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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 775 records · Page 43
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NASA NTRS1978

Perturbations in two- and three-dimensional transonic flows

The difficulty of treating the perturbation of transonic flow, during which shock waves change position, can be overcome by using a distorted coordinate system in which the locations of all shock waves do not change; the distortion is found as part of the solution. This device leads to a relation that allows a range of flows, with differing shock locations, to be related algebraically to two known 'calibration' flows. Results for flows around finite wings, including those with multiple, intersecting shock waves, are presented. A typical computing time for such examples is 0.3 sec on a CDC 7600 computer.

Nixon, D.↗
NASA NTRS1978

Direct numerical solution of the transonic perturbation integral equation for lifting and nonlifting airfoils

The linear transonic perturbation integral equation previously derived for nonlifting airfoils is formulated for lifting cases. In order to treat shock wave motions, a strained coordinate system is used in which the shock location is invariant. The tangency boundary conditions are either formulated using the thin airfoil approximation or by using the analytic continuation concept. A direct numerical solution to this equation is derived in contrast to the iterative scheme initially used, and results of both lifting and nonlifting examples indicate that the method is satisfactory.

Nixon, D.↗
NASA NTRS1979

The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.

Meyer, C. D., Jr.↗
NASA NTRS1979

Evolution of the rotation of an artificial earth satellite under the influence of a perturbing moment which is constant in fixed axes

The change in the modulus of the vector of the kinetic moment of a satellite which is noted during the determination of the actual orientation of an artificial earth is discussed. The change is due to the presence of a small perturbing moment, which is constant in fixed axes relative to the satellite. It is also shown that the averaged equations in this problem can be integrated.

Neyshtadt, A. I.↗
NASA NTRS1979

Matrix perturbation for analytical model improvement

A matrix perturbation method is proposed to calculate the Jacobian matrix and to compute the new eigendata for the parameter estimation procedure. The advantages of the method are the applicability to large complex structures without knowing the analytical expressions for the mass and stiffness matrices, and a cost effective approach for the re-computation of the eigendata. This method also allows the use of other measurements such as modal forces, kinetic energy distribution, and strain energy distributions in the estimation procedure. A realistic sample problem is presented to demonstrate the effectiveness of the proposed method.

Chen, J. C.↗
NASA NTRS1979

Second-order estimates in singular perturbation of output regulator problems

A method of order reduction in singular perturbation problems due to Chow and Kokotovic is studied. The method is used for an output regulator problem in control theory. The quadratic term in the asymptotic expansion of Chow and Kokotovic is calculated and it is shown by some examples how this term can give evidence of the accuracy of the procedure.

Rublein, G.↗
NASA NTRS1979

Singular perturbation techniques for on-line optimal flight path control

This paper presents a partial evaluation on the use of singular perturbation methods for developing computer algorithms for on-line optimal control of aircraft. The evaluation is based on a study of the minimum time intercept problem using F-4 aerodynamic and propulsion data as a base line. The extensions over previous work on this subject are that aircraft turning dynamics (in addition to position and energy dynamics) are included in the analysis, the algorithm is developed for a moving end point and is adaptive to unpredictable target maneuvers, and short range maneuvers that do not have a cruise leg are included. Particular attention is given to identifying those quantities that can be precomputed and stored (as a function of aircraft total energy), thus greatly reducing the onboard computational load. Numerical results are given that illustrate the nature of the optimal intercept flight paths, and an estimate is given for the execution time and storage requirements of the control algorithm.

Calise, A. J.↗
NASA NTRS1979

The adiabatic semiclassical perturbation theory for vibrationally inelastic scattering. I - Collinear calculations. II - Three-dimensional treatment

A semiclassical approximation to treat vibrationally inelastic scattering is developed. The vibrational basis set used is adiabatic with respect to a reference potential which is chosen to be as close as possible to the true potential and also gives easily obtainable solutions to the vibrational wave equation. The radial wave functions are obtained using the WKB approximation, and the coupled Schroedinger equations are solved by a first-order perturbation method to yield a phase shift matrix which is exponentiated to give the full scattering matrix. Results were obtained for all the cases computed by Secrest and Johnson and by Clark and Dickinson, and the agreement is better than 10% for half of the cross-sections and rarely off by more than a factor of 2.

Cross, R. J., Jr.↗
NASA NTRS1979

Application of singular perturbation techniques /SPT/ and continuation methods for on-line aircraft trajectory optimization

The singular perturbation theory (SPT) approximation of optimal feedback control laws is presented and methods for on-line application of these approximations are discussed. It is demonstrated that SPT control laws break down when the current state is near the terminal target state. The use of continuation methods to improve the accuracy of the SPT approximation and to obtain global solutions of two-point boundary value problems is also discussed. As an illustration, consideration is given to the minimum-time control of a supersonic aircraft for a three-dimensional intercept problem.

Washburn, R. B.↗
NASA NTRS1979

Nonlinear singularly perturbed optimal control problems with singular arcs

Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.

Ardema, M. D.↗
NASA NTRS1980

Baroclinic instability with variable gravity: A perturbation analysis

Solutions for a quasigeostrophic baroclinic stability problem in which gravity is a function of height were obtained. Curvature and horizontal shear of the basic state flow were omitted and the vertical and horizontal temperature gradients of the basic state were taken as constant. The effect of a variable dielectric body force, analogous to gravity, on baroclinic instability for the design of a spherical, baroclinic model for Spacelab was determined. Such modeling could not be performed in a laboratory on the Earth's surface because the body force could not be made strong enough to dominate terrestrial gravity. A consequence of the body force variation and the preceding assumptions was that the potential vorticity gradient of the basic state vanished. The problem was solved using a perturbation method. The solution gives results which are qualitatively similar to Eady's results for constant gravity; a short wavelength cutoff and a wavelength of maximum growth rate were observed. The averaged values of the basic state indicate that both the wavelength range of the instability and the growth rate at maximum instability are increased. Results indicate that the presence of the variable body force will not significantly alter the dynamics of the Spacelab experiment. The solutions are also relevant to other geophysical fluid flows where gravity is constant but the static stability or Brunt-Vaisala frequency is a function of height.

Giere, A. C.↗
NASA NTRS1980

A singular perturbation analysis of minimum time long range intercept

The application of singular perturbation theory for deriving algorithms suitable for on board real time computation of optimal aircraft trajectory control was investigated. Minimum time intercept in three dimensions was selected as a pilot problem formulation, and data for an early version F-4 aircraft was used to represent aircraft aerodynamic and propulsion characteristics. Results include the derivation of nonlinear, near optimal feedback control laws that are readily implementable in an aircraft flight computer, performance results for a variety of initial conditions (including optimal intercept at short ranges), and a point mass three dimensional simulation suitable for representing fighter aircraft under closed loop optimal control.

Calise, A.↗
NASA NTRS1978

Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

Brandt, A.↗
NASA NTRS1979

A perturbative treatment of aerosol scattering of infrared radiation

Calculations of long-wave atmospheric heating and cooling rates using the rate equations of Rodgers and Walshaw (1966) with the Malkmus (1967) random band model are presented. A perturbation scheme is developed for the inclusion of aerosol scattering effects in the numerical calculation. Unlike the flux differencing method for calculating long-wave heating and cooling rates, this scheme allows aerosol effects to be included in a simple manner with only a small additional use of computer time. The calculations indicate good agreement with those of previous investigators and demonstrate the expected equivalence of the flux-differencing method and the flux-divergence equation of Rodgers and Walshaw (1966), even at stratospheric altitudes. It is found that aerosols lead to a net heating in the lower troposphere due to infrared scattering and absorption.

Yueh, W. R.↗
NASA NTRS1979

On the 'thickness' of Saturn's rings caused by satellite and solar perturbations and by planetary precession

In the present paper, long-period and secular variations of the longitude of ascending node are derived for a particle orbiting an oblate precessing planet subjected to perturbation by an exterior satellite moving along a low-inclination orbit. It is shown that precession of Saturn under the solar torque, which causes the Laplace plane to be noninertial, is also effective in producing a forced inclination. The height above the Laplace plane associated with this variation is several meters for a particle located in the middle of the ring.

Burns, J. A.↗
NASA NTRS1979

Mean-spherical model for soft potentials - The hard core revealed as a perturbation

The mean-spherical approximation for fluids is extended to treat the case of dense systems interacting via soft potentials. The extension takes the form of a generalized statement concerning the behavior of the direct-correlation function c(r) and the radial-distribution function g(r). From a detailed analysis that views the hard-core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

Rosenfeld, Y.↗
NASA NTRS1980

Atmospheric bromine and ozone perturbations in the lower stratosphere

The role of bromine compounds in the photochemistry of the natural and perturbed stratosphere has been reexamined using an expanded reaction scheme and the results of recent laboratory studies of several key reactions. The most important finding is that through the reaction BrO + ClO yielding Br + Cl + O2 there is a synergistic effect between bromine and chlorine which results in an efficient catalytic destruction of ozone in the lower stratosphere. One-dimensional photochemical model results indicate that BrO is the major bromine species throughout the stratosphere, followed by BrONO2, HBr, HOBr and Br. It is shown from the foregoing that bromine is more efficient than chlorine as a catalyst for destroying ozone, and the implications for stratospheric ozone of possible future growth in the industrial and agricultural use of bromine are discussed. Bromine concentrations of 20 pptv (2 x 10 to the -11th power), as suggested by recent observations, can decrease the present-day integrated ozone column density by 2.4%, and can enhance ozone depletion from steady-state chlorofluoromethane release at 1973 rates by a factor of 1.1-1.2.

Yung, Y. L.↗