Numerical analysis of circular straight mufflers equipped with three chambers at high-order-modes

Abstract

Plane wave theory has been used in predicting the acoustical performance of one-chamber straight mufflers. But, the acoustical effect of the mufflers at higher frequencies that are beyond the threshold of the cut-off frequency has been neglected. In addition, there is a need for a more compact muffler design for use inside a space-constrained working area. In order to improve the acoustical performance of straight mufflers, a space-constrained multi-chamber muffler using a more accurate predicting model in conjunction with an optimizer is proposed.In this paper, an eigen function that uses a three dimensional wave propagation to deduce the acoustical field as a four-pole matrix form is applied. An overall four-pole system matrix that multiplies individual matrices is adopted in evaluating the Transmission Loss (TL) for the hybrid mufflers. A circular and three-chamber straight muffler is introduced and optimized for various targeted tones using both Genetic Algorithm (GA) and Simulated Annealing (SA) Methods in conjunction with five objective functions (case A–case E). Before the optimization process is carried out, an accuracy check of the mathematical models for the circular one-chamber muffler is carried out. In order to verify the reliability of the GA and SA methods, a single-objective optimization of the three-chamber straight muffler at a targeted tone of 2000 Hz using GA method and SA method has been executed. Results reveal that the TL can be maximized at the targeted frequency when using either the GA method or the SA method. In addition, the noise reduction will increase if the number of chambers increases. Moreover, the acoustical performance of the mufflers will be reversely proportional to the diameter of the inlet/outlet tubes. Consequently, results reveal that the TL of the circular hybrid mufflers at targeted frequencies can be simultaneously improved by using the fourth and fifth strategies of objective functions in which the inverse of the summation summing up the individual target frequency’s deviation square between the targeted transmission loss and the predicted transmission loss has been built.