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At least 145 records · Page 8

Gas Generator Feedline Orifice Sizing Methodology: Effects of Unsteadiness and Non-Axisymmetric Flow

Engine LH2 and LO2 gas generator feed assemblies were modeled with computational fluid dynamics (CFD) methods at 100% rated power level, using on-center square- and round-edge orifices. The purpose of the orifices is to regulate the flow of fuel and oxidizer to the gas generator, enabling optimal power supply to the turbine and pump assemblies. The unsteady Reynolds-Averaged Navier-Stokes equations were solved on unstructured grids at second-order spatial and temporal accuracy. The LO2 model was validated against published experimental data and semi-empirical relationships for thin-plate orifices over a range of Reynolds numbers. Predictions for the LO2 square- and round-edge orifices precisely match experiment and semi-empirical formulas, despite complex feedline geometry whereby a portion of the flow from the engine main feedlines travels at a right-angle through a smaller-diameter pipe containing the orifice. Predictions for LH2 square- and round-edge orifice designs match experiment and semi-empirical formulas to varying degrees depending on the semi-empirical formula being evaluated. LO2 mass flow rate through the square-edge orifice is predicted to be 25 percent less than the flow rate budgeted in the original engine balance, which was subsequently modified. LH2 mass flow rate through the square-edge orifice is predicted to be 5 percent greater than the flow rate budgeted in the engine balance. Since CFD predictions for LO2 and LH2 square-edge orifice pressure loss coefficients, K, both agree with published data, the equation for K has been used to define a procedure for orifice sizing.

Rothermel, Jeffry↗

Delineation of vulnerable areas to water erosion in a mountain region using SDR-InVEST model: A case study of the Ourika watershed, Morocco

The Ourika watershed is characterized by higher than average flood flows, a rugged topography, a sparse vegetation cover and a friable substrate that makes it vulnerable to soil erosion. Soil is an important non-renewable asset capital, providing several ecosystem services that sustain life through physical and biological regulation processes. The loss, or otherwise, redistribution of biota by soil erosion in the Ourika watershed has received little attention and thus constitutes a key knowledge gap that needs to be addressed. This study quantifies the level of erosion and maps its spatial distribution in the watershed using the Sediment Delivery Ratio (SDR) of the Integrated Valuation of Ecosystem Services and Tradeoffs model (InVEST3.6.0). The SDR maps the overland sediment generation and delivery to the stream at the watershed level using rainfall, soil properties, topography, cover management and cropping practices as predefined set of input variables. Recommended internal model calibration was used and results were compared to similar studies carried out in different parts of Morocco for validation. The results reveal that 93% of the watershed is subject to a strong rainfall aggressiveness greater than 50 MJ mm ha–1 h–1 yr1 under an average rainfall intensity of 541 mm/year, rainfall capacity to initiate the detachment and transport of soil particles by runoff, and only 11.5% of the watershed area is protected with vegetative cover. We find that overall, the Ourika watershed is losing its soil to erosion at an alarming average rate of 258.48 ton.ha–1.yr–1, a rate well above the tolerable threshold of 7ton.ha–1.yr–1. The spatial distribution of this loss shows areas that need to be urgently remedied. The primary factors for soil erosion in the Ourika watershed appear to be related to the aggressive nature of local rainfall and the inherent susceptibility of soils, which can be costly to this cash-crop region. Because rainfall intensity, soil properties, and topography are intrinsic characteristics of the watershed, we suggest that seasonally adapted cropping rotations that maintains conservative practices with a high cover management may reduce soil erosion in the Ourika watershed.

Erosion↗

A space-time stochastic model of rainfall for satellite remote-sensing studies

A model of the spatial and temporal distribution of rainfall is described that produces random spatial rainfall patterns with these characteristics: (1) the model is defined on a grid with each grid point representing the average rain rate over the surrounding grid box, (2) rain occurs at any one grid point, on average, a specified percentage of the time and has a lognormal probability distribution, (3) spatial correlation of the rainfall can be arbitrarily prescribed, and (4) time stepping is carried out so that large-scale features persist longer than small-scale features. Rain is generated in the model from the portion of a correlated Gaussian random field that exceeds a threshold. The portion of the field above the threshold is rescaled to have a lognormal probability distribution. Sample output of the model designed to mimic radar observations of rainfall during the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE), is shown. The model is intended for use in evaluating sampling strategies for satellite remote-sensing of rainfall and for development of algorithms for converting radiant intensity received by an instrument from its field of view into rainfall amount.

Bell, Thomas L.↗

Reflectance-Based Sensor Validation Over Ice Surfaces

During this period work was performed in the following areas. These areas are defined in the Work Schedule presented in the original proposal: BRDF development, Data acquisition and processing, THR Table generation and Presentations and Publications. BRDF development involves creating and/or modifying a reflectance model of the Antarctic surface. This model must, for a temporal and spatial average, be representative of the East Antarctic plateau and be expressed in terms of the three standard surface angles: solar zenith angle (SolZA), view zenith angle (SatZA), and relative azimuth angle (RelAZ). We successfully acquired a limited amount of NOAA-9 AVHRR data for radiance validation. The data were obtained from the Laboratory for Terrestrial Physics at Goddard Space Flight Center. We developed our own reading and unpacking software, which we used to select Channel 1 data (visible). We then applied geographic subsetting criteria (same as used for TOMS), and wrote only the relevant data to packed binary files. We proceeded with analysis of these data, which is not yet complete.

Jaross, Glen↗

The Characterization of a DIRSIG Simulation Environment to Support the Inter-Calibration of Spaceborne Sensors

Climate change studies require long-term, continuous records that extend beyond the lifetime, and the temporal resolution, of a single remote sensing satellite sensor. The inter-calibration of spaceborne sensors is therefore desired to provide spatially, spectrally, and temporally homogeneous datasets. The Digital Imaging and Remote Sensing Image Generation (DIRSIG) tool is a first principle-based synthetic image generation model that has the potential to characterize the parameters that impact the accuracy of the inter-calibration of spaceborne sensors. To demonstrate the potential utility of the model, we compare the radiance observed in real image data to the radiance observed in simulated image from DIRSIG. In the present work, a synthetic landscape of the Algodones Sand Dunes System is created. The terrain is facetized using a 2-meter digital elevation model generated from NASA Goddard's LiDAR, Hyperspectral, and Thermal (G-LiHT) imager. The material spectra are assigned using hyperspectral measurements of sand collected from the Algodones Sand Dunes System. Lastly, the bidirectional reflectance distribution function (BRDF) properties are assigned to the modeled terrain using the Moderate Resolution Imaging Spectroradiometer (MODIS) BRDF product in conjunction with DIRSIG's Ross-Li capability. The results of this work indicate that DIRSIG is in good agreement with real image data. The potential sources of residual error are identified and the possibilities for future work are discussed..

Ambeau, Brittany L.↗

Carrier generation, recombination, trapping, and transport in semiconductors with position-dependent composition

The spatial variation of the chemical composition of a semiconductor modifies the ideal one-electron energy band model as well as the Shockley equations for carrier recombination and transport in two important ways. The random component of the spatial variation introduces localized states in the energy gap by perturbing the band states. The nonrandom component gives rise to the position dependences of the conduction and valence band edges or the electron affinity and the energy gap. This paper gives the modifications of the Shockley equations from these two effects as well as an example of the steady-state recombination rate from distributed gap states in junction solar cells

Sah, C.-T.↗

Stationary auroral current oscillations resulting from the magnetospheric generator

The origin of the steady state spatial current oscillations in the auroral field-aligned currents, which was detected in the measurements by the two Dynamics Explorer (DE) satellites DE 1 and DE 2, is explained in the framework of a simple steady state model of the magnetosphere-ionosphere current system. The model has only three parameters, including the magnetic-field-aligned conductivity, the ionospheric height-integrated Pedersen conductivity, and the conductivity of a generator or dynamo at the magnetospheric equator. Good agreement between this model and the measurements from the DE satellites was obtained.

Weimer, D. R.↗

Flow Characterization of the NASA Langley Unitary Plan Wind Tunnel, Test Section 2: Computational Results

This is an abstract for an invited paper at the AIAA Aviation Conference, June 2021. The work described here is part of an effort of coordinated experiments in the Unitary Plan Wind Tunnel (UPWT) facility at the NASA Langley Research Center (LaRC) and matching CFD simulations. The primary goal of the work is to assess the productivity and true predictive accuracy of CFD, absent any guidance from experiment, in the high supersonic speed range as compared to experiments performed at the NASA LaRC’s UPWT facility. This report concerns CFD simulation of the primary flow-path in the empty wind tunnel, including the settling chamber, nozzle, test section, and some of the tunnel downstream of the test section. The Mach number in the test section ranges from M~2.4 to M~4.6, and the required area ratio variation is achieved by translation of a nozzle block which constricts the area of a loosely S-shaped throat. Flow past protuberances in the settling chamber and into this S-bend throat are predicted by CFD to generate streamwise vorticity that may, or may not, persist through the throat and into the test section as coherent vortices. Some flow conditions are notably unsteady at frequencies well below those of turbulence, due to unsteady separated flow ahead of the nozzle block. The bulk flow moves at velocities ranging from 'walking speed' in the settling chamber to M~4.6 in the test section. Heat transfer to the settling chamber walls and buoyancy are significant at high Mach number. Subtle variations in surface curvature in the nozzle generate Mach waves that propagate into the test section. CFD of the empty tunnel serves two purposes. Firstly, the full-tunnel simulations are used to provide upstream boundary conditions for CFD of vehicle aerodynamics which are generally performed in a domain confined to the wind tunnel test section; these companion studies are addressed in other papers. Secondly, it is a challenging test for CFD to resolve all of the empty tunnel flow phenomena relevant to flow in the test section. It requires a more complete definition of geometry than was originally anticipated. In addition, it requires good spatial and temporal accuracy, and turbulence modeling that performs well on specific phenomena such as corner flows. The boundary conditions and solution algorithms must perform well from incompressible to almost hypersonic speeds. The final state of the pre-test CFD was a product of an iterative self-improvement process. The initial simulations of the empty tunnel were deficient in many respects, but hints to those deficiencies were recognized in the solutions, and remedies were implemented. Possible further improvements will be studied in the post-test phase when comparisons with experimental data are possible. The CFD was performed by five separate collaborative teams using four different flow solvers: FUN3D, Overflow, Star-CCM+ and USM3D. The level of effort of these teams varied significantly, but each made important contributions to the goals of the work. A concerted effort to use uncertainty quantification methods (UQ) in CFD is also a goal of this work. To this end, variations in CFD results due to grid refinement, turbulence modeling, and boundary conditions have been characterized. Code-to-code variation is another means of assessing CFD uncertainty. All CFD solvers predict similarity among the primary flow features; these include the variation of Mach number due to changes in Reynolds number, and the bulk flow angularity due to tunnel-wall curvature. All CFD solvers also predict similar trends in secondary flows, such as the downwash in the side-wall boundary layers. Three of the high-spatial resolution simulations give similar predictions of a complex secondary flow phenomena, streamwise vortices generated in the S-bend throat that persist into the side-wall boundary layers of the test section. Two of the highest-resolution simulations, run with the same turbulence model in different CFD solvers, gave encouragingly similar predictions of a complex tertiary flow phenomenon, small transient "sprites" of upwash flows, resulting from vortices that presumably originate in the separated flow near the leading edge of the nozzle block. While the CFD was done in a "blind pre-test" mode, requests from the experimental team for CFD results pertaining to unsteadiness and total temperature variations in the test section resulted in CFD runs that included a cooled wall in settling chamber. This then led to a change in the standard practice for running the Overflow results, which would not have occurred without this "release" of this experimental information. CFD was also used to guide some measurements. The paper will focus on establishing the consensus among CFD results and understanding differences among those results. Initial findings from the efforts to characterize CFD uncertainty have been done and will be included in the paper.

Robert Edward Childs↗

Linear mixing model applied to coarse spatial resolution data from multispectral satellite sensors

A linear mixing model was applied to coarse spatial resolution data from the NOAA Advanced Very High Resolution Radiometer. The reflective component of the 3.55-3.95 micron channel was used with the two reflective channels 0.58-0.68 micron and 0.725-1.1 micron to run a constrained least squares model to generate fraction images for an area in the west central region of Brazil. The fraction images were compared with an unsupervised classification derived from Landsat TM data acquired on the same day. The relationship between the fraction images and normalized difference vegetation index images show the potential of the unmixing techniques when using coarse spatial resolution data for global studies.

Holben, Brent N.↗

Radiative Importance of Aerosol-Cloud Interaction

Aerosol particles are input into the troposphere by biomass burning, among other sources. These aerosol palls cover large expanses of the earth's surface. Aerosols may directly scatter solar radiation back to space, thus increasing the earth's albedo and act to cool the earth's surface and atmosphere. Aerosols also contribute to the earth's energy balance indirectly. Hygroscopic aerosol act as cloud condensation nuclei (CCN) and thus affects cloud properties. In 1977, Twomey theorized that additional available CCN would create smaller but more numerous cloud droplets in a cloud with a given amount of liquid water. This in turn would increase the cloud albedo which would scatter additional radiation back to space and create a similar cooling pattern as the direct aerosol effect. Estimates of the magnitude of the aerosol indirect effect on a global scale range from 0.0 to -4.8 W/sq m. Thus the indirect effect can be of comparable magnitude and opposite in sign to the estimates of global greenhouse gas forcing Aerosol-cloud interaction is not a one-way process. Just as aerosols have an influence on clouds through the cloud microphysics, clouds have an influence on aerosols. Cloud droplets are solutions of liquid water and CCN, now dissolved. When the cloud droplet evaporates it leaves behind an aerosol particle. This new particle does not have to have the same properties as the original CCN. In fact, studies show that aerosol particles that result from cloud processing are larger in size than the original CCN. Optical properties of aerosol particles are dependent on the size of the particles. Larger particles have a smaller backscattering fraction, and thus less incoming solar radiation will be backscattered to space if the aerosol particles are larger. Therefore, we see that aerosols and clouds modify each other to influence the radiative balance of the earth. Understanding and quantifying the spatial and seasonal patterns of the aerosol indirect forcing may have even greater consequences. Presently we know that through the use of fossil fuel and land-use changes we have increased the concentration of greenhouse gases in the atmosphere. In parallel, we have seen a modest increase of global temperature in the last century. These two observations have been linked as cause and effect by climate models, but this connection is still experimentally not verified. The spatial and seasonal distribution of aerosol forcing is different from that of greenhouse gases, thus generating a different spatial fingerprint of climate change. This fingerprint was suggested as a method to identify the response of the climate system to anthropogenic forcing of greenhouse gases and aerosol. The aerosol fingerprint may be the only way to firmly establish the presence (or absence) of human impact on climate. Aerosol-cloud interaction through the indirect effect will be an important component of establishing this fingerprint.

Tsay, Si-Chee↗

Dynamic Hurricane Data Analysis Tool

A dynamic hurricane data analysis tool allows users of the JPL Tropical Cyclone Information System (TCIS) to analyze data over a Web medium. The TCIS software is described in the previous article, Tropical Cyclone Information System (TCIS) (NPO-45748). This tool interfaces with the TCIS database to pull in data from several different atmospheric and oceanic data sets, both observed by instruments. Users can use this information to generate histograms, maps, and profile plots for specific storms. The tool also displays statistical values for the user-selected parameter for the mean, standard deviation, median, minimum, and maximum values. There is little wait time, allowing for fast data plots over date and spatial ranges. Users may also zoom-in for a closer look at a particular spatial range. This is version 1 of the software. Researchers will use the data and tools on the TCIS to understand hurricane processes, improve hurricane forecast models and identify what types of measurements the next generation of instruments will need to collect.

Knosp, Brian W.↗

Understanding Climate Policy Data Needs. NASA Carbon Monitoring System Briefing: Characterizing Flux Uncertainty, Washington D.C., 11 January 2012

Climate policy in the United States is currently guided by public-private partnerships and actions at the local and state levels. This mitigation strategy is made up of programs that focus on energy efficiency, renewable energy, agricultural practices and implementation of technologies to reduce greenhouse gases. How will policy makers know if these strategies are working, particularly at the scales at which they are being implemented? The NASA Carbon Monitoring System (CMS) will provide information on carbon dioxide fluxes derived from observations of earth's land, ocean and atmosphere used in state of the art models describing their interactions. This new modeling system could be used to assess the impact of specific policy interventions on CO2 reductions, enabling an iterative, results-oriented policy process. In January of 2012, the CMS team held a meeting with carbon policy and decision makers in Washington DC to describe the developing modeling system to policy makers. The NASA CMS will develop pilot studies to provide information across a range of spatial scales, consider carbon storage in biomass, and improve measures of the atmospheric distribution of carbon dioxide. The pilot involves multiple institutions (four NASA centers as well as several universities) and over 20 scientists in its work. This pilot study will generate CO2 flux maps for two years using observational constraints in NASA's state-of -the-art models. Bottom-up surface flux estimates will be computed using data-constrained land and ocean models; comparison of the different techniques will provide some knowledge of uncertainty in these estimates. Ensembles of atmospheric carbon distributions will be computed using an atmospheric general circulation model (GEOS-5), with perturbations to the surface fluxes and to transport. Top-down flux estimates will be computed from observed atmospheric CO2 distributions (ACOS/GOSAT retrievals) alongside the forward-model fields, in conjunction with an inverse approach based on the CO2 model of GEOS ]Chem. The forward model ensembles will be used to build understanding of relationships among surface flux perturbations, transport uncertainty and atmospheric carbon concentration. This will help construct uncertainty estimates and information on the true spatial resolution of the top-down flux calculations. The relationship between the top-down and bottom-up flux distributions will be documented. Because the goal of NASA CMS is to be policy relevant, the scientists involved in the flux modeling pilot need to understand and be focused on the needs of the climate policy and decision making community. If policy makers are to use CMS products, they must be aware of the modeling effort and begin to design policies that can be evaluated with information. Improving estimates of carbon sequestered in forests, for example, will require information on the spatial variability of forest biomass that is far more explicit than is presently possible using only ground observations. Carbon mitigation policies being implemented by cities around the United States could be designed with the CMS data in mind, enabling sequential evaluation and subsequent improvements in incentives, structures and programs. The success of climate mitigation programs being implemented in the United States today will hang on the depth of the relationship between scientists and their policy and decision making counterparts. Ensuring that there is two-way communication between data providers and users is important for the success both of the policies and the scientific products meant to support them..

Brown, Molly E.↗

Photogrammetry Measurements During a Tanking Test on the Space Shuttle External Tank, ET-137

On November 5, 2010, a significant foam liberation threat was observed as the Space Shuttle STS-133 launch effort was scrubbed because of a hydrogen leak at the ground umbilical carrier plate. Further investigation revealed the presence of multiple cracks at the tops of stringers in the intertank region of the Space Shuttle External Tank. As part of an instrumented tanking test conducted on December 17, 2010, a three dimensional digital image correlation photogrammetry system was used to measure radial deflections and overall deformations of a section of the intertank region. This paper will describe the experimental challenges that were overcome in order to implement the photogrammetry measurements for the tanking test in support of STS-133. The technique consisted of configuring and installing two pairs of custom stereo camera bars containing calibrated cameras on the 215-ft level of the fixed service structure of Launch Pad 39-A. The cameras were remotely operated from the Launch Control Center 3.5 miles away during the 8 hour duration test, which began before sunrise and lasted through sunset. The complete deformation time history was successfully computed from the acquired images and would prove to play a crucial role in the computer modeling validation efforts supporting the successful completion of the root cause analysis of the cracked stringer problem by the Space Shuttle Program. The resulting data generated included full field fringe plots, data extraction time history analysis, section line spatial analyses and differential stringer peak ]valley motion. Some of the sample results are included with discussion. The resulting data showed that new stringer crack formation did not occur for the panel examined, and that large amounts of displacement in the external tank occurred because of the loads derived from its filling. The measurements acquired were also used to validate computer modeling efforts completed by NASA Marshall Space Flight Center (MSFC).

Littell, Justin D.↗

Spherical harmonic analysis of a model-generated climatology

Monthly mean fields of 850 mb temperature (T850), 500 mb geopotential height (G500) and sea level pressure (SLP) were generated in the course of a five-year climate simulation run with a global general circulation model. Both the model-generated climatology and an observed climatology were subjected to spherical harmonic analysis, with separate analyses of the globe and the Northern Hemisphere. Comparison of the dominant harmonics of the two climatologies indicates that more than 95% of the area-weighted spatial variance of G500 and more than 90% of that of T850 are explained by fewer than three components, and that the model adequately simulates these large-scale characteristics. On the other hand, as many as 25 harmonics are needed to explain 95% of the observed variance of SLP, and the model simulation of this field is much less satisfactory. The model climatology is also evaluated in terms of the annual cycles of the dominant harmonics.

Christidis, Z. D.↗

Evaluating Coastal Landscape Response to Sea-Level Rise in the Northeastern United States - Approach and Methods

The U.S. Geological Survey is examining effects of future sea-level rise on the coastal landscape from Maine to Virginia by producing spatially explicit, probabilistic predictions using sea-level projections, vertical land movement rates (due to isostacy), elevation data, and land-cover data. Sea-level-rise scenarios used as model inputs are generated by using multiple sources of information, including Coupled Model Intercomparison Project Phase 5 models following representative concentration pathways 4.5 and 8.5 in the Intergovernmental Panel on Climate Change Fifth Assessment Report. A Bayesian network is used to develop a predictive coastal response model that integrates the sea-level, elevation, and land-cover data with assigned probabilities that account for interactions with coastal geomorphology as well as the corresponding ecological and societal systems it supports. The effects of sea-level rise are presented as (1) level of landscape submergence and (2) coastal response type characterized as either static (that is, inundation) or dynamic (that is, landform or landscape change). Results are produced at a spatial scale of 30 meters for four decades (the 2020s, 2030s, 2050s, and 2080s). The probabilistic predictions can be applied to landscape management decisions based on sea-level-rise effects as well as on assessments of the prediction uncertainty and need for improved data or fundamental understanding. This report describes the methods used to produce predictions, including information on input datasets; the modeling approach; model outputs; data-quality-control procedures; and information on how to access the data and metadata online.

terrain↗

Influence of atmospherically induced random wave fronts on diffraction imagery - A computer simulation model for testing image reconstruction algorithms

This paper is devoted to the development of a two-dimensional computer-simulation model that is based on the rigid constraints of optical diffraction theory with careful attention paid to the generation of sample realizations of Gaussian-distributed, spatially random, isotropic wave fronts that have zero-mean and prescribed-covariance functions. Given a sample realization of the wave front, the corresponding centered point-spread function and optical-transfer function are evaluated. A detailed study is made of the statistics of random wave-front tilt, point-spread function, modulus squared of transfer function, and phase of transfer function.

Barakat, Richard↗

On the Computation of Sound by Large-Eddy Simulations

The effect of the small scales on the source term in Lighthill's acoustic analogy is investigated, with the objective of determining the accuracy of large-eddy simulations when applied to studies of flow-generated sound. The distribution of the turbulent quadrupole is predicted accurately, if models that take into account the trace of the SGS stresses are used. Its spatial distribution is also correct, indicating that the low-wave-number (or frequency) part of the sound spectrum can be predicted well by LES. Filtering, however, removes the small-scale fluctuations that contribute significantly to the higher derivatives in space and time of Lighthill's stress tensor T(sub ij). The rms fluctuations of the filtered derivatives are substantially lower than those of the unfiltered quantities. The small scales, however, are not strongly correlated, and are not expected to contribute significantly to the far-field sound; separate modeling of the subgrid-scale density fluctuations might, however, be required in some configurations.

Piomelli, Ugo↗

Simulation of a Periodic Jet in a Crossflow with a RANS Solver Using an Unstructured Grid

A second-order unstructured-grid code, developed and used primarily for steady aerodynamic simulations, is applied to the synthetic jet in a cross flow. The code, FUN3D, is a vertex-centered finite-volume method originally developed by Anderson[1, 2], and is currently supported by members of the Fast Adaptive Aerospace Tools team at NASA Langley. Used primarily for design[3] and analysis[4] of steady aerodynamic configurations, FUN3D incorporates a discrete adjoint capability, and supports parallel computations using MPI. A detailed description of the FUN3D code can be found in the references given above. The code is under continuous development and contains a variety of flux splitting algorithms for the inviscid terms, two methods for computing gradients, several turbulence models, and several solution methodologies; all in varying states of development. Only the most robust and reliable components, based on experiences with steady aerodynamic simulations, were employed in this work. As applied in this work, FUN3D solves the Reynolds averaged Navier-Stokes equations using the one equation turbulence model of Spalart and Allmaras[5]. The spatial discretization is formed on unstructured meshes using a vertex-centered approach. The inviscid terms are evaluated by a flux-difference splitting formulation using least-squares reconstruction and Roe-type approximate Riemann fluxes. Green-Gauss gradient evaluations are used for viscous and turbulence modeling terms. The discrete spatial operator is combined with a backward time operator which is then solved iteratively using point or line Gauss-Seidel and local time stepping in a pseudo time. For steady flows, the physical time step is set to infinity and the pseudo time step is ramped up with the iteration count. A second-order backward in time operator is used for time accurate flows with 20 to 50 steps in the pseudo time applied at each physical time step. For this effort, FUN3D was modified to support spatially varying boundary and initial conditions, and unsteady boundary conditions. Also, a specialized in/out flow boundary condition was implemented to model the action of the diaphragm. This boundary condition is described below in more detail. The grids were generated using the internally developed codes GridEX[6] for meshing the surfaces and inviscid regions of the domain, and for CAD access; and MesherX[7] for meshing the viscous regions. Grid spacing in on the surfaces and in the inviscid regions are indirectly controlled by specifying sources. The viscous layers are generated using an advancing layer technique. MeshersX allows the user to control the spatial variation of the first step off the surface, growth rates, and the termination criterion by providing small problem dependent subroutines.

Atkins, H. L.↗