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Research Papers: Internal Combustion Engines

Simulating Area Conservation and the Gas-Wall Interface for One-Dimensional Based Diesel Particulate Filter Models

[+] Author and Article Information
Christopher Depcik1

Department of Mechanical Engineering, The University of Kansas, 3120 Learned Hall, 1530 West 15th Street, Lawrence, KS 66045-7609depcik@ku.edu

Dennis Assanis

Department of Mechanical Engineering, The University of Michigan, 2045 W.E. Lay Automotive Laboratory, 1231 Beal Avenue, Ann Arbor, MI 48109

1

Corresponding author.

J. Eng. Gas Turbines Power 130(6), 062807 (Aug 22, 2008) (18 pages) doi:10.1115/1.2939002 History: Received April 20, 2007; Revised April 23, 2008; Published August 22, 2008

Researchers have been using one-dimensional based models of diesel particulate filters (DPFs) for over two decades with good success in comparison to measured experimental data. Recent efforts in literature have expanded the classical model to account for the effects of varying soot layer thickness on the flow area of the gases. However, some discrepancies exist with respect to this formulation and the physical phenomena modeled in the channel equations. In addition, there is still some discussion regarding the calculation of the gas temperature within the soot and wall layers. As a result, this paper presents a model to discuss these different phenomena to remove or validate previous assumptions. In specific, formulation of the flow equations in area-conserved format (or quasi-one-dimensional) allows the model to account for the changes in the gaseous area as a function of soot loading. In addition, imposing thermodynamic equilibrium at the interface of the channels and wall layers allows the model to capture the thermal entrance lengths. These tasks were undertaken to illustrate whether or not the results justify the effort is worthwhile and this additional complexity needs to be incorporated within the model. By utilizing linear density interpolation in the wall to increase the computational efficiency of the code, it was determined that the classical model assumptions of neglecting soot thickness and gas temperature in the wall are valid within the range of typical DPF applications.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Flow schematic of a DPF

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Figure 2

Square channel schematic illustrating the important geometric and soot parameters

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Figure 3

Fully developed Nusselt number correlations based on suction and injection values of the wall Reynolds number for (a) circular tube and (b) square channel

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Figure 4

(a) Packed bed and staggered cylinder correlations as a function of Reynolds and Prandtl numbers and (b) 2D illustration of particles and voids used in adapting packed-bed heat transfer correlation

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Figure 5

Variable differentiation utilized in soot and wall layer energy equations

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Figure 6

Comparison between the classical flow model and area-conserved model of the authors for gas (a) pressure and (b) velocity during isothermal run

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Figure 7

Density comparison between the classical flow model and area-conserved model at halfway point in the axial direction during isothermal run

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Figure 8

(a). Comparison of heat transfer correlations during artificial step change numerical experiment and (b) effect of Peclet number on the heat transfer

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Figure 9

Contour plots of different heat transfer correlations during temperature step change numerical experiment

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Figure 10

(a) Pressure drop as a function of soot loading versus experimental data (77) and previous literature (74) results and (b) the percent error in approximating the flow through the wall using an average velocity

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Figure 11

Velocity and pressure contour plots in the soot and wall layers as a function of soot loading

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Figure 12

Comparison of three different soot loading events with respect to (a) pressure and (b) particulate layer thickness

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Figure 13

Model versus experimental results for (a) warm-up of loaded SiC DPF containing only inert N2 and (b) cooldown and oxidation test with 18% O2

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Figure 14

Reaction enthalpy calculations of soot oxidation by O2 at different partial oxidation factors

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Figure 15

Exit mass flow rate difference from omitting the gain in mass due to soot oxidation reactions in Eq. 4

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Figure 16

Instantaneous Nusselt number in the inlet and outlet channels for the oxidation experiment

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