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NASA NTRS2014

A Walsh Function Module Users' Manual

The solution of partial differential equations (PDEs) with Walsh functions offers new opportunities to simulate many challenging problems in mathematical physics. The approach was developed to better simulate hypersonic flows with shocks on unstructured grids. It is unique in that integrals and derivatives are computed using simple matrix multiplication of series representations of functions without the need for divided differences. The product of any two Walsh functions is another Walsh function - a feature that radically changes an algorithm for solving PDEs. A FORTRAN module for supporting Walsh function simulations is documented. A FORTRAN code is also documented with options for solving time-dependent problems: an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the usage of the Walsh function module including such features as operator overloading, Fast Walsh Transforms in multi-dimensions, and a Fast Walsh reciprocal.

Gnoffo, Peter A.↗

NASA NTRS2004

Multi-Element Unstructured Analyses of Complex Valve Systems

The safe and reliable operation of high pressure test stands for rocket engine and component testing places an increased emphasis on the performance of control valves and flow metering devices. In this paper, we will present a series of high fidelity computational analyses of systems ranging from cryogenic control valves and pressure regulator systems to cavitating venturis that are used to support rocket engine and component testing at NASA Stennis Space Center. A generalized multi-element framework with sub-models for grid adaption, grid movement and multi-phase flow dynamics has been used to carry out the simulations. Such a framework provides the flexibility of resolving the structural and functional complexities that are typically associated with valve-based high pressure feed systems and have been difficult to deal with traditional CFD methods. Our simulations revealed a rich variety of flow phenomena such as secondary flow patterns, hydrodynamic instabilities, fluctuating vapor pockets etc. In the paper, we will discuss performance losses related to cryogenic control valves, and provide insight into the physics of the dominant multi-phase fluid transport phenomena that are responsible for the choking like behavior in cryogenic control elements. Additionally, we will provide detailed analyses of the modal instability that is observed in the operation of the dome pressure regulator valve. Such instabilities are usually not localized and manifest themselves as a system wide phenomena leading to an undesirable chatter at high flow conditions.

Sulyma, Peter↗

NASA NTRS1986

Assimilation of scatterometer winds into surface pressure fields using a variational method

A variational formulation was used to assimilate Seasat-A scatterometer (SASS) surface wind measurements near and during a severe storm in the North Atlantic into conventional National Meteorological Center sea level pressure fields. An estimate of the relative vorticity at every point on a grid was calculated using each of these two data sets. A solution to a modified geostrophic stream function is found subject to the constraints that (1) the relative vorticities calculated from the data agree as closely as possible with the relative vorticities from the variational solution, and that (2) the average kinetic energy is a minimum. Results are obtained which support the idea that averaged satellite data can be treated as synoptic data. Direct substitution rather than a time-weighted insertion made from SASS winds generally resulted in more accurate pressure analyses. In addition, this relatively simple model provides surface pressure fields which agree extremely well with surface truth and the results of other investigators who required additional sources of input data into more complex models. It will be possible to obtain improved wind field maps from future scatterometer pressure fields in mid-latitudes.

Harlan, J., Jr.↗

NASA NTRS2007

Estimating Irrigation Water Requirements using MODIS Vegetation Indices and Inverse Biophysical Modeling

An inverse process approach using satellite-driven (MODIS) biophysical modeling was used to quantitatively assess water resource demand in semi-arid and arid agricultural lands by comparing the carbon and water flux modeled under both equilibrium (in balance with prevailing climate) and non-equilibrium (irrigated) conditions. Since satellite observations of irrigated areas show higher leaf area indices (LAI) than is supportable by local precipitation, we postulate that the degree to which irrigated lands vary from equilibrium conditions is related to the amount of irrigation water used. For an observation year we used MODIS vegetation indices, local climate data, and the SiB2 photosynthesis-conductance model to examine the relationship between climate and the water stress function for a given grid-cell and observed leaf area. To estimate the minimum amount of supplemental water required for an observed cell, we added enough precipitation to the prevailing climatology at each time step to minimize the water stress function and bring the soil to field capacity. The experiment was conducted on irrigated lands on the U.S. Mexico border and Central Asia and compared to estimates of irrigation water used.

Imhoff, Marc L.↗

NASA NTRS2003

Modeling and Visualizing Uncertainty in Continuous Variables Predicted using Remotely Sensed Data

The use of remotely sensed images to map continuous biophysical variables, such as those related to terrestrial vegetation amount, sea surface temperature, and many other targets of NASA s Earth Observing System (EOS), includes variable, parametric, positional, spatial support and structural sources of uncertainty. A complete description of uncertainty will lead to a probability distribution at each location, allowing the exploration of the spatial dimension of uncertainty, that is, where the field is not well quantified. To achieve this purpose, convenient visualization tools are required. We have produced such a tool, called PDFVis, that facilitates the display of probability density functions (pdfs) on a per-grid-cell basis. The density estimate from Monte-Carlo generated realizations is interactively displayed as well as parametric and non-parametric summaries of the pdf field (such as mean, median, quartiles, standard deviation, number of modes, and locations of modes). Shaded surface renderings of pdfs along a transect can also be projected onto a plane. This tool will become more useful as richer descriptions of spatial uncertainty become available.

Dungan, Jennifer L.↗

NASA NTRS2011

NEXT Propellant Management System Integration With Multiple Ion Thrusters

As a critical part of the NEXT test validation process, a multiple-string integration test was performed on the NEXT propellant management system and ion thrusters. The objectives of this test were to verify that the PMS is capable of providing stable flow control to multiple thrusters operating over the NEXT system throttling range and to demonstrate to potential users that the NEXT PMS is ready for transition to flight. A test plan was developed for the sub-system integration test for verification of PMS and thruster system performance and functionality requirements. Propellant management system calibrations were checked during the single and multi-thruster testing. The low pressure assembly total flow rates to the thruster(s) were within 1.4 percent of the calibrated support equipment flow rates. The inlet pressures to the main, cathode, and neutralizer ports of Thruster PM1R were measured as the PMS operated in 1-thruster, 2-thruster, and 3-thruster configurations. It was found that the inlet pressures to Thruster PM1R for 2-thruster and 3-thruster operation as well as single thruster operation with the PMS compare very favorably indicating that flow rates to Thruster PM1R were similar in all cases. Characterizations of discharge losses, accelerator grid current, and neutralizer performance were performed as more operating thrusters were added to the PMS. There were no variations in these parameters as thrusters were throttled and single and multiple thruster operations were conducted. The propellant management system power consumption was at a fixed voltage to the DCIU and a fixed thermal throttle temperature of 75 C. The total power consumed by the PMS was 10.0, 17.9, and 25.2 W, respectively, for single, 2-thruster, and 3-thruster operation with the PMS. These sub-system integration tests of the PMS, the DCIU Simulator, and multiple thrusters addressed, in part, the NEXT PMS and propulsion system performance and functionality requirements.

Sovey, James S.↗

NASA NTRS2016

FUN3D Analyses in Support of the Second Aeroelastic Prediction Workshop

This paper presents the computational aeroelastic results generated in support of the second Aeroelastic Prediction Workshop for the Benchmark Supercritical Wing (BSCW) configurations and compares them to the experimental data. The computational results are obtained using FUN3D, an unstructured grid Reynolds- Averaged Navier-Stokes solver developed at NASA Langley Research Center. The analysis results include aerodynamic coefficients and surface pressures obtained for steady-state, static aeroelastic equilibrium, and unsteady flow due to a pitching wing or flutter prediction. Frequency response functions of the pressure coefficients with respect to the angular displacement are computed and compared with the experimental data. The effects of spatial and temporal convergence on the computational results are examined.

Chwalowski, Pawel↗

NASA NTRS2018

GMI-IPS: Python Processing Software for Aircraft Campaigns

NASA's Atmospheric Tomography Mission (ATom) seeks to understand the impact of anthropogenic air pollution on gases in the Earth's atmosphere. Four flight campaigns are being deployed on a seasonal basis to establish a continuous global-scale data set intended to improve the representation of chemically reactive gases in global atmospheric chemistry models. The Global Modeling Initiative (GMI), is creating chemical transport simulations on a global scale for each of the ATom flight campaigns. To meet the computational demands required to translate the GMI simulation data to grids associated with the flights from the ATom campaigns, the GMI ICARTT Processing Software (GMI-IPS) has been developed and is providing key functionality for data processing and analysis in this ongoing effort. The GMI-IPS is written in Python and provides computational kernels for data interpolation and visualization tasks on GMI simulation data. A key feature of the GMI-IPS, is its ability to read ICARTT files, a text-based file format for airborne instrument data, and extract the required flight information that defines regional and temporal grid parameters associated with an ATom flight. Perhaps most importantly, the GMI-IPS creates ICARTT files containing GMI simulated data, which are used in collaboration with ATom instrument teams and other modeling groups. The initial main task of the GMI-IPS is to interpolate GMI model data to the finer temporal resolution (1-10 seconds) of a given flight. The model data includes basic fields such as temperature and pressure, but the main focus of this effort is to provide species concentrations of chemical gases for ATom flights. The software, which uses parallel computation techniques for data intensive tasks, linearly interpolates each of the model fields to the time resolution of the flight. The temporally interpolated data is then saved to disk, and is used to create additional derived quantities. In order to translate the GMI model data to the spatial grid of the flight path as defined by the pressure, latitude, and longitude points at each flight time record, a weighted average is then calculated from the nearest neighbors in two dimensions (latitude, longitude). Using SciPya's Regular Grid Interpolator, interpolation functions are generated for the GMI model grid and the calculated weighted averages. The flight path points are then extracted from the ATom ICARTT instrument file, and are sent to the multi-dimensional interpolating functions to generate GMI field quantities along the spatial path of the flight. The interpolated field quantities are then written to a ICARTT data file, which is stored for further manipulation. The GMI-IPS is aware of a generic ATom ICARTT header format, containing basic information for all flight campaigns. The GMI-IPS includes logic to edit metadata for the derived field quantities, as well as modify the generic header data such as processing dates and associated instrument files. The ICARTT interpolated data is then appended to the modified header data, and the ICARTT processing is complete for the given flight and ready for collaboration. The output ICARTT data adheres to the ICARTT file format standards V1.1. The visualization component of the GMI-IPS uses Matplotlib extensively and has several functions ranging in complexity. First, it creates a model background curtain for the flight (time versus model eta levels) with the interpolated flight data superimposed on the curtain. Secondly, it creates a time-series plot of the interpolated flight data. Lastly, the visualization component creates averaged 2D model slices (longitude versus latitude) with overlaid flight track circles at key pressure levels. The GMI-IPS consists of a handful of classes and supporting functionality that have been generalized to be compatible with any ICARTT file that adheres to the base class definition. The base class represents a generic ICARTT entry, only defining a single time entry and 3D spatial positioning parameters. Other classes inherit from this base class; several classes for input ICARTT instrument files, which contain the necessary flight positioning information as a basis for data processing, as well as other classes for output ICARTT files, which contain the interpolated model data. Utility classes provide functionality for routine procedures such as: comparing field names among ICARTT files, reading ICARTT entries from a data file and storing them in data structures, and returning a reduced spatial grid based on a collection of ICARTT entries. Although the GMI-IPS is compatible with GMI model data, it can be adapted with reasonable effort for any simulation that creates Hierarchical Data Format (HDF) files. The same can be said of its adaptability to ICARTT files outside of the context of the ATom mission. The GMI-IPS contains just under 30,000 lines of code, eight classes, and a dozen drivers and utility programs. It is maintained with GIT source code management and has been used to deliver processed GMI model data for the ATom campaigns that have taken place to date.

Damon, M. R.↗

NASA NTRS1993

A Regional Analysis of Cloudy Mean Spherical Albedo over the Marine Stratocumulus Region and the Tropical Atlantic Ocean

Since clouds are the largest variable in Earth's radiation budget, it is critical to determine both the spatial and temporal characteristics of their radiative properties. This study examines the relationships between cloud properties and cloud fraction in order to supplement grid scale parameterizations. The satellite data used in this study is from three hourly ISCCP (International Satellite Cloud Climatology Project) and monthly ERBE (Earth Radiation Budget Experiment) data on a 2.50 x 2.50 latitude-longitude grid. Mean cloud spherical albedo, the mean optical depth distribution and cloud fraction are examined and compared off the coast of California and the mid-tropical Atlantic for July 1987 and 1988. Individual grid boxes and spatial averages over several grid boxes are correlated to Coakleys (1991) theory of reflection for uniform and broken layered cloud and to Kedem, et al.(1990) findings that rainfall volume and fractional area of rain in convective systems is linear. Kedem's hypothesis can be expressed in terms of cloud properties. That is, the total volume of liquid in a box is a linear function of cloud fraction. Results for the marine stratocumulus regime indicate that albedo is often invariant for cloud fractions of 20% to 80%. Coakley's satellite model of small and large clouds with cores (1 km) and edges (100 in) is consistent with this observation. The cores maintain high liquid water concentrations and large droplets while the edges contain low liquid water concentrations and small droplets. Large clouds are just a collection of cores. The mean optical depth (TAU) distributions support the above observation with TAU values of 3.55 to 9.38 favored across all cloud fractions. From these results, a method based upon Kedem, et al. theory is proposed to separate the cloud fraction and liquid water path (LWP) calculations in a general circulation model (GCM). In terms of spatial averaging, a linear relationship between albedo and cloud fraction is observed. For tropical locations outside the Intertropical Convergence Zone (ITCZ), results of cloud fraction and albedo spatial averaging followed that of the stratus boxes containing few overcast scenes. Both the ideas of Coakley and Kedem, et al. apply. Within the ITCZ, the grid boxes tended to have the same statistical properties as stratus boxes containing many overcast scenes. Because different dynamical forcing mechanisms are present, it is difficult to devise a method for determining subgrid scale variations. Neither of the theories proposed by Kedem, et al. or Coakley works well for the boxes with numerous overcast scenes.

Ginger, Kathryn M.↗

NASA NTRS1993

A regional analysis of cloudy mean spherical albedo over the marine stratocumulus region and the tropical Atlantic Ocean

Since clouds are the largest variable in Earth's radiation budget, it is critical to determine both the spatial and temporal characteristics of their radiative properties. The relationships between cloud properties and cloud fraction are studied in order to supplement grid scale parameterizations. The satellite data used is from three hourly ISCCP (International Satellite Cloud Climatology Project) and monthly ERBE (Earth Radiation Budget Experiment) data on a 2.5 deg x 2.5 deg latitude-longitude grid. Mean cloud spherical albedo, the mean optical depth distribution, and cloud fraction are examined and compared off the coast of California and the mid-tropical Atlantic for July 1987 and 1988. Individual grid boxes and spatial averages over several grid boxes are correlated to Coakley's theory of reflection for uniform and broken layered cloud and to Kedem, et al.'s findings that rainfall volume and fractional area of rain in convective systems is linear. Kedem's hypothesis can be expressed in terms of cloud properties. That is, the total volume of liquid in a box is a linear function of cloud fraction. Results for the marine stratocumulus regime indicate that albedo is often invariant for cloud fractions of 20% to 80%. Coakley's satellite model of small and large clouds with cores (1 km) and edges (100 m) is consistent with this observation. The cores maintain high liquid water concentrations and large droplets while the edges contain low liquid water concentrations and small droplets. Large clouds are just a collection of cores. The mean optical depth (TAU) distributions support the above observation with TAU values of 3.55 to 9.38 favored across all cloud fractions. From these results, a method based upon Kedem, et al's theory is proposed to separate the cloud fraction and liquid water path (LWP) calculations in a general circulation model (GCM). In terms of spatial averaging, a linear relationship between albedo and cloud fraction is observed. For tropical locations outside the Intertropical Convergence Zone (ITCZ), results of cloud fraction and albedo spatial averaging followed that of the stratus boxes containing few overcast scenes. Both the ideas of Coakley and Kedem, et al. apply. Within the ITCZ, the grid boxes tended to have the same statistical properties as stratus boxes containing many overcast scenes. Because different dynamical forcing mechanisms are present, it is difficult to devise a method for determining subgrid scale variations. Neither of the theories proposed by Kedem, et al. or Coakley works well for the boxes with numerous overcast scenes.

Ginger, Kathryn M.↗

NASA NTRS2019

Characterization of Low-Temperature, Co-Fired Ceramic-Manufactured Electrostatic Thruster-Closeout Report

The goal of the project was to evaluate prototypes of an experimental thruster developed by the University of Arkansas (UA), Fayetteville, AR. The design under evaluation is a radio frequency (RF) electrostatic thruster that was fabricated using the low-temperature, co-fired ceramic (LTCC) materials and fabrication process. This materials system is analogous to printed circuit board (PCB) technology with the most significant difference being that the laminate is replaced by a ceramic material and the copper layer is replaced by printed sinterable silver paste. LTCC designs are baked after fabrication and assembled to realize an entirely monolithic structure with internal conductors, vias, and cavities. In this process, the LTCC electrostatic thruster (LTCC-ET) that is the subject of the present work becomes a monolithic ceramic thruster capable of withstanding temperatures in excess of 500 ºC. The UA and NASA Marshall Space Flight Center (MSFC) jointly performed prototype testing on the LTCC-ET under a NASA Cooperative Agreement Notice (CAN) award. The LTCC-ET was tested at MSFC in May 2018 over a 1-week period. There were two goals for the test program: (1) Testing to determine the operating parameters required to create plasma ignition in the test articles. This was explored by setting a propellant flowrate and increasing RF power until plasma ignition was observed. Testing was conducted with both argon and krypton. (2) Investigate the thrust and specific impulse (Isp) performance of the thruster as a function of propellant flowrate and grid voltage. This goal was not met during the project as technical challenges in maintaining stable plasma ignition arose due to stress and heating of the RF power feed. In summary, a prototype thruster design (consisting of three packaged units) was fabricated by UA and tested for the first time under vacuum conditions at MSFC to experimentally determine basic performance metrics and functionality. It was found that the design was not sufficiently optimized or robust enough in its initial iteration to support a significant test campaign or characterization program. It was concluded that the propellant outlet channels must be reduced in size with the flowpaths adjusted to increase propellant residence time in the thruster, and that the RF connector must be replaced with a version capable of handling higher power throughput and heating. However, even in its unoptimized form, a plasma could be produced in the LTCCET, demonstrating the efficacy of the design approach. The design is especially compelling due to its low cost to manufacture and, more importantly, its scalability of size and power throughput. Low cost and scalability are also important in that additional functionalities, such as thrust vectoring and plume charge neutralization, can be integrated into future designs with minimal additional cost. This project has matured the LTCC-ET development Technology Readiness Level (TRL) from 1 to 2. The low-cost RF plasma source portion of the LTCC device was matured from TRL 2 to 4 through the demonstration of RF plasma ignition under vacuum conditions.

Huang, P.-H. A.↗

NASA NTRS2005

Full Multigrid Flow Solver

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Mineck, Raymond E.↗

NASA NTRS1986

A combined integrating and differentiating matrix formulation for boundary value problems on rectangular domains

Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.

Lakin, W. D.↗

NASA NTRS1986

A combined integrating- and differentiating-matrix formulation for boundary-value problems on rectangular domains

Lakin, W. D.↗

NASA NTRS2017

The Effects of Vegetative Type, Edges, Fire History, Rainfall and Management in Fire-Maintained Ecosystems

The combined effects of repeated fires, climate, and landscape features (e.g., edges) need greater focus in fire ecology studies, which usually emphasize characteristics of the most recent fire and not fire history. Florida scrub-jays are an imperiled, territorial species that prefer medium (1.2-1.7 m) shrub heights. We measured short, medium, and tall habitat quality states annually within 10 ha grid cells that represented potential territories because frequent fires and vegetative recovery cause annual variation in habitat quality. We used multistate models and model selection to test competing hypotheses about how transition probabilities between states varied annually as functions of environmental covariates. Covariates included vegetative type, edges, precipitation, openings (gaps between shrubs), mechanical cutting, and fire characteristics. Fire characteristics not only included an annual presenceabsence of fire covariate, but also fire history covariates: time since the previous fire, the maximum fire-free interval, and the number of repeated fires. Statistical models with support included many covariates for each transition probability, often including fire history, interactions and nonlinear relationships. Tall territories resulted from 28 years of fire suppression and habitat fragmentation that reduced the spread of fires across landscapes. Despite 35 years of habitat restoration and prescribed fires, half the territories remained tall suggesting a regime shift to a less desirable habitat condition. Measuring territory quality states and environmental covariates each year combined with multistate modeling provided a useful empirical approach to quantify the effects of repeated fire in combinations with environmental variables on transition probabilities that drive management strategies and ecosystem change.

Breininger, David R.↗

NASA NTRS2018

The Effects of Vegetative Type, Edges, Fire History, Rainfall and Management in Fire-Maintained Habitat

The combined effects of fire history, climate, and landscape features (e.g., edges) on habitat specialists need greater focus in fire ecology studies, which usually only emphasize characteristics of the most recent fire. Florida scrub-jays are an imperiled, territorial species that prefer medium (1.2-1.7 m) shrub heights, which are dynamic because of frequent fires. We measured short, medium, and tall habitat quality states annually within 10 ha grid cells (that represented potential territories) because fires and vegetative recovery cause annual variation in habitat quality. We used multistate models and model selection to test competing hypotheses about how transition probabilities vary between states as functions of environmental covariates. Covariates included vegetative type, edges (e.g., roads, forests), precipitation, openings (gaps between shrubs), mechanical cutting, and fire characteristics. Fire characteristics not only included an annual presence/absence of fire covariate, but also fire history covariates: time since the previous fire, the longest fire-free interval, and the number of repeated fires. Statistical models with support included many covariates for each transition probability, often including fire history, interactions and nonlinear relationships. Tall territories resulted from 28 years of fire suppression and habitat fragmentation that reduced the spread of fires across landscapes. Despite 35 years of habitat restoration and prescribed fires, half the territories remained tall suggesting a regime shift to a less desirable habitat condition. Edges reduced the effectiveness of fires in setting degraded scrub and flatwoods into earlier successional states making mechanical cutting an important tool to compliment frequent prescribed fires.

Breininger, David R.↗

NASA NTRSDate not supplied

F-ANG+: A 3-D Augmented-Stencil Face-Averaged Nodal-Gradient Cell-Centered Finite-Volume Method for Hypersonic Flows

We describe the extension of a 2-D simplified face-averaged nodal-gradient (F-ANG) method to 3-D and demonstrate that the 3-D simplified F-ANG method is accomplished by augmenting the nodecentered gradient least squares stencil. This augmented stencil F-ANG method is shown to result in advection and diffusion schemes that are stable for hexahedral, prismatic, pyramidal and tetrahedral cells without having to resort to cell-averaged nodal gradients. In addition, we describe the modifications to the augmented stencil required to support the use of wall function boundary conditions. Finally we describe a consistent, face-stencil based multi-dimensional limiter procedure (MLP), and show it to be fully consistent and compatible with the linearity-preserving unstructured- MUSCL (LP-U-MUSCL) scheme for all values of kappa. These methods and schema are implemented in the cell-centered finite-volume code VULCAN-CFD, which is then used to investigate whether the robustness improvements demonstrated in 2-D carry over to 3-D by computing hypersonic flows using mixed-element grids as well as highly adapted tetrahedral grids.

Weighted Least-Squares↗

NASA NTRS2013

FUN3D Analyses in Support of the First Aeroelastic Prediction Workshop

This paper presents the computational aeroelastic results generated in support of the first Aeroelastic Prediction Workshop for the Benchmark Supercritical Wing (BSCW) and the HIgh REynolds Number AeroStructural Dynamics (HIRENASD) configurations and compares them to the experimental data. The computational results are obtained using FUN3D, an unstructured grid Reynolds-averaged Navier-Stokes solver developed at NASA Langley Research Center. The analysis results for both configurations include aerodynamic coefficients and surface pressures obtained for steady-state or static aeroelastic equilibrium (BSCW and HIRENASD, respectively) and for unsteady flow due to a pitching wing (BSCW) or modally-excited wing (HIRENASD). Frequency response functions of the pressure coefficients with respect to displacement are computed and compared with the experimental data. For the BSCW, the shock location is computed aft of the experimentally-located shock position. The pressure distribution upstream of this shock is in excellent agreement with the experimental data, but the pressure downstream of the shock in the separated flow region does not match as well. For HIRENASD, very good agreement between the numerical results and the experimental data is observed at the mid-span wing locations.

Chwalowski, Pawel↗