SEARCH · Engineering Papers

Results for “Convex approximation”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

77 records · Page 5

All sources NASA NTRS DOE OSTI

NASA NTRS2004

Adjoint Formulation for an Embedded-Boundary Cartesian Method

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.

Nemec, Marian↗

NASA NTRS1993

Experimental study of void formation during aluminum solidification in reduced gravity

Void formation due to volumetric shrinkage and liquid/vapor reorientation during aluminum solidification was observed in real time by using a radiographic viewing system in normal and reduced gravity. An end-chill directional solidification furnace with water quench was designed and constructed to solidify aluminum samples during the approximately 16 sec of reduced gravity (+/-0.02g) achieved by flying an aircraft through a parabolic trajectory. In the first series of tests the aluminum was contained in a vacuum sealed, pyrolytic boron nitride crucible. An ullage space was present during each test. Void formation was recorded for two cases: a nonwetting system, and a wetting system where wetting occurred between the aluminum and the crucible lid. The void formation in the nonwetting case was similar in normal and reduced gravity, with a single vapor cavity forming at the top of the crucible. In the wetting case during reduced gravity surface tension caused two voids to form in the top corners of the crucible, but during normal gravity only one large void formed across the top. In the second series of tests the aluminum was contained in a pyrolytic boron nitride crucible that was placed in a stainless steel container and sealed in an environment of argon plus 4 percent hydrogen. An ullage space was present during each test. Void formation was recorded for two cases: a nonwetting system, and a wetting system where wetting occurred between the aluminum and one side wall and the lid. The void for nation in the nonwetting case was similar in normal and reduced gravity, with a single vapor cavity forming at the top of the crucible, although the meniscus became more convex in reduced gravity. In the wetting case the aluminum did not climb up the corners in 1g, and one large symmetric void resulted at the top when the aluminum had solidified. In the wetting case during reduced gravity the molten aluminum was drawn up the wetted wall and partially across the lid by a capillary underpressure; however, on the nonwetting wall the aluminum moved down. One void resulted along the nonwetting side of the container continuing to the top on the same side.

Chiaramonte, Francis Paul, III↗

NASA NTRS2003

Long Focal Length Large Mirror Fabrication System

The goals of this ambitious program are (1) to develop systems to make large superpolished optical mirrors, (2) to develop low scatter polishing techniques using centrifugal elutriation, (3) to develop a means of measuring scatter at any point on the mirror, (4) to polish a Hindle sphere to measure the optical figure of a one meter diameter convex mandrel, and (5) to fabricate low scatter, large adaptive optic graphite filled, cyanate ester replica transfer mirrors using these mandrels. Deliverables are a 30 cm diameter superpolished composite AO mirror. We fabricated a 1/3rd meter superpolished zerodur flat mandrel and with the support of our major subcontractor, Composite Mirror Applications Inc (CMA) we have demonstrated a 30 cm lightweight cyanate ester mirror with an rms microroughness between 0.6 and 0.8 nm and 8 faceplate influence function of 5 cm. The influence function was chosen to be comparable to the atmospheric correlation coefficient r(sub 0) which is about 5 cm at sea level. There was no print-thru of the graphite fibers in the cyanate ester surface (the bane of many previous efforts to use cyanate ester mirrors). Our subcontractor has devised a means for developing a 30-50 nm thick layer of graphite free pure ester resin on the surface of the mirrors. This graphite fiber filled material has a thermal expansion coefficient in the 10(exp -8) centimeter per Kelvin range (the same range of expansion coefficient as Zerodur and ULE glasses) and does not take up water and swell, so it is a nearly ideal mirror material in these areas. Unfortunately for these 0.8mm thick faceplates, the number of plies is not enough to result in isometric coverage. Isolated figure irregularities can appear, making it necessary to go to thicker faceplates. The influence function will then only approximate the length of r(sub 0), at higher altitudes or longer wavelengths. The influence function goes as the cube of the thickness, so we are now making a faceplate optimized for an infrared wavelength, possibly that used for the AO system of the Keck telescope, instead of 0.63 microns. We have polished a 55 cm diameter mandrel to better than 1/20th wave optical figure in the visible using centrifugal elutriation. CMA has just told us that it needs to retool to get optimum mirror faceplate quality in this size, so implementing the 55 cm AO mirror may be delayed somewhat. We expect to complete our 1/3 rd meter AO mirror on time using novel piezoelectric actuators with a throw of one micrometer per volt, as compared to 0.005 micrometers per volt for conventional piezoelectric actuators. We will then demonstrate its AO performance interferometrically.

Bennett, H. E.↗

NASA NTRS2022

Human Stability While Exercising on a VIS Device in Zero Gravity

BACKGROUND: A Vibration Isolation and Stabilization (VIS) system is being designed for use with the European Enhanced Exploration Exercise Device (E4D) [1]. The exercise bar is attached to cables that extend and retract through openings in the E4D platform, which the subject stands on while exercising. Since the E4D is mounted on a moving VIS device, the whole system moves under the subject’s feet. While tension in the cables does help stabilize a crew member in 0g by bracing him or her against the moving platform, flexible cables do not offer full support against falling. This raises the question of whether various exercises that are successfully performed in 1g on a stationary device can be performed without losing balance in 0g on a moving device. Quantifying stability conditions and establishing stability requirements for exercise countermeasure systems is a long-standing challenge and this work helped to inform this specific need for integrated E4D/VIS flight project development. METHODS AND RESULTS: A simplified stability analysis can be attempted based on platform accelerations generated by the VIS device simulation. In this type of analysis, the subject is conceived as standing on the platform in 0g while being held down to it by the tension in the cables. If the sideways acceleration of the platform is such that the cables cannot generate a sufficient moment relative to, e.g., the heels or the toes of the subject to overcome the tipping moment from the inertial forces on the accelerated subject’s body, the subject becomes unstable. This approach, which we refer to as the ‘static’ approximation, indicated failure of all the exercises that were considered in the comprehensive VIS analysis of the E4D. It was realized, however, that platform accelerations are not externally imposed but are themselves induced by the motion of the subject’s body during exercise, and a model calculation confirmed that this drastically altered the tipping moment on the subject, with the potential to even switch the direction in which the body would tip over. This made it imperative to consider in a coupled manner both the motion of the exercising subject’s body and the induced VIS platform motion while considering stability. The coupled dynamics requirement was met by the VIS simulation incorporating time-dependent human mass properties atop the platform and driven by the inertial forces from the prescribed subject motion relative to the platform based on motion-capture recorded human trajectories in 1g on a stationary E4D [2]. To analyze simulation results, a stability criterion was also needed. We do not know how to account for the human ‘control system’ that would take visual and vestibular cues as inputs as the platform moves in 0g. We thus chose to follow an approach we had previously used to analyze the dynamic feasibility of performing a task in lunar gravity along the human body trajectory recorded in 1g [3]. In this approach, one analyzes the center of pressure (COP) between the shoes and the ground (or platform) and checks if the COP remains within the convex hull of the footprints on the ground (or platform), commonly referred to as base of support (BOS). Since pressure is vertical and, in the absence of foot restraints, positive, the COP going outside the BOS indicates that the trajectory recorded in 1g is not dynamically feasible in microgravity and/or on the moving platform of the device. The outcome of the COP-based analysis was that some of the key exercises, especially the deadlift and the back squat exercises, were found to be dynamically feasible for at least some number of the exercise cycles, this number increasing with the cable tension. While this type of stability analysis does not account for the likely alteration of the exercise trajectory from its 1g form in space, it does show that there exist at least some realistic trajectories that pass the dynamic feasibility criterion. This adds confidence that, with further adjustment by the subject of the exercise form in 0g on a moving device, a number of exercises can be performed without losing balance.

D Frenkel↗

NASA NTRS2013

The Face that Launched a Thousand Slips

Helene, (approximately 17.6 kilometers mean radius) is an L4 Trojan co-orbital of Saturn's moon Dione. Its hemisphere features an unusual morphology consisting of broad depressions and a generally smooth surface patterned with streaks and grooves. The streaks appear to be oriented down-gradient, as are the grooves. This pattern suggests intensive mass-wasting as a dominant process on the leading hemisphere. Kilometer-scale impact craters are very sparse on the leading hemisphere other than the degraded kilometer-scale basins defining the overall satellite shape, and many small craters have a diffuse appearance suggesting ongoing mass wasting. Thus mass wasting must dominate surface-modifying processes at present. In fact, the mass wasting appears to have been sufficient in magnitude to narrow the divides between adjacent basins to narrow septa, similar, but in lower relief, to the honeycomb pattern of Hyperion. The prominent groves occur primarily near topographic divides and appear have cut into a broad, slightly lower albedo surface largely conforming to the present topography but elevated a few meters above the smooth surfaces undergoing mass wasting flow. Low ridges and albedo markings on the surface suggest surface flow of materials traveling up to several kilometers. Diffusive mass wasting produces smooth surfaces - such a pattern characterizes most of the low-lying surfaces. The grooves, however, imply that the transport process is advective at those locations where they occur, that is, erosion tends to concentrate along linear pathways separated by divides. In fact, in many places grooves have a fairly regular spacing of 125-160 meters, defining a characteristic erosional scale. Several questions are prompted by the unusual morphology of Helene: 1) What is the nature of the surface materials? 2) Are the transport processes gradual or catastrophic motion from one or a few events? 3) What mechanisms drive mass wasting and groove development? 4) Have the formative processes been active in the recent past? 5) Finally, is the surface accreting or eroding? The smooth character of the leading edge hemisphere of Helene and the dominance of mass wasting suggest that the surface is composed of fine-grained debris, probably dominated by dust-size to small gravel particles. The Lagrangian points of saturnian satellites are locations where planetesimals might have accreted to form co-orbital satellites such as and they may capture ejecta from their master moon. Published models suggest that Helene is a site of net accretion, but we find no extant explanation for the dominance of fine grain sizes for the surface (and probable subsurface) composition of Helene and the other Lagrangian satellites. Observation of the mass wasting tracks on Helene suggests the presence of well-defined streams of debris with low bordering levees that may be depositional features or remnants of the dissected higher surface. Some flows in grazing illumination appear to have a convex cross-section. This mass-flow morphology might be consistent with the occurrence of large-scale flow events, but which might have occurred through rapid emplacement or slow glacier-like creep. On the other hand, small craters appear to have been "softened" by creep-like processes, indicating ongoing mass wasting.

honeycomb pattern of Hyperion↗