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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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337 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Further development of XTRAN3S computer program

This report describes modifications and enhancements to XTRAN3S, a computer program for aerodynamic, static aeroelastic, and dynamic aeroelastic analysis of three-dimensional wings in the transonic speed regime. Modifications to the program include incorporation of a viscous boundary layer, modified coefficient and generalized force integration, direct input of airfoil surface coordinates and slopes, variable dimensions of computational arrays and a modified grid mapping transformation to improve computational stability for highly swept and tapered planforms. Results obtained with the modified program are included. Modifications discussed but not incorporated include a state matrix integration method, enhanced vectorization, and use of a cartesian physical mesh.

Borland, C. J.↗
NASA NTRS1983

A zonal approach for the steady transonic simulation of inviscid rotational flow

A finite difference zonal method is developed to compute steady inviscid transonic flow by coupling a semi-flux split form of the Euler equations in a vorticity producing zone with a zone of scalar and vector (i.e., dual) potential equations. The dual potential equations permit vorticity convection, but not production, and are efficiently solved as an iteratively decoupled set of scalar equations. Zonal results presented for a nonlifting biconvex airfoil on a stretched Cartesian grid show substantial savings in CPU time compared to solving the semi-flux split Euler equations alone. The dual potential equations also provide an alternate way of treating potential flows with circulation. This has been demonstrated by computing a subcritical flow over a lifting airfoil using generalized curvilinear coordinates.

Chaderjian, N. M.↗
DOE OSTI2022

A conservative implicit-PIC scheme for the hybrid kinetic-ion fluid-electron plasma model on curvilinear meshes

We report that the hybrid kinetic-ion fluid-electron plasma model is widely used to study challenging multi-scale problems in space and laboratory plasma physics. Here, a novel conservative scheme for this model employing implicit particle-in-cell techniques is extended to arbitrary coordinate systems via curvilinear maps from logical to physical space. The scheme features a fully non-linear electromagnetic formulation with a multi-rate time advance - including sub-cycling and orbit-averaging for the kinetic ions. By careful choice of compatible particle-based kinetic-ion and mesh-based fluid-electron discretizations in curvilinear coordinates, as well as particle-mesh interpolations and implicit midpoint time advance, the scheme is proven to conserve total energy for arbitrary curvilinear meshes. In the electrostatic limit, the method is also proven to conserve total momentum for arbitrary curvilinear meshes. Although momentum is not conserved for arbitrary curvilinear meshes in the electromagnetic case, it is for an important subset of Cartesian tensor-packed meshes. The scheme and its novel conservation properties are demonstrated for several challenging numerical problems using different curvilinear meshes, including a merging flux-rope simulation for a space weather application, and a helical m = 1 mode simulation for magnetic fusion energy application.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Numerical solution of the Navier-Stokes equations with topography

A finite difference scheme for solving the equations of fluid motion in a generalized coordinate system has been constructed. The scheme conserves mass and all the first integral moments of the motion. The scheme also advectively 'almost conserves' second moments, in that the magnitude of implicit numerical smoothing is typically about an order smaller than explicit viscosity and diffusion. Calculations with the model support the theoretical conjecture that the difference scheme is stable whenever the analogous Cartesian scheme is stable. The scheme has been used to calculate dry atmospheric convection due to differential heating between top and bottom of mountainous terrain. The general small-scale characteristics of mountain up-slope winds have been simulated. In addition, the results have demonstrated the crucial role played by the eddy diffusivities and the environmental stability, in determining both the quantitative and the qualitative features of the circulation.

Gal-Chen, T.↗
NASA NTRS1988

Turbofan forced mixer lobe flow modeling. 2: Three-dimensional inviscid mixer analysis (FLOMIX)

A three-dimensional potential analysis (FLOMIX) was formulated and applied to the inviscid flow over a turbofan foced mixer. The method uses a small disturbance formulation to analytically uncouple the circumferential flow from the radial and axial flow problem, thereby reducing the analysis to the solution of a series of axisymmetric problems. These equations are discretized using a flux volume formulation along a Cartesian grid. The method extends earlier applications of the Cartesian method to complex cambered geometries. The effects of power addition are also included within the potential formulation. Good agreement is obtained with an alternate small disturbance analysis for a high penetration symmetric mixer in a planar duct. In addition, calculations showing pressure distributions and induced secondary vorticity fields are presented for practical trubofan mixer configurations, and where possible, comparison was made with available experimental data. A detailed description of the required data input and coordinate definition is presented along with a sample data set for a practical forced mixer configuration. A brief description of the program structure and subroutines is also provided.

Barber, T.↗
NASA NTRS2004

Overview of Transonic to Hypersonic Stage Separation Tool Development for Multi-Stage-to-Orbit Concepts

An overview of research efforts at NASA in support of the stage separation and ascent aerothermodynamics research program is presented. The objective of this work is to develop a synergistic suite of experimental, computational, and engineering tools and methods to apply to vehicle separation across the transonic to hypersonic speed regimes. Proximity testing of a generic bimese wing-body configuration is on-going in the transonic (Mach numbers 0.6, 1.05, and 1.1), supersonic (Mach numbers 2.3, 3.0, and 4.5) and hypersonic (Mach numbers 6 and 10) speed regimes in four wind tunnel facilities at the NASA Langley Research Center. An overset grid, Navier-Stokes flow solver has been enhanced and demonstrated on a matrix of proximity cases and on a dynamic separation simulation of the bimese configuration. Steady-state predictions with this solver were in excellent agreement with wind tunnel data at Mach 3 as were predictions via a Cartesian-grid Euler solver. Experimental and computational data have been used to evaluate multi-body enhancements to the widely-used Aerodynamic Preliminary Analysis System, an engineering methodology, and to develop a new software package, SepSim, for the simulation and visualization of vehicle motions in a stage separation scenario. Web-based software will be used for archiving information generated from this research program into a database accessible to the user community. Thus, a framework has been established to study stage separation problems using coordinated experimental, computational, and engineering tools.

Murphy, Kelly J.↗
NASA NTRS2018

Symmetric Equations on the Surface of a Sphere as Used by Model GISS:IB

Standard vector calculus formulas of Cartesian three space are projected onto the surface of a sphere. This produces symmetric equations with three nonindependent horizontal velocity components. Each orthogonal axis has a velocity component that rotates around its axis (eastward velocity rotates around the north–south axis) and a specific angular momentum component that is the product of the velocity component multiplied by the cosine of axis’ latitude. Angular momentum components align with the fixed axes and simplify several formulas, whereas the rotating velocity components are not orthogonal and vary with location. Three symmetric coordinates allow vector resolution and calculus operations continuously over the whole spherical surface, which is not possible with only two coordinates. The symmetric equations are applied to one-layer shallow water models on cubed-sphere and icosahedral grids, the latter being computationally simple and applicable to an ocean domain. Model results are presented for three different initial conditions and five different resolutions.

Icosahedral grid↗
NASA NTRS2018

Acoustic Radiation Pressure

The theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from finite deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in Lagrangian coordinates (not Eulerian coordinates) and that the terms in the BST are not the momentum flux density and mean excess Eulerian stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in Eulerian coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean Eulerian pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the Eulerian pressure. It is shown that the transformation between Lagrangian and Eulerian quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of finite deformation theory, which are defined in terms of the displacement gradients. Finite deformation theory leads to the result that for laterally unconfined, plane waves the Lagrangian and Eulerian radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the Lagrangian radiation pressure in the propagation direction is equal to (2K) and the BST result that the Eulerian radiation pressure in that direction is the momentum flux density.

Finite deformation theory↗
NASA NTRS1986

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗
NASA NTRS1989

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗
NASA NTRS2001

Legato: Personal Computer Software for Analyzing Pressure-Sensitive Paint Data

'Legato' is personal computer software for analyzing radiometric pressure-sensitive paint (PSP) data. The software is written in the C programming language and executes under Windows 95/98/NT operating systems. It includes all operations normally required to convert pressure-paint image intensities to normalized pressure distributions mapped to physical coordinates of the test article. The program can analyze data from both single- and bi-luminophore paints and provides for both in situ and a priori paint calibration. In addition, there are functions for determining paint calibration coefficients from calibration-chamber data. The software is designed as a self-contained, interactive research tool that requires as input only the bare minimum of information needed to accomplish each function, e.g., images, model geometry, and paint calibration coefficients (for a priori calibration) or pressure-tap data (for in situ calibration). The program includes functions that can be used to generate needed model geometry files for simple model geometries (e.g., airfoils, trapezoidal wings, rotor blades) based on the model planform and airfoil section. All data files except images are in ASCII format and thus are easily created, read, and edited. The program does not use database files. This simplifies setup but makes the program inappropriate for analyzing massive amounts of data from production wind tunnels. Program output consists of Cartesian plots, false-colored real and virtual images, pressure distributions mapped to the surface of the model, assorted ASCII data files, and a text file of tabulated results. Graphical output is displayed on the computer screen and can be saved as publication-quality (PostScript) files.

Schairer, Edward T.↗
DOE OSTI2020

Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

In this work, we develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that outperforms a Cartesian basis decomposition on rotated grids. The discretization is based on high order Summation-By-Parts (SBP) operators and preserves both symmetry and positive definiteness of the contravariant metric tensor. To improve accuracy and decrease computational cost, we also derive a modified discretization of the metric tensor that leads to a conditionally stable discretization. Bounds are derived that yield a point-wise condition that can be evaluated to check for stability of the modified discretization. This condition shows that the interpolation operators should be constructed such that their norm is close to one.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Electronic Absolute Cartesian Autocollimator

An electronic absolute Cartesian autocollimator performs the same basic optical function as does a conventional all-optical or a conventional electronic autocollimator but differs in the nature of its optical target and the manner in which the position of the image of the target is measured. The term absolute in the name of this apparatus reflects the nature of the position measurement, which, unlike in a conventional electronic autocollimator, is based absolutely on the position of the image rather than on an assumed proportionality between the position and the levels of processed analog electronic signals. The term Cartesian in the name of this apparatus reflects the nature of its optical target. Figure 1 depicts the electronic functional blocks of an electronic absolute Cartesian autocollimator along with its basic optical layout, which is the same as that of a conventional autocollimator. Referring first to the optical layout and functions only, this or any autocollimator is used to measure the compound angular deviation of a flat datum mirror with respect to the optical axis of the autocollimator itself. The optical components include an illuminated target, a beam splitter, an objective or collimating lens, and a viewer or detector (described in more detail below) at a viewing plane. The target and the viewing planes are focal planes of the lens. Target light reflected by the datum mirror is imaged on the viewing plane at unit magnification by the collimating lens. If the normal to the datum mirror is parallel to the optical axis of the autocollimator, then the target image is centered on the viewing plane. Any angular deviation of the normal from the optical axis manifests itself as a lateral displacement of the target image from the center. The magnitude of the displacement is proportional to the focal length and to the magnitude (assumed to be small) of the angular deviation. The direction of the displacement is perpendicular to the axis about which the mirror is slightly tilted. Hence, one can determine the amount and direction of tilt from the coordinates of the target image on the viewing plane.

Leviton, Douglas B.↗