Brief Presentation of CATFOAM: LTTE Foam Particulate Filter Modeling Approach and Software Volos, December 2000 University of Thessaly Mechanical Engineering Department Laboratory of Thermodynamics & Thermal Engines

2 LTTE Foam Particulate Filter Model Specifications CategoryItems Calculation Domaincylindrical filter with given diameter and length Boundary ConditionsEngine operation condition (exhaust gas mass flow rate and exhaust gas temperature at filter inlet) Possibility to assign radial velocity and temperature profile at inlet face Heat loss from the canning surface Initial ConditionInitial filter temperature Initial accumulated soot mass (including clean filter) Mode of RegenerationThermal Regeneration, Catalytic Regeneration ExpandabilityPossible to consider various foam structures, materials and sizes Future activity to cover geometric design optimization

Input Parameters and Data List (1/3) Filter Design Parameter CategoryItems 12-hedral cell structurePore size (mean, STD) Strut thickness (mean, STD) Irregularities’ coefficient Active volume fraction for filtration Fibers’ volume fraction Irregularities’ volume fraction Tuning parameters for diffusion filtration/SBA Filter sizeLength Diameter CanningOutside diameter Thickness Insulation material - thickness

Input Parameters and Data List (2/3): Operating Point Data CategoryItems Boundary conditionInlet gas velocity or flow rate with radial gradient Inlet gas temperature with radial gradient Heat loss from outer filter shell Initial ConditionInitial filter temperature Initial soot mass in filter / bulk mass gradient

Input Parameters and Data List (3/3): Material Properties CategoryItems Ceramic FoamBulk density Specific heat capacity Thermal conductivity Soot depositMean Porosity Mean Density Indicative size distribution

Output Data List CategoryItems Spatial and Temporal Profiles during Regeneration Filter temperature and temperature gradient Species : O2, CO, CO2, NO, HC, H2O Exhaust gas temperature evolution with time Pressure drop evolution with time Particulate mass evolution with time Output Files and Graphics Exported to MS Excel Spreadsheets with graphs updated by means of MS Excel macros

Foam Filter Modeling: Published Journal Papers 1.A Mathematical Model for the Dynamic Particulate Filtration in Diesel Foam Filters. Particulate Science & Technology, 17: , Dynamic Filtration Modeling in Foam Filters for Diesel Exhaust Chem. Eng. Com., 188: 21-46, 2001

Modeling and validation of the filtration, loading and regeneration characteristics of foam filters The core of the model accounts for the pressure drop, filtration efficiency and soot accumulation of a foam filter. It also includes a basic submodel for the regeneration process of the foam filter. Testing procedures for the assessment of filtration, loading & regeneration characteristics are defined. As regards the backpressure and filtration efficiency prediction, the model has been validated against the results of filtration and loading tests on specific foam filter types. A preliminary computational assessment of the effect of filter geometry has been attempted with the aid of commercial CFD code (CFX). The catalytic regeneration model is not yet validated.

Modeling Assumptions (1/2) This is an application oriented engineering model for the prediction of diesel foam filter operation. The following phenomena are taken into account by the model: the actual size distribution of the emitted particulate (usually approximated by a log-normal distribution) the geometric structure properties of the foam filter variation of the filtration efficiency with time, as the filter is being loaded the axial distribution of the accumulated particulate along the filter induced backpressure as function of filter geometry and loading heat transfer between exhaust gas and foam filter thermal soot oxidation by exhaust gas oxygen

Modeling Assumptions (2/2) The filter pore structure is considered to consist of 12hedral elements (cells). The specific geometry is described by the number of pores per linear inch (ppi) and the filter porosity. In practice, the 12hedral structure is reproduced with significant inaccuracies, resulting in numerous "blocked" passages. It may be assumed that the perfectly reproduced 12hedral cells filter the particulate in a "deep-bed" mode, whereas the "struts" act as fiber elements. In the blocked passages, the assumption of a "cake" filtration is reasonable to employ. Thus, the filtration of the foam is modeled by two parallel mechanisms, namely deep-bed and cake filtration. In order to simulate the cell structure with equivalent "fiber" filtering elements, the dimensions of the cell structure (pore size and strut thickness) must be known. In real filters these parameters are not uniform for the entire filter. Actually, a normal distribution around a mean value of the strut thickness may approximate the real conditions. The mean value and the standard deviation of the strut thickness for a specific foam structure can be estimated from photographs. A third mechanism accounts for the filtration due to accumulated soot. As filtration proceeds, a soot particle layer develops around the struts. Accumulated particles, forming irregularly shaped dendrites, act as very efficient collectors, enhancing filtration. The blocking of some passages due to manufacturing inaccuracies is quantified with a "specific blocked area" (SBA), that is, the total area of blocked passages, projected in the direction of the flow per unit volume of the filter. This is a tunable parameter, varying between filters of different pore density and different material or manufacturing technology. Tuning is performed against test results of filtration efficiency.

LTTE approach in the development of CAE Methodologies and Tools Development of models and software packages (apparent kinetics – systems approach) Development of kinetic parameter estimation methodologies and tools Development of emissions measurements quality assurance methodologies and tools Design and implementation of critical experiments to improve understanding and modeling of exhaust after-treatment systems’ components