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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.

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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Comparison of Implicit Collocation Methods for the Heat Equation

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Kouatchou, Jules↗
NASA NTRS2002

High Order Finite Difference Methods for Multiscale Complex Compressible Flows

The classical way of analyzing finite difference schemes for hyperbolic problems is to investigate as many as possible of the following points: (1) Linear stability for constant coefficients; (2) Linear stability for variable coefficients; (3) Non-linear stability; and (4) Stability at discontinuities. We will build a new numerical method, which satisfies all types of stability, by dealing with each of the points above step by step.

Sjoegreen, Bjoern↗
NASA NTRS2003

A Reduced-Order Model for Efficient Simulation of Synthetic Jet Actuators

A new reduced-order model of multidimensional synthetic jet actuators that combines the accuracy and conservation properties of full numerical simulation methods with the efficiency of simplified zero-order models is proposed. The multidimensional actuator is simulated by solving the time-dependent compressible quasi-1-D Euler equations, while the diaphragm is modeled as a moving boundary. The governing equations are approximated with a fourth-order finite difference scheme on a moving mesh such that one of the mesh boundaries coincides with the diaphragm. The reduced-order model of the actuator has several advantages. In contrast to the 3-D models, this approach provides conservation of mass, momentum, and energy. Furthermore, the new method is computationally much more efficient than the multidimensional Navier-Stokes simulation of the actuator cavity flow, while providing practically the same accuracy in the exterior flowfield. The most distinctive feature of the present model is its ability to predict the resonance characteristics of synthetic jet actuators; this is not practical when using the 3-D models because of the computational cost involved. Numerical results demonstrating the accuracy of the new reduced-order model and its limitations are presented.

Yamaleev, Nail K.↗
NASA NTRS2003

Control Law Design in a Computational Aeroelasticity Environment

A methodology for designing active control laws in a computational aeroelasticity environment is given. The methodology involves employing a systems identification technique to develop an explicit state-space model for control law design from the output of a computational aeroelasticity code. The particular computational aeroelasticity code employed in this paper solves the transonic small disturbance aerodynamic equation using a time-accurate, finite-difference scheme. Linear structural dynamics equations are integrated simultaneously with the computational fluid dynamics equations to determine the time responses of the structure. These structural responses are employed as the input to a modern systems identification technique that determines the Markov parameters of an "equivalent linear system". The Eigensystem Realization Algorithm is then employed to develop an explicit state-space model of the equivalent linear system. The Linear Quadratic Guassian control law design technique is employed to design a control law. The computational aeroelasticity code is modified to accept control laws and perform closed-loop simulations. Flutter control of a rectangular wing model is chosen to demonstrate the methodology. Various cases are used to illustrate the usefulness of the methodology as the nonlinearity of the aeroelastic system is increased through increased angle-of-attack changes.

Newsom, Jerry R.↗
NASA NTRS1997

Micromechanics Analysis Code (MAC) Developed

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers in performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions, it must be based on a micromechanics approach that uses physically based deformation and life constitutive models, and it must allow one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Only then can such a model be used by a material scientist to investigate the effect of different deformation mechanisms on the overall response of the composite and, thereby, identify the appropriate constituents for a given application. However, if a micromechanical model is to be used in a large-scale structural analysis it must be (1) computationally efficient, (2) able to generate accurate displacement and stress fields at both the macro and micro level, and (3) compatible with the finite element method. In addition, new advancements in processing and fabrication techniques now make it possible to engineer the architectures of these advanced composite systems. Full utilization of these emerging manufacturing capabilities require the development of a computationally efficient micromechanics analysis tool that can accurately predict the effect of microstructural details on the internal and macroscopic behavior of composites. Computational efficiency is required because (1) a large number of parameters must be varied in the course of engineering (or designing) composite materials and (2) the optimization of a material's microstructure requires that the micromechanics model be integrated with optimization algorithms. From this perspective, analytical approaches that produce closed-form expressions which describe the effect of a material's internal architecture on the overall material behavior are preferable to numerical methods such as the finite element or finite difference schemes.

Source record↗
NASA NTRS1997

SWIFT: Multistage Turbomachinery Analysis Code Developed

A new turbomachinery analysis code called SWIFT has been developed at the NASA Lewis Research Center. SWIFT solves thin-layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and an explicit finite-difference scheme. Preconditioning allows the code to be used for all speed ranges, from incompressible to supersonic flows. Multiblock capability allows three types of grids to be patched together to simulate many types of turbomachinery geometries, including hub and tip clearances. In addition, code users can analyze multistage turbomachinery by using a steady averaging-plane approach. This approach uses linearized characteristic boundary conditions to pass information accurately between the stages.

Chima, Rodrick V.↗
NASA NTRS2006

A Computational and Experimental Investigation of Shear Coaxial Jet Atomization

The instability and subsequent atomization of a viscous liquid jet emanated into a high-pressure gaseous surrounding is studied both computationally and experimentally. Liquid water issued into nitrogen gas at elevated pressures is used to simulate the flow conditions in a coaxial shear injector element relevant to liquid propellant rocket engines. The theoretical analysis is based on a simplified mathematical formulation of the continuity and momentum equations in their conservative form. Numerical solutions of the governing equations subject to appropriate initial and boundary conditions are obtained via a robust finite difference scheme. The computations yield real-time evolution and subsequent breakup characteristics of the liquid jet. The experimental investigation utilizes a digital imaging technique to measure resultant drop sizes. Data were collected for liquid Reynolds number between 2,500 and 25,000, aerodynamic Weber number range of 50-500 and ambient gas pressures from 150 to 1200 psia. Comparison of the model predictions and experimental data for drop sizes at gas pressures of 150 and 300 psia reveal satisfactory agreement particularly for lower values of investigated Weber number. The present model is intended as a component of a practical tool to facilitate design and optimization of coaxial shear atomizers.

Ibrahim, Essam A.↗
NASA NTRS2010

Direct CFD Predictions of Low Frequency Sounds Generated by a Helicopter Main Rotor

The use of CFD to directly predict helicopter main rotor noise is shown to be quite promising as an alternative mean for low frequency source noise evaluation. Results using existing state-of-the-art grid structures and finite-difference schemes demonstrated that small perturbation pressures, associated with acoustics radiation, can be extracted with some degree of fidelity. Accuracy of the predictions are demonstrated via comparing to predictions from conventional acoustic analogy-based models, and with measurements obtained from wind tunnel and flight tests for the MD-902 helicopter at several operating conditions. Findings show that the direct CFD approach is quite successfully in yielding low frequency results due to thickness and steady loading noise mechanisms. Mid-to-high frequency contents, due to blade-vortex interactions, are not predicted due to CFD modeling and grid constraints.

Sim, Ben W.↗
NASA NTRS2010

Development of Implicit Methods in CFD NASA Ames Research Center 1970's - 1980's

The focus here is on the early development (mid 1970's-1980's) at NASA Ames Research Center of implicit methods in Computational Fluid Dynamics (CFD). A class of implicit finite difference schemes of the Beam and Warming approximate factorization type will be addressed. The emphasis will be on the Euler equations. A review of material pertinent to the solution of the Euler equations within the framework of implicit methods will be presented. The eigensystem of the equations will be used extensively in developing a framework for various methods applied to the Euler equations. The development and analysis of various aspects of this class of schemes will be given along with the motivations behind many of the choices. Various acceleration and efficiency modifications such as matrix reduction, diagonalization and flux split schemes will be presented.

Pulliam, Thomas H.↗
NASA NTRSDate not supplied

On A Stabilization of the Ingard-Myers Impedance Boundary Condition

It has been well-known that the Ingard-Myers impedance condition, while simple to apply, is subject to the hydrodynamic Kelvin-Helmholtz instability due to its use of a vortex sheet in modeling the flow at the liner boundary. Recently, in the development of a time domain boundary element method for acoustic scattering by treated surfaces, it was found that by neglecting a certain second-order spatial derivative term in the Ingard-Myers formulation, the hydrodynamic instability can be avoided. The present paper aims to provide further analysis of this modified condition, hereby referred to as Truncated Ingard-Myers Impedance Boundary Condition (TIMIBC). It will be shown, based on the dispersion relations of linear waves, that the instability intrinsic to the Ingard-Myers condition is eliminated in the proposed new formulation. Quantitative assessments on the accuracy of TIMIBC for scattering of acoustic waves by lined surfaces will be carried out, and its effectiveness will be demonstrated by numerical examples. Specifically, the accuracy is assessed by comparing solutions obtained by the Ingard-Myers condition with that by the proposed TIMIBC where theoretical reflection coefficients at a lined surface are derived for cases of plane and spherical incident waves. It is found that the TIMIBC provides a good approximation to the original Ingard-Myers condition for flows of low to mid subsonic Mach numbers. Time domain implementations of TIMIBC are also discussed and illustrated with a numerical example using a finite difference scheme. As many studies have shown the Ingard-Myers condition to be the correct limit of boundary layer thickness going to zero, the proposed TIMIBC can offer a practical solution for overcoming the intrinsic instability associated with the Ingard-Myers condition.

Time Domain BEM↗
NASA NTRSDate not supplied

On A Stabilization of the Ingard-Myers Impedance Boundary Condition

It has been well-known that the Ingard-Myers impedance condition, while simple to apply, is subject to the hydrodynamic Kelvin-Helmholtz instability due to its use of a vortex sheet in modeling the flow at the liner boundary. Recently, in the development of a time domain boundary element method for acoustic scattering by treated surfaces, it was found that by neglecting a certain second-order spatial derivative term in the Ingard-Myers formulation, the hydrodynamic instability can be avoided. The present paper aims to provide further analysis of this modified condition, hereby referred to as Truncated Ingard-Myers Impedance Boundary Condition (TIMIBC). It will be shown, based on the dispersion relations of linear waves, that the instability intrinsic to the Ingard-Myers condition is eliminated in the proposed new formulation. Quantitative assessments on the accuracy of TIMIBC for scattering of acoustic waves by lined surfaces will be carried out, and its effectiveness will be demonstrated by numerical examples. Specifically, the accuracy is assessed by comparing solutions obtained by the Ingard-Myers condition with that by the proposed TIMIBC where theoretical reflection coefficients at a lined surface are derived for cases of plane and spherical incident waves. It is found that the TIMIBC provides a good approximation to the original Ingard-Myers condition for flows of low to mid subsonic Mach numbers. Time domain implementations of TIMIBC are also discussed and illustrated with a numerical example using a finite difference scheme. As many studies have shown the Ingard-Myers condition to be the correct limit of boundary layer thickness going to zero, the proposed TIMIBC can offer a practical solution for overcoming the intrinsic instability associated with the Ingard-Myers condition.

Time Domain BEM↗
DOE OSTI2022

Assessment of Numerical Diffusion in NRELAP5 Code for Density Wave Oscillations Applications

Density wave oscillation (DWO) in a boiling channel can be a delicate phenomenon, and the precision of numerical tools can influence predictions. In this paper, relevant numerical diffusion was analyzed for the finite difference schemes used in the NRELAP5 code. The numerical diffusion in NRELAP5 was investigated under both single-phase and two-phase conditions. A unique perturbation technique called the “V” ramping approach was introduced, and the NRELAP5-predicted DWO results were then compared to test data.

Numerical diffusion, NRELAP5, RELAP5-3D, density w↗
NASA NTRS1990

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

Bates, J. R.↗
NASA NTRS1992

Scheme For Finite-Difference Computations Of Waves

Compact algorithms generating and solving finite-difference approximations of partial differential equations for propagation of waves obtained by new method. Based on concept of discrete dispersion relation. Used in wave propagation to relate frequency to wavelength and is key measure of wave fidelity.

Davis, Sanford↗
NASA NTRS1996

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, K. J.↗
NASA NTRS1996

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, Kenneth J.↗
NASA NTRS1991

A study of the response of nonlinear springs

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Hyer, M. W.↗
NASA NTRS1995

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Skarda, J. Raymond Lee↗