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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 109 records · Page 6

Electromagnetic characterization of conformal antennas

The ultimate objective of this project is to develop a new technique which permits an accurate simulation of microstrip patch antennas or arrays with various feed, superstrate and/or substrate configurations residing in a recessed cavity whose aperture is planar, cylindrical or otherwise conformed to the substructure. The technique combines the finite element and boundary integral methods to formulate a system suitable for solution via the conjugate gradient method in conjunction with the fast Fourier transform. The final code is intended to compute both scattering and radiation patterns of the structure with an affordable memory demand. With upgraded capabilities, the four included papers examined the radar cross section (RCS), input impedance, gain, and resonant frequency of several rectangular configurations using different loading and substrate/superstrate configurations.

Volakis, John L.↗

Computational methods to obtain time optimal jet engine control

Dynamic Programming and the Fletcher-Reeves Conjugate Gradient Method are two existing methods which can be applied to solve a general class of unconstrained fixed time, free right end optimal control problems. New techniques are developed to adapt these methods to solve a time optimal control problem with state variable and control constraints. Specifically, they are applied to compute a time optimal control for a jet engine control problem.

Basso, R. J.↗

Krylov subspace methods on supercomputers

A short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers is presented. Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three-dimensional models gain importance. A conservative approach to derive effective iterative techniques for supercomputers has been to find efficient parallel/vector implementations of the standard algorithms. The main source of difficulty in the incomplete factorization preconditionings is in the solution of the triangular systems at each step. A few approaches consisting of implementing efficient forward and backward triangular solutions are described in detail. Polynomial preconditioning as an alternative to standard incomplete factorization techniques is also discussed. Another efficient approach is to reorder the equations so as to improve the structure of the matrix to achieve better parallelism or vectorization. An overview of these and other ideas and their effectiveness or potential for different types of architectures is given.

Saad, Youcef↗

Sub-domain decomposition methods and computational controls for multibody dynamical systems

This paper presents a concurrent methodology to simulate the dynamics of flexible multibody systems with a large number of degrees of freedom. A general class of open-loop structures is treated and a redundant coordinate formulation is adopted. A range space method is used in which the constraint forces are calculated using a preconditioned conjugate gradient method. By using a preconditioner motivated by the regular ordering of the directed graph of the structures, it is shown that the method is order N in the total number of coordinates of the system. The overall formulation has the advantage that it permits fine parallelization and does not rely on system topology to induce concurrency. It can be efficiently implemented on the present generation of parallel computers with a large number of processors. Validation of the method is presented via numerical simulations of space structures incorporating large number of flexible degrees of freedom.

Menon, R. G.↗

Some iterative schemes for transonic potential flows

The minimal residual (MR) method for the numerical solution of transonic potential flows is closely related to the conjugate gradient method, which has found widespread use in the solution of large sparse, symmetric, and positive-definite linear equations. The primary advantage of the MR method is its applicability to both symmetric and nonsymmetric matrices.

Wong, Y. S.↗

Microwave Imaging on Metal Objects

This final report for the project discusses the attempts to model, using different methods, microwave image reconstruction. Maximum Entropy Method was not successful. Attempts to use Singular Value Decomposition (SVD) got some good results after initial failure. SVD is based upon a theory of linear algebra, to the effect that any M X N Matrix A whose number of rows M is greater than or equal to its number of columns, N can be written as the product of an M X N column-orthogonal matrix U, an N X N diagonal Matrix, W, with m positive or zero elements (the singular values) and the transposition of an N X N orthogonal matrix V. In microwave imaging, the scattered fields can be expressed by the induced current distribution. The SVD method required more contiguous computer memory than was available. Work was also done on the Conjugate Gradient Method (CGM), which didn't work well when tried earlier. It was found that separation of the imaginary part and the real part during calculation may work. This work was considered incomplete as of the end of the grant period.

Tolliver, C. L.↗

A new formulation for the epsilon method applied to the minimum-time-to-climb problem

Balakrishnan's epsilon technique is used to compute minimum-time profiles for the F-104 airplane. This technique differs from the classical gradient method in that a quadratic penalty on the error in satisfying the equation of motion is included in the cost function to be minimized as a means of eliminating the requirement of satisfying the equations of motion. Although the number of unknown independent functions is increased to include the state variables, the evaluation of the gradient of the cost function is simplified, resulting in considerable computational savings, thereby making it appear feasible to use the epsilon method for real-time application.

Taylor, L. W., Jr.↗

Numerical Study of Solidification Crack Susceptibility in Novel Refractory Alloy Systems

Calculation of Phase Diagrams (CALPHAD) -based solidification computa­tions, such as Scheil or equilibrium computations, have been utilized to propose crack solidification susceptibility indices (CSSIs) of cracking. These CSSIs have been proposed in order to predict the cracking susceptibility of an alloy in the solidification range, as a function of its solidification frac­tion and as dependent upon its wt.% elemental composition through the CALPHAD computation & via comparative methods between one composition & the next. Recently Kou at al. have proposed a novel CSSI where the gradient of the e.x. Scheil solidification curve is obtained in the critical solidification cracking region of greater than 0.95 fraction of solid. Therefore, a direct Temperature dependent metric is now available for the prediction, and presumably the control, of solidification cracking. In this TM, the researchers apply this Kou gradient method to refractory alloys for the first time & discuss justification for the approach via Spearman rank correlation with Varestraint cracking test data as well as by comparisons with Thermocalc based vulnerability time CSSI calculations. A Python Pycalphad module example of the approach is provided & can be utilized as an open-source resource that utilizes also open-source available thermodynamical databases, making the CSSI quantitative aspect of ICME more available and freely available to practitioners.

ICME integrated computational materials engineerin↗

Trajectory optimization for an asymmetric launch vehicle

A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.

Sullivan, Jeanne Marie↗

Martian Aerocapture Terminal Point Guidance: A Reference Path Optimization Study

An effective method of terminal point guidance is to employ influence coefficients, which are solved from a set of differential equations adjoint to the linearized perturbations of the equations of motion about a reference trajectory. Hence, to optimize this type of guidance, one must first optimize the reference trajectory that the guidance is based upon. This study concentrates on various methods to optimize a reference trajectory for a Martian aerocapture maneuver, including a parametric analysis and first order gradient method. Resulting reference trajectories were tested in separate 2000 6-DOF Monte Carlo runs, using the Atmospheric Guidance Algorithm Testbed for the Mars Surveyor Program 2001 (MSP '01) Orbiter. These results were compared to an August 1998 study using the same terminal point control guidance algorithm and simulation testbed. Satisfactory improvements over the 1998 study are amply demonstrated.

Ro, Theodore U.↗

High-performance equation solvers and their impact on finite element analysis

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

Poole, Eugene L.↗

High-performance equation solvers and their impact on finite element analysis

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number od operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

Poole, Eugene L.↗

Variational approaches to CFD: Applications to potential Euler and Navier-Stokes equations

Flow simulations based on variational techniques are discussed. Variational techniques are applied for the problem formulation, for the construction of discrete schemes, and for the solution procedures. Inviscid transonic flows, as well as viscous incompressible and compressible flows, are analyzed by several methods. Variational techniques to solve the discrete systems of equations are well known. The most popular one is the conjugate gradient method. Extensions to nonsymmetric and nonpositive definite systems were under investigation for the last two decades. Variational techniques were used for convergence acceleration of iterative procedures. Some of these ideas based on recent work are examined. The lectures are organized in three parts including numerical simulation of inviscid as well as viscous incompressible and compressible flows.

Hafez, M.↗

Scattering of impact wave by a crack in composite plate

The surface responses due to impact load on an infinite uniaxial graphite/epoxy plate with and without delamination cracks are investigated both in time and frequency domain by using a hybrid method combining the finite element discretization of the near-field with boundary integral representation of the field outside a contour enclosing completely the crack. This combined method leads to a set of linear unsymmetric complex matrix equations which are solved to obtain the response in the frequency domain by biconjugate gradient method. The time domain response is then obtained by using an FFT. In order to capture the time-domain characteristics accurately, high order finite elements have been used. Also, both the six node singular elements and eight node transition elements are used around the crack tips to model the crack-tip singularity. It is shown that from the numerical results for surface responses both depth and length of this crack can be identified.

Ju, T. H.↗

UltraSail CubeSat Solar Sail Flight Experiment

UltraSail is a next-generation, highrisk, high-payoff sail system for the launch, deployment, stabilization, and control of very large (km2 class) solar sails enabling high payload mass fractions for interplanetary and deep space spacecraft. UltraSail is a non-traditional approach to propulsion technology achieved by combining propulsion and control systems developed for formation- flying microsatellites with an innovative solar sail architecture to achieve controllable sail areas approaching 1 km2, sail subsystem area densities approaching 1 g/m2, and thrust levels many times those of ion thrusters used for comparable deep space missions. UltraSail can achieve outer planetary rendezvous, a deep-space capability now reserved for high-mass nuclear and chemical systems. There is a twofold rationale behind the UltraSail concept for advanced solar sail systems. The first is that sail-andboom systems are inherently size-limited. The boom mass must be kept small, and column buckling limits the boom length to a few hundred meters. By eliminating the boom, UltraSail not only offers larger sail area, but also lower areal density, allowing larger payloads and shorter mission transit times. The second rationale for UltraSail is that sail films present deployment handling difficulties as the film thickness approaches one micrometer. The square sail requires that the film be folded in two directions for launch, and similarly unfolded for deployment. The film is stressed at the intersection of two folds, and this stress varies inversely with the film thickness. This stress can cause the film to yield, forming a permanent crease, or worse, to perforate. By rolling the film as UltraSail does, creases are prevented. Because the film is so thin, the roll thickness is small. Dynamic structural analysis of UltraSail coupled with dynamic control analysis shows that the system can be designed to eliminate longitudinal torsional waves created while controlling the pitch of the blades, while using solar photon pressure to slew the spin axis. Vacuum tests have also verified that electrostatic and molecular adhesion forces can substantially be eliminated by making the film electrically conductive, reducing the peel force of the film off the storage roll to levels of 100s of micro-N. The innovation demonstrated the capability of deploying a six-micron aluminum- coated film from a reel through a slit in vacuum. The innovation also demonstrated a spin-stabilized method for deploying a long reel of solar sail film using solar pressure to spin-up and orbit raise the satellite, and also a gravity gradient method for deploying a long reel of solar sail film using solar pressure to orbit raise the satellite. The solar sail mass fraction of 25% is consistent with high specific impulse ion systems, but without the added weight and cost of a power source and processing unit. The large sail area, coupled with low film density, is giving UltraSail a high payload fraction. The UltraSail deployment scheme unrolls a micrometerscale reflection-coated polyimide film from a storage mandrel to a maximum length of several kilometers with the aid of a blade tip satellite.

Carroll, David↗

Finite Element Methods for real-time Haptic Feedback of Soft-Tissue Models in Virtual Reality Simulators

We have applied the linear elastic finite element method to compute haptic force feedback and domain deformations of soft tissue models for use in virtual reality simulators. Our results show that, for virtual object models of high-resolution 3D data (>10,000 nodes), haptic real time computations (>500 Hz) are not currently possible using traditional methods. Current research efforts are focused in the following areas: 1) efficient implementation of fully adaptive multi-resolution methods and 2) multi-resolution methods with specialized basis functions to capture the singularity at the haptic interface (point loading). To achieve real time computations, we propose parallel processing of a Jacobi preconditioned conjugate gradient method applied to a reduced system of equations resulting from surface domain decomposition. This can effectively be achieved using reconfigurable computing systems such as field programmable gate arrays (FPGA), thereby providing a flexible solution that allows for new FPGA implementations as improved algorithms become available. The resulting soft tissue simulation system would meet NASA Virtual Glovebox requirements and, at the same time, provide a generalized simulation engine for any immersive environment application, such as biomedical/surgical procedures or interactive scientific applications.

Frank, Andreas O.↗

Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite element method

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique.

Jin, Jian-Ming↗

Large-scale computation of incompressible viscous flow by least-squares finite element method

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Jiang, Bo-Nan↗