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NASA NTRS1979

Numerical methods for large-scale, time-dependent partial differential equations

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Turkel, E.↗

NASA NTRS1979

Optimization of multi-layer front-contact grid patterns for solar cells

In a front-contact grid pattern for a solar cell there is a trade-off necessary between shadowing loss and excessive power loss due to voltage drop in the metalization itself. If the metalization is too little there may be excessive contact resistance to the underlying semiconductor and insufficient coverage to control losses in the thin front-surface layer of the solar cell. Optimization of grid pattern area and geometry is considered analytically to minimize total losses. Worthwhile performance advantages are shown to be possible, particularly in concentrator systems, if multi-layer grid patterns are used. The current carrying fingers should be approximately square in metal cross section and the main current feedout bars should not only be wider but also thicker than the primary collecting fingers. This is termed multi-level metalization. Effective use of multi-level grid metalization allows much greater concentration-to-loss ratio for a cell of large area and permits good performance from cells of high front-layer sheet resistance.

Flat, A.↗

NASA NTRS1981

A potential-flow/boundary-layer method for calculating subsonic and transonic airfoil flow with trailing-edge separation

The development of a potential-flow/boundary-layer method for calculating subsonic and transonic turbulent flow past airfoils with trailing-edge separation is reported. A moment-of-momentum integral boundary-layer method is used which employs the law-of-the-wall/law-of-the-wake velocity profile and a two-layer eddy-viscosity model and ignores the laminar sublayer. All integrals across the boundary layer are obtained in closed form. Separation is assumed to occur when the shearing-stress velocity vanishes. A closed-form solution is derived for separated-flow regions where the shearing stress is negligible. In the potential-flow method, the exact form of the airfoil boundary condition is used, but it is applied at the chord line rather than the airfoil surface. This allows the accurate computation of flow about airfoils at large angles of attack but permits the use of body-oriented Cartesian computational grids. The governing equation for the perturbation velocity potential contains several terms in addition to the classical small-disturbance terms.

Barnwell, R. W.↗

NASA NTRS1982

Numerical simulation of wall-bounded turbulent shear flows

Developments in three dimensional, time dependent numerical simulation of turbulent flows bounded by a wall are reviewed. Both direct and large eddy simulation techniques are considered within the same computational framework. The computational spatial grid requirements as dictated by the known structure of turbulent boundary layers are presented. The numerical methods currently in use are reviewed and some of the features of these algorithms, including spatial differencing and accuracy, time advancement, and data management are discussed. A selection of the results of the recent calculations of turbulent channel flow, including the effects of system rotation and transpiration on the flow are included.

Moin, P.↗

NASA NTRS1982

Numerical simulation of wall-bounded turbulent shear flows

Moin, P.↗

NASA NTRS1989

Euler/Navier-Stokes calculations of transonic flow past fixed- and rotary-wing aircraft configurations

Computational fluid dynamics has an increasingly important role in the design and analysis of aircraft as computer hardware becomes faster and algorithms become more efficient. Progress is being made in two directions: more complex and realistic configurations are being treated and algorithms based on higher approximations to the complete Navier-Stokes equations are being developed. The literature indicates that linear panel methods can model detailed, realistic aircraft geometries in flow regimes where this approximation is valid. As algorithms including higher approximations to the Navier-Stokes equations are developed, computer resource requirements increase rapidly. Generation of suitable grids become more difficult and the number of grid points required to resolve flow features of interest increases. Recently, the development of large vector computers has enabled researchers to attempt more complex geometries with Euler and Navier-Stokes algorithms. The results of calculations for transonic flow about a typical transport and fighter wing-body configuration using thin layer Navier-Stokes equations are described along with flow about helicopter rotor blades using both Euler/Navier-Stokes equations.

Deese, J. E.↗

NASA NTRS1994

Atmospheric parameters of field subdwarf B stars

High signal-to-noise ratio optical spectrophotometry of a sample of field subluminous B stars drawn largely from the Palomar Green ultraviolet-excess survey is analyzed with a new grid of model atmospheres and synthetic spectra. The stellar effective temperatures, surface gravities, and photospheric helium abundances are determined simultaneously from a detailed analysis of hydrogen and helium absorption line profiles. The derived temperatures and gravities place the subluminous B stars in the theoroetical Hertzsprung-Russell (H-R) diagram along and bounded below by theoretical sequences of the zero-age extended horizontal branch, lending strong support to the hypothesis that these stars are composed of helium-burning cores of approximately 0.5 solar mass overlain by very thin layers of hydrogen (approximately less than 0.02 solar mass). Various scenarios for their past evolutionary history are examined in the context of their probable future evolution into white dwarfs of lower than average mass.

Saffer, Rex A.↗

NASA NTRS1996

A General Interface Method for Aeroelastic Analysis of Aircraft

The aeroelastic analysis of an aircraft requires an accurate and efficient procedure to couple aerodynamics and structures. The procedure needs an interface method to bridge the gap between the aerodynamic and structural models in order to transform loads and displacements. Such an interface method is described in this report. This interface method transforms loads computed by any aerodynamic code to a structural finite element (FE) model and converts the displacements from the FE model to the aerodynamic model. The approach is based on FE technology in which virtual work is employed to transform the aerodynamic pressures into FE nodal forces. The displacements at the FE nodes are then converted back to aerodynamic grid points on the aircraft surface through the reciprocal theorem in structural engineering. The method allows both high and crude fidelities of both models and does not require an intermediate modeling. In addition, the method performs the conversion of loads and displacements directly between individual aerodynamic grid point and its corresponding structural finite element and, hence, is very efficient for large aircraft models. This report also describes the application of this aero-structure interface method to a simple wing and an MD-90 wing. The results show that the aeroelastic effect is very important. For the simple wing, both linear and nonlinear approaches are used. In the linear approach, the deformation of the structural model is considered small, and the loads from the deformed aerodynamic model are applied to the original geometry of the structure. In the nonlinear approach, the geometry of the structure and its stiffness matrix are updated in every iteration and the increments of loads from the previous iteration are applied to the new structural geometry in order to compute the displacement increments. Additional studies to apply the aero-structure interaction procedure to more complicated geometry will be conducted in the second phase of the present contract.

Tzong, T.↗

NASA NTRS2004

A Study of the Response of Deep Tropical Clouds to Mesoscale Processes: Sensitivities to Microphysics, Radiation, and Surface Fluxes - Part 2

The Goddard Cumulus Ensemble (GCE) model is used to examine the sensitivities of surface fluxes, explicit radiation, and ice microphysical processes on multi-day simulations of deep tropical convection over the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE). The simulations incorporate large-scale advective temperature and moisture forcing, as well as large-scale momentum, that are updated every time step on a periodic lateral boundary grid. This study shows that when surface fluxes are eliminated, the mean atmosphere is much cooler and drier, convection and CAPE are much weaker, precipitation is less, and cloud coverage in stratiform regions much greater. Surface fluxes using the TOGA COARE flux algorithm are weaker than with the aerodynamic formulation, but closer to the observed fluxes. In addition, similar trends noted above for the case without surface fluxes are produced for the TOGA flux case, albeit to a much lesser extent. The elimination of explicit shortwave and longwave radiation is found to have only minimal effects on the mean thermodynamics, convection, and precipitation. However explicit radiation does have a significant impact on cloud temperatures and structure above 200 mb and on the overall mean vertical circulation. The removal of ice processes produces major changes in the structure of the cloud. Much of the liquid water is transported aloft and into anvils above the melting layer (600 mb), leaving narrow, but intense bands of rainfall in convective regions. The elimination of melting processes leads to greater hydrometeor mass below the melting layer, and produces a much warmer and moister boundary layer, leading to a greater mean CAPE. Finally, the elimination of the graupel species has only a small impact on mean total precipitation, thermodynamics, and dynamics of the simulation, but does produce much greater snow mass just above the melting layer. Some of these results differ from previous CRM studies of tropical systems, which is likely due to the type of simulated system, total time integration, and model setup.

Johnson, Daniel↗

NASA NTRS2013

Path Forward to Space Solar Power using the O'Neill - Glaser Model Modified for Climate Change Demand and Considering the Increasing Risk of Human Self-Extinction if Confined to Earth

The cost of energy is humanity's economic exchange rate with the universe. Space solar power is the first great step that our technological species has to utilize the energy of its star. The classic Peter Glaser Solar Power Satellite, SPS, and later designs collect a large area of solar energy in space and beam it back to Earth for use in the electric grid, but even with optimistic launch costs and technology innovation a clear economic path is not evident using Earth launch of SPS. O Neill in 1969 solved the transportation costs problem by a model that uses lunar and asteroid materials to build SPS and locates the labor force permanently in space (O Neill free space habitats). This solution closes the economics and predicts large profits after 17-35 years. However the costs of time have up to now prevented this solution. We discuss a strategy to move forward in SPS with the motivations to stop global warming and prevent human selfextinction. There are near term steps that can be taken that place us on this path forward. First, we must reevaluate the technologies for the classic model and update the parameters to current technology. As technological capability continues to increase exponentially, we need to understand when the monetary potential energy hills are small as the technology gets larger. But the chance for self-extinction, if humanity remains in a single vulnerable habitat, also increased exponentially with time. The path forward is to identify investment points while assessing the risks of non-action.

Curreri, Peter A.↗

NASA NTRS2013

Forecasting Propagation and Evolution of CMEs in an Operational Setting: What Has Been Learned

One of the major types of solar eruption, coronal mass ejections (CMEs) not only impact space weather, but also can have significant societal consequences. CMEs cause intense geomagnetic storms and drive fast mode shocks that accelerate charged particles, potentially resulting in enhanced radiation levels both in ions and electrons. Human and technological assets in space can be endangered as a result. CMEs are also the major contributor to generating large amplitude Geomagnetically Induced Currents (GICs), which are a source of concern for power grid safety. Due to their space weather significance, forecasting the evolution and impacts of CMEs has become a much desired capability for space weather operations worldwide. Based on our operational experience at Space Weather Research Center at NASA Goddard Space Flight Center (http://swrc.gsfc.nasa.gov), we present here some of the insights gained about accurately predicting CME impacts, particularly in relation to space weather operations. These include: 1. The need to maximize information to get an accurate handle of three-dimensional (3-D) CME kinetic parameters and therefore improve CME forecast; 2. The potential use of CME simulation results for qualitative prediction of regions of space where solar energetic particles (SEPs) may be found; 3. The need to include all CMEs occurring within a ~24 h period for a better representation of the CME interactions; 4. Various other important parameters in forecasting CME evolution in interplanetary space, with special emphasis on the CME propagation direction. It is noted that a future direction for our CME forecasting is to employ the ensemble modeling approach.

forecasting↗

NASA NTRS2024

Regimes of Cloud Vertical Structure From Active Observations

We introduce a new type of cloud class, which we call “active cloud regime” (ACR), owing to its provenance from active (lidar and cloud radar) spaceborne cloud observations. ACRs intend to provide a climatological description based on cloud vertical structure (CVS) of the most prevalent monthly CVS mixtures encountered at large spatial scales of ~400 km. ACRs are thus a way to create a gridded dataset of a vertically-resolved cloud mask that can facilitate joint analysis with other gridded datasets. The detailed 2D cloud mask comes from the 2B-CLDCLASS-LIDAR CloudSat dataset fusing CALIPSO (lidar) and CloudSat (cloud radar) cloud detections. We show that the global classification of cloudiness under the ACR framework provides valuable insights on how the world’s dominant cloud systems regulate the two major components of atmospheric energetics, precipitation and radiative cooling. NASA’s GEOS model allows us to demonstrate the feasibility of applying the ACR concept in Earth System Models that have the capability to produce subgrid cloudiness obeying pre-specified vertical overlap rules. Comparison of observed and simulated ACRs provides thus another means to assess the realism of modeled clouds.

cloud vertical structure↗

NASA NTRS1994

Large Eddy simulation of turbulence: A subgrid scale model including shear, vorticity, rotation, and buoyancy

The Reynolds numbers that characterize geophysical and astrophysical turbulence (Re approximately equals 10(exp 8) for the planetary boundary layer and Re approximately equals 10(exp 14) for the Sun's interior) are too large to allow a direct numerical simulation (DNS) of the fundamental Navier-Stokes and temperature equations. In fact, the spatial number of grid points N approximately Re(exp 9/4) exceeds the computational capability of today's supercomputers. Alternative treatments are the ensemble-time average approach, and/or the volume average approach. Since the first method (Reynolds stress approach) is largely analytical, the resulting turbulence equations entail manageable computational requirements and can thus be linked to a stellar evolutionary code or, in the geophysical case, to general circulation models. In the volume average approach, one carries out a large eddy simulation (LES) which resolves numerically the largest scales, while the unresolved scales must be treated theoretically with a subgrid scale model (SGS). Contrary to the ensemble average approach, the LES+SGS approach has considerable computational requirements. Even if this prevents (for the time being) a LES+SGS model to be linked to stellar or geophysical codes, it is still of the greatest relevance as an 'experimental tool' to be used, inter alia, to improve the parameterizations needed in the ensemble average approach. Such a methodology has been successfully adopted in studies of the convective planetary boundary layer. Experienc e with the LES+SGS approach from different fields has shown that its reliability depends on the healthiness of the SGS model for numerical stability as well as for physical completeness. At present, the most widely used SGS model, the Smagorinsky model, accounts for the effect of the shear induced by the large resolved scales on the unresolved scales but does not account for the effects of buoyancy, anisotropy, rotation, and stable stratification. The latter phenomenon, which affects both geophysical and astrophysical turbulence (e.g., oceanic structure and convective overshooting in stars), has been singularly difficult to account for in turbulence modeling. For example, the widely used model of Deardorff has not been confirmed by recent LES results. As of today, there is no SGS model capable of incorporating buoyancy, rotation, shear, anistropy, and stable stratification (gravity waves). In this paper, we construct such a model which we call CM (complete model). We also present a hierarchy of simpler algebraic models (called AM) of varying complexity. Finally, we present a set of models which are simplified even further (called SM), the simplest of which is the Smagorinsky-Lilly model. The incorporation of these models into the presently available LES codes should begin with the SM, to be followed by the AM and finally by the CM.

Canuto, V. M.↗

NASA NTRS2001

The Sensitivity of West African Squall Line Water Budgets to Land Cover

This study used a two-dimensional coupled land/atmosphere (cloud-resolving) model to investigate the influence of land cover on the water budgets of squall lines in the Sahel. Study simulations used the same initial sounding and one of three different land covers, a sparsely vegetated semi-desert, a grassy savanna, and a dense evergreen broadleaf forest. All simulations began at midnight and ran for 24 hours to capture a full diurnal cycle. In the morning, the latent heat flux, boundary layer mixing ratio, and moist static energy in the boundary layer exhibited notable variations among the three land covers. The broadleaf forest had the highest latent heat flux, the shallowest, moistest, slowest growing boundary layer, and significantly more moist static energy per unit area than the savanna and semi-desert. Although all simulations produced squall lines by early afternoon, the broadleaf forest had the most intense, longest-lived squall lines with 29% more rainfall than the savanna and 37% more than the semi-desert. The sensitivity of the results to vegetation density, initial sounding humidity, and grid resolution was also assessed. There were greater differences in rainfall among land cover types than among simulations of the same land cover with varying amounts of vegetation. Small changes in humidity were equivalent in effect to large changes in land cover, producing large changes in the condensate and rainfall. Decreasing the humidity had a greater effect on rainfall volume than increasing the humidity. Reducing the grid resolution from 1.5 km to 0.5 km decreased the temperature and humidity of the cold pools and increased the rain volume.

Mohr, Karen I.↗

NASA NTRS2004

Validation of EOS Aqua AMSR Sea Ice Products for East Antarctica

This paper presents results from AMSR-E validation activities during a collaborative international cruise onboard the RV Aurora Australis to the East Antarctic sea ice zone (64-65 deg.S, 110-120 deg.E) in the early Austral spring of 2003. The validation strategy entailed an IS-day survey of the statistical characteristics of sea ice and snowcover over a Lagrangian grid 100 x 50 km in size (demarcated by 9 drifting ice beacons) i.e. at a scale representative of Ah4SR pixels. Ice conditions ranged h m consolidated first-year ice to a large polynya offshore from Casey Base. Data sets collected include: snow depth and snow-ice interface temperatures on 24 (?) randomly-selected floes in grid cells within a 10 x 50 km area (using helicopters); detailed snow and ice measurements at 13 dedicated ice stations, one of which lasted for 4 days; time-series measurements of snow temperature and thickness at selected sites; 8 aerial photography and thermal-IR radiometer flights; other satellite products (SAR, AVHRR, MODIS, MISR, ASTER and Envisat MERIS); ice drift data; and ancillary meteorological (ship-based, meteorological buoys, twice-daily radiosondes). These data are applied to a validation of standard AMSR-E ice concentration, snowcover thickness and ice-temperature products. In addition, a validation is carried out of ice-surface skin temperature products h m the NOAA AVHRR and EOS MODIS datasets.

Massom, Rob↗

NASA NTRS1995

Euler Technology Assessment program for preliminary aircraft design employing SPLITFLOW code with Cartesian unstructured grid method

This report documents results from the Euler Technology Assessment program. The objective was to evaluate the efficacy of Euler computational fluid dynamics (CFD) codes for use in preliminary aircraft design. Both the accuracy of the predictions and the rapidity of calculations were to be assessed. This portion of the study was conducted by Lockheed Fort Worth Company, using a recently developed in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages for this study, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaptation of the volume grid during the solution convergence to resolve high-gradient flow regions. This proved beneficial in resolving the large vortical structures in the flow for several configurations examined in the present study. The SPLITFLOW code predictions of the configuration forces and moments are shown to be adequate for preliminary design analysis, including predictions of sideslip effects and the effects of geometry variations at low and high angles of attack. The time required to generate the results from initial surface definition is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.

Finley, Dennis B.↗

NASA NTRS1991

A method for interactive specification of multiple-block topologies

A method is presented for dealing with the vast amount of topological and other data which must be specified to generate a multiple-block computational grid. Specific uses of the graphical capabilities of a powerful scientific workstation are described which reduce the burden on the user of collecting and formatting such large amounts of data. A program to implement this method, 3DPREP, is described. A plotting transformation algorithm, some useful software tools, notes on programming, and a database organization are also presented. Example grids developed using the method are shown.

Sorenson, Reese L.↗

NASA NTRS1985

Three-dimensional inviscid analysis of radial turbine flow and a limited comparison with experimental data

The three-dimensional inviscid DENTON code is used to analyze flow through a radial-inflow turbine rotor. Experimental data from the rotor are compared with analytical results obtained by using the code. The experimental data available for comparison are the radial distributions of circumferentially averaged values of absolute flow angle and total pressure downstream of the rotor exit. The computed rotor-exit flow angles are generally underturned relative to the experimental values, which reflect the boundary-layer separation at the trailing edge and the development of wakes downstream of the rotor. The experimental rotor is designed for a higher-than-optimum work factor of 1.126 resulting in a nonoptimum positive incidence and causing a region of rapid flow adjustment and large velocity gradients. For this experimental rotor, the computed radial distribution of rotor-exit to turbine-inlet total pressure ratios are underpredicted due to the errors in the finite-difference approximations in the regions of rapid flow adjustment, and due to using the relatively coarser grids in the middle of the blade region where the flow passage is highly three-dimensional. Additional results obtained from the three-dimensional inviscid computation are also presented, but without comparison due to the lack of experimental data. These include quasi-secondary velocity vectors on cross-channel surfaces, velocity components on the meridional and blade-to-blade surfaces, and blade surface loading diagrams. Computed results show the evolution of a passage vortex and large streamline deviations from the computational streamwise grid lines. Experience gained from applying the code to a radial turbine geometry is also discussed.

Choo, Y. K.↗