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All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Trifluoroacetic Acid from Degradation of HCFCs and HFCs: A Three-Dimensional Modeling Study

Trifluoroacetic acid (TFA; CF3COOH) is produced by the degradation of the halocarbon replacements HFC-134a, HCFC-124, and HCFC-123. The formation of TFA occurs by HFC/HCFC reacting with OH to yield CF3COX (X = F or CI), followed by in-cloud hydrolysis of CF3COX to form TFA. The TFA formed in the clouds may be reevaporated but is finally deposited onto the surface by washout or dry deposition. Concern has been expressed about the possible long-term accumulation of TFA in certain aquatic environments, pointing to the need to obtain information on the concentrations of TFA in rainwater over scales ranging from local to continental. Based on projected concentrations for HFC-134a, HCFC-124, and HCFC-123 of 80, 10, and 1 pptv in the year 2010, mass conservation arguments imply an annually averaged global concentration of 0.16 micro g/L if washout were the only removal mechanism for TFA. We present 3-D simulations of the HFC/HCFC precursors of TFA that include the rates of formation and deposition of TFA based on assumed future emissions. An established (GISS/Harvard/ UCI) but coarse-resolution (8 deg latitude by 10 deg longitude) chemical transport model was used. The annually averaged rainwater concentration of 0.12 micro g/L (global) was calculated for the year 2010, when both washout and dry deposition are included as the loss mechanism for TFA from the atmosphere. For some large regions in midnorthern latitudes, values are larger, 0.15-0.20 micro g/L. The highest monthly averaged rainwater concentrations of TFA for northern midlatitudes were calculated for the month of July, corresponding to 0.3-0.45 micro g/L in parts of North America and Europe. Recent laboratory experiments have suggested that a substantial amount of vibrationally excited CF3CHFO is produced in the degradation of HFC-134a, decreasing the yield of TFA from this compound by 60%. This decrease would reduce the calculated amounts of TFA in rainwater in the year 2010 by 26%, for the same projected concentrations of precursors.

Kotamarthi, V. R.↗
NASA NTRS1998

Trifluoroacetic Acid from Degradation of HCFCs and HFCs: A Three-Dimensional Modeling Study

Trifluoroacetic acid (TFA; CF3 COOH) is produced by the degradation of the halocarbon replacements HFC-134a, HCFC-124, and HCFC-123. The formation of TFA occurs by HFC/HCFC reacting with OH to yield CF3COX (X = F or CI), followed by in-cloud hydrolysis of CF to form TFA. The TFA formed in the clouds may be reevaporated but is finally deposited onto the surface by washout or dry deposition. Concern has been expressed about the possible long-term accumulation of TFA in certain aquatic environments, pointing to the need to obtain information on the concentrations of TFA in rainwater over scales ranging from local to continental. Based on projected concentrations for HFC-134a, HCFC-124, and HCFC-123 of 80, 10, and 1 pptv in the year 2010, mass conservation arguments imply an annually averaged global concentration of 0.16 micro g/L if washout were the only removal mechanism for TFA. We present 3-D simulations of the HFC/HCFC precursors of TFA that include the rates of formation and deposition of TFA based on assumed future emissions. An established (GISS[Harvard/ UCI) but coarse-resolution (8 deg latitude by 10 deg longitude) chemical transport model was used. The annually averaged rainwater concentration of 0.12 micro g/L (global) was calculated for the year 2010, when both washout and dry deposition are included as the loss mechanism for TFA from the atmosphere. For some large regions in midnorthern latitudes, values are larger. 0.15-0.20 micro g/L. The highest monthly averaged rainwater concentrations of TFA for northern midlatitudes were calculated for the month of July, corresponding to 0.3 - 0.45 micro g/L in parts of North America and Europe. Recent laboratory experiments have suggested that a substantial amount of vibrationally excited CF3CHFO is produced in the degradation of HFC-134a, decreasing the yield of TFA from this compound by 60%. This decrease would reduce the calculated amounts of TFA in rainwater in the year 2010 by 26%, for the same projected concentrations of precursors.

Kotamarthi, V. R.↗
NASA NTRS2001

Dynamics of Aqueous Foam Drops

We develop a model for the nonlinear oscillations of spherical drops composed of aqueous foam. Beginning with a simple mixture law, and utilizing a mass-conserving bubble-in-cell scheme, we obtain a Rayleigh-Plesset-like equation for the dynamics of bubbles in a foam mixture. The dispersion relation for sound waves in a bubbly liquid is then coupled with a normal modes expansion to derive expressions for the frequencies of eigenmodal oscillations. These eigenmodal (breathing plus higher-order shape modes) frequencies are elicited as a function of the void fraction of the foam. A Mathieu-like equation is obtained for the dynamics of the higher-order shape modes and their parametric coupling to the breathing mode. The proposed model is used to explain recently obtained experimental data.

Akhatov, Iskander↗
NASA NTRS2001

Rheology of Foam Near the Order-Disorder Transition

The first part of our research results are summarized in the recent journal publication: J. Gregory McDaniel and R. Glynn Holt, 'Measurement of aqueous foam rheology by acoustic levitation', Phys. Rev. E 61, 2204 (2000). This aspect of the work was a combination of experiment and analysis. We built a levitation system capable of acoustically levitating small samples of aqueous foam of arbitrary gas and liquid volume fractions. We then modulated the acoustic field to induce normal mode oscillations of the foam samples. The observables from the experiment were frequency and mode number. For dry (roughly > 70% gas by volume) foams and small deformations, we developed an effective medium, normal-modes analysis which took the frequency and mode number from experiment, and gave us the shear elastic modulus of the foam as a function of Poisson's ratio. The second part of our results may be found in a soon-to-be submitted manuscript 'Dynamics of aqueous foam drops', I.Sh. Akhatov, J.G. McDaniel and R.G. Holt, describing our modeling in the wet foam limit by considering the acoustic problem. This aspect of the research is purely theoretical. Beginning from a mass-conserving mixture law, the fully nonlinear equations of motion for a wet (roughly < 10% gas by volume) foam drop of initially spherical shape were derived. The frequencies for normal mode oscillations were derived in the linear inviscid limit. The nonlinear equations were numerically solved to elicit the motion of a foam drop under acoustic excitation. The role of the time-varying void fraction in breathing-mode oscillations is of particular interest. As of the end of the current (NAG#3-2121) grant, this work was not yet concluded. We continue to work on this aspect in order to extend the analysis to cover the transition regime of gas volume fractions, as well as to compare to experiments in the wet regime.

Holt, R. Glynn↗
NASA NTRS2000

Thermocapillary Flow and Aggregation of Bubbles on a Solid Wall

During the electrolytic evolution of oxygen bubbles forming on a vertically oriented transparent tin oxide electrode, bubbles were found to be mutually attractive. The mechanism of the aggregation had never been explained satisfactorily until Guelcher et al. attributed it to thermocapillary flow. The gradient of surface tension of the liquid at the bubble's surface, which was established because of reaction heat and ohmic heat loss at the electrode wall, drives flow of the liquid adjacent to each bubble; the bubble "pumps" fluid along its surface away from the wall. Fluid flows toward the bubble to conserve mass and entrains nearby bubbles in the flow pattern. The same logic would apply when two bubbles of equal size are adjacent to each other on a warm wall. Each bubble drives thermocapillary flow and hence entrains the other in its flow pattern, which drives the aggregation. Our objective here is to perform experiments where the temperature gradient at the wall is well known and controlled. The theory can be quantitatively tested by studying aggregation of bubble pairs of equal size, and by varying system parameters such as temperature gradient, bubble size and fluid viscosity. The results are then compared with the theory in a quantitatively rigorous manner. We demonstrate that the theory without adjustable parameters is capable of quantitatively modeling the rate of aggregation of two bubbles. The equations governing the thermocapillary flow around a single stationary bubble on a heated or cooled wall in a semi-infinite domain were solved. Both Reynolds number and Marangoni number were much less than unity. The critical result is that liquid in the vicinity of a warm wall flows toward a stationary collector bubble. Consequently the thermocapillary flow around the stationary bubble entrains another bubble toward itself. The bubbles undergo hindered translation parallel to the wall with velocity U while the fluid flow field is described with u. Two velocities were equated by using a wall hindrance parameter q: U = qu [1] which shows the velocity of bubble is proportional to the entraining velocity. The hindrance parameter q can experimentally be measured independently. q can also be calculated by solving the equations of motion for a bubble translating parallel to a solid wall. The experimental cell is cylindrical with an ID of 10 cm and consists of a 1 cm deep main cell filled with silicone oil and flanked by two thermal reservoirs. The upper thermal reservoir was heated and the lower thermal reservoir was cooled so that the bubbles aggregate. Two types of silicone oil (eta = 0.02 and 0.50 Pa s) were used. Two equal sized air bubbles were injected into the cell with a syringe. The center-to-center distance of bubbles was observed through a microscope. Bubble radius ranged from 0.40 mm to 0.65 mm and the temperature gradients along with the cell ranged from 1400 to 5000 K/m. The bubbles aggregated when heat flows from the wall to the fluid. The velocities of bubbles were in the range of 1 - 10 microns/s. The separation r decreased more quickly when the temperature gradient was higher, bubble size was larger, and the oil viscosity was lower. r decreased more rapidly as the bubbles approached each other. Dimensionless time was arbitrarily set to be zero when the dimensionless center-to-center distance between the bubbles was 4. All the bubble trajectories fall onto one line, especially in the range of dimensionless distance from 4 to 3. This means the relative movement of the bubble pair is proportional to the temperature gradient and bubble size and it is inversely proportional to the viscosity of the oil. This result strongly suggests that the thermocapillary flow-based aggregation mechanism is correct. A value of q can be estimated by fitting the scaled data to Eq. [1]. A best fit value of q was obtained as q = 0.26 with a standard deviation of 0.03. Independent experimental results for q for a 0.5 mm radius bubble, give values of q in the range 0.11 to 0.23. The value of q obtained from solving the equations of motion reveals q has values in the range 0.23 - 0.30. Since the full scale of possible values of q is zero to one, the maximum deviation of independently determined values of q from the best fit value was 15% of this full scale. Thus reasonable quantitative agreement between theory and experiment has been obtained.

Kasumi, Hiroki↗
NASA NTRS2002

Definition of Contravariant Velocity Components

This is an old issue in computational fluid dynamics (CFD). What is the so-called contravariant velocity or contravariant velocity component? In the article, we review the basics of tensor analysis and give the contravariant velocity component a rigorous explanation. For a given coordinate system, there exist two uniquely determined sets of base vector systems - one is the covariant and another is the contravariant base vector system. The two base vector systems are reciprocal. The so-called contravariant velocity component is really the contravariant component of a velocity vector for a time-independent coordinate system, or the contravariant component of a relative velocity between fluid and coordinates, for a time-dependent coordinate system. The contravariant velocity components are not physical quantities of the velocity vector. Their magnitudes, dimensions, and associated directions are controlled by their corresponding covariant base vectors. Several 2-D (two-dimensional) linear examples and 2-D mass-conservation equation are used to illustrate the details of expressing a vector with respect to the covariant and contravariant base vector systems, respectively.

Hung, Ching-Mao↗
NASA NTRS2003

Deviation of Long-Period Tides from Equilibrium: Kinematics and Geostrophy

New empirical estimates of the long-period fortnightly (Mf) tide obtained from TOPEX/Poseidon (T/P) altimeter data confirm significant basin-scale deviations from equilibrium. Elevations in the low-latitude Pacific have reduced amplitude and lag those in the Atlantic by 30 deg or more. These interbasin amplitude and phase variations are robust features that are reproduced by numerical solutions of the shallow-water equations, even for a constant-depth ocean with schematic interconnected rectangular basins. A simplified analytical model for cooscillating connected basins also reproduces the principal features observed in the empirical solutions. This simple model is largely kinematic. Zonally averaged elevations within a simple closed basin would be nearly in equilibrium with the gravitational potential, except for a constant offset required to conserve mass. With connected basins these offsets are mostly eliminated by interbasin mass flux. Because of rotation, this flux occurs mostly in a narrow boundary layer across the mouth and at the western edge of each basin, and geostrophic balance in this zone supports small residual offsets (and phase shifts) between basins. The simple model predicts that this effect should decrease roughly linearly with frequency, a result that is confirmed by numerical modeling and empirical T/P estimates of the monthly (Mm) tidal constituent. This model also explains some aspects of the anomalous nonisostatic response of the ocean to atmospheric pressure forcing at periods of around 5 days.

Egbert, Gary D.↗
NASA NTRS2003

Second Law of Thermodynamics Applied to Metabolic Networks

We present a simple algorithm based on linear programming, that combines Kirchoff's flux and potential laws and applies them to metabolic networks to predict thermodynamically feasible reaction fluxes. These law's represent mass conservation and energy feasibility that are widely used in electrical circuit analysis. Formulating the Kirchoff's potential law around a reaction loop in terms of the null space of the stoichiometric matrix leads to a simple representation of the law of entropy that can be readily incorporated into the traditional flux balance analysis without resorting to non-linear optimization. Our technique is new as it can easily check the fluxes got by applying flux balance analysis for thermodynamic feasibility and modify them if they are infeasible so that they satisfy the law of entropy. We illustrate our method by applying it to the network dealing with the central metabolism of Escherichia coli. Due to its simplicity this algorithm will be useful in studying large scale complex metabolic networks in the cell of different organisms.

Nigam, R.↗
NASA NTRS2005

Incorporation of a Chemical Equilibrium Equation of State into LOCI-Chem

Renewed interest in development of advanced high-speed transport, reentry vehicles and propulsion systems has led to a resurgence of research into high speed aerodynamics. As this flow regime is typically dominated by hot reacting gaseous flow, efficient models for the characteristic chemical activity are necessary for accurate and cost effective analysis and design of aerodynamic vehicles that transit this regime. The LOCI-Chem code recently developed by Ed Luke at Mississippi State University for NASA/MSFC and used by NASA/MSFC and SSC represents an important step in providing an accurate, efficient computational tool for the simulation of reacting flows through the use of finite-rate kinetics [3]. Finite rate chemistry however, requires the solution of an additional N-1 species mass conservation equations with source terms involving reaction kinetics that are not fully understood. In the equilibrium limit, where the reaction rates approach infinity, these equations become very stiff. Through the use of the assumption of local chemical equilibrium the set of governing equations is reduced back to the usual gas dynamic equations, and thus requires less computation, while still allowing for the inclusion of reacting flow phenomenology. The incorporation of a chemical equilibrium equation of state module into the LOCI-Chem code was the primary objective of the current research. The major goals of the project were: (1) the development of a chemical equilibrium composition solver, and (2) the incorporation of chemical equilibrium solver into LOCI-Chem. Due to time and resource constraints, code optimization was not considered unless it was important to the proper functioning of the code.

Cox, Carey F.↗
NASA NTRS2005

Journal Bearing Analysis Suite Released for Planetary Gear System Evaluation

Planetary gear systems are an efficient means of achieving high reduction ratios with minimum space and weight. They are used in helicopter, aerospace, automobile, and many industrial applications. High-speed planetary gear systems will have significant dynamic loading and high heat generation. Hence, they need jet lubrication and associated cooling systems. For units operating in critical applications that necessitate high reliability and long life, that have very large torque loading, and that have downtime costs that are significantly greater than the initial cost, hydrodynamic journal bearings are a must. Computational and analytical tools are needed for sufficiently accurate modeling to facilitate optimal design of these systems. Sufficient physics is needed in the model to facilitate parametric studies of design conditions that enable optimal designs. The first transient journal bearing code to implement the Jacobsson-Floberg-Olsson boundary conditions, using a mass-conserving algorithm devised by Professor Emeritus Harold Elrod of Columbia University, was written by David E. Brewe of the U.S. Army at the NASA Lewis Research Center1 in 1983. Since then, new features and improved modifications have been built into the code by several contributors supported through Army and NASA funding via cooperative agreements with the University of Toledo (Professor Ted Keith, Jr., and Dr. Desikakary Vijayaraghavan) and National Research Council Programs (Dr. Vijayaraghavan). All this was conducted with the close consultation of Professor Elrod and the project management of David Brewe.

Brewe, David E.↗
NASA NTRS2006

Accuracy Quantification of the Loci-CHEM Code for Chamber Wall Heat Transfer in a GO2/GH2 Single Element Injector Model Problem

A robust rocket engine combustor design and development process must include tools which can accurately predict the multi-dimensional thermal environments imposed on solid surfaces by the hot combustion products. Currently, empirical methods used in the design process are typically one dimensional and do not adequately account for the heat flux rise rate in the near-injector region of the chamber. Computational Fluid Dynamics holds promise to meet the design tool requirement, but requires accuracy quantification, or validation, before it can be confidently applied in the design process. This effort presents the beginning of such a validation process for the Loci-CHEM CFD code. The model problem examined here is a gaseous oxygen (GO2)/gaseous hydrogen (GH2) shear coaxial single element injector operating at a chamber pressure of 5.42 MPa. The GO2/GH2 propellant combination in this geometry represents one the simplest rocket model problems and is thus foundational to subsequent validation efforts for more complex injectors. Multiple steady state solutions have been produced with Loci-CHEM employing different hybrid grids and two-equation turbulence models. Iterative convergence for each solution is demonstrated via mass conservation, flow variable monitoring at discrete flow field locations as a function of solution iteration and overall residual performance. A baseline hybrid was used and then locally refined to demonstrate grid convergence. Solutions were obtained with three variations of the k-omega turbulence model.

West, Jeff↗
NASA NTRS2006

Transient Flow Dynamics in Optical Micro Well Involving Gas Bubbles

The Lab-On-a-Chip Application Development (LOCAD) team at NASA s Marshall Space Flight Center is utilizing Lab-On-a-Chip to support technology development specifically for Space Exploration. In this paper, we investigate the transient two-phase flow patterns in an optic well configuration with an entrapped bubble through numerical simulation. Specifically, the filling processes of a liquid inside an expanded chamber that has bubbles entrapped. Due to the back flow created by channel expansion, the entrapped bubbles tend to stay stationary at the immediate downstream of the expansion. Due to the huge difference between the gas and liquid densities, mass conservation issues associated with numerical diffusion need to be specially addressed. The results are presented in terms of the movement of the bubble through the optic well. Bubble removal strategies are developed that involve only pressure gradients across the optic well. Results show that for the bubble to be moved through the well, pressure pulsations must be utilized in order to create pressure gradients across the bubble itself.

Johnson, B.↗
NASA NTRS2006

Accuracy Quantification of the Loci-CHEM Code for Chamber Wall Heat Fluxes in a G02/GH2 Single Element Injector Model Problem

A robust rocket engine combustor design and development process must include tools which can accurately predict the multi-dimensional thermal environments imposed on solid surfaces by the hot combustion products. Currently, empirical methods used in the design process are typically one dimensional and do not adequately account for the heat flux rise rate in the near-injector region of the chamber. Computational Fluid Dynamics holds promise to meet the design tool requirement, but requires accuracy quantification, or validation, before it can be confidently applied in the design process. This effort presents the beginning of such a validation process for the Loci- CHEM CPD code. The model problem examined here is a gaseous oxygen (GO2)/gaseous hydrogen (GH2) shear coaxial single element injector operating at a chamber pressure of 5.42 MPa. The GO2/GH2 propellant combination in this geometry represents one the simplest rocket model problems and is thus foundational to subsequent validation efforts for more complex injectors. Multiple steady state solutions have been produced with Loci-CHEM employing different hybrid grids and two-equation turbulence models. Iterative convergence for each solution is demonstrated via mass conservation, flow variable monitoring at discrete flow field locations as a function of solution iteration and overall residual performance. A baseline hybrid grid was used and then locally refined to demonstrate grid convergence. Solutions were also obtained with three variations of the k-omega turbulence model.

West, Jeff↗
NASA NTRS2012

The NEWS Water Cycle Climatology

NASA's Energy and Water Cycle Study (NEWS) program fosters collaborative research towards improved quantification and prediction of water and energy cycle consequences of climate change. In order to measure change, it is first necessary to describe current conditions. The goal of the first phase of the NEWS Water and Energy Cycle Climatology project was to develop "state of the global water cycle" and "state of the global energy cycle" assessments based on data from modern ground and space based observing systems and data integrating models. The project was a multi-institutional collaboration with more than 20 active contributors. This presentation will describe the results of the water cycle component of the first phase of the project, which include seasonal (monthly) climatologies of water fluxes over land, ocean, and atmosphere at continental and ocean basin scales. The requirement of closure of the water budget (i.e., mass conservation) at various scales was exploited to constrain the flux estimates via an optimization approach that will also be described. Further, error assessments were included with the input datasets, and we examine these in relation to inferred uncertainty in the optimized flux estimates in order to gauge our current ability to close the water budget within an expected uncertainty range.

Rodell, Matthew↗
NASA NTRS2013

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

Carpenter, Mark H.↗
NASA NTRS2014

Convective and Diffusive O2 Transport Components of Peak Oxygen Uptake Following Long-duration Spaceflight

Spaceflight reduces aerobic capacity and may be linked with maladaptations in the O2 transport pathway. The aim was to 1) evaluate the cardiorespiratory adaptations following 6 months aboard the International Space Station and 2) model the contributions of convective (Q (raised dot) O2) and peripheral diffusive (DO2) components of O2 transport to changes in peak O2 uptake (V (raised dot) O2PEAK). To date, 1 male astronaut (XX yrs) completed an incremental exercise test to measure V (raised dot) O2PEAK prior to and 2 days post-flight. Cardiac output (Q (raised dot) ) was measured at three submaximal work rates via carbon dioxide rebreathing. The Q (raised dot) :V (raised dot) O2 relationship was extrapolated to V (raised dot) O2PEAK to determine Q (raised dot) PEAK. Hemoglobin concentration was measured at rest via a venous blood sample. These measurements were used to model the changes in Q (raised dot) O2 and DO2 using Fick's principle of mass conservation and Law of Diffusion as established by Wagner and colleagues (Annu. Rev. Physiol 58: 21-50, 1996 and J. Appl. Physiol. 73: 1067-1076, 1992). V (raised dot) O2PEAK decreased postflight from 3.72 to 3.45 l min-1, but Q (raised dot) PEAK increased from 24.5 to 27.7 l min-1. The decrease in V (raised dot) O2PEAK post-flight was associated with a 21.2% decrease in DO2, an 18.6% decrease in O2 extraction, but a 3.4% increase in Q (raised dot) O2. These preliminary data suggest that long-duration spaceflight reduces peripheral diffusing capacity and that it largely contributes to the post-flight decrease in aerobic capacity.

Ade, Carl J.↗
NASA NTRS2015

Entropy Stable Staggered Grid Spectral Collocation for the Burgers' and Compressible Navier-Stokes Equations

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Carpenter, Mark H.↗
NASA NTRS2014

A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

electric propulsion↗