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NASA NTRS1978

Finite element concepts in computational aerodynamics

Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.

Baker, A. J.↗

NASA NTRS2003

Thermocapillary Convection Due to a Stationary Bubble - A Paradox

We analyze the velocity and temperature fields at steady state due to thermocapillary convection around a gas bubble that is stationary in a liquid. A linear temperature field is imposed in the undisturbed liquid. Our interest is in investigating the effect of convective transport of momentum and energy on the velocity and temperature fields. We assume the pertinent physical properties to be constant, and that buoyant convection is negligible. Suitably defined Reynolds and Marangoni numbers are assumed to be small compared with unity. When both the Reynolds and Marangoni numbers are set equal to zero, a solution can be found. In this solution, far from the bubble, the velocity field decays as the inverse of the distance from the bubble, and the disturbance temperature field decays as the inverse of the square of this distance. We now attempt to obtain a solution when the Reynolds number is zero, but the Marangoni number is small, but non-zero, by a perturbation expansion in the Marangoni number. When the temperature field is expanded in a regular perturbation series in the Marangoni number, we show that the problem for the first correction field is ill-posed. The governing equation for this perturbation field contains an inhomogeneity, and the corresponding particular solution neither decays far from the bubble, nor can be canceled by a homogeneous solution. Additional information is included in the original extended abstract.

Balasubramaniam, R.↗

NASA NTRS1991

High frequency scattering from corrugated stratified cylinders

Interest in applying radar remote sensing for the study of forested areas led to the development of a model for scattering from corrugated stratified dielectric cylinders. The model is used to investigate the effect of bark and its roughness on scattering from tree trunks and branches. The outer layer of the cylinder (bark) is assumed to be a low-loss dielectric material and to have a regular (periodic) corrugation pattern. The inner layers are treated as lossy dielectrics with smooth boundaries. A hybrid solution based on the moment method and the physical optics approximation is obtained. In the solution, the corrugations are replaced with polarization currents that are identical to those of the local tangential periodic corrugated surface, and the stratified cylinder is replaced with equivalent surface currents. New expressions for the equivalent physical-optics currents are used which are more convenient than the standard ones. It is shown that the bark layer and its roughness both reduce the radar cross-section. It is also demonstrated that the corrugations can be replaced by an equivalent anisotropic layer.

Sarabandi, Kamal↗

NASA NTRS1993

Multigrid properties of upwind-biased data reconstructions

The multigrid properties of two data reconstruction methods used for achieving second-order spatial accuracy when solving the two-dimensional Euler equations are examined. The data reconstruction methods are used with an implicit upwind algorithm which uses linearized backward-Euler time-differencing. The solution of the resulting linear system is performed by an iterative procedure. In the present study only regular quadrilateral grids are considered, so a red-black Gauss-Seidel iteration is used. Although the Jacobian is approximated by first-order upwind extrapolation, two alternative data reconstruction techniques for the flux integral that yield higher-order spatial accuracy at steady state are examined. The first method, probably most popular for structured quadrilateral grids, is based on estimating the cell gradients using one-dimensional reconstruction along curvilinear coordinates. The second method is based on Green's theorem. Analysis and numerical results for the two dimensional Euler equations show that data reconstruction based on Green's theorem has superior multigrid properties as compared to the one-dimensional data reconstruction method.

Warren, Gary P.↗

NASA NTRS2006

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗

NASA NTRS2007

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗

NASA NTRS1991

Sinc-Galerkin estimation of diffusivity in parabolic problems

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

Smith, Ralph C.↗

NASA NTRS1987

Self-pulsing and bichromatic emission in homogeneously broadened bidirectional ring lasers

The effects of saturation-induced Bragg gratings on the mode structure and dynamics of bidirectional homogeneously broadened ring lasers are studied. The grating is viewed as a distributed feedback medium in a ring cavity and modes appropriate to such a structure are used. A Fourier decomposed rate equation model is developed to study the behavior of these modes above threshold. The difference in the properties of these solutions from the modes of an unfilled ring cavity lead to the possibility of bichromatic emission and both regular undamped and irregular damped self-pulsing.

Rabinovich, W. S.↗

NASA NTRS2001

A New Analytical Approach to Predict Spacing Selection in Lamellar and Rod Eutectic Systems

In this paper, we reexamine the Jackson and Hunt (JH) theory and relax the assumption of isothermal solid/liquid interface(SLI) used in their treatment. A modification of the term B. in the expression of the solute concentration profile is also proposed. Based on the predictions of this modified theory the traditional definitions of regular and irregular eutectics are discussed. For regular eutectics the new model identifies a range of spacing within the limits defined by the minimum undercooling of the alpha and beta phase. For the irregular Al-Si eutectic system in particular we identified two different spacing selection mechanisnis: a) for a particular growth rate, a nearly isothermal interface can be achieved at a unique minimum spacing lambda(sub I); b) the average spacing in the microstructure (lambda(sub av) > lambda(sub I)) is essentially dictated by the undercooling of the faceted phase. Based on the modified theoretical model a semi-empirical expression has been developed to account for the influence of the temperature gradient. The theoretical calculations have been found to be in good agreement with the published experimental measurements.

Catalina, Adrian V.↗

NASA NTRS1991

A shooting approach to suboptimal control

The shooting method is used to solve the suboptimal control problem where the control history is assumed to be piecewise linear. Suboptimal solutions can be obtained without difficulty and can lead to accurate approximate controls and good starting multipliers for the regular shooting method by increasing the number of nodes. Optimal planar launch trajectories are presented for the advanced launch system.

Hull, David G.↗

NASA NTRS1983

Hybrid perturbation/Bubnov-Galerkin technique for nonlinear thermal analysis

A two step hybrid analysis technique to predict the nonlinear steady state temperature distribution in structures and solids is presented. The technique is based on the regular perturbation expansion and the classical Bubnov-Galerkin approximation. The functions are obtained by using the regular perturbation method. These functions are selected as coordinate functions and the classical Bubnov-Galerkin technique is used to compute their amplitudes. The potential of the proposed hybrid technique for the solution of nonlinear thermal problems is discussed. The effectiveness of this technique is demonstrated by the effects of conduction, convection, and radiation modes of heat transfer. It is indicated that the hybrid technique overcomes the two major drawbacks of the classical techniques: (1) the requirement of using a small parameter in the regular perturbation method; and (2) the arbitrariness in the choice of the coordinate functions in the Bubnov-Galerkin technique. The proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of the Bubnov-Galerkin technique.

Noor, A. K.↗

NASA NTRS1982

ORACLS - A linear-quadratic-Gaussian computer-aided design package

ORACLS, an acronym denoting Optimal Regular Algorithms for the Control of Linear Systems, is a collection of FORTRAN coded subroutines dedicated to the formulation and solution of the Linear-Quadratic-Gaussian (LQG) design problem modeled in both continuous and discrete form. The ORACLS system is under continuous development at the NASA Langley Research Center, Hampton, Virginia, and is widely used by universities and industry within the U.S.A. The current (operational) ORACLS version as well as new software under development is described.

Armstrong, E. S.↗

NASA NTRS1986

Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators

The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.

Golubitsky, Martin↗

NASA NTRS2000

Magnetic Field Suppression of Flow in Semiconductor Melt

One of the most promising approaches for the reduction of convection during the crystal growth of conductive melts (semiconductor crystals) is the application of magnetic fields. Current technology allows the experimentation with very intense static fields (up to 80 KGauss) for which nearly convection free results are expected from simple scaling analysis in stabilized systems (vertical Bridgman method with axial magnetic field). However, controversial experimental results were obtained. The computational methods are, therefore, a fundamental tool in the understanding of the phenomena accounting during the solidification of semiconductor materials. Moreover, effects like the bending of the isomagnetic lines, different aspect ratios and misalignments between the direction of the gravity and magnetic field vectors can not be analyzed with analytical methods. The earliest numerical results showed controversial conclusions and are not able to explain the experimental results. Although the generated flows are extremely low, the computational task is a complicated because of the thin boundary layers. That is one of the reasons for the discrepancy in the results that numerical studies reported. Modeling of these magnetically damped crystal growth experiments requires advanced numerical methods. We used, for comparison, three different approaches to obtain the solution of the problem of thermal convection flows: (1) Spectral method in spectral superelement implementation, (2) Finite element method with regularization for boundary layers, (3) Multiquadric method, a novel method with global radial basis functions, that is proven to have exponential convergence. The results obtained by these three methods are presented for a wide region of Rayleigh and Hartman numbers. Comparison and discussion of accuracy, efficiency, reliability and agreement with experimental results will be presented as well.

Fedoseyev, A. I.↗

NASA NTRS2010

Separation of Lift-Generated Vortex Wakes Into Two Diverging Parts

As part of an ongoing study of the spreading rate of lift-generated vortex wakes, the present investigation considers possible reasons as to why segments of lift-generated wakes sometimes depart from the main part of the wake to move rapidly in either an upward or downward direction. It is assumed that deficiencies or enhancements of the lift carry over across the fuselage-shrouded wing are the driving mechanism for departures of wake-segments. The computations presented first indicate that upwardly departing wake segments that were observed and photographed could have been produced by a deficiency in lift carryover across the fuselage-shrouded part of the wing. Computations made of idealized vortex wakes indicate that upward departure of a wake segment requires a centerline reduction in the span loading of 70% or more, whether the engines are at idle or robust thrust. Similarly, it was found that downward departure of wake segments is produced when the lift over the center part of the wing is enhanced. However, it was also found that downward departures do not occur without the presence of robust engine-exhaust streams (i.e., engines must NOT be at idle). In those cases, downward departures of a wake segment occurs when the centerline value of the loading is enhanced by any amount between about 10% to 100%. Observations of condensation trails indicate that downward departure of wake segments is rare. Upward departures of wake segments appears to be more common but still rare. A study to determine the part of the aircraft that causes wake departures has not been carried out. However, even though departures of wake segments rarely occur, some aircraft do regularly shed these wake structures. If aircraft safety is to be assured to a high degree of reliability, and a solution for eliminating them is not implemented, existing guidelines for the avoidance of vortex wakes [1,3] may need to be broadened to include possible increases in wake sizes caused by vertical departures of wake segments. Further study may indicate that it is not possible to modify existing aircraft enough to prevent wake departures. Wake-avoidance guidelines must then be adjusted to provide the desired degree of safety. It appears that steps to avoid upwardly moving wake segments have already been incorporated into the avoidance procedures used for aircraft on approach to runways at the Frankfurt Airport [6,7]. The uncertainty in the prospects for compromises in flight safety caused by rapidly upwardly or downwardly moving wake segments suggest that it be specified that aircraft do not fly above or below each other during operations in the airport vicinity where aircraft are likely to be closely spaced [20].

Rossow, Vernon J.↗

NASA NTRSDate not supplied

Space Crop Production Gaps and Challenges

As astronauts venture farther from Earth, and stay for longer periods, the space food system will increase in importance. Crop production can supplement a pre-packaged space diet to provide nutrition and dietary variety for space crews. In future missions, bioregenerative approaches may be used to generate a larger percentage of the diet, as well as help to reduce life support system burdens and resupply from Earth. Plants may also provide behavioral health benefits to crew members living in the isolated, confined environment of a space habitat. A number of unique challenges exist for growth of plants in microgravity and on other reduced gravity surfaces like the moon and Mars. Testing plant growth inside the Veggie and Advanced Plant Habitat (APH) chambers on the International Space Station is allowing us to understand the impacts of gravity and spaceflight on crop growth, nutritional content, acceptability, and the importance of plants to astronauts living and working away from Earth. We are also gaining a better understanding of food safety concerns and the behavior of space plant microbiomes and plant pathogens, but major gaps in knowledge remain. As we move from research towards operational space crop production to enable exploration, there are numerous gaps in technology, knowledge, and practice related to space crop growth that must be addressed. Research and development in key focus areas such as effective water and nutrient delivery at variable gravity levels, autonomous plant health monitoring, growth system cleaning and disinfection, and selection of ideal space crops are needed to fill these gaps. Breeding or engineering custom space crops may impact areas including plant growth and development, plant physiology, produce nutrition, organoleptic acceptability, and post-harvest characteristics, and these may further enable space crop production scenarios. Space crop challenges are multifaceted and require diverse interdisciplinary teams working together to develop effective solutions. Solving these requires an array of skill sets from across the biological and physical sciences, engineering, and human social sciences. Solutions to help ensure food security off-Earth may also translate to more sustainable terrestrial crop production approaches, and regular dialog between industry, academia, and government organizations working in related fields benefit all. Additional help can come from engagement with student researchers at various levels through courses, participatory science projects, and open science activities which can provide useful data. Global coordination and integration between space agencies and partners will be essential.

Gioia Donna Massa↗

NASA NTRSDate not supplied

Space Crop Production Gaps and Challenges

Gioia Massa↗

NASA NTRS1997

Frictionless Contact of Multilayered Composite Half Planes Containing Layers With Complex Eigenvalues

A previously developed local-global stiffness matrix methodology for the response of a composite half plane, arbitrarily layered with isotropic, orthotropic or monoclinic plies, to indentation by a rigid parabolic punch is further extended to accommodate the presence of layers with complex eigenvalues (e.g., honeycomb or piezoelectric layers). First, a generalized plane deformation solution for the displacement field in an orthotropic layer or half plane characterized by complex eigenvalues is obtained using Fourier transforms. A local stiffness matrix in the transform domain is subsequently constructed for this class of layers and half planes, which is then assembled into a global stiffness matrix for the entire multilayered half plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the half plane indented by a rigid punch results in an integral equation for the unknown pressure in the contact region. The integral possesses a divergent kernel which is decomposed into Cauchy-type and regular parts using the asymptotic properties of the local stiffness matrix and a relationship between Fourier and finite Hilbert transform of the contact pressure. The solution of the resulting singular integral equation is obtained using a collocation technique based on the properties of orthogonal polynomials developed by Erdogan and Gupta. Examples are presented that illustrate the important influence of low transverse properties of layers with complex eigenvalues, such as those exhibited by honeycomb, on the load versus contact length response and contact pressure distributions for half planes containing typical composite materials.

Zhang, Wang↗