Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “time discretization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Creep Life of Ceramic Components Using a Finite-Element-Based Integrated Design Program (CARES/CREEP)

The desirable properties of ceramics at high temperatures have generated interest in their use for structural applications such as in advanced turbine systems. Design lives for such systems can exceed 10,000 hours. The long life requirement necessitates subjecting the components to relatively low stresses. The combination of high temperatures and low stresses typically places failure for monolithic ceramics in the creep regime. The objective of this paper is to present a design methodology for predicting the lifetimes of structural components subjected to creep rupture conditions. This methodology utilized commercially available finite element packages and takes into account the time-varying creep strain distributions (stress relaxation). The creep life of a component is discretized into short time steps, during which the stress and strain distributions are assumed constant. The damage is calculated for each time step based on a modified Monkman-Grant creep rupture criterion. Failure is assumed to occur when the normalized accumulated damage at any point in the component is greater than or equal to unity. The corresponding time will be the creep rupture life for that component. Examples are chosen to demonstrate the CARES/CREEP (Ceramics Analysis and Reliability Evaluation of Structures/CREEP) integrated design programs, which is written for the ANSYS finite element package. Depending on the component size and loading conditions, it was found that in real structures one of two competing failure modes (creep or slow crack growth) will dominate. Applications to benechmark problems and engine components are included.

Gyekenyesi, J. P.↗
NASA NTRS2015

2nd-Order CESE Results For C1.1: Transonic Ringleb Flow

The Conservation Element and Solution Element (CESE) method was used as implemented in the NASA research code ez4d (an unstructured Navier-Stokes solver coded in C++ with serial and parallel versions available.) The CESE method is a time-accurate formulation with flux-conservation in both space and time. The method treats the discretized derivatives of space and time identically and while the 2nd-order accurate version was used, high-order versions exist.

Numerical Analysis↗
NASA NTRS2015

2nd-Order CESE Results For C1.4: Vortex Transport by Uniform Flow

The Conservation Element and Solution Element (CESE) method was used as implemented in the NASA research code ez4d. The CESE method is a time accurate formulation with flux-conservation in both space and time. The method treats the discretized derivatives of space and time identically and while the 2nd-order accurate version was used, high-order versions exist, the 2nd-order accurate version was used. In regards to the ez4d code, it is an unstructured Navier-Stokes solver coded in C++ with serial and parallel versions available. As part of its architecture, ez4d has the capability to utilize multi-thread and Messaging Passage Interface (MPI) for parallel runs.

Space-time CE/SE method↗
NASA NTRS1989

Doppler radar with multiphase modulation of transmitted and reflected signal

A microwave radar signal is generated and split by a circulator. A phase shifter introduces a series of phase shifts into a first part of the split signal which is then transmitted by antenna. A like number of phase shifts is introduced by the phase shifter into the return signal from the target. The circulator delivers the phase shifted return signal and the leakage signal from the circulator to a mixer which generates an IF signal output at the Doppler frequency. The IF signal is amplified, filtered, counted per unit of time, and the result displayed to provide indications of target sense and range rate. An oscillator controls rate of phase shift in the transmitted and received radar signals and provides a time base for the counter. The phase shift magnitude increases may be continuous and linear or discrete functions of time.

Shores, Paul W.↗
NASA NTRS1995

Experimental confirmation of a PDE-based approach to design of feedback controls

Issues regarding the experimental implementation of partial differential equation based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented.

Banks, H. T.↗
NASA NTRS1985

Optimal generalized multistep integration formulae for real-time digital simulation

The problem of discretizing a dynamical system for real-time digital simulation is considered. Treating the system and its simulation as stochastic processes leads to a statistical characterization of simulator fidelity. A plant discretization procedure based on an efficient matrix generalization of explicit linear multistep discrete integration formulae is introduced, which minimizes a weighted sum of the mean squared steady-state and transient error between the system and simulator outputs.

Moerder, D. D.↗
NASA NTRS1997

Dynamics of Numerics & Spurious Behaviors in CFD Computations

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

Yee, Helen C.↗
NASA NTRS1975

A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

Womble, M. E.↗
NASA NTRS1984

Interpretation of planetary stress systems: Determination of tectonic over-printing in Northwest Wyoming

Structural and tectonic interpretations of planetary surfaces rely strongly on visual determination of regional structural grain. This grain can be very complex and confusing, and sorting out of discrete trends in time and space is of utmost importance. This study is a test of these techniques applied to a well known area having several discrete structural grains. In the Bighorn Basin region of Wyoming, a largely overlooked N10E structural grain has been verified with detailed structural analysis and indicates a significant change in stress orientation at the end of the Laramide orogeny.

Wise, D. U.↗
NASA NTRS2015

Auralization of Tonal Rotor Noise Components of a Quadcopter Flyover

The capabilities offered by small unmanned vertical lift aerial vehicles, for example, quadcopters, continue to captivate entrepreneurs across the private, public, and civil sectors. As this industry rapidly expands, the public will be exposed to these devices (and to the noise these devices generate) with increasing frequency and proximity. Accordingly, an assessment of the human response to these machines will be needed shortly by decision makers in many facets of this burgeoning industry, from hardware manufacturers all the way to government regulators. One factor of this response is that of the annoyance to the noise that is generated by these devices. This paper presents work currently being pursued by NASA toward this goal. First, physics-based (CFD) predictions are performed on a single isolated rotor typical of these devices. The result of these predictions are time records of the discrete tonal components of the rotor noise. These time records are calculated for a number of points that appear on a lattice of locations spread over the lower hemisphere of the rotor. The source noise is then generated by interpolating between these time records. The sound from four rotors are combined and simulated-propagation techniques are used to produce complete flyover auralizations.

Christian, Andrew W.↗
NASA NTRS2010

Improving Customer Waiting Time at a DMV Center Using Discrete-Event Simulation

Virginia's Department of Motor Vehicles (DMV) serves a customer base of approximately 5.6 million licensed drivers and ID card holders and 7 million registered vehicle owners. DMV has more daily face-to-face contact with Virginia's citizens than any other state agency [1]. The DMV faces a major difficulty in keeping up with the excessively large customers' arrival rate. The consequences are queues building up, stretching out to the entrance doors (and sometimes even outside) and customers complaining. While the DMV state employees are trying to serve at their fastest pace, the remarkably large queues indicate that there is a serious problem that the DMV faces in its services, which must be dealt with rapidly. Simulation is considered as one of the best tools for evaluating and improving complex systems. In this paper, we use it to model one of the DMV centers located in Norfolk, VA. The simulation model is modeled in Arena 10.0 from Rockwell systems. The data used is collected from experts of the DMV Virginia headquarter located in Richmond. The model created was verified and validated. The intent of this study is to identify key problems causing the delays at the DMV centers and suggest possible solutions to minimize the customers' waiting time. In addition, two tentative hypotheses aiming to improve the model's design are tested and validated.

Arnaout, Georges M.↗
NASA NTRS1984

A new multifunction acousto-optic signal processor

An acousto-optic architecture for simultaneously obtaining time integration correlation and high-speed power spectrum analysis was constructed using commercially available TeO2 modulators and photodiode detector-arrays. The correlator section of the processor uses coherent interferometry to attain maximum bandwidth and dynamic range while achieving a time-bandwidth product of 1 million. Two correllator outputs are achieved in this system configuration. One is optically filtered and magnified 2 : 1 to decrease the spatial frequency to a level where a 25-MHz bandwidth may be sampled by a 62-mm array with elements on 25-micro centers. The other output is magnified by a factor of 10 such that the center 4 microseconds of information is available for estimation of time-difference-of-arrival to within 10 ns. The Bragg cell spectrum-analyzer section, which also has two outputs, resolves a 25-MHz instantaneous bandwidth to 25 kHz and can determine discrete-frequency reception time to within 15 microseconds. A microprocessor combines spectrum analysis information with that obtained from the correlator.

Berg, N. J.↗
NASA NTRS2008

Adjoint-Based Methodology for Time-Dependent Optimization

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Yamaleev, N. K.↗
NASA NTRS2007

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Campbell, Joel↗
NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux-difference splitting method has been extended to treat two-dimensional viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-stage Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗
NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux difference splitting method was extended to treat 2-D viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-state Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗
NASA NTRS1987

Piloted simulator study of allowable time delays in large-airplane response

A piloted simulation was performed to determine the permissible time delay and phase shift in the flight control system of a specific large transport-type airplane. The study was conducted with a six degree of freedom ground-based simulator and a math model similar to an advanced wide-body jet transport. Time delays in discrete and lagged form were incorporated into the longitudinal, lateral, and directional control systems of the airplane. Three experienced pilots flew simulated approaches and landings with random localizer and glide slope offsets during instrument tracking as their principal evaluation task. Results of the present study suggest a level 1 (satisfactory) handling qualities limit for the effective time delay of 0.15 sec in both the pitch and roll axes, as opposed to a 0.10-sec limit of the present specification (MIL-F-8785C) for both axes. Also, the present results suggest a level 2 (acceptable but unsatisfactory) handling qualities limit for an effective time delay of 0.82 sec and 0.57 sec for the pitch and roll axes, respectively, as opposed to 0.20 sec of the present specifications for both axes. In the area of phase shift between cockpit input and control surface deflection,the results of this study, flown in turbulent air, suggest less severe phase shift limitations for the approach and landing task-approximately 50 deg. in pitch and 40 deg. in roll - as opposed to 15 deg. of the present specifications for both axes.

Grantham, William D.↗
NASA NTRS1974

The UCSD/MIT hard X-ray and low energy gamma ray experiment for HEAO-A

An HEAO-A spacecraft is described which is scheduled for launch in April 1977 to survey the sky in the 0.15 keV to 10 MeV range of X-rays with improved sensitivity and angular resolution. The spectral and time variations of discrete sources, and the spectrum and isotropy of the diffuse component will be measured. A hard X-ray and low energy gamma ray experiment is described which will use as an array of seven (NaI)(Tl)/CsI(Na) phoswich detectors and eight large CsI(Na) shields. Detector events are pulse-height analyzed with a selectable time resolution of 0.1, 0.005, or 0.00002 sec. The instrument background is expected to be comprised of approximately equal parts of diffuse gamma rays entering the aperture, radioactive decay of spallation products, and gamma ray leakage through the shields. Detailed background predictions are presented, and sensitivity estimates indicate that the Crab nebula should be detected up to approximately 5 MeV. Approximate 1% isotropy limits for the diffuse component of cosmic gamma rays should be achieved, and its spectrum measured with improved precision.

Matteson, J. L.↗