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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 181 records · Page 10
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NASA NTRS1972

Asymptotic theory of a slender rotating beam with end masses.

The method of matched asymptotic expansions is employed to solve the singular perturbation problem of the vibrations of a rotating beam of small flexural rigidity with concentrated end masses. The problem is complicated by the appearance of the eigenvalue in the boundary conditions. Eigenfunctions and eigenvalues are developed as power series in the perturbation parameter beta to the 1/2 power, and results are given for mode shapes and eigenvalues through terms of the order of beta.

Whitman, A. M.↗
NASA NTRS1972

The large Reynolds number - Asymptotic theory of turbulent boundary layers.

A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.

Mellor, G. L.↗
NASA NTRS1973

Use of multivariable asymptotic expansions in a satellite theory

Initial conditions and perturbative force of satellite are restricted to yield motion of equatorial satellite about oblate body. In this manner, exact analytic solution exists and can be used as standard of comparison in numerical accuracy comparisons. Detailed numerical accuracy studies of uniformly valid asymptotic expansions were made.

Dallas, S. S.↗
NASA NTRS1972

Asymptotic expansion of an impulse for an optimal finite burn

Closed form expressions are derived for the position and velocity of a spacecraft during a finite burn using the method involving the theory of asymptotic expansion of the optimal impulsive solution. The small parameter is given by the reciprocal of the mass flow rate. The expansion is given in terms of the impulsive solution and holds up through third-order for the velocity and fourth-order for the position.

Pines, S.↗
NASA NTRS1973

Asymptotic solution of the problem for a thin axisymmetric cavern

The boundary value problem which describes the axisymmetric separation of the flow around a body by a stationary infinite stream is considered. It is understood that the cavitation number varies over the length of the cavern. Using the asymptotic expansions for the potential of a thin body, the orders of magnitude of terms in the equations of the problem are estimated. Neglecting small quantities, a simplified boundary value problem is obtained.

Serebriakov, V. V.↗
NASA NTRS1973

Asymptotic solution to the tangential low thrust energy increase trajectory

A approximate analytic solution to the low thrust constant acceleration energy increase trajectory using a tangential steering program is presented. The solution is based on a two-variable asymptotic expansion of the equations of motion formulated in regularized variables. The high accuracy of the second order solution derived is demonstrated by comparing it with numerically integrated trajectories.

Schwenzfeger, K. J.↗
NASA NTRS1974

Asymptotic solution for solar electric low thrust orbit raising with eclipse penalty

This paper describes an analytic solution for the solar electric low thrust orbit raising problem derived by application of the two-variable asymptotic expansion method. Included in the formulation are the effects of (1) high initial eccentricity, (2) large change of inclination, (3) variable mass, and (4) earth shadow penalty including the rotation of the shadow axis relative to the osculating orbit. An advantage of this mathematical strategy is that the effects of various steering policies can be evaluated readily from a physical point of view.

Flandro, G. A.↗
NASA NTRS1975

Asymptotic analytical methods in fluid mechanics related to drag prediction

Some recent theoretical work of a purely analytical nature is described which promises to provide engineering predictions for the important drag-related phenomena of flow in the stall regime. This analytical work deals with rigorous asymptotic studies of the complete Navier-Stokes equations that govern the viscous flow around any aerodynamic body under conditions where boundary layer separation takes place from the body surface.

Inger, G. R.↗
NASA NTRS1976

Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method

An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000.

Rudy, D. H.↗
NASA NTRS1976

Solution of the minimum time-to-climb problem by matched asymptotic expansions

Application of singular perturbation techniques to trajectory optimization problems of flight mechanics is discussed. The method of matched asymptotic expansions is used to obtain an approximate solution to the aircraft minimum time-to-climb problem. Outer, boundary-layer, and composite solutions are obtained to zeroth and first orders. A stability criterion is derived for the zeroth-order boundary-layer solutions (the theory requires a form of boundary-layer stability). A numerical example is considered for which it is shown that the stability criterion is satisfied and a useful numerical solution is obtained. The zeroth-order solution proves to be a poor approximation, but the first-order solution gives a good approximation for both the trajectory and the minimum time-to-climb. The computational cost of the singular perturbation solution is considerably less than that of a steepest descent solution. Thus singular perturbation methods appear to be promising for the solution of optimal control problems.

Ardema, M. D.↗
NASA NTRS1976

A NASTRAN implementation of the doubly asymptotic approximation for underwater shock response

A detailed description is given of how the decoupling approximation known as the doubly asymptotic approximation is implemented with NASTRAN to solve shock problems for submerged structures. The general approach involves locating the nonsymmetric terms (which couple structural and fluid variables) on the right hand side of the equations. This approach results in coefficient matrices of acceptable bandwidth but degrades numerical stability, requiring a smaller time step size than would otherwise be used. It is also shown how the structure's added (virtual) mass matrix, is calculated with NASTRAN.

Everstine, G. C.↗
NASA NTRS1976

Asymptotic residual pump transmission characteristics in laser-induced stimulated Brillouin scattering

The considered asymptotic relationship is investigated and an expression is sought for the slope of the curve representing the relation between the residual fractional transmitted pump and the pump excitation in backward-traveling-wave amplification. It is found that the characteristic -2 slope of the oscillation curve is a unique property. Rapid exponential decay may very well constitute an inherent limiting factor for efficient energy conversion.

Hsu, H.↗
NASA NTRS1977

An asymptotic analysis of a general class of signal detection algorithms

For applications to the problem of radio frequency interference identification, or in the search for extraterrestrial intelligence, it is important to have a basic understanding of signal detection algorithms. A general technique for assessing the asymptotic sensitivity of a broad class of signal detection algorithms is given. In these algorithms, the decision is based on the value of X sub 1 + X sub 2...+ X sub n where the X sub 1's are obtained by sampling and preliminary processing of a physical process.

Mceliece, R. J.↗
NASA NTRS1978

Use of asymptotic methods in vibration analysis

The derivation of dynamic differential equations, suitable for studying the vibrations of rotating, curved, slender structures was examined, and the Hamiltonian procedure was advocated for this purpose. Various reductions of the full system are displayed, which govern the vibrating troposkien when various order of magnitude restrictions are placed on important parameters. Possible advantages of the WKB asymptotic method for solving these classes of problems are discussed. A special case of this method is used illustratively to calculate eigenvalues and eigenfunctions for a flat turbine blade with small flexural stiffness.

Ashley, H.↗
NASA NTRS1979

Computer analysis of shells of revolution using asymptotic results

It is suggested that asymptotic results for the behavior of thin shells can be incorporated in a general computer code for the analysis of a complex shell structure. The advantage when compared to existing finite difference or finite element codes is a substantial reduction in computational labor with the capability of working to a specified level of accuracy. A reduction in user preparation time and dependance on user judgment is also gained, since mesh spacing can be internally generated. The general theory is described in this paper, as well as the implementation in the computer code FAST 1 (Functional Algorithm for Shell Theory) for the analysis of the general axisymmetric shell structure with axisymmetric loading.

Steele, C. R.↗
NASA NTRS1979

Asymptotic effective potentials for electron-hydrogen scattering

The asymptotic effective potential for electron- or positron-hydrogen elastic scattering is derived, correct to order x to the -7th, where x is the positron projectile coordinate, using the Feshbach optical potential as a starting point in the manner of Kleinman et al (1968). To order x to the -6th the potential agrees with the close-coupling results of Seaton and Steenman-Clark (1977) but not to order x to the -7th, where the present calculation gives the result + or - 213/2(x to the 7th) for electron and positron respectively. This coefficient differs considerably from the approximate value of Seaton and Steenman-Clark, and the discrepancy is traced to the omission of d states in their calculation.

Drachman, R. J.↗