4  Evaluation of the Acoustic Properties of the Engine

A sound power spectrum, surface intensity patterns, the sound pressure at points in space and the radiation ratio curves for the engine's structural mode shapes are some of the acoustic properties that are useful to the design engineer. Methods for predicting the acoustic properties of the isolated engine from the surface vibration can be based on the Rayleigh integral method (RIM) or the boundary element method. There is also a simple method for estimating the sound power termed the sound power integral method (SPIM). These methods are reviewed in this section and their suitability for predicting the acoustic properties of the air surrounding the engine block is studied.

4.1  The Sound Power Integral Method

Assuming that the sum of the sound powers from each point on the surface radiating independently is equal to the total sound power allows us to derive the sound power integral method. The method is very crude and it is inappropriate for the estimation of the other acoustic properties. The method is equivalent to assuming that the radiation ratio is equal to one at all wavenumbers. Loosely speaking, for engines the radiation ratio is roughly unity for frequencies greater than approximately 1kHz and the method can therefore yield a rough estimate of the sound power at these higher frequencies. An assumed radiation efficiency curve may be used to modify the predicted frequency spectrum below 1kHz, such that better correlation is obtained with experience. The method has the benefit of being computationally cheap and it has been widely used in this application. An example of its use is given in Croker (1987a,b).

4.2  The Rayleigh Integral Method

Assuming that the engine is made up of a set of flat plates which radiate independently allows us to apply the Rayleigh integral method. Applying the method to the faces where the vibration is strongest can give satisfactory approximations to the local acoustic properties. The sound power and radiation ratio calculated via this method are usually reasonably accurate for in-line engines. There are several reported applications of this method to the engine noise problem, for example see references Yorke (1975) and Croker (1987a,b).

4.3  The Boundary Element Method

The boundary element method is the general term given to numerical methods for the solution of partial differential equations where the method is derived from a boundary integral equation formulation. The method is applicable to a wide range of physical or engineering problems (Brebbia (1978), Banerjee and Butterfield (1981)). For the problem we consider in this section the equation we need to solve is the Helmholtz equation or reduced wave equation in a region exterior to an arbitrary surface with a velocity boundary condition at the surface. The derivation of a reliable BEM for the solution of this problem has interested researchers for several decades. The method introduced in Schenck (1968) is now a popular BEM for the computation of the properties of the acoustic field surrounding a vibrating body. However, though this method is reasonably easy to implement, it is difficult to automate for general surfaces. On the other hand, methods based on the integral equations introduced in Kussmaul (1969) and Burton and Miller (1971) have been found much easier to automate but more difficult to implement. For reviews on these methods see, for example, Burton (1976), Kleinmann and Roach (1974).
From the theoretical point of view, the BEM is clearly well-suited to the problem of predicting the acoustic properties of the air surrounding a vibrating engine. It is able to closely represent the physical situation of the engine in free-space or in an anechoic chamber. The main difference between the physical problem and the model is that the engine surface must be idealised as a simple closed surface so that many details will need to be omitted.
There have been a number of reports on the application of the BEM to engine and machine noise problems. Hall (1982), Koopman (1982), Planchard, Guisnel and Smadja (1985), Sas and VandePonseele (1985), Seybert and Holt (1985), Soenarko and Seybert (1985), Seybert Wu and Li (1989) and Riehle, Allen and Branch (1990). These reports consider the applicability of the method and give some calculated results. However previous research generally discusses the potential of the BEM and generally present results at only one or two frequencies. The method is generally regarded as being computationally expensive.

4.4  Summary

The potential for success or otherwise in the use of the different methods for evaluating the acoustic properties of the air surrounding a vibrating engine for noise purposes is illustrated in the table in figure 4. It must be realised that for engine noise purposes, the most important region of the frequency range is generally approximately 0.5kHz to 2.5kHz and that the acoustic properties need not be evaluated to high numerical accuracy.

Figure 4. A comparison of methods of engine noise estimation.