1 Introduction

Compared with gasoline engine, the diesel engine has the advantages of high efficiency, better power performance, low fuel consumption, and strong reliability. It has been widely used in various fields such as large commercial vehicles, ships, engineering machinery, and so on [1]. However, diesel engines can emit harmful substances, including nitrogen oxides (NOx), hydrocarbons (HC), particulate matter (PM), and so on which violates the requirements of advocating energy conservation, emission reduction, and environmental protection [2,3,4]. Therefore, many countries have promulgated and implemented strict emission regulations [5, 6]. At present, relying on the traditional in-cylinder purification technology of diesel engine is not sufficient to achieve effective PM reduction targets. The most widely used solution is the addition of diesel particulate filter (DPF). [7,8,9].

The interior of DPF is a porous honeycomb structure with one section open and one section blocked. The engine exhaust gas passes through the walls of the channel and is filtered and purified by the porous media, which adsorbs the particulates in the exhaust in the wall slits [10, 11]. A large number of studies have proved that the filtration efficiency of DPF can reach more than 90% [12,13,14]. However, the accumulation of large amounts of soot leads to a reduction in filter wall permeability and an increase in backpressure, which leads to a reduction in engine fuel efficiency and an increase in fuel consumption, so the captured PM must be regenerated by oxidation through the filter [15, 16]. To increase the soot capture volume and filtration area, an asymmetric channel DPF has been introduced, and the channel shape has been derived from octagonal channels in addition to the usual square channel. At present, a large number of scholars have studied the pressure drop and regeneration characteristics of asymmetric channel DPFs through experiments or the development of relevant mathematical models [17]. Lee et al. [18] adopted a one-channel mathematics model to predict the transient thermal response of the DPF. The effect of the ratio of length to width, cell density, the amount of soot loading on the temporal thermal response, and regeneration characteristics were investigated. They found that under “city driving mode,” the maximum wall temperature of regeneration decreases with the increase of the ratio of length to width and the maximum temperature decreased with increasing cell density. Li Zhijun et al. [19] developed a DPF pressure drop model to compare the variation of DPF pressure drop in symmetrical and asymmetrical channel with uneven soot distribution and found that both had the lowest pressure drop in the case of thick soot in the front and thin soot in the back, but the DPF pressure drop was lower in the case of asymmetrical channel with the same soot distribution. Hidemasa Iwata et al. [20] studied the pressure drop and soot regeneration rate of asymmetric plugging layout diesel particulate filters (VPL-DPF) with different wall thickness; they found that the transient pressure drop of thick wall type DPF was lower than that of conventional DPF, but the soot oxidation rate during regeneration was lower. Zhang X et al. [21] studied the flow field distribution of the DPF with an asymmetric channel structure during the capture process and analyzed the pressure drop and gas velocity at the inlet and outlet. They found that the pressure drop of the asymmetric DPF was higher than that of the symmetric channel, but when the soot load increased to a certain value, the pressure drop was just the opposite one. Ge Xiao et al. [22] proposed a novel type of asymmetric channel wall-flow filter, including the regular hexagonal and triangular channels, as well as the rectangular channels and developed corresponding mathematical models to study pressure drop characteristics. The results found that the novel asymmetric channel filter can effectively reduce the lifetime pressure drop by increasing the utilization ratio of the filtration wall and the filtration area.

In this study, based on a common square asymmetric channel DPF, the corresponding capturing, pressure drop, and regeneration models are developed. During the verification of regeneration model, the engine is used to first carry out soot accumulation on the DPF, and then the soot deposited DPF is loaded into the new system through off-line regeneration for regeneration verification. By varying the width ratio of inlet and outlet channels (CRD), the effect of the change in the ratio size on the DPF pressure drop, capturing efficiency, pressure drop composition, and soot distribution is investigated. The effect of the change in CRD on the regeneration characteristics of the DPF was analyzed in terms of peak wall temperature and regeneration rate.

2 Construction of the Computational Model

In this paper, GT-Power software is mainly used to simulate soot capture and regeneration process of DPF. The geometric parameters of the asymmetric channel filter were introduced before mathematical modeling was established. Figure 1 is an asymmetric DPF calculation unit. The ends of the inlet channel of the DPF and its outlet channel were blocked. Exhaust gas enters the outlet channel from the inlet channel through the wall surface, and then exits through the channel. As seen in Fig. 1, d1 is the side length of the inlet channel, and d2 is the side length of the outlet channel.

Fig. 1
figure 1

The asymmetric DPF calculation unit

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CRD (ratio of inlet to outlet channel width) of asymmetric channel DPF is:

$$CRD=\frac{d_1}{d_2}$$
(1)

Before establishing the DPF mathematics model, it is necessary to make reasonable assumptions to simplify the model. The specific assumptions are expressed as follows:

  1. 1.

    The physical parameters of all parts in the clean wall are consistent

  2. 2.

    The particulate matter in the exhaust gas only includes soot, without SOF, sulfate, etc.

  3. 3.

    Only considering laminar flow when the exhaust gas flows inside the DPF channel [23]

2.1 Pressure Drop Model of Asymmetric Channel DPF

The pressure drop is an important parameter in measuring the working performance of the DPF. Exhaust gas in through the inlet channel and out through the outlet channel via the porous media at the wall, and PM is filtered through this process and deposited on the wall surface. A pressure drop model based on Darcy’s law can solve for the pressure loss caused by the DPF working process (including the soot loading and regeneration process) with the following equation [24, 25]:

$$\varDelta P=\varDelta {P}_1+\varDelta {P}_2+\varDelta {P}_3+\varDelta {P}_4+\varDelta {P}_5+\varDelta {P}_6+\varDelta {P}_7$$
(2)
$$\varDelta {P}_1=\frac{\xi_{contraction}{\rho}_{inlet}{U}_{inlet}^2}{2}$$
(3)
$$\varDelta {P}_2=\frac{\mu Q}{2{V}_{trap}}{\left(D+{w}_{wall}\right)}^2\frac{4F{L}^2}{3}\left(\frac{1}{{\left(D-2{w}_{soot}\right)}^4}\right)$$
(4)
$$\varDelta {P}_3=\frac{\mu {U}_{w,1}\left(D-2{w}_{soot}-2{w}_{ash}\right)}{2{k}_{soot}}\mathit{\ln}\left(\frac{D}{D-2{w}_{soot}-2{w}_{ash}}\right)+{\beta}_{soot}\rho {w}_{soot}{U}_{w,1}^2$$
(5)
$$\varDelta {P}_4=\frac{\mu_w{U}_{w1-2}}{2{k}_{ash}}\left(D-2{w}_{ash}\right)\mathit{\ln}\left(\frac{D}{D-2{w}_{ash}}\right)+{\beta}_{ash}\rho {w}_{soot}{U}_{w,1-2}^2$$
(6)
$$\varDelta {P}_5={\sum}_i\left(\frac{\mu {U}_{w,2}{w}_{slab,i}}{k_{wall,i}}+{\beta}_{wall}\rho {w}_{slab,i}{U}_{w,2}^2\right)$$
(7)
$$\varDelta {P}_6=\frac{\mu Q}{2{V}_{trap}}{\left(D+{w}_{wall}\right)}^2\frac{4F{L}^2}{3}\left(\frac{1}{D^4}\right)$$
(8)
$$\varDelta {P}_7=\frac{\xi_{expansion}{\rho}_{outlet}{U}_{outlet}^2}{2}$$
(9)

where ∆P1 represents the pressure drop caused by the contraction at the inlet, ∆P2 represents the pressure drop caused by the friction between the gas in the inlet channel and the wall, ∆P3 represents the pressure drop caused by the gas passing through the soot cake layer, ∆P4 represents the pressure drop caused by the gas passing through the ash layer, ∆P5 represents the pressure drop caused by the gas passing through the DPF carrier wall, and ∆P6 represents the pressure drop caused by the friction between the gas and the wall in the outlet channel. ∆P7 represents the pressure drop caused by the contraction of the outlet. In the formula, ξcontraction and ξexpansion represent contraction pressure drop coefficient and expansion pressure drop coefficient of the carrier, respectively; the coefficient usually varies from 0.3 to 5. Uinlet and Uoutlet indicates the flow rate at the inlet and the outlet respectively, m/s.

2.2 Soot Capture Model of Asymmetric Channel DPF

In the process of DPF capture, the soot is captured by the deep bed and intercepted by the wall pores of the DPF carrier channel. As the soot gradually increases, it enters the cake layer capture stage. The soot layer is covered on the wall of the DPF carrier channel, and the soot is burned after regeneration.

In the deep-bed capturing stage of DPF, the variation relationship of soot capture with time is as follows:

$${m}_{wall}(t)={\sum}_{i=1}^N\left[{m}_{in}\left(i,t\right)E\left(i,t-1\right)\right]$$
(10)

The mass of the soot cake layer after entering the filter cake capture stage can be expressed as follows:

$${m}_{cake}={m}_{engine- out}\cdot \Phi \cdot {E}_{cake}$$
(11)

The thickness of the soot cake layer can be expressed as:

$${w}_{cake}=\frac{D_1-\sqrt{{D_1}^2-\frac{m_{cake}}{N_{cell}{L}_{eff}{\rho}_{cake}}}}{2}$$
(12)

2.3 Regenerative Soot Combustion Model of Asymmetric Channel DPF

Based on the assumptions, the governing equation of DPF regeneration process is shown below:

Mass balance:

$$\frac{d\left({\rho}_i{u}_i{D}_i^2\right)}{dz}={\left(-1\right)}^i4{D}_i{\rho}_w{u}_w$$
(13)

where i = 1 is the inlet channel; i = 2 is the outlet channel; ρi is the density of gas flow in the channel; ρw is the density of gas flow passing through the filter wall; ui is the flow velocity in the channel, uw is the filtration velocity of the air flow; Di is the width of the channel, and z is axial direction.

Momentum balance:

$$\frac{d\left({p}_i+{\rho}_i{u}_i^2\right)}{dz}=-\frac{\alpha {\mu}_i{u}_i}{D_i^2}$$
(14)

where pi is the gas pressure in the channel; μi is the dynamic viscosity; α is the dimensionless frictional resistance coefficient.

Considering that the flow profile across the channel is not flat, the momentum convection term in the momentum balance should have a momentum flux correction factor [26, 27]:

$$\beta =\frac{1}{A{\overline{u}}^2}\int {u}^2\mathrm{d}A$$
(15)

Gas energy balance:

$${\rho}_i{u}_i\frac{D_i}{4}{c}_g\frac{d{T}_i}{dz}+\left[{h}_i+{\left(-1\right)}^i{c}_g{\rho}_w{u}_w\right]\left({T}_w-{T}_i\right)=0$$
(16)

where Tw is the gas temperature of the filter wall; Ti is the gas temperature in the channel; hi is the heat transfer by conduction (for forced convection along a channel); cg is the heat transfer coefficient of the filter wall and flow.

The total heat transferred to the wall by the inlet [28]:

$${c}_p S\rho {u}_{z2}\frac{\partial {T}_1}{\partial z}=\varPi \left({h}_c-{c}_p{\rho}_w{v}_w\right)\left({T}_w-{T}_1\right)$$
(17)

where cp is the gas-specific heat capacity; S is the total surface of the volume; ρ is the gas density; hc is the amount of heat transferred through conduction from the channel to the wall; on the perimeter Π, the normal component of velocity is vw (pointing outward) for the inlet channel.

Darcy’s law of pressure drop:

$$dp=\left\{\begin{array}{c}\frac{\mu_w}{k_p}{u}_w dx,x\in \left(0,w\right]\\ {}\frac{\mu_w}{k_s}{u}_w dx,x\in \left(w,{w}_s\right)\end{array}\right.$$
(18)

where kp is the permeability of the particle; ks is the permeability of the filter wall; μw is the dynamic viscosity of the gas through the wall; w is the thickness of the soot cake layer; ws is the thickness of the filter wall.

During active regeneration, the temperature of DPF is higher than 600 °C, at which point the soot reacts with oxygen to generate CO and CO2 [29]. The soot oxidation and filter regeneration model was constructed on the basis of the following global mechanism, considering thermal reaction kinetics.

Soot oxidation reaction:

$$C+\left(1-{f}_{\mathrm{CO}}/2\right){O}_2\to {f}_{\mathrm{CO}}\mathrm{CO}+\left(1-{f}_{\mathrm{CO}}\right)\mathrm{C}{\mathrm{O}}_2$$
(19)
$${f}_{CO}=\frac{1}{1+{k}_f\bullet {y}_{O_2}^{P_2}\bullet \mathit{\exp}\left(\frac{P_3}{R_0\bullet T}\right)}$$
(20)

where fCO is the selectivity of soot oxidize CO, which determines the concentration of CO and CO2 as the soot is oxidized.

The soot oxidation rate over the above reaction is given by:

$${\dot{r}}_{soot}=-{K}_{thm}{S}_p{\rho}_w{Y}_{oxygen}\frac{M_C}{M_{oxygen}}$$
(7)

Where the thermal reaction rates of progress is given by [30]:

$${K}_{thm}={A}_T{\mathit{\exp}}^{-\left(\frac{E_T}{T}\right)}$$
(8)

In the preceding equations, MC is the molecular weight of soot; Moxygen is the molecular weight of oxygen; Sp is the surface area in the substrate layer; Yoxygen is the mass fraction of O2, and its value is 0.1; ρw is the gas phase density in the substrate; Kthm is the rate constant for thermal reaction; AT is the thermal frequency factor, and its value is 1.43 × 106/s; ET is the thermal activation temperature, and its value is 139.46/(kJ mol−1); T is the filter substrate temperature, and its value is 860 K.

3 Model Validation

According to the user manual of GT-POWER, the calibration of the soot accumulation model mainly involves three factors: the permeability constant controls the pressure drop at the turning point from deep bed filtration to cake filtration, which usually varies in the range of 0.85~0.95 (constant without unit); the soot accumulation density of the filter wall varies in the range of 8~20 kg/m3, and it controls the slope of pressure drop curve with respect to time during deep bed passing. The cumulative density of soot layer controls the slope of the pressure drop curve of cake filtration stage in relation to time. Since the cumulative density of soot can be expressed by the formula including the porosity of soot layer, the porosity of soot layer is taken as the parameter to be calibrated in the calibration process, and its variation range is 0.56~0.96.

The back pressure of clean DPF depends on its wall permeability kw. By modifying the wall permeability parameter of the model, the relationship between simulated pressure drop and exhaust flow rate is close to the test results, which verifies the reliability and accuracy of the pressure drop model.

Clean and soot-free asymmetric channel DPF was selected to adjust engine working conditions, so that the mass flow rate of exhaust gas through DPF varied in 50–200 kg/h with little temperature difference, and the inlet temperature of DPF was about 490 K. The main parameters of DPF are shown in Table 1. Table 2 shows the main parameters of the diesel engine. The comparison between the measurement value and the simulated value is shown in Fig. 2. When the wall permeability kw is 3 × 10−13 m2, the maximum relative error between the simulated value and the measurement value is less than 5%, which indicates that the established pressure drop model is relatively close to the actual test situation and has certain reliability and accuracy.

Table 1 The fundamental parameters of the DPF
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Table 2 Parameters of diesel engine
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Fig. 2
figure 2

DPF pressure drop simulation value and measurement value change with exhaust flow rate

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Since the exhaust parameters of the diesel engine are unstable during operation, in order to reduce the influence of factors such as diesel exhaust parameters, the verification experiment in this paper adopts the offline regeneration method, and the aged filter (DPF after soot capture) was put into the built system for regeneration to achieve accurate control of environmental conditions. While verifying the feasibility of the regeneration scheme, the experiment results can be used as a reference for the validation of chemical reaction kinetic parameters. The soot filtration experiment was carried out in the exhaust environment of a high-pressure common rail four-cylinder diesel engine to obtain the filter loading required for the offline regeneration experiment. The main material used for DPF was silicon carbide. The main parameters of DPF and diesel engine are shown in Tables 1 and 2. The filtration process was carried out under the condition of 1800 r/min and 50% load rate of the diesel engine. During the capture process, the relationship between pressure drop and time was recorded. The engine is only used for soot loading, not for regeneration studies.

Based on the soot capture experiment, the pressure drop data obtained by the experiment was compared with the simulated value, and the value of the optimization function was set as the sum of squares of the difference between the two. The solution of the optimization function at the minimum value was obtained, and the permeability constant P was 0.9, the soot density on the wall of the DPF ρwall was 22 kg/m3, and the porosity of the soot layer εsoot was 0.83 (all three values are fitting parameters). Figure 3 shows the comparison results between the obtained DPF simulated pressure drop and the experiment measured values. It can be seen that the DPF pressure drop curve is similar to the experiment results, indicating that the calibrated DPF capture model is more accurate.

Fig. 3
figure 3

Comparison of simulated and experimental values of DPF pressure drop

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The offline regeneration experiment system diagram is shown in Fig. 4. These include gas heaters, temperature control boxes, oxygen sensors, differential pressure gauges, thermocouples, and other devices. The intake gas is O2/N2 mixture. Before the experiment, N2 was added to discharge the original gas in the pipeline. During the experiment, the intake air was heated to 858 K by a temperature-controlled gas heater to reach the temperature required for regeneration. The intake gas ratio was changed by adjusting the valves and the flow meter, and the total inlet flow rate was 1400 L/min. The pressure drop data can be obtained by means of differential manometer.

Fig. 4
figure 4

Offline regeneration system

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As shown in Fig. 5, when mass concentration of initial soot in DPF was 6.5 g/L, the error in predicted backpressure was not more than 7%. Therefore, the established DPF model is relatively accurate and can reflect the experiment results better. Based on this mathematical model, further effect analysis on regeneration of DPF can be conducted.

Fig. 5
figure 5

Simulation value and measurement value of pressure drop of DPF

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4 Results and Discussion

4.1 Influence of CRD on the Capture Process

In order to study the influence of asymmetric carriers on DPF pressure drop, DPF carriers with inlet to outlet channel width ratios of 1, 1.1, 1.2, 1.3, and 1.4 are selected to calculate the change in DPF pressure drop and capture efficiency with time. The mass concentration of soot in exhaust is 1.7 E−4 kg/m3, the exhaust temperature is 550 K, and the exhaust flow rate is 200 kg/h. The DPF pressure drop of different inlet to outlet channel width ratios varied with time, as shown in Fig. 5.

As can be seen in Fig. 6a, at the beginning of the capture, with the CRD of the DPF increases from 1 to 1.4, the initial pressure drop of the DPF increases from 1.4 to 1.9 kPa. The increase of CRD will lead to the decrease of the volume of the outlet channel; consequently, the wall permeability of DPF becomes poor, and the backpressure across the DPF increases. During the period of 0–250 s of capture process, the five filters are in the deep-bed filtration stage, the pressure drop increases rapidly, and the growth trend is consistent. However, the increase of CRD will increase the surface area of the inlet channel and increase the amount of soot that can be carried inside the wall. Therefore, the DPF deep-bed filtration stage last longer when the CRD is 1.4. At 500–2400 s of the capture process, the soot mass in the DPF wall reached saturation, and soot starts to accumulate on the inner surface of the channels. Compared with the saturated carrier wall, the soot layer permeability is larger, so the pressure drop of DPF increases slowly with time. Due to the large surface area of the asymmetric filter inlet channel, the thickness of soot accumulated in the channel is thin, and the rate of increase of the DPF pressure drop is also smaller.

Fig. 6
figure 6

Pressure drop (a) and capture efficiency (b) of DPF with different CRD over time

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Figure 6 b shows the relationship between the capture efficiency of DPF carriers with different CRD over time. When DPF was clean, the capture efficiency decreased with the increase in CRD. When CRD increased, the carrier area that exhaust gas can pass through from the intake channel to the outlet channel decreases, that is, the actual filtration volume decreases. At 0–500 s of the capture process, soot accumulation within the carrier surface until the saturated state, five kinds of DPF capture efficiency is increased rapidly. With the increase in the CRD, the capture efficiency curve of the DPF deep-bed filtration stage migrated downward as a whole.

4.2 Pressure Drop Composition

In order to explore the reasons for the large pressure drop of asymmetric DPF in the initial stage of capture, the pressure drop composition in the clean state of DPF should be studied first. The pressure drop in DPF in the clean state is mainly composed of five parts: inlet channel pressure drop, outlet channel pressure drop, inlet channel contraction pressure drop, outlet channel expansion pressure drop, and wall pressure drop. Set the inlet flow as 200 kg/h, the initial soot load as 0 g/L, exhaust temperature as 550 K, filter cell density as 300 cspi, and wall thickness as 9 mil. The DPF length is 178 mm. The pressure drop composition of asymmetric DPF was investigated.

Figure 7 shows the composition of the total backpressure across a DPF at different inlet and outlet channel width ratios in the clean state. It can be seen from the figure that, in the clean state, the inlet channel contraction pressure drop and the outlet channel expansion pressure drop were small, accounting for only about 3% of the total pressure drop. The pressure rises with the flow expansion at the exit of a filter. With the increase of the CRD, the inlet channel side length increased, and the outlet channel side length decreased. Therefore, the inlet channel pressure drop and inlet channel contraction pressure drop gradually decreased, while the outlet channel pressure drop and outlet channel expansion pressure drop gradually increased. It can also be seen from the figure that the wall pressure drop accounted for a higher proportion of the total pressure drop, and with the increase of CRD, the total area of the filter channel wall will increase, resulting in a small decrease in the wall pressure drop [22]. When the CRD is 1.4, the vent passage pressure drop rose greatly, resulting in a larger increase in the total pressure drop of DPF. Therefore, the total pressure drop of DPF will increase with the increase of CRD in the clean state.

Fig. 7
figure 7

Pressure drop composition of DPF with different proportion of inlet and outlet in clean state

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Figure 8 shows the pressure drop composition of DPF with different CRD when soot load was 6 g/L, and the soot is uniformly distributed within the DPF. As can be seen from the figure, when the soot load was 6 g/L, the total pressure drop of DPF decreased from 6.2 to 5.4 kPa as the CRD increased from 1 to 1.4. The changed rule of DPF is the same as that in the clean state. With the increase of CRD, the pressure drop at inlet channel and inlet channel contraction decreases gradually, while the pressure drop at outlet channel and outlet channel expansion increases gradually. However, different from the composition of clean DPF, the soot layer pressure drop of DPF under the condition of 6 g/L soot load accounted for a large proportion of the total pressure drop. Since the increase in CRD can increase the internal surface area of the intake passage and reduce the thickness of the captured soot layer, the pressure drop of the soot layer decreases, and the decrease amplitude is larger than that of the pressure drop in the air vent. Therefore, in the clean state, the pressure drop of asymmetric channel filter is larger than that of symmetric channel filter, but when the internal soot load of the carrier is large, the pressure drop of asymmetric channel filter is smaller.

Fig. 8
figure 8

The pressure drop of the DPF with different CRD when the soot load was 6 g/L

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4.3 Soot Distribution in the Channel

In the cake trapping stage, the captured soot was distributed on the inner surface of the intake passage. In order to study the distribution of soot in DPF with different CRD, the thickness of soot in the axial of DPF was simulated and calculated. Set the inlet flow as 200 kg/h, the initial soot load as 6 g/L, exhaust temperature as 550 K, filter cell density as 300 cspi, and wall thickness as 9 mil. The DPF length is 178 mm. Figure 9 shows the axial soot deposition thickness of DPF with different CRD when the soot load was 6 g/L. The axial relative position \(s=\frac{X}{L}\), X represents the distance between the monitoring point and the DPF entry section, and L represents the total length of the DPF.

Fig. 9
figure 9

The axial soot thickness of the DPF with different CRD when the soot load was 6 g/L

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As can be seen from Fig. 9, soot presents concave distribution in the DPF. The thickness of soot deposited at the front and back ends of the carrier axis was larger, while the thickness deposited at the middle of the axis was smaller. As shown in Fig. 10, with the increase of CRD, the actual filtration area of DPF increased, and the overall thickness of the soot layer of the channel decreased. As the thickness of the soot layer in the channel decreases, the soot floating on the wall tends to move along with the exhaust flow, aggravating the non-uniformity of the axial distribution of the soot, resulting in a large difference between the thickness of the back-end soot and that of the front-end soot, which is not conducive to the regeneration process of DPF.

Fig. 10
figure 10

Effect of CRD on filtration area

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4.4 Effect of CRD on Regeneration Process

Due to the special design of inlet and outlet of asymmetric channel will affect the regeneration process. In this paper, the influence of asymmetric structure on the regeneration process of DPF is investigated on two bases, which are wall peak temperature and regeneration rate. The width and length of the DPF are set to 145 mm and 178 mm, the exhaust flow rate is 50 kg/h, and the exhaust temperature is 860 K. The initial soot load was 25 g. The selected filter CRD is 1, 1.2, and 1.4, respectively. The peak wall temperature and regeneration rate during regeneration process are shown in Fig. 11.

Fig. 11
figure 11

Peak wall temperature (a) and the change of soot load mass (b) during DPF regeneration with different CRD

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It can be seen from Fig. 11a that the symmetric DPF reached the peak wall temperature of 1230 K at 220 s, DPF with CRD of 1.2 reached the peak wall temperature of 1308 K at 190 s, and DPF with CRD of 1.4 reached the peak wall temperature of 1412 K at 170 s. Therefore, when the DPF of larger CRD was regenerated, a higher peak wall temperature was generated, and the peak temperature appeared earlier. The logical explanation for this phenomenon is that with the increase of CRD, the volume of the outlet passage decreased, which was not conducive for the flow of exhaust gas in DPF, resulting in slower heat loss from soot oxidation. In addition, the larger the CRD, the larger the contact area between gas and soot, which is more conducive to the combustion and oxidation of soot. The more intense the oxidation, the higher the temperature, the faster the combustion speed and the full oxidation, so the peak temperature increases with the increase of CRD. The faster the rate of oxidation and combustion, the faster the temperature rises.

Figure 11 b shows the change of soot load mass in DPF over time. It can be seen from the figure that at the early stage of regeneration, the soot load of asymmetric DPF with CRD of 1.4 began to decline first, and the trend of decline was the most rapid. That is, the regeneration rate was faster. After the end of the regeneration process, the residual soot in DPF carrier with CRD of 1.2 and 1.4 was smaller. The increase in CRD increased the area of the soot layer on the inlet channel surface and the contact area with the exhaust. In the process of regeneration, due to the slow heat discharge from asymmetric channel filter, there was more heat exchange between exhaust and carrier wall, resulting in faster regeneration rate and increase in the overall regeneration efficiency.

5 Conclusions

Due to the serious environmental pollution, it is important to study and optimize the capture and regeneration performance of DPF. In this paper, the regeneration and soot models of asymmetric DPF have been established, verified, and analyzed. The main conclusions are as follows.

  1. 1.

    In the early stage of capture, the initial pressure drop rises from 1.4 to 1.9 kPa as the CRD goes from 1 to 1.4. This indicates that the pressure drop of asymmetric channel DPF is higher than that of symmetric channel DPF. The capture efficiency of asymmetric channel DPF decreases with the increase of CRD, but the final capture efficiency can reach more than 99%.

  2. 2.

    In the clean state of DPF, with the increase of CRD, the inlet channel pressure drop and wall pressure drop decrease, but the total pressure drop increases. When the DPF soot load is 6 g/L, the pressure drop decreases except for the increase of the outlet channel pressure drop. In the axial position of DPF, the soot is thick at both ends and thin in the middle. With the increase of CRD, the actual filter area of DPF increases, and the total thickness of the soot layer decreases.

  3. 3.

    The increase of CRD has a certain effect on the regeneration performance of asymmetric DPF, and the regeneration peak temperature can be reached quickly during regeneration, which promotes the oxidation and regeneration of soot. With the increase of CRD, the regeneration oxidation rate of soot increased, and the residual soot was less.