Search NASA⌕ Search

SEARCH · Search NASA

Results for “satisfiability problems”

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.

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

At least 307 records · Page 17

Interlaminar stress analysis of dropped-ply laminated plates and shells by a mixed method

A mixed method of approximation based on Reissner's variational principle is developed for the linear analysis of interlaminar stresses in laminated composites, with special interest in laminates that contain terminated internal plies (dropped-ply laminates). Two models are derived, one for problems of generalized plane deformation and the other for the axisymmetric response of shells of revolution. A layerwise approach is taken in which the stress field is assumed with an explicit dependence on the thickness coordinate in each layer. The dependence of the stress field on the thickness coordinate is determined such that the three-dimensional equilibrium equations are satisfied by the approximation. The solution domain is reduced to one dimension by integration through the thickness. Continuity of tractions and displacements between layers is imposed. The governing two-point boundary value problem is composed of a system of both differential and algebraic equations (DAE's) and their associated boundary conditions. Careful evaluation of the system of DAE's was required to arrive at a form that allowed application of a one-step finite difference approximation. A two-stage Gauss implicit Runge-Kutta finite difference scheme was used for the solution because of its relatively high degree of accuracy. Patch tests of the two models revealed problems with solution accuracy for the axisymmetric model of a cylindrical shell loaded by internal pressure. Parametric studies of dropped-ply laminate characteristics and their influence on the interlaminar stresses were performed using the generalized plane deformation model. Eccentricity of the middle surface of the laminate through the ply drop-off was found to have a minimal effect on the interlaminar stresses under longitudinal compression, transverse tension, and in-plane shear. A second study found the stiffness change across the ply termination to have a much greater influence on the interlaminar stresses.

Harrison, Peter N.↗

Accurate boundary conditions for exterior problems in gas dynamics

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Hagstrom, Thomas↗

A Survey of the Spacecraft Line-Of-Sight Jitter Problem

Predicting, managing, controlling, and testing spacecraft Line-of-Sight (LoS) jit- ter due to on-board internal disturbance sources is a challenging multi- disciplinary systems engineering problem, especially for those observatories hosting extremely sensitive optical sensor payloads with stringent requirements on allowable LoS jitter. Some specific spacecraft jitter engineering challenges will be introduced and described in this survey paper. Illustrative examples of missions where dynamic interactions have to be addressed to satisfy demanding payload instrument LoS jitter requirements will be provided. Some lessons learned and a set of recommended rules of thumb are also presented to provide guidance for analysts on where to initiate and how to approach a new spacecraft jitter design problem. These experience-based spacecraft jitter lessons learned and rules of thumb are provided in the hope they can be leveraged on new space system development projects to help overcome unfamiliarity with previously identified jitter technical pitfalls and challenges.

Dennehy, Cornelius J.↗

Radiation from a parallel-plate waveguide into a dielectric or plasma layer.

An analytical solution for radiation from a truncated parallel-plate waveguide into a dielectric or plasma slab is obtained by solving the Hilbert problem associated with a certain singular integral equation. The technique has the advantage that the edge condition is easily shown to be satisfied, and numerical results can be obtained with excellent accuracy. Numerical results are presented for a variety of dielectric and plasma slabs, parallel-plate separations, and aperture-to-slab distances.

Kostelnicek, R. J.↗

On some properties of force-free magnetic fields in infinite regions of space

Techniques for solving boundary value problems (BVP) for a force free magnetic field (FFF) in infinite space are presented. A priori inequalities are defined which must be satisfied by the force-free equations. It is shown that upper bounds may be calculated for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of the region can be shown to decay sufficiently fast at infinity. The results are employed to prove a nonexistence theorem for the BVP for the FFF in the spatial region. The implications of the theory for modeling the origins of solar flares are discussed.

Aly, J. J.↗

The computational treatment of supersonic wake flows in INCOREL

Supersonic wake flows are computed in both conical and three-dimensional full potential flows by modeling the wake as a planar cut with a potential discontinuity. Continuity of pressure is satisfied exactly on the wake cut by computing the necessary potential jump at each wake cut grid point. In the conical wake problem, the jump in potential vanishes in the crossflow symmetry plane. Generally, good correlation is achieved for fully three-dimensional wake flows with the planar wake approximation. Matching pressures in the isolated wake flow leads to small variations in the spanwise jump in potential. On the other hand, a small variation in the jump in potential near the wing tip flow can lead to a significant loading in the wake flow if the pressures are not matched.

Siclari, M. J.↗

A dynamic systems engineering methodology research study. Phase 2: Evaluating methodologies, tools, and techniques for applicability to NASA's systems projects

A study of NASA's Systems Management Policy (SMP) concluded that the primary methodology being used by the Mission Operations and Data Systems Directorate and its subordinate, the Networks Division, is very effective. Still some unmet needs were identified. This study involved evaluating methodologies, tools, and techniques with the potential for resolving the previously identified deficiencies. Six preselected methodologies being used by other organizations with similar development problems were studied. The study revealed a wide range of significant differences in structure. Each system had some strengths but none will satisfy all of the needs of the Networks Division. Areas for improvement of the methodology being used by the Networks Division are listed with recommendations for specific action.

Paul, Arthur S.↗

Obstacle avoidance for redundant robots using configuration control

The article presents a new and simple solution to the obstacle avoidance problem for redundant robots. In the proposed approach, called configuraiton control, the redundancy is utilized to configure the robot so as to satisfy a set of kinematic inequality constraints representing obstacle avoidance, while the end-effector is tracking a desired trajectory. The robot control scheme is very simple, and uses on-line adaptation to eliminate the need for the complex dynamic model and parameter values of the robot. Several simulation results for a four-link planar robot are presented to illustrate the versatility of the approach. These include reaching around a stationary obstacle, simultaneous avoidance of two obstacles, robot reconfiguration to avoid a moving obstacle, and avoidance of rectangular obstacles.

Colbaugh, R.↗

Space Shuttle Main Engine performance analysis

For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.

Santi, L. Michael↗

The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.

Hewitt, R. E.↗

Electrolytic Removal of Nitrate From CELSS Crop Residues

The controlled ecological life support system (CELSS) resource recovery system is a waste processing system using aerobic and anaerobic bioreactors to recover plant nutrients and secondary foods from inedible biomass. Crop residues contain significant amounts of nitrate which presents two problems: (1) both CELSS biomass production and resource recovery consume large quantities of nitric acid, (2) nitrate causes a variety of problems in both aerobic and anaerobic bioreactors. A technique was proposed to remove the nitrate from potato inedible biomass leachate and to satisfy the nitric acid demand using a four compartment electrolytic cell.

Colon, Guillermo↗

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

A stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

N.D. Sandham↗

Accurate boundary conditions for exterior problems in gas dynamics

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far-field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far-field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Hagstrom, Thomas↗

Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows

A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.

Wilson, Robert V.↗

Summary and recommendations for the NASA/MIT workshop on short haul air transport

The material is summarized that was covered by the MIT/NASA Waterville Valley workshop which dealt with the institutional, socio-economic, operational and technological problems associated with introducing new forms of short haul domestic air transportation. It was found that future air systems hold great potential in satisfying society's needs for a low noise, low landspace, high access, high speed, large network system for public travel over distances between 5 and 500 miles. It is concluded that quiet air systems are necessary for obtaining community approval, and is recommended that extremely high priority be assigned to the development of quiet aircraft for future short haul air systems.

Simpson, R. W.↗

Satellites for distress alerting and locating: Report by Interagency Committee for Search and Rescue Ad Hoc Working Group

The background behind the congressional legislation that led to the requirement for the Emergency Locator Transmitter (ELT) and the Emergency Position-Indicating Radio Beacon (EPIRB) to be installed on certain types of aircraft and inspected marine vessels respectively is discussed. The DAL problem is discussed for existing ELT and EPIRB equipped aircraft and ships. It is recognized that the DAL requirement for CONUS and Alaska and the maritime regions are not identical. In order to address the serious DAL problem which currently exists in CONUS and Alaska, a low orbiting satellite system evolves as the most viable and cost effective alternative that satisfies the overall SAR system design requirements. A satellite system designed to meet the needs of the maritime regions could be either low orbiting or geostationary. The conclusions drawn from this report support the recommendation to proceed with the implementation of a SAR orbiting satellite system.

Ehrlich, E.↗

Spacelab 2 pointed experiments

Thirteen experiments have been selected for development for the multidisciplinary Spacelab 2 mission. They include three solar physics instruments and an atmospheric physics investigation mounted on the Instrument Pointing System (IPS), a two-axis gimballed X-ray experiment, an infrared telescope scanned about a single axis, and several fixed instruments. Integration of the IPS with its instruments and integration of the entire experiment complement into a flight mission has been a most demanding, complex task which has evolved as the Shuttle carrier vehicle, Spacelab, the IPS, and the experiments have matured. Mechanical interactions between all of these elements, thermal design restrictions, Shuttle and IPS operational constraints, mission duration, pointed instrument collision avoidance, and many other factors have impacted the scientific and engineering objectives of all of the experiments. Not all of the impacts have been adverse, however, and four types of joint science between previously unrelated experiments have so far been generated. This paper summarizes the current state of mission planning, particularly as it relates to the achievement of the scientific and engineering objectives of the pointed experiments. It discusses some of the compromises that have been made to satisfy the diverse requirements and capabilities of the hardware, the planning to date for joint solar observations from the IPS, and some system problems which remain.

Urban, E. W.↗