Difference analogues of quasi-linear elliptic Dirichlet problems with mixed derivatives
Difference analogs of Dirichlet problem for second order quasi-linear elliptic operators with mixed derivatives, using discretization method
Stepleman, R. S.↗
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Recent advances in the development of implicit schemes for the equations of fluid dynamics
Innovations and extensions of implicit schemes for equations of fluid dynamics are presented. The notation and theory for linear multistep methods are reviewed, and extensions of work by Beam and Warming (1979) include the implementation of one-leg methods, ADI methods for equations with mixed derivatives, flux vector splitting, the P-dimensional wave equation, and boundary conditions. Numerical experiments indicate that implicit treatment of the boundary conditions is necessary for unconditional stability, and the improvement and implementation of the boundary condition theory should improve the implicit algorithms for gas dynamic equations.
Warming, R. F.↗
Stratospheric HF mixing ratio profiles in the northern and southern hemispheres
Spectra obtained by balloon-borne Michelson interferometers over South Australia in 1977 and New Mexico in 1978 have been analyzed to obtain HF mixing ratios using a recently developed, sensitive analysis method for Fourier transform spectroscopy. The stratospheric HF mixing ratio appears to be significantly larger in the northern hemisphere than in the southern hemisphere for similar respective latitudes with the profiles having a similar vertical shape: the HF mixing ratio increases from 20 to 25 km, stays approximately constant between 25 and 35 km, and increases upward from 35 km. A brief discussion is given of possible causes for HF profile shape.
Park, J. H.↗
Fast laser-induced aerosol formation for visualization of gas flows
A technique for aerosol seeding of gas flows by laser-induced particle formation is demonstrated using a pulsed Nd:YAG laser (1.06 microns) for optical breakdown of a mixture of SF6 and H2 in an inert carrier gas. It is noted that, contrary to the smoke-wire approach, the laser-induced particles form first in zones of high turbulence, since mixing enhances coagulation. The method also allows seeding to be performed in locations hardly accessible otherwise and is mechanically nonintrusive. Finally, a study of the mixture and the breakdown effects indicates that for H2:SF6 ratios between 3:1 and 15:1 the particle formation is only limited by the physics of the gas/particle conversion.
Hassa, C.↗
A time-based concept for terminal-area traffic management
An automated air-traffic-management concept that has the potential for significantly increasing the efficiency of traffic flows in high-density terminal areas is discussed. The concept's implementation depends on the techniques for controlling the landing time of all aircraft entering the terminal area, both those that are equipped with on-board four dimensional guidance systems as well as those aircraft types that are conventionally equipped. The two major ground-based elements of the system are a scheduler which assigns conflict-free landing times and a profile descent advisor. Landing times provided by the scheduler are uplinked to equipped aircraft and translated into the appropriate four dimensional trajectory by the on-board flight-management system. The controller issues descent advisories to unequipped aircraft to help them achieve the assigned landing times. Air traffic control simulations have established that the concept provides an efficient method for controlling various mixes of four dimensional-equipped and unequipped, as well as low-and high-performance, aircraft.
Erzberger, H.↗
A time-based concept for terminal-area traffic management
An automated air-traffic-management concept that has the potential for significantly increasing the efficiency of traffic flows in high-density terminal areas is discussed. The concept's implementation depends on techniques for controlling the landing time of all aircraft entering the terminal area, both those that are equipped with on-board four-dimensional (4D) guidance systems as well as those aircraft types that are conventionally equipped. The two major ground-based elements of the system are a scheduler which assigns conflict-free landing times and a profile descent advisor. Landing time provided by the scheduler is uplinked to equipped aircraft and translated into the appropriate 4D trajectory by the-board flight-management system. The controller issues descent advisories to unequipped aircraft to help them achieve the assigned landing times. Air traffic control simulations have established that the concept provides an efficient method for controlling various mixes of 4D-equipped and unequipped, as well as low- and high-performance, aircraft. Piloted simulations of profiles flown with the aid of advisories have verified the ability to meet specified descent times with prescribed accuracy.
Erzberger, Heinz↗
Response of some Thematic Mapper band ratios to variation in soil water content
Bidirectional reflectance to nadir in the reflective TM bands and the 1.15-1.3-micron band was measured in the laboratory as moisture content was varied in ten soils. Stronger absorption by water in TM5 and TM7 was expected to cause ratios of other bands to TM5 and TM7 to increase with water content, but in most cases these ratios were constant or decreased at low to intermediate water content and increased only at high moisture levels. Because these ratios were found to decrease as illumination elevation angle decreased, it was suggested that increased roughness resulting from the methods of moistening and mixing the soil may have tended to counteract the expected ratio increases.
Musick, H. Brad↗
Screening For Alcohol-Producing Microbes
Dye reaction rapidly identifies alcohol-producing microbial colonies. Method visually detects alcohol-producing micro-organisms, and distinguishes them from other microbial colonies that do not produce alcohol. Method useful for screening mixed microbial populations in environmental samples.
Schubert, Wayne W.↗
Optical Detection Of Cryogenic Leaks
Conceptual system identifies leakage without requiring shutdown for testing. Proposed device detects and indicates leaks of cryogenic liquids automatically. Detector makes it unnecessary to shut equipment down so it can be checked for leakage by soap-bubble or helium-detection methods. Not necessary to mix special gases or other materials with cryogenic liquid flowing through equipment.
Wyett, Lynn M.↗
A study on the thermal and moisture influences on the free-edge delamination of laminated composites
A simple delamination analysis method is presented here. It is based on a shear-type deformation theory and includes hygrothermal effects. These environmental conditions are applied to the strain energy release rate and interlaminar shear stresses. The method is applied to mixed mode edge delamination specimens made of T300/5208 graphite/epoxy material. Residual thermal and moisture stresses significantly influenced the strain energy release rate and interlaminar stresses. Both experienced large increases when thermal conditions were added to the mechanical strains. These effects were alleviated when moisture stresses were included. Thermal effects on the interlaminar shear stress and total energy release rate were totally alleviated for the same specific moisture content. Moreover, the value of the moisture content was not significantly affected by the stacking sequence for the laminates considered.
Mahler, Mary A.↗
A weak Hamiltonian finite element method for optimal control problems
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Hodges, Dewey H.↗
A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle
A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.
Hodges, Dewey H.↗
Weak Hamiltonian finite element method for optimal control problems
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Hodges, Dewey H.↗
A weak Hamiltonian finite element method for optimal control problems
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Hodges, Dewey H.↗
Prediction of thermal cycling induced cracking in polymer matrix composites
This report summarizes the work done in the period February 1993 through July 1993 on the 'Prediction of Thermal Cycling Induced Cracking In Polymer Matrix Composites' program. An oral presentation of this work was given to Langley personnel in September of 1993. This document was prepared for archival purposes. Progress studies have been performed on the effects of spatial variations in material strength. Qualitative agreement was found with observed patterns of crack distribution. These results were presented to NASA Langley personnel in November 1992. The analytical methodology developed by Prof. McManus in the summer of 1992 (under an ASEE fellowship) has been generalized. A method for predicting matrix cracking due to decreasing temperatures and/or thermal cycling in all plies of an arbitrary laminate has been implemented as a computer code. The code also predicts changes in properties due to the cracking. Experimental progressive cracking studies on a variety of laminates were carried out at Langley Research Center. Results were correlated to predictions using the new methods. Results were initially mixed. This motivated an exploration of the configuration of cracks within laminates. A crack configuration study was carried out by cutting and/or sanding specimens in order to examine the distribution of cracks within the specimens. These investigations were supplemented by dye-penetrant enhanced X-ray photographs. The behavior of thin plies was found to be different from the behavior of thicker plies (or ply groups) on which existing theories are based. Significant edge effects were also noted, which caused the traditional metric of microcracking (count of cracks on a polished edge) to be very inaccurate in some cases. With edge and configuration taken into account, rough agreement with predictions was achieved. All results to date were reviewed with NASA Langley personnel in September 1993.
Mcmanus, Hugh L.↗
A large eddy simulation scheme for turbulent reacting flows
The recent development of the dynamic subgrid-scale (SGS) model has provided a consistent method for generating localized turbulent mixing models and has opened up great possibilities for applying the large eddy simulation (LES) technique to real world problems. Given the fact that the direct numerical simulation (DNS) can not solve for engineering flow problems in the foreseeable future (Reynolds 1989), the LES is certainly an attractive alternative. It seems only natural to bring this new development in SGS modeling to bear on the reacting flows. The major stumbling block for introducing LES to reacting flow problems has been the proper modeling of the reaction source terms. Various models have been proposed, but none of them has a wide range of applicability. For example, some of the models in combustion have been based on the flamelet assumption which is only valid for relatively fast reactions. Some other models have neglected the effects of chemical reactions on the turbulent mixing time scale, which is certainly not valid for fast and non-isothermal reactions. The probability density function (PDF) method can be usefully employed to deal with the modeling of the reaction source terms. In order to fit into the framework of LES, a new PDF, the large eddy PDF (LEPDF), is introduced. This PDF provides an accurate representation for the filtered chemical source terms and can be readily calculated in the simulations. The details of this scheme are described.
Gao, Feng↗
Modeling of turbulent chemical reaction
Viewgraphs are presented on modeling turbulent reacting flows, regimes of turbulent combustion, regimes of premixed and regimes of non-premixed turbulent combustion, chemical closure models, flamelet model, conditional moment closure (CMC), NO(x) emissions from turbulent H2 jet flames, probability density function (PDF), departures from chemical equilibrium, mixing models for PDF methods, comparison of predicted and measured H2O mass fractions in turbulent nonpremixed jet flames, experimental evidence of preferential diffusion in turbulent jet flames, and computation of turbulent reacting flows.
Chen, J.-Y.↗
High Performance, Robust Control of Flexible Space Structures: MSFC Center Director's Discretionary Fund
Many spacecraft systems have ambitious objectives that place stringent requirements on control systems. Achievable performance is often limited because of difficulty of obtaining accurate models for flexible space structures. To achieve sufficiently high performance to accomplish mission objectives may require the ability to refine the control design model based on closed-loop test data and tune the controller based on the refined model. A control system design procedure is developed based on mixed H2/H(infinity) optimization to synthesize a set of controllers explicitly trading between nominal performance and robust stability. A homotopy algorithm is presented which generates a trajectory of gains that may be implemented to determine maximum achievable performance for a given model error bound. Examples show that a better balance between robustness and performance is obtained using the mixed H2/H(infinity) design method than either H2 or mu-synthesis control design. A second contribution is a new procedure for closed-loop system identification which refines parameters of a control design model in a canonical realization. Examples demonstrate convergence of the parameter estimation and improved performance realized by using the refined model for controller redesign. These developments result in an effective mechanism for achieving high-performance control of flexible space structures.
Whorton, M. S.↗