASA NTRS1992

A two-phase restricted equilibrium model for combustion of metalized solid propellants

An Eulerian-Lagrangian two-phase approach was adopted to model the multi-phase reacting internal flow in a solid rocket with a metalized propellant. An Eulerian description was used to analyze the motion of the continuous phase which includes the gas as well as the small (micron-sized) particulates, while a Lagrangian description is used for the analysis of the discrete phase which consists of the larger particulates in the motor chamber. The particulates consist of Al and Al2O3 such that the particulate composition is 100 percent Al at injection from the propellant surface with Al2O3 fraction increasing due to combustion along the particle trajectory. An empirical model is used to compute the combustion rate for agglomerates while the continuous phase chemistry is treated using chemical equilibrium. The computer code was used to simulate the reacting flow in a solid rocket motor with an AP/HTPB/Al propellant. The computed results show the existence of an extended combustion zone in the chamber rather than a thin reaction region. The presence of the extended combustion zone results in the chamber flow field and chemical being far from isothermal (as would be predicted by a surface combustion assumption). The temperature in the chamber increases from about 2600 K at the propellant surface to about 3350 K in the core. Similarly the chemical composition and the density of the propellant gas also show spatially non-uniform distribution in the chamber. The analysis developed under the present effort provides a more sophisticated tool for solid rocket internal flow predictions than is presently available, and can be useful in studying apparent anomalies and improving the simple correlations currently in use. The code can be used in the analysis of combustion efficiency, thermal load in the internal insulation, plume radiation, etc.

Sabnis, J. S.↗
DOE OSTI2024

Verification of the kinetic electron role in the microinstabilities in a negative triangularity model equilibrium

Effect of kinetic electrons on negative triangularity plasmas has been investigated and compared against the corresponding positive triangularity plasmas, using the global gyrokinetic code X-point Gyrokinetic Code with scale-separated delta-f option without Coulomb collisions. Our model magnetic equilibria have strong positive and negative triangularities and weak magnetic shear. However, unusually large ρ i > a and low density plasmas are chosen to maximize the nonlocal effect to investigate the finite ρ i effect and to be clearly away from kinetic ballooning modes. Similar conclusions to previous flux tube and global simulations have been obtained in this highly nonlocal model plasma: it is essential to include kinetic electrons in the micro-instability study of negative triangularity plasmas. Most physics findings agree with existing reports, with some disagreement. We offer a new “effective trapping fraction” concept that can add to the explanation of the growth rate difference between NT and PT plasmas, pointing to the significant variation in trapped particle fractions that have turning points in the mode growth regions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Downstream Separation of Formic Acid with Anion-Exchange Resin from Electrocatalytic Carbon Dioxide (CO 2 ) Conversion: Adsorption, Kinetics, and Equilibrium Modeling

The electrocatalytic carbon dioxide reduction reaction (CO 2 RR) that produces liquid formic acid (FA) is one potential route to minimize the CO 2 concentration in the atmosphere by utilizing CO 2 as a feedstock. However, one of the main disadvantages of this route is the high energy demand required for purification through conventional distillation. This method of purification has been shown to result in a large carbon footprint in life-cycle analysis (LCA). Therefore, finding an alternative purification technique that can integrate with an electrochemical CO 2 RR process with the potential to lower the carbon footprint would be of great interest. Under the experimental conditions of the CO 2 RR, FA remains in its basic form as the formate anion in the catholyte. Anion exchange resins with their basic properties can separate the formate anion from the catholyte mixture as an alternative to energy intensive distillation. In this work, three anion exchange resins with increasing basicity order: Amberlite IRA-96 < Amberlite IRA-910 < Ambersep 900 are tested to separate FA in the presence of aqueous solution of potassium bicarbonate catholyte with varying levels of resin and FA. Kinetics and equilibrium studies data for the FA adsorption are interpreted using several kinetics and isotherm models. The kinetics data fit well with a pseudo-first-order model at high initial FA concentrations and a pseudo-second-order model at low initial FA concentrations. The experimental data can be best explained with the Freundlich isotherm model. The fitted results show that strongly basic Ambersep 900 is more effective at separating FA, with a maximum adsorption capacity of 336.7 mg/g compared to Amberlite IRA-96 (275.2 mg/g) and Amberlite IRA-910 (209.2 mg/g) in neutral water. However, weakly basic Amberlite IRA-96 (110.8 mg/g) can separate FA more efficiently from potassium bicarbonate catholyte than Amberlite IRA-910 (99.9 mg/g) and Ambersep 900 (40.0 mg/g). As a result, competitive adsorption occurs in the presence of potassium bicarbonate catholyte, but the formic acid adsorption capacity is still sufficient for adequate separation.

20 FOSSIL-FUELED POWER PLANTS↗
NASA NTRS2008

Errors in Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) Kinetic Temperature Caused by Non-Local Thermodynamic Equilibrium Model Parameters

The vast set of near global and continuous atmospheric measurements made by the SABER instrument since 2002, including daytime and nighttime kinetic temperature (T(sub k)) from 20 to 105 km, is available to the scientific community. The temperature is retrieved from SABER measurements of the atmospheric 15 micron CO2 limb emission. This emission separates from local thermodynamic equilibrium (LTE) conditions in the rarefied mesosphere and thermosphere, making it necessary to consider the CO2 vibrational state non-LTE populations in the retrieval algorithm above 70 km. Those populations depend on kinetic parameters describing the rate at which energy exchange between atmospheric molecules take place, but some of these collisional rates are not well known. We consider current uncertainties in the rates of quenching of CO2 (v2 ) by N2 , O2 and O, and the CO2 (v2 ) vibrational-vibrational exchange to estimate their impact on SABER T(sub k) for different atmospheric conditions. The T(sub k) is more sensitive to the uncertainty in the latter two and their effects depend on altitude. The T(sub k) combined systematic error due to non-LTE kinetic parameters does not exceed +/- 1.5 K below 95 km and +/- 4-5 K at 100 km for most latitudes and seasons (except for polar summer) if the Tk profile does not have pronounced vertical structure. The error is +/- 3 K at 80 km, +/- 6 K at 84 km and +/- 18 K at 100 km under the less favourable polar summer conditions. For strong temperature inversion layers, the errors reach +/- 3 K at 82 km and +/- 8 K at 90 km. This particularly affects tide amplitude estimates, with errors of up to +/- 3 K.

Garcia-Comas, Maya↗
NASA NTRS1993

Equilibrium models of mass distribution and collisional lifetimes of asteroids

An understanding of the steady state distribution expected in the present day asteroid belt is important to our understanding of the collisional evolution of the asteroids and their physical properties. We have extended earlier work to show that, in the absence of gravity, a simple power law distribution as a function of mass with constant exponent will give an equilibrium distribution of asteroids for all bodies much smaller than the largest asteroids. This result holds for realistic fragmentation mechanisms and is independent of the physical properties of the asteroids. Inclusion of the effects of gravity on disruption and fragmentation of asteroids precludes an analytic solution to this problem, and rules out a simple power law distribution. We are currently calculating numerical solutions in order to determine the expected steady state mass distribution in the asteroid belt.

Williams, David R.↗
DOE OSTI2025

Modeling Equilibrium Solid–Liquid Interfaces under Effective Constant Chemical Potential Using Machine Learning Interatomic Potentials

The chemical potential (μ) of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot maintain constant chemical potential with reference to a targeted concentration or chemical potential under nonequilibrium or dynamic conditions, as solute species can migrate to the interface and deplete (or enrich) the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative quasi-constant chemical potential molecular dynamics (iqCμMD) simulation, which helps simulate targeted molar concentrations of species in solution. iqCμMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target bulk concentration (chemical potential), which allows simulation of the interface under the bulk conditions comparable to experiment. We demonstrate our approach using machine learning interatomic potential (MLIP)-based MD simulations of the Na 2 SO 4,aq –graphene interface, and to show the transferability of our approach, we also perform classical force field-based MD simulations of NaCl aq –air and NaCl aq –graphite interfaces, which produce comparable results to previous CμMD simulations. Our results also show that the iqCμMD approach efficiently achieves the desired bulk ion concentration within two iterations, and by utilizing MLIPs, we can achieve converged results using relatively small-scale simulations compared to previous CμMD simulations. By combining iqCμMD with MLIP-driven simulations, solid–liquid interfaces can be modeled under an effective constant chemical potential with DFT-level accuracy. Here, we show that iqCμMD offers a robust and simple computational framework for constant chemical potential simulations, as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

Chemical structure↗
DOE OSTI2025

Thermal properties and Thermodynamic Equilibrium Modeling of Cementitious Waste Forms

INTRODUCTION Cementitious matrices are used in the US DOE complex and worldwide to solidify aqueous radioactive, hazardous, mixed salt solutions, and sludges to meet low-level radioactive waste (LLW) disposal requirements. Blended formulations are used for most waste form mix designs. Substitution of pozzolans for Class F fly ash has the potential to alter the processing properties and stabilization properties of the resulting waste forms because they add chemical and mineralogical complexity to the final material. The Savannah River Site saltstone waste form was selected as the test case material. CemGEMS software was chosen as the model for predicting hydrated cementitious phases assemblages and phase evolution. Isothermal calorimetry was used as the method for evaluating processing and properties of fresh, uncured waste forms. The test cases consisted of reference case saltstone, and five natural pozzolan substituted saltstone mixes.

Bustamante, Michael E. [Savannah River National La↗
NASA NTRS1976

The relativistic equations of stellar structure and evolution. Stars with degenerate neutron cores. 1: Structure of equilibrium models

The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."

Thorne, K. S.↗
NASA NTRS1984

Equilibrium model of thin magnetic flux tubes

The existence of a physically realizable domain in which approximations that lead to a self consistent solution for flux tube stratification in the solar atmosphere, without ad hoc hypotheses, is proved. The transfer equation is solved assuming that no energy transport other than radiative is present. Convective motions inside the tube are assumed to be suppressed by magnetic forces. Only one parameter, the plasma beta at tau = 0, must be specified, and this can be estimated from observations of spatially resolved flux tubes.

Bodo, G.↗
NASA NTRS1990

Equilibrium models of self-gravitating inviscid disks resulting from the collapse of rotating clouds

A method is presented for the construction of velocity and surface density profiles of infinitely thin, self-gravitating disks formed from the collapse of spherical clouds, under the condition that the angular momentum of each material parcel is conserved. Results are presented for initially uniformly rotating clouds with density distributions varying as R exp -n and n = 0, 1, 2. The resulting disk surface density distributions are well represented by power laws in the cylindrical radius over most of their extent. The form of the zeroth-order approximation provides a useful representation of the final surface density function near the center for all three cases, and for n = 2 this result holds throughout the disk. This result is not generally true for the velocity functions, however.

Stemwedel, Sally W.↗
DOE OSTI2024

Equilibrium core modeling of a pebble bed reactor similar to the Xe-100 with SCALE

As the nuclear industry moves towards licensing and constructing advanced reactors, new attention has been focused on the advanced reactor designs that have past operational experience, such as pebble-bed high-temperature gas-cooled reactors (PB-HTGRs). Pebble-bed reactor designs have many advantages, such as their higher operating temperatures and online refueling capabilities. However, high-fidelity computational modeling of pebble-bed reactor designs, from reactor startup to operation at equilibrium, is more challenging compared to conventionally fueled reactors due to the continuous movement of the fuel pebbles through the reactor during operation. In previous work at Oak Ridge National Laboratory (ORNL), the SCALE Leap-In method for Cores at Equilibrium (SLICE) was developed around tools within the SCALE code system. This iterative method can effectively generate pebble-bed reactor zone-wise fuel inventories at equilibrium core operation within a reasonable computational time. The objective of this work was to further verify the ORNL SLICE method and to investigate the impact of considering temperature profiles during the application of the method. The SLICE method was applied to a modular high-temperature gas-cooled reactor design based upon publicly available design specifications of the Xe-100 pebble-bed reactor. Upon comparing the results from the SLICE method to published literature, the differences in the eigenvalue k effective were on the order of several hundred pcm (percent millirho). To investigate one possible cause of these differences, a study looking at the sensitivity of the full-core equilibrium k effective and discharge nuclide inventory to temperature was performed by developing equilibrium cores of two additional temperature profiles. From this temperature study, differences on the order of hundreds of pcm for the full-core equilibrium k effective , and up to 15% difference for the discharge inventories were found. In conclusion, these results indicated the strong dependence on temperature that needs to be considered for future work in equilibrium modeling of PB-HTGRs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗