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Development of Acoustic Models for High Frequency Resonators for Turbocharged IC-Engines

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ABSTRACT
Automotive turbo compressors generate high frequency noisein the air intake system. This sound generation is of importance for the perceived sound quality of luxury cars andmay need to be controlled by the use of silencers. Thesilencers usually contain resonators with slits, perforates andcavities. The purpose of the present work is to developacoustic models for these resonators where relevant effectssuch as the effect of a realistic mean flow on losses and 3Deffects are considered.An experimental campaign has been performed where thetwo-port matrices and transmission loss of sample resonatorshave been measured without flow and for two different meanflow speeds.Models for two resonators have been developed using 1Dlinear acoustic theory and a FEM code (COMSOL Multi- physics). For some resonators a separate linear 1D Matlabcode has also been developed. Different models, from theliterature, for including the effect of mean flow on theacoustic losses at slits and perforates have been implementedin the codes and compared to the experimental data.Correct modeling of acoustic losses for resonators withcomplicated geometry is important for the simulation anddevelopment of new and improved silencers, and the presentwork contributes to this understanding. The developedmodels give acceptable agreement with the measured resultseven with flow but can be improved for 3D FEM if correctCAD data is available. The 1D linear theory can be used for simple geometries and to get a general overview related to theresonance frequencies and damping level.
INTRODUCTION
Automotive intake system noise is normally caused by engine pulsations and by flow separation [1]. The pulsations whichare due to the pressure generated by the pumping of the pistons travel upstream through the different components inthe air intake system. These pressure pulsations are finallyemitted either through the walls of the components in theintake system as shell noise or through the intake orifice. Theamplitude of the intake noise can be high enough to make it asignificant contributor to the interior noise especially when itmatches the acoustic resonances of the intake system.Turbochargers often add noise with much higher frequencydue to the high speed revolution of the compressor wheel andgenerally higher flow velocity. Transient effects from rapidevacuation of the charged part of the intake system will alsocreate broad banded noise. Several types of resonators areused to reduce high frequency turbocharger noise. The problem usually has to be solved with the range of a number of important parameters strongly restricted. As aconsequence, it is necessary to perform optimization asefficiently as possible without too much time consuming andcostly testing, which means that accurate modeling tools areneeded [2].
Development of Acoustic Models for HighFrequency Resonators for Turbocharged IC-Engines
2012-01-1559
Published06/13/2012
Sabry Allam
KTH-Competence Centre for Gas Exchange
Magnus Knutsson
Volvo Car Corporation
Hans Boden
KTH-Competence Centre for Gas Exchange
Copyright © 2012 SAE Internationaldoi:10.4271/2012-01-1559
In the present paper resonators for control of turbo generatednoise are studied. Passive noise control using resonators can provide noise suppression over a wide frequency range at thekHz level [3,4]. If the resonant frequency of the resonator can be tuned dynamically [5] or statically to the noise frequency,the resonator will work for a wide range of frequencies. Dueto the complexity of the dynamic method, the easiest andmost applicable way is to tune the resonant frequency of theresonators statically, which can be done, using an array of resonators. This array can be arranged in series to give highdamping, and can also be parallel for a wide frequency range.A combination of both series and parallel can also beintegrated in the same resonator [6-7].In this paper a combination of resonators in series and parallel arrangements inside a single cavity has been studiedover a wide frequency range, see Fig. 1. In general to buildand model such kind of acoustic array resonators is not aneasy task. In this paper, an attempt to develop acousticmodels for turbocharged IC-engine intake system highfrequency resonators will be presented. In order to have agood understanding of the acoustic characteristics of theresonators, acoustical two-port measurements were madewithout and with flow.Considering the modeling of sound transmission in intakesystems, there are two types of simulation approaches thatcan be used, non-linear time domain and linear frequencydomain models [8]. Linear frequency domain models areusually used because of their lower level of complexity and better possibilities to include losses. In this paper 1D modelsand 3D Finite Element COMSOL Multiphysics [9] models inthe linear frequency domain models are used. In order tovalidate the models and also to get better understanding thecharacteristics of the high frequency resonators, comparison between simulations and measurements of transmission loss(
TL
) will be presented.
SUMMARY OF EXPERIMENTALPROCEDURE
Experiments were carried out at room temperature using theflow acoustic test facility at the Marcus WallenbergLaboratory (MWL) for Sound and Vibration research atKTH. The test duct used during the experiments consisted of a standard steel-pipe with a wall thickness of 3 mm, ductinner diameter
d
i
=57 mm and overall length of approximately7 meters. Four loudspeakers were used as external acousticsources, and they were divided equally between the upstreamand downstream side as shown in Fig. 2. The distances between the loudspeakers were chosen to avoid any pressureminima at the source position. Six flush mounted condenser microphones (B&K 4938) were used, three upstream andthree downstream of the test object for the plane wavedecomposition. The microphone separations are chosen tofulfill the frequency ranges of interest from 30 to 3000 Hz.All measurements were performed using the source switchingtechnique [10] and the flow speed was measured upstream of the test section using a small pitot-tube connected to an
Figure 1. The flow directions of all the 4 resonators.
electronic manometer, SWEMA AIR 300, fixed at a distanceof 1000 mm from the upstream loudspeaker section.
MODELING
GENERAL INTRODUCTION
A resonator reduces noise by an impedance mismatch thatcauses reflection of the incident acoustic energy andattenuation in the resonators neck. When a resonator isattached to a duct by a side branch, as depicted in Fig. 3, the basic assumption is that plane waves propagate in the ductand the reflected waves from downstream are eliminated byusing an anechoic termination in the absence of mean flow.Considering the effects of grazing flow, if the mean flowvelocity is less than
M
= 0.1 where
M
is the Mach number,this effect can be neglected. The sound pressure (
p
) and thevolume velocity (
q
) can be expressed as follows:
(1)
and
(2)
Figure 2. Measurement set up during the Two-port experimental procedure and samples of the measured results.
The transfer-matrix form uses the acoustic pressure
p
and thevolume velocity
q
, i.e. between two points and
X
= [
p
1
,
q
1
]and
Y
= [
p
2
,
q
2
] here “
1
” and “
2
” represent two differentducts cross-section. If there are no internal sources inside thetwo-port element the transfer-matrix can be written in thefollowing form [7]:
(3)
Where the transfer matrix can be written as:
(4)
where,
Z
t
= Z
h
+
Z
c
, are the total impedance, hole impedanceand cavity impedance respectively. The cavity impedance can be calculated as
Z
c
= −
j
cot (
k h
) where
h
is defined as thecavity height. More details about the hole impedance will be presented in the following text.Figure 4 and 5 illustrate the serial and parallel arrangement of different resonators. Regarding the TL change when thenumber of resonators is increased, the serial identicalarrangement mainly increases the magnitude of TL at theresonance frequency. The parallel arrangementlogarithmically increases the magnitude of
TL
and the bandwidth. But for the non-identical arrangements, the TLvaries according to the resonator volumes and the distance between them. These characteristics give the resonator arrayhigh TL over a wide frequency band. In this sense, a silencer can be designed by using multiple array resonators havingdifferent resonance frequencies, which are included in thetarget frequency band.
SERIAL ARRANGEMENT
The transfer matrix can be written as:
(5)
where T
1
, T
3
are the transfer matrices for the two resonatorsand T
2
is the pipe transfer matrix, and
N
is depending on thenumber of resonator.
PARALLEL ORGANIZATION
The transfer matrix can be written as:
(6)
The equivalent impedance Z
eq
for a parallel arrangement isobtained as follows:
(7)
Considering a number (N) of identical resonators in parallel,the transfer matrix between point 1 and point 2 can be writtenas
(8)
Figure 3. Helmholtz resonator in a duct. A & B incident, and reflected wave amplitude, S
c
& h cavity cross sectional area and height, S
1
& S
2
cross sectional area of upstream and downstream duct, and D & l are the neck diameter and length.
For more a series of parallel arrangement,
(9)
The transmission matrix for general combination of paralleland serial arrangements as shown Figure 6 can be writen as
(10)
where, Z
eq1
is the equaivlent impedance as shown in equation(7) of the parallel arrangments and Z
t1
is the impedance of the resonator 3 and is defined in the test after equation (4).Existing models for perforate impedances subject to a meanflow are all semi-empirical. Several studies have beenconducted which has resulted in a number of models, see e.g.Refs. [11,12,13,14,15,16,17,18,19,20,21,22]. In spite of thislarge number of publications a single verified global modeldoes not exist. So one task of this work was to test differentmodels to determine which give the best fit with measuredtransmission but due to the complexity of the test objects, itwas decided to depend on the formula presented by Bauer [11] that is verified by Allam and Åbom and used in Ref. [12]to calculate transmission loss data for simple through and
Figure 4. Serial resonator arrangement and its effect on sound transmission loss. Sc = 0.0013 m2, S1 = 0.0020 m2, l1 = 0.002m, D1 = 0.005 m, h1 = 0.04 m, L = 0.1m.Figure 5. Parallel resonator arrangement and its effect on sound transmission loss.

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