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NASA NTRS1997

Toward Understanding Wake Vortices and Atmospheric Turbulence Interactions Using Large-Eddy Simulation

The vortices produced by an aircraft in flight are a complex phenomena created from a 'sheet of vorticity' leaving the trailing edge of the aircraft surfaces. This sheet tends to roll-up into two counter-rotating vortices. After a few spans downstream of the aircraft, the roll-up process is complete and the vortex pair may be characterized in a simple manner for modeling purposes. Our research will focus on what happens to these post roll-up vortices in the vicinity of an airport terminal. As the aircraft wake vortices descend, they are transported by the air mass which they are embedded and are decayed by both internal and external processes. In the vicinity of the airport, these external influences are usually due to planetary boundary layer (PBL) turbulence. Using large-eddy simulation (LES), one may simulate a variety of PBL conditions. In the LES method, turbulence is generated in the PBL as a response to surface heat flux, horizontal pressure gradient, wind shear, and/or stratification, and may produce convective or unstably stratified, neutral, or stably stratified PBL's. Each of these PBL types can occur during a typical diurnal cycle of the PBL. Thus it is important to be able to characterize these conditions with the LES method. Once this turbulent environment has been generated, a vortex pair will be introduced and the interactions are observed. The objective is to be able to quantify the PBL turbulence vortex interaction and be able to draw some conclusions of vortex behavior from the various scale interactions. This research is ongoing, and we will focus on what has been accomplished to date and the future direction of this research. We will discuss the model being used, show results that validate its use in the PBL, and present a nested-grid method proposed to analyze the entire PBL and vortex pair simultaneously.

DeCroix, David↗

NASA NTRS1979

Off-axis impact of unidirectional composites with cracks: Dynamic stress intensification

The dynamic response of unidirectional composites under off axis (angle loading) impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. The analytical method utilizes Fourier transform for the space variable and Laplace transform for the time variable. The off axis impact is separated into two parts, one being symmetric and the other skew-symmetric with reference to the crack plane. Transient boundary conditions of normal and shear tractions are applied to a crack embedded in the matrix of the unidirectional composite. The two boundary conditions are solved independently and the results superimposed. Mathematically, these conditions reduce the problem to a system of dual integral equations which are solved in the Laplace transform plane for the transformation of the dynamic stress intensity factor. The time inversion is carried out numerically for various combinations of the material properties of the composite and the results are displayed graphically.

Sih, G. C.↗

NASA NTRS1989

Local grid refinement for transonic flow problems

The present use of locally refined Cartesian grids to solve transonic flow problems about three-dimensional aircraft configurations obviates surface-conforming grid generation through an embedding of surface-geometry paneling in the grid. Accurate resolution of flow close to the boundary, and in regions with strong velocity gradients, is achieved via hierarchical local refinement which subdivides a given grid cell into eight cells. Fast and reliable convergence is obtained by combining several preconditioners and damping strategies. Methods are suggested for preclusion of global convergence problems.

Melvin, Robin G.↗

NASA NTRS1987

An embedded function approach for turbulent flow prediction

In conventional prediction methods for turbulent flow influence on surface properties, very small mesh sizes and considerable computational effort is required to adequately resolve the intense velocity and temperature profile variations that occur in the wall-layer region. In this study, an approach is described wherein an outer region numerical solution is smoothly matched to a set of embedded analytic profile functions in the near-wall region; these wall-layer profile functions having been derived through consideration of the coherent structure of the time-dependent near-wall flow provide analytic expressions for the mean velocity and enthalpy profiles in the wall layer. The concept is demonstrated through example applications to turbulent boundary-layer flows in two dimensions. The technique is shown to be very efficient and it is demonstrated that a reduction of approximately half the mesh points across the 2-D layer may be realized (as compared to conventional methods) with no degradation in accuracy.

Walker, J. D. A.↗

NASA NTRS1993

Dynamic characteristics of specialty composite structures with embedded damping layers

Damping mechanics for simulating the damped dynamic characteristics in specialty composite structures with compliant interlaminar damping layers are presented. Finite-element based mechanics incorporating a discrete layer (or layer-wise) laminate damping theory are utilized to represent general laminate configurations in terms of lay-up and fiber orientation angles, cross-sectional thickness, shape, and boundary conditions. Evaluations of the method with exact solutions and experimental data illustrate the accuracy of the method. Additional applications investigate the potential for significant damping enhancement in angle-ply composite laminates with cocured interlaminar damping layers.

Saravanos, D. A.↗

NASA NTRSDate not supplied

Uncertainty Estimates for Sonic-Boom Pressure Signatures and Loudness Carpets

A non-intrusive uncertainty quantification method is applied to computational analysis of supersonic, low-boom aircraft. The mean and standard deviation statistics of the pressure waveforms and loudness metrics are evaluated through use of numerical quadrature. The probability density function (p.d.f.) of these outputs is evaluated via kernel density estimation. The simulations use an inviscid, embedded-boundary Cartesian-mesh flow solver in the nearfield combined with an augmented Burgers’ equation solver for propagation in the farfield. The results show that the p.d.f. of the waveform is bimodal at shocks, which makes the mean and standard deviation statistics inappropriate. Despite this limitation, we show that the moment statistics can provide effective assessment of discrepancies when comparing with experimental data. This is demonstrated by presenting uncertainty analysis of a wind-tunnel test and showing that we significantly improve the predictions when we include the test uncertainties in the simulation. Normal distributions are obtained for the ground signature and loudness metrics, which is primarily due to the careful shaping of the low-boom waveform. Separation of variables and error control are used to reduce computational cost. We demonstrate that this is an efficient approach in the sense of balancing numerical errors in the statistics quadrature with discretization errors in the solvers.

ARMD↗

NASA NTRS1980

Normal and shear impact of layered composite with a crack - Dynamic stress intensification

The dynamic response of a layered composite under normal and shear impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. One of the objectives was to develop an analytical method for determining dynamic stress solutions which should lead to a numerical method which utilizes Fourier transform for the space variable and Laplace transform for the time variable. The time-dependent angle loading is separated into two parts: a symmetric and a skew-symmetric with reference to the crack plane. By superposition, the transient boundary conditions consist of applying normal and shear tractions to a crack embedded in a layered composite; one phase of the composite could represent the fiber while the other could be the matrix. Mathematically, these conditions reduce the problem to a system of dual integral equations solved in the transform plane for the transform of the dynamic stress-intensity factor.

Sih, G. C.↗

NASA NTRS2006

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Nguyen, Nhan↗

NASA NTRS1996

Development of a Higher Order Laminate Theory for Modeling Composites with Induced Strain Actuators

A refined higher order plate theory is developed to investigate the actuation mechanism of piezoelectric materials surface bonded or embedded in composite laminates. The current analysis uses a displacement field which accurately accounts for transverse shear stresses. Some higher order terms are identified by using the conditions that shear stresses vanish at all free surfaces. Therefore, all boundary conditions for displacements and stresses are satisfied in the present theory. The analysis is implemented using the finite element method which provides a convenient means to construct a numerical solution due to the discrete nature of the actuators. The higher order theory is computationally less expensive than a full three dimensional analysis. The theory is also shown to agree well with published experimental results. Numerical examples are presented for composite plates with thicknesses ranging from thin to very thick.

Chattopadhyay, Aditi↗

NASA NTRS2001

Deriving the Coronal Magnetic Field Using Parametric Transformation Analysis

When plasma-beta greater than 1 then the gas pressure dominates over the magnetic pressure. This ratio as a function along the coronal magnetic field lines varies from beta greater than 1 in the photosphere at the base of the field lines, to beta much less than 1 in the mid-corona, to beta greater than 1 in the upper corona. Almost all magnetic field extrapolations do not or cannot take into account the full range of beta. They essentially assume beta much less than 1, since the full boundary conditions do not exist in the beta greater than 1 regions. We use a basic parametric representation of the magnetic field lines such that the field lines can be manipulated to match linear features in the EUV and SXR coronal images in a least squares sense. This research employs free-form deformation mathematics to generate the associated coronal magnetic field. In our research program, the complex magnetic field topology uses Parametric Transformation Analysis (PTA) which is a new and innovative method to describe the coronal fields that we are developing. In this technique the field lines can be viewed as being embedded in a plastic medium, the frozen-in-field-line concept. As the medium is deformed the field lines are similarly deformed. However the advantage of the PTA method is that the field line movement represents a transformation of one magnetic field solution into another magnetic field solution. When fully implemented, this method will allow the resulting magnetic field solution to fully match the magnetic field lines with EUV/SXR coronal loops by minimizing the differences in direction and dispersion of a collection of PTA magnetic field lines and observed field lines. The derived magnetic field will then allow beta greater than 1 regions to be included, the electric currents to be calculated, and the Lorentz force to be determined. The advantage of this technique is that the solution is: (1) independent of the upper and side boundary conditions, (2) allows non-vanishing magnetic forces, and (3) provides a global magnetic field solution, which contains high- and low-beta regimes and maximizes the similarity between the field lines structure and all the coronal images of the region. The coronal image analysis is crucial to the investigation and for the first time these images can be exploited to derive the coronal magnetic field in a well-posed mathematical formulation. This program is an outgrowth of an investigation in which an extrapolated potential field was required to be "inflated" in order to have the field lines match the Yohkoh/SXT images. The field lines were radially stretched resulting in a better match to the coronal loops of an active region. The PTA method of radial and non-radial deformations of field lines to provide a match to the EUV/SXR images will be presented.

Gary, G. Allen↗

NASA NTRS1986

Computation of multi-dimensional viscous supersonic flow

A method has been developed for two- and three-dimensional computations of viscous supersonic jet flows interacting with an external flow. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases associated with supersonic jet flow is presented and compared with other calculations for axisymmetric cases. Demonstration calculations indicate that the computational technique has great promise as a tool for calculating a wide range of supersonic flow problems including jet flow. Finally, a User's Manual is presented for the computer code used to perform the calculations.

Buggeln, R. C.↗

NASA NTRS1993

Integrated analysis and design of thick composite structures for optimal passive damping characteristics

The development of novel composite mechanics for the analysis of damping in composite laminates and structures and the more significant results of this effort are summarized. Laminate mechanics based on piecewise continuous in-plane displacement fields are described that can represent both intralaminar stresses and interlaminar shear stresses and the associated effects on the stiffness and damping characteristics of a composite laminate. Among other features, the mechanics can accurately model the static and damped dynamic response of either thin or thick composite laminates, as well as, specialty laminates with embedded compliant damping layers. The discrete laminate damping theory is further incorporated into structural analysis methods. In this context, an exact semi-analytical method for the simulation of the damped dynamic response of composite plates was developed. A finite element based method and a specialty four-node plate element were also developed for the analysis of composite structures of variable shape and boundary conditions. Numerous evaluations and applications demonstrate the quality and superiority of the mechanics in predicting the damped dynamic characteristics of composite structures. Finally, additional development was focused on the development of optimal tailoring methods for the design of thick composite structures based on the developed analytical capability. Applications on composite plates illustrated the influence of composite mechanics in the optimal design of composites and the potential for significant deviations in the resultant designs when more simplified (classical) laminate theories are used.

Saravanos, D. A.↗

NASA NTRS2018

Use of Simple Continuum Solutions in Finite Element Alternating Method for Fracture Problems

The performance of the finite element alternating (FEAM) method for two-dimensional crack problems is studied with respect to a polynomial pressure distribution fitted to the crack face stresses. The FEAM alternates between the analytical solution of crack in an infinite plate subjected to arbitrary polynomial distribution and a finite element solution of an uncracked body to satisfy the required boundary conditions in the crack problem. In this paper, the FEAM is applied to embedded crack and edge crack problems. For embedded crack problems, all of the constant, linear, and quadratic ( N=0,1, or 2, respectively) pressure distributions yield very accurate results with this algorithm with 4 to 5 iterations. The edge crack problems, on the other hand, require much higher order polynomials distributions (N=5 to 6) to yield accurate solutions. For slant edge crack problems, the mode-I stress-intensity factors have better accuracy than the mode-II stress-intensity factors for the same convergence tolerance.

Krishnamurthy, T.↗

NASA NTRS1992

Hover performance analysis of advanced rotor blades

This is an effort aimed at validating recent hover prediction methods. The experimental basis for this validation work is an extensive set of loads, wake and performance data, which were obtained from a pressure instrumented model UH-60 rotor tested at the Sikorsky hover test facility and at Duits-Nederlandse Windtunnel (DNW). This model was equipped with replaceable tips - including a tapered and a BERP-type tip - which permitted studies of the effects of rotor geometry. The central prediction method studied is a free-wake, vortex embedded, full-potential CFD method - called HELIX-I. It is found that the HELIX-I code produces very good comparisons with the data including wake, surface pressure and performance. Comparisons with the measured radial load distributions have permitted an improved understanding of the wake resolution modelling requirements of CFD methods. Since HELIX-I is a combined Eulerian/Lagrangian method, limited comparisons are also made with a Lagrangian boundary element code (called EHPIC) and an Eulerian Navier-Stokes code (called TURNS). In most cases all methods produce good comparisons with the data. It is found that the HELIX-I code provides a good compromise between the speed of boundary integral methods and the comprehensive nature of Navier-Stokes methods.

Tung, C.↗

NASA NTRS1997

Analysis of Smart Composite Structures Including Debonding

Smart composite structures with distributed sensors and actuators have the capability to actively respond to a changing environment while offering significant weight savings and additional passive controllability through ply tailoring. Piezoelectric sensing and actuation of composite laminates is the most promising concept due to the static and dynamic control capabilities. Essential to the implementation of these smart composites are the development of accurate and efficient modeling techniques and experimental validation. This research addresses each of these important topics. A refined higher order theory is developed to model composite structures with surface bonded or embedded piezoelectric transducers. These transducers are used as both sensors and actuators for closed loop control. The theory accurately captures the transverse shear deformation through the thickness of the smart composite laminate while satisfying stress free boundary conditions on the free surfaces. The theory is extended to include the effect of debonding at the actuator-laminate interface. The developed analytical model is implemented using the finite element method utilizing an induced strain approach for computational efficiency. This allows general laminate geometries and boundary conditions to be analyzed. The state space control equations are developed to allow flexibility in the design of the control system. Circuit concepts are also discussed. Static and dynamic results of smart composite structures, obtained using the higher order theory, are correlated with available analytical data. Comparisons, including debonded laminates, are also made with a general purpose finite element code and available experimental data. Overall, very good agreement is observed. Convergence of the finite element implementation of the higher order theory is shown with exact solutions. Additional results demonstrate the utility of the developed theory to study piezoelectric actuation of composite laminates with pre-existing debonding. Significant changes in the modes shapes and reductions in the control authority result due to partially debonded actuators. An experimental investigation addresses practical issues, such as circuit design and implementation, associated with piezoelectric sensing and actuation of composite laminates. Composite specimens with piezoelectric transducers were designed, constructed and tested to validate the higher order theory. These specimens were tested with various stacking sequences, debonding lengths and gains for both open and closed loop cases. Frequency changes of 15% and damping on the order of more than 20% of critical damping, via closed loop control, was achieved. Correlation with the higher order theory is very good. Debonding is shown to adversely affect the open and closed loop frequencies, damping ratios, settling time and control authority.

Chattopadhyay, Aditi↗

NASA NTRS1985

Constitutive Modeling of Superalloy Single Crystals and Directionally Solidified Materials

A unified viscoplastic constitutive relation based on crystallographic slip theory was developed for the deformation analysis of nickel base face centered cubic superalloy single crystals at elevated temperature. The single crystal theory is embedded in a self consistent method to derive a constitutive relation for a directionally solidified material comprised of a polycrystalline aggregate of columnar cylindrical grains. One of the crystallographic axes of the cylindrical crystals points in the columnar direction while the remaining crystallographic axes are oriented at random in the basal plane perpendicular to the columnar direction. These constitutive formulations are coded in FORTRAN for use in nonlinear finite element and boundary element programs.

Walker, K. P.↗

NASA NTRS1987

Analytical electron microscopy of extraterrestrial materials - Results from microtome sections of carbonaceous chondrites and interplanetary dust particles

The paper describes a method for embedding, sectioning, and observing two types of extraterrestrial materials, including hydrated interplanetary dust particles (IDPs) and carbonaceous chondrite meteorites. The technique, which produces large thin areas suitable for both high-resolution imaging and thin-film microanalysis, was applied to study the petrology of the IDP Ames-DE C86-11, the Murchison carbonaceous chondrite matrix, and the Allende dark inclusion. The technique makes it possible to maintain delicate interfaces, boundaries, and phase relationships between grains. Because phases are held in place, layer lattice silicates and other minerals with strong preferred orientations can be viewed in any orientation, including the orientation normal to their basal planes.

Blake, D. F.↗

NASA NTRS1980

Analytic and approximate boundary-fitted coordinate systems for fluid flow simulation

A method for constructing a direct functional relation between the computational and physical domains such that boundaries in the computational domain map into boundaries in the physical domain is presented. This method which is called the 'two-boundary technique' is based on generating functions that represent two disconnected boundaries in the physical domain and an independent function which connects one boundary with another to generate grids. The suggested connecting functions are simple linear and cubic parametric polynomials with parameters based on position and derivatives at the disconnected boundaries. The boundaries can be defined by analytical, approximate, and tension spline functions; the grid density in specified regions is controlled by embedding contraction functions in either the boundary representation or the connecting function.

Smith, R. E.↗