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NASA NTRSDate not supplied

Numerical Behaviour of a Smooth Local Correlation-based Transition Model in a Newton-Krylov Flow Solver

The numerical behaviour of transport-equation-based transition models, including both iterative and grid convergence, is influenced by the source terms. Transition models contain source terms that are large and highly nonlinear, and can be destabilizing in a strong implicit solver. Linearization strategies with varying levels of coupling are evaluated in conjunction with a source-term time step restriction to determine best-practices for solving the SA-sLM2015smooth local correlation-based transition model in an implicit Newton-Krylov flow solver. Achieving deep iterative convergence facilitates a detailed investigation of the grid convergence of these free-transition simulations, which are evaluated relative to fully-turbulent simulations performed using the Spalart-Allmaras turbulence model. Simulations of the NLF0416 general aviation airfoil, VA-2 supercritical airfoil, and NASA CRM-NLF wing-body geometry are performed over a range of grid levels. The results demonstrate that both a fully-coupled linearization strategy and a source-term time step restriction improve nonlinear convergence as the complexity of the free-transition simulations increases. In general, additional grid resolution is required for free-transition simulations relative to fully-turbulent simulations in order to achieve a similar level of accuracy, with the grid convergence of free-transition simulations sensitive to the streamwise grid spacings in the transition regions.

AATT↗
NASA NTRS2022

Simulating Reflected Light Coronagraphy of Earth-like Exoplanets with a Large IR/O/UV Space Telescope: Impact and Calibration of Smooth Exozodiacal Dust

Observing Earth-like exoplanets orbiting within the habitable zone of Sun-like stars and studying their atmospheres in reflected starlight requires contrasts of ∼1e–10 in the visible. At such high contrast, starlight reflected by exozodiacal dust is expected to be a significant source of contamination. Here, we present high-fidelity simulations of coronagraphic observations of a synthetic solar system located at a distance of 10 pc and observed with a 12 m and an 8 m circumscribed aperture diameter space telescope operating at 500 nm wavelength. We explore different techniques to subtract the exozodi and stellar speckles from the simulated images in the face-on, the 30 deg inclined, and the 60 deg inclined case and quantify the remaining systematic noise as a function of the exozodiacal dust level of the system. We find that in the face-on case, the exozodi can be subtracted down to the photon noise limit for exozodi levels up to ∼1000 zodi using a simple toy model for the exozodiacal disk, whereas in the 60 deg inclined case this only works up to ∼50 zodi. We also investigate the impact of larger wave front errors and larger system distance, finding that while the former has no significant impact, the latter has a strong (negative) impact. Ultimately, we derive a penalty factor as a function of the exozodi level and system inclination that should be considered in exoplanet yield studies as a realistic estimate for the excess systematic noise from the exozodi.

Exoplanet detection methods↗
NASA NTRS1992

A variational method for finite element stress recovery: Applications in one-dimension

It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.

Riggs, H. Ronald↗
NASA NTRS1998

Potential Mars Surveyor 2001 Landing Sites: Low-Elevation Cratered "Highlands" in Central and Eastern Sinus Meridiani and Near Amenthes Fossae

The main scientific goal for the Mars Surveyor Program 2001 (MSP 01) landed mission is to collect and characterize 91 rock and 13 soil core samples using an integrated instrument suite onboard the Athena Rover. If possible, these samples will be retrieved and returned to Earth via a MSP 05 or MSP 07 mission. Preliminary engineering constraints for the MSP 01 landing site call for a location that lies between 15 S and 30 N, and below about 2 km elevation (based on Viking-era topography). Desirable landing sites for MSP 01 are to be located "in the ancient highlands where the environmental conditions may have been favorable to the preservation of evidence of possible prebiotic or biotic processes including the emergence (and, potentially, the persistence) of life". We interpret this to mean that the desirable sites include those that have evidence of aqueous sediments that might have been deposited during the Noachian and/or Hesperian Epochs of Mars' history. In addition to the search for subaqueous sedimentary deposits, we took into consideration the fact that the rover, Athena, will need to be able to access these materials. Thus, a site where aeolian deflation has occurred might be desirable because it might expose, in situ, layered sedimentary deposits. Deflated areas, of course, might include potential landing hazards in the form of meterscale buttes and mesas (e.g., Christmas Lake Valley, OR), thus careful study of such sites with high resolution images will be required before a decision is made to land. We have been examining three regions that have potential to be considered for MSP 01 landing sites. This work is based on Viking (VIS, IRTM) and Phobos 2 (Termoskan) observations and should be regarded as preliminary because we believe that the final site selection should also be based upon analysis of Mars Global Surveyor observations that help constrain mineralogy (TES) and local geomorphology (MOC, MOLA). (1) Eastern Sinus Meridiani Region (proposed by K. S. Edgett) Sinus Meridiani is a persistent low-albedo (< 0. 16) region on the martian equator that has been recognized for about 400 years. All of Sinus Meridiani is below the 2 km elevation constraint for MSP 01. The region includes cratered highlands, valley networks, aeolian dunes, and possible aqueous sedimentary deposits. The landing site study region is located in the eastern portion of Sinus Meridiani. It is bounded by latitudes 10 S to 2 N, longitudes 355 W to 345 W, and the elevations are mostly 1-2 km. The center of this area contains a medium-albedo (0.19-0.21), relatively smooth-surfaced deposit that was suggested by Rice to be a lacustrine deposit. Several potential landing areas can be suggested within this region. Based on Viking and Phobos 2 data, the favored sites so far are centered at 7.6 S, 346.9 W and 0.8 S, 349 W. Thermal inertias are 3.2-7.0 x 10(exp -3) cal /sq cm s(exp -0.5)/K; and rock abundances are around 2-6%. The site at 7.6 S, 346.9 W is at the southern end of the smooth, medium-albedo unit that might have a lacustrine origin. At this location, numerous channels appear to have drained toward the smooth unit. Viking images from orbit 747A show this area at about 15 m/pixel ground resolution. The images reveal that aeolian deflation has occurred along the deposit's margins. Bright (i.e., albedo >= 0.21) aeolian dunes are present on the channel floors and in some of the depressions on the smooth unit. The bright, apparently active dunes might consist of material (perhaps lakedeposited sands) that has been eroded from the smooth unit. The site at approximately 0.8 S, 349 W is selected because it offers an opportunity to solve a long-standing puzzle about Mars remote sensing. There are three main "color" units on Mars: "dark red, dark gray, and bright red". This landing site would allow the Athena rover an opportunity to investigate all three materials within close proximity (the best place on Mars to do so). There are no high resolution (better than 100 m/pixel) Viking or Mariner images of this site. (2) Central Sinus Meridiani Region (proposed by K. S. Edgett and T. J. Parker) Central Sinus Meridiani is characterized by two types of surfaces [4]. One is like typical martian cratered highlands elsewhere- there are old valley networks and old impact craters. The other is relatively smooth and flat. These two units are in contact around 3.1 S between 5 W and 4 E longitudes. Valley networks- including one at 6'S, 358 W that rivals the Grand Canyon of Arizona- once drained toward the smooth unit. Edgett and Parker [4] proposed that the smooth unit might consist of sediments laid down in a large Noachian-aged sea/ocean that would have covered much of the northern hemisphere. Schultz and Lutz [I I I suggested that it is a paleopolar layered deposit. Regardless, the smooth unit where it contacts the cratered terrain would make an excellent site for Athena rover to investigate. The site is best seen in Viking high resolution images from orbits 408B (about 30 m/pixel) and 746A (about 12 m/pixel). These images suggest that aeolian deflation has occurred along the margin of the smooth unit, and this deflation has exposed horizontal larrs of material. The elevation is about 0.5 km; thermal inertias are 6.5-8.0 x 10(exp -3) cal /sq cm s(exp -0.5) / K; rock abundances are 2-4%; and the surface is probably sandy with dark drifts and ripples but almost no actual dunes. We suggest a landing around 3.2 S, 3.0 W would test the aqueous sediment hypothesis and provide a potentially smooth surface on which to land. (3) Amenthes Fossae Region (proposed by S. N. Huntwork and K. S. Edgett) The Amenthes Fossae are a series of graben/fissures that are circumferential to the southeast side of Isidis Planitia. These fissures cross a variety of ancient, heavily cratered Noachian terrain and younger, Hesperian and Amazonian terrain. We focused our search on a region 0-15 N, 250 - 270 W. Elevations are -0.5 to 2 km. Depending upon whether Isidis Planitia was ever a water-rich environment, this region might have been influenced by aqueous sedimentation. Valley networks are common, and they drained toward the north and northwest. We focused our work on a set of Viking orbiter high-resolution images, 719A 1-48. These have resolutions 16-24 rri/pixel. We examined images 20-23, centered at 2 N, 258 W. This site, on the plains just southwest of a 42 km-diameter crater, includes a valley network channel, a relatively young crater ejecta deposit, a few buttes composed of presumably ancient, Noachian bedrock, and a "plains" unit. The plains might make an ideal landing surface, except for the presence of some fine-scale ridges (oriented approximately N-S). The ridges are probably yardangs, thus this site offers a place where aeolian deflation has probably exposed some of the layered rock units that comprise the "plains". Thermal inertias are 7.9-8.3 x 10(exp -3) cal/sq cm s(exp -0.5) /K and rock abundances are 10-15%. A rover traverse might include the opportunity to go down to the floor (and sample along the walls) of the valley network channel at 2 N 258.1 W.

Edgett, K. S.↗
NASA NTRS1994

Accurate interlaminar stress recovery from finite element analysis

The accuracy and robustness of a two-dimensional smoothing methodology is examined for the problem of recovering accurate interlaminar shear stress distributions in laminated composite and sandwich plates. The smoothing methodology is based on a variational formulation which combines discrete least-squares and penalty-constraint functionals in a single variational form. The smoothing analysis utilizes optimal strains computed at discrete locations in a finite element analysis. These discrete strain data are smoothed with a smoothing element discretization, producing superior accuracy strains and their first gradients. The approach enables the resulting smooth strain field to be practically C1-continuous throughout the domain of smoothing, exhibiting superconvergent properties of the smoothed quantity. The continuous strain gradients are also obtained directly from the solution. The recovered strain gradients are subsequently employed in the integration o equilibrium equations to obtain accurate interlaminar shear stresses. The problem is a simply-supported rectangular plate under a doubly sinusoidal load. The problem has an exact analytic solution which serves as a measure of goodness of the recovered interlaminar shear stresses. The method has the versatility of being applicable to the analysis of rather general and complex structures built of distinct components and materials, such as found in aircraft design. For these types of structures, the smoothing is achieved with 'patches', each patch covering the domain in which the smoothed quantity is physically continuous.

Tessler, Alexander↗
NASA NTRS1991

Investigation of the influence of a step change in surface roughness on turbulent heat transfer

The use is studied of smooth heat flux gages on the otherwise very rough SSME fuel pump turbine blades. To gain insights into behavior of such installations, fluid mechanics and heat transfer data were collected and are reported for a turbulent boundary layer over a surface with a step change from a rough surface to a smooth surface. The first 0.9 m length of the flat plate test surface was roughened with 1.27 mm hemispheres in a staggered, uniform array spaced 2 base diameters apart. The remaining 1.5 m length was smooth. The effect of the alignment of the smooth surface with respect to the rough surface was also studied by conducting experiments with the smooth surface aligned with the bases or alternatively with the crests of the roughness elements. Stanton number distributions, skin friction distributions, and boundary layer profiles of temperature and velocity are reported and are compared to previous data for both all rough and all smooth wall cases. The experiments show that the step change from rough to smooth has a dramatic effect on the convective heat transfer. It is concluded that use of smooth heat flux gages on otherwise rough surfaces could cause large errors.

Taylor, Robert P.↗
NASA NTRS1994

Topological analysis of the CfA redshift survey

We study the topology of large-scale structure in the Center for Astrophysics Redshift Survey, which now includes approximately 12,000 galaxies with limiting magnitude m(sub B) is less than or equal to 15.5. The dense sampling and large volume of this survey allow us to compute the topology on smoothing scales from 6 to 20/h Mpc; we thus examine the topology of structure in both 'nonlinear' and 'linear' regimes. On smoothing scales less than or equal to 10/h Mpc this sample has 3 times the number of resolution elements of samples examined in previous studies. Isodensity surface of the smoothed galaxy density field demonstrate that coherent high-density structures and large voids dominate the galaxy distribution. We compute the genus-threshold density relation for isodensity surfaces of the CfA survey. To quantify phase correlation in these data, we compare the CfA genus with the genus of realizations of Gaussian random fields with the power spectrum measured for the CfA survey. On scales less than or equal to 10/h Mpc the observed genus amplitude is smaller than random phase (96% confidence level). This decrement reflects the degree of phase coherence in the observed galaxy distribution. In other words the genus amplitude on these scales is not good measure of the power spectrum slope. On scales greater than 10/h Mpc, where the galaxy distribution is rougly in the 'linear' regime, the genus ampitude is consistent with the random phase amplitude. The shape of the genus curve reflects the strong coherence in the observed structure; the observed genus curve appears broader than random phase (94% confidence level for smoothing scales less than or equal to 10/h Mpc) because the topolgoy is spongelike over a very large range of density threshold. This departre from random phase consistent with a distribution like a filamentary net of 'walls with holes.' On smoothing scales approaching approximately 20/h Mpc the shape of the CfA genus curve is consistent with random phase. There is very weak evidence for a shift of the genus toward a 'bubble-like' topology. To test cosmological models, we compute the genus for mock CfA surveys drawn from large (L greater than or approximately 400/h Mpc) N-body simulations of three variants of the cold dark matter (CDM) cosmogony. The genus amplitude of the 'standard' CDM model (omega h = 0.5, b = 1.5) differs from the observations (96% confidence level) on smoothing scales is less than or approximately 10/h Mpc. An open CDM model (omega h = 0.2) and a CDM model with nonzero cosmological constant (omega h = 0.24, lambda (sub 0) = 0.6) are consistent with the observed genus amplitude over the full range of smoothing scales. All of these models fail (97% confidence level) to match the broadness of the observed genus curve on smoothing scales is less than or equal to 10/h Mpc.

Vogeley, Michael S.↗
NASA NTRS2009

Hardware Implementation of a Bilateral Subtraction Filter

A bilateral subtraction filter has been implemented as a hardware module in the form of a field-programmable gate array (FPGA). In general, a bilateral subtraction filter is a key subsystem of a high-quality stereoscopic machine vision system that utilizes images that are large and/or dense. Bilateral subtraction filters have been implemented in software on general-purpose computers, but the processing speeds attainable in this way even on computers containing the fastest processors are insufficient for real-time applications. The present FPGA bilateral subtraction filter is intended to accelerate processing to real-time speed and to be a prototype of a link in a stereoscopic-machine- vision processing chain, now under development, that would process large and/or dense images in real time and would be implemented in an FPGA. In terms that are necessarily oversimplified for the sake of brevity, a bilateral subtraction filter is a smoothing, edge-preserving filter for suppressing low-frequency noise. The filter operation amounts to replacing the value for each pixel with a weighted average of the values of that pixel and the neighboring pixels in a predefined neighborhood or window (e.g., a 9 9 window). The filter weights depend partly on pixel values and partly on the window size. The present FPGA implementation of a bilateral subtraction filter utilizes a 9 9 window. This implementation was designed to take advantage of the ability to do many of the component computations in parallel pipelines to enable processing of image data at the rate at which they are generated. The filter can be considered to be divided into the following parts (see figure): a) An image pixel pipeline with a 9 9- pixel window generator, b) An array of processing elements; c) An adder tree; d) A smoothing-and-delaying unit; and e) A subtraction unit. After each 9 9 window is created, the affected pixel data are fed to the processing elements. Each processing element is fed the pixel value for its position in the window as well as the pixel value for the central pixel of the window. The absolute difference between these two pixel values is calculated and used as an address in a lookup table. Each processing element has a lookup table, unique for its position in the window, containing the weight coefficients for the Gaussian function for that position. The pixel value is multiplied by the weight, and the outputs of the processing element are the weight and pixel-value weight product. The products and weights are fed to the adder tree. The sum of the products and the sum of the weights are fed to the divider, which computes the sum of products the sum of weights. The output of the divider is denoted the bilateral smoothed image. The smoothing function is a simple weighted average computed over a 3 3 subwindow centered in the 9 9 window. After smoothing, the image is delayed by an additional amount of time needed to match the processing time for computing the bilateral smoothed image. The bilateral smoothed image is then subtracted from the 3 3 smoothed image to produce the final output. The prototype filter as implemented in a commercially available FPGA processes one pixel per clock cycle. Operation at a clock speed of 66 MHz has been demonstrated, and results of a static timing analysis have been interpreted as suggesting that the clock speed could be increased to as much as 100 MHz.

Huertas, Andres↗