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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

A crack problem with four distinct harmonic functions

The problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered. A closed form solution using four distinct harmonic functions (none of which can be taken arbitrarily) is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid. These are obtained by employing Fourier and Kontorovich-Lebedev integral transforms and certain singular solutions of Laplace equations in three dimensions. The variations of the intensity of the local stress field along the crack border are shown graphically. An example is presented, which is in contrast with the conclusion established in the literature that one of the four Papkovich-Neuber functions in three-dimensional elasticity may be arbitrarily set to zero.

Sih, G. C.↗
NASA NTRS1973

Point and path performance of light aircraft: A review and analysis

The literature on methods for predicting the performance of light aircraft is reviewed. The methods discussed in the review extend from the classical instantaneous maximum or minimum technique to techniques for generating mathematically optimum flight paths. Classical point performance techniques are shown to be adequate in many cases but their accuracies are compromised by the need to use simple lift, drag, and thrust relations in order to get closed form solutions. Also the investigation of the effect of changes in weight, altitude, configuration, etc. involves many essentially repetitive calculations. Accordingly, computer programs are provided which can fit arbitrary drag polars and power curves with very high precision and which can then use the resulting fits to compute the performance under the assumption that the aircraft is not accelerating.

Smetana, F. O.↗
NASA NTRS1973

The motion and stability of a dual-spin satellite during the momentum wheel spin-up maneuver.

The stability of a dual-spin satellite system during the momentum wheel spin-up maneuver is treated both analytically and numerically. The dual-spin system consists of a slowly rotating or despun main body, a momentum wheel (or rotor) which is accelerated by a torque motor to change its initial angular velocity relative to the main part to some high terminal value, and a nutation damper. A closed-form solution for the case of a symmetrical satellite indicates that when the nutation damper is physically constrained from movement (i.e., by use of a mechanical clamp) the magnitude of the vector sum of the transverse angular velocity components remains bounded during the wheel spin-up under the influence of a constant motor torque. The analysis is extended to consider such effects as the motion of the nutation damper during spin-up, and the effect of a nonsymmetrical mass distribution.

Sen, S.↗
NASA NTRS1973

Application of Papkovich-Neuber potentials to a crack problem.

The problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered in this paper. A closed form solution using four harmonic functions is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid. These are obtained by employing Fourier and Kontorovich-Lebedev integral transforms and certain singular solutions of Laplace equations in three dimensions. The variations of the intensity of the local stress field along the crack border are shown graphically.

Kassir, M. K.↗
NASA NTRS1974

Effects of turbulence in a planetary atmosphere on radio occultation

A formulation is given for the correlation functions for the log-amplitude and phase fluctuations of both spherical and plane waves propagating in a turbulent medium whose correlation function for refractive index fluctuations is described by the product of a function of the average coordinate and a function of the difference coordinate. The results are applied to radio occultation of a flyby space probe by the atmosphere of Venus, assuming that the turbulence in the atmosphere exists as a layer, that it is localized, isotropic, and smoothly varying, and that the localized turbulence is described by the Kolmogorov spectrum. Closed-form solutions for both variances and frequency spectra of the log-amplitude and phase fluctuations are obtained using Rytov's method, and it is seen that the shape of the frequency spectra depends greatly on the characteristics and extent of the turbulence.

Woo, R.↗
NASA NTRS1974

Prediction of unsteady airloads for oblique blade-gust interaction in compressible flow

The techniques of Galilean-Lorentz transformation and matched asymptotic expansions are used to simplify the procedure of calculating the lift and pressure distribution induced on an infinite-span thin wing interacting with an oblique sinusoidal gust in subsonic flow. This technique requires that the product of the flow Mach number and the reduced frequency be small. Under this condition, the inner region of the transformed space behaves as an incompressible flow, so that existing incompressible flow theories can be used as a basis to construct closed-form solutions for the airload induced on the wing. This approach is an extension of the GASP approximation developed by Amiet and Sears (1970). Results are obtained for both the magnitude and the phase of the unsteady lift due to interaction with gust. These results are compared with available numerical results. Some discrepancies are noted and discussed.

Chu, S.↗
NASA NTRS1974

Some analytical results for radiative transfer in thick atmospheres

Singular eigenmode expansions are a convenient analytical tool with which to study problems of monochromatic radiative transfer in thick or semi-infinite atmospheres. Some closed-form solutions are presented for anisotropic scattering, with the neglect of polarization effects. A basic ingredient for applications to the semi-infinite medium is Chandrasekhar's H-function, which is best defined through the Wiener-Hopf factorization. The solutions of the Milne and albedo problems are discussed in order that the method of matched asymptotic approximations may be used to describe the solution for a thick atmosphere adjacent to a diffusely reflecting ground. Expressions for the emerging distributions are quoted. A possible extension of the general scheme to problems involving polarization is indicated.

Kuscer, I.↗
NASA NTRS1974

A method for determining optimum phasing of a multiphase propulsion system for a single-stage vehicle with linearized inert weight

A general analytical treatment is presented of a single-stage vehicle with multiple propulsion phases. A closed-form solution for the cost and for the performance and a derivation of the optimal phasing of the propulsion are included. Linearized variations in the inert weight elements are included, and the function to be minimized can be selected. The derivation of optimal phasing results in a set of nonlinear algebraic equations for optimal fuel volumes, for which a solution method is outlined. Three specific example cases are analyzed: minimum gross lift-off weight, minimum inert weight, and a minimized general function for a two-phase vehicle. The results for the two-phase vehicle are applied to the dual-fuel rocket. Comparisons with single-fuel vehicles indicate that dual-fuel vehicles can have lower inert weight either by development of a dual-fuel engine or by parallel burning of separate engines from lift-off.

Martin, J. A.↗
NASA NTRS1975

Technical guidance and analytic services in support of SEASAT-A

The design of a high resolution radar for altimetry and ocean wave height estimation was studied. From basic principles, it is shown that a short pulse wide beam radar is the most appropriate and recommended technique for measuring both altitude and ocean wave height. To achieve a topographic resolution of + or - 10 cm RMS at 5.0 meter RMS wave heights, as required for SEASAT-A, it is recommended that the altimeter design include an onboard adaptive processor. The resulting design, which assumes a maximum likelihood estimation (MLE) processor, is shown to satisfy all performance requirements. A design summary is given for the recommended radar altimeter, which includes a full deramp STRETCH pulse compression technique followed by an analog filter bank to separate range returns as well as the assumed MLE processor. The feedback loop implementation of the MLE on a digital computer was examined in detail, and computer size, estimation accuracies, and bias due to range sidelobes are given for the MLE with typical SEASAT-A parameters. The standard deviation of the altitude estimate was developed and evaluated for several adaptive and nonadaptive split-gate trackers. Split-gate tracker biases due to range sidelobes and transmitter noise are examined. An approximate closed form solution for the altimeter power return is derived and evaluated. The feasibility of utilizing the basic radar altimeter design for the measurement of ocean wave spectra was examined.

Brooks, W. L.↗
NASA NTRS1975

Nonlinear hyperbolic theory of thermal waves in metals

A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.

Wilhelm, H. E.↗
NASA NTRS1975

The low frequency sound from multipole sources in axisymmetric shear flows, with applications to jet noise

A closed-form solution for the sound radiation from multipole sources imbedded in an infinite cylindrical jet with an arbitrary velocity profile is obtained. It is valid in the limit where the wavelength is large compared with the jet radius. Simple formulae for the acoustic pressure field due to convected point sources are also obtained. The results show (in a simple way) how the mean flow affects the radiation pattern from the sources. For convected lateral quadrupoles it causes the exponent of the Doppler factor multiplying the far-field pressure signal to be increased from the value of 3 used by Lighthill to 5.

Goldstein, M. E.↗
NASA NTRS1975

Flutter analysis of two parallel elastically coupled flat plates

Flutter of two parallel elastically coupled flat plates was investigated analytically. A closed-form solution including both aerodynamic and structural damping is presented for flutter of flat orthotropic plates coupled by an elastic medium. Both plates are simply supported along the side edges but are supported by deflectional, rotational, and torsional springs of arbitrary stiffness at the leading and trailing edges. Two-dimensional quasi-steady aerodynamics was utilized in the solution. Since the large number of variables present in the problem precludes extensive parametric studies, results are presented to indicate the basic flutter characteristics of coupled two-plate systems and to assess the validity of previously published modal solutions for similar problems.

Shore, C. P.↗
NASA NTRS1976

Face-seal lubrication. 2: Theory of response to angular misalignement

A theoretical analysis was made of a hypothetical seal operating mode. The hypothetical seal model provides for three degrees of primary ring motion and includes the force and moments induced by primary ring response to seat angular misalignment. This ring response causes a relative angular misalignment between the faces of the primary seal. Hydrodynamic pressure generation is produced by this misalignment. The analysis is based on the Reynolds equation in short bearing form and on a balance of forces and moments that arise from hydrodynamic and secondary seal friction effects. A closed form solution was obtained that can be solved for film thickness and relative angular misalignment.

Ludwig, L. P.↗
NASA NTRS1976

Finite element computer program to analyze cracked orthotropic sheets

A two dimensional orthotropic sheet with through-the-thickness cracks and temperature gradient was analyzed. The program includes special crack tip elements that account for singular stress fields associated with crack opening and crack sliding displacements at the crack tip. The program also includes a linear spring element and a constant strain, triangular element. A number of problems for which closed form solutions exist were analyzed to demonstrate the capabilities of the program.

Chu, C. S.↗
NASA NTRS1976

Predicting a vehicle's attitude response to a single yo despin

The method developed for analysis of single yo despin systems is a two step process. The first step utilizes the despin equations for a yo or yo-yo system to compute the cable tension force and its point of application on the body throughout the despin process. The second step considers the actual body configuration and treats the force just discussed as a prescribed external force acting on the surface of the body at the physical location of the despin system. The resulting vehicle coning angle is first computed using a digital computer program for a body with no initial coning prior to despin. Closed form solutions which utilize the previous results are then used to treat the effects of initial conditions.

Bensimon, M.↗
NASA NTRS1976

Orifice resistance for ejection into a grazing flow

To explain the decrease in orifice resistance with the addition of grazing flow, the flow from an orifice was modeled by using an inviscid analysis which is valid when the orifice flow total pressure is nearly the same as the free stream grazing flow total pressure. For steady outflow from an orifice into a grazing flow, the orifice flow can enter the main grazing flow in an inviscid manner without generating large eddies to dissipate the kinetic energy of the jet. From the analysis, a simple closed-form solution was developed for the steady resistance for ejection from an orifice into a grazing-flow field. The calculated resistance compare favorably with data for a flow regime where the total pressure difference between the grazing flow and the orifice flow is small.

Baumeister, K. J.↗
NASA NTRS1977

Some MACSYMA program for solving difference equations

A set of MACSYMA programs are described for finding closed form solutions to linear recurrence relations in equations having either constant or variable coefficients. In the homogenous case, a polymonial equation is obtained and the solution to the recurrence relation can be written as a linear combination of the roots of the polynomial. Exponential generating functions are used to solve variable coefficient relations. Taking successive derivatives and using the recurrence relation, an ordinary differential equation is obtained. Expanding the solution to the differential equation in a Taylor series, shows that the nth term of the series is the solution to the recurrence relation. For second order recurrences, a check is made for those that can be solved in terms of Bessel functions.

Ivie, J.↗
NASA NTRS1977

An approximate method for design and analysis of an ALOHA system

An approximate method for the design and performance prediction of a multiaccess communication system which employs the ALOHA packet-switching technique is developed, based on the use of a diffusion process approximation of an ALOHA-like system (with or without time-slotting). A simple closed-form solution for the variable Q(t), a variant of the number of backlog messages at time t, is given in terms of a few system and user parameters. Final results are expressed in terms of ordinary performance measures such as throughput and average delay. Several numerical examples are given to demonstrate the usefulness of the approximation technique developed.

Kobayashi, H.↗