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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2013

Application and Evaluation of a Snowmelt Runoff Model in the Tamor River Basin, Eastern Himalaya Using a Markov Chain Monte Carlo (MCMC) Data Assimilation Approach

Previous studies have drawn attention to substantial hydrological changes taking place in mountainous watersheds where hydrology is dominated by cryospheric processes. Modelling is an important tool for understanding these changes but is particularly challenging in mountainous terrain owing to scarcity of ground observations and uncertainty of model parameters across space and time. This study utilizes a Markov Chain Monte Carlo data assimilation approach to examine and evaluate the performance of a conceptual, degree-day snowmelt runoff model applied in the Tamor River basin in the eastern Nepalese Himalaya. The snowmelt runoff model is calibrated using daily streamflow from 2002 to 2006 with fairly high accuracy (average Nash-Sutcliffe metric approx. 0.84, annual volume bias <3%). The Markov Chain Monte Carlo approach constrains the parameters to which the model is most sensitive (e.g. lapse rate and recession coefficient) and maximizes model fit and performance. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall compared with simulations using observed station precipitation. The average snowmelt contribution to total runoff in the Tamor River basin for the 2002-2006 period is estimated to be 29.7+/-2.9% (which includes 4.2+/-0.9% from snowfall that promptly melts), whereas 70.3+/-2.6% is attributed to contributions from rainfall. On average, the elevation zone in the 4000-5500m range contributes the most to basin runoff, averaging 56.9+/-3.6% of all snowmelt input and 28.9+/-1.1% of all rainfall input to runoff. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall versus snowmelt compared with simulations using observed station precipitation. Model experiments indicate that the hydrograph itself does not constrain estimates of snowmelt versus rainfall contributions to total outflow but that this derives from the degree-day melting model. Lastly, we demonstrate that the data assimilation approach is useful for quantifying and reducing uncertainty related to model parameters and thus provides uncertainty bounds on snowmelt and rainfall contributions in such mountainous watersheds.

runoff↗
NASA NTRS2015

The Parameterization of Top-Hat Particle Sensors with Microchannel-Plate-Based Detection Systems and its Application to the Fast Plasma Investigation on NASA's Magnetospheric MultiScale Mission

The most common instrument for low energy plasmas consists of a top-hat electrostatic analyzer geometry coupled with a microchannel-plate (MCP)-based detection system. While the electrostatic optics for such sensors are readily simulated and parameterized during the laboratory calibration process, the detection system is often less well characterized. Furthermore, due to finite resources, for large sensor suites such as the Fast Plasma Investigation (FPI) on NASA's Magnetospheric Multiscale (MMS) mission, calibration data are increasingly sparse. Measurements must be interpolated and extrapolated to understand instrument behavior for untestable operating modes and yet sensor inter-calibration is critical to mission success. To characterize instruments from a minimal set of parameters we have developed the first comprehensive mathematical description of both sensor electrostatic optics and particle detection systems. We include effects of MCP efficiency, gain, scattering, capacitive crosstalk, and charge cloud spreading at the detector output. Our parameterization enables the interpolation and extrapolation of instrument response to all relevant particle energies, detector high voltage settings, and polar angles from a small set of calibration data. We apply this model to the 32 sensor heads in the Dual Electron Sensor (DES) and 32 sensor heads in the Dual Ion Sensor (DIS) instruments on the 4 MMS observatories and use least squares fitting of calibration data to extract all key instrument parameters. Parameters that will evolve in flight, namely MCP gain, will be determined daily through application of this model to specifically tailored in-flight calibration activities, providing a robust characterization of sensor suite performance throughout mission lifetime. Beyond FPI, our model provides a valuable framework for the simulation and evaluation of future detection system designs and can be used to maximize instrument understanding with minimal calibration resources.

Instrument-model↗
NASA NTRS2016

Model Order Reduction of Aeroservoelastic Model of Flexible Aircraft

This paper presents a holistic model order reduction (MOR) methodology and framework that integrates key technological elements of sequential model reduction, consistent model representation, and model interpolation for constructing high-quality linear parameter-varying (LPV) aeroservoelastic (ASE) reduced order models (ROMs) of flexible aircraft. The sequential MOR encapsulates a suite of reduction techniques, such as truncation and residualization, modal reduction, and balanced realization and truncation to achieve optimal ROMs at grid points across the flight envelope. The consistence in state representation among local ROMs is obtained by the novel method of common subspace reprojection. Model interpolation is then exploited to stitch ROMs at grid points to build a global LPV ASE ROM feasible to arbitrary flight condition. The MOR method is applied to the X-56A MUTT vehicle with flexible wing being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies demonstrated that relative to the fullorder model, our X-56A ROM can accurately and reliably capture vehicles dynamics at various flight conditions in the target frequency regime while the number of states in ROM can be reduced by 10X (from 180 to 19), and hence, holds great promise for robust ASE controller synthesis and novel vehicle design.

aeroelasticity↗
NASA NTRS2015

Quantifying Libya-4 Surface Reflectance Heterogeneity With WorldView-1, 2 and EO-1 Hyperion

The land surface imaging (LSI) virtual constellation approach promotes the concept of increasing Earth observations from multiple but disparate satellites. We evaluated this through spectral and spatial domains, by comparing surface reflectance from 30-m Hyperion and 2-m resolution WorldView-2 (WV-2) data in the Libya-4 pseudoinvariant calibration site. We convolved and resampled Hyperion to WV-2 bands using both cubic convolution and nearest neighbor (NN) interpolation. Additionally, WV-2 and WV-1 same-date imagery were processed as a cross-track stereo pair to generate a digital terrain model to evaluate the effects from large (>70 m) linear dunes. Agreement was moderate to low on dune peaks between WV-2 and Hyperion (R2 <; 0.4) but higher in areas of lower elevation and slope (R2 > 0.6). Our results provide a satellite sensor intercomparison protocol for an LSI virtual constellation at high spatial resolution, which should start with geolocation of pixels, followed by NN interpolation to avoid tall dunes that enhance surface reflectance differences across this internationally utilized site.

Hyperion↗
NASA NTRS2016

High Resolution Image Reconstruction from Projection of Low Resolution Images DIffering in Subpixel Shifts

In this paper, we demonstrate a simple algorithm that projects low resolution (LR) images differing in subpixel shifts on a high resolution (HR) also called super resolution (SR) grid. The algorithm is very effective in accuracy as well as time efficiency. A number of spatial interpolation techniques using nearest neighbor, inverse-distance weighted averages, Radial Basis Functions (RBF) etc. used in projection yield comparable results. For best accuracy of reconstructing SR image by a factor of two requires four LR images differing in four independent subpixel shifts. The algorithm has two steps: i) registration of low resolution images and (ii) shifting the low resolution images to align with reference image and projecting them on high resolution grid based on the shifts of each low resolution image using different interpolation techniques. Experiments are conducted by simulating low resolution images by subpixel shifts and subsampling of original high resolution image and the reconstructing the high resolution images from the simulated low resolution images. The results of accuracy of reconstruction are compared by using mean squared error measure between original high resolution image and reconstructed image. The algorithm was tested on remote sensing images and found to outperform previously proposed techniques such as Iterative Back Projection algorithm (IBP), Maximum Likelihood (ML), and Maximum a posterior (MAP) algorithms. The algorithm is robust and is not overly sensitive to the registration inaccuracies.

0↗
NASA NTRS2016

Near-Body Grid Adaption for Overset Grids

A solution adaption capability for curvilinear near-body grids has been implemented in the OVERFLOW overset grid computational fluid dynamics code. The approach follows closely that used for the Cartesian off-body grids, but inserts refined grids in the computational space of original near-body grids. Refined curvilinear grids are generated using parametric cubic interpolation, with one-sided biasing based on curvature and stretching ratio of the original grid. Sensor functions, grid marking, and solution interpolation tasks are implemented in the same fashion as for off-body grids. A goal-oriented procedure, based on largest error first, is included for controlling growth rate and maximum size of the adapted grid system. The adaption process is almost entirely parallelized using MPI, resulting in a capability suitable for viscous, moving body simulations. Two- and three-dimensional examples are presented.

Buning, Pieter G.↗
NASA NTRS2016

Spline Trajectory Algorithm Development: Bezier Curve Control Point Generation for UAVs

A greater need for sophisticated autonomous piloting systems has risen in direct correlation with the ubiquity of Unmanned Aerial Vehicle (UAV) technology. Whether surveying unknown or unexplored areas of the world, collecting scientific data from regions in which humans are typically incapable of entering, locating lost or wanted persons, or delivering emergency supplies, an unmanned vehicle moving in close proximity to people and other vehicles, should fly smoothly and predictably. The mathematical application of spline interpolation can play an important role in autopilots' on-board trajectory planning. Spline interpolation allows for the connection of Three-Dimensional Euclidean Space coordinates through a continuous set of smooth curves. This paper explores the motivation, application, and methodology used to compute the spline control points, which shape the curves in such a way that the autopilot trajectory is able to meet vehicle-dynamics limitations. The spline algorithms developed used to generate these curves supply autopilots with the information necessary to compute vehicle paths through a set of coordinate waypoints.

Howell, Lauren R.↗
NASA NTRS2016

Observed Trend in Surface Wind Speed Over the Conterminous USA and CMIP5 Simulations

There has been no spatial surface wind map even over the conterminous USA due to the difficulty of spatial interpolation of wind field. As a result, the reanalysis data were often used to analyze the statistics of spatial pattern in surface wind speed. Unfortunately, no consistent trend in wind field was found among the available reanalysis data, and that obstructed the further analysis or projection of spatial pattern of wind speed. In this study, we developed the methodology to interpolate the observed wind speed data at weather stations using random forest algorithm. We produced the 1-km daily climate variables over the conterminous USA from 1979 to 2015. The validation using Ameriflux daily data showed that R2 is 0.59. Existing studies have found the negative trend over the Eastern US, and our study also showed same results. However, our new datasets also revealed the significant increasing trend over the southwest US especially from April to June. The trend in the southwestern US represented change or seasonal shift in North American Monsoon. Global analysis of CMIP5 data projected the decrease trend in mid-latitude, while increase trend in tropical region over the land. Most likely because of the low resolution in GCM, CMIP5 data failed to simulate the increase trend in the southwest US, even though it was qualitatively predicted that pole ward shift of anticyclone help the North American Monsoon.

simulations↗
NASA NTRS2017

Genetic Algorithm-Guided, Adaptive Model Order Reduction of Flexible Aircrafts

This paper presents a methodology for automated model order reduction (MOR) of flexible aircrafts to construct linear parameter-varying (LPV) reduced order models (ROM) for aeroservoelasticity (ASE) analysis and control synthesis in broad flight parameter space. The novelty includes utilization of genetic algorithms (GAs) to automatically determine the states for reduction while minimizing the trial-and-error process and heuristics requirement to perform MOR; balanced truncation for unstable systems to achieve locally optimal realization of the full model; congruence transformation for "weak" fulfillment of state consistency across the entire flight parameter space; and ROM interpolation based on adaptive grid refinement to generate a globally functional LPV ASE ROM. The methodology is applied to the X-56A MUTT model currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that X-56A ROM with less than one-seventh the number of states relative to the original model is able to accurately predict system response among all input-output channels for pitch, roll, and ASE control at various flight conditions. The GA-guided approach exceeds manual and empirical state selection in terms of efficiency and accuracy. The adaptive refinement allows selective addition of the grid points in the parameter space where flight dynamics varies dramatically to enhance interpolation accuracy without over-burdening controller synthesis and onboard memory efforts downstream. The present MOR framework can be used by control engineers for robust ASE controller synthesis and novel vehicle design.

Numerical Analysi↗
NASA NTRS2017

Development and Assessment of the SMAP Enhanced Passive Soil Moisture Product

Launched in January 2015, the National Aeronautics and Space Administration (NASA) Soil Moisture Active Passive (SMAP) observatory was designed to provide frequent global mapping of high-resolution soil moisture and freeze-thaw state every two to three days using a radar and a radiometer operating at L-band frequencies. Despite a hardware mishap that rendered the radar inoperable shortly after launch, the radiometer continues to operate nominally, returning more than two years of science data that have helped to improve existing hydrological applications and foster new ones.Beginning in late 2016 the SMAP project launched a suite of new data products with the objective of recovering some high-resolution observation capability loss resulting from the radar malfunction. Among these new data products are the SMAP Enhanced Passive Soil Moisture Product that was released in December 2016, followed by the SMAPSentinel-1 Active-Passive Soil Moisture Product in April 2017.This article covers the development and assessment of the SMAP Level 2 Enhanced Passive Soil Moisture Product (L2_SM_P_E). The product distinguishes itself from the current SMAP Level 2 Passive Soil Moisture Product (L2_SM_P) in that the soil moisture retrieval is posted on a 9 km grid instead of a 36 km grid. This is made possible by first applying the Backus-Gilbert optimal interpolation technique to the antenna temperature (TA) data in the original SMAP Level 1B Brightness Temperature Product to take advantage of the overlapped radiometer footprints on orbit. The resulting interpolated TA data then go through various correctioncalibration procedures to become the SMAP Level 1C Enhanced Brightness Temperature Product (L1C_TB_E). The L1C_TB_E product, posted on a 9 km grid, is then used as the primary input to the current operational SMAP baseline soil moisture retrieval algorithm to produce L2_SM_P_E as the final output. Images of the new product reveal enhanced visual features that are not apparent in the standard product. Based on in situ data from core validation sites and sparse networks representing different seasons and biomes all over the world, comparisons between L2_SM_P_E and in situ data were performed for the duration of April 1, 2015 October 30, 2016. It was found that the performance of the enhanced 9 km L2_SM_P_E is equivalent to that of the standard 36 km L2_SM_P, attaining a retrieval uncertainty below 0.040 m(exp 3)/m(exp 3) unbiased root-mean-square error (ubRMSE) and a correlation coefficient above 0.800. This assessment also affirmed that the Single Channel Algorithm using the V-polarized TB channel (SCA-V) delivered the best retrieval performance among the various algorithms implemented for L2_SM_P_E, a result similar to a previous assessment for L2_SM_P.

Enhanced↗
NASA NTRS2018

File Specification for M2AMIP Products: Version Number - 1.0

The Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) is an atmospheric reanalysis computed with the Goddard Earth Observing (EOS) System, Version 5.12.4 (GEOS) data assimilation system (Gelaro et al., 2017). To supplement the reanalysis, the GEOS General Circulation Model (GCM) used in MERRA-2 has been used to generate a 10-member ensemble of simulations, configured following the convention of the Atmospheric Model Intercomparison Project (AMIP; Gates et al., 1992). Each ensemble member was initialized using meteorological fields from a different date in November 1979. The AMIP simulations used the sea-surface temperature (SST) and sea-ice boundary conditions that were used in MERRA-2 (Bosilovich et al., 2016). This 10-member ensemble of AMIP simulations, denoted M2AMIP, is available for download in a group of self-describing files, which are documented in this office note. All data collections are provided on the same horizontal grid as MERRA-2. This grid has 576 points in the longitudinal direction and 361 points in the latitudinal direction, corresponding to a resolution of 0.625 degrees by 0.5 degrees. Although data collections are available at this grid, all fields are computed on a cubed-sphere grid with an approximate resolution of 50 km by 50 km and are then spatially interpolated to the latitude-longitude grid. There are no changes in the vertical grids used: variables are provided on either the native vertical grid of 72 model layers, or interpolated to 42 standard pressure levels. Unlike MERRA, no data collections are available at the vertical layer edges. More details on the grid are provided in Section 4. MERRA-2 introduced observation-based precipitation forcing for the land surface parameterization and the corresponding variable PRECTOTCORR in the MERRA-2 FLX (surface turbulent fluxes and related quantities) and LFO (land-surface forcing) collections (see Section 6; Reichle et al., 2017). While this variable is still available for M2AMIP, there was no observation-based forcing, making the value identical to the model derived precipitation, PRECTOT. Similarly, without data assimilation, the values for the analysis increments, D*DTANA, in the tendency and vertically integrated file collections are zero. The M2AMIP data are available for download online through the NASA Center for Climate Simulation (NCCS) DataPortal (https://portal.nccs.nasa.gov/datashare/gmao_m2amip/). Data are arranged in subdirectories based on ensemble member, followed by year and month. Control files that are compatible with the Grid Analysis and Display System (GrADS) are available in the ctl_daily and ctl_monthly directories for the hourly, three hourly, and monthly mean data. Control files for the monthly mean diurnal cycle can be found in the ctl_diurnal subdirectory within the directory for each individual ensemble member.

M2AMIP↗
NASA NTRS2018

Deriving Three Dimensional Reservoir Bathymetry from Multi-Satellite Datasets

We evaluate different techniques that rebuild reservoir bathymetry by combining multi-satellite imagery of surface water elevation and extent. Digital elevation models (DEMs) are processed in two distinct ways in order to determine 3-D reservoir bathymetry. They are defined as (a) linear extrapolation and (b) linear interpolation. The first one linearly extrapolates the land slope, defining the bottom as the intersection of all extrapolated lines. The second linearly interpolates the uppermost and lowermost pixels of the reservoir's main river, repeating the process for all other tributaries. A visible bathymetry, resulting from the combination of radar altimetry and water extent masks, can be coupled with the DEM, improving the accuracy of techniques (a) and (b). Envisat-and Altika-based altimetric time series is combined to a Landsat-based water extent database over the2002-2016 period in order to generate the visible bathymetry, and topography is derived from the 3-arcsecHydroSHEDS DEM. Fourteen 3-D bathymetries derived from the combination of these techniques and datasets, plus the inclusion of upstream and downstream riverbed elevations, are evaluated over Lake Mead. Accuracy is measured using ground observations, and show that metrics improve as a function of added data requirement and processing. Best bathymetry estimates are obtained when the visible bathymetry, linear extrapolation technique and riverbed elevation are combined. Water storage variability is also evaluated and shows that best results are derived from the aforementioned combination. This study contributes to our understanding and representation of reservoir water impoundment impacts on the hydrological cycle.

HydroSHEDS↗
NASA NTRS2018

MODIS Solar Diffuser Degradation Determination and Its Spectral Dependency

This study presents a modeling approach to improve solar diffuser (SD) degradation determination from SD stability monitor (SDSM) measurements. The MODIS instrument uses a SDto calibrate its reflective solar bands (RSBs) on-orbit. Due to the imperfectly designed SDSM sun view screen, the SD reflectance tracked by SDSM has large noise. The SDSM measurements noise is spectrally coherent and can be minimized by normalizing measurements to the least degradeddetector 9 (936 nm). In this study, a SD degradation model is used to determine the SDdegradation's wavelength dependency and the detector 9 degradation is estimated by the model solution.The results show the SD degradations measured at 6 SDSM detectors (554 _ 936 nm) have stable relationships, where the degradation is inversely proportion to 1/wavelength^4. The model estimated SD degradation at SDSM detector 9 wavelength (936 nm) is ~0.9% from 2002 to 2018.Based on the SD degradation model solution, the SD degradation at short/mid wave bands are estimated to improve short/mid wave bands calibration. The model can also be used to improve interpolating SD degradation at SDSM detectors to RSB wavelengths. Compared to linear interpolation, bands 9 and 10 show the largest differences of up to 0.3 and 0.4% respectively. These differences directly impact the calibration coefficients of these bands.

radiometric calibration↗
NASA NTRS2018

Super Resolution of Remote Sensing Images Using Edge-Directed Radial Basis Functions

Edge-Directed Radial Basis Functions (EDRBF) are used to compute super resolution(SR) image from a given set of low resolution (LR) images differing in subpixel shifts. The algorithm is tested on remote sensing images and compared for accuracy with other well-known algorithms such as Iterative Back Projection (IBP), Maximum Likelihood (ML) algorithm, interpolation of scattered points using Nearest Neighbor (NN) and Inversed Distance Weighted (IDW) interpolation, and Radial Basis Functin(RBF) . The accuracy of SR depends on various factors besides the algorithm (i) number of subpixel shifted LR images (ii) accuracy with which the LR shifts are estimated by registration algorithms (iii) and the targeted spatial resolution of SR. In our studies, the accuracy of EDRBF is compared with other algorithms keeping these factors constant. The algorithm has two steps: i) registration of low resolution images and (ii) estimating the pixels in High Resolution (HR) grid using EDRBF. Experiments are conducted by simulating LR images from a input HR image with different sub-pixel shifts. The reconstructed SR image is compared with input HR image to measure the accuracy of the algorithm using sum of squared errors (SSE). The algorithm has outperformed all of the algorithms mentioned above. The algorithm is robust and is not overly sensitive to the registration inaccuracies.

Mareboyana, Manohar M.↗
NASA NTRS2019

Auralization of Unsteady Rotor Noise Using a Solution to the Ffowcs Williams-Hawkings Equation

Auralization of unsteady helicopter flight operations is needed to better understand the impact of maneuvers on community noise. Previous source sound synthesis methods were based on interpolated data, which may lead to artifacts in generating sound for helicopter maneuvers where sound pressure directivity may change rapidly. In this paper, the source sound is synthesized at every time sample using a solution to the Ffowcs Williams-Hawkings Equation along the path of the emission angle between the source and a ground observer. The synthesized sound is then propagated to the ground observer for auralization. Since no interpolation is performed, maneuvers with rapidly changing sound pressure directivities may be more accurately synthesized and auralized. The framework for accomplishing this synthesis and auralization is described, which couples the Fundamental Rotorcraft Acoustic Modeling from Experiments, the second-generation Aircraft NOise Prediction Program, and the NASA Auralization Framework. Synthesis of a hovering rotor is presented to compare with previous synthesis methods. Two examples with a periodic signals are then presented to demonstrate synthesis and auralization of unsteady rotor noise.

Krishnamurthy, Siddhartha↗
NASA NTRS2019

Adjoint-Based Anisotropic Mesh Adaptation for a Stabilized Finite-Element Flow Solver

An adjoint solver is implemented in the FUN3D stabilized finite-element flow solver. The adjoint solution is used to generate anisotropic, adapted meshes to control error in scalar out- put functionals, such as lift or drag coefficient. The inviscid and turbulent adjoints are verified with a finite-difference derivative approximation and can be used in design optimization in addition to mesh adaptation. The adjoint capability represents an extension of previous research using the FUN3D stabilized finite-element capability with metric-based mesh adaptation and interpolation-based error estimates to generate highly anisotropic adapted meshes for turbulent flows. In the present work, a metric-based approach is again utilized, where the adjoint and the primal solutions both contribute to the generation of a metric tensor field that is subsequently used to produce the required anisotropic mesh for each adaptation cycle. Adaptive results are then shown for an inviscid supersonic flow over a diamond airfoil, inviscid transonic flow over the ONERA M6 wing, and viscous laminar flow over the NACA 0012 airfoil, all using drag force as the output functional. Adjoint-based adaptation is compared with a multiscale solution-based approach that controls the L norm of Mach number interpolation error to demonstrate the effectiveness and effciency of the adjoint-based adaptive mesh technology.

Balan, Aravind↗
NASA NTRS2019

Aeroelastic Indicial Response Reduced-Order Modeling for Flexible Flight Vehicles

A reduced-order modeling method capable of providing computationally efficient predictions of the nonlinear, unsteady aerodynamics encountered by flexible flight vehicles under- going forced oscillations is presented. Models are developed using indicial response theory, which characterizes a vehicle’s dynamics through identification of time-accurate aerodynamic responses due to step changes in the vehicle-state parameters, e.g., angle-of-attack, pitch rate. A coupled computational fluid dynamics aeroelastic analysis is proposed for identifying step (indicial) responses of flexible vehicles. In this approach, aeroelastic indicial responses are simulated via prescribed rigid body motions, while fluid-structure interactions are captured at the subiterative level through coupling to a linear modal structural solver. A nonlinear extension of indicial response theory is applied through time-dependent linear interpolation of a database of locally linear aeroelastic step responses. Reduced-order models are then created using the mathematical principle of convolution applied to the interpolated aeroelastic indicial responses to predict the time-dependent aerodynamic response of a flexible vehicle to any arbitrary prescribed flight maneuver. The NASA FUN3D computational fluid dynamics solver is utilized for simulating full-order trajectories and indicial response functions. Aerodynamic predictions were generated for the X-56A aircraft undergoing a series of harmonic forced oscillations. The s are shown to provide a practical option for evaluating the unsteady aerodynamics of flexible vehicles using high-fidelity simulations.

Hiller, Brett↗
NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗