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Journal of Vibration and Acoustics | Volume 128 | Issue 3 | TECHNICAL PAPERS
TECHNICAL PAPERS

Modeling and Testing of After-Treatment Devices

[+] Author and Article Information
Sabry Allam

The Marcus Wallenberg Laboratory for Sound and Vibration Research, KTH, SE-10044 Stockholm, Sweden

Mats Åbom

The Marcus Wallenberg Laboratory for Sound and Vibration Research, KTH, SE-10044 Stockholm, Swedenmatsabom@kth.se

J. Vib. Acoust 128(3), 347-356 (Nov 10, 2005) (10 pages) doi:10.1115/1.2172262 History: Received February 28, 2005; Revised November 10, 2005
Article
References
Figures
Tables
Citing Articles

Driven by emission regulations in the US and the EU exhaust systems on new diesel engines are equipped with both a catalytic converter (CC) and a diesel particulate filter (DPF). The CC and DPF are normally placed after each other in an expansion chamber, to create a complete after-treatment device (ATD) to reduce the exhaust pollutants. The ATD unit can also affect the acoustical performance of an exhaust system. In this paper, an acoustic model of a complete ATD for a passenger car is presented. The model is made up of four basic elements: (i) straight pipes; (ii) conical inlet/outlet; (iii) CC unit, and (iv) DPF unit. For each of these elements, a two-port model is used and, with the exception of the DPF unit, known models from the literature are available. For the DPF unit, a new model suggested by the authors has been used. Using the models, the complete acoustic two-port model for the investigated ATD unit has been calculated and used to predict the sound transmission loss. The predictions have been compared to experimental data taken at cold conditions for various flow speeds and show a good agreement.
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References

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Konstandopoulos, A. G., and Johnson, J. H., 1989, “Wall-Flow Diesel Particulate Filters- Their Pressure Drop and Collection Efficiency,” SAE Tech. Paper. No. 890405.
3
Konstandopoulos, A. G., Kostoglou, M., and Skaperdas, E., 2000, “Fundamental Studies of Diesel Particulate Filters: Transient Loading, Regeneration and Aging,” SAE Tech. Paper No. 2000-01-1016.
4
Masoudi, M., Zink, U., Then, P., Thompson, D., and Heibe, A., 2000, “Predicting Pressure Drop of Ceramic Wall-Flow Diesel Particulate Filters—Theory and Experiment,” SAE Tech. Paper No. 2000-01-0184.
5
Allam, S., and Åbom, M., 2005, “Acoustic Modeling and Testing of Diesel Particulate Filters,” J. Sound Vib., 288 , pp. 255–273.
6
Allam, S., 2004, “Acoustic Modelling and Testing of Advanced Exhaust System Components for Automotive Engines,” Ph.D. thesis, Royal Inst. of Technology, Stockholm, TRITA-AVE 2004:43.
7
Munjal, M. L., 1987, "Acoustic of Ducts and Mufflers", Wiley, New York, pp. 42–124.
8
Dokumaci, E., 1997, “A Note on Transmission of Sound in a Wide Pipe With Mean flow and Viscothermal Attenuation,” J. Sound Vib., 208 (4), pp. 653–655.
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Davies, P. O. A. L., and Doak, P. E., 1990, “Spherical Wave Propagation in A Conical Pipe With Mean Flow,” J. Sound Vib., 137 (2), pp. 343–346.
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Davies, P. O. A. L., and Doak, P. E., 1990, “Wave Transfer to and From Conical Diffusers With Mean Flow,” J. Sound Vib., 138 (2), pp. 345–350.
11
Easwaran, V., and Munjal, M. L., 1991, “Transfer Matrix Modeling of Hyperbolic and Parabolic Ducts With Incompressible Mean Flow,” J. Acoust. Soc. Am.  [CrossRef], 90 (4), pp. 2163–2172.
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Åbom, M., 1987, “An Analytical Model for Reactive Silencers Based on Bragg-Scattering,” J. Sound Vib., 112 (2), pp. 384–388.
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Glav, R., 1994, “On Acoustic Modelling of Silencers,” Ph.D. thesis, Royal Inst. of Technology, Stockholm, TRITA-FKT9435.
14
Glav, R., Boden, H., and Åbom, M., 1988, “An Acoustic Model for Automobile Catalytic Converters,” "Proceedings of Inter-Noise 88", INCE, Avignon, France, pp. 1261–1266.
15
Morse, P. M., and Ingard, K. U., 1968, "Theoretical Acoustics", McGraw-Hill, New York.
16
Ingard, U., and Singhal, V. K., 1974, “Sound Attenuation in Turbulent Pipe Flow,” J. Acoust. Soc. Am.  [CrossRef], 55 , pp. 535–538.
17
Dokumaci, E., 1995, “Sound Transmission in Narrow Pipes With Superimposed Uniform Mean Flow and Modeling the Automobile Catalytic Converters,” J. Sound Vib.  [CrossRef], 182 , pp. 799–808.
18
Dokumaci, E., 1998, “On Transmission of Sound in Circular and Rectangular Narrow Pipes With Superimposed Mean Flow,” J. Sound Vib.  [CrossRef], 210 (3), pp. 375–389.
19
Astley, R. J., and Cummings, A., 1995, “Wave Propagation in Catalytic Converter: Formulation of the Problem and Finite Element Scheme,” J. Sound Vib.  [CrossRef], 188 (5), pp. 635–657.
20
Peat, K., 1994, “A First Approximation to the Effects of Mean Flow on Sound Propagation in Capillary Tubes,” J. Sound Vib.  [CrossRef], 175 (4), pp. 475–489.
21
Ih, J.-G., Park, C. M., and Kim, H.-J., 1996, “A Model for Sound Propagation in Capillary Ducts With Mean Flow,” J. Sound Vib.  [CrossRef], 190 (2), pp. 163–175.
22
Jeong, K.-W., and Ih, J.-G., 1996, “A Numerical Study on the Propagation of Sound Through Capillary Tubes With Mean Flow,” J. Sound Vib.  [CrossRef], 198 (1), pp. 67–79.
23
Peat, K., 1997, “Convected Acoustic Wave Motion Along a Capillary Duct With an Axial Temperature Gradient,” J. Sound Vib.  [CrossRef], 203 (5), pp. 855–866.
24
Peat, K., and Kirby, R., 2000, “Acoustic Wave Motion Along a Narrow Cylindrical Duct in the Presence of an Axial Mean Flow and Temperature Gradient,” J. Acoust. Soc. Am.  [CrossRef], 107 (4), pp. 1859–1867.
25
Dokumaci, E., 2001, “An Approximate Dispersion Equation for Sound Waves in a Narrow Pipe With Ambient Gradients,” J. Sound Vib., 240 (4), pp. 637–646.
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Keefe, D. H., 1984, “Acoustical Wave Propagation in Cylindrical Ducts: Transmission Line Parameter Approximations for Isothermal and Nonisothermal Boundary Conditions,” J. Acoust. Soc. Am.  [CrossRef], 75 (1), pp. 58–62.
28
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Figures

Grahic Jump Location
+Transmission loss versus frequency for the ATD at M=0.1 in the inlet pipe and T=293K. —, predicted, °°°°, measured.
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Transmission loss versus frequency for the ATD at M=0.1 in the inlet pipe and T=293K. —, predicted, °°°°, measured.
Figure 13

Transmission loss versus frequency for the ATD at M=0.1 in the inlet pipe and T=293K. —, predicted, °°°°, measured.

Grahic Jump Location
+Transmission loss versus frequency for the ATD at M=0.15 in the inlet pipe and T=293K. —, predicted, °°°°, measured.
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Transmission loss versus frequency for the ATD at M=0.15 in the inlet pipe and T=293K. —, predicted, °°°°, measured.
Figure 14

Transmission loss versus frequency for the ATD at M=0.15 in the inlet pipe and T=293K. —, predicted, °°°°, measured.

Grahic Jump Location
+Photograph of the investigated after-treatment device (ATD) together with a drawing of the various parts: (1) flexible inlet; (2) straight pipe; (3) a diverging conical duct; (4) straight pipe; (5) straight pipe; (6) catalytic converter; (7) straight pipe; (8) diesel particulate trap; (9) straight pipe; (10) straight pipe; (11) A converging conical duct; and (12) straight pipe. Geometrical data for all the elements is given in Appendix .
View Large  |  Save Figure  |  Download Slide (.ppt)
Photograph of the investigated after-treatment device (ATD) together with a drawing of the various parts: (1) flexible inlet; (2) straight pipe; (3) a diverging conical duct; (4) straight pipe; (5) straight pipe; (6) catalytic converter; (7) straight pipe; (8) diesel particulate trap; (9) straight pipe; (10) straight pipe; (11) A converging conical duct; and (12) straight pipe. Geometrical data for all the elements is given in Appendix .
Figure 1

Photograph of the investigated after-treatment device (ATD) together with a drawing of the various parts: (1) flexible inlet; (2) straight pipe; (3) a diverging conical duct; (4) straight pipe; (5) straight pipe; (6) catalytic converter; (7) straight pipe; (8) diesel particulate trap; (9) straight pipe; (10) straight pipe; (11) A converging conical duct; and (12) straight pipe. Geometrical data for all the elements is given in Appendix .

Grahic Jump Location
+Approximation of a conical horn using piecewise constant area straight duct sections with constant length
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Approximation of a conical horn using piecewise constant area straight duct sections with constant length
Figure 2

Approximation of a conical horn using piecewise constant area straight duct sections with constant length

Grahic Jump Location
+Cross section of a unit cell in a DPF split into five sections, each described by an acoustic two-port model. Note, the filter section (II) is actually an acoustic four-port but can be reduced to a two-port due to the hard walls in sections I and III. Typical cross dimensions for the quadratic narrow channels in section II are 1–2mm with a wall thickness of 0.3–0.5mm.
View Large  |  Save Figure  |  Download Slide (.ppt)
Cross section of a unit cell in a DPF split into five sections, each described by an acoustic two-port model. Note, the filter section (II) is actually an acoustic four-port but can be reduced to a two-port due to the hard walls in sections I and III. Typical cross dimensions for the quadratic narrow channels in section II are 1–2mm with a wall thickness of 0.3–0.5mm.
Figure 3

Cross section of a unit cell in a DPF split into five sections, each described by an acoustic two-port model. Note, the filter section (II) is actually an acoustic four-port but can be reduced to a two-port due to the hard walls in sections I and III. Typical cross dimensions for the quadratic narrow channels in section II are 1–2mm with a wall thickness of 0.3–0.5mm.

Grahic Jump Location
+Neighboring channels in a DPF unit. The flow and the acoustic waves enter the channels (1) open upstream and closed downstream, then pass through the porous walls into the channels (2) closed upstream and open downstream.
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Neighboring channels in a DPF unit. The flow and the acoustic waves enter the channels (1) open upstream and closed downstream, then pass through the porous walls into the channels (2) closed upstream and open downstream.
Figure 4

Neighboring channels in a DPF unit. The flow and the acoustic waves enter the channels (1) open upstream and closed downstream, then pass through the porous walls into the channels (2) closed upstream and open downstream.

Grahic Jump Location
+Real part of the propagation constants versus normalized shear wave number (sa) for a typical DPF. No flow is assumed, and the filter data are taken from Table 2 and To=293K. °°°, Γ1; —, −Γ2 propagation constants for uncoupled waves and ◇◇◇, propagation constant from Dokumaci (18). +++, Γ3 and ---, −Γ4 propagation constants for coupled waves.
View Large  |  Save Figure  |  Download Slide (.ppt)
Real part of the propagation constants versus normalized shear wave number (sa) for a typical DPF. No flow is assumed, and the filter data are taken from Table 2 and To=293K. °°°, Γ1; —, −Γ2 propagation constants for uncoupled waves and ◇◇◇, propagation constant from Dokumaci (18). +++, Γ3 and ---, −Γ4 propagation constants for coupled waves.
Figure 5

Real part of the propagation constants versus normalized shear wave number (sa) for a typical DPF. No flow is assumed, and the filter data are taken from Table 2 and To=293K. °°°, Γ1; —, −Γ2 propagation constants for uncoupled waves and ◇◇◇, propagation constant from Dokumaci (18). +++, Γ3 and ---, −Γ4 propagation constants for coupled waves.

Grahic Jump Location
+Imaginary part of the propagation constants (−Γ) versus normalized shear wave number (sa) for a typical DPF. No flow is assumed, and the filter data are taken from Table 2 at To=293K. °°°, Γ1; —, Γ2 propagation constants for uncoupled waves and ◇◇◇, propagation constant from Dokumaci (18). +++, Γ3 and ---, Γ4 propagation constants for coupled waves.
View Large  |  Save Figure  |  Download Slide (.ppt)
Imaginary part of the propagation constants (−Γ) versus normalized shear wave number (sa) for a typical DPF. No flow is assumed, and the filter data are taken from Table 2 at To=293K. °°°, Γ1; —, Γ2 propagation constants for uncoupled waves and ◇◇◇, propagation constant from Dokumaci (18). +++, Γ3 and ---, Γ4 propagation constants for coupled waves.
Figure 6

Imaginary part of the propagation constants (−Γ) versus normalized shear wave number (sa) for a typical DPF. No flow is assumed, and the filter data are taken from Table 2 at To=293K. °°°, Γ1; —, Γ2 propagation constants for uncoupled waves and ◇◇◇, propagation constant from Dokumaci (18). +++, Γ3 and ---, Γ4 propagation constants for coupled waves.

Grahic Jump Location
+Transmission loss versus frequency at M=0.02 before the inlet of the DPF and Tav=775K(6). Effect of different acoustic coupling conditions at the inlet and outlet: +++, with energy losses on both sides; —, with the conservation of energy at the inlet and conservation of momentum at the outlet.
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Transmission loss versus frequency at M=0.02 before the inlet of the DPF and Tav=775K(6). Effect of different acoustic coupling conditions at the inlet and outlet: +++, with energy losses on both sides; —, with the conservation of energy at the inlet and conservation of momentum at the outlet.
Figure 7

Transmission loss versus frequency at M=0.02 before the inlet of the DPF and Tav=775K(6). Effect of different acoustic coupling conditions at the inlet and outlet: +++, with energy losses on both sides; —, with the conservation of energy at the inlet and conservation of momentum at the outlet.

Grahic Jump Location
+Layout of the test rig for mufflers at MWL/KTH. The two-microphone technique was used for the wave decomposition and to cover the desired frequency range (30–1200Hz); 2 microphone pairs were used.
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Layout of the test rig for mufflers at MWL/KTH. The two-microphone technique was used for the wave decomposition and to cover the desired frequency range (30–1200Hz); 2 microphone pairs were used.
Figure 8

Layout of the test rig for mufflers at MWL/KTH. The two-microphone technique was used for the wave decomposition and to cover the desired frequency range (30–1200Hz); 2 microphone pairs were used.

Grahic Jump Location
+Transmission loss versus frequency for the CC at M=0.01 before the inlet and T=293K. ---, simulated using Kirchhoff equation 4; —, simulated using Dokumaci (18); °°°°, measured.
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Transmission loss versus frequency for the CC at M=0.01 before the inlet and T=293K. ---, simulated using Kirchhoff equation 4; —, simulated using Dokumaci (18); °°°°, measured.
Figure 9

Transmission loss versus frequency for the CC at M=0.01 before the inlet and T=293K. ---, simulated using Kirchhoff equation 4; —, simulated using Dokumaci (18); °°°°, measured.

Grahic Jump Location
+Transmission loss versus frequency for the CC at M=0.02 before the inlet and T=293K. ---, simulated using Kirchhoff equation 4; —, simulated using Dokumaci (18); °°°°, measured.
View Large  |  Save Figure  |  Download Slide (.ppt)
Transmission loss versus frequency for the CC at M=0.02 before the inlet and T=293K. ---, simulated using Kirchhoff equation 4; —, simulated using Dokumaci (18); °°°°, measured.
Figure 10

Transmission loss versus frequency for the CC at M=0.02 before the inlet and T=293K. ---, simulated using Kirchhoff equation 4; —, simulated using Dokumaci (18); °°°°, measured.

Grahic Jump Location
+Measured and predicted transmission loss for the DPF at M=0.01 before the inlet and T=293K. °°°°, Measured; —, predicted using theory in Sec. 22; …, predicted using modified 1D model, Sec. 24.
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Measured and predicted transmission loss for the DPF at M=0.01 before the inlet and T=293K. °°°°, Measured; —, predicted using theory in Sec. 22; …, predicted using modified 1D model, Sec. 24.
Figure 11

Measured and predicted transmission loss for the DPF at M=0.01 before the inlet and T=293K. °°°°, Measured; —, predicted using theory in Sec. 22; …, predicted using modified 1D model, Sec. 24.

Grahic Jump Location
+Measured and predicted transmission loss for the DPF at M=0.02 before the inlet and T=293K. °°°°, Measured; —, predicted using theory in Sec. 22; …, predicted using modified 1D model, Sec. 24.
View Large  |  Save Figure  |  Download Slide (.ppt)
Measured and predicted transmission loss for the DPF at M=0.02 before the inlet and T=293K. °°°°, Measured; —, predicted using theory in Sec. 22; …, predicted using modified 1D model, Sec. 24.
Figure 12

Measured and predicted transmission loss for the DPF at M=0.02 before the inlet and T=293K. °°°°, Measured; —, predicted using theory in Sec. 22; …, predicted using modified 1D model, Sec. 24.

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