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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
NASA NTRS1952

Two-and three-dimensional unsteady lift problems in high-speed flight

The problem of transient lift on two- and three-dimensional wings flying at high speeds is discussed as a boundary-value problem for the classical wave equation. Kirchoff's formula is applied so that the analysis is reduced, just as in the steady state, to an investigation of sources and doublets. The applications include the evaluation of indicial lift and pitching-moment curves for two-dimensional sinking and pitching wings flying at Mach numbers equal to 0, 0.8, 1.0, 1.2 and 2.0. Results for the sinking case are also given for a Mach number of 0.5. In addition, the indicial functions for supersonic-edged triangular wings in both forward and reverse flow are presented and compared with the two-dimensional values.

Lomax, Harvard↗
NASA NTRS1994

Unsteady jet flow computation towards noise prediction

An attempt has been made to combine a wave solution method and an unsteady flow computation to produce an integrated aeroacoustic code to predict far-field jet noise. An axisymmetric subsonic jet is considered for this purpose. A fourth order space accurate Pade compact scheme is used for the unsteady Navier-Stokes solution. A Kirchhoff surface integral for the wave equation is employed through the use of an imaginary surface which is a circular cylinder enclosing the jet at a distance. Information such as pressure and its time and normal derivatives is provided on the surface. The sound prediction is performed side by side with the jet flow computation. Retarded time is also taken into consideration since the cylinder body is not acoustically compact. The far-field sound pressure has the directivity and spectra show that low frequency peaks shift toward higher frequency region as the observation angle increases from the jet flow axis.

Soh, Woo-Yung↗
NASA NTRS1994

A Galerkin method for linear PDE systems in circular geometries with structural acoustic applications

A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic, and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the two dimensional wave equations on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems.

Smith, Ralph C.↗
NASA NTRS1995

Calculated coupling efficiency between an elliptical-core optical fiber and an optical waveguide over temperature

To determine the feasibility of coupling the output of a single-mode optical fiber into a single-mode rib waveguide in a temperature varying environment, a theoretical calculation of the coupling efficiency between the two was investigated. Due to the complex geometry of the rib guide, there is no analytical solution to the wave equation for the guided modes, thus, approximation and/or numerical techniques must be utilized to determine the field patterns of the guide. In this study, three solution methods were used for both the fiber and guide fields; the effective-index method (EIM), Marcatili's approximation, and a Fourier method. These methods were utilized independently to calculate the electric field profile of each component at two temperatures, 20 C and 300 C, representing a nominal and high temperature. Using the electric field profile calculated from each method, the theoretical coupling efficiency between an elliptical-core optical fiber and a rib waveguide was calculated using the overlap integral and the results were compared. It was determined that a high coupling efficiency can be achieved when the two components are aligned. The coupling efficiency was more sensitive to alignment offsets in the y direction than the x, due to the elliptical modal field profile of both components. Changes in the coupling efficiency over temperature were found to be minimal.

Tuma, Margaret L.↗
NASA NTRS1995

Representation of feedback operators for hyperbolic systems

We consider the problem of obtaining integral representation of feedback operators for damped hyperbolic control systems. We show that for the wave equation with Kelvin-Voigt damping and non-compact input operator, the feedback gain operator is Hilbert-Schmidt. This result is then used to provide an explicit integral representation for the feedback operator in terms of functional gains. Numerical results are given to illustrate the role that damping plays in the smoothness of these gains.

Burns, John A.↗
NASA NTRS1995

Feasibility of Coupling Between a Single-Mode Elliptical-Core Fiber and a Single Mode Rib Waveguide Over Temperature

To determine the feasibility of coupling the output of an optical fiber to a rib waveguide in a temperature environment ranging from 20 C to 300 C, a theoretical calculation of the coupling efficiency between the two was investigated. This is a significant problem which needs to be addressed to determine whether an integrated optic device can function in a harsh temperature environment. Because the behavior of the integrated-optic device is polarization sensitive, a polarization-preserving optic fiber, via its elliptical core, was used to couple light with a known polarization into the device. To couple light energy efficiently from an optical fiber into a channel waveguide, the design of both components should provide for well-matched electric field profiles. The rib waveguide analyzed was the light input channel of an integrated-optic pressure sensor. Due to the complex geometry of the rib waveguide, there is no analytical solution to the wave equation for the guided modes. Approximation or numerical techniques must be utilized to determine the propagation constants and field patterns of the guide. In this study, three solution methods were used to determine the field profiles of both the fiber and guide: the effective-index method (EIM), Marcatili's approximation, and a Fourier method. These methods were utilized independently to calculate the electric field profile of a rib channel waveguide and elliptical fiber at two temperatures, 20 C and 300 C. These temperatures were chosen to represent a nominal and a high temperature that the device would experience. Using the electric field profile calculated from each method, the theoretical coupling efficiency between the single-mode optical fiber and rib waveguide was calculated using the overlap integral and results of the techniques compared. Initially, perfect alignment was assumed and the coupling efficiency calculated. Then, the coupling efficiency calculation was repeated for a range of transverse offsets at both temperatures. Results of the calculation indicate a high coupling efficiency can be achieved when the two components were properly aligned. The coupling efficiency was more sensitive to alignment offsets in the y direction than the x, due to the elliptical modal profile of both components. Changes in the coupling efficiency over temperature were found to be minimal.

Tuma, Margaret L.↗
NASA NTRS1995

Triggering of longitudinal combustion instabilities in solid rocket motors: Nonlinear combustion response

Pulsed oscillations in solid rocket motors are investigated with emphasis on nonlinear combustion response. The study employs a wave equation governing the unsteady motions in a two-phase flow, and a solution technique based on spatial- and time-averaging. A wide class of combustion response functions is studied to second-order in fluctuation amplitude to determine if, when, and how triggered instabilities arise. Conditions for triggering are derived from analysis of limit cycles, and regions of triggering are found in parametric space. Based on the behavior of model dynamical systems, introduction of linear cross-coupling and quadratic self-coupling among the acoustic modes appears to be the manner in which the nonlinear combustion response produces triggering to a stable limit cycle. Regions of initial conditions corresponding to stable pulses were found, suggesting that stability depends on initial phase angle and harmonic content, as well as the composite amplitude, of the pulse.

Wicker, J. M.↗
NASA NTRS1996

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, Kenneth J.↗
NASA NTRS1996

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Kreider, Kevin L.↗
NASA NTRS1997

Development of Improved Surface Integral Methods for Jet Aeroacoustic Predictions

The accurate prediction of aerodynamically generated noise has become an important goal over the past decade. Aeroacoustics must now be an integral part of the aircraft design process. The direct calculation of aerodynamically generated noise with CFD-like algorithms is plausible. However, large computer time and memory requirements often make these predictions impractical. It is therefore necessary to separate the aeroacoustics problem into two parts, one in which aerodynamic sound sources are determined, and another in which the propagating sound is calculated. This idea is applied in acoustic analogy methods. However, in the acoustic analogy, the determination of far-field sound requires the solution of a volume integral. This volume integration again leads to impractical computer requirements. An alternative to the volume integrations can be found in the Kirchhoff method. In this method, Green's theorem for the linear wave equation is used to determine sound propagation based on quantities on a surface surrounding the source region. The change from volume to surface integrals represents a tremendous savings in the computer resources required for an accurate prediction. This work is concerned with the development of enhancements of the Kirchhoff method for use in a wide variety of aeroacoustics problems. This enhanced method, the modified Kirchhoff method, is shown to be a Green's function solution of Lighthill's equation. It is also shown rigorously to be identical to the methods of Ffowcs Williams and Hawkings. This allows for development of versatile computer codes which can easily alternate between the different Kirchhoff and Ffowcs Williams-Hawkings formulations, using the most appropriate method for the problem at hand. The modified Kirchhoff method is developed primarily for use in jet aeroacoustics predictions. Applications of the method are shown for two dimensional and three dimensional jet flows. Additionally, the enhancements are generalized so that they may be used in any aeroacoustics problem.

Pilon, Anthony R.↗
NASA NTRS1998

The Radiated Field Generated by a Monopole Source in a Short, Rigid, Rectangular Duct

This thesis develops a method to model the acoustic field generated by a monopole source placed in a moving rectangular duct. The walls of the duct are assumed to be infinitesimally thin and the source is placed at the center of the duct. The total acoustic pressure is written in terms of the free-space pressure, or incident pressure, and the scattered pressure. The scattered pressure is the augmentation to the incident pressure due to the presence of the duct. It satisfies a homogeneous wave equation and is discontinuous across the duct walls. Utilizing an integral representation of the scattered pressure, a set of singular boundary integral equations governing the unknown jump in scattered pressure is derived. This equation is solved by the method of collocation after representing the jump in pressure as a double series of shape functions. The solution obtained is then substituted back into the integral representation to determine the scattered pressure, and the total acoustic pressure at any point in the field. A few examples are included to illustrate the influence of various geometric and kinematic parameters on the radiated sound field.

Lakota, Barbara Anne↗
NASA NTRS1996

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

Balakrishnan, A. V.↗
NASA NTRS1998

Angular Broadening: Effects of Nonzero, Spatially Varying Plasma Frequency Between the Source and Observer

Angular broadening of radiation due to scattering by density irregularities is usually described using geometric optics (GO) or the parabolic wave equation (PWE) with the assumptions that the radiation frequency f greatly exceeds the local plasma frequency f(sub p0) or that f(sub p0)/f is constant along the path. These assumptions are inappropriate for many solar system radio phenomena. Here the PWE and GO formalisms are extended to treat angular broadening in plasmas with nonzero, spatially varying ratios, f(sub p0)(z)/f < 1. The new PWE results show that the correlation function, scattered angular spectrum, and other quantities are modified by inclusion of a denominator factor [1 - f(sup 2, sub p0)(z prime)/f prime] inside the path integral over z prime, while the mean-square scattering angle depends on both f(sub p0)(z)/f at the observer and the foregoing factor inside the path integral. The PWE and GO predictions for are identical and involve equivalent assumptions. Previous GO and PWE results are recovered in the limits that f(sub p0)(z prime)/f is constant or zero. The new PWE and GO results will permit more accurate calculation of angular broadening for solar system and astrophysical sources. Moreover and importantly, due to the PWE and GO results for being identical, previous GO analyses of in solar system contexts are essentially correct, except for the neglect of or minor deficiencies in the treatment of nonzero, spatially varying f(sub p0)/f effects. The identical GO and PWE results for and the form of the PWE equation for the correlation function raise questions as to whether diffraction is unimportant for angular broadening (under the usual PWE conditions). Future direct comparisons of the PWE predictions with angular spectra calculated using existing GO ray-tracing codes should answer these questions. Diffraction effects are probably important when the medium and turbulence are not sufficiently homogeneous transverse to the central ray path. The implications are also discussed for studies of the 2-3.5 kHz radiation observed in the outer heliosphere.

Cairns, Iver H.↗
NASA NTRS2000

Single Airfoil Gust Response Problem

An unsteady aerodynamic code, called GUST3D, has been developed to solve the single, non-constant coefficient, inhomogeneous convective wave equation for flows with periodic vortical disturbance. The code uses a frequency-domain approach with second-order central differences and a Sommerfeld radiation condition in the far field. It has been extensively validated on model problems with analytical solutions. GUST3D requires as input certain mean flow quantities which are calculated separately by a potential flow solver. This solver calculates the mean flow using a Gothert's Rule approximation. On the airfoil surface, it uses the solution calculated by the potential code FL036. A figure shows the mean pressure along the airfoil surface. To calculate the unsteady pressure, GUST3D was run oil systematically refined grids to obtain a converged solution at each frequency. It was found that 24 points per wavelength was sufficient for convergence. The location of the outer grid boundary was also varied to check for sensitivity to the far-field boundary condition.

Scott, James R.↗
NASA NTRS2003

Spectral Characteristics of Wake Vortex Sound During Roll-Up

This report presents an analysis of the sound spectra generated by a trailing aircraft vortex during its rolling-up process. The study demonstrates that a rolling-up vortex could produce low frequency (less than 100 Hz) sound with very high intensity (60 dB above threshold of human hearing) at a distance of 200 ft from the vortex core. The spectrum then drops o rapidly thereafter. A rigorous analytical approach has been adopted in this report to derive the spectrum of vortex sound. First, the sound pressure was solved from an alternative treatment of the Lighthill s acoustic analogy approach [1]. After the application of Green s function for free space, a tensor analysis was applied to permit the removal of the source term singularity of the wave equation in the far field. Consequently, the sound pressure is expressed in terms of the retarded time that indicates the time history and spacial distribution of the sound source. The Fourier transformation is then applied to the sound pressure to compute its spectrum. As a result, the Fourier transformation greatly simplifies the expression of the vortex sound pressure involving the retarded time, so that the numerical computation is applicable with ease for axisymmetric line vortices during the rolling-up process. The vortex model assumes that the vortex circulation is proportional to the time and the core radius is a constant. In addition, the velocity profile is assumed to be self-similar along the aircraft flight path, so that a benchmark vortex velocity profile can be devised to obtain a closed form solution, which is then used to validate the numerical calculations for other more realistic vortex profiles for which no closed form solutions are available. The study suggests that acoustic sensors operating at low frequency band could be profitably deployed for detecting the vortex sound during the rolling-up process.

Booth, Earl R., Jr.↗
NASA NTRS2000

Acoustic Radiation From Rotating Blades: The Kirchhoff Method in Aeroacoustics

This paper reviews the current status of discrete frequency noise prediction for rotating blade machinery in the time domain. There are two major approaches both of which can be classified as the Kirchhoff method. These methods depend on the solution of two linear wave equations called the K and FW-H equations. The solutions of these equations for subsonic and supersonic surfaces are discussed and some important results of the research in the past years are presented. This paper is analytical in nature and emphasizes the work of the author and coworkers at NASA Langley Research Center.

Farassat, F.↗
NASA NTRS1999

Verification and Analysis of Formulation 4 of Langley for the Study of Noise From High Speed Surfaces

There are several approaches to the prediction of the noise from sources on high speed surfaces. Two of these are the Kirchhoff and the Ffowcs williams-Hawkings methods. It can be shown that both of these methods depend on the solution of the wave equation with mathematically similar inhomogeneous source terms. Two subsonic solutions known as Formulation 1 and 1A of Langley are simple and efficient for noise prediction. The supersonic solution known as Formulation 3 is very complicated and difficult to code. Because of the complexity of the result, the computation time is longer than the subsonic formulas. Furthermore, it is difficult to assess the accuracy of noise prediction. We have been searching for a new and simpler supersonic formulation without these shortcomings. In the last AIAA Aeroacoustics Conference in Toulouse, Farassat, Dunn and Brentner presented a paper in which such a result was presented and called Formulation 4 of Langley. In this paper we will present two analytic tests of the validity this Formulation: 1) the noise from dipole distribution on the unit circle whose strength varies radially with the square of the distance from the center and 2) the noise from dipole distribution on the unit sphere whose strength varies with the cosine of the angle from the polar axis. We will discuss the question of singularities of Formulation 4.

Farassat, F.↗
NASA NTRS1986

Aerodynamics Via Acoustics: Application of Acoustic Formulas for Aerodynamic Calculations

Prediction of aerodynamic loads on bodies in arbitrary motion is considered from an acoustic point of view, i.e., in a frame of reference fixed in the undisturbed medium. An inhomogeneous wave equation which governs the disturbance pressure is constructed and solved formally using generalized function theory. When the observer is located on the moving body surface there results a singular linear integral equation for surface pressure. Two different methods for obtaining such equations are discussed. Both steady and unsteady aerodynamic calculations are considered. Two examples are presented, the more important being an application to propeller aerodynamics. Of particular interest for numerical applications is the analytical behavior of the kernel functions in the various integral equations.

Farassat, F.↗