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NASA NTRS1967

A Study to Analyze the Permeation of High Density Gases and Propellant Vapors Through Single Layer Teflon or Teflon Structure Materials and Laminations

This report contains the results of a fifteen month analytical and experimental study of the leakage rate of the pressurant gases (N2, He) and the propellant vapors (N2O4,N2H4) through bladder structures consisting of two layers of Teflon separated by a metallic foil diffusion barrier containing microscopic or larger holes. Results were obtained for the steady state leakage rate through circular holes and long rectangular openings in the barrier for arbitrary thicknesses of the two Teflon layers. The effect of hole shape and relative hole position on the leakage rate were studied. The transient problem was analyzed and it was shown that steady state calculations are adequate for estimating the leakage rate. A computer program entitled "Diffusion Analyzer Program" was developed to calculate the leakage rate, both transient and steady state. Finally, the analytical results were compared to experimentally determined values of the leakage rate through a model laminated bladder structure. The results of the analysis are in good agreement with experiment. The experimental effort (Part II of the Bladder Permeation Program) measured the solubility, diffusion coefficient and permeability of helium, nitrogen and nitrogen tetroxide vapor through Teflon TFE and FEP membranes. Data were obtained in the temperature range of 25 to 100 C at pressures ranging from near vacuum to about 20 atmospheres. Results of the experimental effort were compared with the limited data previously reported. As a verification to the applicability of results to actual bladder systems, counter diffusion tests were performed with a laminated sample containing aluminum foil with a selected group of holes.

Johnson, R. L.↗

NASA NTRS1984

Finite difference solutions of heat conduction problems in multi-layered bodies with complex geometries

A numerical procedure is presented for analyzing a wide variety of heat conduction problems in multilayered bodies having complex geometry. The method is based on a finite difference solution of the heat conduction equation using a body fitted coordinate system transformation. Solution techniques are described for steady and transient problems with and without internal energy generation. Results are found to compare favorably with several well known solutions.

Masiulaniec, K. C.↗

NASA NTRS1990

An adaptive grid algorithm for one-dimensional nonlinear equations

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

Gutierrez, William E.↗

NASA NTRS1964

The study of transient heat transfer problems Quarterly progress report VI, 1 Jun. - 31 Aug. 1964

Data collection on transient heat transfer problems in calorimeter test section for intermediate range, high temperature hot gas test facility

DATA ACQUISITION↗

NASA NTRS1980

Grid evolution in time asymptotic problems

A technique for generating systems of coordinates for solving time asymptotic problems is described which provides a simple way of moving the mesh points in physical space and reduces the error in the solution relative to that obtained using a fixed mesh. First order partial differential equations are formulated for the grid point velocity in transient problems. Local flow information and boundary motion are used to determine the interior grid point motion.

Rai, M. M.↗

NASA NTRS1983

Mixed time integration schemes for transient conduction forced-convection analysis

A partition procedure for forced-convection conduction transient problems is presented. Mixed time partitions are defined wherein coupled conduction force-matrix equations are discretized using an implicit integration method, followed by derivation of a mixed time integration technique. Explicit-implicit and explicit-explicit partitions are performed for a stability analysis for transient conditions, e.g., those found in an actively air-cooled engine and airframe structure.

Liu, W. K.↗

NASA NTRS1980

Corotational velocity strain formulations for nonlinear analysis of beams and axisymmetric shells

Finite element formulations for large strain, large displacement problems are formulated using a kinematic description based on the corotational components of the velocity strain. The corotational components are defined in terms of a system that rotates with each element and approximates the rotation of the material. To account for rotations of the material relative to this element system, extra terms are introduced in the velocity strain equations. Although this formulation is incremental, in explicitly integrated transient problems it compares very well with formulations that are not.

Belytschko, T.↗

NASA NTRS1997

Modeling of Structural-Acoustic Interaction Using Coupled FE/BE Method and Control of Interior Acoustic Pressure Using Piezoelectric Actuators

A coupled finite element (FE) and boundary element (BE) approach is presented to model full coupled structural/acoustic/piezoelectric systems. The dual reciprocity boundary element method is used so that the natural frequencies and mode shapes of the coupled system can be obtained, and to extend this approach to time dependent problems. The boundary element method is applied to interior acoustic domains, and the results are very accurate when compared with limited exact solutions. Structural-acoustic problems are then analyzed with the coupled finite element/boundary element method, where the finite element method models the structural domain and the boundary element method models the acoustic domain. Results for a system consisting of an isotropic panel and a cubic cavity are in good agreement with exact solutions and experiment data. The response of a composite panel backed cavity is then obtained. The results show that the mass and stiffness of piezoelectric layers have to be considered. The coupled finite element and boundary element equations are transformed into modal coordinates, which is more convenient for transient excitation. Several transient problems are solved based on this formulation. Two control designs, a linear quadratic regulator (LQR) and a feedforward controller, are applied to reduce the acoustic pressure inside the cavity based on the equations in modal coordinates. The results indicate that both controllers can reduce the interior acoustic pressure and the plate deflection.

Mei, Chuh↗

NASA NTRS1988

Solutions to time variant problems of real-time expert systems

Real-time expert systems for monitoring and control are driven by input data which changes with time. One of the subtle problems of this field is the propagation of time variant problems from rule to rule. This propagation problem is even complicated under a multiprogramming environment where the expert system may issue test commands to the system to get data and to access time consuming devices to retrieve data for concurrent reasoning. Two approaches are used to handle the flood of input data. Snapshots can be taken to freeze the system from time to time. The expert system treats the system as a stationary one and traces changes by comparing consecutive snapshots. In the other approach, when an input is available, the rules associated with it are evaluated. For both approaches, if the premise condition of a fired rule is changed to being false, the downstream rules should be deactivated. If the status change is due to disappearance of a transient problem, actions taken by the fired downstream rules which are no longer true may need to be undone. If a downstream rule is being evaluated, it should not be fired. Three mechanisms for solving this problem are discussed: tracing, backward checking, and censor setting. In the forward tracing mechanism, when the premise conditions of a fired rule become false, the premise conditions of downstream rules which have been fired or are being evaluated due to the firing of that rule are reevaluated. A tree with its root at the rule being deactivated is traversed. In the backward checking mechanism, when a rule is being fired, the expert system checks back on the premise conditions of the upstream rules that result in evaluation of the rule to see whether it should be fired. The root of the tree being traversed is the rule being fired. In the censor setting mechanism, when a rule is to be evaluated, a censor is constructed based on the premise conditions of the upstream rules and the censor is evaluated just before the rule is fired. Unlike the backward checking mechanism, this one does not search the upstream rules. This paper explores the details of implementation of the three mechanisms.

Yeh, Show-Way↗

NASA NTRS1974

Nonstationary homogeneous nucleation

The theory of homogeneous condensation is reviewed and equations describing this process are presented. Numerical computer solutions to transient problems in nucleation (relaxation to steady state) are presented and compared to a prior computation.

Harstad, K. G.↗

NASA NTRS1981

Steady and nonsteady supersonic turbulent afterbody flow

The effect of the specific heat ratio gamma of the incoming ideal gas on the flow properties, especially on pressure distributions along the base and sting surfaces and on reattachment distance, was investigated. The specific heat ratios considered were gamma = 1.2, 1.4, and 1.667. Also, effects of other major parameters, such as eddy-viscosity coefficient (or effective Reynolds number) and Mach number, on the afterbody pressure and reattachment distance were studied and are discussed. Evolution of shock induced flow and stabilization time were examined and are discussed for a transient problem. The important influence of the flow-field geometry, pressure distributions, and reattachment distance on the aerodynamics radiative heat transfer for an atmosphere entry probe in high speed flight are briefly described.

Yoshikawa, K. K.↗

NASA NTRS1980

P78-2 satellite and payload responses to electron beam operations on March 30, 1979

The operating modes of the SC4-1 payload, the resultant charging of the spacecraft frame and sample materials on the spacecraft exterior and recorded transient pulses are reported. Arcing was detected by pulse monitors in several electron beam modes of operation. The ejection of a beam of 6 mA of 3 keV electrons caused three distinct payload failures and created a transient problem in the telemetry system. The exact time, nature, and cause of these failures was determined and component failure and why they failed was identified. Analytical and modeling techniques are used to examine possible spacecraft and payload responses to the electron beam ejection which might have contributed to the arcing and payload failures.

Cohen, H. A.↗

NASA NTRS1983

Flutter and forced response of mistuned rotors using standing wave analysis

A standing wave approach is applied to the analysis of the flutter and forced response of tuned and mistuned rotors. The traditional traveling wave cascade airforces are recast into standing wave arbitrary motion form using Pade approximants, and the resulting equations of motion are written in the matrix form. Applications for vibration modes, flutter, and forced response are discussed. It is noted that the standing wave methods may prove to be more versatile for dealing with certain applications, such as coupling flutter with forced response and dynamic shaft problems, transient impulses on the rotor, low-order engine excitation, bearing motions, and mistuning effects in rotors.

Dugundji, J.↗

NASA NTRS1983

Flutter and forced response of mistuned rotors using standing wave analysis

Bundas, D. J.↗

NASA NTRS1989

Development of higher-order modal methods for transient thermal and structural analysis

A force-derivative method which produces higher-order modal solutions to transient problems is evaluated. These higher-order solutions converge to an accurate response using fewer degrees-of-freedom (eigenmodes) than lower-order methods such as the mode-displacement or mode-acceleration methods. Results are presented for non-proportionally damped structural problems as well as thermal problems modeled by finite elements.

Camarda, Charles J.↗

NASA NTRS1994

Visualization of unsteady computational fluid dynamics

A brief summary of the computer environment used for calculating three dimensional unsteady Computational Fluid Dynamic (CFD) results is presented. This environment requires a super computer as well as massively parallel processors (MPP's) and clusters of workstations acting as a single MPP (by concurrently working on the same task) provide the required computational bandwidth for CFD calculations of transient problems. The cluster of reduced instruction set computers (RISC) is a recent advent based on the low cost and high performance that workstation vendors provide. The cluster, with the proper software can act as a multiple instruction/multiple data (MIMD) machine. A new set of software tools is being designed specifically to address visualizing 3D unsteady CFD results in these environments. Three user's manuals for the parallel version of Visual3, pV3, revision 1.00 make up the bulk of this report.

Haimes, Robert↗

NASA NTRS1995

Visualization of unsteady computational fluid dynamics

The current computing environment that most researchers are using for the calculation of 3D unsteady Computational Fluid Dynamic (CFD) results is a super-computer class machine. The Massively Parallel Processors (MPP's) such as the 160 node IBM SP2 at NAS and clusters of workstations acting as a single MPP (like NAS's SGI Power-Challenge array) provide the required computation bandwidth for CFD calculations of transient problems. Work is in progress on a set of software tools designed specifically to address visualizing 3D unsteady CFD results in these super-computer-like environments. The visualization is concurrently executed with the CFD solver. The parallel version of Visual3, pV3 required splitting up the unsteady visualization task to allow execution across a network of workstation(s) and compute servers. In this computing model, the network is almost always the bottleneck so much of the effort involved techniques to reduce the size of the data transferred between machines.

Haimes, Robert↗

NASA NTRS1982

Algorithmic aspects of transient heat transfer problems in structures

It is noted that the application of finite element or finite difference techniques to the solution of transient heat transfer problems in structures often results in a stiff system of ordinary differential equations. Such systems are usually handled most efficiently by implicit integration techniques which require the solution of large and sparse systems of algebraic equations. The assembly and solution of these systems using the incomplete Cholesky conjugate gradient algorithm is examined. Several examples are used to demonstrate the advantage of the algorithm over other techniques.

Haftka, R. T.↗