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At least 523 records · Page 29

Calculating Viscous/Inviscid Interactions

Report describes some experiences in numerical simulation of compressible, viscous flows by finite-difference approximations of Navier-Stokes equations. Focuses upon viscous/inviscid-interaction approach, in which flow mathematically modeled with interacting zones, within each of which different model of viscous or inviscid flow applies. Reduces task of computation by taking advantage of simpler models and coarser grids in some of zones.

Van Dalsem, W. R.↗

Diffusion Of Mass In Evaporating Multicomponent Drops

Report summarizes study of diffusion of mass and related phenomena occurring in evaporation of dense and dilute clusters of drops of multicomponent liquids intended to represent fuels as oil, kerosene, and gasoline. Cluster represented by simplified mathematical model, including global conservation equations for entire cluster and conditions on boundary between cluster and ambient gas. Differential equations of model integrated numerically. One of series of reports by same authors discussing evaporation and combustion of sprayed liquid fuels.

Bellan, Josette↗

Modeling the Restraint of Liquid Jets by Surface Tension in Microgravity

An axisymmetric phase field model is developed and used to model surface tension forces on liquid jets in microgravity. The previous work in this area is reviewed and a baseline drop tower experiment selected 'for model comparison. A mathematical model is developed which includes a free surface. a symmetric centerline and wall boundaries with given contact angles. The model is solved numerically with a compact fourth order stencil on a equally spaced axisymmetric grid. After grid convergence studies, a grid is selected and all drop tower tests modeled. Agreement was assessed by comparing predicted and measured free surface rise. Trend wise agreement is good but agreement in magnitude is only fair. Suspected sources of disagreement are suspected to be lack of a turbulence model and the existence of slosh baffles in the experiment which were not included in the model.

Chato, David J.↗

Ice Sheet Change Detection by Satellite Image Differencing

Differencing of digital satellite image pairs highlights subtle changes in near-identical scenes of Earth surfaces. Using the mathematical relationships relevant to photoclinometry, we examine the effectiveness of this method for the study of localized ice sheet surface topography changes using numerical experiments. We then test these results by differencing images of several regions in West Antarctica, including some where changes have previously been identified in altimeter profiles. The technique works well with coregistered images having low noise, high radiometric sensitivity, and near-identical solar illumination geometry. Clouds and frosts detract from resolving surface features. The ETM(plus) sensor on Landsat-7, ALI sensor on EO-1, and MODIS sensor on the Aqua and Terra satellite platforms all have potential for detecting localized topographic changes such as shifting dunes, surface inflation and deflation features associated with sub-glacial lake fill-drain events, or grounding line changes. Availability and frequency of MODIS images favor this sensor for wide application, and using it, we demonstrate both qualitative identification of changes in topography and quantitative mapping of slope and elevation changes.

Bindschadler, Robert A.↗

Theory, Modeling, Software and Hardware Development for Analytical and Computational Materials Science

The focus of this Cooperative Agreement between the Computational Materials Laboratory (CML) of the Processing Science and Technology Branch of the NASA Glenn Research Center (GRC) and the Department of Theoretical and Applied Mathematics at The University of Akron was in the areas of system development of the CML workstation environment, modeling of microgravity and earth-based material processing systems, and joint activities in laboratory projects. These efforts complement each other as the majority of the modeling work involves numerical computations to support laboratory investigations. Coordination and interaction between the modelers, system analysts, and laboratory personnel are essential toward providing the most effective simulations and communication of the simulation results. Toward these means, The University of Akron personnel involved in the agreement worked at the Applied Mathematics Research Laboratory (AMRL) in the Department of Theoretical and Applied Mathematics while maintaining a close relationship with the personnel of the Computational Materials Laboratory at GRC. Network communication between both sites has been established. A summary of the projects we undertook during the time period 9/1/03 - 6/30/04 is included.

Young, Gerald W.↗

The solution of coupled Schroedinger equations using an extrapolation method

In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.

Goorvitch, D.↗

Study of high-g effects in animals

General aspects of animal centrifugation are examined. It is shown that once a covariance is established and the nature of the kinetics is determined it is possible to calculate a regression of the biological change (with suitable numerical transforms of the data) upon field strength. This should yield a rather simple equation containing two arbitrary constants: a, the zero intercept (a mathematical prediction of the magnitude of the parameter y, when G = 0); and b, the proportionality coefficient, the change in the parameter y per unit change in G: Y = a + bG.

Smith, A. H.↗

A three dimensional calculation of elastic equilibrium for composite materials

A compact scheme is applied to three-dimensional elasticity problems for composite materials, involving simple geometries. The mathematical aspects of this approach are discussed, in particular the iteration method. A vector processor code implementing the compact scheme is presented, and several numerical experiments are summarized.

Lustman, Liviu R.↗

Local intermodal energy transfer of the secondary instability in a plane channel

A mathematical technique for analyzing local energy-transfer rates among wave-vector triads is developed and applied to the data generated by direct numerical simulations of waves with various types of initial conditions. Starting the simulation with a primary two-dimensional wave and random noise produced structures very similar to those which evolved from three-dimensional center modes. The local transfer rates determined in this case help to explain the eventual deformation of the primary two-dimensional wave which was observed in wind-tunnel experiments. Including weak streamwise vortices in the initial flow field results in large amounts of energy being transferred to the K-type modes early in the simulation. The later development of the waves (and hence the energy-transfer rates) is similar to the previous case.

Singer, Bart A.↗

A three dimensional calculation of elastic equilibrium for composite materials

A compact scheme is applied to three-dimensional elasticity problems for composite materials, involving simple geometries. The mathematical aspects of this approach are discussed, in particular the iteration method. A vector processor code implementing the compact scheme is presented, and several numerical experiments are summarized.

Lustman, Liviu R.↗

High-order state space simulation models of helicopter flight mechanics

This paper describes the formulation and validation of a high-order linearized mathematical model of helicopter flight mechanics, which includes rotor flap and lag degrees of freedom as well as inflow dynamics. The model is extracted numerically from an existing nonlinear, blade element, time simulation model. Extensive modifications in the formulation and solution process of the nonlinear model, required for a theoretically rigorous linearization, are described in detail. The validation results show that the linearized model successfully captures the coupled rotor-fuselage dynamics in the frequency band most critical for the design of advanced flight control systems. Additional results quantify the extent to which the order of the model can be reduced without loss of fidelity.

Kim, Frederick D.↗

High-order state space simulation models of helicopter flight mechanics

This paper describes the formulation and validation of a high-order linearized mathematical model of helicopter flight mechanics, which includes rotor flap and lag degrees of freedom as well as inflow dynamics. The model is extracted numerically from an existing nonlinear, blade element, real-time simulation model. Extensive modifications in the formulation and solution process of the nonlinear model, required for a theoetically rigorous linearization, are described in detail. The validation results show that the linearized model successfully captures the coupled rotor-fuselage dynamics in the frequency band most critical for the design of advanced flight control systems. Additional results quantify the extent to which the order of the model can be reduced without loss of fidelity.

Kim, Frederick D.↗

Space proton transport in one dimension

An approximate evaluation procedure is derived for a second-order theory of coupled nucleon transport in one dimension. An analytical solution with a simplified interaction model is used to determine quadrature parameters to minimize truncation error. Effects of the improved method on transport solutions with the BRYNTRN data base are evaluated. Comparisons with Monte Carlo benchmarks are given. Using different shield materials, the computational procedure is used to study the physics of space protons. A transition effect occurs in tissue near the shield interface and is most important in shields of high atomic number.

NASA Discipline Number 45-10↗

Constructing the 'Best' Reliability Data for the Job - Developing Generic Reliability Data from Alternative Sources Early in a Product's Development Phase

Reliability practitioners advocate getting reliability involved early in a product development process. However, when assigned to estimate or assess the (potential) reliability of a product or system early in the design and development phase, they are faced with lack of reasonable models or methods for useful reliability estimation. Developing specific data is costly and time consuming. Instead, analysts rely on available data to assess reliability. Finding data relevant to the specific use and environment for any project is difficult, if not impossible. Instead, analysts attempt to develop the "best" or composite analog data to support the assessments. Industries, consortia and vendors across many areas have spent decades collecting, analyzing and tabulating fielded item and component reliability performance in terms of observed failures and operational use. This data resource provides a huge compendium of information for potential use, but can also be compartmented by industry, difficult to find out about, access, or manipulate. One method used incorporates processes for reviewing these existing data sources and identifying the available information based on similar equipment, then using that generic data to derive an analog composite. Dissimilarities in equipment descriptions, environment of intended use, quality and even failure modes impact the "best" data incorporated in an analog composite. Once developed, this composite analog data provides a "better" representation of the reliability of the equipment or component. It can be used to support early risk or reliability trade studies, or analytical models to establish the predicted reliability data points. It also establishes a baseline prior that may updated based on test data or observed operational constraints and failures, i.e., using Bayesian techniques. This tutorial presents a descriptive compilation of historical data sources across numerous industries and disciplines, along with examples of contents and data characteristics. It then presents methods for combining failure information from different sources and mathematical use of this data in early reliability estimation and analyses.

Kleinhammer, Roger K.↗

An economical method of analyzing transient motion of gas-lubricated rotor-bearing systems.

A method of economically evaluating the hydrodynamic forces generated in a gas-lubricated tilting-pad bearing is presented. The numerical method consists of solving the case of the infinite width bearing and then converting this solution to the case of the finite bearing by accounting for end leakage. The approximate method is compared to the finite-difference solution of Reynolds equation and yields acceptable accuracy while running about one-hundred times faster. A mathematical model of a gas-lubricated tilting-pad vertical rotor systems is developed. The model is capable of analyzing a two-bearing-rotor system in which the rotor center of mass is not at midspan by accounting for gyroscopic moments. The numerical results from the model are compared to actual test data as well as analytical results of other investigators.

Falkenhagen, G. L.↗

Analysis of Radiation-natural Convection Interactions in 1-g and low-g Environments using the Discrete Exchange Factor Method

A new numerical method is presented for the analysis of combined natural convection and radiation heat transfer with applications in many engineering situations such as materials processing, combustion and fire research. Because of the recent interest in the low gravity environment of space, attention is devoted to both 1-g and low-g applications. The two-dimensional mathematical model is represented by a set of coupled nonlinear integro-partial differential equations. Radiative exchange is formulated using the Discrete Exchange Factor method (DEF). This method considers point to point exchange and provides accurate results over a wide range of radiation parameters. Numerical results show that radiation significantly influences the flow and heat transfer in both low-g and 1-g applications. In the low-g environment, convection is weak, and radiation can easily become the dominant heat transfer mode. It is also shown that volumetric heating by radiation gives rise to an intricate cell pattern in the top heated enclosure.

Kassemi, M.↗

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗

Modeling techniques of thin walled beams with open cross sections

A composite element is presented which includes the effects of warping and offset shear centers. It is shown to be mathematically consistent with thin walled open beam theory and can be incorporated into any structural analysis program by use of NASTRAN'S standard elements. A numerical example analyzing the vibration of a channel beam is presented, and, by using the composite element, the numerical results agreed well with theoretical data.

Skattum, K. S.↗