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NASA NTRS2010

Adaptive Numerical Algorithms in Space Weather Modeling

Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics based space weather modeling and even forecasting.

Toth, Gabor↗

NASA NTRS2006

Domed, 40-cm-Diameter Ion Optics for an Ion Thruster

Improved accelerator and screen grids for an ion accelerator have been designed and tested in a continuing effort to increase the sustainable power and thrust at the high end of the accelerator throttling range. The accelerator and screen grids are undergoing development for intended use as NASA s Evolutionary Xenon Thruster (NEXT) a spacecraft thruster that would have an input-power throttling range of 1.2 to 6.9 kW. The improved accelerator and screen grids could also be incorporated into ion accelerators used in such industrial processes as ion implantation and ion milling. NEXT is a successor to the NASA Solar Electric Propulsion Technology Application Readiness (NSTAR) thruster - a state-of-the-art ion thruster characterized by, among other things, a beam-extraction diameter of 28 cm, a span-to-gap ratio (defined as this diameter divided by the distance between the grids) of about 430, and a rated peak input power of 2.3 kW. To enable the NEXT thruster to operate at the required higher peak power, the beam-extraction diameter was increased to 40 cm almost doubling the beam-extraction area over that of NSTAR (see figure). The span-to-gap ratio was increased to 600 to enable throttling to the low end of the required input-power range. The geometry of the apertures in the grids was selected on the basis of experience in the use of grids of similar geometry in the NSTAR thruster. Characteristics of the aperture geometry include a high open-area fraction in the screen grid to reduce discharge losses and a low open-area fraction in the accelerator grid to reduce losses of electrically neutral gas atoms or molecules. The NEXT accelerator grid was made thicker than that of the NSTAR to make more material available for erosion, thereby increasing the service life and, hence, the total impulse. The NEXT grids are made of molybdenum, which was chosen because its combination of high strength and low thermal expansion helps to minimize thermally and inertially induced deflections of the grids. A secondary reason for choosing molybdenum is the availability of a large database for this material. To keep development costs low, the NEXT grids have been fabricated by the same techniques used to fabricate the NSTAR grids. In tests, the NEXT ion optics have been found to outperform the NSTAR ion optics, as expected.

Soulas, George C.↗

NASA NTRS2002

Computational Modeling of Vortex Generators for Turbomachinery

In this work computational models were developed and used to investigate applications of vortex generators (VGs) to turbomachinery. The work was aimed at increasing the efficiency of compressor components designed for the NASA Ultra Efficient Engine Technology (UEET) program. Initial calculations were used to investigate the physical behavior of VGs. A parametric study of the effects of VG height was done using 3-D calculations of isolated VGs. A body force model was developed to simulate the effects of VGs without requiring complicated grids. The model was calibrated using 2-D calculations of the VG vanes and was validated using the 3-D results. Then three applications of VGs to a compressor rotor and stator were investigated: 1) The results of the 3-D calculations were used to simulate the use of small casing VGs used to generate rotor preswirl or counterswirl. Computed performance maps were used to evaluate the effects of VGs. 2) The body force model was used to simulate large part-span splitters on the casing ahead of the stator. Computed loss buckets showed the effects of the VGs. 3) The body force model was also used to investigate the use of tiny VGs on the stator suction surface for controlling secondary flows. Near-surface particle traces and exit loss profiles were used to evaluate the effects of the VGs.

Chima, R. V.↗

NASA NTRS1986

Models for application of radiation boundary condition for MHD waves in collapse calculations

The problem of reflection of magnetohydrodynamic (MHD) waves at the boundary of a numerical grid has to be resolved in order to obtain reliable results for the end state of the (isothermal) collapse of a rotating, magnetic protostellar cloud. Since the goal of investigating magnetic braking in collapse simulations is to see if the transport of angular momentum via alfven waves is large enough to solve the angular momentum problem an approximation that artificially suppresses large amplitudes in the MHD waves can be self-defeating. For this reason, four alternate methods of handling reflected waves where no assumptions are made regarding the amplitudes of the waves were investigated. In order to study this problem (of reflection) without interference from other effects these methods were tried on two simpler cases. The four methods are discussed.

Vanajakshi, C. T.↗

NASA NTRS1994

Evaluating GCM land surface hydrology parameterizations by computing river discharges using a runoff routing model: Application to the Mississippi basin

To relate general circulation model (GCM) hydrologic output to readily available river hydrographic data, a runoff routing scheme that routes gridded runoffs through regional- or continental-scale river drainage basins is developed. By following the basin overland flow paths, the routing model generates river discharge hydrographs that can be compared to observed river discharges, thus allowing an analysis of the GCM representation of monthly, seasonal, and annual water balances over large regions. The runoff routing model consists of two linear reservoirs, a surface reservoir and a groundwater reservoir, which store and transport water. The water transport mechanisms operating within these two reservoirs are differentiated by their time scales; the groundwater reservoir transports water much more slowly than the surface reservior. The groundwater reservior feeds the corresponding surface store, and the surface stores are connected via the river network. The routing model is implemented over the Global Energy and Water Cycle Experiment (GEWEX) Continental-Scale International Project Mississippi River basin on a rectangular grid of 2 deg X 2.5 deg. Two land surface hydrology parameterizations provide the gridded runoff data required to run the runoff routing scheme: the variable infiltration capacity model, and the soil moisture component of the simple biosphere model. These parameterizations are driven with 4 deg X 5 deg gridded climatological potential evapotranspiration and 1979 First Global Atmospheric Research Program (GARP) Global Experiment precipitation. These investigations have quantified the importance of physically realistic soil moisture holding capacities, evaporation parameters, and runoff mechanisms in land surface hydrology formulations.

Liston, G. E.↗

NASA NTRS1995

Surface modeling and grid generation for aeropropulsion CFD

The efforts in geometry modeling and grid generation at the NASA Lewis Research Center, as applied to the computational fluid dynamic (CFD) analysis of aeropropulsion systems, are presented. The efforts are mainly characterized by a focus on the analysis of components of an aeropropulsion system, which involve turbulent viscous flow with heat transfer and chemistry. Thus, this discussion will follow that characterization and will sequence through the components of typical propulsion systems consisting of inlets, compressors, combustors, turbines, and nozzles. For each component, some applications of CFD analysis will be presented to show how CFD is used to compute the desired performance information, how geometry modeling and grid generation are performed, and what issues have developed related to geometry modeling and grid generation. The discussion will illustrate the following needs related to geometry modeling and grid generation as observed in aeropropulsion analysis: (1) accurate and efficient resolution of turbulent viscous and chemically-reacting flowfields; (2) easy-to-use interfaces with CAD data for automated grid generation about complex geometries; and (3) automated batch grid generation software for use with design and optimization software.

Choo, Yung K.↗

NASA NTRSDate not supplied

A NASA GISTEMP Observational Uncertainty Ensemble: Regional and Monthly Uncertainty

The historical global temperature record is an essential data product for quantifying the variability and change of the Earth system. In recent years, better characterization of observational uncertainty in global and hemispheric trends has become available, but the methodologies are not necessarily applicable to analyses at smaller regional areas, or monthly means, where station sparsity and other systematic issues contribute to greater uncertainty. This work details a gridded uncertainty ensemble of historical temperature anomalies from the Goddard Institute for Space Studies (GISS) Surface Temperature product (GISTEMP) product. This ensemble characterizes the complex spatial and temporal correlation structure of uncertainty in gridded historical temperature, enabling proper uncertainty propagation for climate and social science at regional and monthly scales. This work details the methodology for generating the uncertainty ensemble, key statistics of the uncertainty evolution over space and time, and provides best practices for using the uncertainty ensemble in future studies. Summary statistics from the uncertainty ensemble are in good agreement with production GISTEMP. Two applications of the uncertainty ensemble are also presented. First, the warmest year on record is shown to most likely be 2016 with a 53.2% chance and 2020 as the second most likely with a 44.4% chance. Second, it is shown that the arctic is warming 2.5 - 5 times faster than the globe, significantly faster than the regularly quoted twice as fast.

GISTEMP↗

NASA NTRS2016

Annular Ion Engine Concept and Development Status

The Annular Ion Engine (AIE) concept represents an evolutionary development in gridded ion thruster technology with the potential for delivering revolutionary capabilities. It has this potential because the AIE concept: (a) enables scaling of ion thruster technology to high power at specific impulse (Isp) values of interest for near-term mission applications, 5000 sec; and (b) it enables an increase in both thrust density and thrust-to-power (FP) ratio exceeding conventional ion thrusters and other electric propulsion (EP) technology options, thereby yielding the highest performance over a broad range in Isp. The AIE concept represents a natural progression of gridded ion thruster technology beyond the capabilities embodied by NASAs Evolutionary Xenon Thruster (NEXT) [1]. The AIE would be appropriate for: (a) applications which require power levels exceeding NEXTs capabilities (up to about 14 kW [2]), with scalability potentially to 100s of kW; and/or (b) applications which require FP conditions exceeding NEXTs capabilities.

ion engine↗

NASA NTRS1975

Sinter of uniform, predictable, blemish-free nickel plaque for large aerospace nickel cadmium cells

A series of nickel slurry compositions were tested. Important slurry parameters were found to be the nature of the binder, a pore former and the method of mixing. A slow roll mixing which is non-turbulent successfully eliminated entrapped air so that bubbles and pockets were avoided in the sinter. A slurry applicator was developed which enabled an equal quantity of slurry to be applied to both sides of the grid. Sintering in a furnace having a graded atmosphere characteristic, ranging from oxidizing to strongly reducing, improved adhesion of porous sinter to grid and resulted in a uniform welding of nickel particles to each other throughout the plaque. Sintering was carried out in a horizontal furnace having three heating zones and 16 heating control circuits. Tests used for plaque evaluation include (1) appearance, (2) grid location and adhesion, (3) mechanical strength, (4) thickness, (5) weight per unit area, (6) void volume per unit area, (7) surface area and (8) electrical resistance. Plaque material was impregnated using Heliotek proprietary processes and 100 AH cells were fabricated.

Seiger, H. N.↗

NASA NTRS1977

Splines under tension in integral transfer problems

Splines under tension are used to develop an interpolatory representation of integral radiation operators. A quantitative measure of the stability of this representation is derived and approximated in terms of local grid lengths and the tension parameter. Cubic splines (zero tension parameter) are shown to be approximately stable when the ratio of successive grid lengths lies within a specific range. Scaling procedures for determining the tension constant from the structure of the grids and the characteristics of the problem are discussed, and the utility of these procedures is illustrated by application to the formation of resonance lines in two-dimensional media with exponential height variation of opacity.

Jones, H. P.↗

NASA NTRS1983

Some recent applications of XTRAN3S

A time marching finite difference code, XTRAN3S that solves the three dimensional transonic small perturbation equation for flow over isolated wings was developed. During initial applications of the program, problems were encountered in the prediction of unsteady forces. The use of a revised grid and force calculation scheme improved those predictions. Comparisons are made between predicted and experimental pressure data for a rectangular supercritical wing. Comparisons of steady and unsteady data at M sub infinity = 0.700 show good agreement between calculated and experimental values. A comparison of steady data at M sub infinity 0.825 shows poor agreement between calculations and experiment. Program difficulties were encountered with swept and tapered configurations.

Seidel, D. A.↗

NASA NTRS1983

Some recent applications of XTRAN3S

A time-marching finite difference code, XTRAN3S, that solves the three-dimensional transonic small perturbation equation for flow over isolated wings has recently been developed. During initial applications of the program, problems were encountered in the prediction of unsteady forces. The use of a revised grid and force calculation scheme improved those predictions. Comparisons are made between predicted and experimental pressure data for a rectangular supercritical wing. Comparisons of steady and unsteady data at freestream Mach number = 0.700 show good agreement between calculated and experimental values. A comparison of steady data at freestream Mach number = 0.825 shows poor agreement between calculations and experiment. Program difficulties have been encountered with swept and tapered configurations.

Seidel, D. A.↗

NASA NTRS1983

Numerical computation of transonic flow governed by the full-potential equation

Basic concepts associated with the numerical solution of elliptic partial differential equations are introduced, and procedures used to solve the full potential equation for transonic flow fields are discussed. Governing equations, classical relaxation schemes and concepts regarding transonic, full potential equation algorithms are covered. The equation transformation and grid generation procedures; full potential spatial differencing schemes; full potential iteration schemes, emphasizing convergence acceleration; and three dimensional applications are presented.

Holst, T. L.↗

NASA NTRS1989

Euler flutter analysis of airfoils using unstructured dynamic meshes

Modifications to a two-dimensional unsteady Euler code for the aeroelastic analysis of airfoils are described. The modifications involve including the structural equations of motion and their simultaneous time-integration with the governing flow equations. A novel aspect of the capability is that the solutions are obtained using unstructured grids made up of triangles. Comparisons are made with parallel calculations performed using linear theory and a structured grid Euler code to assess the accuracy of the unstructured grid Euler results. Results are presented for a flat plate airfoil and the NACA 0012 airfoil to demonstrate applications of the Euler code for generalized force computations and aeroelastic analysis. In these comparisons, two different finite-volume discretizations of the Euler equations on unstructured meshes were employed. Sensitivity of the Euler results to changes in numerical parameters were also investigated.

Rausch, Russ D.↗

NASA NTRS1993

Virtual zone Navier-Stokes computations for oscillating control surfaces

A new zoning method called 'virtual zones' has been developed for application to an unsteady finite difference Navier-Stokes code. The virtual zoning method simplifies the zoning and gridding of complex configurations for use with patched multi-zone flow codes. An existing interpolation method has been extensively modified to bring the run time for the interpolation procedure down to the same level as for the flow solver. Unsteady Navier-Stokes computations have been performed for transonic flow over a clipped delta wing with an oscillating control surface. The computed unsteady pressure and response characteristics of the control-surface motion compare well with experimental data.

Klopfer, G. H.↗

NASA NTRS1996

Numerical Modeling of Spray Combustion with an Unstructured-Grid Method

The present unstructured-grid method follows strictly the basic finite volume forms of the conservation laws of the governing equations for the entire flow domain. High-order spatially accurate formulation has been employed for the numerical solutions of the Navier-Stokes equations. A two-equation k-epsilon turbulence model is also incorporated in the unstructured-grid solver. The convergence of the resulted linear algebraic equation is accelerated with preconditioned Conjugate Gradient method. A statistical spray combustion model has been incorporated into the present unstructured-grid solver. In this model, spray is represented by discrete particles, rather than by continuous distributions. A finite number of computational particles are used to predict a sample of total population of particles. Particle trajectories are integrated using their momentum and motion equations and particles exchange mass, momentum and energy with the gas within the computational cell in which they are located. The interaction calculations are performed simultaneously and eliminate global iteration for the two-phase momentum exchange. A transient spray flame in a high pressure combustion chamber is predicted and then the solution of liquid-fuel combusting flow with a rotating cup atomizer is presented and compared with the experimental data. The major conclusion of this investigation is that the unstructured-grid method can be employed to study very complicated flow fields of turbulent spray combustion. Grid adaptation can be easily achieved in any flow domain such as droplet evaporation and combustion zone. Future applications of the present model can be found in the full three-dimensional study of flow fields of gas turbine and liquid propulsion engine combustion chambers with multi-injectors.

Shang, H. M.↗

NASA NTRS1998

Low Dissipative High Order Shock-Capturing Methods using Characteristic-Based Filters

An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Olsson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

Yee, H. C.↗

NASA NTRS1998

Low Dissipative High Order Shock-Capturing Methods Using Characteristic-Based Filters

An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Oisson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

Yee, H. C.↗