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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Optimal Angle of Attack Control for Aerocapture Maneuvers

Recent investigations of aerocapture maneuvers have considered direct force control as a promising alternative to bank angle control. By modulating the angle of attack and sideslip angle independently, the longitudinal and lateral channels can be decoupled and thus solved separately. However, the optimal angle of attack profile for minimizing post-atmospheric propellant expenditure was previously unknown. This research applies principles of optimal control theory to numerically solve for the optimal angle of attack profile for control of the longitudinal channel. Direct methods are first employed to discretize the angle of attack profile and show that an optimal solution follows a nearly bang-bang (full lift up then full lift down) structure under a variety of conditions along the flight path angle corridor. To corroborate these results, indirect methods were also applied to scope the Optimal Control Problem (OCP) as a Two Point Boundary Value Problem (2P-BVP) which could then be solved numerically. The indirect optimization results aligned closely with the direct results, providing further evidence that a bang-bang structure provides a good approximation for the optimal angle of attack profile for aerocapture maneuvers using direct force control.

aerocapture↗
NASA NTRS1989

Structural zooming research and development of an interactive computer graphical interface for stress analysis of cracks

Engineering problems sometimes involve the numerical solution of boundary value problems over domains containing geometric feature with widely varying scales. Often, a detailed solution is required at one or more of these features. Small details in large structures may have profound effects upon global performance. Conversely, large-scale conditions may effect local performance. Many man-hours and CPU-hours are currently spent in modeling such problems. With the structural zooming technique, it is now possible to design an integrated program which allows the analyst to interactively focus upon a small region of interest, to modify the local geometry, and then to obtain highly accurate responses in that region which reflect both the properties of the overall structure and the local detail. A boundary integral equation analysis program, called BOAST, was recently developed for the stress analysis of cracks. This program can accurately analyze two-dimensional linear elastic fracture mechanics problems with far less computational effort than existing finite element codes. An interactive computer graphical interface to BOAST was written. The graphical interface would have several requirements: it would be menu-driven, with mouse input; all aspects of input would be entered graphically; the results of a BOAST analysis would be displayed pictorially but also the user would be able to probe interactively to get numerical values of displacement and stress at desired locations within the analysis domain; the entire procedure would be integrated into a single, easy to use package; and it would be written using calls to the graphic package called HOOPS. The program is nearing completion. All of the preprocessing features are working satisfactorily and were debugged. The postprocessing features are under development, and rudimentary postprocessing should be available by the end of the summer. The program was developed and run on a VAX workstation, and must be ported to the SUN workstation. This activity is currently underway.

Gerstle, Walter↗
DOE OSTI2025

Image-Driven Hybrid Structural Analysis Based on Continuum Point Cloud Method with Boundary Capturing Technique

Conventional approaches for the structural health monitoring of infrastructures often rely on physical sensors or targets attached to structural members, which require considerable preparation, maintenance, and operational effort, including continuous on-site adjustments. This paper presents an image-driven hybrid structural analysis technique that combines digital image processing (DIP) and regression analysis with a continuum point cloud method (CPCM) built on a particle-based strong formulation. Polynomial regressions capture the boundary shape change due to the structural loading and precisely identify the edge and corner coordinates of the deformed structure. The captured edge profiles are transformed into essential boundary conditions. This allows the construction of a strongly formulated boundary value problem (BVP), classified as the Dirichlet problem. Capturing boundary conditions from the digital image is novel, although a similar approach was applied to the point cloud data. It was shown that the CPCM is more efficient in this hybrid simulation framework than the weak-form-based numerical schemes. Unlike the finite element method (FEM), it can avoid aligning boundary nodes with regression points. A three-point bending test of a rubber beam was simulated to validate the developed technique. The simulation results were benchmarked against numerical results by ANSYS and various relevant numerical schemes. The technique can effectively solve the Dirichlet-type BVP, yielding accurate deformation, stress, and strain values across the entire problem domain when employing a linear strain model and increasing the number of CPCM nodes. In addition, comparative analysis with conventional displacement tracking techniques verifies the developed technique’s robustness. The proposed technique effectively circumvents the inherent limitations of traditional monitoring methods resulting from the reliance on physical gauges or target markers so that a robust and non-contact solution for remote structural health monitoring in real-scale infrastructures can be provided, even in unfavorable experimental environments.

Chemistry↗
DOE OSTI2021

Wave-driven torques to drive current and rotation

In the classic Landau damping initial value problem, where a planar electrostatic wave transfers energy and momentum to resonant electrons, a recoil reaction occurs in the nonresonant particles to ensure momentum conservation. To explain how net current can be driven in spite of this conservation, the literature often appeals to mechanisms that transfer this nonresonant recoil momentum to ions, which carry negligible current. However, this explanation does not allow the transport of net charge across magnetic field lines, precluding E X B rotation drive. In this study, we show that in steady state, this picture of current drive is incomplete. Using a simple Fresnel model of the plasma, we show that for lower hybrid waves, the electromagnetic energy flux (Poynting vector) and momentum flux (Maxwell stress tensor) associated with the evanescent vacuum wave become the Minkowski energy flux and momentum flux in the plasma and are ultimately transferred to resonant particles. Thus, the torque delivered to the resonant particles is ultimately supplied by the electromagnetic torque from the antenna, allowing the nonresonant recoil response to vanish and rotation to be driven. We present a warm fluid model that explains how this momentum conservation works out locally, via a Reynolds stress that does not appear in the one-dimensional initial value problem. This model is the simplest that can capture both the nonresonant recoil reaction in the initial-value problem, and the absence of a nonresonant recoil in the steady-state boundary value problem, thus forbidding rotation drive in the former while allowing it in the latter.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1979

Linearization of the boundary-layer equations of the minimum time-to-climb problem

Ardema (1974) has formally linearized the two-point boundary value problem arising from a general optimal control problem, and has reviewed the known stability properties of such a linear system. In the present paper, Ardema's results are applied to the minimum time-to-climb problem. The linearized zeroth-order boundary layer equations of the problem are derived and solved.

Ardema, M. D.↗
NASA NTRS1976

Numerical solutions of the triple-deck equations for laminar trailing-edge stall

The problem of determining the effect of laminar boundary layers on the lift of thin wings in subsonic flow at high Reynolds numbers is considered. The boundary value problem is formulated in the framework of the triple-deck theory of Brown and Stewartson. The resulting fourth-order boundary value was solved by an iterative finite-difference technique. An inverse iteration procedure provides proper treatment of the trailing-edge singularity, and asymptotic far-field expansions and coordinate stretchings are used to deal with the problem of the slow algebraic decay of the solution.

Chow, R.↗
DOE OSTI2021

Relativistic levels of mesic atoms

We revisit the derivation of the covariant two-body scalar-fermion equation with a Coulomb interaction, presented in a previous paper. We show that it can be given the formal aspect of a Dirac equation, but for the fact that the eigenvalue is also contained in one of the coefficients and thus it is not linearly included. The discussion of the boundary value problem is therefore different, although some properties of the Dirac equation can be recovered in an approximation bringing back to the concept of reduced mass. We discuss a mixed analytic-numerical method of solution which allows to obtain very accurate results and we calculate the lowest levels, states and QED corrections for pionic and kaonic atoms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Rapid optimization of multiple-burn rocket flights.

Different formulations of the fuel optimization problem for multiple burn trajectories are considered. It is shown that certain customary idealizing assumptions lead to an ill-posed optimization problem for which no solution exists. Several ways are discussed for avoiding such difficulties by more realistic problem statements. An iterative solution of the boundary value problem is presented together with efficient coast arc computations, the right end conditions for various orbital missions, and some test results.

Brown, K. R.↗
NASA NTRS1979

Energy deposition in the earth's atmosphere due to impact of solar activity-generated disturbances

Energy deposition in and dynamic responses of the terrestrial atmosphere to solar flare-generated shocks and other physical processes - such as particle precipitation and local heating - are investigated self-consistently in the context of hydrodynamics, the problem being treated as an initial boundary-value problem. It is extremely difficult to construct a general model for the line solar activity-magnetosphere-atmosphere; however, a limited model for this link is possible. The paper describes such a model, and presents some results on energy deposition into the earth's atmosphere due to solar activity-generated disturbances. Results from the present calculations are presented and discussed.

Wu, S. T.↗
NASA NTRS1985

Stable boundary conditions and difference schemes for Navier-Stokes equations

The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

Dutt, P.↗
NASA NTRS1996

Effective Numerical Methods for Solving Elliptical Problems in Strengthened Sobolev Spaces

Fourth-order elliptic boundary value problems in the plane can be reduced to operator equations in Hilbert spaces G that are certain subspaces of the Sobolev space W(sub 2)(exp 2)(Omega) is identical with G(sup (2)). Appearance of asymptotically optimal algorithms for Stokes type problems made it natural to focus on an approach that considers rot w is identical with (D(sub 2)w - D(sub 1)w) is identical with vector of u as a new unknown vector-function, which automatically satisfies the condition div vector of u = 0. In this work, we show that this approach can also be developed for an important class of problems from the theory of plates and shells with stiffeners. The main mathematical problem was to show that the well-known inf-sup condition (normal solvability of the divergence operator) holds for special Hilbert spaces. This result is also essential for certain hydrodynamics problems.

D'yakonov, Eugene G.↗
NASA NTRS1997

An Application of the Difference Potentials Method to Solving External Problems in CFD

Numerical solution of infinite-domain boundary-value problems requires some special techniques that would make the problem available for treatment on the computer. Indeed, the problem must be discretized in a way that the computer operates with only finite amount of information. Therefore, the original infinite-domain formulation must be altered and/or augmented so that on one hand the solution is not changed (or changed slightly) and on the other hand the finite discrete formulation becomes available. One widely used approach to constructing such discretizations consists of truncating the unbounded original domain and then setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The role of the ABC's is to close the truncated problem and at the same time to ensure that the solution found inside the finite computational domain would be maximally close to (in the ideal case, exactly the same as) the corresponding fragment of the original infinite-domain solution. Let us emphasize that the proper treatment of artificial boundaries may have a profound impact on the overall quality and performance of numerical algorithms. The latter statement is corroborated by the numerous computational experiments and especially concerns the area of CFD, in which external problems present a wide class of practically important formulations. In this paper, we review some work that has been done over the recent years on constructing highly accurate nonlocal ABC's for calculation of compressible external flows. The approach is based on implementation of the generalized potentials and pseudodifferential boundary projection operators analogous to those proposed first by Calderon. The difference potentials method (DPM) by Ryaben'kii is used for the effective computation of the generalized potentials and projections. The resulting ABC's clearly outperform the existing methods from the standpoints of accuracy and robustness, in many cases noticeably speed up the multigrid convergence, and at the same time are quite comparable to other methods from the standpoints of geometric universality and simplicity of implementation.

Ryaben 'Kii, Victor S.↗
DOE OSTI2021

An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ 2 ) in the L∞(Ω) norm, which is optimal considering the O(δ 2 ) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Finally, based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ 2 ) convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Solving Eco-Driving Problems Using Indirect Collocation Method and Smooth Representation

Here, we discuss the eco-driving problem, considering both electric and conventional powertrains, and presents a pathway to solving it numerically using an indirect collocation method. Despite the low-order system dynamics, the piecewise fuel/efficiency map, gear shifting, and real-world traffic/road situations bring system discontinuities/switchings and pure state constraints into the problem formulation, which make the problem highly nonlinear and nontrivial to solve. This letter introduces smooth approximations to convert the original problem to an unconstrained (and penalized) smooth boundary-value problem. This approach eliminates the discussion of the switching structure and leads to a lightweight Newton-method-based solution procedure.

42 ENGINEERING↗