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At least 199 records · Page 11

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NASA NTRS1980

A dynamic analysis of the motion of a low-wing general aviation aircraft about its calculated equilibrium flat spin mode

The properties of the flat spin mode of a general aviation configuration have been studied through analysis of rotary balance data, numerical simulation, and analytical study of the equilibrium state. The equilibrium state is predicted well from rotary balance data. The variations of yawing moment and pitching moment as functions of sideslip have been shown to be of great importance in obtaining accurate modeling. These dependencies are not presently available with sufficient accuracy from previous tests or theories. The stability of the flat spin mode has been examined extensively using numerical linearization, classical perturbation methods, and reduced order modeling. The stability exhibited by the time histories and the eigenvalue analyses is shown to be strongly dependent on certain static cross derivatives and more so on the dynamic derivatives. Explicit stability criteria are obtained from the reduced order models.

Tischler, M. B.↗

NASA NTRS1982

Asymptotic Expansions and Estimates for the Capillary Problem

The asymptotic properties for the small Bond number B of the equilibrium capillary interface interior to a circular cylindrical tube vertically dipped in an infinite reservoir of liquid are discussed. (The Bond number B is a dimensionless parameter which is the ratio of gravitational to capillary forces.) The formal expansion in powers of B of the solution to the differential equation describing the equilibrium surface (as can be obtained by standard perturbation methods) is proved to be truly asymptotic -- to all orders and uniformly in the variable and parameter gamma, the contact angle. Sequences of general estimates, in closed form, from above and from below, are also given for the solution and related functions. The M-th term in these sequences are asymptotically exact to order m. An idiosyncrasy of the problem, crucial in obtaining these estimates, is the absolute monotonicity of the structural function of the system in integral form.

Brulois, F. P.↗

NASA NTRS1982

Singular perturbation techniques for real time aircraft trajectory optimization and control

The usefulness of singular perturbation methods for developing real time computer algorithms to control and optimize aircraft flight trajectories is examined. A minimum time intercept problem using F-8 aerodynamic and propulsion data is used as a baseline. This provides a framework within which issues relating to problem formulation, solution methodology and real time implementation are examined. Theoretical questions relating to separability of dynamics are addressed. With respect to implementation, situations leading to numerical singularities are identified, and procedures for dealing with them are outlined. Also, particular attention is given to identifying quantities that can be precomputed and stored, thus greatly reducing the on-board computational load. Numerical results are given to illustrate the minimum time algorithm, and the resulting flight paths. An estimate is given for execution time and storage requirements.

Calise, A. J.↗

NASA NTRS1982

Transonic perturbation analysis of wing-fuselage-nacelle-pylon configurations with powered jet exhausts

A transonic small perturbation method has been developed for the analysis of general wing-fuselage-nacelle-pylon configurations with powered jet exhausts. Finite difference successive line relaxation algorithm is used to solve the small disturbance potential equation in conservative form. The nacelle tangency condition and the jet exhaust plume contact conditions are fulfilled in a quasi-cylindrical fashion on a surface fitting the Cartesian grid. The pylon tangency condition is treated in a quasi-planar manner as for the wing. Viscous displacement effects on the wing are modeled by suitable shape changes including the placement of a viscous ramp at the base of the shock. Computed results of a transport configuration show satisfactory correlation with test data.

Wai, J. C.↗

NASA NTRS1983

Complex eigenvalues for the stability of Couette flow

The eigenvalue problem for the linear stability of Couette flow between rotating concentric cylinders to axisymmetric disturbances is considered. It is shown by numerical calculations and by formal perturbation methods that when the outer cylinder is at rest there exist complex eigenvalues corresponding to oscillatory damped disturbances. The structure of the first few eigenvalues in the spectrum is discussed. The results do not contradict the principle of exchange of stabilities, namely, for a fixed axial wavenumber the first mode to become unstable as the speed of the inner cylinder is increased is nonoscillatory as the stability boundary is crossed.

Diprima, R. C.↗

NASA NTRS1983

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

Strelkov, S. A.↗

NASA NTRS1984

Flow in a differentially rotated cylindrical drop at moderate Reynolds number

Galerkin finite-element approximations are combined with computer-implemented perturbation methods for tracking families of solutions to calculate the steady axisymmetric flows in a differentially rotated cylindrical drop as a function of Reynolds number Re, drop aspect ratio and the rotation ratio between the two end disks. The flows for Reynolds numbers below 100 are primarily viscous and reasonably described by an asymptotic analysis. When the disks are exactly counter-rotated, multiple steady flows are calculated that bifurcate to higher values of Re from the expected solution with two identical secondary cells stacked symmetrically about the axial midplane. The new flows have two cells of different size and are stable beyond the critical value Re sub c. The slope of the locus of Re sub c for drops with aspect ratio up to 3 disagrees with the result for two disks of infinite radius computed assuming the similarity form of the velocity field. Changing the rotation ratio for exact counter-rotation ruptures the junction of the multiple flow fields into two separated flow families.

Harriott, G. M.↗

NASA NTRS1984

Solution influence on biomolecular equilibria - Nucleic acid base associations

Various attempts to construct an understanding of the influence of solution environment on biomolecular equilibria at the molecular level using computer simulation are discussed. First, the application of the formal statistical thermodynamic program for investigating biomolecular equilibria in solution is presented, addressing modeling and conceptual simplications such as perturbative methods, long-range interaction approximations, surface thermodynamics, and hydration shell. Then, Monte Carlo calculations on the associations of nucleic acid bases in both polar and nonpolar solvents such as water and carbon tetrachloride are carried out. The solvent contribution to the enthalpy of base association is positive (destabilizing) in both polar and nonpolar solvents while negative enthalpies for stacked complexes are obtained only when the solute-solute in vacuo energy is added to the total energy. The release upon association of solvent molecules from the first hydration layer around a solute to the bulk is accompanied by an increase in solute-solvent energy and decrease in solvent-solvent energy. The techniques presented are expectd to displace less molecular and more heuristic modeling of biomolecular equilibria in solution.

Pohorille, A.↗

NASA NTRS1985

Unsteady Heat Transfer Due to Time-dependent Free Stream Velocity

The present work was undertaken in order to study the unsteady combined convection from a horizontal circular cylinder to a transverse flow. A coordinate perturbation method is used to transform the governing set of partial differential equations into a system of ordinary differential equations. The free stream time-dependent velocity was assumed to be sinusoidal and the boundary layer response due to both low as well as high frequencies of oscillation will be studied. Currently numerical solutions are being obtained for the distribution of the unsteady Nusselt number and the friction factor.

Gorla, R. S. R.↗

NASA NTRS1985

Relativistic electron in curved magnetic fields

Making use of the perturbation method based on the nonlinear differential equation theory, the author investigates the classical motion of a relativistic electron in a class of curved magnetic fields which may be written as B=B(O,B sub phi, O) in cylindrical coordinates (R. phi, Z). Under general astrophysical conditions the author derives the analytical expressions of the motion orbit, pitch angle, etc., of the electron in their dependence upon parameters characterizing the magnetic field and electron. The effects of non-zero curvature of magnetic field lines on the motion of electrons and applicabilities of these results to astrophysics are also discussed.

An, S.↗

NASA NTRS1985

Shuttle glow emissions due to radiative relaxation of highly vibrationally excited NO molecules produced by surface reflection

A new mechanism is proposed for the Space Shuttle glow, which is due to the radiative relaxation of ambient nitric-oxide molecules that are excited to very high vibrational levels by collisions with the Shuttle surface. Many of the particles colliding with the Shuttle surface at a very high speed (about 8 km/sec) would bounce off, exciting vibrational and rotational motions of molecules up to the level of vibrational quantum number v not greater than 35. Radiative transfer from these high levels should cause emissions in the spectrum range from infrared (IR) to visible red depending upon the transition paths. A perturbation method is used to calculate the transition probability and the emission intensity for the transitions of Delta-v not greater than 4. The result indicates that the Delta-v not greater than 4 transitions from high vibrational levels dominates the other transitions; the Delta-v = 4 transitions generally occur at the IR range.

Shimazaki, T.↗

NASA NTRS1986

Equations for the vibration of a slewing flexible spacecraft

The derivation of the equations describing the vibration of a flexible spacecraft is presented in the context of a perturbation method permitting a maneuver strategy independent of the vibration control. A straightforward open-loop minimum-time rotational maneuver strategy is developed for the spacecraft regarded as a rigid body. Actuator dynamics are considered in the formulation. A maneuver force distribution is developed which excites the least amount of elastic deformation of the flexible parts of the spacecraft. An efficient technique for simulating structural vibrations during a maneuver is presented. Numerical results demonstrate the maneuver strategy and highlight the vibration caused by rotational maneuvers.

Quinn, R. D.↗

NASA NTRS1986

Maneuver and vibration control of SCOLE

This paper is concerned with the simultaneous maneuver and vibration control of the Spacecraft Control Laboratory Experiment (SCOLE). Summaries of the derivation of the equations of motion and of a perturbation method permitting a maneuver strategy independent of the vibration control are presented. Some of the problems encountered in dynamical modeling of a flexible spacecraft in an earth-based laboratory are high-lighted and solved. Numerical results demonstrating rotational maneuvers of the SCOLE model are included.

Quinn, R. D.↗

NASA NTRS1987

Motion and decay of vortex rings submerged in a rotational flow

The interaction between vortex rings of finite strength and an axisymmetric rotational background flow is studied by a singular perturbation method, because it is difficult to use a finite-difference method to analyze the viscous decay in the small core of a vortex ring. The analysis is carried out by combining a composite solution of a vortex ring and an unsteady Euler solution for the background rotational flow. Using the method of averaging, a numerical scheme is developed to obtain an Euler solution in which the grid and time-step sizes depend solely on the length and velocity scales of the background flow. Numerical results are presented to illustrate the interaction between the trajectories and decay rates of the vortex rings and the background rotational flow.

Ishii, K.↗

NASA NTRS1987

Interaction of a decaying vortex ring with a rotational background flow bounded by a solid wall

The interaction between a vortex ring of finite strength and an axisymmetric rotational background flow bounded by a solid wall is studied by a singular perturbation method. The analysis is carried out by combining a composite solution of a vortex ring and an unsteady Navier-Stokes solution for the background rotational flow. Using the method of averaging, numerical scheme is developed to obtain a Navier-Stokes solution in which the grid and time-step sizes depend solely on the length and velocity scales of the background flow. Numerical results are presented to illustrate the separation of the boundary layer on a solid wall and its interaction with the vortex ring.

Ishii, K.↗

NASA NTRS1985

Cellular interface morphologies in directional solidification. III - The effects of heat transfer and solid diffusivity

The shape and stability of two-dimensional finite-amplitude cellular interfaces arising during directional solidification are compared for several solidification models that account differently for latent heat released at the interface, unequal thermal conductivities of melt and solid, and solute diffusivity in the solid. Finite-element analysis and computer-implemented perturbation methods are used to analyze the families of steadily growing cellular forms that evolve from the planar state. In all models a secondary bifurcation between different families of finite-amplitude cells exists that halves the spatial wavelength of the stable interface. The quantitative location of this transition is very dependent on the details of the model. Large amounts of solute diffusion in the solid retard the growth of large-amplitude cells.

Ungar, Lyle H.↗

NASA NTRS1987

Maneuvering and vibration control of flexible spacecraft

This paper is concerned with the problem of slewing a large structure in space and suppressing any vibration at the same time. The structure is assumed to undergo large rigid-body motions and small elastic deformations. A perturbation method permits a maneuver strategy independent of the vibration control. Optimal control and pole placement techniques, formulated to include first-order actuator dynamics, are used to suppress the vibration during maneuver. The theory is illustrated by simultaneous maneuvering and vibration control of the Spacecraft Control Laboratory Experiment (SCOLE) model in a space environment.

Meirovitch, L.↗

NASA NTRS1988

Variance and bias confidence criteria for ERA modal parameter identification

For the ERA system identification algorithm, perturbation methods are used to develop expressions for variance and bias of the identified modal parameters. Based on the statistics of the measurement noise, the variance results serve as confidence criteria by indicating how likely the true parameters are to lie within any chosen interval about their identified values. This replaces the use of expensive and time-consuming Monte Carlo computer runs to obtain similar information. The bias estimates help guide the ERA user in his choice of which data points to use and how much data to use in order to obtain the best results, performing the trade-off between the bias and scatter. Also, when the uncertainty in the bias is sufficiently small, the bias information can be used to correct the ERA results. In addition, expressions for the variance and bias of the singular values serve as tools to help the ERA user decide the proper modal order.

Longman, Richard W.↗