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NASA NTRS1994

A combined algorithm for minimum time slewing of flexible spacecraft

The use of Pontryagin's Maximum Principle for the large-angle slewing of large flexible structures usually results in the so-called two-point boundary-value problem (TPBVP), in which many requirements (e.g., minimum time, small flexible amplitude, and limited control powers, etc.) must be satisfied simultaneously. The successful solution of this problem depends largely on the use of an efficient numerical computational algorithm. There are many candidate algorithms available for his problem (e.g., quasilinearization, gradient, and shooting, etc.). In this paper, a proposed algorithm, which combines the quasilinearization method with a time shortening technique and a shooting method, is applied to the minimum-time, three-dimensional, and large-angle maneuver of flexible spacecraft, particularly the orbiting Spacecraft Control Laboratory Experiment (SCOLE) configuration. Theoretically, the nonlinear TPBVP can be solved only through the shooting method to find the 'exact' switching times for the bang-bang controls. However, computationally, a suitable guess for the missing initial costates is crucial because the convergence range of the unknown initial costates is usually narrow, especially for systems with high dimensions and when a multi-bang-bang control strategy is needed. On the other hand, the problems of near minimum time attitude maneuver of general rigid spacecraft and fast slewing of flexible spacecraft have been examined by the authors through a numerical approach based on the quasilinearization algorithm with a time shortening technique. Computational results have demonstrated its broad convergence range and insensitivity to initial costate choices. Consequently, a combined approach is naturally suggested here to solve the minimum time slewing problem. That is, in the computational process, the quasilinearization method is used first to obtain a near minimum time solution. Then, the acquired converged initial costates from the quasilinearization approach are transformed (tailored) to and used as the initial costate guess for starting the shooting method. Finally, the shooting method takes over the remaining calculations until the minimum-time solution converges. The nonlinear equations of motion of the SCOLE are formulated by using Lagrange's equations, with the mast modeled as a continuous beam subject to three-dimensional deformations. The numerical results will be presented and some related computational issues will also be discussed.

Bainum, P. M.↗
NASA NTRS2020

Durability of YSZ Coated Ti2AlC in 1300 °C Mach 0.3 Burner Rig Tests

A thermal barrier coating system survived burner rig testing at 1300 °C for 500 h. A 160 µm thick yttria stabilized zirconia (YSZ) coating was applied to a Ti2AlC MAX phase bar sample by plasma spray physical vapor deposition (PS-PVD) and tested face-on in an atmospheric Mach 0.3 jet fuel burner, using 5-h thermal cycles. No thermal barrier coating (TBC) spallation or recession was observed, only a 2.4 mg/cm2 mass gain. The modest weight gain precluded severe volatility losses under high velocity burner conditions. The coating surface exhibited colonies of (111)flourite fiber-textured columns separated by craze patterns, with no visible moisture attack. The metastable tetragonal t' YSZ phase was obtained initially, transitioning to equilibrium teq and cubic YSZ, but with little detrimental monoclinic. The thickness of the alumina TGO was ~21 to 23 μm under the heated YSZ face and ~13 to 15 μm on the uncoated, cooler backside. The backside exhibited removal of initial transient TiO2 nodules and partial etching of the underlying Al2O3 scale by volatile hydroxides formed in high temperature, high velocity water vapor. Aerodynamic forces produced some bending of the cantilevered sample via creep. The test indicated exceptional stability of YSZ coatings on Ti2AlC under turbine conditions, with thermal expansion matching playing a key role. The purpose of this study was to demonstrate long term durability of YSZ/MAX phase system in aggressive high temperature burner rig testing. MAX phases have been keenly studied because of their unique crystal structure and intriguing properties (Refs. 1 and 2). Having Mn+1(Al,Si)(C,N)n general composition, they are defined as ceramics, but possess unusual desirable attributes such as high conductivity, thermal shock resistance, easy machinability, and deformation tolerance. The mechanical properties derive from weak M-(Al,Si) bonding in the basal plane that leads to sliding and kinking in preference to catastrophic crack growth. Like most ceramics they are phase stable at high temperatures, generally up to 1500 °C. High temperature oxidation resistance is excellent for alumina-forming Ti3AlC2, Ti2AlC, and Cr2AlC, as reviewed by Tallman, et al. (Ref. 3). Compatibility with α-Al2O3 scales is further enhanced in cyclic exposures by a close matching of thermal expansion coefficients, (Ref. 4) i.e., (~9.3, 10.2, 11.3×10–6/K for Al2O3, Ti2AlC, and YSZ, to be discussed). Turbine environments generally contain 10 percent water vapor in the combustion gases, therefore moisture effects can be a concern for some materials (Ref. 5). Furnace tests of MAX phases in high temperature steam generally showed little effect on Al2O3 scale growth (Ref. 6). However, high velocity and high pressure gas can influence scale losses by the formation of volatile reaction products, such as TiO(OH)2 and Al(OH)3 (Refs. 7 to 10). This phenomenon had been discussed for 1100 to 1300 °C high pressure burner rig tests of Ti2AlC (Ref. 11). A single cubic growth rate parameter kcubic was measurably lower than comparable furnace TGA data, but it could be matched reasonably well if corrected for a slight volatility term. In general, a two-parameter cubic-linear growth-volatility law was believed to apply. Corresponding scale volatility loss rates, directly measured at 1300 °C on a pre-oxidized sample, were moderate (0.012 mg/cm2/h) and largely attributed to removal of the initial TiO2 transient scale. A related CH4 burner study of high purity Cr2AlC MAX phase demonstrated 1200 °C durability after 500 rapid (5 min. heat and 2 min. cool) thermal shock cycling (29 h hot time) (Ref. 12). Heating and cooling rates were ~1000 and 500 °C per minute, with a gas velocity of 5 m/s, producing a 75 °C/mm gradient. A 7 μm Al2O3 surface scale and a 13 μm Cr7C3 depletion zone formed with no signs of failure. No evidence of scale volatility was evident, although weight change was not provided, the velocity was moderate, and the total hot time was not extensive. The same high gradient BRT was used to produce 1400 °C surface temperatures for a YSZ/Cr2AlC/IN738 system in the first study of MAX phases used as bond coats for thermal barrier coatings (TBC) (Ref. 25). Here TBC failure was reported after 745 cycles, with only a 1.5 μm Al2O3 scale entrained within a porous, Cr7C3 bondcoat depletion phase. YSZ thermal barrier coatings have been considered to be a compatible complement to Al-MAX phases because of thermal expansion matching and extremely low volatility in water vapor. Initial studies showed superior oxidative stability up to 1300 °C, for long times (at least 500 h) for Ti2AlC substrates and less (268 h) for Cr2AlC, while withstanding large alumina TGO scale thickness (~35 to 40 μm) (Refs. 13 and 14). By comparison, typical superalloy systems can only survive 1150 °C maximum interface temperatures for extended periods, with a maximum sustained TGO below 10 μm (Ref. 15). High temperature SiC based systems are known to form slow-growing SiO2 scales. But these are subject to rate enhancement and volatile Si(OH)4 products in the presence of water vapor, as described comprehensively by Opila, et al. (Refs. 5, 16 to 19). Net weight losses are generally observed in high velocity, high pressure burner rig studies (e.g., 0.084 mg/cm2/h at 1300 °C) (Ref. 20). Furthermore, the loss rates have been shown from chemical physics to scale with v1/2 and pH2O 2 (Ref. 16). Low activity, moisture-resistant environmental barrier coatings (EBC), such as rare earth silicates, are needed to prevent substrate recession under turbine conditions (Refs. 21 to 23).

Smialek, James L.↗
NASA NTRS2002

Motion of Drops on Surfaces with Wettability Gradients

A liquid drop present on a solid surface can move because of a gradient in wettability along the surface, as manifested by a gradient in the contact angle. The contact angle at a given point on the contact line between a solid and a liquid in a gaseous medium is the angle between the tangent planes to the liquid and the solid surfaces at that point and is measured within the liquid side, by convention. The motion of the drop occurs in the direction of increasing wettability. The cause of the motion is the net force exerted on the drop by the solid surface because of the variation of the contact angle around the periphery. This force causes acceleration of an initially stationary drop, and leads to its motion in the direction of decreasing contact angle. The nature of the motion is determined by the balance between the motivating force and the resisting hydrodynamic force from the solid surface and the surrounding gaseous medium. A wettability gradient can be chemically induced as shown by Chaudhury and Whitesides who provided unambiguous experimental evidence that drops can move in such gradients. The phenomenon can be important in heat transfer applications in low gravity, such as when condensation occurs on a surface. Daniel et al have demonstrated that the velocity of a drop on a surface due to a wettability gradient in the presence of condensation can be more than two orders of magnitude larger than that observed in the absence of condensation. In the present research program, we have begun to study the motion of a drop in a wettability gradient systematically using a model system. Our initial efforts will be restricted to a system in which no condensation occurs. The experiments are performed as follows. First, a rectangular strip of approximate dimensions 10 x 20 mm is cut out of a silicon wafer. The strip is cleaned thoroughly and its surface is exposed to the vapor from an alkylchlorosilane for a period lasting between one and two minutes inside a desiccator. This is done using an approximate line source of the vapor in the form of a string soaked in the alkylchlorosilane. Ordinarily, many fluids, including water, wet the surface of silicon quite well. This means that the contact angle is small. But the silanized surface resists wetting, with contact angles that are as large as 100 degs. Therefore, a gradient of wettability is formed on the silicon surface. The region near the string is highly hydrophobic, and the contact angle decreases gradually toward a small value at the hydrophilic end away from this region. The change in wettability occurs over a distance of several mm. The strip is placed on a platform within a Plexiglas cell. Drops of a suitable liquid are introduced on top of the strip near the hydrophobic end. An optical system attached to a video camera is trained on the drop so that images of the moving drop can be captured on videotape for subsequent analysis. We have performed preliminary experiments with water as well as ethylene glycol drops. Results from these experiments will be presented in the poster. Future plans include the refinement of the experimental system so as to permit images to be recorded from the side as well as the top, and the conduct of a systematic study in which the drop size is varied over a good range. Experiments will be conducted with different fluids so as to obtain the largest possible range of suitably defined Reynolds and Capillary numbers. Also, an effort will be initiated on theoretical modeling of this motion. The challenges in the development of the theoretical description lie in the proper analysis of the region in the vicinity of the contact line, as well as in the free boundary nature of the problem. It is known that continuum models assuming the no slip condition all the way to the contact line fail by predicting that the stress on the solid surface becomes singular as the contact line is approached. One approach for dealing with this issue has been to relax the no-slip boundary condition using the Navier model. Molecular dynamics simulations of the contact line region show that for a non-polar liquid on a solid surface, the no-slip boundary condition is in fact incorrect near the contact line. Furthermore, the same simulations also show that the usual relationship between stress and the rate of deformation breaks down in the vicinity of the contact line. In developing continuum theoretical models of the system, we shall accommodate this knowledge to the extent possible.

Subramanian, R. Shankar↗
NASA NTRS2000

Overcoming Dynamic Disturbances in Imaging Systems

We develop and discuss a methodology with the potential to yield a significant reduction in complexity, cost, and risk of space-borne optical systems in the presence of dynamic disturbances. More robust systems almost certainly will be a result as well. Many future space-based and ground-based optical systems will employ optical control systems to enhance imaging performance. The goal of the optical control subsystem is to determine the wavefront aberrations and remove them. Ideally reducing an aberrated image of the object under investigation to a sufficiently clear (usually diffraction-limited) image. Control will likely be distributed over several elements. These elements may include telescope primary segments, telescope secondary, telescope tertiary, deformable mirror(s), fine steering mirror(s), etc. The last two elements, in particular, may have to provide dynamic control. These control subsystems may become elaborate indeed. But robust system performance will require evaluation of the image quality over a substantial range and in a dynamic environment. Candidate systems for improvement in the Earth Sciences Enterprise could include next generation Landsat systems or atmospheric sensors for dynamic imaging of individual, severe storms. The technology developed here could have a substantial impact on the development of new systems in the Space Science Enterprise; such as the Next Generation Space Telescope(NGST) and its follow-on the Next NGST. Large Interferometric Systems of non-zero field, such as Planet Finder and Submillimeter Probe of the Evolution of Cosmic Structure, could benefit. These systems most likely will contain large, flexible optomechanical structures subject to dynamic disturbance. Furthermore, large systems for high resolution imaging of planets or the sun from space may also benefit. Tactical and Strategic Defense systems will need to image very small targets as well and could benefit from the technology developed here. We discuss a novel speckle imaging technique with the potential to separate dynamic aberrations from static aberrations. Post-processing of a set of image data, using an algorithm based on this technique, should work for all but the lowest light levels and highest frequency dynamic environments. This technique may serve to reduce the complexity of the control system and provide for robust, fault-tolerant, reduced risk operation. For a given object, a short exposure image is "frozen" on the focal plane in the presence of the environmental disturbance (turbulence, jitter, etc.). A key factor is that this imaging data exhibits frame-to-frame linear shift invariance. Therefore, although the Point Spread Function is varying from frame to frame, the source is fixed; and each short exposure contains object spectrum data out to the diffraction limit of the imaging system. This novel speckle imaging technique uses the Knox-Thompson method. The magnitude of the complex object spectrum is straightforward to determine by well-established approaches. The phase of the complex object spectrum is decomposed into two parts. One is a single-valued function determined by the divergence of the optical phase gradient. The other is a multi-valued function determined by the circulation of the optical phase gradient-"hidden phase." Finite difference equations are developed for the phase. The novelty of this approach is captured in the inclusion of this "hidden phase." This technique allows the diffraction-limited reconstruction of the object from the ensemble of short exposure frames while simultaneously estimating the phase as a function of time from a set of exposures.

Young, Eric W.↗
NASA NTRS2000

Overcoming Dynamic Disturbances in Imaging Systems

We develop and discuss a methodology with the potential to yield a significant reduction in complexity, cost, and risk of space-borne optical systems in the presence of dynamic disturbances. More robust systems almost certainly will be a result as well. Many future space-based and ground-based optical systems will employ optical control systems to enhance imaging performance. The goal of the optical control subsystem is to determine the wavefront aberrations and remove them. Ideally reducing an aberrated image of the object under investigation to a sufficiently clear (usually diffraction-limited) image. Control will likely be distributed over several elements. These elements may include telescope primary segments, telescope secondary, telescope tertiary, deformable mirror(s), fine steering mirror(s), etc. The last two elements, in particular, may have to provide dynamic control. These control subsystems may become elaborate indeed. But robust system performance will require evaluation of the image quality over a substantial range and in a dynamic environment. Candidate systems for improvement in the Earth Sciences Enterprise could include next generation Landsat systems or atmospheric sensors for dynamic imaging of individual, severe storms. The technology developed here could have a substantial impact on the development of new systems in the Space Science Enterprise; such as the Next Generation Space Telescope(NGST) and its follow-on the Next NGST. Large Interferometric Systems of non-zero field, such as Planet Finder and Submillimeter Probe of the Evolution of Cosmic Structure, could benefit. These systems most likely will contain large, flexible optormechanical structures subject to dynamic disturbance. Furthermore, large systems for high resolution imaging of planets or the sun from space may also benefit. Tactical and Strategic Defense systems will need to image very small targets as well and could benefit from the technology developed here. We discuss a novel speckle imaging technique with the potential to separate dynamic aberrations from static aberrations. Post-processing of a set of image data, using an algorithm based on this technique, should work for all but the lowest light levels and highest frequency dynamic environments. This technique may serve to reduce the complexity of the control system and provide for robust, fault-tolerant, reduced risk operation. For a given object, a short exposure image is "frozen" on the focal plane in the presence of the environmental disturbance (turbulence, jitter, etc.). A key factor is that this imaging data exhibits frame-to-frame linear shift invariance. Therefore, although the Point Spread Function is varying from frame to frame, the source is fixed; and each short exposure contains object spectrum data out to the diffraction limit of the imaging system. This novel speckle imaging technique uses the Knox-Thompson method. The magnitude of the complex object spectrum is straightforward to determine by well-established approaches. The phase of the complex object spectrum is decomposed into two parts. One is a single-valued function determined by the divergence of the optical phase gradient. The other is a multi-valued function determined by, the circulation of the optical phase gradient-"hidden phase." Finite difference equations are developed for the phase. The novelty of this approach is captured in the inclusion of this "hidden phase." This technique allows the diffraction-limited reconstruction of the object from the ensemble of short exposure frames while simultaneously estimating the phase as a function of time from a set of exposures.

Young, Eric W.↗