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NASA NTRS1995

Dynamic sensitivity analysis of frictional contact/impact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic frictional contact/impact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response to variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the nodal displacements, and the Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. Temporal integration is performed by using Newmark method. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented from the frictional contact/impact response of a composite spherical cap impacting on a rigid plate.

Karaoglan, Levent↗

NASA NTRS1994

Estimation and classification by sigmoids based on mutual information

An estimate of the probability density function of a random vector is obtained by maximizing the mutual information between the input and the output of a feedforward network of sigmoidal units with respect to the input weights. Classification problems can be solved by selecting the class associated with the maximal estimated density. Newton's s method, applied to an estimated density, yields a recursive maximum likelihood estimator, consisting of a single internal layer of sigmoids, for a random variable or a random sequence. Applications to the diamond classification and to the prediction of a sun-spot process are demonstrated.

Baram, Yoram↗

NASA NTRS1995

Development of a two-equation turbulence model for hypersonic flows: Evaluation of a low Reynolds number correction to the Kappa - epsilon two equation compressible turbulence model - Volume 1

The objective of the current research is the development of an improved k-epsilon two-equation compressible turbulence model for turbulent boundary layer flows experiencing strong viscous-inviscid interactions. The development of an improved model is important in the design of hypersonic vehicles such as the National Aerospace Plane (NASP) and the High Speed Civil Transport (HSCT). Improvements have been made to the low Reynolds number functions in the eddy viscosity and dissipation of solenoidal dissipation of the k-epsilon turbulence mode. These corrections offer easily applicable modifications that may be utilized for more complex geometries. The low Reynolds number corrections are functions of the turbulent Reynolds number and are therefore independent of the coordinate system. The proposed model offers advantages over some current models which are based upon the physical distance from the wall, that modify the constants of the standard model, or that make more corrections than are necessary to the governing equations. The code has been developed to solve the Favre averaged, boundary layer equations for mass, momentum, energy, turbulence kinetic energy, and dissipation of solenoidal dissipation using Keller's box scheme and the Newton spatial marching method. The code has been validated by removing the turbulent terms and comparing the solution with the Blasius solution, and by comparing the turbulent solution with an existing k-epsilon model code using wall function boundary conditions. Excellent agreement is seen between the computed solution and the Blasius solution, and between the two codes. The model has been tested for both subsonic and supersonic flat-plate turbulent boundary layer flow by comparing the computed skin friction with the Van Driest II theory and the experimental data of Weighardt; by comparing the transformed velocity profile with the data of Weighardt, and the Law of the Wall and the Law of the Wake; and by comparing the computed results of an adverse pressure gradient with the experimental data of Fernando and Smits. Good agreement is obtained with the experimental correlations for all flow conditions.

Knight, Doyle D.↗

NASA NTRS1999

NPARC v3.1 User's Guide: A Companion to the NPARC v3.0 User's Guide

NPARC v3.1 is a modification to the NPARC v3.0 computer program which expands the capabilities for time-accurate computations through the use of a Newton iterative implicit method, time-varying boundary conditions, and planar dynamic grids. This document discusses some of the changes from the NPARC v3.0, specifically: changes to the directory structure and execution, changes to the input format. background on new methods, new boundary conditions. dynamic grids, new options for output, usage concepts, and some test cases to serve as tutorials. This document is intended to be used in conjunction with the NPARC v3.0 user's guide.

Chung, Joongkee↗

NASA NTRS1995

Optimization of Time-Dependent Particle Tracing Using Tetrahedral Decomposition

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation and step-size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations or expensive matrix inversions. Integration accuracy is maintained using an adaptive step-size control scheme which is regulated by the path line curvature. The problem of cell-searching, point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells yet produces almost identical particle trajectories.

Kenwright, David↗

NASA NTRS2000

Computer Modeling of the Earliest Cellular Structures and Functions

In the absence of extinct or extant record of protocells (the earliest ancestors of contemporary cells). the most direct way to test our understanding of the origin of cellular life is to construct laboratory models of protocells. Such efforts are currently underway in the NASA Astrobiology Program. They are accompanied by computational studies aimed at explaining self-organization of simple molecules into ordered structures and developing designs for molecules that perform proto-cellular functions. Many of these functions, such as import of nutrients, capture and storage of energy. and response to changes in the environment are carried out by proteins bound to membrane< We will discuss a series of large-scale, molecular-level computer simulations which demonstrate (a) how small proteins (peptides) organize themselves into ordered structures at water-membrane interfaces and insert into membranes, (b) how these peptides aggregate to form membrane-spanning structures (eg. channels), and (c) by what mechanisms such aggregates perform essential proto-cellular functions, such as proton transport of protons across cell walls, a key step in cellular bioenergetics. The simulations were performed using the molecular dynamics method, in which Newton's equations of motion for each item in the system are solved iteratively. The problems of interest required simulations on multi-nanosecond time scales, which corresponded to 10(exp 6)-10(exp 8) time steps.

Pohorille, Andrew↗

NASA NTRSDate not supplied

Variational Asymptotic Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites

The objective of this paper is to develop a constitutive model for finitely deformed viscoelastic-viscoplastic materials and a micromechanics approach to homogenizing composites consisting of such materials. The development of the constitutive model involves establishing a thermodynamic framework based on finite strain theory, developing a viscoelasticity and a viscoplasticity model based on the thermodynamic framework, developing a radial return algorithm based on a classic framework, and deriving a closed-from incremental constitutive relation in the spatial configuration. The development of the micromechanics approach involves pulling-back the above constitutive relation to the material configuration, formulating a variational statement with the resulting constitutive relation, discretizing variational statement in a finite-dimensional space, and solving the discretized variational statement using an Euler–Newton predictor–corrector method. The constitutive model is calibrated via monotonic uniaxial compression tests on a polymer, and the calibrated model is validated by comparing its predictions with the cyclic test data. It is shown capable of characterizing viscoelasticity, viscoplasticity, and complex loading paths. The micromechanics approach’s capabilities are demonstrated through homogenizing a unidirectional fiber-reinforced composite, subjected to uniaxial, biaxial, and shear loading, at different strain rates. It is demonstrated to be capable of handling rate dependence and complex loading paths. The present framework can be further improved by implementing more sophisticated viscoelasticity and viscoplasticity models in future work.

Finite element analysis↗

NASA NTRS1987

Spatially random models, estimation theory, and robot arm dynamics

Spatially random models provide an alternative to the more traditional deterministic models used to describe robot arm dynamics. These alternative models can be used to establish a relationship between the methodologies of estimation theory and robot dynamics. A new class of algorithms for many of the fundamental robotics problems of inverse and forward dynamics, inverse kinematics, etc. can be developed that use computations typical in estimation theory. The algorithms make extensive use of the difference equations of Kalman filtering and Bryson-Frazier smoothing to conduct spatial recursions. The spatially random models are very easy to describe and are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. The models can also be used to generate numerically the composite multibody system inertia matrix. This is done without resorting to the more common methods of deterministic modeling involving Lagrangian dynamics, Newton-Euler equations, etc. These methods make substantial use of human knowledge in derivation and minipulation of equations of motion for complex mechanical systems.

Rodriguez, G.↗

NASA NTRS1998

A Generalized Fluid System Simulation Program to Model Flow Distribution in Fluid Networks

This paper describes a general purpose computer program for analyzing steady state and transient flow in a complex network. The program is capable of modeling phase changes, compressibility, mixture thermodynamics and external body forces such as gravity and centrifugal. The program's preprocessor allows the user to interactively develop a fluid network simulation consisting of nodes and branches. Mass, energy and specie conservation equations are solved at the nodes; the momentum conservation equations are solved in the branches. The program contains subroutines for computing "real fluid" thermodynamic and thermophysical properties for 33 fluids. The fluids are: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride and ammonia. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. Seventeen different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include: pipe flow, flow through a restriction, non-circular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, and a Joule-Thompson device. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. This paper also illustrates the application and verification of the code by comparison with Hardy Cross method for steady state flow and analytical solution for unsteady flow.

Majumdar, Alok↗

NASA NTRS2004

Generalized Fluid System Simulation Program

A general purpose program implemented on a computer analyzes steady state and transient flow in a complex fluid network, modeling phase changes, compressibility, mixture thermodynamics and external body forces such as gravity and centrifugal force. A preprocessor provides for the inter- active development of a fluid network simulation having nodes and branches. Mass, energy, and specie conservation equations are solved at the nodes, and momentum conservation equations are solved in the branches. Contained herein are subroutines for computing "real fluid" thermodynamic and thermophysical properties for 12 fluids, and a number of different source options are provided for model- ing momentum sources or sinks in the branches. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. Application and verification of this invention are provided through an example problem, which demonstrates that the predictions of the present invention compare most reasonably with test data.

Alok Kumar Majumdar↗

NASA NTRS2005

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

Majumdar, Alok↗

NASA NTRS2009

Method and Apparatus for Predicting Unsteady Pressure and Flow Rate Distribution in a Fluid Network

A method and apparatus for analyzing steady state and transient flow in a complex fluid network, modeling phase changes, compressibility, mixture thermodynamics, external body forces such as gravity and centrifugal force and conjugate heat transfer. In some embodiments, a graphical user interface provides for the interactive development of a fluid network simulation having nodes and branches. In some embodiments, mass, energy, and specific conservation equations are solved at the nodes, and momentum conservation equations are solved in the branches. In some embodiments, contained herein are data objects for computing thermodynamic and thermophysical properties for fluids. In some embodiments, the systems of equations describing the fluid network are solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods.

Majumdar, Alok K.↗

NASA NTRS2016

Generalized Fluid System Simulation Program, Version 6.0

The Generalized Fluid System Simulation Program (GFSSP) is a general purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors, and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. Two thermodynamic property programs (GASP/WASP and GASPAK) provide required thermodynamic and thermophysical properties for 36 fluids: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutene, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride, ammonia, hydrogen peroxide, and air. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. The users can also supply property tables for fluids that are not in the library. Twenty-four different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include pipe flow, flow through a restriction, noncircular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, Joule-Thompson device, control valve, heat exchanger core, parallel tube, and compressible orifice. The program has the provision of including additional resistance options through User Subroutines. GFSSP employs a finite volume formulation of mass, momentum, and energy conservation equations in conjunction with the thermodynamic equations of state for real fluids as well as energy conservation equations for the solid. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. The application and verification of the code has been demonstrated through 30 example problems.

Majumdar, A. K.↗

NASA NTRS2019

A Finite Volume Procedure for Thermo-Fluid System Analysis in a Flow Network

This paper describes a finite volume procedure for network flow analysis in a thermofluid system. A flow network is defined as a group of inter-connected control volumes called “nodes” that are connected by “branches”. The mass and energy conservation equations are solved at the nodes and momentum conservation equations are solved at the branches. The flow network also includes solid nodes to account for fluid to solid heat transfer. The heat conduction equation is solved at the solid nodes in conjunction with the flow equations. The properties of a real fluid are calculated using a thermodynamic property program and used in the conservation equations. The system of equations describing the fluid-solid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution method. This procedure has been incorporated into a general-purpose computer program, the Generalized Fluid System Simulation Program, GFSSP. This paper also presents the application and verification of the method by comparison with test data for several applications that include (a) internal flow in a rocket engine turbo-pump, (b) pressurization and loading of a cryogenic propellant tank, (c) fluid transient during sudden opening of valve for priming of an evacuated feed line, and (d) chill down of a cryogenic transfer line with phase change and two phase flows.

Majumdar, Alok↗

NASA NTRS2002

P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems

The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning

Kang, Kab S.↗

NASA NTRS2014

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Mazaheri, Alireza R.↗

NASA NTRS2017

Quasi-Periodic Pulse Amplitude Modulation in the Accreting Millisecond Pulsar IGR J00291+5934

We introduce a new method for analyzing the a periodic variability of coherent pulsations in accreting millisecond X-ray pulsars (AMXPs). Our method involves applying a complex frequency correction to the time-domain lightcurve, allowing for the aperiodic modulation of the pulse amplitude to be robustly extracted in the frequency domain. We discuss the statistical properties of the resulting modulation spectrum and show how it can be correlated with the non-pulsed emission to determine if the periodic and a periodic variability are coupled processes. Using this method, we study the 598.88 Hz coherent pulsations of the AMXP IGR J00291+5934 as observed with the Rossi X-ray Timing Explorer and XMM-Newton. We demonstrate that our method easily confirms the known coupling between the pulsations and a strong 8 mHz quasi-periodic oscillation (QPO) in XMM-Newton observations. Applying our method to the RXTE observations, we further show, for the first time, that the much weaker 20 mHz QPO and its harmonic are also coupled with the pulsations. We discuss the implications of this coupling and indicate how it may be used to extract new information on the underlying accretion process.

stars↗

NASA NTRS1975

An algorithm and computer program to locate real zeros of real polynomials

A method for reliably extracting real zeros of real polynomials using an expanded two-point secant and bisection method is formed into an algorithm for a digital computer, and a computer program based on this algorithm is presented. The results obtained with the program show that the proposed method compares favorably with the Laguerre, Newton-Raphson, and Jenkins-Traub methods when the polynomial has all real zeros, and is more efficient when the polynomial has complex zeros.

Hedgley, D. R., Jr.↗