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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
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 NTRS1990

Acoustic radiation from lifting airfoils in compressible subsonic flow

The far field acoustic radiation from a lifting airfoil in a three-dimensional gust is studied. The acoustic pressure is calculated using the Kirchhoff method, instead of using the classical acoustic analogy approach due to Lighthill. The pressure on the Kirchhoff surface is calculated using an existing numerical solution of the unsteady flow field. The far field acoustic pressure is calculated in terms of these values using Kirchhoff's formula. The method is validated against existing semi-analytical results for a flat plate. The method is then used to study the problem of an airfoil in a harmonic three-dimensional gust, for a wide range of Mach numbers. The effect of variation of the airfoil thickness and angle of attack on the acoustic far field is studied. The changes in the mechanism of sound generation and propagation due to the presence of steady loading and nonuniform mean flow are also studied.

Atassi, Hafiz M.↗
NASA NTRS1990

Acoustic radiation from lifting airfoils in compressible subsonic flow

The far field acoustic radiation from a lifting airfoil in a three-dimensional gust is studied. The acoustic pressure is calculated using the Kirchhoff method, instead of using the classical acoustic analogy approach due to Lighthill. The pressure on the Kirchhoff surface is calculated using an existing numerical solution of the unsteady flow field. The far field acoustic pressure is calculated in terms of these values using Kirchhoff's formula. The method is validated against existing semi-analytical results for a flat plate. The method is then used to study the problem of an airfoil in a harmonic three-dimensional gust, for a wide range of Mach numbers. The effect of variation of the airfoil thickness and angle of attack on the acoustic far field is studied. The changes in the mechanism of sound generation and propagation due to the presence of steady loading and non-uniform mean flow are also studied.

Atassi, Hafiz M.↗
NASA NTRS1994

Computation of helicopter rotor acoustics in forward flight

This paper presents a new method for computing acoustic signals from helicopter rotors in forward flight. The aerodynamic and acoustic solutions in the near field are computed with a finite-difference solver for the Euler equations. A nonrotating cylindrical Kirchhoff surface is then placed around the entire rotor system. This Kirchhoff surface moves subsonically with the rotor in forward flight. The finite-difference solution is interpolated onto this cylindrical surface at each time step and a Kirchhoff integration is used to carry the acoustic signal to the far field. Computed values for high-speed impulsive noise show excellent agreement with model-rotor and flight-test experimental data. Results from the new method offer high accuracy with reasonable computer resource requirements.

Strawn, Roger↗
NASA NTRS1996

New Computational Methods for the Prediction and Analysis of Helicopter Noise

This paper describes several new methods to predict and analyze rotorcraft noise. These methods are: 1) a combined computational fluid dynamics and Kirchhoff scheme for far-field noise predictions, 2) parallel computer implementation of the Kirchhoff integrations, 3) audio and visual rendering of the computed acoustic predictions over large far-field regions, and 4) acoustic tracebacks to the Kirchhoff surface to pinpoint the sources of the rotor noise. The paper describes each method and presents sample results for three test cases. The first case consists of in-plane high-speed impulsive noise and the other two cases show idealized parallel and oblique blade-vortex interactions. The computed results show good agreement with available experimental data but convey much more information about the far-field noise propagation. When taken together, these new analysis methods exploit the power of new computer technologies and offer the potential to significantly improve our prediction and understanding of rotorcraft noise.

Strawn, Roger C.↗
NASA NTRS1982

The radar cross section of dielectric disks

A solution is presented for the backscatter (nonstatic) radar cross section of dielectric disks of arbitrary shape, thickness and dielectric constant. The result is obtained by employing a Kirchhoff type approximation to obtain the fields inside the disk. The internal fields induce polarization and conduction currents from which the scattered fields and the radar cross section can be computed. The solution for the radar cross section obtained in this manner is shown to agree with known results in the special cases of normal incidence, thin disks and perfect conductivity. The solution can also be written as a product of the reflection coefficient of an identically oriented slab times the physical optics solution for the backscatter cross section of a perfectly conducting disk of the same shape. This result follows directly from the Kirchhoff type approximation without additional assumptions.

D M Le Vine↗
NASA NTRS1984

The radar cross section of dielectric disks

A solution is presented for the backscatter (monostatic) radar cross section of dielectric disks of arbitrary shape, thickness, and dielectric constant. The result is obtained by employing a Kirchhoff-type approximation to obtain the fields inside the disk. The internal fields induce polarization and conduction currents from which the scattered fields and the radar cross section can be computed. The solution for the radar cross section obtained in this manner will be shown to agree with known results in the special cases of normal incidence, thin disks, and perfect conductivity. It will also be shown that the solution can be written as a product of the reflection coefficient of an identically oriented slab times the physical optics solution for the backscatter cross section of a perfectly conducting disk of the same shape. This result follows directly from the Kirchhoff-type approximation without additional assumptions.

Radar cross section↗
NASA NTRS1984

Classical free-streamline flow over a polygonal obstacle

In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to use except for very simple obstacles, because the conformal mapping problem has been too difficult. This paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time. We achieve this high speed and flexibility by working with a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon. This integral and its associated parameter problem are treated numerically by methods developed earlier by Trefethen for standard Schwarz-Christoffel maps.

Elcrat, A. R.↗
NASA NTRS1986

Classical free-streamline flow over a polygonal obstacle

In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to use except for very simple obstacles, because the conformal mapping problem has been too difficult. This paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time. We achieve this high speed and flexibility by working with a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon. This integral and its associated parameter problem are treated numerically by methods developed earlier by Trefethen for standard Schwarz-Christoffel maps.

Elcrat, A. R.↗
NASA NTRS1987

Geometrical acoustics and transonic helicopter sound

A new method is presented for predicting the impulsive noise generated by a transonic rotor blade. The method is a combined approach involving computational fluid dynamics and geometrical acoustics. A full-potential finite-difference method is used to obtain the pressure field close to the blade. A Kirchhoff integral formulation is then used to extend these finite-difference results into the far field. This Kirchhoff formula is based on geometrical acoustics approximations. It requires initial data across a plane at the sonic radius in a blade-fixed coordinate system. This data is provided by the finite-difference solution. Acoustic pressure predictions show good agreement with hover experimental data for cases with hover tip Mach numbers of 0.88 through 0.96. The cases above 0.92 tip Mach number are dominated by non-linear transonic effects seen as strong shocks on and off the blade tip. This paper gives the first successful predictions of far-field acoustic pressures for high-speed impulsive noise over a range of Mach numbers after delocalization.

Isom, Morris↗
NASA NTRS1989

A prediction of high-speed rotor noise

A combined computational (CFD) and integral approach solves the acoustic pressure fields of two high-speed helicopter rotors. A CFD code supplies boundary data to a non-linear type of Kirchhoff integral formulation to find the far-field pressures. Direct calculations of pressures are given by the CFD code up to the sonic cylinder where the Kirchhoff method takes over. This paper shows predictions and measurements of High-Speed Impulsive (HSI) noise in hover for two different rotor geometries. One rotor has a conventional rectangular planform, while the other rotor is highly swept and tapered. The swept rotor analysis forms the majority of this paper. Test data from both rotors are shown and compared with predictions for a range of tip Mach numbers from .85 to .95 (including delocalization). The correlation with the near-field pressures from the straight bladed experiment is excellent and good to excellent correlation is seen for the far-field pressures from both experiments.

Purcell, Timothy W.↗
NASA NTRS1988

CFD and transonic helicopter sound

A computational method which predicts far-field impulsive noise from a transonic motor blade is demonstrated. This method couples near-field results from a full-potential finite-difference method with a new Kirchhoff integral formulation to extend the finite-difference results into the acoustic far-field. This Kirchhoff formula is written in a blade-fixed coordinate system. It requires initial data from the potential code on a plane at the sonic radius. A recent hovering rotor experiment is described where accurate pressure measurements were recorded on the sonic cylinder and at 2 and 3 radii. The potential code prediction of sonic cylinder pressures is excellent. Acoustic far-field pressure predictions show good agreement with hover experimental data over the range of speeds from 0.85 to 0.92 tip Mach number, the latter of which have delocalized transonic flow. These results are some of the first successful predictions for peak pressure amplitudes using a computational code.

Purcell, Timothy W.↗
NASA NTRS1990

Boundary element analysis of sound scattered by a moving surface

A solution for the acoustic field scattered from a uniformly moving rigid body in the presence of a harmonic incident source has been obtained using a boundary integral method. A derivation of the Kirchhoff formula given by Farassat and Myers (1988) for moving surfaces forms the basis for the analysis, and the development of a boundary integral method for the solution of scattering problems from moving rigid bodies is described. Finite elements are used in conjunction with the Galerkin method in order to solve the integral equation that results from the Kirchhoff formula when the observer point is placed on the moving body surface. Once appropriate surface field values are known they are inserted back into the formula in order to predict the field scattered off the body. Tests, including the so called superposition method, are carried out in order to validate the technique and to establish some confidence in its accuracy. Application of the superposition method to moving bodies is presented, and results of the two approaches are discussed. Sample calculations of scattering from a simple body are presented to illustrate the effects of variations in relevant parameters.

Myers, M. K.↗
NASA NTRS1990

Near-nadir radar backscatter from a well-developed sea

The Kirchhoff approximation for the case of well-developed seas is analyzed. In this peculiar case, the equilibrium range in the wave number spectrum corresponds to a cascade pattern in the surface geometry. Its high wave number cutoff is shown to be a major factor of the radar backscatter. This intrinsic scale is evaluated, and both the geometrical and the physical optics terms are related to major parameters of wind-wave dynamics. The range of validity of the Kirchhoff approximation and the relative importance of the diffraction correction are analyzed. Finally, the radar cross section sigma exp 0 of well-developed seas is compared with that of poorly developed seas. The great qualitative difference shown in the wind speed dependence of sigma exp 0 for these two regimes is pointed out as a source of a considerable error trend recently discovered in satellite altimeter wind measurements.

Glazman, Roman E.↗
NASA NTRS1991

The first ANDES elements: 9-DOF plate bending triangles

New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) formulation of finite elements, which has recently attracted attention as an effective method for constructing high-performance elements for linear and nonlinear analysis. The ANDES formulation is based on an extended parametrized variational principle developed in recent publications. The key concept is that only the deviatoric part of the strains is assumed over the element whereas the mean strain part is discarded in favor of a constant stress assumption. Unlike conventional ANS elements, ANDES elements satisfy the individual element test (a stringent form of the patch test) a priori while retaining the favorable distortion-insensitivity properties of ANS elements. The first application of this formulation is the development of several Kirchhoff plate bending triangular elements with the standard nine degrees of freedom. Linear curvature variations are sampled along the three sides with the corners as gage reading points. These sample values are interpolated over the triangle using three schemes. Two schemes merge back to conventional ANS elements, one being identical to the Discrete Kirchhoff Triangle (DKT), whereas the third one produces two new ANDES elements. Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements.

Militello, Carmelo↗
NASA NTRS1992

Homogenization models for 2-D grid structures

In the past several years, we have pursued efforts related to the development of accurate models for the dynamics of flexible structures made of composite materials. Rather than viewing periodicity and sparseness as obstacles to be overcome, we exploit them to our advantage. We consider a variational problem on a domain that has large, periodically distributed holes. Using homogenization techniques we show that the solution to this problem is in some topology 'close' to the solution of a similar problem that holds on a much simpler domain. We study the behavior of the solution of the variational problem as the holes increase in number, but decrease in size in such a way that the total amount of material remains constant. The result is an equation that is in general more complex, but with a domain that is simply connected rather than perforated. We study the limit of the solution as the amount of material goes to zero. This second limit will, in most cases, retrieve much of the simplicity that was lost in the first limit without sacrificing the simplicity of the domain. Finally, we show that these results can be applied to the case of a vibrating Love-Kirchhoff plate with Kelvin-Voigt damping. We rely heavily on earlier results of (Du), (CS) for the static, undamped Love-Kirchhoff equation. Our efforts here result in a modification of those results to include both time dependence and Kelvin-Voigt damping.

Banks, H. T.↗
NASA NTRS1991

Analyses of near- and far-field two-lobe patterns outside the output endface of a two-mode fiber

The behaviors of the near- and far-field two-lobe radiation patterns from a circular-core two-mode fiber are studied by using both the mode and Kirchhoff diffraction theories. The electric field outside the output endface of the fiber is derived from the electric field distribution of the LP sub 01 and LP sub 11 modes at the fiber endface using the Kirchhoff diffraction formula. Different phenomena are studied by solving this expression numerically at near-and far-fields. The Gouy phase shifts are quantitatively evaluated at cross-sections of the near field. The results reveal the distortion and dislocation of the far-field two-lobe pattern induced by an inclination angle of the fiber endface.

Wang, A.↗
NASA NTRS1992

Dependence of the surface backscattering coefficients on roughness, frequency and polarization states

This paper summarizes the properties of the surface backscattering coefficient as a function of roughness, incidence angle, frequency and polarization state. Results are presented in the form of like- and cross-polarized backscattering coefficient curves versus the incidence angle and the polarization state for different values of the surface roughness parameters and frequency. It is seen that there is a gradual transition from the standard small perturbation scattering model into the Kirchhoff scattering model as frequency increases. It is also shown that in the intermediate frequency region neither the small perturbation nor the Kirchhoff model is applicable. The maximum value of the polarized backscattering coefficient occurs at VV polarization and its two minimum values occur at zero ellipticity and orientation angles between 0 deg and 45 deg and between 135 deg and 180 deg. The cross-polarized scattering coefficient has two maximum values which occur in the same polarization state regions as the minima of the polarized coefficients.

Fung, A. K.↗