Topic: TSF: Thermal Systems and Fluid Mechanics

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1 The 23 rd Conference of the Mechanical Engineering Network of Thailand November 4 7, 2009, Chiang Mai Validation of a 3D Model for Predicting Pressure Drop of a Clean Diesel Particulate Filter Ekathai Wirojsakunchai Department of Mechanical Engineering, Kasetsart University, Bangkok, Thailand fengeka@ku.ac.th, Tel ext Abstract The Computational Fluid Dynamics (CFD) package, Fluent, was employed to study the internal flow field of each channel in the clean Diesel Particulate Filter (DPF). A 3-D CAD model was generated in SolidWorks, meshed in Gambit, and later transported to Fluent to perform the analysis. The simulation results were compared against experimental data. Good agreements were found comparing the pressure drop at various filtration velocities among all method. With the current model setup, the complications of flow distribution that arise in the DPF can be studied in more details. Integrations of the filtration model to the existing CFD code in Fluent will be done in the future work. This will give many opportunities to gain more access to study the impacts of parameters, whose measurements are limited and/or hardly adjusted in the real experiment, on the filtration processes. Keywords: Computational Fluid Dynamic, Fluent, Diesel Particulate Filter, Pressure Drop 1. Introduction Particulate Matter (PM), or sometimes referred to as smoke, is one of the most important emissions from diesel engines. It has been known that PM is said to be a cause of premature death, asthma, and cancer. To control PM emissions, DPFs (Figure 1) have been developed to collect and oxidize PM from diesel engine exhaust gases [1]. The DPF substrate consists of many parallel channels alternatively plugged at either ends. The exhaust gas is forced through the substrate walls of the inlet channels. PMs are deposited in the porous media pores and later form a thin, porous soot cake. After sufficient mass of PMs have been collected and the exhaust back pressure increases, regeneration is performed. It is expected that DPF will be an essential component of the future diesel exhaust aftertreatment systems [2]. One of the drawbacks of integrating the DPF into the exhaust system is the increase of exhaust back pressure due to the flow over the substrate. Most of the recent DPF researches are therefore focusing on the design of DPF substrate that provides low pressure drop with high filtration efficiency [3, 4, 5]. The

2 pressure drop is highly dependent on not only substrate porous material and velocity magnitude but also the flow characteristics inside DPF [2, 6, 7]. Figure 1. Schematic of the DPF Substrate (above) and a Pair of its Inlet/Outlet Channels (below) adapted from [2] Due to the nature of the flow field in DPF, the computing limitations, and the different orders of magnitude of interesting parameters, the scale in DPF simulation has been classified into three levels [8], namely zero dimensional model (wallscale), one dimensional scale (single channel scale), and multi-dimensional scale (multiple channel scale). See Ref. [1, 9, 10], Ref. [11, 12], and Ref. [13, 14] for more details on 0-D, 1-D, and 3-D setup, respectively. However, multichannel dimensional models using state-of-the-art CFD codes to solve a set of partial differential equations were rarely employed in literatures and mostly done on in-house software packages [15, 16]. The results depend on the behavior of these CFD codes. In addition, the grid generation was a very complicated and tedious task. The objective of the current study is to construct a CFD model by using CFD packages available commercially to study flow characteristics inside the DPF. The modeler can quickly benchmark the design and the result will also offer insightful details of the interaction of various parameters that affect DPF performance. At the point when this paper is written, the model is built and tested only in the cold flow environment (no soot deposition inside the DPF) by comparing to experimental results on a flow bench setup (no soot generator, only clean air at room temperature were drawn to the test cell). In the future, the soot filtration and regeneration model from the literatures will be integrated to the software code. The structure of the paper is as follows. First, details of the experimental setup of the DPF flow bench apparatus are fully discussed. Then, the simulation setup including the 3-D CAD model is presented. The results of pressure drop at various flow rates on a clean DPF from the simulation were compared to those from the experiment. Finally, a preliminary result of the flow field inside a clean DPF is investigated. 2. Experimental Setup The schematic of the flow bench test apparatus is shown in Figure 2. The system consists of an air pump drawing air through the test specimen (in this case, a DPF), a differential (U-tube) manometer measuring test pressure, an inclined manometer measuring pressure drop across the test specimen, and thermocouples monitoring temperatures at various locations. The test piece is attached in series with the pump

3 and measuring elements. A short flow straightening pipe is installed upstream of the DPF to help promote the uniform flow distribution before entering the DPF. By using air at room temperature as the working fluid, the pressure drop across a DPF was measured within a range of flow rates similar to the engine exhaust. A plot between pressure drop and wall filtration velocity (see Eq.4 for more detailed description of the wall filtration velocity) can then be constructed. DPF Figure 2. DPF Flow Bench Setup (adapted from [17]) 2.1 DPF Specifications Four DPF samples were tested in this study. A summary of important parameters for the examined filter is given in Table 1. Filter 1, 2, and 3 has the same dimension. The only difference lies in their coatings. Filter 4 is made of different material, has different dimension (bigger than Filter 1, 2, and 3), and therefore is used as a reference. Table 1. DPF Specifications Designation Substrate Cordierite Silicon- Carbide Cell Density, N Wall Thickness (mil) Geometric Filter Area (m 2 /l) Substrate Porosity, ε (%) Median Pore Diameter, d50 Substrate Vl Washcoat V (l) no yes yes yes Pt Loading (g/l) Pressure Drop Model Once a plot between pressure drop and filtration velocity are constructed, a quadratic regression analysis was performed to estimate the values of global permeability (k global ) and inertial parameter (ζ) from Eq.1 to Eq.3. Eq.1 to Eq.3 demonstrates the analytical pressure drop model first proposed by Ref. [17] and later was modified by Ref. [19]. Each pressure drop term represents the pressure drop across various DPF geometries as shown in Figure 1. DPF inlet conditions are assumed to be radially uniform and therefore solving the model for two consecutive channels (inlet/outlet) is equivalent to solving for the entire trap.

4 clean = wall, clean cone cells µ wth 2 = vwall + βρw thvwall k global Forchheimer Darcy wall, clean cells 2 ρ Af 2 cells cells = ζ.. vwall 2 OFA + cone Eq.1 Eq.2 Eq.3 The ρ and µ terms are fluid density and kinematic viscosity, respectively. OFA and A f are filter open frontal area and the filtration area inside each channel, respectively. The parameter is pressure drop. cone and cone in Equation 1 were neglected due to their small contributions to the overall pressure drop value. Assuming Darcy s law, the Forcheimer term in Equation 2 was also neglected. w th is the wall thickness. Lastly, v wall is the wall filtration velocity defined as follows. v wall Flow Rate in Each Channel = / ε A f Eq.4 Where ε is the wall porosity. 3. Simulation Setup A Computational Fluid Dynamic (CFD) package, Fluent, has been employed to study the flow field inside the DPF. Since the PM deposition process is one of major interests in this research effort, the ultimate goal is to use CFD to study the characteristics of the velocity distribution on the surface of the inlet channel. A 3-D CAD model was generated in SolidWorks, meshed in Gambit, and later transported to Fluent. Figure 3 shows the computational domain of the current study in Fluent. The following conditions were chosen to perform the simulation as recommended in Fluent s manual [20]. Physical Model: Turbulent Flow (k-ε RNG) Mesh: 3D hexahedral mesh No. of Cell: 238,640 Inlet: velocity- Outlet: pressure-outlet Pressure at the inlet tube is set at atmospheric pressure (0 kpa gage pressure) Porous Media Model: Flow through Packed Bed (Given k, z, and Porosity using Darcy s Law to predict the pressure drop) a) Front View of DPF Substrate b) Zoom-in of the Circle Area c) Computational Domain Compared to the Actual Area Figure 3. Model Setup in Fluent 4. Results 4.1 Experimental Results Results from flow bench experiments are shown in Figure 4. The values of k global, ζ, and R 2 from the quadratic curve fits according to Eq.2 for all DPFs are shown in Table 2. Filter 2 and 3 has similar k and ζ values as expected since adding catalyst has slight impact on pressure drop. On the other hand, adding washcoat (Filter 2) to a bare substrate (Filter 1) increases flow restriction across the wall (porosity decreases as seen in Table 2) and promotes flow losses through the contraction and expansion of the inlet and outlet channels due to the deposition of the washcoat at the corners of the square channel

5 ceramic monolith [21]. Filter 4 has the largest volume resulting in the highest k value. Filter Pressure Drop [kpa] Filter Pressure Drop [kpa] Catalyzed + Filter Sic DPF Washcoated Filter Cordierite 2 DPF Bare Cordierite DPF 0.2 Filter 3 Catalyzed Filter Cordierite 4 DPF Wall Filtration Velocity [cm/s] Wall Filtration Velocity [cm/s] Figure 4. Filter Pressure Drop vs. Filtration Velocities of Tested DPFs Note that values of filter pressure drops shown in Figure 4 are calculated based on Eq.5. This is done since we would like to correct measured pressure drop such that the filter pressure drop only contributes to the flow in the channel, the value we obtain from the simulation model. Eq.5 P filter = measured cell cells Table 2. Properties of Tested DPFs from Cold Flow Bench Tests Filter Permeability, C/E coefficient, k global [m 2 ] ζ [-] R 2 Value x x x x Simulation Results An example of velocity contour plot at the filtration velocity of 4 cm/s is shown in Figure 5. The velocity at the inlet channel is set at 4 cm/s representing in green color at the entrance of the channel. As flow starts traveling along the channel, the velocity magnitude increases (representing in yellow and red colors). This is due to the boundary layer developing at the entrance region. Once passing this region, the velocity start decreasing until becoming zero at the end of the channel. Similar observation is found in Ref. [16]. It is believed that by having the flow distribution as shown in Figure 5, the PM deposition process would occur mostly at the entrance of the channel. Figure 5. Velocity Contour Plot of an Inlet DPF Channel at the Filtration Velocity of 4cm/s 4.3 Comparisons of Simulation Results with Experimental Data on Cold Flow Test To gain confidence in the CFD simulation results, a comparison of the pressure drop was made between the simulation and experimental data for Filter 1. These results are illustrated in Figure 6. Values of parameters k and ζ were derived from the cold flow experiment (Table 2) and applied to the porous media model in Fluent. Based on the results shown in Figure 6, good agreement can be found between the simulation and experimental data during the wall filtration velocity of 0 to 3 cm/s. Beyond 3 cm/s, the simulation gives the pressure drop lower than that of the experiment. One possible explanation would be the same observation made in Figure 4 regarding to losses due to the deposition of the washcoat at the corners of the square channel ceramic monolith. This effect is not included in

6 the CAD model. However, most of the DPF operating conditions are within 1 to 3 cm/s range. Therefore, the model is considered to be able to capture flow characteristics as it occurs in the real DPF operation. Filter Pressure Drop [kpa] Experiment -- Simulation Wall Filtration Velocity [cm/s] Figure 6. Comparison of the Filter Pressure Drop between Simulation and Experimental Results 5. Conclusions A 3-D model of an inlet/outlet channel segment of a DPF are successfully constructed and implemented in a commercial CFD package, namely Fluent. Various clean DPFs are tested in cold flow bench experiments. The permeability and inertial coefficient of the DPF can be found by the analytical pressure drop model. Washcoating process has significant impact on the value of the DPF permeability. Results from Fluent showing flow characteristics inside the inlet channel correspond to results from other in-house software package. The model was employed to simulate the flow inside the DPF inlet/outlet channel. The results confirmed good agreement between the experiment and the simulation. In the future work, the filtration model will be integrated into Fluent s CFD code in order to study the flow characteristics during the filtration process. 6. References 1. Konstandopoulos, A.G. and Johnson, J.H. (1989). Wall-Flow Diesel Particulate Filters- Their Pressure Drop and Collection Efficiency, SAE Paper No , Warrendale, PA, Konstandopoulos, A.G. et al. (2000). Fundamental Studies of Diesel Particulate Filters: Transient Loading, Regeneration, and Aging, presented at SAE World Congress, SAE Paper No , Miller, R.K., et al. (2002). Design, Development and Performance of a Composite Diesel Particulate Filter, presented at SAE World Congress, SAE Paper No , Merkel, G.A., et al., Effects of Microstructure and Cell Geometry on Performance of Cordierite Diesel Particulate Filters, presented at SAE World Congress, SAE Paper No , Ohno, K., et al., Characterization of High Porosity SiC-DPF, presented at SAE World Congress, SAE Paper No , Konstandopoulos, A.G. et al. (2005). Progress in Diesel Particulate Filter Simulation, presented at SAE World Congress, SAE Paper No , Ranalli, M., Klement, J., Hoehnen, M., and Rosenberger, R., Soot Distribution in DPF Systems: A Simple and Cost Effective

7 Measurement Method for Series Development, presented at SAE World Congress, SAE Paper No , Konstandopoulos, A.G. and Kostoglou, M., Microstructural Aspects of Soot Oxidation in Diesel Particulate Filters, presented at SAE World Congress, SAE Paper No , Bisset, E.J. and Shadman, F., Thermal Regeneration of Diesel Particulate Monolith Filters, AlChE J., Vol. 31, pp. 753, Konstandopoulos, A.G. and Kostoglou, M., A Mathematical Model of Soot Oxidation on Catalytically Coated Ceramic Filters, Advances in Vehicle Control and Safety (AVCS 98), Amiens, France, July 1-3, Bisset, E.J., Mathematical Model of the Thermal Regeneration of a Wall-Flow Monolith Diesel Particulate Filter, Chemical Eng. Sci., Vol. 39, No. 7/8, pp , Huynh, C.T., Johnson, J.H., Yang, S.L., Bagley, S.T., and Warner, J.R., A One- Dimensional Computational Model for Studying the Filtration and Regeneration Characteristics of a Catalyzed Wall-Flow Diesel Particulate Filter, presented at SAE World Congress, SAE Paper No , Opris, C.N., and Johnson, J.H., A 2-D Computational Model Describing the Heat Transfer, Reaction Kinetics, and Regeneration Characteristics of a Ceramic Diesel Particulate Trap, presented at SAE World Congress, SAE Paper No , Konstandopoulos, A.G. et al., Multichannel Simulation of Soot Oxidation in Diesel Particulate Filters, presented at SAE World Congress, SAE Paper No , Wangard, W. et al. (2004). CFD Simulations of Transient Soot Trapping and Regeneration in a Diesel Particulate Filter, presented at SAE World Congress, SAE Paper No , Piscaglia, F. et al. (2005). Development of a CFD Model to Study the Hydrodynamic Characteristics and the Soot Deposition Mechanism on the Porous Wall of a Diesel Particulate Filter, presented at SAE World Congress, SAE Paper No , Flowbench%20Design.pdf 18. Suresh, A., et al. (2000). An Experimental and Modeling Study of Cordierite Traps Pressure Drop and Permeability of Clean and Particulate Loaded Traps, presented at SAE World Congress, SAE Paper No , Konstandopoulos, A.G. (2003). Flow Resistance Descriptors for Diesel Particulate Filters: Definitions, Measurements and Testing, presented at SAE World Congress, SAE Paper No , Fluent 6 User s guide, Fluent Inc., Lebanon, NH, USA, December Heck, R.M., Farrauto, R.J., and Gulati, S.T., Catalytic Air Pollution Control: Commercial Technology, John Wiley & Sons, Inc., New York, 2002.

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