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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.

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At least 37 records · Page 2

A strategy for the efficient simulation of viscous compressible flows using a multi-domain pseudospectral method

The viscous compressible flow in a quasi-1D nozzle is presently simulated by means of a novel multidomain pseudospectral method in which interface-point flow variables are advanced in time on the basis of the second-order time-marching scheme used for the interior points. A spectrally accurate modification of Van Leer's (1982) flux-vector flux-splitting method is used to evaluate the spatial derivatives of the inviscid flux vector; these derivatives are alternately evaluated from neighboring subdomains, and the scheme is found to be spectrally accurate and to resolve shock waves without oscillations.

Hanley, Patrick↗

Boundary conditions for implicit solutions to the compressible Navier-Stokes equations in finite computational domains

The admissible boundary conditions for the unsteady Navier-Stokes equations are insufficient to determine completely the flow variables at grid points on the boundaries of a finite computational domain. A general method is presented in which the boundary conditions are supplemented by conservatively differenced forms of the flow equations. For implicit algorithms, the method provides a fully implicit coupling between boundary and interior points. Implicit boundary-point computation schemes are given for most types of flow boundary encountered in internal and external flow problems. Convergence to steady state is generally faster than with locally explicit boundary-point schemes.

Thomas, P. D.↗

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles, theory

The theoretical foundation and formulation of a numerical method for predicting the viscous flowfield in and about isolated three dimensional nozzles of geometrically complex configuration are presented. High Reynolds number turbulent flows are of primary interest for any combination of subsonic, transonic, and supersonic flow conditions inside or outside the nozzle. An alternating-direction implicit (ADI) numerical technique is employed to integrate the unsteady Navier-Stokes equations until an asymptotic steady-state solution is reached. Boundary conditions are computed with an implicit technique compatible with the ADI technique employed at interior points of the flow region. The equations are formulated and solved in a boundary-conforming curvilinear coordinate system. The curvilinear coordinate system and computational grid is generated numerically as the solution to an elliptic boundary value problem. A method is developed that automatically adjusts the elliptic system so that the interior grid spacing is controlled directly by the a priori selection of the grid spacing on the boundaries of the flow region.

Thomas, P. D.↗

Thermohydrodynamic analysis for laminar lubricating films

A Galerkin-type analysis to include thermal effects in laminar lubricating films was performed. The lubricant properties were assumed constant except for a temperature-dependent Newtonian viscosity. The cross-film temperature profile is established by collocation at the film boundaries and two interior Lobatto points. The interior temperatures are determined by requiring that the zeroth and first moment of the energy equation be satisfied across the film. The fluidity is forced to conform to a third--degree polynomial appropriate to the Lobatto-point temperatures. Preliminary indications are that the use of just two such sampling points enables satisfactory prediction of bearing performance even in the presence of substantial viscosity variation.

Elrod, H. G.↗

Optimal Control Problems with Switching Points

The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

Seywald, Hans↗

Gas Motion in a Local Supersonic Region and Conditions of Potential-Flow Breakdown

For a certain Mach number of the oncoming flow, the local velocity first reaches the value of the local velocity of sound (M = 1) at some point on the surface of the body located within the flow. This Mach number is designated the critical Mach number M(sub cr). By increasing the flow velocity, a supersonic local region is formed bounded by the body contour and the line of transition from subsonic to supersonic velocity. As is shown by observations with the Toepler apparatus, at a certain flow Mach number M > M(sub cr) a shock wave is formed near the body that closes the local supersonic region from behind. The formation of the shock wave is associated with the appearance of an additional resistance defined as the wave drag. In this paper, certain features are described of the flow in the local supersonic region, which is bounded by the contour of the body and the transition line, and conditions are sought for which the potential flow with the local supersonic region becomes impossible and a shock wave occurs. In the first part of the paper, the general properties of the potential flow in the local supersonic region, bounded by the contour of the profile and the transition line, are established. It is found that at the transition line, if it is not a line of discontinuity, the law of monotonic variation of the angle of inclination of the velocity vector holds (monotonic law). An approximation is given for the change in velocity at the contour of the body. The flow about a contour having a straight part is studied. In the second part of the paper, an approximation is given of the magnitudes of the accelerations at the interior points of the supersonic region. With the aid of these approximations, it is shown that for profiles convex to the flow the breakdown of the potential flow,associated with an increase of the Mach number of the oncoming flow, cannot be due to the formation of an envelope of the characteristics within the supersonic region. On the basis of the monotonic law, the transitional Mach number M is found, beyond which the potential flow with local supersonic region becomes impossible.

Nikolskii, A. A.↗

Spacecraft Modeling, Attitude Determination, and Control: Quaternion-Based Approach

Spacecraft attitude determination and control is an important part of a spacecraft to achieve its designed mission. As of today, many spacecrafts have been successfully launched, and most of them have performed well as they were designed. Many research papers have been published to address the attitude determination and control design problems. Several text books are available for students to learn the technology and for engineers to use as references. The most popular spacecraft models for attitude determination algorithms and control design methods are the Euler angle models and the quaternion models . The Euler angle models have been proved very efficient as the linearized models are controllable, and all standard linear control system design methods are directly applicable. The drawbacks related to the Euler angle methods are (a) the designs based on linearized models may not globally stabilize the original nonlinear spacecraft, i.e., the design may not work when the attitude of the spacecraft is far away from the point where the linearization is performed; (b) the models depend on the rotational sequences, this can be error prone if several teams work on the same project and they use different rotational sequences; (c) for any rotational sequence, there is a singular point where the model is not applicable; and (d) since most attitude determination methods use quaternion to represent the spacecraft attitude, there is a need to transform quaternion into Euler angles. On the other hand, for quaternion models, people have found controllers that can globally stabilize nonlinear spacecraft systems; the models do not depend on rotational sequences and they have no singular point; and the quaternion is provided by attitude determination system and ready to use. The main problem with the quaternion model based control system design is that the linearized quaternion model is not controllable. Therefore, most published design methods heavily rely on Lyapunov functions for the nonlinear spacecraft system. But there is no systematic way to obtain a desired Lyapunov functions. Moreover, the Lyapunov function based designs focus on the closed-loop system stability but pay little attention to the closed-loop system performance. In a series of papers, the author proposed some reduced quaternion models which lead to some controllable linearized spacecraft models. Therefore, all standard linear system theory can be directly applied to analyze and design the spacecraft control systems. We showed that, in some cases, the designed control system is not only optimal for the linearized system, but also globally stabilize the original nonlinear system . Clearly, the reduced quaternion models do not depend on rotational sequences. Due to the special structure of the linearized spacecraft model, some most important design methods, such as LQR design and robust pole assignment design are very simple, enjoy the analytical solutions for some problems, have direct connection to the performance measures, such as settling time, rising time , and percentage of overshoot . All these features are attractive for high quality control system designs. The idea mentioned above is then extended to more spacecraft control problems using specific actuators such as magnetic torque bars and control momentum gyroscopes. These types of actuators may not provide exactly desired torques. Most existing methods use different conversions to get approximate solutions, meaning that these actuators may generate a torque close to but not equal to the desired one. Using the reduced quaternion models that incorporate the actuators into the system model, the control inputs are not torques but the operational parameters. The main benefit of this idea is that the control actions are not approximate but accurate. As all actuators have their operational limit, design with input constraints are also considered in this book by using recently developed interior-point optimization techniques. This book grows up from my research on the spacecraft attitude determination and control design methods in more than a decade which is focused on using reduced quaternion models because of their merits stated above. The book provides all necessary background materials on orbital dynamics, rotations and quaternion, frequently used reference frames, transformations between reference frames, space environment and disturbance torques, ephemeris astronomical vector calculations and measurement instruments, spacecraft control actuators and their models, so that the readers will get a global picture and can apply all these information into the spacecraft system modeling, attitude determination, and spacecraft control system designs, which is the main purpose of this book. This book is different from existing books in that we focus on quaternion based spacecraft control system designs and we consider only attitude control system design related problems, from spacecraft modeling, to attitude determination and estimation, to control system design method selection, to control algorithm development, and to the simulation of the control system designs. Moreover, this book addresses different attitude control tasks in the spacecraft life cycle, including spacecraft maneuver, orbit raising, attitude control, and rendezvous. Finally, this book emphasizes the state space design methods rather than the classical frequency design methods.

Attitude determination and control↗

Subsonic, transonic, and supersonic nozzle flow by the inverse technique.

The inverse technique is used to obtain a mathematically and physically consistent solution of the flowfield in a nozzle from the mass generation surface through the supersonic region. The inverse method employs an assumed centerline function which is of the Cauchy type in that the values and the derivatives of the function are known. Since the Cauchy boundary conditions can give rise to numerical instabilities, the governing gasdynamic equations for rotational steady flow were transformed into a form which puts the geometry into a rectangular shape, and which spaces the network of interior points more finely in regions of the greatest gradients of the dependent variables. For arbitrarily specified centerline data, the solution of the governing flow equations may not exist, and if it does it may not depend continuously on the data.

Norton, D. J.↗

Matrix operator theory of radiative transfer. I - Rayleigh scattering.

An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; and (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions.

Plass, G. N.↗

Geometrically constrained observability

This paper deals with observed processes in situations in which observations are available only when the state vector lies in certain regions. For linear autonomous observed processes, necessary and sufficient conditions are obtained for half-space observation regions. These results are shown to contain a theorem dual to a controllability result proved by the author for a linear autonomous control system whose control restraint set does not contain the origin as an interior point. Observability results relating to continuous observation systems and sampled data systems are presented, and an example of observing the state of an electrical network is given.

Brammer, R. F.↗

Lagrange duality theory for convex control problems

The Lagrange dual to a control problem is studied. The principal result based on the Hahn-Banach theorem proves that the dual problem has an optimal solution if there exists an interior point for the constraint set. A complementary slackness condition holds, if the primal problem has an optimal solution. A necessary and sufficient condition for the optimality of solutions to the primal and the dual problem is also presented.

Hager, W. W.↗

Forced baroclinic ocean motions. II - The linear equatorial bounded case

Results obtained in the first part of this paper (1976), which studied forced baroclinic ocean motions in the linear equatorial unbounded case, are extended to the case of an ocean bounded by two meridians. A complete solution for the linear spin-up in response to a switched-on, x-dependent wind stress is obtained in terms of five components: the unbounded nonoscillatory response to the wind stress forcing; the inertia-gravity waves generated when the forcing switches on, together with their reflections; the quasi-geostrophic Rossby modes forming the eastern boundary response and a western boundary layer; and the equatorial Kelvin wave component of the western boundary response. Kelvin waves are generated if the forcings include a zonal wind component that is symmetric about the equator or an antisymmetric meridional wind stress. For non-Kelvin symmetries, spin-up occurs entirely by the effects of Rossby waves emanating from the eastern boundary. The state approaches the steady solution as increasing numbers of these reach an interior point. In Kelvin symmetries, the Rossby waves act to bring the sea surface tilt to the steady value and the spin-up of the tilt proceeds as in non-Kelvin cases.

Cane, M. A.↗

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Fleury, C.↗

Fully implicit shock tracking

A tracking method for solving hyperbolic free boundary problems arising in fluid dynamics is presented. The principal feature of the new approach is that the implicit form is used to simultaneously treat both interior points and boundary conditions. In particular, the location of the free boundary (shock) surface is treated implicitly and coupled with all other unknowns. The method is presented in the context of unsteady one-dimensional flow in a variable area duct with an internal shock wave. The fully implicit method and other strategies for advancing the shock are compared for computing a steady solution via a time asymptotic approach. Issues regarding extension of the method to multiple dimensions are also discussed.

Bell, J. B.↗

Fracture behavior of the Space Shuttle thermal protection system

Stable crack-growth and fracture-toughness experiments were conducted using precracked specimens machined from LI-900 reusable surface insulation (RSI) tiles of the Space Shuttle thermal protection system (TPS) at room temperature. Similar fracture experiments were conducted on fracture specimens with preexisting cracks at the interface of the tile and the strain isolation pad (SIP). Stable crack growth was not observed in the LI-900 tile fracture specimens which had a fracture toughness of 12.0 kPa sq rt of m. The intermittent subcritical crack growth at the tile-pad interface of the fracture specimens was attributed to successive local pull-outs due to tensile overload in the LI-900 tile and cannot be characterized by linear elastic fracture mechanics. No subcritical interfacial crack growth was observed in the fracture specimens with densified LI-900 tiles where brittle fracture initiated at an interior point away from the densification.

Komine, A.↗

Effect of crack curvature on stress intensity factors for ASTM standard compact tension specimens

The stress intensity factors (SIF) are calculated using the method of lines for the compact tension specimen in tensile and shear loading for curved crack fronts. For the purely elastic case, it was found that as the crack front curvature increases, the SIF value at the center of the specimen decreases while increasing at the surface. For the higher values of crack front curvatures, the maximum value of the SIF occurs at an interior point located adjacent to the surface. A thickness average SIF was computed for parabolically applied shear loading. These results were used to assess the requirements of ASTM standards E399-71 and E399-81 on the shape of crack fronts. The SIF is assumed to reflect the average stress environment near the crack edge.

Alam, J.↗

Prediction of Acoustical Response of Three-dimensional Cavities Using an Indirect Boundary Element Method

A technique which characterizes the acoustics of generalized cavities with the minimum model possible is developed. All boundary element methods have two advantages over finite element methods: (1) the models are smaller; and (2) the assumed variable behavior, inherent in the method to allow discretization, is harmonic rather than polynomial. Further, IBEM often requires one rather than two numerical boundary integrals as required by DBEM. Thus, a quadratic, isoparametric IBEM program was developed. The source distribution in this solution is continuous and quadratically variable rather than continuous and constant. The program was also formulated to include the additional capability of interior point sources and impedance boundary conditions. To test the quadratic, isoparametric IBEM program, several simple cavity enclosure problems where studied. Results are shown.

Bernhard, R. J.↗