On the flow-acoustic modelling of the exhaust system of a reciprocating internal combustion engine

Abstract

Reciprocating machines, such as internal?combustion engines, compressors, etc., are among the dominant producers of noise. For a suitable design of noise?reducing equipment-primarily mufflers-the noise?generating sources have to be analysed together with the mufflers. The frequency?domain analysis of mufflers is quite convenient but requires prior knowledge of the source characteristics. The time?domain analysis, on the other hand, offers a completely independent formalism for muffler analysis because it eliminates the necessity of knowing the source characteristics beforehand. However, in view of the ease of muffler design in the frequency domain, it is desirable to evaluate the source characteristics. Contemporary methods for source characterization rely mainly on experiments. These methods produce inaccurate results in the low?frequency band, where the characteristics are especially important. Moreover, experimental methods cannot be used at the design stage. Hence, a numerical technique to obtain the source characteristics is desirable. This can readily be done by combining information from the time?domain simulation with the two?load method. The time?domain analysis of exhaust systems is usually performed using the method of characteristics, which employs either the moving?frame method or the fixed?frame method. The fixed?frame method is more convenient because it avoids the difficulties of graphical computation. In this thesis, the fixed?frame computational scheme, along with the appropriate boundary conditions, has been implemented. Analyses of a uniform tube, a cavity杙ipe junction, and simple area discontinuities are presented. The analysis has been performed accounting for wall friction and heat transfer for one?dimensional unsteady flow. In the process, a few inconsistencies in previously reported formulations have been identified and corrected. The results obtained from the simulations show good agreement with experimental observations. The pressure?time history and mass?flux time history thus obtained have been used, along with the two?load method, to compute the source characteristics. Two new computational methods for obtaining the source characteristics are also described. These are much simpler and computationally more economical than a full time?domain simulation using the method of characteristics. In the case of internal?combustion engines, however, nonlinearities are introduced because of large piston motion, the acoustic?diode effect of the initial blowdown, and the presence of the exhaust valve. Therefore, the source characteristics for an engine exhaust system are not unique; that is, they are not independent of the loads (impedances) selected for the two?load method. This has been confirmed by the numerical computations reported in the thesis. Nevertheless, these characteristics can still be used for a gross estimation of noise radiation and insertion loss. Conventionally, the frequency?domain variables and the linear perturbations of the time?domain variables form a Fourier?transform pair. In the case of muffler theory, however, such correspondence between aeroacoustic frequency?domain analysis and time?domain analysis using unsteady gas dynamics is not well established, although Soedel has made some progress in this direction. To address this, a new approach-called the convolution approach-has been developed. However, although the time?domain and frequency?domain analyses are consistent within themselves, the basic equations underlying the two approaches do not form an exact Fourier?transform pair. Therefore, when the two are used together through Soedel抯 approach or the present convolution approach, numerical instability arises. This inconsistency is shown to stem from the application of instantaneous steady?flow equations at the cavity杙ipe junction to obtain perturbations over the steady flow. This, in turn, leads to the question of equivalence between unsteady gas dynamics and linear perturbations about steady flow. As a first step toward establishing this equivalence, and in order to ensure continuity of mass flux and energy balance for unsteady compressible flow, two new state variables-called aeroacoustic variables-have been suggested. These would be truly aeroacoustic in nature compared to those used for incompressible flow, which account only for the convective effects of mean flow.