A computer program for the determination of the acoustic pressure signature of helicopter rotors due to blade thickness

A computer program is presented for the determination of the thickness noise of helicopter rotors. The results were obtained in the form of an acoutic pressure time history. The parameters of the program are the rotor geometry and the helicopter motion descriptors, and the formulation employed is valid in the near and far fields. The blade planform must be rectangular, but the helicopter motion is arbitrary; the observer position is fixed with respect to the ground with a maximum elevation of 45 deg above or below the rotor plane. With these restrictions, the program can also be used for the calculation of thickness noise of propellers

Acoustic analysis of the propfan

A review of propeller noise prediction technology is presented. Two methods for the prediction of the noise from conventional and advanced propellers in forward flight are described. These methods are based on different time domain formulations. Brief descriptions of the computer algorithms based on these formulations are given. The output of the programs (the acoustic pressure signature) was Fourier analyzed to get the acoustic pressure spectrum. The main difference between the two programs is that one can handle propellers with supersonic tip speed while the other is for subsonic tip speed propellers. Comparisons of the calculated and measured acoustic data for a conventional and an advanced propeller show good agreement in general

User's manual for a computer program to calculate discrete frequency noise of conventional and advanced propellers

A user's manual is presented for a computer program for the calculation of discrete frequency noise of conventional and advanced propellers. The structure of the program and the subroutines describing the input functions are discussed. Input variables and their default values and the variables in the output data sheet are defined. Two versions of the program are available. These differ only in the graphic output capability. One version has only printed output capability. A second version with extensive graphic output capability is available for the computer system at Langley. This Manual includes four detailed examples of both the printed and graphic outputs. These examples may be reproduced by users to check their code on their computer system

A numerical technique for calculation of the noise of high-speed propellers with advanced blade geometry

A numerical technique and computer program were developed for the prediction of the noise of propellers with advanced geometry. The blade upper and lower surfaces are described by a curvilinear coordinate system, which was also used to divide the blade surfaces into panels. Two different acoustic formulations in the time domain were used to improve the speed and efficiency of the noise calculations: an acoustic formualtion with the Doppler factor singularity for panels moving at subsonic speeds and the collapsing sphere formulation for panels moving at transonic or supersonic speeds. This second formulation involves a sphere which is centered at the observer position and whose radius decreases at the speed of sound. The acoustic equation consisted of integrals over the curve of intersection for both the sphere and the panels on the blade. Algorithms used in some parts of the computer program are discussed. Comparisons with measured acoustic data for two model high speed propellers with advanced geometry are also presented

Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics

Generalized functions have many applications in science and engineering. One useful aspect is that discontinuous functions can be handled as easily as continuous or differentiable functions and provide a powerful tool in formulating and solving many problems of aerodynamics and acoustics. Furthermore, generalized function theory elucidates and unifies many ad hoc mathematical approaches used by engineers and scientists. We define generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support, then introduce the concept of generalized differentiation. Generalized differentiation is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some results of classical analysis, are derived with the generalized function theory. Other applications of the generalized function theory in aerodynamics discussed here are the derivations of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of the finite part of divergent integrals, the derivation of the Oswatitsch integral equation of transonic flow, and the analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics include the derivation of the Kirchhoff formula for moving surfaces, the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation

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

Theory of Noise Generation from Moving Bodies with an Application to Helicopter Rotors

Several expressions for the determination of the acoustic field of moving bodies are presented. The analysis is based on the Ffowcs Williams-Hawkings equation. Applying some proposed criteria, one of these expressions is singled out for numerical computation of acoustic pressure signature. The compactness of sources is not assumed and the main results are not restricted by the observer position. The distinction between compact and noncompact sources on moving surfaces is discussed. Some thickness noise calculations of helicopter rotors and comparison with experiments are included which suggest this mechanism as the source of high-speed blade slap of rotors

The Kirchhoff Formulas for Moving Surfaces in Aeroacoustics - The Subsonic and Supersonic Cases

One of the active areas of computational aeroacoustics is the application of the Kirchhoff formulas to the problems of the rotating machinery noise predictions. The original Kirchhoff formula was derived for a stationary surface. In 1988, Farassat and Myers derived a Kirchhoff Formula obtained originally by Morgans using modem mathematics. These authors gave a formula particularly useful for applications in aeroacoustics. This formula is for a surface moving at subsonic speed. Later in 1995 these authors derived the Kirchhoff formula for a super-sonically moving surface. This technical memorandum presents the viewgraphs of a day long workshop by the author on the derivation of the Kirchhoff formulas. All necessary background mathematics such as differential geometry and multidimensional generalized function theory are discussed in these viewgraphs. Abstraction is kept at minimum level here. These viewgraphs are also suitable for understanding the derivation and obtaining the solutions of the Ffowcs Williams-Hawkings equation. In the first part of this memorandum, some introductory remarks are made on generalized functions, the derivation of the Kirchhoff formulas and the development and validation of Kirchhoff codes. Separate lists of references by Lyrintzis, Long, Strawn and their co-workers are given in this memorandum. This publication is aimed at graduate students, physicists and engineers who are in need of the understanding and applications of the Kirchhoff formulas in acoustics and electromagnetics

Bounds on thickness and loading noise of rotating blades and the favorable effect of blade sweep on noise reduction

The maxima of amplitudes of thickness and loading noise harmonics are established when the radial distribution of blade chord, thickness ratio, and lift coefficient is specified. It is first shown that only airfoils with thickness distribution and chordwise loading distributions which are symmetric with respect to midchord need be considered for finding the absolute maxima of thickness and loading noise. The resulting chordwise thickness and load distributions for these maximum noise conditions require infinite slope at some points along the chord but otherwise are uniform. It is shown that sweeping the blades reduces the thickness and loading noise, but there is no optimum sweep which generates the lowest noise

Advanced turboprop noise prediction: Development of a code at NASA Langley based on recent theoretical results

The development of a high speed propeller noise prediction code at Langley Research Center is described. The code utilizes two recent acoustic formulations in the time domain for subsonic and supersonic sources. The structure and capabilities of the code are discussed. Grid size study for accuracy and speed of execution on a computer is also presented. The code is tested against an earlier Langley code. Considerable increase in accuracy and speed of execution are observed. Some examples of noise prediction of a high speed propeller for which acoustic test data are available are given. A brisk derivation of formulations used is given in an appendix