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NASA NTRS1992

Application of edge-based finite elements and vector ABCs in 3D scattering

A finite element absorbing boundary condition (FE-ABC) solution of the scattering by arbitrary 3-D structures is considered. The computational domain is discretized using edge-based tetrahedral elements. In contrast to the node-based elements, edge elements can treat geometries with sharp edges, are divergence-less, and easily satisfy the field continuity condition across dielectric interfaces. They do, however, lead to a higher unknown count but this is balanced by the greater sparsity of the resulting finite element matrix. Thus, the computation time required to solve such a system iteratively with a given degree of accuracy is less than the traditional node-based approach. The purpose is to examine the derivation and performance of the ABC's when applied to 2-D and 3-D problems and to discuss the specifics of our FE-ABC implementation.

Chatterjee, A.↗

NASA NTRS1982

Particle trajectory computer program for icing analysis of axisymmetric bodies

General aviation aircraft and helicopters exposed to an icing environment can accumulate ice resulting in a sharp increase in drag and reduction of maximum lift causing hazardous flight conditions. NASA Lewis Research Center (LeRC) is conducting a program to examine, with the aid of high-speed computer facilities, how the trajectories of particles contribute to the ice accumulation on airfoils and engine inlets. This study, as part of the NASA/LeRC research program, develops a computer program for the calculation of icing particle trajectories and impingement limits relative to axisymmetric bodies in the leeward-windward symmetry plane. The methodology employed in the current particle trajectory calculation is to integrate the governing equations of particle motion in a flow field computed by the Douglas axisymmetric potential flow program. The three-degrees-of-freedom (horizontal, vertical, and pitch) motion of the particle is considered. The particle is assumed to be acted upon by aerodynamic lift and drag forces, gravitational forces, and for nonspherical particles, aerodynamic moments. The particle momentum equation is integrated to determine the particle trajectory. Derivation of the governing equations and the method of their solution are described in Section 2.0. General features, as well as input/output instructions for the particle trajectory computer program, are described in Section 3.0. The details of the computer program are described in Section 4.0. Examples of the calculation of particle trajectories demonstrating application of the trajectory program to given axisymmetric inlet test cases are presented in Section 5.0. For the examples presented, the particles are treated as spherical water droplets. In Section 6.0, limitations of the program relative to excessive computer time and recommendations in this regard are discussed.

Frost, Walter↗

NASA NTRS1991

A new method for simulating atmospheric turbulence for rotorcraft applications

Simulation of atmospheric turbulence as seen by a rotating blade element involves treatment of cyclostationary processes. Conventional filtering techniques do not lend themselves well to the generation of such turbulence sample functions as are required in rotorcraft flight dynamics simulation codes. A method to generate sample functions containing second order statistics of mean and covariance is presented. Compared to ensemble averaging involving excessive computer time, the novelty is to exploit cycloergodicity and thereby, replace ensemble averaging by averaging over a single path sample function of long duration. The method is validated by comparing its covariance results with the analytical and ensemble averaged results for a widely used 1-D turbulence approximation.

J. Riaz↗

NASA NTRS1992

Development of 3D electromagnetic modeling tools for airborne vehicles

The main goal of this report is to advance the development of methodologies for scattering by airborne composite vehicles. Although the primary focus continues to be the development of a general purpose computer code for analyzing the entire structure as a single unit, a number of other tasks are also being pursued in parallel with this effort. One of these tasks discussed within is on new finite element formulations and mesh termination schemes. The goal here is to decrease computation time while retaining accuracy and geometric adaptability.The second task focuses on the application of wavelets to electromagnetics. Wavelet transformations are shown to be able to reduce a full matrix to a band matrix, thereby reducing the solutions memory requirements. Included within this document are two separate papers on finite element formulations and wavelets.

Volakis, John L.↗

NASA NTRS1992

Adaptive unstructured meshing for thermal stress analysis of built-up structures

An adaptive unstructured meshing technique for mechanical and thermal stress analysis of built-up structures has been developed. A triangular membrane finite element and a new plate bending element are evaluated on a panel with a circular cutout and a frame stiffened panel. The adaptive unstructured meshing technique, without a priori knowledge of the solution to the problem, generates clustered elements only where needed. An improved solution accuracy is obtained at a reduced problem size and analysis computational time as compared to the results produced by the standard finite element procedure.

Dechaumphai, Pramote↗

NASA NTRS1990

A Numerical Method for Direct Simulation of Turbulence in Complex Geometries

The ultimate goal of this work is to study the flow inside a channel with riblets on one of the two walls. The method has been tested for two dimensional flows in the presence of bodies with a geometrical singularity and for three dimensional flows inside domains described by Cartesian coordinates. The results have been compared with previous numerical simulations and with experimental results. The cases considered are: (1) the growth of Orr-Sommerfield waves in plane Poiseulle flow; (2) the flow over a backward facing step; (3) the flow past a wedge; and (4) the flow inside a narrow channel. Finally, the case of a channel with two large riblets on a wall has been simulated. In this case a limited number of grid points is sufficient, and in spite of the slow convergence for the pressure solver, one is able to obtain solutions with a reasonable amount of computer time. At present solutions with very fine grids in all three directions can not be obtained, due to lack of a fast pressure solver for general curvilinear coordinates.

P Orlandi↗

NASA NTRS1992

Altimetry and lidar using AlGaAs lasers modulated with pseudo-random codes

We have demonstrated a prototype laser altimeter and lidar which uses a low power AlGaAs laser modulated with a pseudorandom noise (PN) code, a 20 cm diameter telescope, and a photon counting receiver. Measurements to tree canopies over a 400 m horizontal path show strong signals with 5.3 mW average power and a 6.4 msec averaging time. Computer simulations predict lidar performance for various types of scattering performance.

Abshire, James B.↗

NASA NTRS1992

Lidar multiple scattering: Dependence on atmospheric parameters

Backscatter lidars are very useful tools in gaining information about the atmosphere. Inversion of backscatter signals can be used to retrieve the spatial distribution of clouds and aerosols, e.g., vertical extensions of clouds and aerosol layers, detection of 'subvisible' cirrus, etc., very accurately compared to passive radiometers. To retrieve extinction coefficient profiles, in general, the so-called lidar equation is solved. This equation describes a laser pulse which propagates through an atmosphere with transmission exp(- integral of sigma(z')dz'), which is scattered singly under 180 degrees towards a receiver, and which is attenuated on its way back again by exp(- integral of sigma(z')dz'). For inversion, further information on optical properties of the scatterers are required (extinction to backscatter ratio). However, it is evident that, at least for optically thick clouds and/or large receiver's field-of-views, this approach may be erroneous because of multiply scattered photons. Several studies were performed to simulate multiple scattering in case of collimated beams or pulses including Monte Carlo, transport, and diffusion theory. Unfortunately, most of the approaches require an enormous amount of computer time. Thus, it is meaningful to elaborate approximate methods, and one such method is discussed. Our method is based on Bissonnett (1988). We have improved the numerical simulation of limited field-of-view detectors, and compared the results to Monte Carlo calculations and an exact model of Altmann (1989).

Wiegner, Matthias↗

NASA NTRS1992

Computations of unsteady multistage compressor flows in a workstation environment

High-end graphics workstations are becoming a necessary tool in the computational fluid dynamics environment. In addition to their graphic capabilities, workstations of the latest generation have powerful floating-point-operation capabilities. As workstations become common, they could provide valuable computing time for such applications as turbomachinery flow calculations. This report discusses the issues involved in implementing an unsteady, viscous multistage-turbomachinery code (STAGE-2) on workstations. It then describes work in which the workstation version of STAGE-2 was used to study the effects of axial-gap spacing on the time-averaged and unsteady flow within a 2 1/2-stage compressor. The results included time-averaged surface pressures, time-averaged pressure contours, standard deviation of pressure contours, pressure amplitudes, and force polar plots.

Gundy-Burlet, Karen L.↗

NASA NTRS1992

Application of Computational Fluid Dynamics to the Study of Vortex Flow Control for the Management of Inlet Distortion

The present study demonstrates that the Reduced Navier-Stokes code RNS3D can be used very effectively to develop a vortex generator installation for the purpose of minimizing the engine face circumferential distortion by controlling the development of secondary flow. The computing times required are small enough that studies such as this are feasible within an analysis-design environment with all its constraints of time and costs. This research study also established the nature of the performance improvements that can be realized with vortex flow control, and suggests a set of aerodynamic properties (called observations) that can be used to arrive at a successful vortex generator installation design. The ultimate aim of this research is to manage inlet distortion by controlling secondary flow through an arrangements of vortex generators configurations tailored to the specific aerodynamic characteristics of the inlet duct. This study also indicated that scaling between flight and typical wind tunnel test conditions is possible only within a very narrow range of generator configurations close to an optimum installation. This paper also suggests a possible law that can be used to scale generator blade height for experimental testing, but further research in this area is needed before it can be effectively applied to practical problems. Lastly, this study indicated that vortex generator installation design for inlet ducts is more complex than simply satisfying the requirement of attached flow, it must satisfy the requirement of minimum engine face distortion.

Anderson, Bernhard H.↗

NASA NTRS1991

A new method for simulating atmospheric turbulence for rotorcraft applications

Simulation of atmospheric turbulence as seen by a rotating blade element involves treatment of cyclostationary processes. Conventional filtering techniques do not lend themselves well to the generation of such turbulence sample functions as are required in rotorcraft flight dynamics simulation codes. A method to generate sample functions containing second-order statistics of mean and covariance is presented. Compared to ensemble averaging involving excessive computer time, the novelty is to exploit cycloergodicity and thereby, replace ensemble averaging by averaging over a single-path sample function of long duration. The method is validated by comparing its covariance results with the analytical and ensemble-averaged results for a widely used one-dimensional turbulence approximation.

Prasad, J. V. R.↗

NASA NTRS1991

Computations of unsteady multistage compressor flows in a workstation environment

High-end graphics workstations are becoming a necessary tool in the Computational Fluid Dynamics (CFD) environment. In addition to their graphics capabilities, the latest generation of workstations have powerful floating point operation capabilities. As workstations become common, they could provide valuable computing time for applications, such as turbomachinery flow calculations. This paper discusses the issues involved in implementing an unsteady, viscous multistage turbomachinery code (STAGE-2) on workstations. The workstation version of STAGE-2 has then been used to study the effects of axial-gap spacing on the time-averaged and unsteady flow within a 2 1/2-stage compressor. Results include force polar plots, time-averaged pressure contours, standard deviation of pressure contours, time-averaged surface pressures and pressure amplitudes.

Gundy-Burlet, Karen L.↗

NASA NTRS1991

Discrete ordinate solution of the radiative transfer equation in the 'polarization normal wave representation'

The transfer equations for normal waves in finite, inhomogeneous and plane-parallel magnetoactive media are solved using the discrete ordinate method. The physical process of absorption, emission, and multiple scattering are accounted for, and the medium may be forced both at the top and bottom boundary by anisotropic radiation as well as by internal anisotropic sources. The computational procedure is numerically stable for arbitrarily large optical depths, and the computer time is independent of optical thickness.

Kylling, A.↗

NASA NTRS1992

A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

Bernstein, Ira B.↗

NASA NTRS1992

Arrival and departure impulsive Delta V determination for precessing Mars parking orbits

An attempt is made to develop a method for realistic estimation of the initial LEO mass. The method takes into account the actual geometry between the inbound and outbound hyperbolic asymptotes and the parking orbit, along with precession effects caused by the oblateness of Mars, in calculating the arrival and departure Delta V values. Three mission scenarios alternative to the arbitrarily assumed two tangential periapsis burns are described: a tangential periapsis arrival and an in-plane departure; an in-plane arrival and in-plane departure; and a tangential periapsis arrival and a 3D departure. Results obtained by the method under consideration compared well with a trajectory integration code, where the differences in the initial LEO orbit mass were within one percent, for all three cases. The method is considered to be an ideal tool for preliminary mission design, since it reduces the analysis computation time with minimal loss in accuracy.

Desai, Prasun N.↗

NASA NTRS1992

Adaptive unstructured meshing for thermal stress analysis of built-up structures

Dechaumphai, Pramote↗

NASA NTRS1992

A solar radiation model for use in climate studies

A solar radiation routine is developed for use in climate studies that includes absorption and scattering due to ozone, water vapor, oxygen, carbon dioxide, clouds, and aerosols. Rayleigh scattering is also included. Broadband parameterization is used to compute the absorption by water vapor in a clear atmosphere, and the k-distribution method is applied to compute fluxes in a scattering atmosphere. The reflectivity and transmissivity of a scattering layer are computed analytically using the delta-four-stream discrete-ordinate approximation. The two-stream adding method is then applied to compute fluxes for a composite of clear and scattering layers. Compared to the results of high spectral resolution and detailed multiple-scattering calculations, fluxes and heating rate are accurately computed to within a few percent. The high accuracy of the flux and heating-rate calculations is achieved with a reasonable amount of computing time. With the UV and visible region grouped into four bands, this solar radiation routine is useful not only for climate studies but also for studies on photolysis in the upper atmosphere and photosynthesis in the biosphere.

Chou, Ming-Dah↗

NASA NTRS1992

Equivalent GPS measurements for efficient estimation process

Dual-frequency pseudorange and carrier phase data streams can be analytically combined into a single equivalent data stream, reducing the data volume and computing time in the filtering process for parameter estimation by a factor of 2 to 4. The resulting single data stream is that of carrier phase measurements with both data noise and bias uncertainty strictly defined. Based on these analytical formulas the equivalent GPS measurements can be formed by simple and efficient numerical calculations without any degradation in data strength. Formulation for the equivalent GPS measurements and their covariances are given in closed form; and a numerical simulation is performed to demonstrate the validity and effectiveness of the equivalent measurements.

Wu, S. C.↗