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At least 1,261 records · Page 70

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NASA NTRS1985

Finite-amplitude steady waves in plane viscous shear flows

Computations of two-dimensional solutions of the Navier-Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Milinazzo, F. A.↗

NASA NTRS1989

State-of-the-art surveys on computational mechanics

Topics considered include advances in finite difference techniques for computational fluid dynamics, the spectral element methods for the incompressible Navier-Stokes equations, a review of recent developments in time integration, and advances and trends in element-by-element techniques. Also examined are the algebraic multigrid methods applied to problems in computational structural mechanics, grid generation for the solution of partial differential equations, advances in adaptive improvements, and new computing systems and their impact on computational mechanics.

Noor, Ahmed K.↗

NASA NTRS1989

Compact finite volume methods for the diffusion equation

The paper describes an approach to treating initial-boundary-value problems by finite volume methods in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second-order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and ADI methods.

Rose, Milton E.↗

NASA NTRS1998

Multi-Bandwidth Frequency Selective Surfaces for Near Infrared Filtering: Design and Optimization

Frequency selective surfaces are widely used in the microwave and millimeter wave regions of the spectrum for filtering signals. They are used in telecommunication systems for multi-frequency operation or in instrument detectors for spectroscopy. The frequency selective surface operation depends on a periodic array of elements resonating at prescribed wavelengths producing a filter response. The size of the elements is on the order of half the electrical wavelength, and the array period is typically less than a wavelength for efficient operation. When operating in the optical region, diffraction gratings are used for filtering. In this regime the period of the grating may be several wavelengths producing multiple orders of light in reflection or transmission. In regions between these bands (specifically in the infrared band) frequency selective filters consisting of patterned metal layers fabricated using electron beam lithography are beginning to be developed. The operation is completely analogous to surfaces made in the microwave and millimeter wave region except for the choice of materials used and the fabrication process. In addition, the lithography process allows an arbitrary distribution of patterns corresponding to resonances at various wavelengths to be produced. The design of sub-millimeter filters follows the design methods used in the microwave region. Exacting modal matching, integral equation or finite element methods can be used for design. A major difference though is the introduction of material parameters and thicknesses that may not be important in longer wavelength designs. This paper describes the design of multi- bandwidth filters operating in the 1-5 micrometer wavelength range. This work follows on a previous design. In this paper extensions based on further optimization and an examination of the specific shape of the element in the periodic cell will be reported. Results from the design, manufacture and test of linear wedge filters built using microlithographic techniques and used in spectral imaging applications will be presented.

Cwik, Tom↗

NASA NTRS1999

Multi-Bandwidth Frequency Selective Surfaces for Near Infrared Filtering: Design and Optimization

Frequency selective surfaces are widely used in the microwave and millimeter wave regions of the spectrum for filtering signals. They are used in telecommunication systems for multi-frequency operation or in instrument detectors for spectroscopy. The frequency selective surface operation depends on a periodic array of elements resonating at prescribed wavelengths producing a filter response. The size of the elements is on the order of half the electrical wavelength, and the array period is typically less than a wavelength for efficient operation. When operating in the optical region, diffraction gratings are used for filtering. In this regime the period of the grating may be several wavelengths producing multiple orders of light in reflection or transmission. In regions between these bands (specifically in the infrared band) frequency selective filters consisting of patterned metal layers fabricated using electron beam lithography are beginning to be developed. The operation is completely analogous to surfaces made in the microwave and millimeter wave region except for the choice of materials used and the fabrication process. In addition, the lithography process allows an arbitrary distribution of patterns corresponding to resonances at various wavelengths to be produced. The design of sub-millimeter filters follows the design methods used in the microwave region. Exacting modal matching, integral equation or finite element methods can be used for design. A major difference though is the introduction of material parameters and thicknesses tha_ may not be important in longer wavelength designs. This paper describes the design of multi-bandwidth filters operating in the I-5 micrometer wavelength range. This work follows on previous design [1,2]. In this paper extensions based on further optimization and an examination of the specific shape of the element in the periodic cell will be reported. Results from the design, manufacture and test of linear wedge filters built using micro-lithographic techniques and used ir spectral imaging applications will be presented.

Cwik, Tom↗

NASA NTRS2005

Inference of Ice Cloud Properties from High-spectral Resolution Infrared Observations

The theoretical basis is explored for inferring the microphysical properties of ice crystal from high-spectral resolution infrared observations. A radiative transfer model is employed to simulate spectral radiances to address relevant issues. The extinction and absorption efficiencies of individual ice crystals, assumed as hexagonal columns for large particles and droxtals for small particles, are computed from a combination of the finite- difference time-domain (FDTD) technique and a composite method. The corresponding phase functions are computed from a combination of FDTD and an improved geometric optics method (IGOM). Bulk scattering properties are derived by averaging the single- scattering properties of individual particles for 30 particle size distributions developed from in situ measurements and for additional four analytical Gamma size distributions for small particles. The non-sphericity of ice crystals is shown to have a significant impact on the radiative signatures in the infrared (IR) spectrum; the spherical particle approximation for inferring ice cloud properties may result in an overest&ation of the optical thickness and an inaccurate retrieval of effective particle size. Furthermore, we show that the error associated with the use of the Henyey-Greenstein phase function can be as larger as 1 K in terms of brightness temperature for larger particle effective size at some strong scattering wavenumbers. For small particles, the difference between the two phase functions is much less, with brightness temperatures generally differing by less than 0.4 K. The simulations undertaken in this study show that the slope of the IR brightness temperature spectrum between 790-960/cm is sensitive to the effective particle size. Furthermore, a strong sensitivity of IR brightness temperature to cloud optical thickness is noted within the l050-1250/cm region. Based on this spectral feature, a technique is presented for the simultaneous retrieval of the visible optical thickness and effective particle size from high spectral resolution infrared data under ice cloudy con&tion. The error analysis shows that the uncertainty of the retrieved optical thickness and effective particle size has a small range of variation. The error for retrieving particle size in conjunction with an uncertainty of 5 K in cloud'temperature, or a surface temperature uncertainty of 2.5 K, is less than 15%. The corresponding e m r in the uncertainty of optical thickness is within 5-2096, depending on the value of cloud optical thickness. The applicability of the technique is demonstrated using the aircraft-based High- resolution Interferometer Sounder (HIS) data from the Subsonic Aircraft: Contrail and Cloud Effects Special Study (SUCCESS) in 1996 and the First ISCCP Regional Experiment - Arctic Clouds Experiment (FIRE-ACE) in 1998.

Huang, Hung-Lung↗

DOE OSTI2021

THERMAL/STRUCTURAL ANALYSIS OF THE AXION QUANTUM METROLOGY CAVITY AND ITS COMPONENTS

This research was centered around maximizing the capability to cool dielectric material within a containment unit, or Photonic Band Gap (PBG) cavity, designed for detecting axion dark matter and identifying the unit’s thermal properties. There are multiple types of PBG cavities, but the latest version that axion researchers wish to use has been theorized to contain possible issues related to its thermal properties. Thermal conductivity is an issue with the dielectric material because it is made from alumina which is highly insulative. This is important since the research is being done in a cryogenic environment and the thermal noise affects the quantum bit used for detecting the axion to photon conversion process. Therefore, any improvements to this unit should be justified and implemented but are not entirely limited to thermal contact related aspects of PBG cavities. A prospect of using sapphire in place of alumina also exists, but this is a more expensive, less tested, and more elusive material to justify the creation of a full dielectric structure out of sapphire. Thermal aspects of the cavity were analyzed using finite element method (FEM) and an experiment designed to test different thermal joint materials. FEM was used to check the contraction of the cavity during cooling, the contact quality between the dielectric material and cavity wall, theheat flow rate through the assembly, and helps visualize the cavity’s reaction to different design changes. A simple comparison between thermal conductivity curves justified the usage of sapphire over alumina from a thermal property point of view. Thus, the method of experimentation had an additional dielectric material, sapphire, to test with and compare to alumina. The thermal test identified which material is best to use for a thermal joint but also simultaneously found the conductance of the joint and dielectric material as well as an estimate for what the temperature is inside the larger scale cavity since a thermometer cannot be placed inside the PBG when it cools. Initially, the cavity simulation was tested for structural deformation properties and stress distribution since it is made of copper which contracts heavily in comparison to most other materials. The reduction in volume of the cavity was less than anticipated which gave more room for a possible usage of a modified thermal joint for additional contact area and higher conductivity.

43 PARTICLE ACCELERATORS↗

NASA NTRS2014

Modeling Sound Propagation Through Non-Axisymmetric Jets

A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.

Leib, Stewart J.↗

NASA NTRS1984

Numerical simulation of two-dimensional inlet flowfields

Inlet flowfields for airbreathing missiles are calculated by a two-dimensional computational method. A supersonic freestream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time-marching, finite difference procedure to solve the Euler equations formulated in body-fitted coordinates. The method can be used for a flowfield with both subsonic and supersonic regions and is found to converge rapidly for supercritical inlet operation. For subcritical inlet operation, however, convergence to steady state is slow.

Biringen, S.↗

NASA NTRS2000

A New Method for Accurate Treatment of Flow Equations in Cylindrical Coordinates Using Series Expansions

The motivation of this work is the ongoing effort at the Center for Turbulence Research (CTR) to use large eddy simulation (LES) techniques to calculate the noise radiated by jet engines. The focus on engine exhaust noise reduction is motivated by the fact that a significant reduction has been achieved over the last decade on the other main sources of acoustic emissions of jet engines, such as the fan and turbomachinery noise, which gives increased priority to jet noise. To be able to propose methods to reduce the jet noise based on results of numerical simulations, one first has to be able to accurately predict the spatio-temporal distribution of the noise sources in the jet. Though a great deal of understanding of the fundamental turbulence mechanisms in high-speed jets was obtained from direct numerical simulations (DNS) at low Reynolds numbers, LES seems to be the only realistic available tool to obtain the necessary near-field information that is required to estimate the acoustic radiation of the turbulent compressible engine exhaust jets. The quality of jet-noise predictions is determined by the accuracy of the numerical method that has to capture the wide range of pressure fluctuations associated with the turbulence in the jet and with the resulting radiated noise, and by the boundary condition treatment and the quality of the mesh. Higher Reynolds numbers and coarser grids put in turn a higher burden on the robustness and accuracy of the numerical method used in this kind of jet LES simulations. As these calculations are often done in cylindrical coordinates, one of the most important requirements for the numerical method is to provide a flow solution that is not contaminated by numerical artifacts. The coordinate singularity is known to be a source of such artifacts. In the present work we use 6th order Pade schemes in the non-periodic directions to discretize the full compressible flow equations. It turns out that the quality of jet-noise predictions using these schemes is especially sensitive to the type of equation treatment at the singularity axis. The objective of this work is to develop a generally applicable numerical method for treating the singularities present at the polar axis, which is particularly suitable for highly accurate finite-differences schemes (e.g., Pade schemes) on non-staggered grids. The main idea is to reinterpret the regularity conditions developed in the context of pseudo-spectral methods. A set of exact equations at the singularity axis is derived using the appropriate series expansions for the variables in the original set of equations. The present treatment of the equations preserves the same level of accuracy as for the interior scheme. We also want to point out the wider utility of the method, proposed here in the context of compressible flow equations, as its extension for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical coordinates with finite-differences schemes of various level of accuracy is straightforward. The robustness and accuracy of the proposed technique is assessed by comparing results from simulations of laminar forced-jets and turbulent compressible jets using LES with similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r = 0.

Constantinescu, G.S.↗

NASA NTRS1997

Predictive Modeling in Plasma Reactor and Process Design

Research continues toward the improvement and increased understanding of high-density plasma tools. Such reactor systems are lauded for their independent control of ion flux and energy enabling high etch rates with low ion damage and for their improved ion velocity anisotropy resulting from thin collisionless sheaths and low neutral pressures. Still, with the transition to 300 mm processing, achieving etch uniformity and high etch rates concurrently may be a formidable task for such large diameter wafers for which computational modeling can play an important role in successful reactor and process design. The inductively coupled plasma (ICP) reactor is the focus of the present investigation. The present work attempts to understand the fundamental physical phenomena of such systems through computational modeling. Simulations will be presented using both computational fluid dynamics (CFD) techniques and the direct simulation Monte Carlo (DSMC) method for argon and chlorine discharges. ICP reactors generally operate at pressures on the order of 1 to 10 mTorr. At such low pressures, rarefaction can be significant to the degree that the constitutive relations used in typical CFD techniques become invalid and a particle simulation must be employed. This work will assess the extent to which CFD can be applied and evaluate the degree to which accuracy is lost in prediction of the phenomenon of interest; i.e., etch rate. If the CFD approach is found reasonably accurate and bench-marked with DSMC and experimental results, it has the potential to serve as a design tool due to the rapid time relative to DSMC. The continuum CFD simulation solves the governing equations for plasma flow using a finite difference technique with an implicit Gauss-Seidel Line Relaxation method for time marching toward a converged solution. The equation set consists of mass conservation for each species, separate energy equations for the electrons and heavy species, and momentum equations for the gas. The sheath is modeled by imposing the Bohm velocity to the ions near the walls. The DSMC method simulates each constituent of the gas as a separate species which would be analogous in CFD to employing separate species mass, momentum, and energy equations. All particles including electrons are moved and allowed to collide with one another with the stipulation that the electrons remain tied to the ions consistent with the concept of ambipolar diffusion. The velocities of the electrons are allowed to be modified during collisions and are not confined to a Maxwellian distribution. These benefits come at a price in terms of computational time and memory. The DSMC and CFD are made as consistent as possible by using similar chemistry and power deposition models. Although the comparison of CFD and DSMC is interesting, the main goal of this work is the increased understanding of high-density plasma flowfields that can then direct improvements in both techniques. This work is unique in the level of the physical models employed in both the DSMC and CFD for high-density plasma reactor applications. For example, the electrons are simulated in the present DSMC work which has not been done before for low temperature plasma processing problems. In the CFD approach, for the first time, the charged particle transport (discharge physics) has been self-consistently coupled to the gas flow and heat transfer.

Hash, D. B.↗

DOE OSTI2022

A sixth order Mehrstellen scheme with an application to the Method of Local Corrections for the 3D Poisson equation

We present a sixth order finite difference scheme for Poisson’s equation when discretized with the compact 27-point stencil based on Mehrstellen corrections of the forcing function term f. Our approach results in a sixth order accurate solution error as opposed to a fourth-order error imposed by the classical Mehrstellen correction for the 19-point and 27-point stencils. The present study is a continuation of former work of Spotz and Carey (1996) on compact finite difference schemes for Poisson’s equation where sixth order convergence may be obtained under the assumption that the fourth order derivatives of f are determined analytically. Specifically, we show that sixth order convergence can still be attained when only values of f at grid points are available. The sixth order Mehrstellen scheme is further coupled with a Method of Local Corrections (MLC) 3D Poisson solver improving to sixth order accuracy the results reported in Kavouklis and Colella (2019). The MLC test case considered involves an adaptive grid that comprises 7.5 billion cells.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1982

Solidification of a binary mixture

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

Antar, B. N.↗

NASA NTRS1991

A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities

A Fourier-Chebyshev pseudospectral method for solving steady 3D Navier-Stokes equations in cylindrical cavities is presented and discussed. The general method is pseudo-unsteady and uses a semi-implicit finite difference scheme for the time discretization. The generalized ADI (Alternating Direction Implicit) procedure is then applied to reduce the problem to a successive solution of one-dimensional problems. The spatial approximation uses a Fourier-Galerkin approximation in the periodic direction and a Chebyshev-collocation approximation in the other directions. Difficulties related to the pressure are surmounted by using the artifical compressibility method. A suitable variable change was chosen to avoid the problem of singularity at the axis generated by cylindrical coordinates. The method is first tested on an advection-diffusion equation and then on the Navier-Stokes equations. Finally, the method is illustrated by a convection problem of a differentially heated fluid.

Pulicani, J. P.↗

NASA NTRS1975

Supercritical wing sections 2, volume 108

A mathematical theory for the design and analysis of supercritical wing sections was previously presented. Examples and computer programs showing how this method works were included. The work on transonics is presented in a more definitive form. For design, a better model of the trailing edge is introduced which should eliminate a loss of fifteen or twenty percent in lift experienced with previous heavily aft loaded models, which is attributed to boundary layer separation. How drag creep can be reduced at off-design conditions is indicated. A rotated finite difference scheme is presented that enables the application of Murman's method of analysis in more or less arbitrary curvilinear coordinate systems. This allows the use of supersonic as well as subsonic free stream Mach numbers and to capture shock waves as far back on an airfoil as desired. Moreover, it leads to an effective three dimensional program for the computation of transonic flow past an oblique wing. In the case of two dimensional flow, the method is extended to take into account the displacement thickness computed by a semi-empirical turbulent boundary layer correction.

Bauer, F.↗

NASA NTRS1989

The numerical solution of the Navier-Stokes equations for 3-dimensional, unsteady, incompressible flows by compact schemes

The present numerical method for the solution of unsteady, incompressible three-dimensional flow Navier-Stokes equations using velocity-vorticity variables and irregular Cartesian grids proceeds by solving: (1) equations of Cauchy-Riemann type for the velocity; and (2) transport-diffusion equations for the vorticity, whose solenoidal vorticity components are generated by a Poisson equation for an appropriate scalar potential. Iterations are used to solve the finite difference equations, facilitating the use of vector and parallel-computing methods; numerical experiments have verified the method's second-order spatial and temporal accuracy.

Gatski, T. B.↗

NASA NTRS1989

Computing Viscoplastic Behavior Of A Material

Finite-element implementation developed for Robinson's unified model of viscoplasticity. Implemented via MARC general-purpose finite-element computer program by incorporating all of nonlinearity of material into initial load vector and treating vector as pseudo body force in finite-element equilibrium equations. In technique, each finite increment split into several equal subincrements, constitutive equations integrated by explicit Euler forward-difference method. HYPELA subroutine in MARC includes adaptive integration scheme selecting optimal sizes of subincrements. Spline function smooths discontinuous boundaries in Robinson's model to facilitate finite-element numerical calculations. Method used to calculate elastic, plastic, and creep deformations in solid materials at various temperatures; also used to study thermomechanical behavior of such things as hot pressure vessels and highly stressed components in engines.

Arya, V. K.↗

DOE OSTI2022

Comparison of three state-of-the-art crystal plasticity based deformation twinning models for magnesium alloys

In magnesium alloys, deformation twinning and its interactions with dislocation slip are responsible for a sigmoidal shape stress–strain behavior and an asymmetrical tension–compression yield strength in magnesium alloys. The sensitivity of twinning to the underlying microstructure renders the crystal plasticity method the most commonly adopted modeling approach for magnesium-twinning. This paper compares three state-of-the-art crystal plasticity-based twinning models from the literature, namely the elastic-viscoplastic self-consistent twinning-detwinning (EVPSC-TDT) model, crystal plasticity finite element model based on enhanced predominate twin reorientation approach (CPFE-ePTR), and the crystal plasticity finite element model based on “discrete twinning” approach (CPFE-DT). A polycrystalline microstructure is simulated with all three methods to compare the resulting stress–strain curves and lattice strains to those from the experimentally measured data. All three methods showed the capability of capturing the experimental results with different levels of accuracy. Additionally, the EVPSC-TDT method avoids solving the finite element matrices and showed the highest computational efficiency. The CPFE-ePTR model shows a higher accuracy in capturing the lattice strain. The CPFE-DT relies on high-resolution finite element mesh and is much slower than the other two methods, but it captured the local deformation concentration and stress reversal phenomena near the twin band, which was not possible with the other two methods. Based on the comparison, guidance for the selection of the appropriate model based on the specific modeling target is provided in this paper.

36 MATERIALS SCIENCE↗