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NASA NTRS1982

Computer simulations of optimum boost and buck-boost converters

The development of mathematicl models suitable for minimum weight boost and buck-boost converter designs are presented. The facility of an augumented Lagrangian (ALAG) multiplier-based nonlinear programming technique is demonstrated for minimum weight design optimizations of boost and buck-boost power converters. ALAG-based computer simulation results for those two minimum weight designs are discussed. Certain important features of ALAG are presented in the framework of a comprehensive design example for boost and buck-boost power converter design optimization. The study provides refreshing design insight of power converters and presents such information as weight annd loss profiles of various semiconductor components and magnetics as a function of the switching frequency.

Rahman, S.↗

NASA NTRS1982

A numerical simulation of the magnetospheric gate model for the X-ray bursters

A Lagrangian, stellar interior computer code which assumes radiation transport by diffusion is used to numerically simulate an X-ray burst occurring on a rapidly rotating, 1 solar mass neutron star accreting material from a companion in noncontinuous, episodic fashion. The blob of gas from the companion extends from the surface of the neutron star to a radius of 185 km, is optically thick, has mass of 10 to the -11th solar masses, and is initially at rest with respect to the surface. The gas initially has a temperature of about 10 million K and a surface luminosity of 0.1 that of the sun. The infall results in a burst which lasts about 0.1 second and reaches a peak luminosity and effective temperature of 240,000 suns and nine million K. The burst is followed by a phase of oscillations with a period of 0.2 second. It is found that the burst is too cool and rapid to resemble normal bursts, although the time scale is in agreement with some observations.

Starrfield, S.↗

NASA NTRS1982

Thermonuclear runaways in thick hydrogen rich envelopes of neutron stars

A Lagrangian, fully implicit, one-dimensional hydrodynamic computer code is used to evolve thermonuclear runaways in the accreted hydrogen-rich envelopes of 1.0-solar-mass neutron stars with radii of 10 km and 20 km. The simulations produce outbursts lasting from approximately 750 seconds to approximately one week. The peak effective temperatures and luminosities are 2.6 x 10 to the 7th K and 8 x 10 to the 4th solar luminosities for the 10 km study and 5.3 x 10 to the 6th K and 600 solar luminosities for the 20 km study. It is found that hydrodynamic expansion on the 10 km neutron star produced a precursor lasting approximately 0.0001 second. The study assumes that the bursters and transient X-ray sources occur as a result of mass transfer from a secondary onto a neutron star in a fashion analogous to the nova phenomena. The peak temperatures and luminosities are found to be inversely proportional to the radius of the neutron stars and the calculations here, together with those in the literature, indicate that the actual radii of most neutron stars must be closer to 10 km than 20 km.

Starrfield, S.↗

NASA NTRS1981

Simplified robot arm dynamics for control

A brief summary and evaluation is presented on the use of symbolic state equation techniques in order to represent robot arm dynamics with sufficient accuracy for controlling arm motion. The use of homogeneous transformations and the Lagrangian formulation of mechanics offers a convenient frame for the derivation, analysis and simplification of complex robot dynamics equations. It is pointed out that simplified state equations can represent robot arm dynamics with good accuracy.

Bejczy, A. K.↗

NASA NTRS1982

Geometrically nonlinear analysis of layered composite shells

Two kinds of finite-element analyses are developed for the geometrically nonlinear study of the large deformations in laminated composite structures, especially shells. The first kind of finite-element analysis utilizes the general incremental variational formulation as well as the total Lagrangian description of motion, and a three-dimensional degenerate element is adopted. The second kind of analysis employs a formulation based on deformable shell theory, and the plate-bending element is used. Numerical results for bending are presented for five plate and shell structures of isotropic as well as orthotropic composition, including an isotropic cylindrical panel with uniform loading and a laminated cylindrical panel with uniform loading. The results obtained using these analyses are found to be in good agreement with those available in the literature.

Chao, W. C.↗

NASA NTRS1983

Structural optimization - Challenges and opportunities

A review of developments in structural optimization techniques and their interface with growing computer capabilities is presented. Structural design steps comprise functional definition of an object, an evaluation phase wherein external influences are quantified, selection of the design concept, material, object geometry, and the internal layout, and quantification of the physical characteristics. Optimization of a fully stressed design is facilitated by use of nonlinear mathematical programming which permits automated definition of the physics of a problem. Design iterations terminate when convergence is acquired between mathematical and physical criteria. A constrained minimum algorithm has been formulated using an Augmented Lagrangian approach and a generalized reduced gradient to obtain fast convergence. Various approximation techniques are mentioned. The synergistic application of all the methods surveyed requires multidisciplinary teamwork during a design effort.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1983

An inviscid three-dimensional analysis of the Space Shuttle main engine hot-gas manifold

A numerical study using an inviscid three-dimensional Lagrangian fluid dynamics code has been conducted as a part of an overall effort to understand the flow behavior in the SSME fuel side hot-gas manifold. The model simulates flow from the high-pressure fuel turbine exit through the transfer ducts, including the effects of swirl, inlet flow symmetry, and presence of straightening vanes and struts; a separate, more-detailed effort is in progress that includes viscosity and turbulence effects. The simplified model presented is divided into two parts, the first includes the 180-degree turnaround duct downstream of the turbine exit and the spherical fuel bowl section, while the second models the three transfer ducts. The two parts of the model are coupled together with the interface conditions being updated through iteration. Results indicate that a transverse pressure differential of 165 psi would be imposed on the turbine exit and that unstable flow separation occurs around the vanes, struts, and within the transfer ducts. The three transfer ducts show a mass flux split of approximately 41, 21, and 38 percent. Results to date are encouraging that certain flow characteristics can be usefuly represented using a relatively coarse grid inviscid code.

Liang, P. Y.↗

NASA NTRS1983

Planetary rings - 2-2/3 centuries of nearly total ignorance, 4 years of information explosion

Saturn lies at nearly twice Jupiter's distance from the sun and nearly all parts of its system are characterized by much smaller scales than those which are important in the case of Jupiter. This appears in the structures of the planet's atmosphere, in the sizes of classical satellites other than Titan vis-a-vis those of the Galilean satellites, in the plethora of small Saturnian satellites, especially Lagrangian co-orbiters, in the structure of Saturn's F-Ring as contrasted with that of Jupiter's Ring and finally in the highly structured detail in Saturn's Rings, much finer than seriously considered in past theoretical discussions. Uranus' Rings were unknown until five years ago. The discovery and observation of these rings have revived contributions to theory originally intended for application to Saturn's Rings. Models have also been generated for eccentric rings for application to Uranus' Rings which also apply to those of Saturn. These two classes of model are reviewed in the present paper along with the first tentative steps made down the road to unravelling the complexity of Saturn's Rings.

Cook, A. F.↗

NASA NTRS1983

A simple example of a classical gauge transformation

Attention is given to the manner in which the interaction of a gravitational field with a diffusing gas is induced by a gauge transformation. Since the gas can be thought of as a field, the diffusion process may be represented by a Lagrangian density with the symmetry property of invariance under translation. While this property is lost when the field interacts with a static gravitational field, it is formally restored when an appropriate gauge transformation is performed. This ascription of field properties to a gas offers an illuminating illustration of the coupling of matter to a gauge field within the context of classical mechanics.

Whitten, R. C.↗

NASA NTRS1983

Effect of particle presence on the incompressible inviscid flow through a two dimensional compressor cascade

A computational model for calculating the flow field, in the presence of solid particles, through a two dimensional compressor cascade is presented. The method treats the particle phase in the Lagrangian system and the fluid phase in the Eulerian system. The equations of momentum of the fluid phase are modified to account for the momentum exchange between the two phases. The resulting modified momentum and continuity equations are reduced to the conventional stream function-vorticity formulation. The analysis yields the change in the blade surface pressure distribution, the total pressure and velocity in the flow field. Based on this, it is possible to predict the decrease in compressor performance under the presence of particles.

Balan, C.↗

NASA NTRS1982

Mature thunderstorm cloud top structure - Three-dimensional numerical simulation versus satellite observations

Preliminary results of four runs with a three-dimensional model of the effects of vertical wind shear on cloud top height/temperature structure and the internal properties of isolate midlatitude thunderstorms are reported. The model is being developed as an aid to analyses of GEO remote sensing satellite data. The grid is a 27 x 27 x 20 mesh with 2 km horizontal resolution and 0.9 vertical resolution. The total grid is 54 km on a side and 18 km deep. A second-order Crowley scheme for advecting momentum is extended with a third-order correction for spatial truncation error, and the earth-relative horizontal surface wind components are decreased to 50 percent of their values at 0.45 km. A temperature increase with height is included, together with an initial impulse consisting of a nonrotating cylindrical weak buoyant updraft 10 km in radius. The results of the runs are discussed in terms of the time variation of the vertical velocity extrema, the effects of strong and weak shear on a storm, the cloud top height, the Lagrangian dynamics of a thermal couplet, and data from a real storm.

Schlesinger, R. E.↗

NASA NTRS1983

Blade loss transient dynamics analysis with flexible bladed disk

The transient dynamic response of a flexible bladed disk on a flexible rotor in a two rotor system is formulated by modal synthesis and a Lagrangian approach. Only the nonequilibrated one diameter flexible mode is considered for the flexible bladed disk, while the two flexible rotors are represented by their normal modes. The flexible bladed disk motion is modeled as a combination of two one diameter standing waves, and is coupled inertially and gyroscopically to the flexible rotors. Application to a two rotor model shows that a flexible bladed disk on one rotor can be driven into resonance by an unbalance in the other rotor, and at a frequency equal to the difference in the rotor speeds.

Gallardo, V. C.↗

NASA NTRS1983

Optimal mistuning for enhanced aeroelastic stability of transonic fans

An inverse design procedure was developed for the design of a mistuned rotor. The design requirements are that the stability margin of the eigenvalues of the aeroelastic system be greater than or equal to some minimum stability margin, and that the mass added to each blade be positive. The objective was to achieve these requirements with a minimal amount of mistuning. Hence, the problem was posed as a constrained optimization problem. The constrained minimization problem was solved by the technique of mathematical programming via augmented Lagrangians. The unconstrained minimization phase of this technique was solved by the variable metric method. The bladed disk was modelled as being composed of a rigid disk mounted on a rigid shaft. Each of the blades were modelled with a single tosional degree of freedom.

Hall, K. C.↗

NASA NTRS1983

The movement of water droplets in clouds around the nose of an atmospheric research aircraft

The dynamic interaction between droplets and the airflow around the hemispherical nose of an aircraft was evaluated. The effect of the aircraft nose on droplet sampling for cloud research is explained. The proportion of different droplet sizes and their concentration at each point around the aircraft nose were determined. In a cloud, interaction between droplets is negligible. Each particle acts, for the calculation of the forces applied to it, as if it is alone in the air. The airflow carrying the droplets, on the average, is not influenced by their presence. The trajectory of each droplet was studied separately after calculating dry airflow. Concentrations were found with a Lagrangian method, using two trajectories computed directly close to one another. Theory confirms that to within 3% experimentally measured concentrations are representative of those in a cloud.

Feuillebois, P.↗

NASA NTRS1984

Structural optimization: Challenges and opportunities

Sobieszczanski-Sobieski, J.↗

NASA NTRS1983

Computation of potential flows with embedded vortex rings and applications to helicopter rotor wakes

A finite difference scheme for solving the motion of a number of vortex rings is developed. The method is an adaptation of the 'cloud-in-cell' technique to axisymmetric flows, and is thus a combined Eulerian-Lagrangian technique. A straightforward adaptation of the cloud-in-cell scheme to an axisymmetric flow field is shown to introduce a grid dependent self-induced velocity to each vortex ring. To correct this behavior the potential is considered to consist of two parts, a local and a global field. An improved difference formula is derived, allowing the accurate calculation of the potential at points near vortex locations. The local potential is then subtracted before calculating the velocity, leaving only the influences of the remaining vortices. The correct self-induced velocity is then explicitly added to the vortex velocity. Calculations of the motion of one and two vortex rings are performed, demonstrating the ability of the new method to eliminate the grid dependence of the self-induced velocity. The application of the method to the calculation of helicopter rotor flows in hover is attempted.

Roberts, T. W.↗

NASA NTRS1984

Problems with the process partitioning theory of stratocumulus entrainment

Three different approaches to partitioning were proposed. Ball (1960), Lilly (1968), and Deardorff et al. (1969, 1974) considered the sign of the net buoyancy flux at each level. If the net flux is positive, it is counted as TKE producing; otherwise, it is counted as TKE consuming. This approach can be called Eulerian partitioning. The second approach can be called process partitioning. It is assumed that the various processes acting in concert each produce and consume the same energy as if they acted independently (Manins and Turner, 1978). The total rates of TKE production and consumption are obtained by summing the effects of all the forcing processes. The third approach is Lagrangian partitioning. Each air parcel is considered as either producing or consuming TKE, according to the sign of the product of its density and vertical velocity anomalies. Stage and Businger (1981a,b) have applied process partitioning to the cloud topped mixed layer. One of the most important processes influencing entrainment into such a layer is cloud top radiative cooling. The production and consumption due to entrainment and radiative cooling are thus closely related. Model results are sensitive to the choice of formulation.

Randall, D. A.↗

NASA NTRS1984

A dynamical basis for the parameterization of organized deep convection in large-scale numerical models

A hierarchy of steady, nonlinear, semianalytic models of different types of convection were produced. These provide a theoretical framework for determining cloud outflow fluxes of both dynamic and thermodynamic quantities, which can be used to formulate dynamical transports in parameterization schemes. This was achieved by exploiting certain Lagrangian conservation properties of steady flow, from which an equation for the vertical displacement of particles can be obtained and the outflow entropy, energy and momentum fluxes and the infow/outflow mass fluxes can be determined from solution to the equation. These fluxes are determined in terms of grid scale parameters such as convective available potential energy (CAPE), cloud layer shear, and horizontal pressure gradients. Five main types of system models are identified, respectively representing archtypes of convection in zero shear, large shear, midlatitude squall lines, tropical squall lines and cellular convection. The downdraught is an important aspect in the first four of these and the cloud scale transport of momentum is very distinctive.

Moncrieff, M. W.↗