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NASA NTRS1975

Upwind second-order difference schemes and applications in unsteady aerodynamic flows

Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock waves. The general utility of the operational approach for combining schemes is emphasized by deriving a second-order conservative scheme for the steady transonic small-disturbance potential equation.

Warming, R. F.↗

NASA NTRS1980

Free-stream disturbance, continuous Eigenfunctions, boundary-layer instability and transition

A rational foundation is presented for the application of the linear shear flows to transition prediction, and an explicit method is given for carrying out the necessary calculations. The expansions used are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbances in the inner boundary layer, near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer in that the amplitudes of the discrete Tollmien-Schlicting waves are an extremely small fraction of the amplitude of the disturbance.

Grosch, C. E.↗

NASA NTRS1981

Theoretical and experimental supersonic lateral-directional stability characteristics

A program has been initiated at NASA Langley Research Center to assess several methods for estimation of lateral-directional stability. As a basis for comparison, experimental data are presented for a simple wing-body vertical tail configuration. The methods for estimating the characteristics include a second-order shock expansion and panel method (MISLIFT), a slender body and 'first-order' panel method (APAS), and a 'higher-order' panel method for linearized supersonic flow (PAN AIR). The results show that PAN AIR provides accurate estimates of these characteristics at moderate angles of attack for complete configurations with either single or twin vertical tails. APAS provides estimates for complete configurations at zero angle of attack. However, MISLIFT only provides estimates for the simplest body-vertical tail configurations at zero angle of attack.

Lamb, M.↗

NASA NTRS1985

A theoretical basis for extending surface-paneling methods to transonic flow

The surface integral terms in Green's third identity are often used to solve the Prandtl-Glauert (linear potential-flow) equation with panel methods. This can be done, as in the PAN AIR code, for either subsonic or supersonic flow about complete aircraft. The extension to transonic flow is suggested by the volume integral terms of Green's third identity. The mathematical basis for this extension, without the use of body-fitted grids, is presented. Supercritical transonic results computed from a two-dimensional transonic PAN AIR research code demonstrate the method.

Erickson, L. L.↗

NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗

NASA NTRSDate not supplied

Verification and Validation of Progressive Damage and Failure Analysis Methods for Intralaminar Failure Modes in Thermoplastic Composites

Current progressive damage and failure analysis (PDFA) methods were developed around thermoset material systems and their physical behavior. However, the applicability of these analysis methods has not been evaluated for use in modeling thermoplastic material systems. As part of the Hi-Rate Composite Aircraft Manufacturing (HiCAM) Project sponsored by NASA, intralaminar failure characterization was completed on a thermoplastic material system, AS4D/PEKK-FC, with off-axis tension (OAT) and off-axis compression (OAC) testing. The experiments were able to capture matrix non-linear shear behavior and the failure envelope of the material system. Two PDFA methods, LS-DYNA MAT299 and NASA’s CompDam-DGD, were then employed to simulate individual coupon behavior and simulation results were compared to published verification and validation guidelines from the CMH-17 crashworthiness working group. The results found that the two modeling methods provided suitable representation of material behavior of thermoplastics.

PDFA↗

NASA NTRSDate not supplied

Verification and Validation of Progressive Damage and Failure Analysis Methods for Intralaminar Failure Modes in Thermoplastic Composites

PDFA↗

NASA NTRS1984

Control of large flexible spacecraft by the independent modal-space control method

The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes.

Meirovitch, L.↗

NASA NTRS1976

Some inconsistencies of the finite element method as applied to inelastic response

The inadequacy of a two noded beam-column element with a linear axial and a cubic transverse displacement field for inelastic analysis is demonstrated. For complete equilibrium satisfaction in the linear elastic range a three noded beam-column element is shown to be consistent. Next, the sensitivity of the inelastic response to numerical solutions of the inelastic response of a cantilever beam resulting from approximate integration of strain energy are brought out and finally, consequences of this on the nonlinear transient response of structures are considered.

Kamat, M. P.↗

NASA NTRS1974

Calculation of unsteady transonic aerodynamics for oscillating wings with thickness (computer program)

A computer program has been developed to account approximately for the effects of finite wing thickness in the transonic potential flow over an oscillating wing of finite span. The program is based on the original sonic-box program of Rodemich and Andrew, and accounts for the nonuniform flow caused by finite thickness by application of the local linearization concept. A brief description of each subroutine is given, and the method of input is shown in detail. A sample problem as well as a complete listing of the computer program are presented.

Ruo, S. Y.↗

NASA NTRS1994

A grid generation and flow solution method for the Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Anderson, W. Kyle↗

NASA NTRS1976

Simplified solution for point contact deformation between two elastic solids

A linear-regression by the method of least squares is made on the geometric variables that occur in the equation for point contact deformation. The ellipticity and the complete eliptic integrals of the first and second kind are expressed as a function of the x, y-plane principal radii. The ellipticity was varied from 1 (circular contact) to 10 (a configuration approaching line contact). These simplified equations enable one to calculate easily the point-contact deformation to within 3 percent without resorting to charts or numerical methods.

Brewe, D. E.↗

NASA NTRS1980

Free-stream disturbances, continuous eigenfunctions, boundary-layer instability and transition

A rational foundation is provided for the application of the linear stability theory of parallel shear flows to transition prediction. An explicit method is given for carrying out the necessary calculations. The expansions are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbance in the inner boundary layer near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer, in that the amplitudes of the discrete Tollmein-Schlichting waves are an extremely small fraction of the amplitude of the disturbance.

Salwen, H.↗

NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗

NASA NTRS2018

Realistic Covariance Generation for the GPM Spacecraft

A covariance realism process for NASA's Global Precipitation Measurement (GPM) spacecraft is detailed. The GPM spacecraft is in a low earth orbit, and performs collision avoidance maneuvers few times a year. Currently GPM is below the International Space Station (ISS). So, in addition to cataloged debris objects, GPM must contend with smallsat/cubesat objects that are deployed from the ISS. Both operational scenarios require complete knowledge of the expected GPM prediction errors as a function of time. In this study, we present a method for generating realistic predicted covariance that uses linear propagation of the covariance with the addition of process noise. Further analyses are presented for the process noise ''tuning'' that generates an inflation factor based on the observed error statistics of the predictive satellite trajectories when compared to the definitive ones. Different tuning strategies are considered and compared via a Goodness-of-Fit testing for the Gaussian properties of the scaled covariance. SpaceNav's realistic covariance generation approach takes into account the contribution of predicted maneuver errors in the increased propagation uncertainty. Corresponding maneuver uncertainty is injected into the state uncertainty, and is used within the collision avoidance process to determine the collision risk for close approach events that follow a maneuver. This is a critical step in the maneuver planning process that provides the satellite operator with an accurate quantification of the collision probability for planned maneuvers. Using this information, an informed decision can be made to proceed with a maneuver if the collision risk is acceptable. This approach is validated by Monte-Carlo simulations and results are presented.

spacecraft uncertainty propagation↗

NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. IV: Coherent Backscattering

The problem of backscattering of light by a discrete random medium illuminated by an obliquely incident plane electromagnetic wave is considered.The analysis is performed in a linear-polarization basis and includes a complete derivation of the cross reflection matrix for a layer with densely and sparsely distributed particles, the design of an approximate method for computing the ladder and cross reflection matrices in the case of a semi-infinite medium with a sparse distribution of particles, the derivation of the relations between the elements of the ladder and cross reflection matrices in the exact backscattering direction for dense and sparse media, and the development of practical algorithms for solving the underlying integral equations by the method of Picard iterations and the discrete ordinate method. Simulation results for particles with large size parameters are also presented.

Adrian Doicu↗

NASA NTRS1967

Computer program provides linear sampled- data analysis for high order systems

Computer program performs transformations in the order S-to W-to Z to allow arithmetic to be completed in the W-plane. The method is based on a direct transformation from the S-plane to the W-plane. The W-plane poles and zeros are transformed into Z-plane poles and zeros using the bilinear transformation algorithm.

Bunn, D. B.↗

NASA NTRS1975

Initialization procedures for primitive equation models

A linear analysis and comparison of the damping properties of six dynamic initialization schemes is presented, indicating that the Okamura-Rivas scheme has the most efficient damping properties over the whole frequency range, and suggesting that it should be faster than the other methods and given more stable results. The results obtained with a nonlinear shallow water equations model agree well with the linear analysis. The Okamura-Rivas scheme attains complete balance in the equivalent of 5 to 6 hours of leapfrog forecasting, and requires in this model an order of magnitude less computation than the balance equation solution.

Grant, W. K. F.↗