Optimal guidance with transition partial derivative matrices.
Newton method for boundary value problem associated with differential equations applied to Lambert, rendezvous and orbital transfer problems
Ingram, H. L.↗
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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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Partial derivatives of matrices representing rigid body rotations
Applying method for computing partial derivatives of matrices representing rigid body rotations to formulation of RTCC processor for lunar landing mission
Cockrell, B. F.↗
Approaches to polymer-derived CMC matrices
The use of polymeric precursors to ceramics permits the fabrication of large, complex-shaped ceramic matrix composites (CMC's) at temperatures which do not degrade the fiber. Processing equipment and techniques readily available in the resin matrix composite industry can be adapted for CMC fabrication using this approach. Criteria which influence the choice of candidate precursor polymers, the use of fillers, and the role of fiber architecture and ply layup are discussed. Three polymer systems, polycarbosilanes, polysilazanes, and polysilsesquioxanes, are compared as candidate ceramic matrix precursors.
Hurwitz, Frances I.↗
Approaches to polymer-derived CMC matrices
The use of polymeric precursors to ceramics permits the fabrication of large, complex-shaped ceramic matrix composites (CMC's) at temperatures which do not degrade the fiber. Processing equipment and techniques readily available in the resin matrix composite industry can be adapted for CMC fabrication using this approach. Criteria which influence the choice of candidate precursor polymers, the use of fillers, and the role of fiber architecture and ply layup are discussed. Three polymer systems, polycarbosilanes, polysilazanes, and polysilsesquioxanes, are compared as candidate ceramic matrix precursors.
Hurwitz, Frances I.↗
Closed-form solutions for atomspheric flight with applications to shuttle guidance
Closed-form solutions for the motion of a rocket-powered vehicle during atmospheric ascent and closed-form solutions for unpowered atmospheric reentry are developed. These closed-form solutions are then used to develop a simplified guidance scheme and to develop a variation-of-parameters integration of more accurate equations of motion with the closed-form solutions as base solutions. The variation-of-parameters integration of the more accurate equations of motion also allows the transition partial derivative matrices associated with these equations to be easily developed. Then the partial derivative transition matrices are used to develop a guidance scheme based on the more accurate equations of motion instead of the less accurate closed-form solutions.
Ingram, H. L.↗
Natural frequencies of an orbiting space station
The technique of modal synthesis is applied to find the natural frequencies of space stations. The station is modeled as an assemblage of rigid modules, joined by massless elastic constraints, and flexible modules characterized by deformation functions. The equations of motion are derived and system mass and stiffness matrices derived. The method is applied to the Skylab orbiting space station. The frequencies of the lowest 65 modes are given and selected mode shapes illustrated. The technique is feasible for analysis of a complex system and suitable for response studies including damping and attitude control system effects.
Bernstein, E. L.↗
A fast algorithm for spectral differentiation
A simple algorithm is presented for matrix multiplication in just over half the number of operations entailed by the conventional algorithm, in cases where the matrix possesses the degree of symmetry widely exhibited by derivative matrices. The algorithm is used to multiply the Chebyshev derivative matrix by a vector. For the larger values of n, the ratio of execution times approached the expected value of 2.
Solomonoff, Alex↗
Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes
High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel Benchmarks (NPB). In this paper, we present some interesting performance results of ow OpenMP parallel implementation on different architectures such as the SGI Origin2000, SGI Altix, and Cray MTA-2.
Feng, Huiyu↗
Preconditioning matrices for Chebyshev derivative operators
The problem of preconditioning the matrices arising from pseudo-spectral Chebyshev approximations of first order operators is considered in both one and two dimensions. In one dimension a preconditioner represented by a full matrix which leads to preconditioned eigenvalues that are real, positive, and lie between 1 and pi/2, is already available. Since there are cases in which it is not computationally convenient to work with such a preconditioner, a large number of preconditioners were studied which were more sparse (in particular three and four diagonal matrices). The eigenvalues of such preconditioned matrices are compared. The results were applied to the problem of finding the steady state solution to an equation of the type u sub t = u sub x + f, where the Chebyshev collocation is used for the spatial variable and time discretization is performed by the Richardson method. In two dimensions different preconditioners are proposed for the matrix which arises from the pseudo-spectral discretization of the steady state problem. Results are given for the CPU time and the number of iterations using a Richardson iteration method for the unpreconditioned and preconditioned cases.
Rothman, Ernest E.↗
Flux Jacobian Matrices For Equilibrium Real Gases
Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.
Vinokur, Marcel↗
Nonlinear consider covariance analysis using a sigma-point filter formulation
The research reported here extends the mathematical formulation of nonlinear, sigma-point estimators to enable consider covariance analysis for dynamical systems. This paper presents a novel sigma-point consider filter algorithm, for consider-parameterized nonlinear estimation, following the unscented Kalman filter (UKF) variation on the sigma-point filter formulation, which requires no partial derivatives of dynamics models or measurement models with respect to the parameter list. It is shown that, consistent with the attributes of sigma-point estimators, a consider-parameterized sigma-point estimator can be developed entirely without requiring the derivation of any partial-derivative matrices related to the dynamical system, the measurements, or the considered parameters, which appears to be an advantage over the formulation of a linear-theory sequential consider estimator. It is also demonstrated that a consider covariance analysis performed with this 'partial-derivative-free' formulation yields equivalent results to the linear-theory consider filter, for purely linear problems.
covariance↗
Active Metal Brazing and Characterization of Brazed Joints in C-C and C-SiC Composites to Copper-Clad-Molybdenum System
Carbon/carbon composites with CVI and resin-derived matrices, and C/SiC composites reinforced with T-300 carbon fibers in a CVI SiC matrix were joined to Cu-clad Mo using two Ag-Cu braze alloys, Cusil-ABA (1.75% Ti) and Ticusil (4.5% Ti). The brazed joints revealed good interfacial bonding, preferential precipitation of Ti at the composite/braze interface, and a tendency toward delamination in resin-derived C/C composite. Extensive braze penetration of the inter-fiber channels in the CVI C/C composites was observed. The Knoop microhardness (HK) distribution across the C/C joints indicated sharp gradients at the interface, and a higher hardness in Ticusil than in Cusil-ABA. For the C/SiC composite to Cu-clad-Mo joints, the effect of composite surface preparation revealed that ground samples did not crack whereas unground samples cracked. Calculated strain energy in brazed joints in both systems is comparable to the strain energy in a number of other ceramic/metal systems. Theoretical predictions of the effective thermal resistance suggest that such joined systems may be promising for thermal management applications.
Singh, M.↗
Thermostructural Properties Of Sic/Sic Panels With 2.5d And 3d Fiber Architectures
CMC hot-section components in advanced engines for power and propulsion will typically require high cracking strength, high ultimate strength and strain, high creep- rupture resistance, and high thermal conductivity in all directions. In the past, NASA has demonstrated fabrication of a variety of SiC/SiC flat panels and round tubes with various 2D fiber architectures using the high-modulus high-performance Sylramic-iBN Sic fiber and Sic-based matrices derived by CVI, MI, and/or PIP processes. The thermo- mechanical properties of these CMC have shown state-of-the-art performance, but primarily in the in-plane directions. Currently NASA is extending the thermostructural capability of these SiC/SiC systems in the thru-thickness direction by using various 2.5D and 3D fiber architectures. NASA is also using specially designed fabrication steps to optimize the properties of the BN-based interphase and Sic-based matrices. In this study, Sylramic-iBN/SiC panels with 2D plain weave, 2.5D satin weave, 2.5D ply-to-ply interlock weave, and 3D angle interlock fiber architectures, all woven at AITI, were fabricated using matrix densification routes previously established between NASA and GEPSC for CVI-MI processes and between NASA and Starfire-Systems for PIP processes. Introduction of the 2.5 D fiber architecture along with an improved matrix process was found to increase inter-laminar tensile strength from 1.5 -2 to 3 - 4 ksi and thru-thickness thermal conductivity from 15-20 to 30-35 BTU/ft.hr.F with minimal reduction in in-plane strength and creep-rupture properties. Such improvements should reduce thermal stresses and increase the thermostructural operating envelope for SiC/SiC engine components. These results are analyzed to offer general guidelines for selecting fiber architectures and constituent processes for high-performance SiC/SiC engine components.
Yun, H. M.↗
Experimental measurements of hydrodynamic radial forces and stiffness matrices for a centrifugal pump-impeller
Measurements of the steady-state hydrodynamic forces on a centrifugal pump impeller are presented as a function of position within two geometrically different volutes. These correspond to the forces experienced by the impeller at zero whirl frequency. The hydrodynamic force matrices derived from these measurements exhibit both diagonal and off-diagonal terms of substantial magnitude. These terms are of the form which would tend to excite a whirl motion in a rotordynamic analysis of the pump; this may be the cause of 'rough running' reported in many pumps. Static pressure measurements in the impeller discharge flow show that the hydrodynamic force on the impeller contains a substantial component due to the nonisotropy of the net momentum flux leaving the impeller. A similar breakdown of the contributions to the stiffness matrices reveals that the major component of these matrices results from the nonisotropy of the momentum flux.
Chamieh, D. S.↗
Behavior of triangular shell element stiffness matrices associated with polyhedral deflection distributions
Stiffness matrices derived for triangular shell elements associated with polyhedral deflection distributions
Melosh, R. J.↗
A refined mixed-type plate bending element.
Triangular plate bending element using Herrmann variational method, deriving matrices for finite elements
Visser, W.↗
Atmospheric particulate analysis using angular light scattering
Using the light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit from the library data for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distributions. A real index of 1.50 and an imaginary index of -0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.
Hansen, M. Z.↗
Atmospheric particulate analysis using angular light scattering
Using light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distribution. A real index of 1.50 and an imaginary index of -0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.
Hansen, M. Z.↗