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At least 307 records · Page 17

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NASA NTRS1975

Broadband noise generated by turbulent inflow to rotor or stator blades in an annular duct

The Green's function relating the radiated pressure field to the fluctuating forces on rotor or stator blades is developed in the presence of dissipation due to turbulent velocity fluctuations and sound speed fluctuations. The resonances in the output power spectrum which would occur at the cut-off frequencies in the absence of dissipation should be removed and smeared out by the incorporation of dissipation. Wave number dependence is developed for an effective eddy viscosity due to the aforementioned fluctuations in the background medium. The space-time correlation function for blade-normal velocity fluctuations on a single or on two different blades is developed in terms of the velocity correlation tensor for the inflow under the assumptions of isotropy and (Taylor) frozen behavior. The correlation function is then simplified under certain approximations and the behavior of the blade-force correlation function is inferred.

Lnae, F.↗

NASA NTRS1975

Suppression of nonlinear oscillations in combustors with partial length acoustic liners

An analytical model is formulated for a three-dimensional nonlinear stability problem in a rocket motor combustion chamber. The chamber is modeled as a right circular cylinder with a short (multi-orifice) nozzle, and an acoustic linear covering an arbitrary portion of the cylindrical periphery. The combustion is concentrated at the injector and the gas flow field is characterized by a mean Mach number. The unsteady combustion processes are formulated using the Crocco time lag model. The resulting equations are solved using a Green's function method combined with numerical evaluation techniques. The influence of acoustic liners on the nonlinear waveforms is predicted. Nonlinear stability limits and regions where triggering is possible are also predicted for both lined and unlined combustors in terms of the combustion parameters.

Espander, W. R.↗

NASA NTRS1974

Normal-mode approach to wave propagation in the turbulent atmosphere

Recent studies have used the superposition principle (extended Huygens-Fresnel principle) to characterize completely the statistics of a field that has propagated through a thick slab of turbulent air in terms of the statistics for spherical-wave sources. In this paper, we consider the normal-mode decomposition associated with this linear system propagation model. In particular, we use the statistics of the atmospheric impulse response (Green's function) to show that the atmospheric mode decomposition exhibits far-field and near-field regimes very similar to those of free-space propagation. The significance of these results for optical communication through the atmosphere is briefly discussed.

Shapiro, J. H.↗

NASA NTRS1975

On an integro-differential equation model for the study of the response of an acoustically coupled panel

The response of a clamped panel to supersonically convected turbulence is considered. A theoretical model in the form of an integro-differential equation is employed that takes into account the coupling between the panel motion and the surrounding acoustic medium. The kernels of the integrals, which represent induced pressures due to the panel motion, are Green's functions for sound radiations under various moving and stationary sources. An approximate analysis is made by following a finite-element Ritz-Galerkin procedure. Preliminary numerical results, in agreement with experimental findings, indicate that the acoustic damping is the controlling mechanism of the response.

Yen, D. H. Y.↗

NASA NTRS1975

Interaction between a circular inclusion and an arbitrarily oriented crack

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Erdogan, F.↗

NASA NTRS1975

The scattering of electromagnetic pulses by a slit in a conducting screen

A direct method for calculating the impulse response of a slit in a conducting screen is presented which is derived specifically for the analysis of transient scattering by two-dimensional objects illuminated by a plane incident wave. The impulse response is obtained by assuming that the total response is composed of two sequences of diffracted waves. The solution is determined for the first two waves in one sequence by using Green's functions and the equivalence principle, for additional waves in the sequence by iteration, and for the other sequence by a transformation of coordinates. The cases of E-polarization and H-polarization are considered.

Ackerknecht, W. E., III↗

NASA NTRS1975

Vector potential and metric perturbations of a rotating black hole

The assumption of factorized Green's functions together with the inhomogeneous Teukolsky equations are used to derive analytic expressions for homogeneous metric (and vector potential) perturbations of a Kerr black hole. These homogeneous solutions are used to construct solutions to the perturbation equations when sources are present. What one finds are particularly simple formulas for the energy and angular momentum flux in the asymptotic regions at plus or minus infinity.-

Chrzanowski, P. L.↗

NASA NTRS1975

Derivation and application of the reciprocity relations for radiative transfer with internal illumination

A Green's function formulation is used to derive basic reciprocity relations for planar radiative transfer in a general medium with internal illumination. Reciprocity (or functional symmetry) allows an explicit and generalized development of the equivalence between source and probability functions. Assuming similar symmetry in three-dimensional space, a general relationship is derived between planar-source intensity and point-source total directional energy. These quantities are expressed in terms of standard (universal) functions associated with the planar medium, while all results are derived from the differential equation of radiative transfer.

Cogley, A. C.↗

NASA NTRS1975

Combustion instability with partial length acoustic liners

The development is discussed of analytical techniques and numerical methods for the prediction of the stability behavior of liquid propellant rocket combustors with partial length acoustic liners, injector face baffles, and nonlinear combustion responses. Three primary objectives included: (1) extension of the Green's Function integral-iteration technique previously developed so that nonlinear three dimensional wave propagation effects could be included in stability predictions; (2) development of an analytical technique and a computer program for the prediction of the damping effects caused by injector face baffles; and (3) inclusion of a nonlinear, wave distortation dependent, combustion response model in the global stability analysis and determination of its effect on combustor stability.

Mitchell, C. E.↗

NASA NTRS1976

Evidence of the beam pattern concept of subsonic jet noise emission

The methods and results are described of an approach toward positively identifying the apparent location and strength of the sound source in a subsonic jet. The Green's function technique is applied to regenerate the three-dimensional distribution of the acoustic far field from measured data on a two-dimensional plane. The apparent sound-source location is also determined by using geometrical ray acoustics. The results revealed a number of features of the subsonic jet noise mechanisms; they show that the apparent sound source is highly localized within the jet flow and that the spontaneous noise emission from such a compact source volume is in the fashion of a narrow beam with random directions. These observable properties of the sound field offer the basis for a beam pattern concept of subsonic jet noise radiation. A powerful and accurate technique of aerodynamic noise measurement is verified. This technique is expected to have important applications in the development of jet noise reduction technology.

Pao, S. P.↗

NASA NTRS1975

Effect of flow on the acoustic resonances of an open-ended duct

The effect of flow on the acoustic resonances of an open-ended, hard-walled duct is analyzed. The flow produces acoustic losses both in the interior of the duct and at the ends. Unless the duct is very long, typically 100 times the diameter, the losses at the ends dominate. At flow Mach numbers in excess of 0.4 the losses are so large that axial duct resonances are almost completely suppressed. The plane-wave Green's function for the duct with flow is expressed in terms of the (experimentally determined) pressure reflection coefficients at the ends of the duct, and the flow dependence of the complex eigenfrequencies of the duct is obtained. Some observations concerning the noise produced by the flow in the duct are also reported.

Ingard, U.↗

NASA NTRS1976

Microwave remote sensing of a two-layer random medium

A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.

Tsang, L.↗

NASA NTRS1976

A new unified approach for analyzing wing-body-tail configurations with control surfaces

A general theory for steady and unsteady, subsonic and supersonic potential aerodynamics for complex configurations is presented. Special attention is given to the theoretical formulation and the corresponding numerical implementation for coplanar interfering surfaces. Applying the Green's function method to the equation of the velocity potential and discretizing the spatial problem by using the finite-element technique, yields a set of differential-delay equations in time relating the potential to the normal wash. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t less than or equal to 0 (steady state) and of small perturbations around the steady state for time t greater than 0; the solution is obtained in the Laplace domain. From the potential, the aerodynamic pressure and the generalized forces are evaluated. The program SOUSSA (Steady, Oscillatory and Unsteady Subsonic and Supersonic Aerodynamics) is briefly described. Numerical results obtained with SOUSSA are presented.

Tseng, K.↗

NASA NTRS1976

Three-dimensional potential flow over hills and oval mounds

An analysis was made of the potential flow behavior for an initially uniform flow passing over a single axisymmetric hill, an oval mound, and a combination of two hills. Small perturbation theory was used, and the resulting Laplace equation for the perturbation velocity potential was solved by using either a product solution or a Green's function. The three dimensional solution is of interest in calculating the pressure distribution around obstacles, the flow of pollutants carried by the wind, and the augmentation of wind velocity for windmill siting. The augmentation in velocity at the top of a hill was found to be proportional to the hill height relative to a characteristic width dimension of the hill. An axisymmetric hill produced about 20 percent less velocity increase than a two dimensional ridge having the same cross-sectional profile.

Siegel, R.↗

NASA NTRS1977

Aerodynamic interference effects on tilting proprotor aircraft

The Green's function method was used to study tilting proprotor aircraft aerodynamics with particular application to the problem of the mutual interference of the wing-fuselage-tail-rotor wake configuration. While the formulation is valid for fully unsteady rotor aerodynamics, attention was directed to steady state aerodynamics, which was achieved by replacing the rotor with the actuator disk approximation. The use of an actuator disk analysis introduced a mathematical singularity into the formulation; this problem was studied and resolved. The pressure distribution, lift, and pitching moment were obtained for an XV-15 wing-fuselage-tail rotor configuration at various flight conditions. For the flight configurations explored, the effects of the rotor wake interference on the XV-15 tilt rotor aircraft yielded a reduction in the total lift and an increase in the nose-down pitching moment. This method provides an analytical capability that is simple to apply and can be used to investigate fuselage-tail rotor wake interference as well as to explore other rotor design problem areas.

Soohoo, P.↗

NASA NTRS1977

Simple analytical solutions for spherically symmetric production and modulation of energetic solar particles

Exact analytical solutions are presented for the standard time-independent spherically symmetric convection-diffusion-adiabatic deceleration equation governing the transport of cosmic rays in the interplanetary medium for the case in which particles are produced with spherical symmetry at the sun. It is assumed that the solar-wind speed is constant and radial, and that the spatial diffusion coefficient has a power-law dependence on momentum. The Green's function describing the modulation of a monoenergetic production of particles is presented. The solutions provide a useful basis for the study of time-integrated properties of energetic solar-flare particle spectra.

Gross, M. W.↗

NASA NTRS1977

Aerodynamic sound in a relaxing medium

A theory of aerodynamic sound propagation, when inhomogeneities characterized by a relaxation process are present in both the source and propagation region, is formulated. The details of the relaxation process need not be specified at the outset, although the relaxation process is characterized by a relaxation time and by an equilibrium and a frozen sound speed in a propagation region which is otherwise in equilibrium. Propagation is described in terms of a D'Alembertian characterized by the frozen sound speed relaxing toward one characterized by the equilibrium sound speed, while the source is interpreted in terms of a frozen Lighthill stress tensor relaxing toward the equilibrium stress tensor. An appropriate Green's function for the three-dimensional relaxing wave propagation operator is used to construct an exact integral for the aerodynamic sound. The sound generated far from the source is then estimated in terms of the aerodynamic sound source.

Liu, J. T. C.↗

NASA NTRS1978

Artificially created holes in the ionosphere

The artificial creation of ionospheric holes by the release of highly reactive molecules into the F region is investigated. Through ion-atom interchange or charge transfer reactions, H2 or H2O reacts with O(+) to form OH(+) or H2O(+), respectively, which subsequently dissociatively recombines with electrons at a very rapid rate. The diffusion of H2 is also modified by chemical loss to the ambient atomic oxygen atmosphere. The limited spatial and temporal extent of the hole-making process allows several approximations to be made which permit three-dimensional analytic solutions of the continuity equations for the released particles, the O(+) and e(-) densities, and the intermediary molecular ions. A versatile formalism is developed whereby the hole-making capability of virtually any spatial-temporal configuration of released particles can be determined by convolving a set of destruction operators which can be viewed as Green's functions for the problem. As a specific application of the techniques developed, the modification of a winter nighttime ionosphere is described by simulating the release of 1000 kg of water vapor near a height of 300 km.

Mendillo, M.↗