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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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A Chebyshev matrix collocation method is outlined for the solution of the Orr-Sommerfeld equation for the Blausius boundary layer. User information is provided for FORTRAN program ORRBL which solves the equation by the QR method.
Two computers programs, known as Matrix Through-Flow and Matrix Blade-To-Blade, for analyzing the meridional and blade-to-blade flow patterns are described. The numerical solutions are obtained by finite difference approximations to the governing Poisson-type differential equations for the stream function. Solutions for several turbomachines, giving flow patterns and velocity distributions, are included.
Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.
During the assembly flights of the Space Station Freedom (SSF), the Orbiter will either dock with the SSF and retract to the final berthed position, or will grapple the SSF using the Shuttle Remote Manipulator System (SRMS) and maneuver the SRMS coupled vehicles to their final berthed position. The SRMS method is expected to take approximately one to one and a half hours to complete and require periodic attitude corrections by either the Orbiter or the SSF reaction control system (RCS) or continuous control by a control moment gyro (CMG) system with RCS desaturation as required. Free drift of the attached vehicles is not currently thought to be acceptable because the desired system attitude will quickly deteriorate due to unbalanced gravity gradient and aerodynamic torques resulting in power generation problems, thermodynamic control problems, and communications problems. This paper deals with the simulation and control of the SRMS during trunnion/latch interaction dynamics and during RCS maneuvers. The SRMS servo drive joints have highly non-linear elastic characteristics which tend to degrade sensitive control strategies. In addition the system natural frequencies are extremely low and depend on the drive joint deflections and SRMS geometric position. The lowest mean period of oscillation for the Orbiter/SRMS/SSF(MB6) system in brakes hold mode positioned near the final berthed position is approximately 120 seconds. A detailed finite element model of the SRMS has been developed and used in a newly developed SRMS systems dynamics simulation to investigate the non-linear transient response dynamics of the Orbiter/SRMS/SSF systems. The present SRMS control strategy of brakes only recommended by the Charles Draper Labs is contrasted with a robust controller developed by the authors. The robust controller uses an optimal inear quadratic regulator (LQR) to optimally place the closed-loop poles of a multivariable continuous-time system within the common region of an open sector with the sector angle plus or minus 45 degrees from the negative real axis, and the left-hand side of a parallel to the imaginary axis in the complex s-plane. This guarantees that the critical damping ratio for the desired control modes is equal to or in excess of 0.707. The matrix sign function is used for solving the Riccati equations which appear in the controller design procedure. Fast and stable algorithms have recently been developed for the computation of the matrix sign function. Simulation results are given which demonstrate the potential CSI involvement for the current SRMS control system and the proposed control system.
Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.
Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.
The results presented here are part of an ongoing research program to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric matrix materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical 5 plasticity theory definitions of effective stress and effective plastic strain are modified by applying variations of the Drucker-Prager yield criterion. To verify the revised formulation, the shear and tensile deformation of a representative toughened epoxy is analyzed across a wide range of strain rates (from quasi-static to high strain rates) and the results are compared to experimentally obtained values. For the analyzed polymers, both the tensile and shear stress-strain curves computed using the analytical model correlate well with values obtained through experimental tests. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. In the micromechanics, the unit cell is divided up into a number of independently analyzed slices, and laminate theory is then applied to obtain the effective deformation of the unit cell. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite (composed using the representative polymer analyzed for the correlation of the polymer constitutive equations) for several fiber orientation angles across a variety of strain rates. The computed values compare favorably to experimentally obtained results.
Nuclear materials often evolve into two-phase systems comprising a bulk matrix with dispersed inert-gas bubbles. The presence of these bubbles can have consequences to the thermomechanical response of materials and is a key life-limiting factor in some nuclear fuel forms. Understanding the behavior of these two-phase, bubble-matrix systems is, thus, important to improved predictive models and frameworks for many nuclear materials applications. While temperature excursions of these two-phase systems have been characterized, fewer studies have focused on the evolution of inert-gas bubbles under pressure. Here, in this paper, we use x-ray tools to interrogate a He-implanted gold foil to determine the pressure-dependent evolution of the individual components (Au matrix + bubbles), and we compare that total pressure dependence to theoretical equation-of-state descriptions based on mixing rules.
Within the MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) module TRD1, solving physical (coupled) or modal (uncoupled) transient equations of motion is performed using the Newmark-Beta or mode superposition algorithms, respectively. For equations of motion with initial conditions, only the Newmark-Beta integration routine has been available in MSC/NASTRAN solution sequences for solving physical systems and in custom DMAP sequences or alters for solving modal systems. In some cases, one difficulty with using the Newmark-Beta method is that the process of selecting suitable integration time steps for obtaining acceptable results is lengthy. In addition, when very small step sizes are required, a large amount of time can be spent integrating the equations of motion. For certain aerospace applications, a significant time savings can be realized when the equations of motion are solved using an exact integration routine instead of the Newmark-Beta numerical algorithm. In order to solve modal equations of motion with initial conditions and take advantage of efficiencies gained when using uncoupled solution algorithms (like that within TRD1), an exact mode superposition method using MSC/NASTRAN DMAP has been developed and successfully implemented as an enhancement to an existing coupled loads methodology at the NASA Lewis Research Center.
Based on general mass continuity and diffusive transport equations, a mathematical model was developed that simulates the transport of water in Bacon and alkaline-matrix fuel cells. The derived model was validated by using it to analytically reproduce various Bacon and matrix-cell experimental water transport transients.
Progress made toward interpretation of radiometric observations. Paper discusses equation of radiative transfer in three-dimensional, inhomogeneous, scattering medium illuminated from above and bounded below by laterallyinhomogeneous, reflective plane. Representation of radiation field with full three-dimensional variability derived by use of spatial Fourier transform and matrix-operator techniques developed previously for one-dimensional version of problem. Equations useful for radiometric measurements from aircraft and spacecraft. Although derivations and resulting equations complicated, use of Fourier-transform, matrix-operator approach to solve practical problems simpler than direct solution of complete three-dimensional, linear wave equations.
A methodology for predicting the equivalent properties and constituent microstresses for particulate matrix composites, based on the micromechanics approach, is developed. These equations are integrated into a computer code developed to predict the equivalent properties and microstresses of fiber reinforced polymer matrix composites to form a new computer code, ICAN/PART. Details of the flowchart, input and output for ICAN/PART are described, along with examples of the input and output. Only the differences between ICAN/PART and the original ICAN code are described in detail, and the user is assumed to be familiar with the structure and usage of the original ICAN code. Detailed verification studies, utilizing dim dimensional finite element and boundary element analyses, are conducted in order to verify that the micromechanics methodology accurately models the mechanics of particulate matrix composites. ne equivalent properties computed by ICAN/PART fall within bounds established by the finite element and boundary element results. Furthermore, constituent microstresses computed by ICAN/PART agree in average sense with results computed using the finite element method. The verification studies indicate that the micromechanics programmed into ICAN/PART do indeed accurately model the mechanics of particulate matrix composites.
Optical intersubband response of a multiple quantum well (MQW)-embedded microcavity driven by a coherent pump field is studied theoretically. The n-type doped MQW structure with three subbands in the conduction band is sandwiched between a semi-infinite medium and a distributed Bragg reflector (DBR). A strong pump field couples the two upper subbands and a weak field probes the two lower subbands. To describe the optical response of the MQW-embedded microcavity, we adopt a semi-classical nonlocal response theory. Taking into account the pump-probe interaction, we derive the probe-induced current density associated with intersubband transitions from the single-particle density-matrix formalism. By incorporating the current density into the Maxwell equation, we solve the probe local field exactly by means of Green's function technique and the transfer-matrix method. We obtain an exact expression for the probe absorption coefficient of the microcavity. For a GaAs/Al(sub x)Ga(sub 1-x)As MQW structure sandwiched between a GaAs/AlAs DBR and vacuum, we performed numerical calculations of the probe absorption spectra for different parameters such as pump intensity, pump detuning, and cavity length. We find that the probe spectrum is strongly dependent on these parameters. In particular, we find that the combination of the cavity effect and the Autler-Townes effect results in a triplet in the optical spectrum of the MQW system. The optical absorption peak value and its location can be feasibly controlled by varying the pump intensity and detuning.
Here, we utilize a previously constructed thermodynamic T -matrix approach to the quark-gluon plasma (QGP) to derive constaints on its input by using results on Wilson line correlators (WLCs) of a static quark-antiquark pair from 2 + 1-flavor lattice-QCD (lQCD) computations with realistic pion mass. The self-consistent T -matrix results, which include previous constraints from the lQCD equation of state in the light-parton sector, can describe the lQCD data for WLCs fairly well once refinements of its driving kernel are applied. In particular, the input potential requires less screening than what has been inferred from previous T-matrix analyses. Pertinent predictions for the spectral and transport properties of the QGP are discussed, including the spatial diffusion coefficient for heavy quarks; the latter turns out to have a rather weak temperature dependence, in approximate agreement with recent unquenched lQCD results.
An improved technique for the identification and extraction of the exact quantities associated with the degrees of freedom at the element as well as the flexible body level is presented. It is implemented in the dynamic equations of motions based on the recursive formulation of Kane et al. (1987) and presented in a matrix form, integrating the concepts of strain energy, the finite-element approach, modal analysis, and reduction of equations. This technique eliminates the CPU intensive matrix multiplication operations in the code's hot spots for the dynamic simulation of the interconnected rigid and flexible bodies. A study of a simple robot with flexible links is presented by comparing the execution times on a scalar machine and a vector-processor with and without vector options. Performance figures demonstrating the substantial gains achieved by the technique are plotted.
An efficient way to solve the vector radiative transfer equation for plane-parallel turbid media is to Fourier-decompose it in azimuth. This methodology is typically based on the analytical computation of the Fourier components of the phase matrix and is predicated on the knowledge of the coefficients appearing in the expansion of the normalized scattering matrix in generalized spherical functions. Quite often the expansion coefficients have to be determined from tabulated values of the scattering matrix obtained from measurements or calculated by solving the Maxwell equations. In such cases one needs an efficient and accurate computer procedure converting a tabulated scattering matrix into the corresponding set of expansion coefficients. This short communication summarizes the theoretical basis of this procedure and serves as the user guide to a simple public-domain FORTRAN program.
Numerical results of the heat and mass transfer in a porous matrix are presented. The coupled, nonlinear partial differential equations describing this physical phenomenon are solved in finite difference form for two dimensions, using a new iterative technique (the strongly implicit procedure). The influence of the external environment conditions (heating and pressure) is shown to produce two-dimensional flow in the porous matrix. Typical fluid and solid temperature distributions in the porous matrix and internal pressure distributions are presented.
This paper documents the derivation of the data reduction equations for the calibration of the six-component thrust stand located in the CE-22 Advanced Nozzle Test Facility. The purpose of the calibration is to determine the first-order interactions between the axial, lateral, and vertical load cells (second-order interactions are assumed to be negligible). In an ideal system, the measurements made by the thrust stand along the three coordinate axes should be independent. For example, when a test article applies an axial force on the thrust stand, the axial load cells should measure the full magnitude of the force, while the off-axis load cells (lateral and vertical) should read zero. Likewise, if a lateral force is applied, the lateral load cells should measure the entire force, while the axial and vertical load cells should read zero. However, in real-world systems, there may be interactions between the load cells. Through proper design of the thrust stand, these interactions can be minimized, but are hard to eliminate entirely. Therefore, the purpose of the thrust stand calibration is to account for these interactions, so that necessary corrections can be made during testing. These corrections can be expressed in the form of an interaction matrix, and this paper shows the derivation of the equations used to obtain the coefficients in this matrix.