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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A heterogeneous stochastic FEM framework for elliptic PDEs

We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Applications of a direct/iterative design method to complex transonic configurations

The current study explores the use of an automated direct/iterative design method for the reduction of drag in transport configurations, including configurations with engine nacelles. The method requires the user to choose a proper target-pressure distribution and then develops a corresponding airfoil section. The method can be applied to two-dimensional airfoil sections or to three-dimensional wings. The three cases that are presented show successful application of the method for reducing drag from various sources. The first two cases demonstrate the use of the method to reduce induced drag by designing to an elliptic span-load distribution and to reduce wave drag by decreasing the shock strength for a given lift. In the second case, a body-mounted nacelle is added and the method is successfully used to eliminate increases in wing drag associated with the nacelle addition by designing to an arbitrary pressure distribution as a result of the redesigning of a wing in combination with a given underwing nacelle to clean-wing, target-pressure distributions. These cases illustrate several possible uses of the method for reducing different types of drag. The magnitude of the obtainable drag reduction varies with the constraints of the problem and the configuration to be modified.

Smith, Leigh Ann↗
DOE OSTI2021

RISE: robust iterative surface extension for sub-nanometer X-ray mirror fabrication

Precision optics have been widely required in many advanced technological applications. X-ray mirrors, as an example, serve as the key optical components at synchrotron radiation and free electron laser facilities. They are rectangular silicon or glass substrates where a rectangular Clear Aperture (CA) needs to be polished to sub-nanometer Root Mean Squared (RMS) to keep the imaging capability of the incoming X-ray wavefront at the diffraction limit. The convolutional polishing model requires a CA to be extended with extra data, from which the dwell time is calculated via deconvolution. However, since deconvolution is very sensitive to boundary errors and noise, the existing surface extension methods can hardly fulfill the sub-nanometer requirement. On one hand, the figure errors in a CA were improperly modeled during the extension, leading to continuity issues along the boundary. On the other hand, uncorrectable high-frequency errors and noise were also extended. In this study, we propose a novel Robust Iterative Surface Extension (RISE) method that resolves these problems with a data fitting strategy. RISE models the figure errors in a CA with orthogonal polynomials and ensures that only correctable errors are fit and extended. Combined with boundary conditions, an iterative refinement of dwell time is then proposed to compensate the errors brought by the extension and deconvolution, which drastically reduces the estimated figure error residuals in a CA while the increase of total dwell time is negligible. To our best knowledge, RISE is the first data fitting-based surface extension method and is the first to optimize dwell time based on iterative extension. An experimental verification of RISE is given by fabricating two elliptic cylinders (10 mm × 80 mm CAs) starting from a sphere with a radius of curvature around 173 m using ion beam figuring. The figure errors in the two CAs greatly improved from 204.96 nm RMS and 190.28 nm RMS to 0.62 nm RMS and 0.71 nm RMS, respectively, which proves that RISE is an effective method for sub-nanometer level X-ray mirror fabrication.

36 MATERIALS SCIENCE↗
NASA NTRS2016

Optimizing Mars Sphere of Influence Maneuvers for NASA's Evolvable Mars Campaign

NASA's Human Spaceflight Architecture Team is refining human exploration architectures that will extend human presence to the Martian surface. For both Mars orbital and surface missions, NASA's Evolvable Mars Campaign assumes that cargo and crew can be delivered repeatedly to the same destination. Up to this point, interplanetary trajectories have been optimized to minimize the total propulsive requirements of the in-space transportation systems, while the pre-deployed assets and surface systems are optimized to minimize their respective propulsive requirements separate from the in-space transportation system. There is a need to investigate the coupled problem of optimizing the interplanetary trajectory and optimizing the maneuvers within Mars's sphere of influence. This paper provides a description of the ongoing method development, analysis and initial results of the effort to resolve the discontinuity between the interplanetary trajectory and the Mars sphere of influence trajectories. Assessment of Phobos and Deimos orbital missions shows the in-space transportation and crew taxi allocations are adequate for missions in the 2030s. Because the surface site has yet to be selected, the transportation elements must be sized to provide enough capability to provide surface access to all landing sites under consideration. Analysis shows access to sites from elliptical parking orbits with a lander that is designed for sub-periapsis landing location is either infeasible or requires expensive orbital maneuvers for many latitude ranges. In this case the locus of potential arrival perigee vectors identifies the potential maximum north or south latitudes accessible. Higher arrival velocities can decrease reorientation costs and increase landing site availability. Utilizing hyperbolic arrival and departure vectors in the optimization scheme will increase transportation site accessibility and provide more optimal solutions.

Merrill, Raymond G.↗
DOE OSTI2021

Development, Implementation, and Verification of Partially-Ionized Collisional Multifluid Plasma Models in Drekar

We consider the development of multifluid models for partially ionized multispecies plasmas. The models are composed of a standard set of five-moment fluid equations for each species plus a description of electromagnetics. The most general model considered utilizes a full set of fluid equations for each charge state of each atomic species, plus a set of fluid equations for electrons. The fluid equations are coupled through source terms describing electromagnetic coupling, ionization, recombination, charge exchange, and elastic scattering collisions in the low-density coronal limit. The form of each of these source terms is described in detail, and references for required rate coefficients are identified for a diverse range of atomic species. Initial efforts have been made to extend these models to incorporate some higher-density collisional effects, including ionization potential depression and three- body recombination. Some reductions of the general multifluid model are considered. First, a reduced multifluid model is derived which averages over all of the charge states (including neutrals) of each atomic species in the general multifluid model. The resulting model maintains full consistency with the general multifluid model from which it is derived by leveraging a quasi-steady-state collisional ionization equilibrium assumption to recover the ionization fractions required to make use of the general collision models. Further reductions are briefly considered to derive certain components of a single-fluid magnetohydrodynamics (MHD) model. In this case, a generalized Ohm's law is obtained, and the standard MHD resistivity is expressed in terms of the collisional models used in the general multifluid model. A number of numerical considerations required to obtain robust implementations of these multifluid models are discussed. First, an algebraic flux correction (AFC) stabilization approach for a continuous Galerkin finite element discretization of the multifluid system is described in which the characteristic speeds used in the stabilization of the fluid systems are synchronized across all species in the model. It is demonstrated that this synchronization is crucial in order to obtain a robust discretization of the multifluid system. Additionally, several different formulations are considered for describing the electromagnetics portion of the multifluid system using nodal continuous Galerkin finite element discretizations. The formulations considered include a parabolic divergence cleaning method and an implicit projection method for the traditional curl formulation of Maxwell's equations, a purely- hyperbolic potential-based formulation of Maxwell's equations, and a mixed hyperbolic-elliptic potential-based formulation of Maxwell's equations. Some advantages and disadvantages of each formulation are explored to compare solution robustness and the ease of use of each formulation. Numerical results are presented to demonstrate the accuracy and robustness of various components of our implementation. Analytic solutions for a spatially homogeneous damped plasma oscillation are derived in order to verify the implementation of the source terms for electromagnetic coupling and elastic collisions between fluid species. Ionization balance as a function of electron temperature is evaluated for several atomic species of interest by comparing to steady-state calculations using various sets of ionization and recombination rate coefficients. Several test problems in one and two spatial dimensions are used to demonstrate the accuracy and robustness of the discretization and stabilization approach for the fluid components of the multifluid system. This includes standard test problems for electrostatic and electromagnetic shock tubes in the two-fluid and ideal shock-MHD limits, a cylindrical diocotron instability, and the GEM challenge magnetic reconnection problem. A one-dimensional simplified prototype of an argon gas puff configuration as deployed on Sandia's Z-machine is used as a demonstration to exercise the full range of capabilities associated with the general multifluid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1996

Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

Casarin, Mario↗
NASA NTRS2013

Orbital Transfer Techniques for Round-Trip Mars Missions

The human exploration of Phobos and Deimos or the retrieval of a surface sample launched to low-Mars orbit presents a highly constrained orbital transfer problem. In general, the plane of the target orbit will not be accessible from the arrival or departure interplanetary trajectories with an (energetically optimal) tangential burn at periapsis. The orbital design is further complicated by the addition of a high-energy parking orbit for the relatively massive Deep Space Vehicle to reduce propellant expenditure, while the crew transfers to and from the target orbit in a smaller Space Exploration Vehicle. The proposed strategy shifts the arrival and departure maneuvers away from periapsis so that the apsidal line of the parking orbit lies in the plane of the target orbit, permitting highly efficient plane change maneuvers at apoapsis of the elliptical parking orbit. An apsidal shift during the arrival or departure maneuver is approximately five times as efficient as maneuvering while in Mars orbit, thus significantly reducing the propellant necessary to transfer between the arrival, target, and departure orbits.

human missions↗
NASA NTRS1993

Studies on nonequilibrium phenomena in supersonic chemically reacting flows

This study deals with a systematic investigation of nonequilibrium processes in supersonic combustion. The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with nonequilibrium chemistry and thermodynamics, coupled with radiation, for hydrogen-air systems. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. For a basic understanding of the flow physics, premixed flows undergoing finite rate chemical reactions are investigated. Results obtained for specific conditions indicate that the radiative interactions vary substantially, depending on reactions involving HO2 and NO species, and that this can have a noticeable influence on the flowfield. The second part of this study deals with premixed reacting flows under thermal nonequilibrium conditions. Here, the critical problem is coupling of the vibrational relaxation process with the radiative heat transfer. The specific problem considered is a premixed expanding flow in a supersonic nozzle. Results indicate the presence of nonequilibrium conditions in the expansion region of the nozzle. This results in reduction of the radiative interactions in the flowfield. Next, the present study focuses on investigation of non-premixed flows under chemical nonequilibrium conditions. In this case, the main problem is the coupled turbulence-chemistry interaction. The resulting formulation is validated by comparison with experimental data on reacting supersonic coflowing jets. Results indicate that the effect of heat release is to lower the turbulent shear stress and the mean density. The last part of this study proposes a new theoretical formulation for the coupled turbulence-radiation interactions. Results obtained for the coflowing jets experiment indicate that the effect of turbulence is to enhance the radiative interactions.

Tiwari, S. N.↗
NASA NTRS1993

A displacement gradient BEM for accurate stress computation near boundaries in 2-D anisotropic problems

A displacement gradient method for 2D anisotropic elasticity problems is presented, which effectively minimizes the boundary layer effect through a two-step procedure. First, the boundary integral equations are solved for the unknown boundary displacements and tractions. Second, a direct integral equation for displacement gradients is developed in terms of boundary tractions. Three methods based on different evaluation procedures and locations for determining the displacement gradients are proposed. In the first method the displacement gradients are averaged at nodes common to adjacent elements. The second method stores the gradients element-wise. In the third method, the gradients are evaluated at the nodes of discontinuous elements. The three methods are applied to near-isotropic plates with circular and elliptic cutouts. It is concluded that all three methods can yield accurate stress distributions.

Sistla, R.↗
NASA NTRS2003

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

In this paper we present, a comparison of trajectory optimization approaches for the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP). Quasi- Newton and Nelder-Meade Simplex. Several cost function parameterizations are considered for the direct approach. We choose one direct approach that appears to be the most flexible. Both the direct and indirect methods are applied to a variety of test cases which are chosen to demonstrate the performance of each method in different flight regimes. The first test case is a simple circular-to-circular coplanar rendezvous. The second test case is an elliptic-to-elliptic line of apsides rotation. The final test case is an orbit phasing maneuver sequence in a highly elliptic orbit. For each test case we present a comparison of the performance of all methods we consider in this paper.

Hughes, Steven P.↗
DOE OSTI2015

Theoretical study of symmetry of flux onto a capsule

An analytic model to describe the flux asymmetry onto a capsule based on the viewfactor approximation is developed and verified with numerical simulations. By using a nested spheres technique to represent the various sources of flux asymmetry, the model can treat spherically and cylindrically symmetric hohlraums, e.g., cylinder, elliptic, and rugby. This approach includes the more realistic case of frequency-dependent flux asymmetry compared with the more standard frequency-integrated or single-frequency approaches [D. W. Phillion and S. M. Pollaine, Phys. Plasmas 1, 2963 (1994)]. Correspondingly, the approach can be used to assess x-ray preheat asymmetry generated from localized laser absorption in the high-Z hohlraum wall. For spherical hohlraums with 4, 6, or 8 laser entrance holes (LEHs), an optimal configuration of LEHs, laser spot placement, and angle-of-incidence of the single-ringed laser beams is defined. An analogy between minimizing the flux asymmetry onto a capsule and the Thomson problem of point charge placement on a sphere for minimized energy is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1989

An entropy method for induced drag minimization

A fundamentally new approach to the aircraft minimum induced drag problem is presented. The method, a 'viscous lifting line', is based on the minimum entropy production principle and does not require the planar wake assumption. An approximate, closed form solution is obtained for several wing configurations including a comparison of wing extension, winglets, and in-plane wing sweep, with and without a constraint on wing-root bending moment. Like the classical lifting-line theory, this theory predicts that induced drag is proportional to the square of the lift coefficient and inversely proportioinal to the wing aspect ratio. Unlike the classical theory, it predicts that induced drag is Reynolds number dependent and that the optimum spanwise circulation distribution is non-elliptic.

Greene, George C.↗
NASA NTRS1996

A Computational and Experimental Study of Nonlinear Aspects of Induced Drag

Despite the 80-year history of classical wing theory, considerable research has recently been directed toward planform and wake effects on induced drag. Nonlinear interactions between the trailing wake and the wing offer the possibility of reducing drag. The nonlinear effect of compressibility on induced drag characteristics may also influence wing design. This thesis deals with the prediction of these nonlinear aspects of induced drag and ways to exploit them. A potential benefit of only a few percent of the drag represents a large fuel savings for the world's commercial transport fleet. Computational methods must be applied carefully to obtain accurate induced drag predictions. Trefftz-plane drag integration is far more reliable than surface pressure integration, but is very sensitive to the accuracy of the force-free wake model. The practical use of Trefftz plane drag integration was extended to transonic flow with the Tranair full-potential code. The induced drag characteristics of a typical transport wing were studied with Tranair, a full-potential method, and A502, a high-order linear panel method to investigate changes in lift distribution and span efficiency due to compressibility. Modeling the force-free wake is a nonlinear problem, even when the flow governing equation is linear. A novel method was developed for computing the force-free wake shape. This hybrid wake-relaxation scheme couples the well-behaved nature of the discrete vortex wake with viscous-core modeling and the high-accuracy velocity prediction of the high-order panel method. The hybrid scheme produced converged wake shapes that allowed accurate Trefftz-plane integration. An unusual split-tip wing concept was studied for exploiting nonlinear wake interaction to reduced induced drag. This design exhibits significant nonlinear interactions between the wing and wake that produced a 12% reduction in induced drag compared to an equivalent elliptical wing at a lift coefficient of 0.7. The performance of the split-tip wing was also investigated by wing tunnel experiments. Induced drag was determined from force measurements by subtracting the estimated viscous drag, and from an analytical drag-decomposition method using a wake survey. The experimental results confirm the computational prediction.

Smith, Stephen C.↗
DOE OSTI2014

Nonlinear periodic waves solutions of the nonlinear self-dual network equations

The new classes of periodic solutions of nonlinear self-dual network equations describing the breather and soliton lattices, expressed in terms of the Jacobi elliptic functions have been obtained. The dependences of the frequencies on energy have been found. Numerical simulations of soliton lattice demonstrate their stability in the ideal lattice and the breather lattice instability in the dissipative lattice. However, the lifetime of such structures in the dissipative lattice can be extended through the application of ac driving terms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition

We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

A two parameter survey of periodic orbits in the restricted problem of three bodies

Within the context of the restricted problem of three bodies the effects caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass which are numerical continuations of circular orbits in the ordinary problem of two bodies are shown. A recursive power series technique is used to numerically integrate the equations of motion as well as the first variational equations in order to generate a two parameter family of perodic orbits and identify the linear stability characteristics. Seven such families are investigated with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, nearly circular motion of the primaries, and small mass ratios of the primaries. Unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, highly elliptic orbits of the primaries and large mass ratios.

Shelus, P. J.↗
NASA NTRS2018

Systems Engineering for the PRANDTL-D 3c Aircraft

The purpose of the Preliminary Research in AerodyNamicDesign to Lower Drag (PRANDTL-D) project is to show that birds fly using a "bell" shaped spanload rather than using an elliptical shaped spanload and to demonstrate the extensive benefits of this alternative spanload. This validation is done by flying a research glider with a twenty five foot wingspan that collects a range of parameters in flight. To ensure the data collection computers and suite of sensors work together and mesh well with the aircraft, systems engineering principles are applied. Needs for new one-off parts require a systems engineering approach as all the criteria of the plane, such as aerodynamics, structures, and avionics, must be taken into account when making decisions. The result of this approach were effective solutions that had a minimal negative impact on other systems that were not related to the original problem.

Larson, James G.↗
NASA NTRS2019

Weighted Least-Squares Cell-Average Gradient Construction Methods for the VULCAN-CFD Second-Order Accurate Unstructured-Grid Cell-Centered Finite-Volume Solver

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches to augment the number of cells participating in the stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cell-average gradients is described and investigated. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 8 turbulent flow of air around a blunt wedge is computed to demonstrate the robustness and convergence behavior of the new method for constructing stencils of use in a weighted linear least-squares gradient method for a hypersonic flow.

White, Jeffery A.↗