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NASA NTRS1987

Inverse problems in the modeling of vibrations of flexible beams

The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented.

Banks, H. T.↗

NASA NTRS1993

Computational analysis of methods for reduction of induced drag

The purpose of this effort was to perform a computational flow analysis of a design concept centered around induced drag reduction and tip-vortex energy recovery. The flow model solves the unsteady three-dimensional Euler equations, discretized as a finite-volume method, utilizing a high-resolution approximate Riemann solver for cell interface flux definitions. The numerical scheme is an approximately-factored block LU implicit Newton iterative-refinement method. Multiblock domain decomposition is used to partition the field into an ordered arrangement of blocks. Three configurations are analyzed: a baseline fuselage-wing, a fuselage-wing-nacelle, and a fuselage-wing-nacelle-propfan. Aerodynamic force coefficients, propfan performance coefficients, and flowfield maps are used to qualitatively access design efficacy. Where appropriate, comparisons are made with available experimental data.

Janus, J. M.↗

NASA NTRS1966

Solutions of differential equations by evaluations of functions.

Runge-Kutta fourth order formula used to obtain approximate solution to differential equations

RUNGE-KUTTA INTEGRATION↗

NASA NTRS1994

Navier-Stokes, flight, and wind tunnel flow analysis for the F/A-18 aircraft

Computational analysis of flow over the F/A-18 aircraft is presented along with complementary data from both flight and wind tunnel experiments. The computational results are based on the three-dimensional thin-layer Navier-Stokes formulation and are obtained from an accurate surface representation of the fuselage, leading-edge extension (LEX), and the wing geometry. However, the constraints imposed by either the flow solver and/or the complexity associated with the flow-field grid generation required certain geometrical approximations to be implemented in the present numerical model. In particular, such constraints inspired the removal of the empennage and the blocking (fairing) of the inlet face. The results are computed for three different free-stream flow conditions and compared with flight test data of surface pressure coefficients, surface tuft flow, and off-surface vortical flow characteristics that included breakdown phenomena. Excellent surface pressure coefficient correlations, both in terms of magnitude and overall trend, are obtained on the forebody throughout the range of flow conditions. Reasonable pressure agreement was obtained over the LEX; the general correlation tends to improve at higher angles of attack. The surface tuft flow and the off-surface vortex flow structures compared qualitatively well with the flight test results. To evaluate the computational results, a wind tunnel investigation was conducted to determine the effects of existing configurational differences between the flight vehicle and the numerical model on aerodynamic characteristics. In most cases, the geometrical approximations made to the numerical model had very little effect on overall aerodynamic characteristics.

Ghaffari, Farhad↗

NASA NTRS1994

A test of the adhesion approximation for gravitational clustering

We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Melott, Adrian L.↗

NASA NTRS2005

Reliability-Based Control Design for Uncertain Systems

This paper presents a robust control design methodology for systems with probabilistic parametric uncertainty. Control design is carried out by solving a reliability-based multi-objective optimization problem where the probability of violating design requirements is minimized. Simultaneously, failure domains are optimally enlarged to enable global improvements in the closed-loop performance. To enable an efficient numerical implementation, a hybrid approach for estimating reliability metrics is developed. This approach, which integrates deterministic sampling and asymptotic approximations, greatly reduces the numerical burden associated with complex probabilistic computations without compromising the accuracy of the results. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.

Crespo, Luis G.↗

NASA NTRS1985

Factorization and reduction methods for optimal control of distributed parameter systems

A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.

Burns, J. A.↗

NASA NTRS1986

Convection in the vertical midplane of a horizontal cylinder Comparison of two-dimensional approximations with three-dimensional results

Experimental results and numerical data on the flow characteristics of core-driven and boundary-layer-driven regimes (CDRs) and (BLDRs) are compared to two-dimensional solutions for heated convective flow in the vertical midplane of a horizontal cylinder. The data were obtained from laser Doppler velocimetry (LDA) measurements and from three-dimensional numerical solutions. It is shown that the approximate solutions gave the correct Rayleigh-number-dependences and distributions for the velocities in the CDR and BLDR regimes. However, the transition between the CDR and the BLDR, as well as the magnitude of the distribution of velocity components, were found to be dependent on the type of two-dimensional approximation selected. In the case of CDR, core velocities were overestimated by as much as 30 percent by the two-dimensional approximations; and in the case of BLDR, the core velocities were overestimated by 40-50 percent as compared to the measured velocities. A schematic illustration of the flow patterns in the cylinder is provided.

Bontoux, P.↗

NASA NTRS2018

Tetrahedral-Mesh Simulations of Shock-Turbulence Interaction

Despite decades of development of unstructured mesh methods, direct numerical simulations (DNS) of turbulent flows are still predominantly performed on structured or unstructured hexahedral meshes with high-order finite-difference methods, weighted essentially nonoscillatory (WENO) schemes, or hybrid schemes formed by their combinations. Tetrahedral meshes offer easy mesh generation and adaptation around complex geometries and the potential of an orientation-free grid that would benefit the isotropic nature of small-scale dissipation, as well as the solution accuracy of intermediate scales. To advance the state of the art of unstructured-mesh simulation capabilities for shock/turbulence interaction, DNS using pure tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method in this research. By its design, the CESE method is constructed based on a non-dissipative scheme and is a genuinely multidimensional numerical framework that is free from the use of an approximate Riemann-solver. The numerical framework also provides the ability to add numerical dissipation (the nondissipative scheme acts as the reference state like that of the reversible state in thermodynamics) when needed (with justification from mathematics/physics). The above-mentioned features along with the CESE method's consistent shock-capturing approach and strong enforcement of flux conservation in spacetime offers a novel method to accurately simulate turbulent flows and their interaction with shocks using tetrahedral meshes. Two canonical problems, namely, isotropic turbulence interaction with a normal shock and a Mach 2.9 turbulent boundary layer flow over a 24deg compression corner are investigated in this study. Computational results show reasonably good agreement with experimental data and results from structured-mesh, high-order simulations available in the literature. Successful validation of these canonical problems demonstrated here paves the way for future high-fidelity supersonic flow simulations involving complex-geometries.

Venkatachari, Balaji Shankar↗

NASA NTRS1983

Parameter identification in continuum models

Approximation techniques for use in numerical schemes for estimating spatially varying coefficients in continuum models such as those for Euler-Bernoulli beams are discussed. The techniques are based on quintic spline state approximations and cubic spline parameter approximations. Both theoretical and numerical results are presented.

Banks, H. T.↗

NASA NTRS1983

Parameter identification in continuum models

Banks, H. T.↗

NASA NTRS1984

Stability and Convergence of Underintegrated Finite Element Approximations

The effects of underintegration on the numerical stability and convergence characteristics of certain classes of finite element approximations were analyzed. Particular attention is given to hourglassing instabilities that arise from underintegrating the stiffness matrix entries and checkerboard instabilities that arise from underintegrating constrain terms such as those arising from incompressibility conditions. A fundamental result reported here is the proof that the fully integrated stiffness is restored in some cases through a post-processing operation.

Oden, J. T.↗

NASA NTRS1979

Population statistics of faint stellar and non-stellar objects

A disc and halo population model is constructed to fit star counts and color data down to V approximately 23 at absolute value of b = 90 deg. This model is used to predict star counts and colors down to V approximately 30. Deviations from these extrapolated relationships provide constraints on the number of faint quasars and black dwarf stars. It is shown that extra-galactic globular clusters start contributing significantly to star counts at V approximately 25 and are more numerous than stars for V 31. Morphological studies of galaxies with approximately 0.5, were made with the space telescope. Significant constraints on theoretical models that describe the evolution of clusters of galaxies are provided.

Vandenbergh, S.↗

NASA NTRS1992

An implicit Navier-Stokes code for turbulent flow modeling

This paper presents a numerical approach to calculating turbulent flows employing advanced turbulence models. The main features include a line-by-line Gauss-Seidel algorithm using Roe's approximate Riemann solver, TVD numerical schemes, implicit boundary conditions and a decoupled turbulence-model solver. Based on the problems tested so far, the method has consistently demonstrated its ability in offering accuracy, boundedness and a fast rate of convergence to steady-state solution.

Huang, P. G.↗

NASA NTRS2003

MHD Turbulence at Moderate Magnetic Reynolds Number

In the present article we will consider the decay of MHD turbulence under the influence of a strong external magnetic field at moderate magnetic Reynolds numbers. Typical values of R(sub m) that are considered here range from R(sub m) approx. 0.1 to R(sub m) approx. 20. As a comparison, the initial kinetic Reynolds number common to all our simulations is Re(sub L) = 199. This means that the range of Prandtl numbers explored is 5 x 10(exp -4) to 10(exp -1). Our motivation is mainly to exhibit how the transition from the QS approximation to FMHD occurs. At the lowest values of R(sub m) studied here, the QS approximation is shown to model the flow faithfully. However, for the higher values of R(sub m) considered, it is clearly inadequate but can be replaced by another approximation which will be referred to as the Quasi-Linear (QL) approximation. Another objective of the present study is to describe how variations in the magnetic Reynolds number (while maintaining all other parameters constant) affect the dynamics of the flow. This complements past studies where variations in either the strength of the external magnetic field or the kinetic Reynolds number were considered. This article is organized as follows. In section 2 we recall the definition of the quasi-static approximation. Section 3 is devoted to the description of the numerical experiments performed using the quasi-static approximation and full MHD. In section 4 we describe the quasi-linear approximation and test it numerically against full MHD. A concluding summary is given in section 5.

Knaepen, B.↗

NASA NTRS1991

An efficient method for estimating neighboring steady-state numerical solutions to the Euler equations

The paper concentrates on a linear approximation method for predicting the changes occurring in steady-state numerical solutions of the Euler equations as a consequence of small changes in the independent variables which control the problem. The importance of proper boundary-condition treatment and other issues concerning the problem are covered along with the importance of proper algorithm selection for a fully supersonic inviscid flow. The method is applied to a subsonic nozzle involving variation of the pressure on the outflow boundary and to a supersonic inlet involving variation of the inflow Mach number. In the subsonic test case, the comparisons between the predicted and conventional numerical solutions are shown to be good, while in the supersonic test case, the agreement between the approximation method and conventional numerical solution starts out well but rapidly degenerates at some point in the flowfield as the perturbation of the boundary conditions is increased.

Taylor, Arthur C., III↗

NASA NTRS1973

Nonlinear vibrations of rectangular plates.

A finite-difference method is developed to determine the large amplitude dynamic responses of thin elastic plates subjected to uniform pressure pulse-type loads. Four different sets of boundary conditions are considered. Some specific problems are solved. The results are compared with approximate solutions obtained by Yamaki (1961). The numerical method presented provides an accurate and efficient approximate solution to the problem, and should be useful as a check on other approximate methods. The grid-size and the time-step necessary for obtaining numerical stability depend on the particular problem. For many cases the method converges rapidly and a rather large grid-size and time-step is adequate.

Bayles, D. J.↗

NASA NTRS1990

A numerical study of the separation wavenumber in the two-scale scattering approximation

The choice of the separation wavenumber Kd for the two-scale scattering approximation is examined by the comparison of two-scale calculations with exact numerical solutions using the moment method. It was found that the optimal choice of Kd is near k/2 when attempting to optimize for all incidence angles. When optimizing for specific incidence angles, Kd varied from k/5 at low incidence angles to just below k at higher incidence angles. These numerical results are in rough agreement with previous theoretical derivations of the separation wavenumber.

Durden, Stephen L.↗