The exact calculation of quadrupole sources for some incompressible flows

This paper is concerned with the application of the acoustic analogy of Lighthill to the acoustic and aerodynamic problems associated with moving bodies. The Ffowcs Williams-Hawkings equation, which is an interpretation of the acoustic analogy for sound generation by moving bodies, manipulates the source terms into surface and volume sources. Quite often in practice the volume sources, or quadrupoles, are neglected for various reasons. Recently, Farassat, Long and others have attempted to use the FW-H equation with the quadrupole source and neglected to solve for the surface pressure on the body. The purpose of this paper is to examine the contribution of the quadrupole source to the acoustic pressure and body surface pressure for some problems for which the exact solution is known. The inviscid, incompressible, 2-D flow, calculated using the velocity potential, is used to calculate the individual contributions of the various surface and volume source terms in the FW-H equation. The relative importance of each of the sources is then assessed

The Derivation of the Gradient of the Acoustic Pressure on a Moving Surface for Application to the Fast Scattering Code (FSC)

In this paper we develop an analytic expression for calculation of the the acoustic pressure from a rotating blade on a moving surface for application to the Fast Scattering Code (FSC). The analytic result is intended to be used in the helicopter noise prediction code PSU-WOPWOP. One of the goals of the derivation is obtaining a result that will not use any more information than are needed for the prediction of the thickness and loading noise. The result derived here achieves this goal and its incorporation in PSU-WOPWOP is straight forward and attainable

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

The scattering of rotor noise is an area that has received little attention over the years, yet the limited work that has been done has shown that both the directivity and intensity of the acoustic field may be significantly modified by the presence of scattering bodies. One of the inputs needed to compute the scattered acoustic field is the acoustic pressure gradient on a scattering surface. Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. These formulations are presented in this paper. The first formulation is derived by taking the gradient of Farassat's retarded-time Formulation 1A. Although this formulation is relatively simple, it requires numerical time differentiation of the acoustic integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. The acoustic pressure gradient predicted by these new formulations is validated through comparison with the acoustic pressure gradient determined by a purely numerical approach for two model rotors. The agreement between analytic formulations and numerical method is excellent for both stationary and moving observers case

Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions

The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. The pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems. The first formulation is derived from the gradient of the Ffowcs Williams-Hawkings (FW-H) equation. This formulation has a form involving the observer time differentiation outside the integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. The formulations are applied to the rotor noise problems for two model rotors. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases

Increased Fidelity in Prediction Methods For Landing Gear Noise

An aeroacoustic prediction scheme has been developed for landing gear noise. The method is designed to handle the complex landing gear geometry of current and future aircraft. The gear is represented by a collection of subassemblies and simple components that are modeled using acoustic elements. These acoustic elements are generic, but generate noise representative of the physical components on a landing gear. The method sums the noise radiation from each component of the undercarriage in isolation accounting for interference with adjacent components through an estimate of the local upstream and downstream flows and turbulence intensities. The acoustic calculations are made in the code LGMAP, which computes the sound pressure levels at various observer locations. The method can calculate the noise from the undercarriage in isolation or installed on an aircraft for both main and nose landing gear. Comparisons with wind tunnel and flight data are used to initially calibrate the method, then it may be used to predict the noise of any landing gear. In this paper, noise predictions are compared with wind tunnel data for model landing gears of various scales and levels of fidelity, as well as with flight data on fullscale undercarriages. The present agreement between the calculations and measurements suggests the method has promise for future application in the prediction of airframe noise

Computation of Sound Generated by Viscous Flow Over a Circular Cylinder

The Lighthill acoustic analogy approach combined with Reynolds-averaged Navier Stokes is used to predict the sound generated by unsteady viscous flow past a circular cylinder assuming a correlation length of 10 cylinder diameters. The two-dimensional unsteady flow field is computed using two Navier-Stokes codes at a low Mach number over a range of Reynolds numbers from 100 to 5 million. Both laminar flow as well as turbulent flow with a variety of eddy viscosity turbulence models are employed. Mean drag and Strouhal number are examined, and trends similar to experiments are observed. Computing the noise within the Reynolds number regime where transition to turbulence occurs near the separation point is problematic: laminar flow exhibits chaotic behavior and turbulent flow exhibits strong dependence on the turbulence model employed. Comparisons of far-field noise with experiment at a Reynolds number of 90,000, therefore, vary significantly, depending on the turbulence model. At a high Reynolds number outside this regime, three different turbulence models yield self-consistent results

The personal aircraft: Status and issues

Paper summarizes the status of personal air transportation with emphasis upon VTOL and converticar capability. The former obviates the need for airport operations for personal aircraft whereas the latter provides both ground and air capability in the same vehicle. Fully automatic operation, ATC and navigation is stressed along with consideration of acoustic, environmental and cost issues

Towards an Airframe Noise Prediction Methodology: Survey of Current Approaches

In this paper, we present a critical survey of the current airframe noise (AFN) prediction methodologies. Four methodologies are recognized. These are the fully analytic method, CFD combined with the acoustic analogy, the semi-empirical method and fully numerical method. It is argued that for the immediate need of the aircraft industry, the semi-empirical method based on recent high quality acoustic database is the best available method. The method based on CFD and the Ffowcs William- Hawkings (FW-H) equation with penetrable data surface (FW-Hpds ) has advanced considerably and much experience has been gained in its use. However, more research is needed in the near future particularly in the area of turbulence simulation. The fully numerical method will take longer to reach maturity. Based on the current trends, it is predicted that this method will eventually develop into the method of choice. Both the turbulence simulation and propagation methods need to develop more for this method to become useful. Nonetheless, the authors propose that the method based on a combination of numerical and analytical techniques, e.g., CFD combined with FW-H equation, should also be worked on. In this effort, the current symbolic algebra software will allow more analytical approaches to be incorporated into AFN prediction methods

The Devil is in the Details

The accurate prediction of the aeroacoustic eld generated by aerospace vehicles or nonaerospace machinery is necessary for designers to control and reduce source noise. Powerful computational aeroacoustic methods, based on various acoustic analogies (primarily the Lighthill acoustic analogy) and Kirchho methods, have been developed for prediction of noise from complicated sources, such as rotating blades. Both methods ultimately predict the noise through a numerical evaluation of an integral formulation. In this paper, we consider three generic acoustic formulations and several numerical algorithms that have been used to compute the solutions to these formulations. Algorithms for retarded-time formulations are the most e cient and robust, but they are di cult to implement for supersonic-source motion. Collapsing-sphere and emission-surface formulations are good alternatives when supersonicsource motion is present, but the numerical implementations of these formulations are more computationally demanding. New algorithms|which utilize solution adaptation to provide a speci ed error level|are needed. Notation 2 wave operator, D'Alembertian c sound speed in undisturbed medium d6 element of emission (in uence) surface d element of collapsing-sphere surface dS element of source surface f = 0 function that describes the source surface g = 0 surface that describes the collapsing sphere, g = 0 t + r=