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NASA NTRS1985

A three-dimensional Navier-Stokes/Euler code for blunt-body flow computations

The formulation computation method of an improved version of the three-dimensional Navier-Stokes/Euler computation algorithm of Li (1981) for the numerical simulation of blunt-body reentry flows are discussed, and results for five sample problems are presented graphically. The vector notation of the coordinate systems is defined; the governing equations are presented in full; the Jacobian matrices and damping terms of the factorization technique (based on the alternating-direction implicit procedure of Beam and Warming, 1978) are explained; and the capabilities, limitations and proper use of the code are summarized. Examples presented include the equilibrium-flow problem for Shuttle-orbiter reentry at Mach 22 and angle of attack 40.8 deg and the perfect-gas problem of an aerobraking orbital-transfer vehicle with an ellipsoidal/60-deg cone and a toroidal sonic shoulder. The advantages of the improved code in terms of accuracy and computation time are indicated.

Li, C. P.↗

NASA NTRS1985

Magnetic field in the wake of Venus and the formation of ionospheric holes

Magnetic field structures are analyzed for both the ionospheric hole region and the magnetosheath/ionosphere interaction region of the nightside of Venus, in search of possible coupling between these two regimes. A magnetic coordinate system based on the directions of the solar wind and the interplanetary magnetic field is found to order the data reasonably well, allowing consistent superposition of observational data from individual passes of the Pioneer Venus orbiter. The results indicate that the magnetosheath plasma flow in the wake region plays an important role in forming the ionospheric holes through deformation of the nightside ionopause. The results are combined in a model of the three-dimensional magnetic field structure around the ionosphere of Venus.

Marubashi, K.↗

NASA NTRS1984

A kinetic energy analysis of the meso beta-scale severe storm environment

Analyses are performed of the meso beta-scale (20-200 km wavelengths and several hours to one-day periods) severe storm kinetic energy balance on the fifth day of the AVE SESAME campaign of May 1979. A 24-hr interval covering the antecedent, active and post-convective outbreak activity over Oklahoma are considered. Use is made of the kinetic energy budget equation (KEBE) for a finite volume in an isobaric coordinate system. Rawindsonde data with 75 km resolution were treated. The KEBE model covered changes in kinetic energy due to the cross contour flows, horizontal and vertical components of flux divergence, and volumic mass changes on synoptic and subsynoptic scales. The greatest variability was concentrated above 400 mb height and over the most intense storm activity. Energy was generated at the highest rates in divergence and decreased the most in convection. The meso beta-scale lacked sufficient resolution for analyzing mesoscale activity.

Fuelberg, H. E.↗

NASA NTRS1985

On the accuracy of the pseudocompressibility method in solving the incompressible Navier-Stokes equations

The method of pseudocompressibility is being tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite-difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibility for solving the pressure field, coupled with an implicit, approximate-factorization scheme. This coupling is known as the pseudocompressibility method. The pseudocompressibility method introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. However, these waves limit the time-accuracy of the computations. The effects of these waves are analyzed and criteria are set for choosing the pseudocompressibility parameters that govern the pressure wave speed. Test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.

Rogers, S. E.↗

NASA NTRS1985

Numerical simulation of compressible, turbulent, two-phase flow

A computer program for numerically simulating compressible, turbulent, two-phase flows is described and applied. Special attention is given to flows in which dust is ingested into the turbulent boundary layer behind shock waves moving over the earth's surface. it is assumed that the two phases are interpenetrating continua which are coupled by drag forces and heat transfer. The particle phase is assumed to be dilute, and turbulent effects are modeled by zero- and two-equation eddy viscosity models. An important feature of the turbulence modeling is the treatment of surface boundary conditions which control the ingestion of particles into the boundary layer by turbulent friction and diffusion. The numerical method uses second-order implicit upwind differencing of the inviscid terms of the equations and second-order central differencing of the viscous terms. A diagonal form of the implicit algorithm is used to improve efficiency, and the transformation to a curvilinear coordinate system is accomplished by the finite volume techniques. Applications to a series of representative flows include a two-phase nozzle flow, the steady flow of air over a sand bed, and the air flow behind a normal shock wave in uniform motion over a sand bed. Results of the latter two applications are compared with experimental results.

Coakley, t. J.↗

NASA NTRS1985

Implicit lambda methods for three-dimensional compressible flow

This paper derives the three dimensional lambda-formulation equations for a general orthogonal curvilinear coordinate system and provides various block-explicit and block-implicit methods for solving them, numerically. Three model problems, characterized by subsonic, supersonic and transonic flow conditions, are used to assess the reliability and compare the efficiency of the proposed methods.

Napolitano, M.↗

NASA NTRS1985

A two-layer diagnostic model of the long-term physical evolution of warm-core ring 82B

The present shipboard data in the 1982 time series on a single Gulf Stream warm core ring are composited on a cylindrical coordinate system following ring motion; 10 C-isotherm depth measurements are used in a two-layer model of the ring's structure to compute gradient current, kinetic energy, available potential energy (APE), and potential vorticity. The ring's evolution can be divided into two periods: April-late June, while the ring is isolated from strong Gulf Stream interaction, during which the ring loses APE at a low rate, and from July onward, following ring interactions with the Gulf Stream and topography with much higher energy loss. Within measurement errors, the potential vorticity at the center of the ring is conserved from April through August, implying nearly inviscid dynamics.

Olson, D. B.↗

NASA NTRS1986

Algorithm for Calibrating Robot Arms

Robots made to less demanding specifications and yet be more accurate. Method, described in published paper, used on any serial-link robot with any combination of revolute and primatic joints. Increases accuracy of positioning manipulator at any point in workspace relative to fixed coordinate system. Accurate absolute positioning capability particularly useful for those tasks where robot is issued target location by external sensory devices, such as vision system. With new method, ultraprecise manufacturing and high-resolution measurements of robot components unnecessary. Method therefore reduces cost of robots in addition to increasing robot accuracy.

Hayati, S. A.↗

NASA NTRS1985

Development of an explicit multigrid algorithm for quasi-three-dimensional viscous flows in turbo-machinery

A rapid quasi three-dimensional analysis was developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations which are solved by a two-stage Runge-Kutta scheme made efficient by use of vectorization, a variable time-step, and a flux-based multigrid scheme, are described. A stability analysis is presented for the two-stage scheme. Results for a flat-plate model problem show the applicability of the method to axial, radial, and rotating geometries. Results for a centrifugal impeller and a radial diffuser show that the quasi three-dimensional viscous analysis can be a practical design tool.

Chima, R. V.↗

NASA NTRS1985

Kinematics of foldable discrete space cranes

Exact kinematic description of a NASA proposed prototype foldable-deployable discrete space crane are presented. A computer program is developed which maps the geometry of the crane once controlling parameters are specified. The program uses a building block type approach in which it calculates the local coordinates of each repeating cell and then combines them with respect to a global coordinates system.

Nayfeh, A. H.↗

NASA NTRS1986

Viscous compressible flow direct and inverse computation and illustrations

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Yang, T. T.↗

NASA NTRS1986

Analytical ultrasonics for evaluation of composite materials response. Part 1: Physical interpretation

The phenomena associated with the propagation of elastic waves in anisotropic materials are discussed. Wave modes propagating in general directions relative to the material coordinate system are not purely longitudinal nor transverse. Hence the generation of ultrasonic waves by common piezoelectric transducers will generate multiple modes to some extent. The received signals will likely be a combination of different modes. When using two transducers to send and receive ultrasonic waves, deviation of the energy flux vector may reduce the apparent value of the received signal unless the proper orientation of the two transducers with respect to one another is taken into account. And application of reflection from plane boundaries for the purposes of making certain measurements may lead to misinterpretation of results unless one is aware of the differences in multiple mode generation and critical angle phenomena between isotropic and anisotropic materials. When studies or characterizations of composite materials by ultrasonics are to be performed, these phenomena must be taken into consideration so that proper and correct application and interpretation of the measurements can be made. Finally, attention must be drawn again to the fact that composite materials are heterogeneous by definition. The results discussed here have been determined for homogeneous materials only. While the assumption of homogeneity appears to be valid for certain wavelength ranges in composites, future work must continue to study the phenomena of wave propagation in anisotropic, nonhomogeneous materials.

Henneke, E. G., II↗

NASA NTRS1986

Turbulent flow field predictions in sharply curved turn around ducts

In this investigation, two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative indication of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa-epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa-esilon model predictions are included.

Santi, L. M.↗

NASA NTRS1986

Turbulent flow field predictions in sharply curved turn-around ducts

Two-dimensional turbulent flow of incompressible Newtonian fluids in sharply curved 180 deg turn around ducts is studied. Results of an approximate numerical flow field analysis utilizing an orthogonal, body-fitted, curvilinear coordinate system are compared to results based on a traditional cylindrical reference frame. Qualitative induction of general streamfield characteristics as well as quantitative benchmarks for the planning of future experimentation are provided. In addition, preliminary results of an augmented kappa - epsilon turbulence model analysis, which explicitly accounts for the effects of streamline curvature and pressure strain in internal turbulent flows, are presented. Specific model difficulties are discussed and comparisons with standard kappa - epsilon model predictions are included.

Santi, L. M.↗

NASA NTRS1986

Implicit multigrid algorithms for the three-dimensional flux split Euler equations

The full approximation scheme multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computations required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. Results comparing pressure distributions with experimental data using both splitting types are shown. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined. Using the multigrid method on both subsonic and transonic wing calculations, the final lift coefficient is obtained to within 0.1 percent of its final value in a few as 15 cycles for a mesh with over 210,000 points. A spectral radius of 0.89 is achieved for both subsonic and transonic flow over the ONERA M6 wing while a spectral radius of 0.83 is obtained for supersonic flow over an analytically defined forebody. Results compared with experiment for all cases show good agreement.

Anderson, W. K.↗

NASA NTRS1985

Station coordinates, baselines, and earth rotation from Lageos laser ranging - 1976-1984

The orbit of the Lageos satellite is well suited as a reference frame for studying the rotation of the earth and the relative motion of points on the earth's crust. The satellite laser measurements can determine the location of a set of tracking stations in an appropriate terrestrial coordinate system. The motion of the earth's rotation axis relative to this system can be studied on the basis of the established tracking station locations. The present investigation is concerned with an analysis of 7.7 years of Lageos laser ranging data. In the first solution considered, the entire data span was used to adjust a single set of station positions simultaneously with orbit and earth rotation parameters. Attention is given to the accuracy of earth rotation parameters which are determined as an inherent part of the solution process.

Tapley, B. D.↗

NASA NTRS1985

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching-step sizes with the implicit shock fitting procedure. A correlation is found between the marching-step size, Reynolds number and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Kaul, U. K.↗

NASA NTRS1986

Development of an explicit multigrid algorithm for quasi-three-dimensional viscous flows in turbomachinery

A rapid quasi three-dimensional analysis was developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations which are solved b a two-stage Runge-Kutta scheme made efficient by use of vectorization, a variable time-step, and a flux-based multigrid scheme, are described. A stability analysis is presented for the two-stage. Results for a flat-plate model problem show the applicability of the method to axial, radial, and rotating geometries. Results for a centrifugal impeller and a radial diffuser show that the quasi three-dimensional viscous analysis can be a practical design tool.

Chima, R. V.↗