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Effects analysis on diesel soot continuous regeneration performance of a rotary microwave-assisted regeneration diesel particulate filter
Fuel 260 (2020) 116353
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Full Length Article
Effects analysis on diesel soot continuous regeneration performance of a rotary microwave-assisted regeneration diesel particulate filter
T
Jiaqiang Ea,c, Mengyuan Zhaoa, Qingsong Zuob, Bin Zhanga,b, , Zhiqing Zhanga, Qingguo Penga, Dandan Hana, Xiaohuan Zhaoa, Yuanwang Denga,c ⁎
a
College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China College of Mechanical Engineering, Xiangtan University, Xiangtan 411105, China c Institute of New Energy and Energy-Saving & Emission-Reduction Technology, Hunan University, Changsha 410082, China b
GRAPHICAL ABSTRACT Regeneration cavity
Outlet
Inlet
Porous media
Schematic diagram of a rotary DPF
Pressure contour distribution of the rotary DPF
Grid diagram of a rotary DPF
Distribution of cos θ under different flow velocities
ARTICLE INFO
ABSTRACT
Keywords: Rotary microwave-assisted regeneration diesel particulate filter Regeneration performance Continuous regeneration Turbulence model Field synergy
In order to investigate effects of various factors on continuous regeneration performance of a rotary microwave-assisted regeneration diesel particulate filter (MRDPF), a regeneration mathematical model and a field synergy model of the rotary MRDPF are developed, and turbulent kinetic energy distribution and pressure distribution of the rotary MRDPF based on three different turbulence models are analyzed. The results indicate that the RNG k-ε model is more suitable for simulation of the rotary MRDPF and appropriate increment of filter unit number, oxygen content and exhaust gas temperature can result in the regeneration performance improvement of the rotary MRDPF. Inlet flow velocity of exhaust gas can change synergy degree between the velocity field and the temperature field and high synergy area is mainly concentrated in the upper and central parts of the filter unit. Moreover, field synergy degree and regeneration efficiency of the filter unit are both better when the flow velocity reaches 0.3 m/s during regeneration phase, where regeneration optimized area ratio and maximum regeneration efficiency are 0.51 and 91%, respectively. This work provides great reference values for optimizing the continuous regeneration performance of the rotary MRDPF.
⁎
Corresponding author at: College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China. E-mail address: [email protected] (B. Zhang).
https://doi.org/10.1016/j.fuel.2019.116353 Received 8 July 2019; Received in revised form 1 October 2019; Accepted 4 October 2019 Available online 17 October 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
wc ρd cpd λd Td kd ∑sk△Hk qwd β Pw g γd m0c
u \* MERGEFORMAT fluid velocity, m/s; s constituent gas; ws formation rate of gaseous components; i direction; p air pressure, Pa; Si volume force applied to the infinitesimal hexahedron, N; cp specific heat at constant pressure, J/(kg·K); λ thermal conductivity, W/(m·K); QS reaction heat value, J; c particle; a airflow; f filter body; k specific surface area; H heat transfer coefficient, W/(m2·K); DS effective mass diffusivity of components; gas mass percentage in the composition; Ys mc carbon content per unit volume on filter body;
Fc ∂T/∂x ∂T/∂y ∂T/∂z
1. Introduction
particle formation rate; comprehensive density of solid phase, kg/m3; solid specific heat capacity, J/(kg·K); solid phase thermal conductivity, W/(m·K); temperature of the solid phase, K; solid specific surface area; total heat release rate; microwave energy absorbed by solid phase; completeness of combustion oxidation reaction, 0.8; microwave power into the effective area of the filter unit; distance of microwave propagation; attenuation constant of solid relative microwave; amount of particles deposited on the arc of the filter unit along the airflow direction; field synergy number; x-direction temperature gradient; y-direction temperature gradient; z-direction temperature gradient;
channel hydraulic diameter. In addition, the DPF heat transfer properties depend on the heat capacitance ratio and the hydraulic parameters, and the speed of the temperature front can be increased by decreasing the DPF substrate thickness [40]. A synergistic effect among NO2, water and oxygen in the exhaust gas was observed by Soltani et al. [41], and the required exhaust condition was optimized during regeneration phase for maintaining a balance between soot accumulation and soot regeneration. A hexagonal pore filter structure was designed by Tsuneyoshi et al. [42] to reduce the pressure loss of the DPF, which has higher regeneration efficiency compared with the quadrilateral pore structure, but the effect of exhaust parameters and optimal structural parameters for simultaneous improvement of pressure drop and regeneration performance have not been presented. Fang et al. [43] investigated the effect of operating parameters on regeneration characteristics of the diesel particulate filter. The results showed that the exhaust flow rate has negative effect on the maximum temperature, maximum temperature gradient and regeneration performance ratio, but effect of oxygen content has not been considered. These literatures indicated that different structural parameters and exhaust parameters can change flow field, temperature field, heat capacity, heat transfer effect and soot chemical reaction rate, influencing the wall-flow DPF regeneration performance. However, the comprehensive influence analysis of all factors on the wall-flow DPF regeneration performance has not been carried out and the general influence mechanisms related to the rotary DPF regeneration have not been clarified. A current challenge that alternative fuels face is their effect on regeneration performance of the diesel particulate filter. RodriguezFernandez et al. [44] tested different fuels (such as conventional diesel fuel, e-diesel, paraffinic fuels and conventional biodiesel) in a Euro 5 automotive engine with the DPF. Results revealed that a greater ability of soot from paraffinic and oxygenated biofuels to be oxidized under lower temperature conditions, e-diesel soot is the least sensitive to the oxygen concentration and it has the fastest oxidation rate. They also found that biodiesel results in a more economical regeneration through an active process with fuel post-injections due to the biodiesel soot is more reactive than the other fuel samples [45]. These literatures showed that alternative fuels such as biodiesel and paraffinic biofuels have positive effects on the wall-flow DPF regeneration performance as a result of the high reactivity of the soot, and it is worth to carry out effects of these alternative fuels on the regeneration performance of the rotary DPF. The efforts for regeneration influence mechanism analysis and performances enhancement of the wall-flow DPF have been conducted in the published literatures, however, no relative study is reported on the rotary MRDPF. Therefore, it is significant to take further studies
Although the diesel engine has low fuel consumption, strong power performance, reliable performance and a wide application market [1–3], it can produce a considerable amount of particulate matter (PM) [4,5] which results in inevitable environmental pollution. How to reduce the particulate emission of the diesel engine has been being a hot research topic because of an increasing concern on environmental protection and increasingly strict emission regulations [6,7]. Nowadays, blended fuels (such as biodiesel-diesel and ethanol–diesel) [8,9] have been investigated to reduce particle and gaseous emissions [10,11], and simultaneous use of advanced combustion technologies (such as PPCI [12,13], RCCI [14,15] and HCCI [16,17]) and the diesel particulate filter (DPF) [18–20] is viewed as the most effective avenue for fitting PM emission limits of diesel vehicles [21,22]. The key working process of the DPF is soot regeneration [23,24] which includes passive regeneration [25,26], active regeneration [27–29] and composite regeneration [30–32]. In our previous studies [33,34], a microwave assisted regeneration method combining microwave and ceria-manganese base catalytic additive has been employed in a wall-flow DPF, where the continuous regeneration is restricted and battery energy storage of the diesel vehicles can hardly support the microwave energy consumption during regeneration phase. Therefore, a rotary DPF with new type structure and working principle is developed based on microwave assisted regeneration to regenerate the PM continuously and reduce pressure drop by dividing its filter into several rotatable blocks, which avoids the microwave regeneration on the whole filter and saves more energy compared with the wall-flow DPF. It is reported that appropriate structural parameters of the wall-flow DPF and exhaust parameters are beneficial to enhancing DPF regeneration performance based on the large numbers of investigations [35,36]. A lot of numerical studies can be tried to explain the influence mechanism of these parameters. The results showed that an uneven soot combustion exists along the axial coordinate of the filter due to strong temperature gradients inside the filter [37]. The maximum wall temperature of the DPF increases with the rise of the ratio of length to diameter, but it decreases with the rise of cell density because of the improvement of heat conduction and heat capacity [38]. For NO2-assisted regeneration, the regeneration speed is raised up due to the rise of the exhaust gas volume, the exhaust gas temperature, the NO2 concentration and the O2 concentration, but it is decreased with the increment of the filter length and the channel density [39]. A more uniform filtration velocity with a lower pressure drop can be obtained as a result of the reduction of the inlet velocity and the increment of the 2
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about the effects of exhaust parameters and structural parameters on regeneration performance of the rotary MRDPF. Field synergy analysis of the wall-flow DPF [46,47] indicated that for multiple fields in the DPF, the enhancement of fluid flow as well as heat and mass transfer in the filter is not only related to the fluid properties, but also depends on the change of field parameters and the field synergy degree. However, effect of exhaust gas flow velocity on field synergy has not been investigated for the wall-flow DPF especially for the rotary MRDPF which has more complex flow field than the wall-flow one. In this work, a physical–mathematical model and a field synergy model of the rotary MRDPF is established firstly. Then, the turbulence model [48,49] selection is analyzed comparatively, and the effects of filter unit number, oxygen content, exhaust gas temperature and flow velocity on continuous regeneration performance of the rotary MRDPF are investigated. Finally, field synergy optimization between velocity vector and temperature gradient for continuous regeneration performance enhancement of the rotary MRDPF is carried out based on the field synergy theory [50,51], and parameters range is suggested. The results of this work will provide theoretical basis for the microwave assisted regeneration design of the rotary MRDPF, which can reduce the PM emission of the diesel engine.
2. Investigated models of the rotary microwave-assisted regeneration diesel particulate filter In order to investigate effects of different parameters on continuous regeneration performance of the rotary MRDPF, some assumptions of the model should be made as: (a) The exhaust gas of the diesel engine is regarded as ideal gas; (b) The flow through the rotary MRDPF is constant flow; (c) The exhaust gas flow can be considered as incompressible; (d) Particles in the porous media are pure carbon particles with the same size in diameter. 2.1. Physical model of the rotary microwave-assisted regeneration diesel particulate filter The structure schematic diagram of a rotary MRDPF with a SiC foamed ceramics filter is depicted in Fig. 1(a). It shows that the rotary MRDPF can be divided into the intake pipe, the expansion pipe, the filter, the shrink pipe and the exhaust pipe. The SiC foamed ceramics filter (pore density is 50 ppi, length is 135 mm, external diameter is 200 mm, and internal diameter is 80 mm) [52] can be divided into several blocks. In working process of the rotary MRDPF, the filter is
Regeneration cavity
Outlet
Inlet
Porous media
(a) Schematic diagram
(b) Grid diagram Fig. 1. Structure model of a rotary MRDPF. 3
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rotated by a certain angle α (α is the peripheral angle of each filter unit) to start the microwave generator when the exhaust back pressure reaches a certain value. During the regeneration phase, one filter unit is heated by microwave energy and others capture the soot, which can realize continuous regeneration by cycle. A three-dimensional model of the rotary MRDPF is depicted in Fig. 1(b). In order to improve the accuracy and convergence of the calculation, the physical model is simplified by removing inessential structure and the grid area of expansion tube and shrink tube is refined.
follows.
( d Td cpd ) =
C+ O2
uj ui + xj xi
+ Si +
ws ui s
d
=
xj
a
T xj
T ) + k f Hf (Tf
T)
( s · Ys· uj ) =
xj
Ds · s ·
Ys Xj
+ Ws
(3)
cos =
(4)
=
Mass conservation equation of the carbon particles is shown in Eq. (5).
=
wc
(8)
(9)
)
f
(10)
U¯ · ¯T dy¯ = =
Nu RePr
U¯ · ¯T |U¯ | | ¯T |
(11)
T ·u x
+
T ·v y
+
( ) +( ) +( ) T 2 x
T 2 y
T 2 z
T ·w z
· u2 + v 2 + w 2
(12)
where ∂T∕∂x, ∂T∕∂y and ∂T∕∂z is the temperature gradient in x, y and z direction, respectively. u, v and w is the exhaust gas flow velocity in x, y and z direction, respectively. Assuming that the regenerative combustion synergy of regenerative filter unit is optimal when cosθ is larger than 0.8 [53,54], the ratio of the area with cosθ greater than 0.8 to the whole filter unit area (the regeneration optimized area ratio) is shown as follows.
(5) Mass conservation equation of the carbon particles
mc
)CO
where Fc is the synergy number; U is the velocity vector, m/s; θ is the angle between velocity vector and temperature gradient; ∇T is the temperature gradient; Nu is the Nusselt number, Pr is the Planck number, and Re is the Reynold number. For the three-dimensional model used here, the expression of cosθ between the velocity vector and the heat flow temperature vector can be expressed as follows.
The reason for mass change in the micro-hexahedron includes diffusion and chemical reaction. According to Reynolds transport law, the conservation equation of gas component is expressed as Eq. (4).
xj
mc + (1 mc0
cos
(4) Component conservation equation of exhaust gas in the filter
( s ·Ys ) +
=
Fc =
(2)
( uj c p T ) + ws Qs + k c Hc (Tc
0.5)CO2 + 2(1
The field synergy number of the filter unit is defined by the Eq. (11).
Considering the heat release and thermal conductivity in the soot particles combustion reaction, gas energy conservation equation can be written as Eq. (3) according to the first law of thermodynamics.
xj
2(
(9) Field synergy model
(3) Energy conservation equation of exhaust gas in the filter
( cps T ) +
(7)
Since the microwave attenuation constant is different between soot particles and the filter, and the deposited soot mass is different on different area of the filter, the microwave attenuation constant formula of solid phase can be expressed as follows.
According to the law of momentum conservation, the variation of micro-hexahedron momentum with time in the fluid calculation domain is equal to the sum of pressure, volume force and momentum generated by reaction in the micro-element. Gas momentum equation can be expressed as follows.
p + µ xi xi
s k Hk + qwd s
qwc = 2 Pw exp( 2 d g )
(2) Momentum conservation equation of exhaust gas in the filter
D ( · ui ) = D
T) +
When microwave is fed into regeneration cavity, the filter and soot particles begin to absorb microwave energy. The absorbed microwave energy is shown as follows.
(1)
s
ad Hd (Td
(8) Microwave energy equation
There is a restrictive relationship between velocity and density, and the fluid mass increment of a micro-hexahedron which can be taken as the volume element is the total mass of the reaction products in the computational domain. Mass conservation equation of the exhaust gas is shown in Eq. (1).
ws
T xj
An oxidation reaction model is shown in Eq. (5), and β is the complete coefficient of the carbon particles oxidation reaction.
(1) Continuity equation of exhaust gas in the filter
·( · u ) =
d
xj
(7) Oxidation reaction mechanism of the carbon particles
2.2. Mathematical models of the filter
+
(6)
Td = Tc = Tf
=1 cos = 0.8 =1 cos = 0.
× 100%
(13)
(10) Boundary conditions and initial conditions
(5)
The boundary conditions and initial conditions of the simulation model are given as follows: (a) The inlet boundary condition is set as inlet velocity of the exhaust gas, and it is assumed that inlet velocity is uniform without radial component. The value of inlet velocity is set according to working conditions of the diesel engine.
(6) Energy conservation equation of solid phase Assuming that the temperature of carbon particles is same as that of the filter, the solid phase energy conservation equation is shown as 4
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(b) The outlet boundary condition is defined as outlet pressure of the exhaust gas, and it is set to 0 MPa. (c) No slip boundary condition is set on the filter wall. The exhaust gas temperature is set as 573 K and the content of the soot particles in the exhaust gas is set to 0.05 [39]. Moreover, since the specific heat of each gas component will be changed under high temperature condition with the rise of temperature, the specific heat of the gas component such as O2, CO2 and N2 is set to piecewise polynomial, the specific heat of the carbon particles is regarded as constant and that of the overall mixture is set to mix-law.
shown in Fig. 4, the change trends of the simulation results are consistent with the experimental results under the same working condition of the rotary MRDPF. It displays a good agreement between measured values and simulation values under different position, but there is still a smaller difference (the relative error is less than 5.4%) between these results due to model simplification, self-measurement error and instrument precision, etc. Therefore, the mathematical model can be used to predict the flow and reaction characteristics of the rotary MRDPF. 3. Results and discussion
2.3. Grid independence and model verification
3.1. Investigations of different turbulence models
2.3.1. Grid independence In order to obtain a proper grid size for accurate simulation of the flow and reaction characteristics, five various meshes are employed to study the effects of the grid size on the exhaust flow velocity in five different position of the rotary MRDPF. The relationship between the flow velocity and the mesh number is presented in Fig. 2. It can be seen that the flow velocity of five points first decreases and then tends to be a constant with increment of the mesh umber, when the mesh number is increased to 1,246,932, the mesh number has no effect on the flow velocity of each position in the rotary MRDPF. Therefore, the medium mesh with 1,246,932 cells can be employed for obtaining better accuracy and saving computational time.
In this work, simulation results of the rotary MRDPF are different by using three different turbulence models. The turbulent kinetic energy distribution of the DPF is shown in Fig. 5. It can be seen that turbulent kinetic energy of the RNG k-ω model is distributed in the inlet of the rotary MRDPF, that of the k-ω model is distributed in the inlet and outlet of the rotary MRDPF, and that of the RSM is distributed in the inlet, outlet and filter body of the rotary MRDPF. The maximum turbulent kinetic energy of these models appears in the entrance of the rotary MRDPF, which can reach 79.8 m2/s2, 78.8 m2/s2 and 79.2 m2/s2 by using the k-ω model, the RNG k-ε model and the RSM, respectively. Moreover, there is a large turbulent kinetic energy gradient in the entrance of the rotary MRDPF under the k-ω model and the RSM, but it is small under the RNG k-ε model. Therefore, the RNG k-ε model shows a relatively uniform distribution of the turbulent kinetic energy. Fig. 6 presents the pressure contour of the rotary MRDPF. It shows that the pressure is roughly symmetrically distributed, and the pressure at the end of the rotary MRDPF is almost the same. The pressure drop of the rotary MRDPF will increase sharply when the exhaust gas flows through the filter. The pressure tends to be constant when the exhaust gas flows out of the filter and reaches the outlet of the rotary MRDPF, and it slightly increases as the airflow approaches the wall of the rotary MRDPF. Fig. 7 clearly depicts the axial pressure drop distribution of the rotary MRDPF under the different turbulence models. It can be seen that the pressure drop of the filter presents large fluctuations in the axial direction, and three turbulence models have a same variation trend of the pressure drop. The pressure distribution is roughly symmetrical, the pressure drop first decreases and then increases with increment of the axial distance before y = 0.1 m, where the pressure drop reaches the largest value of exceeding 30.1 kPa. This variation trend is repeated between y = 0.1 m and y = 0.175 m due to the outlet pressure
2.3.2 Model verification (1) Experimental methods In the experiment, a single-stage air compressor with the rated discharge pressure 1.6 MPa is used to simulate the exhaust process of the diesel engine. There is little change of the flow rate, temperature and other factors between the air in the experiment and the actual exhaust process of the diesel engine. Considering that the experiment mainly focuses on the study of the distribution characteristics of the flow velocity, the experimental device can satisfy the requirements of the experiment [22]. And airflow velocity is measured by the hot wire anemometer with type AN1002. The Schematic diagram of experimental equipments is shown in Fig. 3. (2) Experimental procedures Since it is difficult to measure the airflow velocity inside the foamed ceramics filter, the axial airflow velocity distribution in section 1 and section 2 are analyzed in the test process. The main experimental steps are described as follows: Step 1: The air compressor is started and kept its power in certain value, and then the regulating valve is switched to control the airflow velocity with a constant value (50 m/s), and then the regulating valve is fixed. Step 2: After the hot wire anemometers with type AN1002 are connected in the section 1 (x = 40 mm) and the section 2 (x = 70 mm), the data sampling intervals of the hot wire anemometers are also set. Step 3: The sampling data of the airflow velocity are recorded in the section 1 (x = 40 mm) and the section 2 (x = 70 mm) when r/R is equal to 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, respectively. And then the air compressor is closed after all sampling data of the airflow velocity are obtained. Step 4: The above steps are repeated three times, then, the sampling data of three groups are obtained. And the arithmetic mean values from the sampling data of three groups are treated as the sampling data of the airflow velocity.
45 40 35
(0, -0.05, 0) (0, 0.10, 0)
v/m. s-1
30
(0, 0, 0) (0, 0.15, 0)
(0, 0.05, 0)
25 20 15 10 5 8.0x105
(3) Experimental verification results
1.2x106
1.6x106
2.0x106
Grid quantity Fig. 2. Grid independence validation based on flow velocity results in the Y direction.
Fig. 4 depicts the airflow velocity comparisons of simulation results based on RNG k-ε model and experimental results in each section. As 5
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J. E, et al.
Sampled-data systems Air compressor Inlet
PC display
Velocity controller
Rotary DPF
Hot wire anemometer 1
Cold dryer
2 Filter
Electric heater
Valve 1
Gas analyzer
Valve 2
Fig. 3. Schematic diagram of experimental equipments.
The volume of a single filter unit decreases with the increment of the filter unit number. If soot particles in the exhaust gas and microwave power remain constant, regeneration time is reduced with rise of the microwave energy obtained by the particles due to decrease of the filter unit volume. On the contrary, regeneration time increases with decrease of the filter unit number, therefore, more microwave energy consumption is required to control the regeneration time, which increases the load of the vehicle battery. Fig. 9 shows the effect of filter unit number on regeneration performance of the rotary MRDPF. Fig. 9(a) indicates that the regeneration efficiency of the rotary MRDPF increases with the increment of the filter unit number under a constant microwave power. The regeneration efficiency increases slightly and the filter tends to be completely regenerated when the filter unit number is more than 10, while it becomes smaller when filter unit number is less than 10. The main reason is that there is insufficient absorbed microwave energy of the soot in the regenerated filter unit with larger volume, which results in incomplete combustion of the soot particles on the filter unit. With the increment of the filter unit number, the filter unit volume becomes smaller and the microwave power is enough to ignite soot particles in most areas of the filter unit, so the regeneration efficiency becomes higher. Fig. 9(b) shows that the regeneration time first increases to a certain maximum value and then decreases with increment of the filter unit number. This is owing to that the small filter unit number results in larger microwave heating area and insufficient absorbed microwave energy per unit volume, and most of soot particles difficultly reach the ignition temperature, which needs longer regeneration time. With the increase of filter unit number from 6 to 8, filed synergy effect becomes poor, which results in the rise of the regeneration time and the appearance of a maximum regeneration time. As the filter unit number is above 8, more and more soot particles can reach the ignition temperature for combustion reaction on the filter unit, the regeneration time is decreased due to the decrease of the filter unit volume and the rise of the average microwave heating amount. With the further increase of filter unit number, the microwave power is enough to ignite the particles in the whole filter unit and the total soot mass on the filter unit decreases, which results in the shorter regeneration time.
55 50 45 40
u /m.s
-1
35 30 25 20 15 10 5 0 -5 0.0
Simulation value of section 1 Measurement value of section 1 Simulation value of section 2 Measurement value of section 2
0.2
0.4
0.6
0.8
1.0
Positon r/R Fig. 4. Comparisons of measurement values and simulation values based on RNG k-ε model.
is smaller than the wall when the exhaust gas flows out of the filter, and the pressure drop decreases after y = 0.175 m. In addition, there is a small difference between the pressure drop curve of the RSM and that of the RNG k-ε model, while that of the k-ω model shows a large deviation compared to former ones. Therefore, the k-ω turbulence model is not suitable for simulation of the rotary MRDPF. To sum up, the RNG k-ε model can be selected in this work based on the simulation results of the turbulent kinetic energy and pressure of the rotary MRDPF. 3.2. Effect of filter unit number on regeneration performance of the rotary microwave-assisted regeneration diesel particulate filter In order to investigate the effect of filter unit number on continuous regeneration of the rotary MRDPF, the filter is divided into several filter units on average, and the volume of each filter unit is as follows.
V=
1 (R22 n
R12)· L
(14)
3.3. Effect of oxygen content on regeneration performance of the rotary microwave-assisted regeneration diesel particulate filter
where n is filter unit number, n = 6–15, R1,R2 and L are internal diameter, external diameter and length of the filter unit, respectively. Fig. 8 shows the structure of filter units of different block numbers.
Fig. 10 depicts the synergistic effect of oxygen content in the exhaust 6
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Fig. 5. Turbulent kinetic energy distribution of the rotary MRDPF.
30.4 RNG k-ε
RSM
k-ω
∆p/kPa
30.2
30.0
29.8
29.6
29.4
0.00
0.05
0.10
0.15
0.20
Axial position/m Fig. 7. Pressure drop of the rotary MRDPF in the Y direction.
content. Fig. 10(b) shows the effect of oxygen content on the regeneration time. The regeneration rate of filter unit increases with the increment of oxygen content, which results in the decrease of regeneration time. Moreover, the regeneration rate changes slowly and the regeneration time decreases slowly when oxygen content is more than 15%. Small filter unit number leads to insufficient average microwave energy absorbed by soot particles, and fewer soot particles involved in the combustion reaction, so the oxygen content has little effect on the regeneration performance of the filter unit. When the filter unit number increases, more and more soot particles can reach the ignition temperature faster. Under this circumstance, less oxygen content is difficult to meet the complete combustion reaction of soot particles, which has a great influence on the regeneration time and regeneration efficiency. If the oxygen content reaches more than 15%, the oxygen content is
Fig. 6. Pressure contour of the rotary MRDPF.
gas and the filter unit number on the regeneration performance of the rotary MRDPF when the exhaust temperature is constant. Fig. 10(a) shows the effect of oxygen content on regeneration efficiency of the rotary MRDPF. It can be seen from Fig. 10(a) that oxygen content has a great influence on the regeneration efficiency when it is less than 15%, and the regeneration efficiency of the filter unit increases with the rise of oxygen content in the exhaust gas. However, when oxygen content exceeds 15%, it has little effect on the regeneration efficiency due to the oxygen content is sufficient for soot oxidation reaction on the filter unit, and the regeneration efficiency is no longer limited by the oxygen 7
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(a) n=6
(b) n=9
(c) n=12
(d) n=15
Fig. 8. Structure of the filter units.
100
100
70 60 50 40 30
0.1m/s-573K 0.1m/s-673K
20
0.15m/s-573K 0.15m/s-673K
5
6
7
8
9
10
n
11
12
13
14
80 70 60 50 40 12
30 5
10 0
90
15
10
O xy
16
(a) Regeneration efficiency
gen
14
10
15
cont
20
ent /%
8 25
30
n
ficiency /%
80
Regeneration ef
Regeneration efficiency/%
90
6
(a) Regeneration efficiency
1100 1000
900 800 700
800
600
8
9
10 11 12 13 14 15 16
n
n
(b) Regeneration time
12
10 14
5
nt
10
co
7
20
n
6
15
ge
5
8
xy
6
500
30 25
O
600
t /%
e/s Regeneration tim
Regeneration time/s
0.15m/s-573K 0.15m/s-673K
en
0.1m/s-573K 0.1m/s-673K
1000
(b) Regeneration time
Fig. 9. Effect of filter unit number on the regeneration performance.
Fig. 10. Effect of oxygen content on the regeneration performance.
sufficient to regenerate the soot completely, therefore, the regeneration performance of the rotary MRDPF is no longer greatly affected by the oxygen content.
unit number on the regeneration performance of the rotary MRDPF when the oxygen content in the exhaust gas is constant. It can be seen in Fig. 11(a) that the exhaust gas temperature can promote the regeneration efficiency of the filter when the oxygen content and filter unit number are constant. With the increase of filter unit number, the influence of exhaust gas temperature decreases gradually. Fig. 11(b) shows the effect of exhaust gas temperature on regeneration time. With
3.4. Effect of exhaust gas temperature on regeneration performance of the rotary microwave-assisted regeneration diesel particulate filter Fig. 11 shows the synergistic effect of flow temperature and filter 8
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the increment of filter unit number, the influence of exhaust gas temperature on regeneration time becomes smaller. For the filter unit number below 10, the regeneration time of the filter unit decreases obviously with the rise of exhaust gas temperature. In addition, the variation of regeneration time becomes smaller when the filter unit number is more than 10. When the filter unit number is small and the microwave power is constant, a little of average microwave energy can be absorbed by soot particles, the soot mainly absorbs heat from the exhaust gas by convection heat transfer due to higher exhaust gas temperature before microwave heating, and then reaches the ignition temperature quickly by the microwave heating. Therefore, exhaust gas temperature can promote the combustion of soot particles, shorten the heating time and improve the regeneration efficiency. With the rise of filter unit number, the average microwave energy absorbed by soot particles becomes larger even if it doesn’t absorb heat from the exhaust gas, and soot ignition temperature can be quickly reached, so the exhaust gas temperature has little influence on regeneration time and regeneration efficiency of the rotary MRDPF gradually.
4. Conclusions In this paper, the appropriate turbulence model for numerical simulation is determined, effects of various factors on continuous regeneration performance of the rotary MRDPF are investigated based the physical–mathematical model, the field synergy analysis for continuous regeneration performance enhancement of the rotary MRDPF is carried out based on the field synergy model, and proper parameters range is obtained. The major conclusions are drawn as follows: According to the model verification results and the simulation results comparison of three turbulence models, the maximum relative error of velocity is only 5.4% between experimental results and simulation results based on the RNG k-ε model. The turbulent energy distribution of RNG k-ε is more uniform and its calculation accuracy is better than others, which is more suitable for the simulation of the rotary MRDPF. The regeneration performance of the rotary MRDPF can be better if oxygen content, the exhaust gas temperature and the filter unit number are appropriately increased. Regeneration time begins to decrease when the filter unit number is above 8. The regeneration efficiency of the rotary MRDPF increases with the increment of the
3.5. Effect of exhaust gas flow velocity on field synergy and regeneration performance
100 90 80 70 60 50 40 30 20
400
flow
12 10
500
tem p
14
8
600
erat
ure /
K
700
n
Regeneration ef
ficiency/%
The valuation of regeneration performance of the rotary MRDPF is mainly based on regeneration time and regeneration efficiency. Improving convective heat transfer of the filter unit during regeneration phase can accelerate regeneration and improve regeneration efficiency. According to the field synergy theory, the convective heat transfer efficiency is not only related to the physical properties of the fluid itself, but also to the angle between the temperature field and the velocity field. This angle has a great influence on the convective heat transfer efficiency. Keeping other boundary conditions unchanged, the effect of inlet flow velocity of exhaust gas on field synergy is investigated, the distribution of cosθ between velocity field and temperature field in the regenerative filter unit is calculated by field synergy model, and the ratio of the area with cosθ greater than 0.8 to the whole filter unit area under different flow velocities is compared. As shown in Fig. 12, the area with high synergy during regeneration of the filter unit is mainly concentrated in the upper and central parts of the filter unit due to high oxygen concentration and high combustion efficiency, and the cosθ value decreases toward to both sides of the filter unit. Since the soot is burned, the flow resistance of the exhaust gas in the central area of the filter unit decreases fast and the overall filter temperature increases, which can accelerate the soot regeneration and increase the seepage velocity and produce better synergy compared with the other area. Fig. 13 shows that the ratio of regeneration area increases with the rise of exhaust gas flow velocity but decreases when it exceeds 0.3 m/s, where the regeneration optimized area ratio is 0.51. The effect of exhaust gas flow velocity on regeneration efficiency is shown in Fig. 14. It can be seen that the regeneration efficiency of the filter unit increases first with the rise of flow velocity but decreases when it exceeds 0.3 m/s, where the maximum regeneration efficiency is 91%. When the flow velocity is very low, oxygen diffuses close to the molecules, and most of the soot particles are difficult to burn due to the lack of oxygen under microwave heating, which results in bad synergy and low regeneration efficiency of the filter unit. With the increase of flow velocity, convective heat transfer is accelerated, more soot particles participate in the combustion reaction and the optimal synergistic area increases, leading to higher regeneration efficiency. When the flow velocity is above 0.3 m/s, the regeneration efficiency becomes small. If it is further increased, more heat in the filter unit is carried away by the exhaust gas flow, and part of soot particles are hard to reach the ignition point, which result in the reduction of regeneration efficiency.
6
(a) Regeneration efficiency
1000
800
600
14
400
ra
flo
n
500 12
pe
10
m
8
tu
re /K
700 600
te
400 6
w
Regeneration tim
e/s
1200
(b) Regeneration time Fig. 11. Effect of exhaust gas temperature on the regeneration performance. 9
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Fig. 12. Distribution of cosθ under different flow velocities.
100
0.5
Regeneration efficiency/%
Optimal ratio of regeneration region
0.6
0.4 0.3 0.2 0.1 0.0
80 60 40 20 0
0.1
0.2
0.3
0.4
0.5
0.6
0.1
0.2
0.3
0.4
v/m.s-1
0.5
0.6
Fig. 14. Effect of flow velocity on the regeneration efficiency.
v/m.s-1 Fig. 13. Variation of regeneration optimized area ratio under different flow velocities.
gas temperature on the regeneration efficiency decreases gradually and that on regeneration time becomes smaller. In addition, exhaust gas temperature can shorten the heating time and improve the regeneration efficiency. When the filter unit number is less than 10, the regeneration time of the filter unit decreases obviously with the increase of exhaust gas temperature, and the regeneration time variation becomes smaller when the filter unit number is above 10. The exhaust gas flow velocity has a great influence on the field synergy and the regeneration efficiency of the rotary MRDPF. The high synergy area is mainly concentrated in the upper and central parts of the filter unit, and the cosθ value decreases toward to both sides of the filter unit. Moreover, the field synergy and the regeneration efficiency of the filter unit are both better when flow velocity reaches 0.3 m/s during regeneration phase, where the regeneration optimized area ratio and the maximum regeneration efficiency are 0.51 and 91%, respectively. Therefore, the appropriate filter unit number, oxygen content and exhaust gas flow velocity are 8–10, 15% and 0.3 m/s, respectively.
filter unit number under a constant microwave power, and it increases slightly and the filter tends to be completely regenerated when the filter unit number is above 10. Moreover, the regeneration time first increases to a maximum value and then decreases with increment of the filter unit number. Oxygen content has a great influence on the regeneration performance of the rotary MRDPF when it is less than 15%, but it is no longer greatly affect the regeneration performance when it is more than 15%. The regeneration efficiency of the filter unit increases and regeneration time decreases with the rise of oxygen content in the exhaust gas. In addition, the oxygen content has little effect on the regeneration performance when the filter unit number is small, but it has a great influence on that with the increment of filter unit number. With the increment of filter unit number, the influence of exhaust 10
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Declaration of Competing Interest
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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work is supported by the National Natural Science Foundation of China under the research grant of 51676066, 51606162, the China Postdoctoral Science Foundation under the research grant of 2018M630897. References [1] Zhao D, Li L. Effect of choked outlet on transient energy growth analysis of a thermoacoustic system. Appl Energy 2015;160:502–10. [2] Zhao D, Chew Y. Energy harvesting from a convection-driven Rijke-Zhao thermoacoustic engine. J Appl Phys 2012;112(11):1–6. 114507. [3] Wu G, Lu Z, Xu X, Pan W, Wu W, Li J, et al. Numerical investigation of aeroacoustics damping performance of a Helmholtz resonator: Effects of geometry, grazing and bias flow. Aerosp Sci Technol 2019;86:191–203. [4] Tan YR, Botero ML, Sheng Y, Dreyer JAH, Xu R, Yang WM, et al. Sooting characteristics of polyoxymethylene dimethyl ether blends with diesel in a diffusion flame. Fuel 2018;224:499–506. [5] Kontses A, Dimaratos A, Keramidas C, Williams R, Hamje H, Ntziachristos L, et al. Effects of fuel properties on particulate emissions of diesel cars equipped with diesel particulate filters. Fuel 2019;255:115879. [6] Jain A, Singh AP, Agarwal AK. Effect of split fuel injection and EGR on NOx and PM emission reduction in a low temperature combustion (LTC) mode diesel engine. Energy 2017;122:249–64. [7] Mohamed Shameer P, Ramesh K, Sakthivel R, Purnachandran R. Effects of fuel injection parameters on emission characteristics of diesel engines operating on various biodiesel: a review. Renew Sustain Energy Rev 2017;67:1267–81. [8] Di YG, Cheung CS, Huang ZH. Comparison of the effect of biodiesel-diesel and ethanol-diesel on the gaseous emission of a direct-injection diesel engine. Atmos Environ 2009;43(17):2721–30. [9] Wang XG, Huang ZH, Kuti OA, Zhang W, Nishida K. Experimental and analytical study on biodiesel and diesel spray characteristics under ultra-high injection pressure. Int J Heat Fluid Flow 2010;31(4):659–66. [10] Wang XG, Cheung CS, Di YG, Huang ZH. Diesel engine gaseous and particle emissions fueled with diesel-oxygenate blends. Fuel 2012;94(1):317–23. [11] Zheng JB, Wang JH, Zhao ZB, Wang DD, Huang ZH. Effect of equivalence ratio on combustion and emissions of a dual-fuel natural gas engine ignited with diesel. Appl Therm Eng 2019;146:738–51. [12] Benajes J, Molina S, García A, Monsalve-Serrano J, Durrett R. Performance and engine-out emissions evaluation of the double injection strategy applied to the gasoline partially premixed compression ignition spark assisted combustion concept. Appl Energy 2014;134:90–101. [13] Benajes J, García A, Domenech V, Durrett R. An investigation of partially premixed compression ignition combustion using gasoline and spark assistance. Appl Therm Eng 2013;52(2):468–77. [14] Benajes J, Molina S, García A, Monsalve-Serrano J. Effects of low reactivity fuel characteristics and blending ratio on low load RCCI (reactivity controlled compression ignition) performance and emissions in a heavy-duty diesel engine. Energy 2015;90:1261–71. [15] Paykani A, Kakaee AH, Rahnama P, Reitz RD. Effects of diesel injection strategy on natural gas/diesel reactivity controlled compression ignition combustion. Energy 2015;90:814–26. [16] Zheng M, Han X, Asad U, Wang J. Investigation of butanol-fuelled HCCI combustion on a high efficiency diesel engine. Energy Convers Manage 2015;98:215–24. [17] Reader GT, Asad U, Zheng M. Energy efficiency trade-off with phasing of HCCI combustion. Int J Energy Res 2013;37(3):200–10. [18] Du YH, Meng ZW, Fang J, Qin Y, Jiang Y, Li S, et al. Characterization of soot deposition and oxidation process on catalytic diesel particulate filter with ash loading through an optimized visualized method. Fuel 2019;243:251–61. [19] Stepien Z, Ziemianski L, Zak G, Wojtasik M, Jeczmionek L, Burnus Z. The evaluation of fuel borne catalyst (FBC's) for DPF regeneration. Fuel 2015;161:278–86. [20] Guo Y, Stevanovic S, Verma P, Jafari M, Jabbour N, Brown R, et al. An experimental study of the role of biodiesel on the performance of diesel particulate filters. Fuel 2019;247:67–76. [21] Konstandopoulos AG, Kostoglou M, Lorentzou S, Vlachos N. Aspects of multifunctional diesel particulate filters and their efficient simulation. Catal Today 2012;188(1):2–13. [22] E JQ, Zhao X, Xie L, Zhang B, Chen J, Zuo Q, et al. Performance enhancement of microwave assisted regeneration in a wall-flow diesel particulate filter based on field synergy theory. Energy 2019;169:719–29. [23] Zuo QS, Zhu XN, Zhang JP, Zhang B, Tang YY, Xie Y, et al. Effects of exhaust parameters on temperature and pressure drop of the gasoline particulate filter in the regeneration equilibrium state. Fuel 2019;257:116019.
11
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Full Length Article
Effects analysis on diesel soot continuous regeneration performance of a rotary microwave-assisted regeneration diesel particulate filter
T
Jiaqiang Ea,c, Mengyuan Zhaoa, Qingsong Zuob, Bin Zhanga,b, , Zhiqing Zhanga, Qingguo Penga, Dandan Hana, Xiaohuan Zhaoa, Yuanwang Denga,c ⁎
a
College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China College of Mechanical Engineering, Xiangtan University, Xiangtan 411105, China c Institute of New Energy and Energy-Saving & Emission-Reduction Technology, Hunan University, Changsha 410082, China b
GRAPHICAL ABSTRACT Regeneration cavity
Outlet
Inlet
Porous media
Schematic diagram of a rotary DPF
Pressure contour distribution of the rotary DPF
Grid diagram of a rotary DPF
Distribution of cos θ under different flow velocities
ARTICLE INFO
ABSTRACT
Keywords: Rotary microwave-assisted regeneration diesel particulate filter Regeneration performance Continuous regeneration Turbulence model Field synergy
In order to investigate effects of various factors on continuous regeneration performance of a rotary microwave-assisted regeneration diesel particulate filter (MRDPF), a regeneration mathematical model and a field synergy model of the rotary MRDPF are developed, and turbulent kinetic energy distribution and pressure distribution of the rotary MRDPF based on three different turbulence models are analyzed. The results indicate that the RNG k-ε model is more suitable for simulation of the rotary MRDPF and appropriate increment of filter unit number, oxygen content and exhaust gas temperature can result in the regeneration performance improvement of the rotary MRDPF. Inlet flow velocity of exhaust gas can change synergy degree between the velocity field and the temperature field and high synergy area is mainly concentrated in the upper and central parts of the filter unit. Moreover, field synergy degree and regeneration efficiency of the filter unit are both better when the flow velocity reaches 0.3 m/s during regeneration phase, where regeneration optimized area ratio and maximum regeneration efficiency are 0.51 and 91%, respectively. This work provides great reference values for optimizing the continuous regeneration performance of the rotary MRDPF.
⁎
Corresponding author at: College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China. E-mail address: [email protected] (B. Zhang).
https://doi.org/10.1016/j.fuel.2019.116353 Received 8 July 2019; Received in revised form 1 October 2019; Accepted 4 October 2019 Available online 17 October 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
wc ρd cpd λd Td kd ∑sk△Hk qwd β Pw g γd m0c
u \* MERGEFORMAT fluid velocity, m/s; s constituent gas; ws formation rate of gaseous components; i direction; p air pressure, Pa; Si volume force applied to the infinitesimal hexahedron, N; cp specific heat at constant pressure, J/(kg·K); λ thermal conductivity, W/(m·K); QS reaction heat value, J; c particle; a airflow; f filter body; k specific surface area; H heat transfer coefficient, W/(m2·K); DS effective mass diffusivity of components; gas mass percentage in the composition; Ys mc carbon content per unit volume on filter body;
Fc ∂T/∂x ∂T/∂y ∂T/∂z
1. Introduction
particle formation rate; comprehensive density of solid phase, kg/m3; solid specific heat capacity, J/(kg·K); solid phase thermal conductivity, W/(m·K); temperature of the solid phase, K; solid specific surface area; total heat release rate; microwave energy absorbed by solid phase; completeness of combustion oxidation reaction, 0.8; microwave power into the effective area of the filter unit; distance of microwave propagation; attenuation constant of solid relative microwave; amount of particles deposited on the arc of the filter unit along the airflow direction; field synergy number; x-direction temperature gradient; y-direction temperature gradient; z-direction temperature gradient;
channel hydraulic diameter. In addition, the DPF heat transfer properties depend on the heat capacitance ratio and the hydraulic parameters, and the speed of the temperature front can be increased by decreasing the DPF substrate thickness [40]. A synergistic effect among NO2, water and oxygen in the exhaust gas was observed by Soltani et al. [41], and the required exhaust condition was optimized during regeneration phase for maintaining a balance between soot accumulation and soot regeneration. A hexagonal pore filter structure was designed by Tsuneyoshi et al. [42] to reduce the pressure loss of the DPF, which has higher regeneration efficiency compared with the quadrilateral pore structure, but the effect of exhaust parameters and optimal structural parameters for simultaneous improvement of pressure drop and regeneration performance have not been presented. Fang et al. [43] investigated the effect of operating parameters on regeneration characteristics of the diesel particulate filter. The results showed that the exhaust flow rate has negative effect on the maximum temperature, maximum temperature gradient and regeneration performance ratio, but effect of oxygen content has not been considered. These literatures indicated that different structural parameters and exhaust parameters can change flow field, temperature field, heat capacity, heat transfer effect and soot chemical reaction rate, influencing the wall-flow DPF regeneration performance. However, the comprehensive influence analysis of all factors on the wall-flow DPF regeneration performance has not been carried out and the general influence mechanisms related to the rotary DPF regeneration have not been clarified. A current challenge that alternative fuels face is their effect on regeneration performance of the diesel particulate filter. RodriguezFernandez et al. [44] tested different fuels (such as conventional diesel fuel, e-diesel, paraffinic fuels and conventional biodiesel) in a Euro 5 automotive engine with the DPF. Results revealed that a greater ability of soot from paraffinic and oxygenated biofuels to be oxidized under lower temperature conditions, e-diesel soot is the least sensitive to the oxygen concentration and it has the fastest oxidation rate. They also found that biodiesel results in a more economical regeneration through an active process with fuel post-injections due to the biodiesel soot is more reactive than the other fuel samples [45]. These literatures showed that alternative fuels such as biodiesel and paraffinic biofuels have positive effects on the wall-flow DPF regeneration performance as a result of the high reactivity of the soot, and it is worth to carry out effects of these alternative fuels on the regeneration performance of the rotary DPF. The efforts for regeneration influence mechanism analysis and performances enhancement of the wall-flow DPF have been conducted in the published literatures, however, no relative study is reported on the rotary MRDPF. Therefore, it is significant to take further studies
Although the diesel engine has low fuel consumption, strong power performance, reliable performance and a wide application market [1–3], it can produce a considerable amount of particulate matter (PM) [4,5] which results in inevitable environmental pollution. How to reduce the particulate emission of the diesel engine has been being a hot research topic because of an increasing concern on environmental protection and increasingly strict emission regulations [6,7]. Nowadays, blended fuels (such as biodiesel-diesel and ethanol–diesel) [8,9] have been investigated to reduce particle and gaseous emissions [10,11], and simultaneous use of advanced combustion technologies (such as PPCI [12,13], RCCI [14,15] and HCCI [16,17]) and the diesel particulate filter (DPF) [18–20] is viewed as the most effective avenue for fitting PM emission limits of diesel vehicles [21,22]. The key working process of the DPF is soot regeneration [23,24] which includes passive regeneration [25,26], active regeneration [27–29] and composite regeneration [30–32]. In our previous studies [33,34], a microwave assisted regeneration method combining microwave and ceria-manganese base catalytic additive has been employed in a wall-flow DPF, where the continuous regeneration is restricted and battery energy storage of the diesel vehicles can hardly support the microwave energy consumption during regeneration phase. Therefore, a rotary DPF with new type structure and working principle is developed based on microwave assisted regeneration to regenerate the PM continuously and reduce pressure drop by dividing its filter into several rotatable blocks, which avoids the microwave regeneration on the whole filter and saves more energy compared with the wall-flow DPF. It is reported that appropriate structural parameters of the wall-flow DPF and exhaust parameters are beneficial to enhancing DPF regeneration performance based on the large numbers of investigations [35,36]. A lot of numerical studies can be tried to explain the influence mechanism of these parameters. The results showed that an uneven soot combustion exists along the axial coordinate of the filter due to strong temperature gradients inside the filter [37]. The maximum wall temperature of the DPF increases with the rise of the ratio of length to diameter, but it decreases with the rise of cell density because of the improvement of heat conduction and heat capacity [38]. For NO2-assisted regeneration, the regeneration speed is raised up due to the rise of the exhaust gas volume, the exhaust gas temperature, the NO2 concentration and the O2 concentration, but it is decreased with the increment of the filter length and the channel density [39]. A more uniform filtration velocity with a lower pressure drop can be obtained as a result of the reduction of the inlet velocity and the increment of the 2
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about the effects of exhaust parameters and structural parameters on regeneration performance of the rotary MRDPF. Field synergy analysis of the wall-flow DPF [46,47] indicated that for multiple fields in the DPF, the enhancement of fluid flow as well as heat and mass transfer in the filter is not only related to the fluid properties, but also depends on the change of field parameters and the field synergy degree. However, effect of exhaust gas flow velocity on field synergy has not been investigated for the wall-flow DPF especially for the rotary MRDPF which has more complex flow field than the wall-flow one. In this work, a physical–mathematical model and a field synergy model of the rotary MRDPF is established firstly. Then, the turbulence model [48,49] selection is analyzed comparatively, and the effects of filter unit number, oxygen content, exhaust gas temperature and flow velocity on continuous regeneration performance of the rotary MRDPF are investigated. Finally, field synergy optimization between velocity vector and temperature gradient for continuous regeneration performance enhancement of the rotary MRDPF is carried out based on the field synergy theory [50,51], and parameters range is suggested. The results of this work will provide theoretical basis for the microwave assisted regeneration design of the rotary MRDPF, which can reduce the PM emission of the diesel engine.
2. Investigated models of the rotary microwave-assisted regeneration diesel particulate filter In order to investigate effects of different parameters on continuous regeneration performance of the rotary MRDPF, some assumptions of the model should be made as: (a) The exhaust gas of the diesel engine is regarded as ideal gas; (b) The flow through the rotary MRDPF is constant flow; (c) The exhaust gas flow can be considered as incompressible; (d) Particles in the porous media are pure carbon particles with the same size in diameter. 2.1. Physical model of the rotary microwave-assisted regeneration diesel particulate filter The structure schematic diagram of a rotary MRDPF with a SiC foamed ceramics filter is depicted in Fig. 1(a). It shows that the rotary MRDPF can be divided into the intake pipe, the expansion pipe, the filter, the shrink pipe and the exhaust pipe. The SiC foamed ceramics filter (pore density is 50 ppi, length is 135 mm, external diameter is 200 mm, and internal diameter is 80 mm) [52] can be divided into several blocks. In working process of the rotary MRDPF, the filter is
Regeneration cavity
Outlet
Inlet
Porous media
(a) Schematic diagram
(b) Grid diagram Fig. 1. Structure model of a rotary MRDPF. 3
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rotated by a certain angle α (α is the peripheral angle of each filter unit) to start the microwave generator when the exhaust back pressure reaches a certain value. During the regeneration phase, one filter unit is heated by microwave energy and others capture the soot, which can realize continuous regeneration by cycle. A three-dimensional model of the rotary MRDPF is depicted in Fig. 1(b). In order to improve the accuracy and convergence of the calculation, the physical model is simplified by removing inessential structure and the grid area of expansion tube and shrink tube is refined.
follows.
( d Td cpd ) =
C+ O2
uj ui + xj xi
+ Si +
ws ui s
d
=
xj
a
T xj
T ) + k f Hf (Tf
T)
( s · Ys· uj ) =
xj
Ds · s ·
Ys Xj
+ Ws
(3)
cos =
(4)
=
Mass conservation equation of the carbon particles is shown in Eq. (5).
=
wc
(8)
(9)
)
f
(10)
U¯ · ¯T dy¯ = =
Nu RePr
U¯ · ¯T |U¯ | | ¯T |
(11)
T ·u x
+
T ·v y
+
( ) +( ) +( ) T 2 x
T 2 y
T 2 z
T ·w z
· u2 + v 2 + w 2
(12)
where ∂T∕∂x, ∂T∕∂y and ∂T∕∂z is the temperature gradient in x, y and z direction, respectively. u, v and w is the exhaust gas flow velocity in x, y and z direction, respectively. Assuming that the regenerative combustion synergy of regenerative filter unit is optimal when cosθ is larger than 0.8 [53,54], the ratio of the area with cosθ greater than 0.8 to the whole filter unit area (the regeneration optimized area ratio) is shown as follows.
(5) Mass conservation equation of the carbon particles
mc
)CO
where Fc is the synergy number; U is the velocity vector, m/s; θ is the angle between velocity vector and temperature gradient; ∇T is the temperature gradient; Nu is the Nusselt number, Pr is the Planck number, and Re is the Reynold number. For the three-dimensional model used here, the expression of cosθ between the velocity vector and the heat flow temperature vector can be expressed as follows.
The reason for mass change in the micro-hexahedron includes diffusion and chemical reaction. According to Reynolds transport law, the conservation equation of gas component is expressed as Eq. (4).
xj
mc + (1 mc0
cos
(4) Component conservation equation of exhaust gas in the filter
( s ·Ys ) +
=
Fc =
(2)
( uj c p T ) + ws Qs + k c Hc (Tc
0.5)CO2 + 2(1
The field synergy number of the filter unit is defined by the Eq. (11).
Considering the heat release and thermal conductivity in the soot particles combustion reaction, gas energy conservation equation can be written as Eq. (3) according to the first law of thermodynamics.
xj
2(
(9) Field synergy model
(3) Energy conservation equation of exhaust gas in the filter
( cps T ) +
(7)
Since the microwave attenuation constant is different between soot particles and the filter, and the deposited soot mass is different on different area of the filter, the microwave attenuation constant formula of solid phase can be expressed as follows.
According to the law of momentum conservation, the variation of micro-hexahedron momentum with time in the fluid calculation domain is equal to the sum of pressure, volume force and momentum generated by reaction in the micro-element. Gas momentum equation can be expressed as follows.
p + µ xi xi
s k Hk + qwd s
qwc = 2 Pw exp( 2 d g )
(2) Momentum conservation equation of exhaust gas in the filter
D ( · ui ) = D
T) +
When microwave is fed into regeneration cavity, the filter and soot particles begin to absorb microwave energy. The absorbed microwave energy is shown as follows.
(1)
s
ad Hd (Td
(8) Microwave energy equation
There is a restrictive relationship between velocity and density, and the fluid mass increment of a micro-hexahedron which can be taken as the volume element is the total mass of the reaction products in the computational domain. Mass conservation equation of the exhaust gas is shown in Eq. (1).
ws
T xj
An oxidation reaction model is shown in Eq. (5), and β is the complete coefficient of the carbon particles oxidation reaction.
(1) Continuity equation of exhaust gas in the filter
·( · u ) =
d
xj
(7) Oxidation reaction mechanism of the carbon particles
2.2. Mathematical models of the filter
+
(6)
Td = Tc = Tf
=1 cos = 0.8 =1 cos = 0.
× 100%
(13)
(10) Boundary conditions and initial conditions
(5)
The boundary conditions and initial conditions of the simulation model are given as follows: (a) The inlet boundary condition is set as inlet velocity of the exhaust gas, and it is assumed that inlet velocity is uniform without radial component. The value of inlet velocity is set according to working conditions of the diesel engine.
(6) Energy conservation equation of solid phase Assuming that the temperature of carbon particles is same as that of the filter, the solid phase energy conservation equation is shown as 4
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(b) The outlet boundary condition is defined as outlet pressure of the exhaust gas, and it is set to 0 MPa. (c) No slip boundary condition is set on the filter wall. The exhaust gas temperature is set as 573 K and the content of the soot particles in the exhaust gas is set to 0.05 [39]. Moreover, since the specific heat of each gas component will be changed under high temperature condition with the rise of temperature, the specific heat of the gas component such as O2, CO2 and N2 is set to piecewise polynomial, the specific heat of the carbon particles is regarded as constant and that of the overall mixture is set to mix-law.
shown in Fig. 4, the change trends of the simulation results are consistent with the experimental results under the same working condition of the rotary MRDPF. It displays a good agreement between measured values and simulation values under different position, but there is still a smaller difference (the relative error is less than 5.4%) between these results due to model simplification, self-measurement error and instrument precision, etc. Therefore, the mathematical model can be used to predict the flow and reaction characteristics of the rotary MRDPF. 3. Results and discussion
2.3. Grid independence and model verification
3.1. Investigations of different turbulence models
2.3.1. Grid independence In order to obtain a proper grid size for accurate simulation of the flow and reaction characteristics, five various meshes are employed to study the effects of the grid size on the exhaust flow velocity in five different position of the rotary MRDPF. The relationship between the flow velocity and the mesh number is presented in Fig. 2. It can be seen that the flow velocity of five points first decreases and then tends to be a constant with increment of the mesh umber, when the mesh number is increased to 1,246,932, the mesh number has no effect on the flow velocity of each position in the rotary MRDPF. Therefore, the medium mesh with 1,246,932 cells can be employed for obtaining better accuracy and saving computational time.
In this work, simulation results of the rotary MRDPF are different by using three different turbulence models. The turbulent kinetic energy distribution of the DPF is shown in Fig. 5. It can be seen that turbulent kinetic energy of the RNG k-ω model is distributed in the inlet of the rotary MRDPF, that of the k-ω model is distributed in the inlet and outlet of the rotary MRDPF, and that of the RSM is distributed in the inlet, outlet and filter body of the rotary MRDPF. The maximum turbulent kinetic energy of these models appears in the entrance of the rotary MRDPF, which can reach 79.8 m2/s2, 78.8 m2/s2 and 79.2 m2/s2 by using the k-ω model, the RNG k-ε model and the RSM, respectively. Moreover, there is a large turbulent kinetic energy gradient in the entrance of the rotary MRDPF under the k-ω model and the RSM, but it is small under the RNG k-ε model. Therefore, the RNG k-ε model shows a relatively uniform distribution of the turbulent kinetic energy. Fig. 6 presents the pressure contour of the rotary MRDPF. It shows that the pressure is roughly symmetrically distributed, and the pressure at the end of the rotary MRDPF is almost the same. The pressure drop of the rotary MRDPF will increase sharply when the exhaust gas flows through the filter. The pressure tends to be constant when the exhaust gas flows out of the filter and reaches the outlet of the rotary MRDPF, and it slightly increases as the airflow approaches the wall of the rotary MRDPF. Fig. 7 clearly depicts the axial pressure drop distribution of the rotary MRDPF under the different turbulence models. It can be seen that the pressure drop of the filter presents large fluctuations in the axial direction, and three turbulence models have a same variation trend of the pressure drop. The pressure distribution is roughly symmetrical, the pressure drop first decreases and then increases with increment of the axial distance before y = 0.1 m, where the pressure drop reaches the largest value of exceeding 30.1 kPa. This variation trend is repeated between y = 0.1 m and y = 0.175 m due to the outlet pressure
2.3.2 Model verification (1) Experimental methods In the experiment, a single-stage air compressor with the rated discharge pressure 1.6 MPa is used to simulate the exhaust process of the diesel engine. There is little change of the flow rate, temperature and other factors between the air in the experiment and the actual exhaust process of the diesel engine. Considering that the experiment mainly focuses on the study of the distribution characteristics of the flow velocity, the experimental device can satisfy the requirements of the experiment [22]. And airflow velocity is measured by the hot wire anemometer with type AN1002. The Schematic diagram of experimental equipments is shown in Fig. 3. (2) Experimental procedures Since it is difficult to measure the airflow velocity inside the foamed ceramics filter, the axial airflow velocity distribution in section 1 and section 2 are analyzed in the test process. The main experimental steps are described as follows: Step 1: The air compressor is started and kept its power in certain value, and then the regulating valve is switched to control the airflow velocity with a constant value (50 m/s), and then the regulating valve is fixed. Step 2: After the hot wire anemometers with type AN1002 are connected in the section 1 (x = 40 mm) and the section 2 (x = 70 mm), the data sampling intervals of the hot wire anemometers are also set. Step 3: The sampling data of the airflow velocity are recorded in the section 1 (x = 40 mm) and the section 2 (x = 70 mm) when r/R is equal to 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, respectively. And then the air compressor is closed after all sampling data of the airflow velocity are obtained. Step 4: The above steps are repeated three times, then, the sampling data of three groups are obtained. And the arithmetic mean values from the sampling data of three groups are treated as the sampling data of the airflow velocity.
45 40 35
(0, -0.05, 0) (0, 0.10, 0)
v/m. s-1
30
(0, 0, 0) (0, 0.15, 0)
(0, 0.05, 0)
25 20 15 10 5 8.0x105
(3) Experimental verification results
1.2x106
1.6x106
2.0x106
Grid quantity Fig. 2. Grid independence validation based on flow velocity results in the Y direction.
Fig. 4 depicts the airflow velocity comparisons of simulation results based on RNG k-ε model and experimental results in each section. As 5
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Sampled-data systems Air compressor Inlet
PC display
Velocity controller
Rotary DPF
Hot wire anemometer 1
Cold dryer
2 Filter
Electric heater
Valve 1
Gas analyzer
Valve 2
Fig. 3. Schematic diagram of experimental equipments.
The volume of a single filter unit decreases with the increment of the filter unit number. If soot particles in the exhaust gas and microwave power remain constant, regeneration time is reduced with rise of the microwave energy obtained by the particles due to decrease of the filter unit volume. On the contrary, regeneration time increases with decrease of the filter unit number, therefore, more microwave energy consumption is required to control the regeneration time, which increases the load of the vehicle battery. Fig. 9 shows the effect of filter unit number on regeneration performance of the rotary MRDPF. Fig. 9(a) indicates that the regeneration efficiency of the rotary MRDPF increases with the increment of the filter unit number under a constant microwave power. The regeneration efficiency increases slightly and the filter tends to be completely regenerated when the filter unit number is more than 10, while it becomes smaller when filter unit number is less than 10. The main reason is that there is insufficient absorbed microwave energy of the soot in the regenerated filter unit with larger volume, which results in incomplete combustion of the soot particles on the filter unit. With the increment of the filter unit number, the filter unit volume becomes smaller and the microwave power is enough to ignite soot particles in most areas of the filter unit, so the regeneration efficiency becomes higher. Fig. 9(b) shows that the regeneration time first increases to a certain maximum value and then decreases with increment of the filter unit number. This is owing to that the small filter unit number results in larger microwave heating area and insufficient absorbed microwave energy per unit volume, and most of soot particles difficultly reach the ignition temperature, which needs longer regeneration time. With the increase of filter unit number from 6 to 8, filed synergy effect becomes poor, which results in the rise of the regeneration time and the appearance of a maximum regeneration time. As the filter unit number is above 8, more and more soot particles can reach the ignition temperature for combustion reaction on the filter unit, the regeneration time is decreased due to the decrease of the filter unit volume and the rise of the average microwave heating amount. With the further increase of filter unit number, the microwave power is enough to ignite the particles in the whole filter unit and the total soot mass on the filter unit decreases, which results in the shorter regeneration time.
55 50 45 40
u /m.s
-1
35 30 25 20 15 10 5 0 -5 0.0
Simulation value of section 1 Measurement value of section 1 Simulation value of section 2 Measurement value of section 2
0.2
0.4
0.6
0.8
1.0
Positon r/R Fig. 4. Comparisons of measurement values and simulation values based on RNG k-ε model.
is smaller than the wall when the exhaust gas flows out of the filter, and the pressure drop decreases after y = 0.175 m. In addition, there is a small difference between the pressure drop curve of the RSM and that of the RNG k-ε model, while that of the k-ω model shows a large deviation compared to former ones. Therefore, the k-ω turbulence model is not suitable for simulation of the rotary MRDPF. To sum up, the RNG k-ε model can be selected in this work based on the simulation results of the turbulent kinetic energy and pressure of the rotary MRDPF. 3.2. Effect of filter unit number on regeneration performance of the rotary microwave-assisted regeneration diesel particulate filter In order to investigate the effect of filter unit number on continuous regeneration of the rotary MRDPF, the filter is divided into several filter units on average, and the volume of each filter unit is as follows.
V=
1 (R22 n
R12)· L
(14)
3.3. Effect of oxygen content on regeneration performance of the rotary microwave-assisted regeneration diesel particulate filter
where n is filter unit number, n = 6–15, R1,R2 and L are internal diameter, external diameter and length of the filter unit, respectively. Fig. 8 shows the structure of filter units of different block numbers.
Fig. 10 depicts the synergistic effect of oxygen content in the exhaust 6
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Fig. 5. Turbulent kinetic energy distribution of the rotary MRDPF.
30.4 RNG k-ε
RSM
k-ω
∆p/kPa
30.2
30.0
29.8
29.6
29.4
0.00
0.05
0.10
0.15
0.20
Axial position/m Fig. 7. Pressure drop of the rotary MRDPF in the Y direction.
content. Fig. 10(b) shows the effect of oxygen content on the regeneration time. The regeneration rate of filter unit increases with the increment of oxygen content, which results in the decrease of regeneration time. Moreover, the regeneration rate changes slowly and the regeneration time decreases slowly when oxygen content is more than 15%. Small filter unit number leads to insufficient average microwave energy absorbed by soot particles, and fewer soot particles involved in the combustion reaction, so the oxygen content has little effect on the regeneration performance of the filter unit. When the filter unit number increases, more and more soot particles can reach the ignition temperature faster. Under this circumstance, less oxygen content is difficult to meet the complete combustion reaction of soot particles, which has a great influence on the regeneration time and regeneration efficiency. If the oxygen content reaches more than 15%, the oxygen content is
Fig. 6. Pressure contour of the rotary MRDPF.
gas and the filter unit number on the regeneration performance of the rotary MRDPF when the exhaust temperature is constant. Fig. 10(a) shows the effect of oxygen content on regeneration efficiency of the rotary MRDPF. It can be seen from Fig. 10(a) that oxygen content has a great influence on the regeneration efficiency when it is less than 15%, and the regeneration efficiency of the filter unit increases with the rise of oxygen content in the exhaust gas. However, when oxygen content exceeds 15%, it has little effect on the regeneration efficiency due to the oxygen content is sufficient for soot oxidation reaction on the filter unit, and the regeneration efficiency is no longer limited by the oxygen 7
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(a) n=6
(b) n=9
(c) n=12
(d) n=15
Fig. 8. Structure of the filter units.
100
100
70 60 50 40 30
0.1m/s-573K 0.1m/s-673K
20
0.15m/s-573K 0.15m/s-673K
5
6
7
8
9
10
n
11
12
13
14
80 70 60 50 40 12
30 5
10 0
90
15
10
O xy
16
(a) Regeneration efficiency
gen
14
10
15
cont
20
ent /%
8 25
30
n
ficiency /%
80
Regeneration ef
Regeneration efficiency/%
90
6
(a) Regeneration efficiency
1100 1000
900 800 700
800
600
8
9
10 11 12 13 14 15 16
n
n
(b) Regeneration time
12
10 14
5
nt
10
co
7
20
n
6
15
ge
5
8
xy
6
500
30 25
O
600
t /%
e/s Regeneration tim
Regeneration time/s
0.15m/s-573K 0.15m/s-673K
en
0.1m/s-573K 0.1m/s-673K
1000
(b) Regeneration time
Fig. 9. Effect of filter unit number on the regeneration performance.
Fig. 10. Effect of oxygen content on the regeneration performance.
sufficient to regenerate the soot completely, therefore, the regeneration performance of the rotary MRDPF is no longer greatly affected by the oxygen content.
unit number on the regeneration performance of the rotary MRDPF when the oxygen content in the exhaust gas is constant. It can be seen in Fig. 11(a) that the exhaust gas temperature can promote the regeneration efficiency of the filter when the oxygen content and filter unit number are constant. With the increase of filter unit number, the influence of exhaust gas temperature decreases gradually. Fig. 11(b) shows the effect of exhaust gas temperature on regeneration time. With
3.4. Effect of exhaust gas temperature on regeneration performance of the rotary microwave-assisted regeneration diesel particulate filter Fig. 11 shows the synergistic effect of flow temperature and filter 8
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the increment of filter unit number, the influence of exhaust gas temperature on regeneration time becomes smaller. For the filter unit number below 10, the regeneration time of the filter unit decreases obviously with the rise of exhaust gas temperature. In addition, the variation of regeneration time becomes smaller when the filter unit number is more than 10. When the filter unit number is small and the microwave power is constant, a little of average microwave energy can be absorbed by soot particles, the soot mainly absorbs heat from the exhaust gas by convection heat transfer due to higher exhaust gas temperature before microwave heating, and then reaches the ignition temperature quickly by the microwave heating. Therefore, exhaust gas temperature can promote the combustion of soot particles, shorten the heating time and improve the regeneration efficiency. With the rise of filter unit number, the average microwave energy absorbed by soot particles becomes larger even if it doesn’t absorb heat from the exhaust gas, and soot ignition temperature can be quickly reached, so the exhaust gas temperature has little influence on regeneration time and regeneration efficiency of the rotary MRDPF gradually.
4. Conclusions In this paper, the appropriate turbulence model for numerical simulation is determined, effects of various factors on continuous regeneration performance of the rotary MRDPF are investigated based the physical–mathematical model, the field synergy analysis for continuous regeneration performance enhancement of the rotary MRDPF is carried out based on the field synergy model, and proper parameters range is obtained. The major conclusions are drawn as follows: According to the model verification results and the simulation results comparison of three turbulence models, the maximum relative error of velocity is only 5.4% between experimental results and simulation results based on the RNG k-ε model. The turbulent energy distribution of RNG k-ε is more uniform and its calculation accuracy is better than others, which is more suitable for the simulation of the rotary MRDPF. The regeneration performance of the rotary MRDPF can be better if oxygen content, the exhaust gas temperature and the filter unit number are appropriately increased. Regeneration time begins to decrease when the filter unit number is above 8. The regeneration efficiency of the rotary MRDPF increases with the increment of the
3.5. Effect of exhaust gas flow velocity on field synergy and regeneration performance
100 90 80 70 60 50 40 30 20
400
flow
12 10
500
tem p
14
8
600
erat
ure /
K
700
n
Regeneration ef
ficiency/%
The valuation of regeneration performance of the rotary MRDPF is mainly based on regeneration time and regeneration efficiency. Improving convective heat transfer of the filter unit during regeneration phase can accelerate regeneration and improve regeneration efficiency. According to the field synergy theory, the convective heat transfer efficiency is not only related to the physical properties of the fluid itself, but also to the angle between the temperature field and the velocity field. This angle has a great influence on the convective heat transfer efficiency. Keeping other boundary conditions unchanged, the effect of inlet flow velocity of exhaust gas on field synergy is investigated, the distribution of cosθ between velocity field and temperature field in the regenerative filter unit is calculated by field synergy model, and the ratio of the area with cosθ greater than 0.8 to the whole filter unit area under different flow velocities is compared. As shown in Fig. 12, the area with high synergy during regeneration of the filter unit is mainly concentrated in the upper and central parts of the filter unit due to high oxygen concentration and high combustion efficiency, and the cosθ value decreases toward to both sides of the filter unit. Since the soot is burned, the flow resistance of the exhaust gas in the central area of the filter unit decreases fast and the overall filter temperature increases, which can accelerate the soot regeneration and increase the seepage velocity and produce better synergy compared with the other area. Fig. 13 shows that the ratio of regeneration area increases with the rise of exhaust gas flow velocity but decreases when it exceeds 0.3 m/s, where the regeneration optimized area ratio is 0.51. The effect of exhaust gas flow velocity on regeneration efficiency is shown in Fig. 14. It can be seen that the regeneration efficiency of the filter unit increases first with the rise of flow velocity but decreases when it exceeds 0.3 m/s, where the maximum regeneration efficiency is 91%. When the flow velocity is very low, oxygen diffuses close to the molecules, and most of the soot particles are difficult to burn due to the lack of oxygen under microwave heating, which results in bad synergy and low regeneration efficiency of the filter unit. With the increase of flow velocity, convective heat transfer is accelerated, more soot particles participate in the combustion reaction and the optimal synergistic area increases, leading to higher regeneration efficiency. When the flow velocity is above 0.3 m/s, the regeneration efficiency becomes small. If it is further increased, more heat in the filter unit is carried away by the exhaust gas flow, and part of soot particles are hard to reach the ignition point, which result in the reduction of regeneration efficiency.
6
(a) Regeneration efficiency
1000
800
600
14
400
ra
flo
n
500 12
pe
10
m
8
tu
re /K
700 600
te
400 6
w
Regeneration tim
e/s
1200
(b) Regeneration time Fig. 11. Effect of exhaust gas temperature on the regeneration performance. 9
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Fig. 12. Distribution of cosθ under different flow velocities.
100
0.5
Regeneration efficiency/%
Optimal ratio of regeneration region
0.6
0.4 0.3 0.2 0.1 0.0
80 60 40 20 0
0.1
0.2
0.3
0.4
0.5
0.6
0.1
0.2
0.3
0.4
v/m.s-1
0.5
0.6
Fig. 14. Effect of flow velocity on the regeneration efficiency.
v/m.s-1 Fig. 13. Variation of regeneration optimized area ratio under different flow velocities.
gas temperature on the regeneration efficiency decreases gradually and that on regeneration time becomes smaller. In addition, exhaust gas temperature can shorten the heating time and improve the regeneration efficiency. When the filter unit number is less than 10, the regeneration time of the filter unit decreases obviously with the increase of exhaust gas temperature, and the regeneration time variation becomes smaller when the filter unit number is above 10. The exhaust gas flow velocity has a great influence on the field synergy and the regeneration efficiency of the rotary MRDPF. The high synergy area is mainly concentrated in the upper and central parts of the filter unit, and the cosθ value decreases toward to both sides of the filter unit. Moreover, the field synergy and the regeneration efficiency of the filter unit are both better when flow velocity reaches 0.3 m/s during regeneration phase, where the regeneration optimized area ratio and the maximum regeneration efficiency are 0.51 and 91%, respectively. Therefore, the appropriate filter unit number, oxygen content and exhaust gas flow velocity are 8–10, 15% and 0.3 m/s, respectively.
filter unit number under a constant microwave power, and it increases slightly and the filter tends to be completely regenerated when the filter unit number is above 10. Moreover, the regeneration time first increases to a maximum value and then decreases with increment of the filter unit number. Oxygen content has a great influence on the regeneration performance of the rotary MRDPF when it is less than 15%, but it is no longer greatly affect the regeneration performance when it is more than 15%. The regeneration efficiency of the filter unit increases and regeneration time decreases with the rise of oxygen content in the exhaust gas. In addition, the oxygen content has little effect on the regeneration performance when the filter unit number is small, but it has a great influence on that with the increment of filter unit number. With the increment of filter unit number, the influence of exhaust 10
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Declaration of Competing Interest
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