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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Remarks on the theory of aerodynamic noise

The accuracy of approximations employed in the Lighthill theory in current aerodynamic noise research is critically evaluated. Based on the method of matched asymptotic expansions, the full Navier-Stokes equations are expanded for small Mach numbers. To the first order, the near-field is generally nonisentropic. The pressure field (pseudo-sound) is generated by the incompressible Reynolds stresses in the turbulent flow and the velocity, pressure perturbation, and their derivatives on the boundaries. In the far-field, the first-order pressure (acoustic) field satisfying a linear wave equation is obtained by matching with the pseudo-sound field. A uniformly valid solution for the pressure field in a stationary or uniformly moving medium is obtained. The solution shows that the generation of the first-order aerodynamic noise does not depend on the viscous, thermal, or entropy effects in the adiabatic flow nor on the shear stress on a smooth rigid boundary.

Pan, Y. S.↗
NASA NTRS1983

A finite element model for sound transmission through panels

A finite element method (FEM) is applied to predicting coupled frequencies and pressures within an acoustic cavity in order to characterize sound transmission through a panel. Structural equations of motion are defined and the FEM model is configured with four-noded plate elements, the lateral displacement and two slopes being the unknowns at every node. Each element then has 12 degrees of freedom (DOF) and the displacement variation is expressed by a 12-term nonconforming polynomial. A consistent mass matrix is used to represent the panel mass matrix and a wave equation governs the acoustic volume. Analysis of pressure and displacement over the panel yields a square coupling matrix, and an eigenanalysis leads to a solution of the forced vibration problem.

Ramakrishnan, J. V.↗
NASA NTRS1965

Attenuation of Sinusoidal Perturbations Superimposed on Laminar Flow of a Liquid in a Long Line

The attenuation constant for sinusoidal pressure and flow perturbations superimposed on the laminar flow of a viscous liquid was measured in a system consisting of a long, straight, cylindrical hydraulic line. The upstream and downstream ends of the line were securely fastened t o the ground. A sinusoidal perturbation was imposed on the mean flow at the upstream end by means of a s m a l l oscillation of a throttle valve abmt a partly open mean position. The downstream end was terminated in a restricting orifice. Pressure perturbations were measured at three locations along the line for frequencies from 15 t o 100 cps. These pressure measurements were reduced by use of a pair of complex damped acoustic one-dimensional wave equations to obtain the attenuation constant along with the phase constant and the dimensionless downstream admittance. For the range of frequencies investigated, the experimental values of the attenuation constant are in good agreement with classical theory.

PERTURBATION↗
NASA NTRS2007

Derivation of Formulations 1 and 1A of Farassat

Formulations 1 and 1A are the solutions of the Ffowcs Williams-Hawkings (FW-H) equation with surface sources only when the surface moves at subsonic speed. Both formulations have been successfully used for helicopter rotor and propeller noise prediction for many years although we now recommend using Formulation 1A for this purpose. Formulation 1 has an observer time derivative that is taken numerically, and thus, increasing execution time on a computer and reducing the accuracy of the results. After some discussion of the Green's function of the wave equation, we derive Formulation 1 which is the basis of deriving Formulation 1A. We will then show how to take this observer time derivative analytically to get Formulation 1A. We give here the most detailed derivation of these formulations. Once you see the whole derivation, you will ask yourself why you did not do it yourself!

Farassat, F.↗
NASA NTRS1989

Sound power spectrum and wave drag of a propeller in flight

Theory is presented for the sound power and sound power spectrum of a single rotation propeller in forward flight. Calculations are based on the linear wave equation with sources distributed over helicoidal surfaces to represent effects of blade thickness and steady loading. Sound power is distributed continuously over frequecy, as would be expected from Doppler effects, rather than in discrete harmonics. The theory is applied to study effects of sweep and Mach number in propfans. An acoustic efficiency is defined as the ratio of radiated sound power to shaft input power. This value is the linear estimate of the effect of wave drag due to the supersonic blade section speeds. It is shown that the acoustic efficiency is somewhat less than 1 percent for a well designed propfan.

Hanson, D. B.↗
NASA NTRS1979

Procedure for noise prediction and optimization of advanced technology propellers

The sound field due to a propeller operating at supersonic tip speed in a uniform flow was investigated. Using the fact that the wave front in a uniform stream is a convected sphere, the fundamental solution to the convected wave equation was easily obtained. The Fourier coefficients of the pressure signature were obtained by a far field approximation, and are expressed as an integral over the blade platform. It is shown that cones of silence exist fore and aft the propeller plane. The semiapex angles are shown. These angles are independent of the individual Mach components such as the flight Mach number and the rotation Mach number. The result is confirmed by the computation of the ray path of the emitted Mach waves. The Doppler amplification factor strengthens the signal behind the propeller while it weakens that upstream.

Jou, W. H.↗
NASA NTRS1985

Molecular processes in a high temperature shock layer

The development of techniques for the calculation of electron capture widths, electronic wave functions, cross sections and rates needed for the description of the dissociative recombination (DR) of molecular ions with electrons were described. The cross sections and rates were calculated by using harmonic oscillator wave functions for the ion and a delta function approximation for the continuum vibrational wave function in the repulsive dissociative channel. In order to obtain DR cross sections of quantitative accuracy, a computer program which solves the one dimensional nuclear motion wave equation was revised to calculate the cross sections and rates. The program and the new results are described. Included is a discussion of large windows found in the dissociative recombination cross sections from excited ion vibrational levels. These windows have not been previously reported in the literature. The magnitude of the DR cross sections for several dissociative routes are sensitive to the location of the crossing of the neutral and ion potential curves. Studies of the effects of basis set and CI wave function size on vertical excitation energies are described. Preliminary studies on N2 and O2 using large scale wave functions are also reported.

Guberman, S. L.↗
NASA NTRS1995

An extension of the Lighthill theory of jet noise to encompass refraction and shielding

A formalism for jet noise prediction is derived that includes the refractive 'cone of silence' and other effects; outside the cone it approximates the simple Lighthill format. A key step is deferral of the simplifying assumption of uniform density in the dominant 'source' term. The result is conversion to a convected wave equation retaining the basic Lighthill source term. The main effect is to amend the Lighthill solution to allow for refraction by mean flow gradients, achieved via a frequency-dependent directional factor. A general formula for power spectral density emitted from unit volume is developed as the Lighthill-based value multiplied by a squared 'normalized' Green's function (the directional factor), referred to a stationary point source. The convective motion of the sources, with its powerful amplifying effect, also directional, is already accounted for in the Lighthill format: wave convection and source convection are decoupled. The normalized Green's function appears to be near unity outside the refraction dominated 'cone of silence', this validates our long term practice of using Lighthill-based approaches outside the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected 'point' source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are shrouding jets: in that case the difference from unity quantifies the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g., hot jets).

Ribner, Herbert S.↗
NASA NTRS1993

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

Moghaddam, M.↗
NASA NTRS1992

The influence of a vertical magnetic field on oscillations in an isothermal stratified atmosphere

The effect of a uniform vertical magnetic field on the modes of an isothermal stratified atmosphere is examined. The general solutions of the wave equation for an isothermal magnetized medium are given. Asymptotic expansions of these solutions are presented in the strong- and weak-field limits. For a weak field, it is found that, to lowest order of the present perturbation expansion, the oscillation spectrum can be analyzed in terms of p- and g-like modes, magnetic Lamb modes, and magnetic or slow modes. The frequency corrections for each of the modes due to coupling with the remaining modes are calculated. It is demonstrated that when the frequencies of different modes are almost identical, strong mode coupling occurs and the waves acquire a mixed character. An analysis of the solutions in the vicinity of the degenerate frequencies is carried out. The solutions reveal the presence of avoided crossings, which occur at the otherwise degenerate frequencies. Examples of different types of avoided crossings are given.

Hasan, S. S.↗
NASA NTRS1971

Nonlinear, nonlaminar-3D computation of electron motion through the output cavity of a klystron

The equations of motion used in the computation are discussed along with the space charge fields and the integration process. The following assumptions were used as a basis for the computation: (1) The beam is divided into N axisymmetric discs of equal charge and each disc into R rings of equal charge. (2) The velocity of each disc, its phase with respect to the gap voltage, and its radius at a specified position in the drift tunnel prior to the interaction gap is known from available large signal one dimensional programs. (3) The fringing rf fields are computed from exact analytical expressions derived from the wave equation assuming a known field shape between the tunnel tips at a radius a. (4) The beam is focused by an axisymmetric magnetic field. Both components of B, that is B sub z and B sub r, are taken into account. (5) Since this integration does not start at the cathode but rather further down the stream prior to entering the output cavity it is assumed that each electron moved along a laminar path from the cathode to the start of integration.

Albers, L. U.↗
NASA NTRSDate not supplied

Modelling Sonic Boom Propagation through Planetary Boundary Layer Turbulence near the Lateral Extent of the Carpet

Nonlinear acoustic propagation of sonic booms in the atmospheric boundary layer is considered in the context of a one-way solution to a third order wave equation. A split-step approach is utilized to compute different physical effects efficiently. Unlike previous approaches, the diffraction effects are computed exactly in the forward direction with no restriction on the angle of propagation. This results in more accurate modelling of sonic boom near the carpet edge. Heterogenous flow effects are incorporated with a wide-angle parabolic approximation. Nonlinear propagation is computed with a Burgers-Hayes method. Turbulence in the medium is constructed by the method of random Fourier modes. The turbulence spectra are constructed using an altitude dependent 3-dimensional von Karman spectrum. The turbulence field is considered frozen, as the eddy turnover time in the atmospheric boundary layer is generally much larger than the propagation time of the acoustic wave. Comparisons with benchmark predictions from the PCBoom software are conducted. The benchmark cases provide insight into the accuracy of the current prediction code for non-turbulent atmospheres. Future work is discussed regarding the prediction of shaped booms, boundary conditions, and predictions near the lateral extent of the boom carpet where previous approaches fail to capture the diffraction effects.

sonic boom↗
NASA NTRS2006

Airframe Noise Prediction by Acoustic Analogy: Revisited

The present work follows a recent survey of airframe noise prediction methodologies. In that survey, Lighthill s acoustic analogy was identified as the most prominent analytical basis for current approaches to airframe noise research. Within this approach, a problem is typically modeled with the Ffowcs Williams and Hawkings (FW-H) equation, for which a geometry-independent solution is obtained by means of the use of the free-space Green function (FSGF). Nonetheless, the aeroacoustic literature would suggest some interest in the use of tailored or exact Green s function (EGF) for aerodynamic noise problems involving solid boundaries, in particular, for trailing edge (TE) noise. A study of possible applications of EGF for prediction of broadband noise from turbulent flow over an airfoil surface and the TE is, therefore, the primary topic of the present work. Typically, the applications of EGF in the literature have been limited to TE noise prediction at low Mach numbers assuming that the normal derivative of the pressure vanishes on the airfoil surface. To extend the application of EGF to higher Mach numbers, the uniqueness of the solution of the wave equation when either the Dirichlet or the Neumann boundary condition (BC) is specified on a deformable surface in motion. The solution of Lighthill s equation with either the Dirichlet or the Neumann BC is given for such a surface using EGFs. These solutions involve both surface and volume integrals just like the solution of FW-H equation using FSGF. Insight drawn from this analysis is evoked to discuss the potential application of EGF to broadband noise prediction. It appears that the use of a EGF offers distinct advantages for predicting TE noise of an airfoil when the normal pressure gradient vanishes on the airfoil surface. It is argued that such an approach may also apply to an airfoil in motion. However, for the prediction of broadband noise not directly associated with a trailing edge, the use of EGF does not appear to offer any advantages over the use of FSGF at the present stage of development. It is suggested here that the applications of EGF for airframe noise analysis be continued. As an example pertinent to airframe noise prediction, the Fast Scattering Code of NASA Langley is utilized to obtain the EGF numerically on the surface of a three dimensional wing with a flap and leading edge slat in uniform rectilinear motion. The interpretation and use of these numerical Green functions are then discussed.

Farassat, F.↗