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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 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Numerical methods for the calculation of three-dimensional nozzle exhaust flow fields

Numerical codes developed for the calculation of three-dimensional nozzle exhaust flow fields associated with hypersonic airbreathing aircraft are described. Both codes employ reference plane grid networks with respect to three coordinate systems. Program CHAR3D is a characteristic code utilizing a new wave preserving network within the reference planes, while program BIGMAC is a finite difference code utilizing conservation variables and a one-sided difference algorithm. Secondary waves are numerically captured by both codes, while the underexpansion shock and plume boundary are treated discretely. The exhaust gas properties consist of hydrogen-air combustion product mixtures in local chemical equilibrium. Nozzle contours are treated by a newly developed geometry package based on dual cubic splines. Results are presented for simple configurations demonstrating two- and three-dimensional multiple wave interactions.

Dash, S. M.↗
NASA NTRS1993

Liquid propellant rocket engine combustion simulation with a time-accurate CFD method

Time-accurate computational fluid dynamics (CFD) algorithms are among the basic requirements as an engineering or research tool for realistic simulations of transient combustion phenomena, such as combustion instability, transient start-up, etc., inside the rocket engine combustion chamber. A time-accurate pressure based method is employed in the FDNS code for combustion model development. This is in connection with other program development activities such as spray combustion model development and efficient finite-rate chemistry solution method implementation. In the present study, a second-order time-accurate time-marching scheme is employed. For better spatial resolutions near discontinuities (e.g., shocks, contact discontinuities), a 3rd-order accurate TVD scheme for modeling the convection terms is implemented in the FDNS code. Necessary modification to the predictor/multi-corrector solution algorithm in order to maintain time-accurate wave propagation is also investigated. Benchmark 1-D and multidimensional test cases, which include the classical shock tube wave propagation problems, resonant pipe test case, unsteady flow development of a blast tube test case, and H2/O2 rocket engine chamber combustion start-up transient simulation, etc., are investigated to validate and demonstrate the accuracy and robustness of the present numerical scheme and solution algorithm.

Chen, Y. S.↗
NASA NTRS1990

Constructing second-order structural models with specified mass submatrix condition numbers

This paper presents a simple new algorithm for constructing second-order models for any given flexible structure, with these models satisfying the constraint that each leading principal submatrix of the mass matrix must have a specified condition number. Now, the effects of rounding errors in practical computation generally increase with increasing condition number, i.e. as the matrix considered approaches singularity. Thus, the new models should prove useful for the systematic testing of the numerical properties of many algorithms in the dynamics and control of flexible structures.

Williams, T.↗
NASA NTRS1986

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

Chen, Y. S.↗
NASA NTRS1984

A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.

Radhakrishnan, K.↗
DOE OSTI2024

Solving the homogeneous Bethe-Salpeter equation with a quantum annealer

The homogeneous Bethe-Salpeter equation (hBSE), describing a bound system in a genuinely relativistic quantum-field theory framework, was solved for the first time by using a D-Wave quantum annealer. After applying standard techniques of discretization, the hBSE, in ladder approximation, can be formally transformed in a generalized eigenvalue problem (GEVP), with two square matrices: one symmetric and the other nonsymmetric. The latter matrix poses the challenge of obtaining a suitable formal approach for investigating the GEVP by means of a quantum annealer, i.e., to recast it as a quadratic unconstrained binary optimization problem. A broad numerical analysis of the proposed algorithms, applied to matrices of dimension up to 64, was carried out by using both the simulated-annealing package and the D-Wave . The numerical results very nicely compare with those obtained with standard classical algorithms, and also show interesting scalability features. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

Algorithms For Integrating Nonlinear Differential Equations

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

Freed, A. D.↗
NASA NTRS2012

Physics of Acoustic Radiation from Jet Engine Inlets

Numerical simulations of acoustic radiation from a jet engine inlet are performed using advanced computational aeroacoustics (CAA) algorithms and high-quality numerical boundary treatments. As a model of modern commercial jet engine inlets, the inlet geometry of the NASA Source Diagnostic Test (SDT) is used. Fan noise consists of tones and broadband sound. This investigation considers the radiation of tones associated with upstream propagating duct modes. The primary objective is to identify the dominant physical processes that determine the directivity of the radiated sound. Two such processes have been identified. They are acoustic diffraction and refraction. Diffraction is the natural tendency for an acoustic wave to follow a curved solid surface as it propagates. Refraction is the turning of the direction of propagation of sound waves by mean flow gradients. Parametric studies on the changes in the directivity of radiated sound due to variations in forward flight Mach number and duct mode frequency, azimuthal mode number, and radial mode number are carried out. It is found there is a significant difference in directivity for the radiation of the same duct mode from an engine inlet when operating in static condition and in forward flight. It will be shown that the large change in directivity is the result of the combined effects of diffraction and refraction.

Tam, Christopher K. W.↗
NASA NTRS1991

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗
NASA NTRS1990

Entry vehicle performance analysis and atmospheric guidance algorithm for precision landing on Mars

Future missions to Mars may require pin-point landing precision, possibly on the order of tens of meters. The ability to reach a target while meeting a dynamic pressure constraint to ensure safe parachute deployment is complicated at Mars by low atmospheric density, high atmospheric uncertainty, and the desire to employ only bank angle control. The vehicle aerodynamic performance requirements and guidance necessary for 0.5 to 1.5 lift drag ratio vehicle to maximize the achievable footprint while meeting the constraints are examined. A parametric study of the various factors related to entry vehicle performance in the Mars environment is undertaken to develop general vehicle aerodynamic design requirements. The combination of low lift drag ratio and low atmospheric density at Mars result in a large phugoid motion involving the dynamic pressure which complicates trajectory control. Vehicle ballistic coefficient is demonstrated to be the predominant characteristic affecting final dynamic pressure. Additionally, a speed brake is shown to be ineffective at reducing the final dynamic pressure. An adaptive precision entry atmospheric guidance scheme is presented. The guidance uses a numeric predictor-corrector algorithm to control downrange, an azimuth controller to govern crossrange, and analytic control law to reduce the final dynamic pressure. Guidance performance is tested against a variety of dispersions, and the results from selected tests are presented. Precision entry using bank angle control only is demonstrated to be feasible at Mars.

Dieriam, Todd A.↗
NASA NTRS1989

Stable Kalman filters for processing clock measurement data

Kalman filters have been used for some time to process clock measurement data. Due to instabilities in the standard Kalman filter algorithms, the results have been unreliable and difficult to obtain. During the past several years, stable forms of the Kalman filter have been developed, implemented, and used in many diverse applications. These algorithms, while algebraically equivalent to the standard Kalman filter, exhibit excellent numerical properties. Two of these stable algorithms, the Upper triangular-Diagonal (UD) filter and the Square Root Information Filter (SRIF), have been implemented to replace the standard Kalman filter used to process data from the Deep Space Network (DSN) hydrogen maser clocks. The data are time offsets between the clocks in the DSN, the timescale at the National Institute of Standards and Technology (NIST), and two geographically intermediate clocks. The measurements are made by using the GPS navigation satellites in mutual view between clocks. The filter programs allow the user to easily modify the clock models, the GPS satellite dependent biases, and the random noise levels in order to compare different modeling assumptions. The results of this study show the usefulness of such software for processing clock data. The UD filter is indeed a stable, efficient, and flexible method for obtaining optimal estimates of clock offsets, offset rates, and drift rates. A brief overview of the UD filter is also given.

Clements, P. A.↗
NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗
NASA NTRS1988

Analysis of long term heart rate variability: methods, 1/f scaling and implications

The use of spectral techniques to quantify short term heart rate fluctuations on the order of seconds to minutes has helped define the autonomic contributions to beat-to-beat control of heart rate. We used similar techniques to quantify the entire spectrum (0.00003-1.0 Hz) of heart rate variability during 24 hour ambulatory ECG monitoring. The ECG from standard Holter monitor recordings from normal subjects was sampled with the use of a phase locked loop, and a heart rate time series was constructed at 3 Hz. Frequency analysis of the heart rate signal was performed after a nonlinear filtering algorithm was used to eliminate artifacts. A power spectrum of the entire 24 hour record revealed power that was inversely proportional to frequency, 1/f, over 4 decades from 0.00003 to 0.1 Hz (period approximately 10 hours to 10 seconds). Displaying consecutive spectra calculated at 5 minute intervals revealed marked variability in the peaks at all frequencies throughout the 24 hours, probably accounting for the lack of distinct peaks in the spectra of the entire records.

Non-NASA Center↗
NASA NTRS1987

Comparison of two numerical techniques for aerodynamic model identification

An algorithm, called the Minimal Residual QR algorithm, is presented to solve subset regression problems. It is shown that this scheme can be used as a numerically reliable implementation of the stepwise regression technique, which is widely used to identify an aerodynamic model from flight test data. This capability as well as the numerical superiority of this scheme over the stepwise regression technique is demonstrated in an experimental simulation study.

Verhaegen, M. H.↗
DOE OSTI2026

A simple fourth order propagator based on the Magnus expansion in the Liouville space: Application to a Λ-system and assessment of the rotating wave approximation

A simple fourth-order propagator [Ture and Jang, J. Phys. Chem. A 128, 2871 (2024)] based on the Magnus expansion is extended to the Liouville space for both closed-system and Lindbladian open-system quantum dynamics. For both dynamics, commutator free versions of fourth-order propagators are provided as well. These propagators are then applied to the dynamics of a driven Λ-system, where Lindblad terms represent the effect of a photonic bath. For both dynamics, the accuracy of the rotating wave approximation (RWA) for the matter–radiation interaction is assessed. We confirmed reasonable performance of RWA for weak and resonant fields. However, small errors appear for moderate fields and substantial errors can be found for strong fields where coherent population trapping can still be expected. We also found that the presence of bath for open-system quantum dynamics consistently reduces the errors of the RWA. These results provide quantitative information on how the RWA breaks down beyond weak field or for non-resonant cases. Major results are benchmarked against results of our sixth-order ME-based propagator. Finally, we also provide numerical comparison of our algorithms with other fourth-order algorithms for the Λ-system. These confirm reasonable performance of our simple propagators and the improvement gained through commutator-free expressions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1996

Multigrid with Overlapping Patches

Solving boundary value problems with optimal efficiency requires adaptivity and multilevel techniques. Previously, an implementation of the AFACx algorithm is presented that is based on rectangular Cartesian grids. This implementation does not allow for the over]ap of grids that lie on the same level of refinement. We investigate the case in which these grids overlap. A standard technique for overlapping grids is the Schwarz algorithm. Some ways of using the Schwarz algorithm in a standard multigrid scheme are presented. Also, a problem that arises in some situations with non-aligned, overlapping grids is described. This situation comes up in a natural way when the Schwarz algorithm is used as a relaxation scheme within a multilevel algorithm. We identify the reason for the bad convergence and show that by more sophisticated interpolation the difficulties can be overcome. Then we present a multiplicative Schwarz algorithm for a large number of grids that has a high potential for parallelization. Finally we give some numerical results for the FACx algorithm with overlapping grids on each refinement level. The implementation of the described codes uses C++ and the array class libraries A++ and P++. Using the A++/P++ programming environment, it was possible to move from a serial code to a parallel code within a few days.

Berndt, Markus↗
NASA NTRS1978

Transonic lifting line theory - Numerical procedure for shock-free flows

An algorithm for computing transonic lifting-line theory without shocks is presented; the numerical procedure relies on two-dimensional analyses developed to solve inviscid flow equations for slender airfoils. From a series of solutions to two-dimensional problems in which span effects appear parametrically, the three-dimensional potential field characterization is obtained. Numerical results are given for a lifting wing with an elliptic (spanwise) distribution of chord and a NACA-0012 cross section (a freestream Mach number of 0.63 and an angle of attack of 2 deg are assumed).

Small, R. D.↗
NASA NTRS1988

In-flight determination of spacecraft magnetic bias independent of attitude

A simple algorithm for the in-flight determination of the magnetic bias of a spacecraft is presented. The algorithm, developed for use during the Hubble Space Telescope mission, determines this bias independently of any attitude estimates and requires no spacecraft sensor data other than that from the spacecraft magnetometer(s). Estimates of the algorithm's accuracy and results from a number of numerical studies on the use of this algorithm are also presented.

Davenport, P. B.↗