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Stress calculator permits speedy conversion of strain data directly into maximum and minimum stresses and also determines stress direction. The calculator has a movable slide with logarithmic and linear scales, and an information and grid board. Its size is flexible for easy manipulation.
The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.
A computational procedure is developed that uses a moving zonal grid concept to model complex flexible aerospace vehicles. The Euler/Navier-Stokes equations are used to model the flow, and computations are made using efficient methods based on both central and upwind schemes. The structure is represented by a finite element method which can model general aerospace vehicles. Provisions are made to accommodate other disciplines such as controls and thermal loads. The code is capable of computing unsteady flows on flexible wings with vortical flows. Adaptation of this procedure for parallel processing and validation for complete aerospace configurations is in progress.
Lifetime cost and performance (LCP) model assists in assessment of design options for photovoltaic systems. LCP is simulation of performance, cost, and revenue streams associated with photovoltaic power systems connected to electric-utility grid. LCP provides user with substantial flexibility in specifying technical and economic environment of application.
The authors have noticed in the recent grid generation literature an emphasis on the automation of structured grid generation. The motivation behind such work is clear; grid generation is easily the most despised task in the grid-analyze-visualize triad of computational analysis (CA). However, because grid generation is closely coupled to both the design and analysis software and because quantitative measures of grid quality are lacking, 'push button' grid generation usually results in a compromise between speed, control, and quality. Overt emphasis on automation obscures the substantive issues of providing users with flexible tools for generating and modifying high quality grids in a design environment. In support of this paper's tongue-in-cheek title, many features of the Gridgen software are described. Gridgen is by no stretch of the imagination an automatic grid generator. Despite this fact, the code does utilize many automation techniques that permit interesting regenerative features.
A flexible framework constructing block structured volume grids for hypersonic Navier-Strokes flow simulations was developed for the analysis of the Shuttle Orbiter Columbia. The development of the framework, which was partially basedon the requirements of the primary flow solvers used resulted in an ability to directly correlate solutions contributed by participating groups on a common surface mesh. A foundation was built through the assessment of differences between differnt solvers, which provided confidence for independent assessment of other damage scenarios by team members. The framework draws on the experience of NASA Langley and NASA Ames Research Centers in structured grid generation, and consists of a grid generation, and consist of a grid generation process implemented through a division of responsibilities. The nominal division of labor consisted of NASA Johnson Space Center coordinating the damage scenarios to be analyzed by the Aerothermodynamics Columbia Accident Investigation (ACAI) team, Ames developing the surface grids that described the computational volume about the Orbiter, and Langley improving grid quality of Ames generated data and constructing the final computational volume grids. Distributing the work among the participant in th ACAI team resulted in significantl less time required to construct complete meshes than possible by any individual participant. The approach demonstrated that the One-NASA grid generation team could sustain the demand of for five new meshes to explore new damage scenarios within an aggressive time-line.
A flexible framework for the development of block structured volume grids for hypersonic Navier-Stokes flow simulations was developed for analysis of the Shuttle Orbiter Columbia. The development of the flexible framework, resulted in an ability to quickly generate meshes to directly correlate solutions contributed by participating groups on a common surface mesh, providing confidence for the extension of the envelope of solutions and damage scenarios. The framework draws on the experience of NASA Langely and NASA Ames Research Centers in structured grid generation, and consists of a grid generation process that is implemented through a division of responsibilities. The nominal division of labor consisted of NASA Johnson Space Center coordinating the damage scenarios to be analyzed by the Aerothermodynamics Columbia Accident Investigation (CAI) team, Ames developing the surface grids that described the computational volume about the orbiter, and Langely improving grid quality of Ames generated data and constructing the final volume grids. Distributing the work among the participants in the Aerothermodynamic CIA team resulted in significantly less time required to construct complete meshes than possible by any individual participant. The approach demonstrated that the One-NASA grid generation team could sustain the demand for new meshes to explore new damage scenarios within a aggressive timeline.
Future spacecraft are being conceived that are highly flexible and of extreme size. The two features of flexibility and size pose new problems in control system design. Since large scale structures are not testable in ground based facilities, the decision on component placement must be made prior to full-scale tests on the spacecraft. Control law research is directed at solving problems of inadequate modelling knowledge prior to operation required to achieve peak performance. Another crucial problem addressed is accommodating failures in systems with smart components that are physically distributed on highly flexible structures. Parameter adaptive control is a method of promise that provides on-orbit tuning of the control system to improve performance by upgrading the mathematical model of the spacecraft during operation. Two specific questions are answered in this work. They are: What limits does on-line parameter identification with realistic sensors and actuators place on the ultimate achievable performance of a system in the highly flexible environment? Also, how well must the mathematical model used in on-board analytic redundancy be known and what are the reasonable expectations for advanced redundancy management schemes in the highly flexible and distributed component environment?
A capability to couple NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This paper summarizes the efforts in applying the installed coupling software to demonstrate/investigate fluid-structure interaction (FSI) between pressure wave and flexible inhibitor inside reusable solid rocket motor (RSRM). First a unified governing equation for both fluid and structure is presented, then an Eulerian-Lagrangian framework is described to satisfy the interfacial continuity requirements. The features of fluid solver, Loci/CHEM and structural solver, CoBi, are discussed before the coupling methodology of the solvers is described. The simulation uses production level CFD LES turbulence model with a grid resolution of 80 million cells. The flexible inhibitor is modeled with full 3D shell elements. Verifications against analytical solutions of structural model under steady uniform pressure condition and under dynamic condition of modal analysis show excellent agreements in terms of displacement distribution and eigen modal frequencies. The preliminary coupled result shows that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor.
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. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.
Postprocessing programs written to analyze the results of a general circulation model are described. The model history data is interpolated to pressure surfaces, converted from 64-bit Cyber words to 32 bit IBM words, and transferred to tape for further analysis. The time average program reads the interpolation output tape and produces 15-day time averages. The model outputs a very detailed record for selected grid points. This data is sent to a tape in Cyber full words. The conversion program changes the format of the tape from 64 bit Cyber words to 32 bit IBM words, processing a month of data at a time. The grid-point history sorting program inputs the converted grid point history tape and sorts it by time. The end product is a tape with a time history of each field for every point. After the PBP data has been stored, it can be plotted. The plotting package is flexible, and allows the choice of fields and grid points. The one-dimensional fields are plotted as functions of time, and a daily summary is also produced. For the two-dimensional fields, time-height cross sections and daily summaries are produced. The model plotting package produces plots for all fields on the time average and pressure tapes. These plots include world maps, polar projections, zonal means, vectors, streamlines, and latitude-height plots.
A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.
Multilevel methods on unstructured grids for elliptic problems are reviewed. The advantages of these techniques are the flexible approximation of the boundaries of complicated physical domains and the ability to adapt the grid to the resolution of fine scaled structures. Multilevel methods, which include multigrid methods and domain decomposition methods, depend on the correct splitting of appropriate finite element spaces. The standard splittings used in the structured grid case cannot be directly extended to unstructured grids due to their requirement for a hierarchical grid structure. Issues related to the application of multilevel methods to unstructured grids are discussed, including how the coarse spaces and transfer operators are defined and how different types of boundary conditions are treated. An obvious way to generate a coarse mesh is to regrid the physical domain several times. Several alternatives are proposed and discussed: node nested coarse spaces, agglomerated coarse spaces and algebraically generated coarse spaces.
An advanced-technology mercury ion thruster designed for operation at high thrust and high thrust-to-power ratio is described. The laboratory-model thruster employs a highly efficient discharge-chamber design that uses high-field-strength samarium-cobalt magnets arranged in a ring-cusp configuration. Ion extraction is achieved using an advanced three-grid ion-optics assembly which utilizes flexible mounts for supporting the screen, accel, and decel electrodes. Performance results are presented for operation at beam currents in the range from 1 to 5 A. The baseline specific discharge power is shown to be about 125 eV/ion, and the acceptable range of net-to-total accelerating-voltage ratio is shown to be in the range of 0.2-0.8 for beam currents in the range of 1-5 A.
A hybrid grid system that combines the Chimera overset grid scheme and an unstructured grid method is developed to study fluid flow and heat transfer problems. With the proposed method, the solid structural region, in which only the heat conduction is considered, can be easily represented using an unstructured grid method. As for the fluid flow region external to the solid material, the Chimera overset grid scheme has been shown to be very flexible and efficient in resolving complex configurations. The numerical analyses require the flow field solution and material thermal response to be obtained simultaneously. A continuous transfer of temperature and heat flux is specified at the interface, which connects the solid structure and the fluid flow as an integral system. Numerical results are compared with analytical and experimental data for a flat plate and a C3X cooled turbine cascade. A simplified drum-disk system is also simulated to show the effectiveness of this hybrid grid system.
The multidimensional self-adaptive grid code, SAGE, has proven to be a flexible and useful tool in the solution of complex flow problems. Both 2- and 3-D examples given in this report show the code to be reliable and to substantially improve flowfield solutions. Since the adaptive procedure is a marching scheme the code is extremely fast and uses insignificant CPU time compared to the corresponding flow solver. The SAGE program is also machine and flow solver independent. Significant effort was made to simplify user interaction, though some parameters still need to be chosen with care. It is also difficult to tell when the adaption process has provided its best possible solution. This is particularly true if no experimental data are available or if there is a lack of theoretical understanding of the flow. Another difficulty occurs if local features are important but missing in the original grid; the adaption to this solution will not result in any improvement, and only grid refinement can result in an improved solution. These are complex issues that need to be explored within the context of each specific problem.
A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.
A mesh-sequencing algorithm and a conservative patched-grid-interface algorithm (hereafter Patch Algorithm ) have been incorporated into the PAB3D code, which is a computer program that solves the Navier-Stokes equations for the simulation of subsonic, transonic, or supersonic flows surrounding an aircraft or other complex aerodynamic shapes. These algorithms are efficient, flexible, and have added tremendously to the capabilities of PAB3D. The mesh-sequencing algorithm makes it possible to perform preliminary computations using only a fraction of the grid cells (provided the original cell count is divisible by an integer) along any grid coordinate axis, independently of the other axes. The patch algorithm addresses another critical need in multi-block grid situation where the cell faces of adjacent grid blocks may not coincide, leading to errors in calculating fluxes of conserved physical quantities across interfaces between the blocks. The patch algorithm, based on the Stokes integral formulation of the applicable conservation laws, effectively matches each of the interfacial cells on one side of the block interface to the corresponding fractional cell area pieces on the other side. This approach is comprehensive and unified such that all interface topology is automatically processed without user intervention. This algorithm is implemented in a preprocessing code that creates a cell-by-cell database that will maintain flux conservation at any level of full or reduced grid density as the user may choose by way of the mesh-sequencing algorithm. These two algorithms have enhanced the numerical accuracy of the code, reduced the time and effort for grid preprocessing, and provided users with the flexibility of performing computations at any desired full or reduced grid resolution to suit their specific computational requirements.