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NASA NTRS1980

Protostellar formation in rotating interstellar clouds. I - Numerical methods and tests

Attention is given to numerical methods and tests of a series of gravitational hydrodynamics computer codes constructed in order to numerically follow the dynamic collapse of spherically symmetric (1-D), axisymmetric (2-D), and non-axisymmetric (3-D) isothermal interstellar clouds. A spherical harmonic expansion is used to solve the Poisson equation for the gravitational potential. It is shown that the use of explicit donor-cell hydrodynamics on a moving spherical coordinate grid ensures mass and momentum conservation and allows the grid to follow the collapse of the fluid. Finally, the performance of the codes is examined.

Boss, A. P.↗

NASA NTRS1980

On the numerical solution of time-dependent viscous incompressible fluid flows involving solid boundaries

An inherent numerical problem associated with the fully explicit pseudospectral numerical simulation of the incompressible Navier-Stokes equation for viscous flows with no-slip walls is described. A semi-implicit scheme which circumvents this numerical difficulty is presented. In this algorithm the equation of continuity rather than the Poisson equation for pressure is solved directly. Pseudospectral formulation of the channel flow problem using Fourier series and Chebyshev polynomials expansions is given for this scheme. An example demonstrating the applicability of the method is given.

Moin, P.↗

NASA NTRS1979

The search for, and study of black holes in the galaxy

The study of the short-term (less than 10 s) time variability of Cygnus X-1 is reviewed, with attention given to measurements of the autocorrelation function and of the cross-correlation between different energy bandwidths, as well as to a simple shot noise model for describing all such short-term variations. Observational questions with regard to Cygnus X-1 are discussed, relating to the average shape of the randomly occurring flares, energy dependence in the cross-correlation and the dependence on energy of the X-ray polarization. Concerning the study of the Cyg X-1-like aperiodic X-ray sources, an estimate is made of what can be accomplished at the limits of sensitivity where Poisson fluctuations are at least as important as the intrinsic variability of the source, considering the third moment due to the source fluctuations.

Weisskopf, M. C.↗

NASA NTRS1980

Prediction and measurement of turbulent aerodynamic trailing edge flows

A viscous-inviscid interaction algorithm is developed for prediction of two-dimensional mean and fluctuating velocity distributions in the wake immediately downstream of an airfoil trailing edge. A composite pressure field is defined, and a Poisson equation solved for transverse pressure variations. A parabolized form of the time-averaged steady Navier-Stokes equations are solved in conjunction with a viscous-augmented two-dimensional inviscid potential flow analysis. A tensor constitutive equation is employed to predict Reynolds stress distributions from solutions of a turbulence kinetic energy two equation closure model. Numerical predictions compared favorably with detailed experimental data for mean and fluctuating velocities, and Reynolds shear stress distributions, in the trailing edge region of a NACA 63-012 airfoil.

Baker, A. J.↗

NASA NTRS1980

Generation of orthogonal boundary-fitted coordinate systems

A method is presented for computing orthogonal boundary fitted coordinate systems for geometries with coordinate distributions specified on all boundaries. The system which has found most extensive use in generating boundary fitted grids is made up of Poisson equations, of which the functions P and Q provide a means for controlling the spacing and density of grid lines in the coordinate system. While questions remain concerning the existence and uniqueness of orthogonal systems, the generating method presented adds to the available, useful techniques for constructing these systems.

Coleman, R. M.↗

NASA NTRS1980

Vortex methods for two- and three-dimensional flow simulations

The point vortex and vortex blob methods for two dimensional flows are presented. Several results are discussed concerning the numerical analysis of the latter scheme, e.g., the preservation of globally conserved quantities and the analysis of the spatial discretization error resulting from the convection of fixed blobs of vorticity. An application to the two dimensional mixing layer is briefly described. The contour dynamics method is also discussed. The simulation of three dimensional flows with vortex methods is discussed. A natural way to represent the vorticity is in the form of closed tubes of filaments of vorticity, although other schemes are examined. Applications to aircraft trailing vortices and to a turbulent spot in a laminar boundary layer are presented. Hybrid schemes that use an Eulerian mesh to solve the Poisson equation for the velocity field are discussed. The goal of these schemes is to avoid the high cost of the Biot-Savart integration if many vortex elements are used while enjoying most of the advantages of pure Lagrangian schemes.

Leonard, A.↗

NASA NTRS1981

On the relationship between engineering properties and delamination of composite laminates

The influence of the coefficient of mutal influence, Poisson's ratio and coefficients of thermal and moisture expansion on delamination is studied. Engineering theories are compared to finite element and experimental results. It is shown that the mismatch in coefficients of mutual influence can have a strong influence on delamination with fiber angles in the 10-15 degree range being critical for adjacent layer combinations. The mismatch in coefficient of mutual influence is reduced by a factor of two and the interlaminar shear stress is reduced significantly when the + or - adjacent layers are interspersed between 0 and 90 degree layers. It is shown how the results can be used for design of composite laminates.

Herakovich, C. T.↗

NASA NTRS1981

Room temperature shear properties of the strain isolator pad for the shuttle thermal protection system

Tests were conducted at room temperature to determine the shear properties of the strain isolator pad (SIP) material used in the thermal protection system of the space shuttle. Tests were conducted on both the .23 cm and .41 cm thick SIP material in the virgin state and after fifty fully reversed shear cycles. The shear stress displacement relationships are highly nonlinear, exhibit large hysteresis effects, are dependent on material orientation, and have a large low modulus region near the zero stress level where small changes in stress can result in large displacements. The values at the higher stress levels generally increase with normal and shear force load conditioning. Normal forces applied during the shear tests reduces the low modulus region for the material. Shear test techniques which restrict the normal movement of the material give erroneous stress displacement results. However, small normal forces do not significantly effect the shear modulus for a given shear stress. Poisson's ratio values for the material are within the range of values for many common materials. The values are not constant but vary as a function of the stress level and the previous stress history of the material. Ultimate shear strengths of the .23 cm thick SIP are significantly higher than those obtained for the .41 cm thick SIP.

Sawyer, J. W.↗

NASA NTRS1979

A study of trends and techniques for space base electronics

The use of dry processing and alternate dielectrics for processing wafers is reported. A two dimensional modeling program was written for the simulation of short channel MOSFETs with nonuniform substrate doping. A key simplifying assumption used is that the majority carriers can be represented by a sheet charge at the silicon dioxide-silicon interface. In solving current continuity equation, the program does not converge. However, solving the two dimensional Poisson equation for the potential distribution was achieved. The status of other 2D MOSFET simulation programs are summarized.

Trotter, J. D.↗

NASA NTRS1979

Trends and Techniques for Space Base Electronics

Simulations of various phosphorus and boron diffusions in SOS were completed and a sputtering system, furnaces, and photolithography related equipment were set up. Double layer metal experiments initially utilized wet chemistry techniques. By incorporating ultrasonic etching of the vias, premetal cleaning a modified buffered HF, phosphorus doped vapox, and extended sintering, yields of 98% were obtained using the standard test pattern. A two dimensional modeling program was written for simulating short channel MOSFETs with nonuniform substrate doping. A key simplifying assumption used is that the majority carriers can be represented by a sheet charge at the silicon dioxide silicon interface. Although the program is incomplete, the two dimensional Poisson equation for the potential distribution was achieved. The status of other Z-D MOSFET simulation programs is summarized.

Trotter, J. D.↗

NASA NTRS1981

Rapid, high-order accurate calculation of flows due to free source or vortex distributions

Fast Fourier transform (FFT) techniques are applied to the problem of finding the flow due to source or vortex distributions in the field outside an airfoil or other two-dimensional body. Either the complex potential or the complex velocity may be obtained to a high order of accuracy, with computational effort similar to that required by second-order fast Poisson solvers. These techniques are applicable to general flow problems with compressibility and rotation. An example is given of their use for inviscid compressible flow.

Halsey, D.↗

NASA NTRS1981

Rigorous numerical treatment of the no-slip condition in a vorticity formulation

It is shown that a rigorous mathematical treatment of the boundary conditions for rigid no-slip surfaces requires, in general, that two passes be made in solving Poisson's equation. A Fourier solution procedure was the key to this realization. It is also shown that a corresponding method exists for finite and, for the same local approximation, the usual one step method gives the same result for the geometry considered here. The more fundamental two step method gives a new insight into the physical significance of boundary vorticity.

Gazdag, J.↗

NASA NTRS1980

Some features of inverted-V events as seen from simulated double layers

Results from a numerical simulation of a double layer show some features similar to those of inverted-V events. The strong heating of thermal and precipitating electrons is observed along with extremely low frequency fluctuations found during inverted-V events. It is suggested that after the acceleration of auroral electrons by the double layer, the precipitating free electrons are heated by the nonlinear effects of the electron beam plasma instability. Fluctuations and pulsations of auroral electron fluxes during auroral events are caused by a relaxation type of oscillation. The finite extent of one dimensional plasma is simulated by solving the Vlasov and Poisson equations as an initial and boundary value problem.

Singh, N.↗

NASA NTRS1981

Simulation of three-dimensional incompressible flows with a vortex-in-cell method

A new method for the numerical simulation of three-dimensional incompressible flows is described. The vortex-in-cell (VIC) method presented traces the motion of the vortex filaments in the velocity field which these filaments create. The velocity field is not calculated directly by the Biot-Savart law of interaction but by creating a mesh-record of the vorticity field, then integrating a Poisson's equation via the fast Fourier transform to generate a mesh-record of the velocity field. The computed scales of motion are assumed to be essentially inviscid. Viscous of subgrid-scale effects are incorporated into a filtering procedure in wave vector space. Results of tracing a periodic array of single vortex rings are compared with a Green's function calculation. The agreement is very good.

Couet, B.↗

NASA NTRS1981

Three-dimensional structures and turbulence closure of the wake developing in a wall shear layer

The turbulent wake interacting with the rotating wall shear layer is investigated analytically and numerically. The turbulent wakes of the rotating blades in a compressor which are interacting with the rotating hub-wall boundary layer are analyzed. A modified version of the closure model of the pressure-strain correlation term in the Reynolds stress transport equation is developed to predict the effect of rotation, which is appreciable for the present flow because the thick hub-wall boundary layer is interacting with the rotor wake. It is noted that the Poisson type equation for the pressure-strain correlation has an extra rotation term when the entire flow field is rotating. This extra rotation term is modeled to accommodate the effect of rotation. In addition, the standard correction for the wall effect is incorporated for the utilized Reynolds stress closure model. The rotation-modified Reynolds stress closure model is used to predict the present flow, and the predictions are compared with the experimental data. The experimental data reveal that the characteristics of the three-dimensional turbulent wake interacting with the wall shear layer are considerably altered by the effects of the wall and the rotation. These features are predicted with good accuracy by the turbulence closure model developed.

Hah, C.↗

NASA NTRS1981

Role of the doubly stochastic Neyman type-A and Thomas counting distributions in photon detection

The sums of Meyman type-A and Thomas random variables are shown to retain their form under the constant multiplication parameter constraint. The conditions under which the two random variables converge in distribution to the fixed multiplicative Poisson, and to the Gaussian, are presented. It is shown that the latter result is important, in that it provides a solution to likelihood-ratio detection, estimation and discrimination problems in the presence of many kinds of signal and noise. Among the explicit applications presented are: (1) the photon-counter scintillation detection of nuclear particles when particle flux is low, (2) the photon-counting detection of weak optical signals in the presence of ionizing radiation, and (3) the design of a star-scanner spacecraft guidance system adequate for hostile space environments.

Teich, M. C.↗

NASA NTRS1981

A new global operator for two-particle delta functions

A new type of global operator to be used in evaluating matrix elements of two-particle delta functions is introduced. It is based, like the Trivedi one-particle operator, on the Poisson equation and is easier to apply than the method of Hiller, Sucher and Feinberg. After a test in the helium isoelectronic sequence, the new method is applied successfully to the interesting problem of hyperfine structure in muonic helium.

Drachman, R. J.↗

NASA NTRS1981

An evaluation of the sandwich beam compression test method for composites

The sandwich beam in a four-point bending compressive test method for advanced composites is evaluated. Young's modulus and Poisson's ratio were obtained for graphite/polyimide beam specimens tested at 117 K, room temperature, and 589 K. Tensile elastic properties obtained from the specimens were assumed to be equal to the compressive elastic properties and were used in the analysis. Strain gages were used to record strain data. A three-dimensional finite-element model was used to examine the effects of the honeycomb core on measured composite mechanical properties. Results of the analysis led to the following conclusions: (1) a near uniaxial compressive stress state existed in the top cover and essentially all the compressive load was carried by the top cover; (2) laminate orientation, test temperature, and type of honeycomb core material were shown to affect the type of beam failure; and (3) the test method can be used to obtain compressive elastic constants over the temperature range 117 to 589 K.

Shuart, M. J.↗