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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

A comparison of design variables for control theory based airfoil optimization

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work in the area it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using either the potential flow or the Euler equations with either a conformal mapping or a general coordinate system. We have also explored three-dimensional extensions of these formulations recently. The goal of our present work is to demonstrate the versatility of the control theory approach by designing airfoils using both Hicks-Henne functions and B-spline control points as design variables. The research also demonstrates that the parameterization of the design space is an open question in aerodynamic design.

Reuther, James↗
NASA NTRS1995

On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory

The consistency of second-order closure models with results from hydrodynamic stability theory is analyzed for the simplified case of homogeneous turbulence. In a recent study, Speziale, Gatski, and MacGiolla Mhuiris showed that second-order closures are capable of yielding results that are consistent with hydrodynamic stability theory for the case of homogeneous shear flow in a rotating frame. It is demonstrated in this paper that this success is due to the fact that the stability boundaries for rotating homogeneous shear flow are not dependent on the details of the spatial structure of the disturbances. For those instances where they are -- such as in the case of elliptical flows where the instability mechanism is more subtle -- the results are not so favorable. The origins and extent of this modeling problem are examined in detail along with a possible resolution based on rapid distortion theory (RDT) and its implications for turbulence modeling.

Speziale, Charles G.↗
NASA NTRS1995

Theory of the water vapor continuum and validations

A far-wing line shape theory based on the binary collision and quasistatic approximations that is applicable for both the low- and high-frequency wings of the vibration-rotational bands has been developed. This theory has been applied in order to calculate the frequency and temperature dependence of the continuous absorption coefficient for frequencies up to 10,000 cm(exp -1) for pure H2O and for H2O-N2 mixtures. The calculations were made assuming an interaction potential consisting of an isotropic Lennard-Jones part with two parameters that are consistent with values obtained from other data, and the leading long-range anisotropic part, together with the measured line strengths and transition frequencies. The results, obtained without the introduction of adjustable parameters, compare well with the existing laboratory data, both in magnitude and in temperature dependence. This leads us to the conclusion that the water continuum can be explained in terms of far-wing absorption. Current work in progress to extend the theory and to validate the theoretically calculated continuum will be discussed briefly.

Tipping, Richard H.↗
NASA NTRS1995

Analytic MHD Theory for Earth's Bow Shock at Low Mach Numbers

A previous MHD theory for the density jump at the Earth's bow shock, which assumed the Alfven M(A) and sonic M(s) Mach numbers are both much greater than 1, is reanalyzed and generalized. It is shown that the MHD jump equation can be analytically solved much more directly using perturbation theory, with the ordering determined by M(A) and M(s), and that the first-order perturbation solution is identical to the solution found in the earlier theory. The second-order perturbation solution is calculated, whereas the earlier approach cannot be used to obtain it. The second-order terms generally are important over most of the range of M(A) and M(s) in the solar wind when the angle theta between the normal to the bow shock and magnetic field is not close to 0 deg or 180 deg (the solutions are symmetric about 90 deg). This new perturbation solution is generally accurate under most solar wind conditions at 1 AU, with the exception of low Mach numbers when theta is close to 90 deg. In this exceptional case the new solution does not improve on the first-order solutions obtained earlier, and the predicted density ratio can vary by 10-20% from the exact numerical MHD solutions. For theta approx. = 90 deg another perturbation solution is derived that predicts the density ratio much more accurately. This second solution is typically accurate for quasi-perpendicular conditions. Taken together, these two analytical solutions are generally accurate for the Earth's bow shock, except in the rare circumstance that M(A) is less than or = 2. MHD and gasdynamic simulations have produced empirical models in which the shock's standoff distance a(s) is linearly related to the density jump ratio X at the subsolar point. Using an empirical relationship between a(s) and X obtained from MHD simulations, a(s) values predicted using the MHD solutions for X are compared with the predictions of phenomenological models commonly used for modeling observational data, and with the predictions of a modified phenomenological model proposed recently. The similarities and differences between these results are illustrated using plots of X and a(s) predicted for the Earth's bow shock. The plots show that the new analytic solutions agree very well with the exact numerical MHD solutions and that these MHD solutions should replace the corresponding phenomenological relations in comparisons with data. Furthermore, significant differences exist between the standoff distances predicted at low M(A) using the MHD models versus those predicted by the new modified phenomenological model. These differences should be amenable to observational testing.

Grabbe, Crockett L.↗
NASA NTRS1996

Theory of Planetary System Formation

Observations and theoretical considerations support the idea that the Solar System formed by the collapse of tenuous interstellar matter to a disk of gas and dust (the primitive solar nebula), from which the Sun and other components separated under the action of dissipative forces and by the coagulation of solid material. Thus, planets are understood to be contemporaneous byproducts of star formation. Because the circumstellar disks of new stars are easier to observe than mature planetary systems, the possibility arises that the nature and variety of planets might be studied from observations of the conditions of their birth. A useful theory of planetary system formation would therefore relate the properties of circumstellar disks both to the initial conditions of star formation and to the consequent properties of planets to those of the disk. Although the broad outlines of such a theory are in place, many aspects are either untested, controversial, or otherwise unresolved; even the degree to which such a comprehensive theory is possible remains unknown.

Cassen, Patrick↗
NASA NTRS1997

Unified Theory for Aircraft Handling Qualities and Adverse Aircraft-Pilot Coupling

A unified theory for aircraft handling qualities and adverse aircraft-pilot coupling or pilot-induced oscillations is introduced. The theory is based on a structural model of the human pilot. A methodology is presented for the prediction of (1) handling qualities levels; (2) pilot-induced oscillation rating levels; and (3) a frequency range in which pilot-induced oscillations are likely to occur. Although the dynamics of the force-feel system of the cockpit inceptor is included, the methodology will not account for effects attributable to control sensitivity and is limited to single-axis tasks and, at present, to linear vehicle models. The theory is derived from the feedback topology of the structural model and an examination of flight test results for 32 aircraft configurations simulated by the U.S. Air Force/CALSPAN NT-33A and Total In-Flight Simulator variable stability aircraft. An extension to nonlinear vehicle dynamics such as that encountered with actuator saturation is discussed.

Hess, R. A.↗
NASA NTRS1960

A Modified Hansen's Theory as Applied to the Motion of Artificial Satellites

This report presents a theory of oblateness perturbations of the orbits of artificial satellites based on Hansen's theory, with modification for adaptation to fast machine computation. The theory permits the easy inclusion of any gravitational terms and is suitable for the deduction of geo-physical and geodetic data from orbit observations on artificial satellites. The computations can be carried out to any desired order compatible with the accuracy of the geodetic parameters.

Musen, Peter↗
NASA NTRS2000

Theory of Type 3 and Type 2 Solar Radio Emissions

The main features of some current theories of type III and type II bursts are outlined. Among the most common solar radio bursts, type III bursts are produced at frequencies of 10 kHz to a few GHz when electron beams are ejected from solar active regions, entering the corona and solar wind at typical speeds of 0.1c. These beams provide energy to generate Langmuir waves via a streaming instability. In the current stochastic-growth theory, Langmuir waves grow in clumps associated with random low-frequency density fluctuations, leading to the observed spiky waves. Nonlinear wave-wave interactions then lead to secondary emission of observable radio waves near the fundamental and harmonic of the plasma frequency. Subsequent scattering processes modify the dynamic radio spectra, while back-reaction of Langmuir waves on the beam causes it to fluctuate about a state of marginal stability. Theories based on these ideas can account for the observed properties of type III bursts, including the in situ waves and the dynamic spectra of the radiation. Type 11 bursts are associated with shock waves propagating through the corona and interplanetary space and radiating from roughly 30 kHz to 1 GHz. Their basic emission mechanisms are believed to be similar to those of type III events and radiation from Earth's foreshock. However, several sub-classes of type II bursts may exist with different source regions and detailed characteristics. Theoretical models for type II bursts are briefly reviewed, focusing on a model with emission from a foreshock region upstream of the shock for which observational evidence has just been reported.

Robinson, P. A.↗
NASA NTRS1994

A Logical Account of Diagnosis with Multiple Theories

Model-based diagnosis is a powerful, first-principles approach to diagnosis. The primary drawback with model-based diagnosis is that it is based on a system model, and this model might be inappropriate. The inappropriateness of models usually stems from the fundamental tradeoff between completeness and efficiency. Recently, Struss has developed an elegant proposal for diagnosis with multiple models. Struss characterizes models as relations and develops a precise notion of abstraction. He defines relations between models and analyzes the effect of a model switch on the space of possible diagnoses. In this paper we extend Struss's proposal in three ways. First, our account of diagnosis with multiple models is based on representing models as more expressive first-order theories, rather than as relations. A key technical contribution is the use of a general notion of abstraction based on interpretations between theories. Second, Struss conflates component modes with models, requiring him to define models relations such as choices which result in non-relational models. We avoid this problem by differentiating component modes from models. Third, we present a more general account of simplifications that correctly handles situations where the simplification contradicts the base theory.

Pandurang, P.↗
NASA NTRS1998

Theory of the Shape of the Heliospheric Termination Shock: Axial Symmetry

The heliospheric termination shock must exhibit asymmetry in its shape, due in part to internal latitude variations in the solar wind, and in part to the special directions defined by the external interstellar flow and/or the galactic magnetic field. This asymmetry shows up naturally in numerical simulations of the interaction between the heliosphere and local interstellar medium. However, to date only one analytical treatment of the theory has appeared, which discussed the modification of the shock shape due to solar wind latitude variations in the presence of spherically symmetric outer boundary conditions. In the present report, we discuss an extension and generalization of this theory to an axially symmetric gasdynamic system, in which departure from spherical symmetry may be due either to internal solar wind variations or to the directional properties of the external interstellar medium. It is shown that for steady flow the post-shock region is characterized by an infinite set of quantities that are conserved along streamlines; among these invariants are the stagnation pressure and a quantity closely related to vorticity. Moreover, for a given latitude profile of the (supersonic) solar wind, the geometry of the termination shock uniquely determines the valued of these invariants at the points where the streamlines emerge from the shock. A self-consistent solution of the problem thus requires a match between the shock geometry and distant boundary conditions. The theory is applied to give estimates of termination-shock asymmetry for various internal and external conditions.

Barnes, Aaron↗
NASA NTRS2002

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Freed, Alan D.↗
NASA NTRS2002

A Thermodynamic Theory of Solid Viscoelasticity: Nonlinear Thermo-viscoelasticity - Part II:

This paper, second in the series of three papers, develops a general, nonlinear, non-isothermal, compressible theory for finite rubber viscoelasticity and specifies it in a form convenient for solving problems important to the rubber, tire, automobile, and air-space industries, among others. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory of differential type has been developed for arbitrary non-isothermal deformations of viscoelastic solids. In this theory, the constitutive equations were presented as the sum of a rubber elastic (equilibrium) and a liquid type viscoelastic (non-equilibrium) terms. These equations have then been simplified using several modeling and simplicity arguments.

Freed, Alan D.↗
NASA NTRS2002

Primer Vector Optimization: Survey of Theory, New Analysis and Applications

In this paper, a summary of primer vector theory is presented. The applicability of primer vector theory is examined in an effort to understand when and why the theory can fail. For example, since the Calculus of Variations is based on "small" variations, singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyse that employ small variations. Two examples, the initialization of an orbit and a line of apsides rotation, are presented. Recommendations, future work, and the possible addition of other optimization techniques are also discussed.

Guzman, J. J.↗
NASA NTRS2002

A Nonlinear Theory for Smart Composite Structures

The paper discusses the following: (1) Development of a completely coupled thermo-piezoelectric-mechanical theory for the analysis of composite shells with segmented and distributed piezoelectric sensor/actuators and shape memory alloys. The higher order displacement theory will be used to capture the transverse shear effects in anisotropic composites. The original theory will be modified to satisfy the stress continuity at ply interfaces. (2) Development of a finite element technique to implement the mathematical model. (3) Investigation of the coupled structures/controls interaction problem to study the complex trade-offs associated with the coupled problem.

Chattopadhyay, Aditi↗
NASA NTRS1991

Spatial Direct Numerical Simulation of Boundary-Layer Transition Mechanisms: Validation of PSE Theory

A study of instabilities in incompressible boundary-layer flow on a flat plate is conducted by spatial direct numerical simulation (DNS) of the Navier-Stokes equations. Here, the DNS results are used to critically evaluate the results obtained using parabolized stability equations (PSE) theory and to study mechanisms associated with breakdown from laminar to turbulent flow. Three test cases are considered: two-dimensional Tollmien-Schlichting wave propagation, subharmonic instability breakdown, and oblique-wave break-down. The instability modes predicted by PSE theory are in good quantitative agreement with the DNS results, except a small discrepancy is evident in the mean-flow distortion component of the 2-D test problem. This discrepancy is attributed to far-field boundary- condition differences. Both DNS and PSE theory results show several modal discrepancies when compared with the experiments of subharmonic breakdown. Computations that allow for a small adverse pressure gradient in the basic flow and a variation of the disturbance frequency result in better agreement with the experiments.

Joslin, R. D.↗
NASA NTRS2004

Network Theory: A Primer and Questions for Air Transportation Systems Applications

A new understanding (with potential applications to air transportation systems) has emerged in the past five years in the scientific field of networks. This development emerges in large part because we now have a new laboratory for developing theories about complex networks: The Internet. The premise of this new understanding is that most complex networks of interest, both of nature and of human contrivance, exhibit a fundamentally different behavior than thought for over two hundred years under classical graph theory. Classical theory held that networks exhibited random behavior, characterized by normal, (e.g., Gaussian or Poisson) degree distributions of the connectivity between nodes by links. The new understanding turns this idea on its head: networks of interest exhibit scale-free (or small world) degree distributions of connectivity, characterized by power law distributions. The implications of scale-free behavior for air transportation systems include the potential that some behaviors of complex system architectures might be analyzed through relatively simple approximations of local elements of the system. For air transportation applications, this presentation proposes a framework for constructing topologies (architectures) that represent the relationships between mobility, flight operations, aircraft requirements, and airspace capacity, and the related externalities in airspace procedures and architectures. The proposed architectures or topologies may serve as a framework for posing comparative and combinative analyses of performance, cost, security, environmental, and related metrics.

Holmes, Bruce J.↗
NASA NTRS1944

The Theory of a Free Jet of a Compressible Gas

In the present report the theory of free turbulence propagation and the boundary layer theory are developed for a plane-parallel free stream of a compressible fluid. In constructing the theory use was made of the turbulence hypothesis by Taylor (transport of vorticity) which gives best agreement with test results for problems involving heat transfer in free jets.

Abramovich, G. N.↗
NASA NTRS2007

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Rubinstein, Robert↗