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.
Issue Section:
Internal Combustion Engines
1.
Howitt
, J. S.
, and Montierth
, M. R.
, 1981, “Cellular Ceramic Diesel Particulate Filter
,” SAE Paper No. 810114.2.
General Motors
, 1979, General Motors Response to EPA Notice of Proposed Rulemaking on Particulate Regulation for Light-Duty Diesel Vehicles Submitted to Environmental Protection Agency.3.
Springer
, K. J.
, and Stahman
, R. C.
, 1977, “Removal of Exhaust Particulate From a Mercedes 300D Diesel Car
,” SAE Paper No. 770716.4.
Tessier
, L. P.
, et al., 1980, “The Development of a High Efficiency Diesel Exhaust Particulate Filter
,” SAE Paper No. 800338.5.
Garner
, C. P.
, and Dent
, J. C.
, 1988, “A Thermal Regeneration Model for Monolithic and Fibrous Diesel Particulate Traps
,” SAE Paper No. 880007.6.
Oh
, S. H.
, et al., 1981, “Mathematical Modeling of Fibrous Filters for Diesel Particulates—Theory and Experiment
,” SAE Paper No. 810113.7.
Shadman
, F.
, and Bissett
, E. J.
, 1983, “Analysis of Thermal Regeneration of Fibrous Diesel-Particulate Filters
,” Ind. Eng. Chem. Prod. Res. Dev.
0196-4321, 22
, pp. 203
–208
.8.
MacDonald
, J. S.
, and Vaneman
, G. L.
, 1981, “Experimental Evaluation of Fibrous Filters for Trapping Diesel-Exhaust Particulates
,” SAE Paper No. 810956.9.
Bissett
, E. J.
, 1984, “Mathematical Model of the Thermal Regeneration of a Wall-Flow Monolith Diesel Particulate Filter
,” Chem. Eng. Sci.
0009-2509, 39
, pp. 1232
–1244
.10.
Koltsakis
, G. C.
, and Stamatelos
, A. M.
, 1997, “Modes of Catalytic Regeneration in Diesel Particulate Filters
,” Ind. Eng. Chem. Res.
0888-5885, 36
, pp. 4155
–4165
.11.
Konstandopoulos
, A. G.
, and Johnson
, J. H.
, 1989, “Wall-Flow Diesel Particulate Filters—Their Pressure Drop and Collection Efficiency
,” SAE Paper No. 890405.12.
Gropi
, G.
, and Tronconi
, E.
, 1996, “Continuous vs. Discrete Models of Nonadiabatic Monolith Catalysts
,” AIChE J.
0001-1541, 42
(8
), pp. 2382
–2387
.13.
Haralampous
, O. A.
, et al., 2003, “Partial Regenerations in Diesel Particulate Filters
,” SAE Paper No. 2003-01-1881.14.
Konstandopoulos
, A. G.
, et al., 2001, “Spatial Non-Uniformities in Diesel Particulate Trap Regeneration
,” SAE Paper No. 2001-01-0908.15.
Kostoglou
, M.
, et al., 2003, “Multi-Channel Simulation of Regeneration in Honeycomb Monolithic Diesel Particulate Filters
,” Chem. Eng. Sci.
0009-2509, 58
, pp. 3273
–3283
.16.
Depcik
, C.
, and Assanis
, D.
, 2005, “One-Dimensional Automotive Catalyst Modeling
,” Prog. Energy Combust. Sci.
0360-1285, 31
(4
), pp. 308
–369
.17.
Bissett
, E. J.
, 1985, “Thermal Regeneration of Particle Filters With Large Conduction
,” Math. Modell.
0270-0255, 6
, pp. 1
–18
.18.
Bissett
, E. J.
, and Shadman
, F.
, 1985, “Thermal Regeneration of Diesel Particulate Monolithic Filters
,” AIChE J.
0001-1541, 31
, pp. 753
–758
.19.
Lee
, W.-T.
, 1992, “Local Preconditioning of the Euler Equations
,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.20.
Roe
, P. L.
, 1986, “Characteristic-Based Schemes for the Euler Equations
,” Annu. Rev. Fluid Mech.
0066-4189, 18
, pp. 337
–365
.21.
Liu
, J.
, et al., 1996, “Comparison Studies on the Method of Characteristics and Finite Difference Methods for One-Dimensional Gas Flow Through IC Engine Manifold
,” SAE Paper No. 960078.22.
Onorati
, A.
, et al., 1999, “Fluid Dynamic Modeling of the Gas Flow With Chemical Specie Transport Through the Exhaust Manifold of a Four Cylinder SI Engine
,” SAE Paper No. 1999-01-0557.23.
Peters
, B. J.
, 2003, “Numerical Simulation of a Diesel Particulate Filter During Loading and Regeneration
,” 2003 Spring Technical Conference of the ASME Internal Combustion Engine Division
, Salzburg, Austria
.24.
Peters
, B. J.
, et al., 2004, “Integrated 1D to 3D Simulation Workflow of Exhaust Aftertreatment Devices
,” SAE Paper No. 2004-01-1132.25.
Haralampous
, O. A.
, et al., 2004, “Study of Catalytic Regeneration Mechanisms in Diesel Particulate Filters Using Coupled Reaction-Diffusion Modeling
,” SAE Paper No. 2004-01-1941.26.
Haralampous
, O. A.
, and Koltsakis
, G. C.
, 2004, “Oxygen Diffusion Modeling in Diesel Particulate Filter Regeneration
,” AIChE J.
0001-1541, 50
(9
), pp. 2008
–2019
.27.
Haralampous
, O. A.
, et al., 2004, “Reaction and Diffusion Phenomena in Catalyzed Diesel Particulate Filters
,” SAE Paper No. 2004-01-0696.28.
Konstandopoulos
, A. G.
, et al., 2005, “Progress in Diesel Particulate Filter Simulation
,” SAE Paper No. 2005-01-0946.29.
Konstandopoulos
, A. G.
, et al., 2003, “Simulation of Triangular-Cell-Shaped, Fibrous Wall-Flow Filters
,” SAE Paper No. 2003-01-0844.30.
Haralampous
, O. A.
, and Koltsakis
, G. C.
, 2002, “Intra-Layer Temperature Gradients During Regeneration of Diesel Particulate Filters
,” Chem. Eng. Sci.
0009-2509, 57
, pp. 2345
–2355
.31.
Depcik
, C.
, et al., 2005, “The Numerical Simulation of Variable-Property Reacting-Gas Dynamics: New Insights and Validation
,” Numer. Heat Transfer, Part A
1040-7782, 47
, pp. 27
–56
.32.
Wooding
, R. A.
, 1957, “Steady State Free Thermal Convection of Liquid in a Saturated Permeable Medium
,” J. Fluid Mech.
0022-1120, 2
, pp. 273
–285
.33.
Brinkman
, H. C.
, 1947, “A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles
,” Appl. Sci. Res., Sect. A
0365-7132, 1
, pp. 27
–34
.34.
Brinkman
, H. C.
, 1947, “On the Permeability of Media Consisting of Closely Packed Porous Particles
,” Appl. Sci. Res., Sect. A
0365-7132, 1
, pp. 81
–86
.35.
Nield
, D. A.
, and Bejan
, A.
, 1999, Convection in Porous Media
, Springer-Verlag
, New York
.36.
Beck
, J. L.
, 1972, “Convection in a Box of Porous Material Saturated With Fluid
,” Phys. Fluids
0031-9171, 15
, pp. 1377
–1383
.37.
Koltsakis
, G. C.
, and Stamatelos
, A. M.
, 1997, “Catalytic Automotive Exhaust Aftertreatment
,” Prog. Energy Combust. Sci.
0360-1285, 23
, pp. 1
–39
.38.
Cheng
, Y. C.
, and Hwang
, G. J.
, 1995, “Experimental Studies of Laminar Flow and Heat Transfer in a One-Porous-Wall Square Duct With Wall Injection
,” Int. J. Heat Mass Transfer
0017-9310, 38
(18
), pp. 3475
–3484
.39.
Cheng
, Y. C.
, et al., 1994, “Developing Laminar Flow and Heat Transfer in a Rectangular Duct With One-Walled Injection and Suction
,” Int. J. Heat Mass Transfer
0017-9310, 37
(17
), pp. 2601
–2613
.40.
Hwang
, G. J.
, et al., 1997, “An Experimental Study of Laminar Heat Transfer in a One-Porous-Wall Square Duct With Suction Flow
,” Int. J. Heat Mass Transfer
0017-9310, 40
(2
), pp. 481
–485
.41.
Hwang
, G. J.
, et al., 1993, “Developing Laminar Flow and Heat Transfer in a Square Duct With One-Walled Injection and Suction
,” Int. J. Heat Mass Transfer
0017-9310, 36
(9
), pp. 2429
–2440
.42.
Kinney
, R. B.
, 1968, “Fully Developed Frictional and Heat Transfer Characteristics of Laminar Flow in Porous Tubes
,” Int. J. Heat Mass Transfer
0017-9310, 11
, pp. 1393
–1401
.43.
Pederson
, R. J.
, and Kinney
, R. B.
, 1971, “Entrance-Region Heat Transfer for Laminar Flow in Porous Tubes
,” Int. J. Heat Mass Transfer
0017-9310, 14
, pp. 159
–161
.44.
Raithby
, G.
, 1971, “Laminar Heat Transfer in the Thermal Entrance Region of Circular Tubes and Two-Dimensional Rectangular Ducts With Wall Suction and Injection
,” Int. J. Heat Mass Transfer
0017-9310, 14
, pp. 223
–243
.45.
Schmidt
, F. M.
, and Newell
, M. E.
, 1967, “Heat Transfer in Fully Developed Laminar Flow Through Rectangular and Isosceles Triangular Ducts
,” Int. J. Heat Mass Transfer
0017-9310, 10
, pp. 1121
–1128
.46.
Yuan
, J.
, et al., 2001, “Simulation of Fully Developed Laminar Heat and Mass Transfer in Fuel Cell Ducts With Different Cross-Sections
,” Int. J. Heat Mass Transfer
0017-9310, 44
, pp. 4047
–4058
.47.
Calmidi
, V. V.
, and Mahajan
, R. L.
, 2000, “Forced Convection in High Porosity Metal Foams
,” ASME J. Heat Transfer
0022-1481, 122
, pp. 557
–565
.48.
Ingham
, D. B.
et al., 2004, Emerging Technologies and Techniques in Porous Media
, Kluwer Academic
, Dordrecht
.49.
Lu
, W.
, et al., 2006, “Thermal Analysis on Metal-foam Filled Heat Exchangers. Part I: Metal-Foam Filled Pipes
,” Int. J. Heat Mass Transfer
0017-9310, 49
, pp. 2751
–2761
.50.
Zhao
, C. Y.
, et al., 2004, “Thermal Transport in High Porosity Cellular Metal Foams
,” J. Thermophys. Heat Transfer
0887-8722, 18
(3
), pp. 309
–317
.51.
Boomsma
, K.
, and Poulikakos
, D.
, 2001, “On the Effective Thermal Conductivity of a Three-Dimensionally Structured Fluid-Saturated Metal Foam
,” Int. J. Heat Mass Transfer
0017-9310, 44
, pp. 827
–836
.52.
Wakao
, N.
, et al., 1979, “Effect of Fluid Dispersion Coefficients on Particle-to-Fluid Heat Transfer Coefficients in Packed Beds
,” Chem. Eng. Sci.
0009-2509, 34
, pp. 325
–336
.53.
Zukauskas
, A. A.
, 1987, “Convective Heat Transfer in Cross-Flow
,” Handbook of Single-Phase Convective Heat Transfer
, Wiley
, New York
.54.
Konstandopoulos
, A. G.
, et al., 2000, “Fundamental Studies of Diesel Particulate Filters: Transient Loading, Regeneration and Aging
,” SAE Paper No. 2000-01-1016.55.
Masoudi
, M.
, et al., 2001, “Validation of a Model and Development of a Simulator for Predicting the Pressure Drop of Diesel Particulate Filters
,” SAE Paper No. 2001-01-0911.56.
Mohammed
, H.
, et al., 2006, “An Advanced 1D 2-Layer Catalyzed Diesel Particulate Filter Model to Simulate: Filtration by the Wall and Particulate Cake, Oxidation in the Wall and Particulate Cake by NO2 and O2, and Regeneration by Heat Addition
,” SAE Paper No. 2006-01-0467.57.
Zhang
, Z.
, et al., 2002, “Modeling and Numerical Simulation of Diesel Particulate Trap Performance During Loading and Regeneration
,” SAE Paper No. 2002-01-1019.58.
Kandylas
, I. P.
, and Koltsakis
, G. C.
, 2002, “Simulation of Continuously Regenerating Diesel Particulate Filters in Transient Driving Cycles
,” Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.)
0954-4070, 216
, pp. 591
–606
.59.
Koltsakis
, G. C.
, and Stamatelos
, A. M.
, 1996, “Modeling Catalytic Regeneration of Wall-Flow Particulate Filters
,” Ind. Eng. Chem. Res.
0888-5885, 35
, pp. 2
–13
.60.
Koltsakis
, G. C.
, and Stamatelos
, A. M.
, 1996, “Modeling Thermal Regeneration of Wall-Flow Diesel Particulate Traps
,” AIChE J.
0001-1541, 42
(6
), pp. 1662
–1672
.61.
Konstandopoulos
, A. G.
, et al., 2003, “Multichannel Simulation of Soot Oxidation in Diesel Particulate Filters
,” SAE Paper No. 2003-01-0839.62.
Guo
, Z.
, and Zhang
, Z.
, 2006, “Multi-Dimensional Modeling and Simulation of Wall-Flow Diesel Particulate Filter During Loading and Regeneration
,” SAE Paper No. 2006-01-0265.63.
Aoki
, H.
, et al., 1993, “Numerical Simulation Model for the Regeneration Process of a Wall-Flow Monolith Diesel Particulate Filter
,” SAE Paper No. 930364.64.
Jacquot
, F.
, et al., 2002, “Kinetics of the Oxidation of Carbon Black by NO2. Influence in the Presence of Water and Oxygen
,” Carbon
0008-6223, 40
, pp. 335
–343
.65.
Neeft
, J. P. A.
, et al., 1997, “Kinetics of the Oxidation of Diesel Soot
,” Fuel
0016-2361, 76
(12
), pp. 1129
–1136
.66.
Pattas
, K. N.
, and Samaras
, Z. C.
, 1989, “Computational Simulation of the Ceramic Trap Transient Operation
,” SAE Paper No. 890403.67.
Romero
, A. F.
, et al., 1995, “Self Regenerating Catalyzed Diesel Aftertreatment System
,” SAE Paper No. 950367.68.
Depcik
, C.
, 2003, “Modeling Reacting Gases and Aftertreatment Devices for Internal Combustion Engines
,” Ph.D. thesis, The University of Michigan, Ann Arbor, MI.69.
Hindmarsh
, A. C.
, 2002, “Serial Fortran Solvers for ODE Initial Value Problems
,” http://www.llnl.gov/CASC/odepack/http://www.llnl.gov/CASC/odepack/.70.
Hirsch
, C.
, 1988, Numerical Computation of Internal and External Flows
, Wiley
, Chichester
.71.
Hirsch
, C.
, 1990, Numerical Computation of Internal and External Flows
, Wiley
, New York
.72.
Roache
, P. J.
, 1972, Computational Fluid Dynamics
, Hermosa
, Albuerque, NM
.73.
Konstandopoulos
, A. G.
, et al., 1999, “Optimized Filter Design and Selection Criteria for Continuously Regenerating Diesel Particulate Traps
,” SAE Paper No. 1999-01-0468.74.
Konstandopoulos
, A. G.
, et al., 2002, “Microstructural Properties of Soot Deposits in Diesel Particulate Traps
,” SAE Paper No. 2002-01-1015.75.
Young
, D. M.
, et al., 2002, “Silicon Carbide for Diesel Particulate Filter Applications: Material Development and Thermal Design
,” SAE Paper No. 2002-01-0324.76.
Konstandopoulos
, A. G.
, and Kostoglou
, M.
, 1999, “Periodically Reversed Flow Regeneration of Diesel Particulate Traps
,” SAE Paper No. 1999-01-0469.77.
Johnson
, J. H.
, et al., 1997, “A Study of the Regeneration Characteristics of Silicon Carbide and Cordierite Diesel Particulate Filters Using a Copper Fuel Additive
,” SAE Paper No. 970187.78.
Gantawar
, A. K.
, et al., 1997, “A Study of the Regeneration Characteristics of a Silicon Carbide and Cordierite Diesel Particulate Filters Using a Copper Fuel Additive
,” SAE Paper No. 970188.79.
Stobbe
, P.
, et al., 1993, “SiC as a Substrate for Diesel Particulate Filters
,” SAE Paper No. 932495.80.
Incropera
, F. P.
, and DeWitt
, D. P.
, 1990, Fundamentals of Heat and Mass Transfer
, Wiley
, New York
.81.
National Institute of Standards and Technologies
, 2007, “NIST Chemistry Webbook
,” http://webbook.nist.gov/chemistry/http://webbook.nist.gov/chemistry/.82.
Day
, J. P.
, 1990, “The Design of a New Ceramic Catalyst Support
,” SAE Paper No. 902167.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.
