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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Flow interaction experiment. Volume 1: Aerothermal modeling, phase 2

An experimental and computational study is reported for the flow of a turbulent jet discharging into a rectangular enclosure. The experimental configurations consisting of primary jets only, annular jets only, and a combination of annular and primary jets are investigated to provide a better understanding of the flow field in an annular combustor. A laser Doppler velocimeter is used to measure mean velocity and Reynolds stress components. Major features of the flow field include recirculation, primary and annular jet interaction, and high turbulence. A significant result from this study is the effect the primary jets have on the flow field. The primary jets are seen to create statistically larger recirculation zones and higher turbulence levels. In addition, a technique called marker nephelometry is used to provide mean concentration values in the model combustor. Computations are performed using three levels of turbulence closures, namely k-epsilon model, algebraic second moment (ASM), and differential second moment (DSM) closure. Two different numerical schemes are applied. One is the lower-order power-law differencing scheme (PLDS) and the other is the higher-order flux-spline differencing scheme (FSDS). A comparison is made of the performance of these schemes. The numerical results are compared with experimental data. For the cases considered in this study, the FSDS is more accurate than the PLDS. For a prescribed accuracy, the flux-spline scheme requires a far fewer number of grid points. Thus, it has the potential for providing a numerical error-free solution, especially for three-dimensional flows, without requiring an excessively fine grid. Although qualitatively good comparison with data was obtained, the deficiencies regarding the modeled dissipation rate (epsilon) equation, pressure-strain correlation model, and the inlet epsilon profile and other critical closure issues need to be resolved before one can achieve the degree of accuracy required to analytically design combustion systems.

Nikjooy, M.↗
NASA NTRS1993

Flow interaction experiment. Volume 2: Aerothermal modeling, phase 2

An experimental and computational study is reported for the flow of a turbulent jet discharging into a rectangular enclosure. The experimental configurations consisting of primary jets only, annular jets only, and a combination of annular and primary jets are investigated to provide a better understanding of the flow field in an annular combustor. A laser Doppler velocimeter is used to measure mean velocity and Reynolds stress components. Major features of the flow field include recirculation, primary and annular jet interaction, and high turbulence. A significant result from this study is the effect the primary jets have on the flow field. The primary jets are seen to create statistically larger recirculation zones and higher turbulence levels. In addition, a technique called marker nephelometry is used to provide mean concentration values in the model combustor. Computations are performed using three levels of turbulence closures, namely k-epsilon model, algebraic second moment (ASM), and differential second moment (DSM) closure. Two different numerical schemes are applied. One is the lower-order power-law differencing scheme (PLDS) and the other is the higher-order flux-spline differencing scheme (FSDS). A comparison is made of the performance of these schemes. The numerical results are compared with experimental data. For the cases considered in this study, the FSDS is more accurate than the PLDS. For a prescribed accuracy, the flux-spline scheme requires a far fewer number of grid points. Thus, it has the potential for providing a numerical error-free solution, especially for three-dimensional flows, without requiring an excessively fine grid. Although qualitatively good comparison with data was obtained, the deficiencies regarding the modeled dissipation rate (epsilon) equation, pressure-strain correlation model, and the inlet epsilon profile and other critical closure issues need to be resolved before one can achieve the degree of accuracy required to analytically design combustion systems.

Nikjooy, M.↗
NASA NTRS1993

Diversity reception for advanced multi-satellite networks: A CDMA approach

Diversity reception for Synchronous CDMA (S-CDMA) is introduced and analyzed. A Gaussian co-channel synchronous and asynchronous interference approximation is derived to evaluate the effects on the system bit error rate. Numerical results are provided for a simple mobile communication system where the signals transmitted by two distinct satellites in visibility are coherently combined by a three fingers Rake receiver. A second example showing performance of an integrated ground/satellite single frequency network for digital audio broadcasting is presented. Results show the capacity advantage of utilizing S-CDMA in combination with diversity reception.

Colzi, E.↗
NASA NTRS2001

High Order Numerical Simulation of Sound Generated by the Kirchhoff Vortex

An improved high order finite difference method for low Mach number computational aeroacoustics (CAA) is described. The improvements involve the conditioning of the Euler equations in perturbation form to minimize numerical cancellation error, and the use of a stable non-dissipative sixth-order central spatial differencing for the interior points and third-order at the boundary points. The spatial difference operator satisfies the summation-by-parts property to guarantee strict stability for linear hyperbolic systems. Spurious high frequency oscillations are damped by a third-order characteristic-based filter. The objective of this paper is to apply these improvements in the simulation of sound generated by the Kirchhoff vortex.

Mueller, Bernhard↗
NASA NTRS2004

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗
NASA NTRS2010

Integrating Radar Image Data with Google Maps

A public Web site has been developed as a method for displaying the multitude of radar imagery collected by NASA s Airborne Synthetic Aperture Radar (AIRSAR) instrument during its 16-year mission. Utilizing NASA s internal AIRSAR site, the new Web site features more sophisticated visualization tools that enable the general public to have access to these images. The site was originally maintained at NASA on six computers: one that held the Oracle database, two that took care of the software for the interactive map, and three that were for the Web site itself. Several tasks were involved in moving this complicated setup to just one computer. First, the AIRSAR database was migrated from Oracle to MySQL. Then the back-end of the AIRSAR Web site was updated in order to access the MySQL database. To do this, a few of the scripts needed to be modified; specifically three Perl scripts that query that database. The database connections were then updated from Oracle to MySQL, numerous syntax errors were corrected, and a query was implemented that replaced one of the stored Oracle procedures. Lastly, the interactive map was designed, implemented, and tested so that users could easily browse and access the radar imagery through the Google Maps interface.

Chapman, Bruce D.↗
NASA NTRS2012

Dual Accelerometer Usage Strategy for Onboard Space Navigation

This work introduces a dual accelerometer usage strategy for onboard space navigation. In the proposed algorithm the accelerometer is used to propagate the state when its value exceeds a threshold and it is used to estimate its errors otherwise. Numerical examples and comparison to other accelerometer usage schemes are presented to validate the proposed approach.

Zanetti, Renato↗
NASA NTRS2014

Lunar Reconnaissance Orbiter Orbit Determination Accuracy Analysis

Results from operational OD produced by the NASA Goddard Flight Dynamics Facility for the LRO nominal and extended mission are presented. During the LRO nominal mission, when LRO flew in a low circular orbit, orbit determination requirements were met nearly 100% of the time. When the extended mission began, LRO returned to a more elliptical frozen orbit where gravity and other modeling errors caused numerous violations of mission accuracy requirements. Prediction accuracy is particularly challenged during periods when LRO is in full-Sun. A series of improvements to LRO orbit determination are presented, including implementation of new lunar gravity models, improved spacecraft solar radiation pressure modeling using a dynamic multi-plate area model, a shorter orbit determination arc length, and a constrained plane method for estimation. The analysis presented in this paper shows that updated lunar gravity models improved accuracy in the frozen orbit, and a multiplate dynamic area model improves prediction accuracy during full-Sun orbit periods. Implementation of a 36-hour tracking data arc and plane constraints during edge-on orbit geometry also provide benefits. A comparison of the operational solutions to precision orbit determination solutions shows agreement on a 100- to 250-meter level in definitive accuracy.

Gravitation↗
NASA NTRS2023

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier-Stokes (RANS) equations are solved using turbulence modeling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been achieved to realize similar performance with two-equation models of the k-w type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k-w type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically renewed mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus, numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the turbulence model. Additionally, in this paper, analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Turbulence↗
NASA NTRS2002

Finite Element A Posteriori Error Estimation for Heat Conduction

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

Lang, Christapher G.↗
NASA NTRS1993

Fourier analysis of numerical algorithms for the Maxwell equations

The Fourier method is used to analyze the dispersive, dissipative, and isotropy errors of various spatial and time discretizations applied to the Maxwell equations on multi-dimensional grids. Both Cartesian grids and non-Cartesian grids based on hexagons and tetradecahedra are studied and compared. The numerical errors are quantitatively determined in terms of phase speed, wave number, propagation direction, gridspacings, and CFL number. The study shows that centered schemes are more efficient than upwind schemes. The non-Cartesian grids yield superior isotropy and higher accuracy than the Cartesian ones. For the centered schemes, the staggered grids produce less errors than the unstaggered ones. A new unstaggered scheme which has all the best properties is introduced. The study also demonstrates that a proper choice of time discretization can reduce the overall numerical errors due to the spatial discretization.

Liu, Yen↗
NASA NTRS2004

Prototype Development of a Geostationary Synthetic Thinned Aperture Radiometer, GeoSTAR

Preliminary details of a 2-D synthetic aperture radiometer prototype operating from 50 to 58 GHz will be presented. The instrument is being developed as a laboratory testbed, and the goal of this work is to demonstrate the technologies needed to do atmospheric soundings with high spatial resolution from Geostationary orbit. The concept is to deploy a large sparse aperture Y-array from a geostationary satellite, and to use aperture synthesis to obtain images of the earth without the need for a large mechanically scanned antenna. The laboratory prototype consists of a Y-array of 24 horn antennas, MMIC receivers, and a digital cross-correlation sub-system. System studies are discussed, including an error budget which has been derived from numerical simulations. The error budget defines key requirements, such as null offsets, phase calibration, and antenna pattern knowledge. Details of the instrument design are discussed in the context of these requirements.

aperture synthesis↗
NASA NTRS1983

N-person differential games. Part 2: The penalty method

The equilibrium strategy for N-person differential games can be found by studying a min-max problem subject to differential systems constraints. The differential constraints are penalized and finite elements are used to compute numerical solutions. Convergence proof and error estimates are given. Numerical results are also included and compared with those obtained by the dual method.

Chen, G.↗
NASA NTRS1983

A numerical method based on the Fourier-Fourier transform approach for modeling 1-D electron plasma evolution

A numerical method is presented for studying one-dimensional electron plasma evolution under typical interplanetary conditions. The method applies the Fourier-Fourier transform approach to a plasma model that is a generalization of the electrostatic Vlasov-Poisson system of equations. Conservation laws that are modified to include the plasma model generalization and also the boundary effects of nonperiodic solutions are given. A new conservation law for entropy in the transformed space is then introduced. These conservation laws are used to verify the numerical solutions. A discretization error analysis is presented. Two numerical instabilities and the methods used for their suppression are treated. It is shown that in interplanetary plasma conditions, the bump-on-tail instability produces significant excitation of plasma oscillations at the Bohm-Gross frequency and its second harmonic. An explanation of the second harmonic excitation is given in terms of wave-wave coupling during the growth phase of the instability.

Klimas, A. J.↗
NASA NTRS1993

Advanced adaptive computational methods for Navier-Stokes simulations in rotorcraft aerodynamics

A phase 2 research and development effort was conducted in area transonic, compressible, inviscid flows with an ultimate goal of numerically modeling complex flows inherent in advanced helicopter blade designs. The algorithms and methodologies therefore are classified as adaptive methods, which are error estimation techniques for approximating the local numerical error, and automatically refine or unrefine the mesh so as to deliver a given level of accuracy. The result is a scheme which attempts to produce the best possible results with the least number of grid points, degrees of freedom, and operations. These types of schemes automatically locate and resolve shocks, shear layers, and other flow details to an accuracy level specified by the user of the code. The phase 1 work involved a feasibility study of h-adaptive methods for steady viscous flows, with emphasis on accurate simulation of vortex initiation, migration, and interaction. Phase 2 effort focused on extending these algorithms and methodologies to a three-dimensional topology.

Stowers, S. T.↗