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Numerical Prediction of Particulate Matter (PM) Collection Efficiency, Loading, and Flow Characteristics in Partially Damaged Particulate Filters with Different PM Size Classes


The objective of the current study is to numerically predict the collection efficiency, particulate matter (PM) loading, pressure drop, and flow characteristics in partially damaged or unplugged filters. Five different PM size classes with mean particle diameters ranging from 25 to 300 nm are considered for loading the filter. These PM classes are transported in the computational domain as scalars and collected in the filter through Brownian diffusion and interception mechanisms. Four different partially damaged filters with varying damaged cross-sections in the outlet face of the filter are considered. Five different exhaust gas flow rates from 50 to 300 kg/h with a transient soot loading condition are considered, which leads to different temporal and spatial soot cake evolutions as well as a different total soot mass in the filter. As expected, plugged filter sections have higher filtration efficiencies which increases monotonically with soot accumulation. For damaged segment, however, efficiency is nonmonotonic and depends strongly on particle size, loading, and prevailing flow conditions. The collection efficiency of damaged segments is less than 40% at all flow rates and damaged cross-sections considered in this study. The overall filter efficiency is evaluated as the sum of flow averaged filtration efficiencies of both plugged and unplugged sections. The overall filter efficiency is less than 100% and this efficiency decreases from filter-1 to filter-4 as the damaged filter section contributes to the efficiency loss. Spatial and temporal evolution of soot cake is different in damaged and undamaged sections. Strong nonuniform soot distribution is observed in the partially damaged filters in both the axial and radial direction. One objective of the current study is to analyze the overall filter collection efficiency with respect to the percentage of damage, which as a result will assist in the roadworthiness studies, on-board diagnostic studies, or periodic technical inspection of the filters or damaged filters.

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Computational fluid dynamics


Channels per square inch (1/in2)


Diesel particulate filter


Gas hourly space velocity (1/s)


Gasoline particulate filter


Particulate matter (soot)


Particulate number (soot, #/m3)


Particulate matter 1 with size class 25 nm


Particulate matter 2 with size class 50 nm


Particulate matter 3 with size class 100 nm


Particulate matter 4 with size class 200 nm


Particulate matter 5 with size class 300 nm

A :

Cross-sectional area (m2)

D p :

Particle diffusion coefficient

d :

Diameter (m)

d c :

Unit collector diameter

d p :

Mean particle diameter

E :

Total filtration efficiency

F :

Friction coefficient ( −)

f :

Fraction of the flow going into plugged filter segment ( −)

\(g\left(\varepsilon \right)\) :

Kuwabara flow field function

Kn :

Knudsen number

k :

Permeability (1/m2)

m :

Mass (kg)

\(\dot{m}\) :

Mass flow rate (kg/s)

l :

Length (channel) (m)

\({N}_{R}\) :

Interception parameter

p :

Pressure (Pa)

Pe :

Peclet number


Time (s)

u i :

Interstitial or pore velocity

u w :

Approach velocity

v :

Velocity (m/s)

w s :

Wall thickness

z :

Coordinate in axial direction (m

δ :

Thickness (m)

\(\varepsilon\) :

Porosity of the

μ :

Dynamic viscosity of the gas (kg/(m s))

η :

Efficiency ( −)

ρ :

Density (kg/(m3))

\(\varnothing\) :

Transported scalar value


Boundary (filter inlet, outlet)






Brownian diffusion efficiency


Damaged filter segment


Effective (length)


Inlet (channel)


Inlet (face)




Outlet (channel)


Outlet (filter)




Overall filtration efficiency


Plugged filter segment


Interception efficiency


Regular filter segment


Dimensionless parameter




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Chittipotula, T. Numerical Prediction of Particulate Matter (PM) Collection Efficiency, Loading, and Flow Characteristics in Partially Damaged Particulate Filters with Different PM Size Classes. Emiss. Control Sci. Technol. 7, 302–320 (2021).

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  • PM size classes
  • Filter collection efficiency
  • Partially damaged filter
  • Transient soot loading
  • Brownian diffusion and interception
  • Nonuniform soot distribution
  • Periodic technical inspection