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Suite of nonparallel benchmark programs, ELAPSE, designed for three tests: comparing efficiency of computer processing via Lisp vs. Ada; comparing efficiencies of several computers processing via Lisp; or comparing several computers processing via Ada. Tests efficiency which computer executes routines in each language. Available for computer equipped with validated Ada compiler and/or Common Lisp system.
Nontrivial benchmark solutions are developed for the galactic heavy ion transport equations in the straightahead approximation with energy and spatial coupling. Analytical representations of the ion fluxes are obtained for a variety of sources with the assumption that the nuclear interaction parameters are energy independent. The method utilizes an analytical LaPlace transform inversion to yield a closed form representation that is computationally efficient. The flux profiles are then used to predict ion dose profiles, which are important for shield design studies.
An experimental effort was implemented in aeroelasticity called the Benchmark Models Program. The primary purpose of this program is to provide the necessary data to evaluate computational fluid dynamic codes for aeroelastic analysis. It also focuses on increasing the understanding of the physics of unsteady flows and providing data for empirical design. An overview is given of this program and some results obtained in the initial tests are highlighted. The tests that were completed include measurement of unsteady pressures during flutter of rigid wing with a NACA 0012 airfoil section and dynamic response measurements of a flexible rectangular wing with a thick circular arc airfoil undergoing shock boundary layer oscillations.
An experimental effort was implemented in aeroelasticity called the Benchmark Models Program. The primary purpose of this program is to provide the necessary data to evaluate computational fluid dynamic codes for aeroelastic analysis. It also focuses on increasing the understanding of the physics of unsteady flows and providing data for empirical design. An overview is given of this program and some results obtained in the initial tests are highlighted. The tests that were completed include measurement of unsteady pressures during flutter of a rigid wing with an NACA 0012 airfoil section and dynamic response measurements of a flexible rectangular wing with a thick circular arc airfoil undergoing shock boundary layer oscillations.
The stochastic robustness of solutions to a benchmark control design problem has been analyzed. The analysis quantifies the controllers' stability and performance robustness with structured uncertainties in up to six system parameters. The analysis provides insights about system response that are not readily derived from other robustness criteria, providing a common ground for judging controllers produced by alternative methods.
An examination is made of the performance of a linear quadratic regulator which is robust to parametric uncertainty. The controller, which feeds back all states, is based upon Petersen's approach. Simulations show, using the benchmark problem, that remarkable performance robustness can be achieved.
The robustness of 10 solutions to a benchmark control design problem presented at the 1990 American Control Conference has been evaluated. The 10 controllers have second-to-eighth-order transfer functions and have been designed using several different methods, including H-infinity optimization, loop-transfer recovery, imaginary-axis shifting, constrained optimization, structured covariance, game theory, and the internal model principle. Stochastic robustness analysis quantifies the controllers' stability and performance robustness with structured uncertainties in up to six system parameters. The analysis provides insights into system response that are not readily derived from other robustness criteria and provides a common ground for judging controllers produced by alternative methods. One important conclusion is that gain and phase margins are not reliable indicators of the probability of instability. Furthermore, parameter variations actually may improve the likelihood of achieving selected performance metrics, as demonstrated by results for the probability of settling-time exceedance.
Recent results regarding quadratic stabilization and disturbance attenuation are applied to the benchmark problem. The authors investigate the minimum achievable levels of disturbance attenuation for different disturbance inputs and controlled outputs. They then design a feedforward tracking controller which tracks step inputs while maintaining the disturbance attenuation properties of the regulator.
Stochastic robustness analysis guides the synthesis of robust linear quadratic Gaussian (LQG) regulators for a benchmark control problem. Probabilities of exceeding allowable design limits, including stability, setting time, and control usage, are estimated by Monte Carlo evaluation. Robust, low-gain compensators that fulfill objectives are designed by numerically minimizing quadratic functions of these probabilities. The method is straightforward and makes use of uncomplicated design principles.
This paper describes selected results from the flutter testing of the Supercritical Wing (SW) model. This model is a rigid semispan wing having a rectangular planform and a supercritical airfoil shape. The model was flutter tested in the Langley Transonic Dynamics Tunnel (TDT) as part of the Benchmark Models Program, a multi-year wind tunnel activity currently being conducted by the Structural Dynamics Division of NASA Langley Research Center. The primary objective of this program is to assist in the development and evaluation of aeroelastic computational fluid dynamics codes. The SW is the second of a series of three similar models which are designed to be flutter tested in the TDT on a flexible mount known as the Pitch and Plunge Apparatus. Data sets acquired with these models, including simultaneous unsteady surface pressures and model response data, are meant to be used for correlation with analytical codes. Presented in this report are experimental flutter boundaries and corresponding steady and unsteady pressure distribution data acquired over two model chords located at the 60 and 95 percent span stations.
The goal of the Benchmark Models Program is to provide data useful in the development and evaluation of aeroelastic computational fluid dynamics (CFD) codes. To that end, a series of three similar wing models are being flutter tested in the Langley Transonic Dynamics Tunnel. These models are designed to simultaneously acquire model response data and unsteady surface pressure data during wing flutter conditions. The supercritical wing is the second model of this series. It is a rigid semispan model with a rectangular planform and a NASA SC(2)-0414 supercritical airfoil shape. The supercritical wing model was flutter tested on a flexible mount, called the Pitch and Plunge Apparatus, that provides a well-defined, two-degree-of-freedom dynamic system. The supercritical wing model and associated flutter test apparatus is described and experimentally determined wind-off structural dynamic characteristics of the combined rigid model and flexible mount system are included.
The QUAD4 and TRIA3 elements are the primary plate/shell elements in NASTRAN. These elements enable the user to analyze thin plate/shell structures for membrane, bending and shear phenomena. They are also very new elements in the NASTRAN library. These elements are extremely versatile and constitute a substantially enhanced analysis capability in NASTRAN. However, with the versatility comes the burden of understanding a myriad of modeling implications and their effect on accuracy and analysis quality. The validity of many aspects of these elements were established through a series of benchmark problem results and comparison with those available in the literature and obtained from other programs like MSC/NASTRAN and CSAR/NASTRAN. Never-the-less such a comparison is never complete because of the new and creative use of these elements in complex modeling situations. One of the important features of QUAD4 and TRIA3 elements is the offset capability which allows the midsurface of the plate to be noncoincident with the surface of the grid points. None of the previous elements, with the exception of bar (beam), has this capability. The offset capability played a crucial role in the design of QUAD4 and TRIA3 elements. It allowed modeling layered composites, laminated plates and sandwich plates with the metal and composite face sheets. Even though the basic implementation of the offset capability is found to be sound in the previous applications, there is some uncertainty in relatively simple applications. The main purpose of this paper is to test the integrity of the offset capability and provide guidelines for its effective use. For the purpose of simplicity, references in this paper to the QUAD4 element will also include the TRIA3 element.
The relationship between management style and program costs is analyzed to determine the feasibility of financing large international space missions. The incorporation of management systems is considered to be essential to realizing low cost spacecraft and planetary surface systems. Several companies ranging from large Lockheed 'Skunk Works' to small companies including Space Industries, Inc., Rocket Research Corp., and Orbital Sciences Corp. were studied. It is concluded that to lower the prices, the ways in which spacecraft and hardware are developed must be changed. Benchmarking of successful low cost space programs has revealed a number of prescriptive rules for low cost managements, including major changes in the relationships between the public and private sectors.
A recent directive at NASA Langley is aimed at numerically predicting principal noise sources. During my summer stay, I worked with high-order ENO code, developed by Dr. Harold Atkins, for solving the unsteady compressible Navier-Stokes equations, as it applies to computational aeroacoustics (CAA). A CAA workshop, composed of six categories of benchmark problems, has been organized to test various numerical properties of code. My task was to determine the robustness of Atkins' code for these test problems. In one category, we tested the nonlinear wave propagation of the code for the one-dimensional Euler equations, with initial pressure, density, and velocity conditions. Using freestream boundary conditions, our results were plausible. In another category, we solved the linearized two-dimensional Euler equations to test the effectiveness of radiation boundary conditions. Here we utilized MAPLE to compute eigenvalues and eigenvectors of the Jacobian given variable and flux vectors. We experienced a minor problem with inflow and outflow boundary conditions. Next, we solved the quasi one dimensional unsteady flow equations with an incoming acoustic wave of amplitude 10(exp -6). The small amplitude sound wave was incident on a convergent-divergent nozzle. After finding a steady-state solution and then marching forward, our solution indicated that after 30 periods the acoustic wave had dissipated (a period is time required for sound wave to traverse one end of nozzle to other end).
This report documents the results of an experimental investigation on the response of a cavity to external flowfields. The primary objective of this research was to acquire benchmark of data on the effects of cavity length, width, depth, upstream boundary layer, and flow temperature on cavity noise. These data were to be used for validation of computational aeroacoustic (CAA) codes on cavity noise. To achieve this objective, a systematic set of acoustic and flow measurements were made for subsonic turbulent flows approaching a cavity. These measurements were conducted in the research facilities of the Georgia Tech research institute. Two cavity models were designed, one for heated flow and another for unheated flow studies. Both models were designed such that the cavity length (L) could easily be varied while holding fixed the depth (D) and width (W) dimensions of the cavity. Depth and width blocks were manufactured so that these dimensions could be varied as well. A wall jet issuing from a rectangular nozzle was used to simulate flows over the cavity.
The proceedings of the Benchmark Problems in Computational Aeroacoustics Workshop held at NASA Langley Research Center are the subject of this report. The purpose of the Workshop was to assess the utility of a number of numerical schemes in the context of the unusual requirements of aeroacoustical calculations. The schemes were assessed from the viewpoint of dispersion and dissipation -- issues important to long time integration and long distance propagation in aeroacoustics. Also investigated were the effect of implementation of different boundary conditions. The Workshop included a forum in which practical engineering problems related to computational aeroacoustics were discussed. This discussion took the form of a dialogue between an industrial panel and the workshop participants and was an effort to suggest the direction of evolution of this field in the context of current engineering needs.
We investigate accurate and efficient time advancing methods for computational aeroacoustics, where non-dissipative and non-dispersive properties are of critical importance. Our analysis pertains to the application of Runge-Kutta methods to high-order finite difference discretization. In many CFD applications, multi-stage Runge-Kutta schemes have often been favored for their low storage requirements and relatively large stability limits. For computing acoustic waves, however, the stability consideration alone is not sufficient, since the Runge-Kutta schemes entail both dissipation and dispersion errors. The time step is now limited by the tolerable dissipation and dispersion errors in the computation. In the present paper, it is shown that if the traditional Runge-Kutta schemes are used for time advancing in acoustic problems, time steps greatly smaller than that allowed by the stability limit are necessary. Low Dissipation and Dispersion Runge-Kutta (LDDRK) schemes are proposed, based on an optimization that minimizes the dissipation and dispersion errors for wave propagation. Optimizations of both single-step and two-step alternating schemes are considered. The proposed LDDRK schemes are remarkably more efficient than the classical Runge-Kutta schemes for acoustic computations. Numerical results of each Category of the Benchmark Problems are presented. Moreover, low storage implementations of the optimized schemes are discussed. Special issues of implementing numerical boundary conditions in the LDDRK schemes are also addressed.
Two new methods for the numerical solution of conservation laws (the Euler equations in particular) are presented: a uniformly second-order accurate upwind scheme and a third-order accurate centered scheme. Results of these schemes are shown for problems 1, 2, and 5 of this workshop's benchmark problems.