Analysis of flow distribution and heat transfer in a diesel particulate filter

Analysis of limiting models of a Diesel Particulate Filter (DPF) provides insight on its design and operating conditions. Analytical expressions for predicting the filtration velocity, pressure drop, filter heat-up time and speed and width of the temperature front in a DPF are presented. A more uniform filtration velocity with a lower pressure drop can be obtained by either decreasing the inlet velocity, increasing the channel hydraulic diameter or by increasing the DPF aspect ratio (D/L) under constant DPF volume and flow rate. The DPF heat transfer properties depend on the heat capacitance ratio (σ) and the effective heat Peclet number (Peh,e) as well as on the hydraulic parameters. The speed of the temperature front can be increased by decreasing the DPF substrate thickness and volumetric heat capacitance. Higher value of Peh,e decreases the DPF front heat-up time and sharpens the temperature front. When Peh,e is smaller than 8, the temperature front covers the whole DPF length. When it is larger than 128, a sharp front forms covering less than 25% of the DPF length. The effective heat Peclet number attains a maximum value at an intermediate inlet velocity and channel hydraulic diameter. Increasing the DPF aspect ratio (D/L) under constant DPF volume and flow rate can help achieve two important design targets, low pressure drop and a wide temperature front.