西门子Analytic Calculation of TL for MCPR and its GA Optimization.pdf

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2021-06-03

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Corrected Analytic Calculation of Transmission Loss for Multi-Chamber Perforate

d Resonator and its GA Optimization

Jin Chang, Zhang Tianpeng

School of Automotive Studies, Tongji University

Abstract

This paper presents the work of Transmission Loss

(TL) calculation and optimization of Multi-

Chamber Perforated Resonator (MCPR) which can

attenuate the high frequency broadband whoosh

noise from air intake system of a turbocharged

engine. The paper presents one-dimension analytic

method by combining the transfer matrix method

and the perforated acoustic impedance model, in the

hypothesis of acoustic linearization, to calculate the

TL of the MCPR. For the non-uniform perforation,

a corrected perforation rate calculation which takes

the thickness of perforation into account was

proposed to improve the accuracy of TL calculation.

The TL of a seven-chamber perforated resonator

was calculated by both corrected analytic method

and acoustic finite element method and verified

experimentally by two-source method. The result

shows that the TL from corrected analytic method

which considering the thickness of perforation has

the best agreement with that from measurement.

Further, by introducing the Genetic Algorithm (GA)

in which the corrected analytic formulation was

embedded with the geometric variable length of

chamber the TL of a seven-chamber perforated

resonator was optimized in the target frequency

range of 1700~3500Hz with given TL amplitude. It

is expected that the corrected analytic method and

GA optimization of MCPR may provide application

reference for the high frequency noise control of

vehicle intake system.

Introduction

For the vehicle fuel economy and low speed torque,

one trend is to equip small displacement

turbocharged engine. One of the challenges in

utilizing the turbocharger in passenger cars is the

NVH issues associated with this hardware.

Turbocharger generated flow or whoosh noise

which is caused by the compressor working at or

near surge line typically at full acceleration

conditions is a high frequency broadband flow noise

[1][2]. This noise inevitably radiates from the air

intake system and seriously affects the ride comfort

[3]. With the feature of broadband frequency the

conventional type of resonators, such as the

Helmholtz and the quarter-wave type, are incapable

of attenuating whoosh noise from air intake system.

A Multi-Chamber Perforated Resonator (MCPR)

which is coupled by multiple single perforated

resonator is capable of attenuating broadband noise.

The resonator consists of main duct and multiple

resonant chambers, which are separated by annular

partitions. The main duct is connected to the

resonant chambers by perforations on the tube. The

Transmission Loss (TL) of MCPR which is an

important acoustic performance indicator can be

computed numerically by either Finite Element

Method (FEM) or Boundary Element Method

(BEM)[4][5]. It is however time consuming to

compute and optimize TL numerically due to the

complex geometry of MCPR. For a quicker

assessment on TL of MCPR, researchers have

introduced one-dimension analytic method

[6]~[11]which combined the transfer matrix method

and the perforated acoustic impedance model with

the hypothesis of acoustic linearization. However

these references did not take the thickness of

perforation into account when calculating the

perforation rate of main duct, which changes the

actual acoustic impedance of perforated area on

main duct and affects the TL calculation. This paper

proposes a corrected perforation rate calculation

that takes the thickness of perforation into account

to improve the accuracy of TL calculation. The TL

of a seven-chamber perforated resonator was

calculated by both corrected analytic method and

FEM and verified experimentally by two-source

method.

For the geometric optimization of MCPR, the

graphical analysis of optimal shape design to

improve the performance of TL on a constrained

single expansion muffler was discussed in the

previous work [12][13]. Bernhard [14] has

introduced the shape optimization of simple

expansion mufflers by using design sensitivity

matrices. But the calculation of design sensitivity

matrices is difficult especially for the mufflers,

which is complicated. Yeh et al.[15] proposed the

four-pole matrix in conjunction with the traditional

gradient method in optimizing the acoustical

performance in a constrained double-chamber

muffler. So as to avoid the drop in local optimum

searching in the traditional gradient methods, a

good starting point in an objective function is

required which will cause inconvenienced and

instability during optimization processing. To

efficiently ultimate the optimal design in muffler,

Min-Chie Chiu has introduced shape optimization

of multi-chamber plug-inlet mufflers in conjunction

with a genetic algorithm (GA) which can locate the

global optimal value in a near zone without extra

information of derivatives and starting design point

of objective function required in classical gradient

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