By Tobias Höffken and Dr. Burkhard Michaelis, Robert Bosch GmbH, Stuttgart, Germany

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Outline of the flow in a Bosch Diesel Particulate Filter, capturing particulate matter (PM)

Robert Bosch GmbH is developing particulate filters for exhaust flows from diesel cars and light commercial vehicles that are based on sintered metals. The filter geometry ensures that there is sufficient space for all deposits likely to accrue during the normal service life of a vehicle, with or without the use of additives to promote filter regeneration. This particular pocket design results in a more complex exhaust gas flow within the filter compared to monolithic filters currently in use.

Hexahedral mesh of the filter pocket space

Unlike ceramic monolithic diesel particulate filters (DPFs), the Bosch DPF consists of a sin-tered compound of metal granulate and a stainless steel mesh that is folded into pockets and arranged around a sealing plate. The soot-laden flow is forced to permeate the filter material where the soot is deposited in an initial deep filtration stage before a soot layer is built up on the filter surface. Soot deposits in the filter are removed by means of regeneration. The open structure and homogeneous flow distribution result in a uniform soot and ash layer. FLUENT is being used to assist in the filter development, understand the soot loading and regeneration behavior, and optimize the filter geometry.

For the CFD model, the rotational symmetry of the domain and flow field is taken into account, and only one pocket of the filter is modeled. This allows for detailed resolution of the filter material and the boundary layer around it, but comes at the price of a narrow geometry with a small angle near the axis of rotation. Periodic boundary conditions are applied to the confining surfaces in the radial direction. Meshing is entirely hexahedral with separate zones for boundary layers at the walls and the filter surface. The complex shaped filter pocket separator is modeled as a wall of zero thickness. A nonconformal interface is introduced between the fluid domain inside the filter pocket and the outside fluid domain. The filter material is modeled in the CFD code as a porous zone with Darcy permeability.

With Reynolds numbers based on the inlet exhaust pipe diameter between 2,000 to more than 100,000, turbulence is clearly an issue. Calculation of the flow without use of any turbulence model gives reasonable results for the pressure drop at lower flow velocities but does not do well at higher flow velocities. When a turbulence model is used, however, the presence of the porous filter poses a challenge. At low permeability, the interface between the fluid and porous zone acts as a no-slip boundary condition for the tangential components of the velocity. Large velocity gradients that develop cause excessive turbulence production that is not balanced by wall treatment of the turbulence quantities. Consequently the flow in the vicinity of the interface is too viscous and agreement with experiments is poor.

To circumvent this problem, adjustments to the turbulence models have been developed at Bosch and tested for this application. The investigation has been limited to the standard k-e and k-w two-equation models. First, the FLUENT “laminar zone” approach [1], which sets the turbulent viscosity and turbulence production to zero locally within the porous region, is extended by an additional damping factor to avoid the transport of turbulent kinetic energy. This is accomplished by fixing the turbulent dissipation (e or w) to a large value within the porous region. In the case of the filter material with pore size on the order of 10 µm and permeability on the order of 1 µm2damping of turbulence can be expected to a large extent. Additional wall treatment modifications are introduced to both the k-e and kw turbulence models. For both approaches,

the goal is the same: to have a more realistic representation of the production of turbulent kinetic energy at the interface between the porous and non-porous zones. Both approaches were checked for plausibility for flow over a porous surface of much simpler geometry. The available experimental data [2, 3] consists of velocity profiles at several stations in a pressure gradient free turbulent boundary layer. The corrected turbulence models yielded superior correlation with the experiments compared to the uncorrected ones.

Comparison of simulated velocity profiles with measurements [2, 3] for three arbitrarily chosen stations as a function of the logarithmic wall distance. Solid lines are FLUENT calculations, dotted lines are experimental dat

Pathlines illustrate the flow inside the diesal particulate filter

To validate the CFD model on the Bosch DPF, flow measurements in the actual filter geometry were performed. The first experiments made use of LDA (laser Doppler anemometry) to measure velocity components in a full-size pocket filter in a transparent canning. However, since the opening between the filter pockets was found to be poorly accessible, this technique was soon abandoned. The next round of experiments involved only one filter pocket, which had similar geometry and flow physics, but better accessibility. Differences between the single-filter and full-filter geometry were enough that the former had to be considered a model geometry. The measurements were recognized as not representative of the exact flow field in the full scale filter but sufficiently close to it to validate the CFD model.

Velocity and pressure measurements for a range of flow rates were compared to CFD simulation results of the actual geometry of the experiment. For the comparison, the Darcy permeability of the filter material in the model was adapted so that the overall pressure drop at a low mass flow is reproduced in a simulation assuming laminar flow. Using the corrected turbulence models, very good agreement was obtained for all of the other mass flow rates as well. The uncorrected turbulence models produce significantly higher pressure drop results due to excess turbulent viscosity.

Velocity measurements using particle image velocimetry (PIV) were also performed, and illustrated some of the characteristic features of the flow, such as recirculation patterns in the gap and location of detachment and stagnation points. The CFD simulations were found to be in good qualitative agreement with the experimental findings. They showed that for the uncorrected k-e and k-w models, unrestrained turbulence production at the filter material surface leads to blocking of the gap between the pocket and wall and thus to an underestimated recirculation in the upstream widening due to reduced backflow from the pocket. Only the corrected models were able to capture these patterns correctly. Also the pressure within the pocket is affected by the excess turbulence viscosity inside the pocket, which is of special importance for the filtration velocity distribution. Comparison of wall pressure measurements to CFD predictions showed that both corrected turbulence models were able to capture the measured values and trends.

References:

1. Fluent Inc. Modeling Turbulence, Fluent 6.1 Documentation, Chapter 10, 2003.
2. Andersen, P.S.; Kays, W.M.; Moffat, R.J.: Zero pressure gradient constant injection, “JFE Data Bank” test case f0241, http://scholar.lib.vt.edu/ejournals/JFE/ data/JFE/DB96-243/d1/f0241, online resource, last viewed 20.11.2004.
3. Moffat, R J.; Kays, W.M.: The Turbulent Boundary Layer on a Porous Plate: Experimental Heat Transfer with Uniform Blowing and Suction. Int. J. Heat Mass Transfer 1968, 11, 1547-1566.

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