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At least 109 records · Page 6

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NASA NTRS1976

Stability derivatives for bodies of revolution at subsonic speeds

The paper considers a rigid pointed body of revolution in a steady uniform subsonic flow. The body performs harmonic small-amplitude pitching oscillations around its zero angle of attack position. The body is assumed to be smooth and sufficiently slender so that the small perturbation concept can be applied. The basis of the method used, following Revell (1960), is the relation of a body-fixed perturbation potential to the general velocity potential. Normal force distributions as well as total force and moment coefficients are calculated for parabolic spindles and the numerical results show good agreement between Revell's second-order slender body theory and the present theory for the static stability derivatives of the parabolic spindles.

Liu, D. D.↗

NASA NTRS1989

Mixed formulation for frictionless contact problems

Simple mixed finite element models and a computational precedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large rotation theory of the structure with the effects of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The element characteristic array are obtained by using a modified form of the two-field Hellinger-Reissner mixed variational principle. The internal forces and the Lagrange multipliers are allowed to be discontinuous at interelement boundaries. The Newton-Raphson iterative scheme is used for the solution of the nonlinear algebraic equations, and the determination of the contact area and the contact pressures.

Noor, Ahmed K.↗

NASA NTRS1974

A General Theory of Unsteady Compressible Potential Aerodynamics

The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the potential is obtained for both supersonic and subsonic flow. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface, sigma, of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface sigma. For the important practical case of small harmonic oscillation around a rest position, the equation reduces to a two-dimensional Fredholm integral equation of second-type. It is shown that this equation reduces properly to the lifting surface theories as well as other classical mathematical formulas. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings.

Morino, L.↗

NASA NTRS1985

A complex T-matrix derivation of a resonance amplitude

Time-dependent perturbation-theory techniques are used to derive a compact expression, valid to arbitrary order and displaying time dependence explicitly, for a quantum-mechanical transition amplitude applicable to the description of resonances. A solution representing a complex-energy generalization of the usual real-energy (nonresonant) amplitude is obtained and generalized to all orders by introducing a complex-energy T matrix. Applications to physical problems such as the extension of the Fermi golden rules to resonances (Norbury and Deutchman, 1984); pion production in relativistic nucleus-nucleus collisions (Norbury et al., 1985); and the determination of resonant cross sections for nuclear, atomic, or molecular processes involving the formation and decay of intermediate discrete or continuum states are indicated.

Norbury, J. W.↗

NASA NTRS1989

Mixed finite element formulation for frictionless contact problems

Simple mixed finite element models and a computational procedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large-rotation theory of the structure with the effect of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (or stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. Numerical examples of axisymmetric deformations of a hemispherical shell and planar deformations of a circular ring are presented. Both structures are pressed against a rigid plate. Detailed information about the response of the structures is presented. The numerical studies demonstrate the high accuracy of the mixed models and the effectiveness of the computational procedure based on combining the geometrically nonlinear terms and the contact conditions in one iteration loop.

Noor, Ahmed K.↗

NASA NTRS1988

Singular perturbation analysis of the atmospheric orbital plane change problem

A three-state model is presented for the aeroassisted orbital plane change problem. A further model order reduction to a single state model is examined using singular perturbation theory. The optimal solution for this single state model compares favorably with the exact numerical solution using a four-state model; however, a separate boundary layer solution is required to satisfy the terminal constraint on altitude. This, in general, involves the solution of a two-point boundary value problem, but for a two-state model. An approximation is introduced to obtain an analytical control solution for lift and bank angle. Included are numerical simulation results of a guidance law derived from this analysis, along with comparison to earlier work by other researchers.

Calise, A. J.↗

NASA NTRS1989

Mixed finite element models for free vibrations of thin-walled beams

Simple, mixed finite element models are developed for the free vibration analysis of curved thin-walled beams with arbitrary open cross section. The analytical formulation is based on a Vlasov's type thin-walled beam theory with the effects of flexural-torsional coupling, transverse shear deformation and rotary inertia included. The fundamental unknowns consist of seven internal forces and seven generalized displacements of the beam. The element characteristic arrays are obtained by using a perturbed Lagrangian-mixed variational principle. Only C(sup o) continuity is required for the generalized displacements. The internal forces and the Lagrange multiplier are allowed to be discontinuous at interelement boundaries. Numerical results are presented to demonstrate the high accuracy and effectiveness of the elements developed. The standard of comparison is taken to be the solutions obtained by using 2-D plate/shell models for the beams.

Noor, Ahmed K.↗

NASA NTRS1989

Mixed finite element models for free vibrations of thin-walled beams

Noor, Ahmed K.↗

NASA NTRS1989

Generalized mathematical models in design optimization

The theory of optimality conditions of extremal problems can be extended to problems continuously deformed by an input vector. The connection between the sensitivity, well-posedness, stability and approximation of optimization problems is steadily emerging. The authors believe that the important realization here is that the underlying basis of all such work is still the study of point-to-set maps and of small perturbations, yet what has been identified previously as being just related to solution procedures is now being extended to study modeling itself in its own right. Many important studies related to the theoretical issues of parametric programming and large deformation in nonlinear programming have been reported in the last few years, and the challenge now seems to be in devising effective computational tools for solving these generalized design optimization models.

Papalambros, Panos Y.↗

NASA NTRS1984

The application of satellite data to study the effects of latent heat release on cyclones

Generalized energetics were studied for nonlinear inviscid symmetric instability (SI). It was found that the linear theory fails to predict the stability in certain cases where the basic state is transitional between stability and instability. The initial growth of the SI perturbations can be fairly well approximated by linear theory, but the long time nonlinear evaluations will be bonded energetically if the SI region is finite. However, a further extension of the energetics to conditional symmetric instability (CSI) shows that the nonlinear evolution of circulation will energetically depend much more on the precipitation in a complicated way. By treating the latent heat as a source which is implicitly related to the motion field, the existence, uniqueness and stability of steady viscous (CSI) circulations are studied. Viscous CSI circulations are proved to be unique and asymptotically stable when the heat sources are weak and less sensitive to the motion perturbations. By considering the fact that moist updrafts are narrow and using eddy viscosity of 0(1,000 m squared/s) the stability criterion suggests that some frontal rainbands were probably dominated by the CSI mechanism even in their mature quasi-steady stage.

Clark, J. H. E.↗

NASA NTRS1991

Theoretical and computational dynamics of a compressible flow

An introduction to the theoretical and computational fluid dynamics of a compressible fluid is presented. The general topics addressed include: thermodynamics and physical properties of compressible fluids; 1D flow of an inviscid compressible fluid; shock waves; fundamental equations of the dynamics of a compressible inviscid non-heat-conducting and radiating fluid, method of small perturbations, linearized theory; 2D subsonic steady potential flow; hodograph and rheograph methods, exact solutions of 2D insentropic steady flow equations, 2D steady transonic and hypersonic flows, method of characteristics, linearized theory of 3D potential flow, nonlinear theory of 3D compressibe flow, anisentropic (rotational) flow of inviscid compressible fluid, electromagnetogasdynamics, multiphase flows, flows of a compressible fluid with transport phenomena.

Pai, Shih-I↗

NASA NTRS1993

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗

NASA NTRS1974

Subsonic potential aerodynamics for complex configurations - A general theory

A general theory of subsonic potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the velocity potential is obtained for both supersonic and subsonic flow. Under the small perturbation assumption, the potential at any point in the field depends only upon the values of the potential and its normal derivative on the surface of the body. On the surface of the body, this representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface. The theory is applied to finite-thickness wings in subsonic steady and oscillatory flows.

Morino, L.↗

NASA NTRS1995

Reduction technique for tire contact problems

A reduction technique and a computational procedure are presented for predicting the tire contact response and evaluating the sensitivity coefficients of the different response quantities. The sensitivity coefficients measure the sensitivity of the contact response to variations in the geometric and material parameters of the tire. The tire is modeled using a two-dimensional laminated anisotropic shell theory with the effects of variation in geometric and material parameters, transverse shear deformation, and geometric nonlinearities included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The elemental arrays are obtained by using a modified two-field, mixed variational principle. For the application of the reduction technique, the tire finite element model is partitioned into two regions. The first region consists of the nodes that are likely to come in contact with the pavement, and the second region includes all the remaining nodes. The reduction technique is used to significantly reduce the degrees of freedom in the second region. The effectiveness of the computational procedure is demonstrated by a numerical example of the frictionless contact response of the space shuttle nose-gear tire, inflated and pressed against a rigid flat surface.

Noor, Ahmed K.↗

NASA NTRS1995

Advances in reduction techniques for tire contact problems

Some recent developments in reduction techniques, as applied to predicting the tire contact response and evaluating the sensitivity coefficients of the different response quantities, are reviewed. The sensitivity coefficients measure the sensitivity of the contact response to variations in the geometric and material parameters of the tire. The tire is modeled using a two-dimensional laminated anisotropic shell theory with the effects of variation in geometric and material parameters, transverse shear deformation, and geometric nonlinearities included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The elemental arrays are obtained by using a modified two-field, mixed variational principle. For the application of reduction techniques, the tire finite element model is partitioned into two regions. The first region consists of the nodes that are likely to come in contact with the pavement, and the second region includes all the remaining nodes. The reduction technique is used to significantly reduce the degrees of freedom in the second region. The effectiveness of the computational procedure is demonstrated by a numerical example of the frictionless contact response of the space shuttle nose-gear tire, inflated and pressed against a rigid flat surface. Also, the research topics which have high potential for enhancing the effectiveness of reduction techniques are outlined.

Noor, Ahmed K.↗

NASA NTRS1996

Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear Tire

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Tanner, John A.↗

NASA NTRS1996

Computational methods for frictional contact with applications to the Space Shuttle orbiter nose-gear tire: Comparisons of experimental measurements and analytical predictions

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical-loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Tanner, John A.↗

NASA NTRSDate not supplied

Metal Hydroxide and Oxyhydroxide Gas Database

In a high temperature combustion situation such as a gas turbine or rocket engine, combustion products include water vapor. This water vapor reacts with oxides in the hot-gas-path to form volatile hydroxides and oxyhydroxides. The oxides may be structural oxide components or protective oxides on alloys or non-oxide ceramics. In either case, this enhanced volatilization leads to degradation of components. Reliable thermochemical data for many metal hydroxides and oxyhydroxides has not been available. We review a database put together at NASA over many years based on experimental and ab initio computations for thermochemical data of Al, Si, Ti, Cr, Mn, Y, Zr, La, Ta, Gd, and Yb hydroxides and oxyhydroxides. Experimental methods for measuring thermodynamic quantities of metal hydroxides and oxyhydroxides are limited since the required high temperatures and high pressures preclude many conventional methods. Nonetheless, transpiration has proven a valuable tool in our laboratories for the Si-O-H, Cr-O-H, and Ti-O-H systems. Data are analyzed with second and third law methods. These data can be leveraged with quantum chemistry to provide reliable free energy functions for the third law calculation and comparison to the derived enthalpies of formation. Both wave function and DFT methods can be utilized for deriving the thermodynamic functions for the various metal hydroxides and oxyhydroxides. We have found that, in general, reasonable molecular geometries and spectroscopic data can be derived with a relatively low level of theory, i.e. DFT with the B3LYP functional. Accurate calculations of the enthalpy of formation require higher levels of theory, such as the Coupled Cluster, Singles, Doubles, and perturbative Triples CCSD(T) approach with complete basis sets (CBS). Also, corrections for hindered rotations and anharmonicity are necessary. For some symmetries, the anharmonic correction has proven to be a challenge and we have found that this is only treated properly by certain codes. The database lists the fHo(298), So(298), and Cp in the form Cp = A + BT + CT2 + D/T + E/T2, where A, B, C, D, and E are the fitting constants. Thus, it can be easily used in any of the common computational thermochemistry codes. To date, the database contains 51 gaseous species of the formula MOx(OH)y.

Metal Hydroxides↗