W. Bell

Boundary integral solutions of three dimensional acoustic radiation problems

Abstract This paper is concerned with the development of a procedure for generating the sound fields radiated by arbitrarily shaped, three dimensional bodies from an integral representation of the solutions of the Helmholtz equation. The method of Burton and Miller is employed to eliminate the non-uniqueness in the external Helmholtz formulae which occurs at the internal eigenfrequencies of the geometry under consideration. Also, a representation of the most singular component in the Burton and Miller formulation is developed resulting in an integral equation which is amenable to numerical solutions. A simple numerical scheme is introduced which reduces the large amounts of computer storage and time normally required for the solution of similar problems. This numerical scheme is then used to obtain solutions for the radiated sound field generated by a vibrating piston set in a sphere. The numerical solutions for the surface and far field sound patterns are compared with exact analytical solutions and deviations of 10% at most are noted. Since the symmetry of the sphere was not taken advantage of in these computations, the numerical schemes employed are applicable to general three dimensional sound radiation problems.

Prediction of the sound field radiated from axisymmetric surfaces

A general analytical method for determining the radiated sound fields from axisymmetric surfaces of arbitrary cross section with general boundary conditions is developed. The method is based on an integral representation for the external solutions of the Helmholtz equation. An integral equation is developed governing the surface potential distribution which gives unique solutions at all wavenumbers. The axisymmetric formulation of the problem reduces its solution to the numerical evaluation of line integrals by Gaussian quadrature. The applicability of the solution approach for both a sphere and finite cylinder is demontrated by comparing the numerical results with exact analytical solutions for both discontinuous and continuous boundary conditions. The method is then applied to a jet‐engine‐inlet configuration and the computed results are in good agreement with exact values.

Predicting the Acoustics of Arbitrarily Shaped Bodies Using an Integral Approach

An integral solution of the Helmoltz equation is developed for predicting the acoustic properties of arbitrarily shaped bodies. With the integral formulation, the acoustic potentials at the surface are solved independently of the internal acoustic field which, effectively, reduces the dimensionality of the problem by one. Considerable reductions in computation time and storage requirements are thus achieved. Efficient numerical techniques for solving the resulting algebraic equations are presented. Numerical results obtained for the two-dimensional problems of a circle and a rectangle agree to within one percent with available exact solutions. The modes of a star-shaped configuration and a duct with a right-angle bend are also determined to demonstrate the applicability of this method to complicated geometries and general boundary conditions. The acoustic properties of a sphere are investigated using an axisymmetric formulation. With the axisymmetric formulation the numerical and exact results agree to three significant figures. I. Introduction T HE prediction of the acoustics of arbitrarily shaped bodies has a variety of applications in aerospace engineering. Among them are the determination of the internal and radiated sound fields from airbreathing propulsion systems and the investigation of the stability limits of rocket combustors. These studies are concerned with obtaining solutions to the Helmholtz equation, which is derived from the wave equation when a sinusoidal time dependence is assumed and which describes the spatial dependence of the oscillations. This equation is included in most standard texts on differential equations of mathematical physics (Ref. 1, Ch. 11) and has been extensively studied in both differential and integral form., The differential form is currently the most widely used.

An investigation of the noise dynamics in a southern illinois underground coal mine.

Noise in an underground coal mine has dominant components generated mainly from three sources: (1) continuous mining machine (CMM), (2) roof bolters, and (3) cars/vehicles which are transporting personnel end/or coal. Each of these three noise sources also has a number of well defined sub‐sources with their own noise characteristics. The CMM noise is comprised mainly of noise generated by coal cutting drum, wet scrubber for dust control, and coal transport conveyor (called also the CMM’s tail). Roof bolter’s noise is generated during the drilling of the roof bolt holes in the bolting process. Personnel and coal transportation vehicles generate noise from the power driven system. The personnel most exposed to these noises are operators of these machines and associated support personnel. Three selected techniques with appropriate instrumentation were used to monitor exposure of the personnel to the noise and noise energy over a period of time. The most common technique is based on the use of personal noise ...

Sound radiation from ducts - A comparison of admittance values

Note typical blocking in classical wind tunnels is of the order of 5% or less. In that case separation on the wall of the type described here is unlikely to happen. However, use of large models and self-streamlining walls, particularly near stall where gradients could be numerically large, may present problems. Alternately, in confined flowfields, as may be encountered between an external store and its rack, it is possible that induced separation of this type could exist. This is particularly likely because the store usually extends well in front of the rack and so a relatively thick boundary layer could be expected. Note that it is possible in a confined flow for the aft separation (as in the source plus one wall) to choke or block the flow and to cause the separation point to move well forward. Flow between a wall and any boattail shape generates a deceleration that causes the wall boundary layer to be particularly susceptible to the latter type of induced separation. Finally, below a critical Mach number the results suggest likelihood of separation may be reduced through the use of aerodynamic interference to accelerate the flow locally.