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Effect analysis on pressure drop of the continuous regeneration-diesel particulate filter based on NO2 assisted regeneration
Applied Thermal Engineering 100 (2016) 356–366
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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Effect analysis on pressure drop of the continuous regeneration-diesel particulate filter based on NO2 assisted regeneration Jiaqiang E a,b,c,*, Wei Zuo a,b,c, Junxu Gao b,c, Qingguo Peng a,b,c, Zhiqing Zhang b,c, Pham Minh Hieu b a
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China c Institute of New Energy and Energy-Saving & Emission-Reduction Technology, Hunan University, Changsha 410082, China b
•
Pressure gauge
Electric dynamometer
Valve 1
Flowmeter 1 Diesel engine
Valve 2
v 1,T1, 1,p1
inlet of the channel
DOC
y v w,Tw,
particale sedim ents
w
z x
Gas analyzer
Flowmeter 3
Flowmeter 2
Valve 5
outer wall
Valve 4
Valve 3
L
Valve 6 Data acquisition card
v 2,T2, 2,p2
outlet of the channel
DPF
D
•
A mathematic model based on the NO2 assisted regeneration is developed and verified. Effect laws of the NO2 assisted regeneration on the pressure drop are obtained. The proper ranges of some key parameters for reducing pressure drop are provided.
A B S T R A C T
wp
•
G R A P H I C A L
ws
H I G H L I G H T S
O2
NO2
PC display
15 Measurement value in case 1 Measurement value in case 2 Measurement value in case 3 Measurement value in case 4 Measurement value in case 5 Measurement value in case 6 Measurement value in case 7 Measurement value in case 8
14 13
8 7
12
p/kPa
11 6
10 9
4 5
8 7 6
3 2 1
5 4 0.0
A R T I C L E
I N F O
Article history: Received 6 November 2015 Accepted 10 February 2016 Available online 23 February 2016 Keywords: Diesel particulate filter (DPF) Continuous regeneration NO2 assisted regeneration Pressure drop characteristics
0.2
0.4
t/t0
0.6
0.8
1.0
A B S T R A C T
In order to enhance the dynamic performance, fuel economy and reduce particulate emissions for a diesel engine, the key is to reduce the pressure drop of continuous regeneration-diesel particulate filter (CRDPF) based on NO2-assisted regeneration. In this work, firstly, a mathematic model based on NO2assisted regeneration is developed. Then, the effects of the exhaust gas parameters and structural parameters of the CR-DPF on pressure drop in the NO2-assisted regeneration process are investigated and verified by experiments. Results show that the pressure drop is decreased under some conditions such as the moderate increase of the low exhaust flow rate, the reduction of the exhaust temperature, the reduction of the NO2 concentration in the exhaust gas and the increase of the channel wall thickness, while the pressure drop is increased under other conditions such as the mass ratio m(NO2)/m(soot) between the NO2 and the soot being less than its threshold in exhaust gas, the increase of the filter length of the CR-DPF and the increase of the channel density when initial amount of the soot in filter is less than its threshold. Moreover, the O2 concentration in exhaust gas has no effect on the pressure drop. Finally, the proper ranges of some key parameters for reducing pressure drop of the CR-DPF have been provided. © 2016 Elsevier Ltd. All rights reserved.
* Corresponding author. Tel.: +86 13187041842; fax: +86 0731 89825335. E-mail address: [email protected] (J. E). http://dx.doi.org/10.1016/j.applthermaleng.2016.02.031 1359-4311/© 2016 Elsevier Ltd. All rights reserved.
J. E et al./Applied Thermal Engineering 100 (2016) 356–366
v 1,T1, 1,p1
v w,Tw,
particale sediments
w
ws
z x outer wall outlet of the channel
v 2,T2, 2,p2
L Fig. 2. Flow model of inside channel in the CR-DPF.
[26–28]. Moreover, pressure drop characteristics is the main performance of the CR-DPF based on NO2 assisted regeneration. It is obvious that higher pressure drop in the CR-DPF will reduce the dynamic performance and fuel economy of a diesel engine. As a result, some theoretical and experimental research such as pressure drop prediction in wall-flow DPFs [20,25], pressure drop control in loaded wall-flow diesel particulate filters [29] and inertial pressure drop distribution and pore structure properties in wall-flow diesel particulate filters [30,31] have been conducted. However, the effects of the exhaust gas parameters and filter structural parameters on pressure drop characteristics of the CR-DPF based on NO2 assisted regeneration are rarely reported in related literatures. In order to improve the regeneration performance of the CRDPF and ensure dynamic equilibrium point between the DOC and the DPF, it is necessary to study the effects of the physical parameters of exhaust gas and the structure parameters of the DPF on pressure drop characteristics of the CR-DPF based on NO2 assisted regeneration and reduce the fine particle emissions from the diesel engines. In this work, a novel pressure drop model of the CR-DPF based on NO2 assisted regeneration is established and tested by experimental data. This work provides theoretical basis on optimizing design of the CR-DPF and reducing particular emissions from the diesel engines into the atmospheric environment. 2. Mathematic model of the CR-DPF 2.1. Governing equations Fig. 2 presents the working principle and the flow model of inside channel in the CR-DPF. As shown in Fig. 2, the exhaust gas from the diesel engine flows into a channel and goes through the ceramic wall, so the soot in the exhaust gas is captured and deposited on the porous wall surface in the CR-DPF. According to the research results of Kandylas et al. [32], some assumptions are made as follows: (a) the thermal radiation loss in the CR-DPF is neglected; (b) the particulate matter (PM) from the exhaust gas is pure soot; (c) the inlet size of channel in the CR-DPF is not affected by particle’s deposition and regeneration reaction on wall surface; (d) the effects of the air temperature inside channel and concentration parameters in the CR-DPF at the radial
DO C
DPF
Exhaust gas from the diesel engine HC, Coal(C) NO x
inlet of the channel y wp
It is well known that diesel engines have been widely used as the vehicle power in the world [1,2] due to their good performance such as low fuel consumption, reliable performance and strong power performance. Unfortunately, the particulate matter (PM) has been always an issue in diffusion flames under compression ignition engines and the development of the diesel engine is challenged seriously for their particulate emissions. Currently, some new combustion modes (PPCI (partially premixed compression ignition) [3,4], RCCI (reactivity controlled compression ignition) [5–7], HCCI (homogeneous charge compression ignition) [8,9], etc.) have been proposed and studied to solve the particulate emissions. However, the diesel particulate filter (DPF) is considered to be one of the most effective and simplest methods for reducing particulate emissions [10,11] and its regeneration technology [12,13] is the key process for actual application of the DPF. At present, the continuous regeneration technology [14–17] including a diesel oxidation catalyst (DOC) and a diesel particulate filter (DPF) (as shown in Fig. 1) has been investigated by lots of researchers. In continuous regeneration process of the DPF [18], the NO from the exhaust gas in the DOC is cataleptically oxidized to the NO2 that is a stronger oxidizer than O2 so that it is more useful for the low temperature combustion of the soot in the DPF without control system or heat sources under the exhaust temperature of 623 K [19]. Moreover, the CO and the HC from the exhaust gas in the DOC are cataleptically oxidized to the CO2 and H2O, and the soluble organic fractions (SOF) in the DOC can be removed from the soot. As a result, the continuous regeneration-diesel particulate filter (CR-DPF) is considered as an after-treatment device with low-cost, simple structure and good performances for reducing carbon emission [20]. In order to reveal the thermodynamic and kinetic mechanism [21–25] for the low temperature combustion of the soot by the NO2, some researches had investigated some factors such as space velocity, temperature, catalyst component and exhaust gas component. For example, Schejbal et al. [21] established a two-dimensional soot oxidation by the NO2 based on detailed kinetics of soot combustion, and the soot conversion and other properties of the systems during the passive regeneration are compared successfully. Azambre et al. [22] investigated the effects of the NO2 on the kinetics of diesel soot oxidation by the thermogravimetric analysis. Tighe et al. [23] investigated the kinetics of oxidation soots by the NO2 at various temperatures (300–550 °C) and [NO2] (20–880 ppm) relevant to regenerating a DPF was analyzed; the results revealed that the regeneration window of the CR-DPF was wider than that of other DPF. Müller et al. [24] investigated the oxidation of soot particulate in the presence of NO2; the results revealed that the NO2 accelerated the oxidation of soot in the low temperature region (250–400 °C) due to an increased surface functionalization with oxygen groups and a subsequent decomposition thereof. Serrano et al. [25] predicted pressure drop in wall-flow DPFs under soot loading conditions by the packed bed of spherical particles. The above results reveal that the CR-DPF based on NO2 assisted regeneration has become an advanced regeneration technique
D
1. Introduction
357
Filter body Fig. 1. Representative CR-DPF.
Filtered exhaust emissions
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direction are both neglected; (e) no chemical reactions happen on wall surface in the CR-DPF filter. Based on the above assumptions, the governing equations of a one-dimensional mathematic model of the single channel are expressed as follows:
Table 1 Main parameters of the DOC.
DOC
1. Mass conservation equation of the exhaust gas
⎧ ∂ ( ρ1v 1 ) ρ1v 1 ∂A 4 ⎪⎪ ∂z + A ∂z + D ρwv w = 0 for inlet channels ⎨ ⎪ ∂ ( ρ2v 2 ) + ρ2v 2 ∂A − 4 ρwv w = 0 ⎪⎩ ∂z for outlet channels A ∂z D
(2)
∂T ⎧ ⎛ 2 ⎞ ⎪⎪c p ⎜⎝ D ρ1v 1 ∂z + 4D ρwv wT1 ⎟⎠ + 4h1D (T C − T1 ) = 0 for inlet channels ⎨ ⎪c p ⎛⎜ D 2ρ2v 2 ∂T + 4D ρwv wT 2 ⎞⎟ − h2D (T C − T 2 ) = 0 ⎠ ⎪⎩ ⎝ for outlet channels ∂z (3) 4. Energy conservation equation of the soot
∂T w = h1 (T1 − T w ) + h2 (T 2 − T w ) ∂t ΔH 2 ⎞ ⎛ ΔH 1 + ρwv wc pw (T1 − T w ) + ⎜ R + R ⎝ M 1 1 M 2 2 ⎟⎠ + λp
∂ ⎛ ∂ 2T ⎞ ∂ ⎛ ∂T w ⎞ ws 2 w ⎟ ⎜⎝ w p ⎟⎠ + λ w ⎜ ∂z ⎝ ∂z ⎠ ∂z ∂z (4)
Reaction rate R1 of the oxygen and reaction rate R2 of the NO2 are expressed by Equations (5) and (6), respectively.
R1 = ρwv wY1 {1 − exp[S pk 1 (1 − α1 2)w s ]}
(5)
R 2 = ρwv wY 2 {1 − exp[S pk 2 (2 − α 2 )w s ]}
(6)
Based on the Arrhenius law, reaction rate constant k1 between the soot and the oxygen is described by Equation (7):
⎛ E ⎞ k 1 = A1T w exp ⎜ − 1 ⎟ ⎝ R 0T w ⎠
(7)
Based on the Arrhenius law, reaction rate constant k2 between the soot and the NO2 is described by Equation (8):
⎛ E ⎞ k 2 = A 2T w exp ⎜ − 2 ⎟ ⎝ R 0T w ⎠
(8)
5. Mass conservation equation of soot on filter wall According to assumption (e), the mass conservation equation of soot on filter wall is described by Equation (9):
⎧ ∂ ( ρwv 1Y1 ) = −k 1S pv 1ρwY1α1 ⎪⎪ ∂w s for inlet channels ⎨ ⎪ ∂ ( ρwv 2Y 2 ) = −k 2S pv 2ρwY 2α 2 ⎪⎩ ∂w s for outlet channels
266 150 0.19 49.1 1.5 1.8
According to the research results [33,34], the deposition layer of soot and inside-wall of the CR-DPF are considered as two connected porous media. Darcy law is applied to calculate the pressure drop between inlet channel and outlet channel [35]; as a result, a novel model of the total pressure drop Δp between inlet channel and outlet channel, including the pressure drop Δpwall through the wall, the pressure drop Δpcarbon through the soot deposition layer, the local pressure loss ΔpL and the friction pressure loss Δpf, is defined by Equation (10):
Δp = Δp wall + Δp carbon + Δp L + Δp f
3. Energy conservation equation of the exhaust gas
(ρpw pc pp + ρww sc pw )
Value
Diameter/mm Length/mm Channel wall thickness/mm Channel diameter/μm Channel width/mm Catalyst amount/(g/L)
(1)
According to assumption (c), it is obvious that cross sectional area of square channels A is a constant. 2. Momentum conservation equation of the exhaust gas
⎧ ∂p 1 ∂ ( ρ1v 12 ) μ1 (T1 )v 1 =0 ⎪⎪ ∂z + ∂z + k D 2 for inlet channels ⎨ 2 ρ ∂ v ( ) T v μ ∂ p ( ) 2 2 ⎪ 2+ + k 2 22 2 = 0 ⎪⎩ ∂z for outlet channels D ∂z
Parameter
(9)
=
(10) μ1v p ρgv 12 ρgv 22 μv μv μ1v w ws + wp +ξ +ξ + F γ 1 21 L + F γ 2 2 2 L ks kp 2 2 D D
2.2. Initial and boundary conditions The initial conditions of this model are defined as follows: the thickness wp of the soot on the deposition layer is equal to initial thickness wb of the particle layer at initial time, and the temperature Tw of filter wall is equal to the temperature Tb of the exhaust gas in inlet channel and outlet channel, as presented in Equation (11).
w p = w b, T w = T b ( when t = 0)
(11)
The boundary conditions of the inlet channel are defined by Equation (12):
⎧T1 = T 0 ⎪v = v ⎪ 1 0 ⎨ v = 0 1 ⎪ ⎪⎩Y1 = Y 0
(when (when (when (when
t t t t
> 0, z > 0, z > 0, z > 0, z
= 0) = 0) = L) = 0)
(12)
The boundary conditions of the outlet channel are defined by Equation (13):
⎧v 2 = 0 ⎪ ⎨p 2 = p 0 ⎪T = T w ⎩ 2
(when t , z = 0) (when t , z = 0) (when t , z = 0)
(13)
3. Results and discussions The key parameters of regeneration performance of the CRDPF are the exhaust gas parameters and structural parameters of the DPF. The exhaust parameters include the exhaust flow rate, the exhaust temperature, the NO2 concentration, the O2 concentration and m(NO2)/m(soot), while structural parameters of filter mainly include length, pore density and channel wall thickness. The cordierite is employed as the filter material of the DOC and its main parameters as well as main parameters of the four DPFs (namely 1#DPF, 2#DPF, 3#DPF and 4#DPF) are given in Table 1. The effects of the exhaust gas parameters and structural parameters on pressure drop characteristics in the CR-DPF are investigated.
J. E et al./Applied Thermal Engineering 100 (2016) 356–366
359
Pressure gauge
Electric dynamometer
Valve 1
Flowmeter 1 Diesel engine
Valve 2 DOC
Gas analyzer
Flowmeter 3
Flowmeter 2
Valve 5 Valve 4
Valve 3
NO2
DPF
Valve 6 Data acquisition card
O2 PC display
(a) Schematic diagram of the test bench
(b) Main equipments in the test bench Fig. 3. Test system of the CR-DPF.
3.1. Experimental verification The test bench is composed of the diesel engine, the CR-DPF, the flowmeter, the pressure gauge, the gas analyzer (AVL AMAi60) and the electric dynamometer (Schenck DYNAS HT350), etc. Continuous regeneration of the DPF test system is shown in Fig. 3(a) and main equipments in the test bench are shown in Fig. 3(b). The direction injection diesel engine YC4A following Chinese emission standard III is used in the experiment and its main parameters are given in Table 2. The electric dynamometer is used in the DPF test system.
Table 2 Technique parameters of the diesel engineYC4A. SN
Parameter
Value
1 2 3 4 5 6 7
Cylinder number Compression ratio ε Air induction Displacement V/L Max velocity n/r·min−1 Max power Pmax/kW Max peak torque T/N·m
4 17.5 Turbocharged/after cooling 4.84 2300 85 450
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Table 3 Test matrix of the CR-DPF.
Engine speed/rpm Engine load/% Exhaust gas recycling rate/% Injection pressure/MPa Initial soot mass/g Exhaust temperature/K Exhaust flow rate/kg·s−1 Volume fraction of the NO2/10−6 m(NO2)/m(soot) Volume fraction of the O2/% Length of the filter/mm Channel diameter/μm Thickness of the channel wall/mm
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Case 8
1#DPF
2#DPF
3#DPF
4#DPF
1#DPF
2#DPF
3#DPF
4#DPF
2000 20.0 5 65 19.1 545 0.40 300 21 20 250 75 0.21
2000 40.0 15 65 19.2 575 0.50 235 15 15.0 300 58 0.31
2000 55.0 20 65 19.2 600 0.60 200 10.5 10.0 350 48 0.41
2000 70.0 25 65 19.1 660 0.70 100 5.0 5.0 400 38 0.51
2000 20.0 5 65 25.5 545 0.40 300 21 20 250 75 0.21
2000 40.0 15 65 25.5 575 0.50 235 15 15 300 58 0.31
2000 55.0 20 65 25.5 600 0.60 200 10.5 10 350 48 0.41
2000 70.0 25 65 25.5 660 0.70 100 5.0 5 400 38 0.51
In order to verify the reliability of experimental device, a test matrix of the CR-DPF is selected as shown in Table 3. The main test steps are as follows: Step 1: Pretreatment for the DPF Step 1.1: Insulation pretreatment for the DPF In order to obtain steady and accurate experimental temperature, glass wool is adopted for insulation treatment of pipeline before starting experiment. Step 1.2: Clean pretreatment for the DPF Apart from the initial use of the new DPF, the DPF must be placed into the oven with the environmental temperature of 600 °C to bake for 10 minutes before each test experiment, ensuring that the residual soot deposition of the DPF is completely oxidized and the catalyst in the DPF does not fail at the environmental temperature of 600 °C. Then, mass Δm1 of the clean DPF is weighted by microgram level balance and placed on the test bench for experiments. Step 2: Soot capture process for the DPF Firstly, the valve 2 is closed and then the valve 1 is opened. When the work case of the diesel engine is stable, the valve 2 is opened firstly and then the valve 1 is closed and soot is captured by the DPF. When the total pressure drop between inlet channel and outlet channel is kept a constant which is greater than 7 kPa, the soot capture process for the DPF is over. Then the mass Δm2 of the DPF with the captured soot is weighed under the temperature 150 °C by microgram level balance. Step 3: NO2 assisted regeneration process for the DPF The inlet flow of the DPF is adjusted by valve 2 and flowmeter 1 and detection parameters are obtained through gas analyzer controlled by the valve 3 and the valve 4. The data about total pressure drop between inlet channel and outlet channel is collected. When the total pressure drop between inlet channel and outlet channel is kept a constant which is less than 2 kPa, the NO2 assisted regeneration process for the DPF ends. Then the mass Δm3 of the regenerated DPF is weighed by microgram level balance under the temperature 150 °C. If |Δm3 − Δm1|/Δm1 is greater than 0.02, the NO2 assisted regeneration process for the DPF must be continued. As depicted in Fig. 4, the regeneration time t0 in the CR-DPF from case 1 to case 8 is 3556 s, 3667 s, 3764 s, 3929 s, 4438 s, 4547 s, 4663 s, and 4834 s respectively. With the increase of the engine load and exhaust gas recycling rate, the NO2 concentration decreased and regeneration time is extended. Moreover, the increase of initial soot mass is another reason resulting in extended regeneration time. Fig. 5(a) depicts the comparison of pressure drop in the CRDPF at the end of soot capture process by simulations and
experiments. As shown in Fig. 5(a), the maximal relative error between the simulation value and measurement value from case 1 to case 8 are 2.56%, 3.53%, 3.06%, 2.75%, 2.88%, 3.48%, 2.38% and 3.52%, respectively. Fig. 5(b) shows the pressure drop comparison between simulation values and measurement values in the CRDPF in the process of NO2 assisted regeneration. It can be seen in Fig. 5(b) that the change trends of the simulation values are consistent with the measurement values in the CR-DPF in the process of NO2 assisted regeneration. The relative error of the simulation value and measurement value of the pressure drop in the CR-DPF probably derives from the following reasons: (1) The permeability kp of soot on deposition layer in computed model is treated as a constant due to nominal value of factory, but the actual permeability kp is a random variable varying from 1.0 × 10−15 m2 to 1.0 × 10−13 m2, which will have a greater impact on the calculation of the pressure drop. (2) The thickness wp of soot deposition layer is treated as an uniform thickness, but it is true that the thickness wp of soot deposition layer gradually increases along the axial direction. (3) There are some unavoidable errors from measuring instrument and testing process. Obviously, simulation results of the one-dimensional mathematic model based on the NO2 assisted thermal-regeneration developed match with experimental results, which proves that the mathematic model can be used to analyze the influence of the different parameters in the CR-DPF on the pressure drop characteristics based on the NO2 assisted regeneration process.
5000
Regeneration time t0/s
Parameters
4000
3000
2000
1000
0
1
2
3
4
5
6
Case Fig. 4. Measurement value of regeneration time.
7
8
J. E et al./Applied Thermal Engineering 100 (2016) 356–366
361
Simulation value Measurement value
14 12
p/kPa
10 8 6 4 2 0
1
2
3
4
5
6
7
8
Case
(a) The pressure drop at the end of soot capture process 15 Measurement value in case 1 Measurement value in case 2 Measurement value in case 3 Measurement value in case 4 Measurement value in case 5 Measurement value in case 6 Measurement value in case 7 Measurement value in case 8
14 13
8 7
12
p/kPa
11 6
10 9
4 5
8 7 6
3 2 1
5 4 0.0
0.2
0.4
t/t0
0.6
0.8
1.0
1- Simulation value in case 1; 2- Simulation value in case 2; 3- Simulation value in case 3; 4- Simulation value in case 4; 5- Simulation value in case 5; 6- Simulation value in case 6; 7- Simulation value in case 7; 8- Simulation value in case 8 (b) Simulation value and measurement value of the pressure drop in the DPF Fig. 5. Comparison between experiment and simulation.
3.2. Effects of exhaust gas parameters on pressure drop characteristics based on the NO2 assisted regeneration process Based on the case 2 shown in the Table 3, the effects of some exhaust parameter on pressure drop characteristics are investigated on condition that the other exhaust gas parameters and the structural parameters of the CR-DPF are kept at a constant. 3.2.1. Exhaust flow rate As shown in Fig. 6(a), the change trend of the pressure drop Δp in the CR-DPF is obtained when the exhaust flow rate is 0.4 kg/s, 0.5 kg/s, 0.6 kg/s and 0.7 kg/s, respectively. With the increase of the exhaust flow rate G, the pressure drop in the DPF is increased. The regeneration endpoint for the CR-DPF appears when the regeneration time is about 4000 s. It is very obvious that the pressure drop Δp1 in the regeneration endpoint is 10.4 kPa at the exhaust flow rate of 0.7 kg/s, while the pressure drop Δp2 in the regeneration endpoint is 4.3 kPa at the exhaust flow rate of 0.4 kg/s. This is due to that the increase of the exhaust flow rate leads to the increase of the frictional pressure loss and the local pressure loss. 3.2.2. Exhaust temperature As shown in Fig. 6(b), the change trend of pressure drop Δp in the CR-DPF is obtained when the exhaust temperature is 545 K,
575 K, 600 K and 660 K, respectively. It can be seen that the initial backpressure of the exhaust gas is higher when the exhaust temperature is increased at initial point of the NO2 assisted regeneration process. When the temperature of the exhaust gas is higher than 600 K, the NO2 is of stronger oxidizing property and its activity and oxidation capacity are gradually enhanced with the increase of the exhaust temperature. As a result, NO2 plays a major role on the main regeneration reaction of the carbon particles and there is a larger decrease of pressure drop. While the exhaust temperature is lower than 600 K, activity and oxidation capacity of the O2 are stronger than that of the NO2, that is to say, O2 plays a major role on the main regeneration reaction of the carbon particles and there is a slight decrease of pressure drop. 3.2.3. NO2 concentration As shown in Fig. 6(c), the change trend of pressure drop Δp in the CR-DPF is obtained by changing the NO2 concentration. In order to gain various NO2 concentrations, the NO2 is added as diluents in the test system as shown in Fig. 3. The results show that the NO2 concentration has a great impact on the pressure drop in the CRDPF. With the increase of the NO2 concentration, the pressure drop of the CR-DPF is reduced. It suggests that the NO2 has great effects on the decrease of the pressure drop in the process of continuous regeneration. The working performance and the service life of the
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14 1 - 100 2 - 200 3 - 235 4 - 300
16
p/kPa
12 2 10
8
2
6
3
4
8
3
4 2
4
6 4
1
10
p/kPa
14
12
1 - 0.70kg/s 2 - 0.60kg/s 3 - 0.50kg/s 4 - 0.40kg/s
1
0
0
-6
10 -6 10 -6 10 -6 10
1000
2000 3000 Regeneration time/s
4000
0
1000
2000
3000
4000
Regeneration time/s
(c) NO2 concentration
(a) Exhaust flow rate 12
1
12
1
3
10
6 4 2
0
8 3 1 - m(NO2)/m(PM)=5.0
1000
2 - m(NO2)/m(PM)=10.5
2000 3000 Regeneration time/s
4 - m(NO2)/m(PM)=21.0 0
4000
4
3 - m(NO2)/m(PM)=15.5
4
2 0
2
6
4
1000
2000 3000 Regeneration time/s
(d) m(NO2)/m(SOOT)
(b) Exhaust temperature 14
1 - 5% 2 - 10% 3 - 15% 4 - 20%
13 12
p/KPa
p/kPa
8
1 - 660K 2 - 600K 3 - 575K 4 - 545K
p/kPa
10
11 2 10
3
9
1 4
8 7
0
1000
2000 3000 Regeneration time/s
4000
(e) Oxygen concentration Fig. 6. Effects of various parameters of exhaust gas on pressure drop of the CR-DPF based on NO2 assisted regeneration.
4000
J. E et al./Applied Thermal Engineering 100 (2016) 356–366
CR-DPF can be improved and extended with the increase of the NO2 concentration.
3.2.4. m(NO2)/m(soot) As shown in Fig. 6(d), the change trend of the pressure drop in the CR-DPF is obtained by changing the m(NO2)/m(soot). The higher the ratio of the m(NO2)/m(soot) is, the faster regeneration rate of the CR-DPF is. When the ratio of the m(NO2)/m(soot) reaches a critical value, it appears a net decrease for the soot. With the increase of the regeneration time, the regeneration process and deposition process of the CR-DPF appear to be in dynamic balance, i.e. the deposition rate is equal to oxidation rate of the soot and the pressure fluctuates in a small range. If the m(NO2)/m(soot) is too low, it appears as a net increase for the soot in the CR-DPF and the pressure drop becomes larger and larger; finally, the CR-DPF cannot work properly. When the CRDPF works in such operating condition for a long time, the power and the fuel economy of the diesel engine are greatly affected. As a result, the pressure drop of CR-DPF will be decreased with the increase of the m(NO2)/m(soot). When the range of ratio m(NO2)/ m(soot) is from 20 to 25, there is a smaller pressure drop in the CR-DPF.
3.2.5. O2 concentration As shown in Fig. 6(e), the change trend of pressure drop Δp in the CR-DPF is obtained by changing the O2 concentration. It can be seen that the pressure drop of the CR-DPF is decreased with the increase of the O2 concentration. It suggests that the O2 has small effects on the decrease of the pressure drop in the process of continuous regeneration. The working performance and the service life of the CR-DPF can barely be improved and extended with the increase of the O2 concentration. Therefore, the decrease of pressure drop of the CR-DPF is limited.
3.3. Effects of filter structural parameters on pressure drop characteristics in NO2 assisted regeneration process Based on the case 2 shown in the Table 3, the effects of some structural parameter on pressure drop characteristics are investigated on condition that the exhaust gas parameters and the other structural parameters of the CR-DPF are kept at a constant.
3.3.1. Filter length As shown in Fig. 7(a), the change trend of the pressure drop in the CR-DPF is obtained by changing the CR-DPF filter length. It is well known that the end of the inlet channel is blocked, so the exhaust gas can only seep from the particle deposition layer and the filter wall to the outlet channel. When the CR-DPF filter length is shortened, the exhaust gas flowing into the channels of the CRDPF filter is blocked alternately and the initial pressure drop is increased. Therefore, the shorter the CR-DPF filter length is and the faster the seepage velocity of the exhaust gas is, the larger the seepage resistance of the CR-DPF is. Furthermore, Fig. 7(a) reveals that the total pressure drop is decreased at a period of equal regeneration time with the increase of the CR-DPF filter length. Moreover, the change of the CR-DPF filter length leads to the change of the total DPF’s volume and affects the regeneration capacity of the filter soot in unit time. Therefore, the two factors such as regeneration capacity and trapping capacity should be both considered when the CR-DPF filter length is determined. When the range of the CR-DPF filter length is from 200 mm to 250 mm, there is the optimal regeneration speed and smaller pressure drop in the CR-DPF.
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3.3.2. Channel diameter The change trend of the pressure drop in the CR-DPF is obtained by changing the channel diameter in the CR-DPF filter. As shown in Fig. 7(b), with the increase of the channel diameter in the CR-DPF filter, the velocity of exhaust gas inside the channel is increased and the frictional resistance from the filter wall will be reduced so that the pressure drop is decreased when the channel wall thickness is kept at a constant. Moreover, when the diameter of the CR-DPF and the thickness of the CR-DPF filter wall are unchanged, the decrease of the channel diameter in the CR-DPF filter will increase the local pressure loss if the exhaust flow rate is kept at a constant. As a result, in the case of the same soot mass concentration, the smaller the channel diameter in the CR-DPF filter is, the higher the blockage probability of the channel in the CR-DPF filter is. 3.3.3. Channel wall thickness Fig. 7(c) presents the effects of the channel wall thickness on the pressure drop of the CR-DPF. As shown in Fig. 7(c), the change of the channel wall thickness has great effects on the pressure drop of the CR-DPF. It is due to the fact that the increased channel wall thickness will cause the increase of seepage resistance of the exhaust flow rate going through soot deposition layer and filter wall in the CR-DPF. The trapping efficiency is affected by the channel wall thickness so that the increase of the channel wall thickness is useful for improving the trapping efficiency of the CR-DPF and prolonging its service life. However, small channel wall thickness will lead to the some difficulties on design and manufacture of the CR-DPF. As a result, two factors such as trapping efficiency and pressure loss are considered to determine the channel wall thickness in the CRDPF. When channel wall thickness is less than 0.31 mm, there is a smaller pressure drop in the CR-DPF. According to above analysis results, the range of some key parameters such as the m(NO2)/m(soot), the filter length and the channel wall thickness are determined for reducing pressure drop of the CR-DPF: (1) When the range of ratio m(NO2)/m(soot) is from 20 to 25, there is a smaller pressure drop in the CR-DPF. (2) When the range of the filter length in the CR-DPF is from 200 mm to 250 mm, there is a smaller pressure drop in the CR-DPF. (3) When channel wall thickness is less than 0.31 mm, there is a smaller pressure drop in the CR-DPF. Obviously, the smaller pressure drop is very useful for preventing particulate matter into the atmosphere. 4. Conclusions 1. In the case of the small flow rate of exhaust gas, the appropriate increase of exhaust flow rate in the CR-PDF is favorable for increasing amount of strong oxidizing agent NO2 and decreasing the pressure drop, and the larger exhaust flow rate leads to the increase of the pressure drop in the CR-DPF. 2. The increase of the exhaust temperature increases the initial pressure drop of the CR-DPF, and it appears the net cost or net increase in the CR-DPF. 3. The increase of the O2 concentration is useful for the decrease of the pressure drop, but the decreasing range is limited. But the oxidant NO2 has great effects on the decrease of the pressure drop in the process of continuous regeneration, and the increase of the NO2 concentration is useful for enhancing the working performance and prolonging the service life. 4. When the exhaust temperature is below 673 K and M(NO2)/ m(soot) is too low, a net increase of the soot inside the channel leads to the increase of the pressure drop and the decrease of the economy and the power of diesel engine fuel.
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(c) Channel wall thickness Fig. 7. Effects of filter structural parameters on pressure drop of the CR-DPF based on NO2 assisted regeneration.
5. The change of the filter length leads to the change of the total DPF’s volume, and the two factors such as regeneration capacity and trapping capacity should be both considered after the filter length is determined. 6. The increase of the channel diameter in the CR-DPF filter is useful for decreasing the pressure drop when the channel wall thickness is kept at a constant. 7. The trapping efficiency is affected by the channel wall thickness so that the increase of the channel wall thickness will improve the trapping efficiency of the CR-DPF and prolong its service life. 8. The proper range of some key parameters such as the m(NO2)/ m(soot), the filter length, and the channel thickness is determined for reducing pressure drop of the CR-DPF.
Acknowledgements The authors would like to acknowledge the project (51176045) supported by the National Natural Science Foundation of China
and the National Studying Abroad Foundation Project (No. 201208430262) supported by the China Scholarship Council. Nomenclature A A1 A2 cp cpp cpw D E1 E2 F h1
Cross-sectional area of the square channel [m2] Pre-exponential factor of the O2, A1 = 2.8 × 10−2 mol·K/(m2·s) Pre-exponential factor of the NO2, A2 = 5.0 × 10−1 mol·K/(m2·s) Specific heat capacity of exhaust gas [J/(kg·K)] Specific heat capacity of deposition carbon particle layer [J/(kg·K)] Specific heat capacity of filter [J/(kg·K)] Side-length of square channel [m] Activation energy of the oxygen, E1 = 125 kJ/mol The activation energy of the NO2, E2 = 40 kJ/mol Friction factor of wall surface for channel, F = 28.454 Heat transfer coefficient between airflow and filter wall in inlet channels, h1 = 1.419cpρ1v1Re1−0.717 W/(m2·K)
J. E et al./Applied Thermal Engineering 100 (2016) 356–366
h2 k k1 k2 kp
ks
M1 M2 L p0 p1 p2 R0 R1 R2 Re1 Re2 Sp T0 T1 T2 Tb TC Tw v0 v1 v2 wb wp ws vw Y0 Y1 Y2 z α1 α2 ρ1 ρ2 ρp ρw μ1 μ2 λp λw ξ γ ΔH1
Heat transfer coefficient between airflow and filter wall in outlet channels, h2 = 1.419cpρ2v2Re2−0.717 W/(m2·K) Pressure coefficient of the channel, k = 28.45 Reaction rate constant between the carbon particles and the oxygen inside channel Reaction rate constant between the carbon particles and the nitrogen dioxide inside channel Permeability of carbon particles on deposition layer, kp = 1.0 × 10−15 m2~1.0 × 10−13 m2 (in this work, kp = 1.0 × 10−14 m2) Permeability of inside wall of filter, ks = 1.8 × 10−14 m2~1.8 × 10−11 m2 (in this work, ks = 1.8 × 10−13 m2) Molar mass of the oxygen [kg/kmol] Molar mass of NO2 [kg/kmol] Length of the filter [m] Atmospheric pressure [Pa] Exhaust pressure in inlet channels [Pa] Exhaust pressure in outlet channels [Pa] Universal gas constant, R0 = 8.314 J/(mol·K) Reaction rate of the oxygen inside channel Reaction rate of the nitrogen dioxide inside channel Reynolds number in inlet channel, Re1 = ρ1v1D/μ1 Reynolds number in outlet channel, Re2 = ρ2v2D/μ2 Specific surface area of carbon particle layer [1/m] Inlet temperature in the channel [K] Exhaust temperature in inlet channels [K] Exhaust temperature in outlet channels [K] Initial temperature at initial time (namely t = 0) [K] Exhaust temperature on particle deposition layer in filter wall [K] Exhaust temperature inside the filter [K] Initial velocity of the exhaust gas in the diesel [m/s] Inlet velocity of the exhaust gas in the channels [m/s] Outlet velocity of the exhaust gas in the channels [m/s] The initial thickness of carbon particle layer at initial time(namely t = 0) [m] Thickness of carbon particle deposition layer [m] The channel wall thickness [m] Exhaust velocity inside the filter [m/s] The oxygen content of the inlet in channel [mol/m3] Mass fraction of the oxygen inside channel Mass fraction of the nitrogen dioxide inside channel Axial direction of channels Selectivity coefficient for completely reaction between O2 and carbon particle, with a range from 0.55 to 0.9 Selectivity coefficient for completely reaction between NO2 and carbon particle, with a range from 1.2 to 1.8 Exhaust density in inlet channels [kg/m3] Exhaust density in outlet channels [kg/m3] Particle density of deposition carbon particle layer [kg/m3] Airflow density inside the filter [kg/m3] Dynamic viscosity of the exhaust gas in the inlet channels [Pa·s], μ1 = 1.364T10.5 Dynamic viscosity of the exhaust gas in the outlet channels [Pa·s], μ2 = 1.364T20.5 Thermal conductivity of carbon particles on deposition layer [W/(m·K)] Thermal conductivity of the filter [W/(m·K)] Partial loss coefficient sum of inlet and outlet’s, ξ = 0.82 Modified coefficient, and modified coefficient γ is equal to 1/3 Enthalpy reacting from the carbon particles and the oxygen [J]
ΔH2 Δp
365
Enthalpy reacting from the carbon particles and the NO2 [J] Total pressure drop [Pa]
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Contents lists available at ScienceDirect
Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Effect analysis on pressure drop of the continuous regeneration-diesel particulate filter based on NO2 assisted regeneration Jiaqiang E a,b,c,*, Wei Zuo a,b,c, Junxu Gao b,c, Qingguo Peng a,b,c, Zhiqing Zhang b,c, Pham Minh Hieu b a
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China c Institute of New Energy and Energy-Saving & Emission-Reduction Technology, Hunan University, Changsha 410082, China b
•
Pressure gauge
Electric dynamometer
Valve 1
Flowmeter 1 Diesel engine
Valve 2
v 1,T1, 1,p1
inlet of the channel
DOC
y v w,Tw,
particale sedim ents
w
z x
Gas analyzer
Flowmeter 3
Flowmeter 2
Valve 5
outer wall
Valve 4
Valve 3
L
Valve 6 Data acquisition card
v 2,T2, 2,p2
outlet of the channel
DPF
D
•
A mathematic model based on the NO2 assisted regeneration is developed and verified. Effect laws of the NO2 assisted regeneration on the pressure drop are obtained. The proper ranges of some key parameters for reducing pressure drop are provided.
A B S T R A C T
wp
•
G R A P H I C A L
ws
H I G H L I G H T S
O2
NO2
PC display
15 Measurement value in case 1 Measurement value in case 2 Measurement value in case 3 Measurement value in case 4 Measurement value in case 5 Measurement value in case 6 Measurement value in case 7 Measurement value in case 8
14 13
8 7
12
p/kPa
11 6
10 9
4 5
8 7 6
3 2 1
5 4 0.0
A R T I C L E
I N F O
Article history: Received 6 November 2015 Accepted 10 February 2016 Available online 23 February 2016 Keywords: Diesel particulate filter (DPF) Continuous regeneration NO2 assisted regeneration Pressure drop characteristics
0.2
0.4
t/t0
0.6
0.8
1.0
A B S T R A C T
In order to enhance the dynamic performance, fuel economy and reduce particulate emissions for a diesel engine, the key is to reduce the pressure drop of continuous regeneration-diesel particulate filter (CRDPF) based on NO2-assisted regeneration. In this work, firstly, a mathematic model based on NO2assisted regeneration is developed. Then, the effects of the exhaust gas parameters and structural parameters of the CR-DPF on pressure drop in the NO2-assisted regeneration process are investigated and verified by experiments. Results show that the pressure drop is decreased under some conditions such as the moderate increase of the low exhaust flow rate, the reduction of the exhaust temperature, the reduction of the NO2 concentration in the exhaust gas and the increase of the channel wall thickness, while the pressure drop is increased under other conditions such as the mass ratio m(NO2)/m(soot) between the NO2 and the soot being less than its threshold in exhaust gas, the increase of the filter length of the CR-DPF and the increase of the channel density when initial amount of the soot in filter is less than its threshold. Moreover, the O2 concentration in exhaust gas has no effect on the pressure drop. Finally, the proper ranges of some key parameters for reducing pressure drop of the CR-DPF have been provided. © 2016 Elsevier Ltd. All rights reserved.
* Corresponding author. Tel.: +86 13187041842; fax: +86 0731 89825335. E-mail address: [email protected] (J. E). http://dx.doi.org/10.1016/j.applthermaleng.2016.02.031 1359-4311/© 2016 Elsevier Ltd. All rights reserved.
J. E et al./Applied Thermal Engineering 100 (2016) 356–366
v 1,T1, 1,p1
v w,Tw,
particale sediments
w
ws
z x outer wall outlet of the channel
v 2,T2, 2,p2
L Fig. 2. Flow model of inside channel in the CR-DPF.
[26–28]. Moreover, pressure drop characteristics is the main performance of the CR-DPF based on NO2 assisted regeneration. It is obvious that higher pressure drop in the CR-DPF will reduce the dynamic performance and fuel economy of a diesel engine. As a result, some theoretical and experimental research such as pressure drop prediction in wall-flow DPFs [20,25], pressure drop control in loaded wall-flow diesel particulate filters [29] and inertial pressure drop distribution and pore structure properties in wall-flow diesel particulate filters [30,31] have been conducted. However, the effects of the exhaust gas parameters and filter structural parameters on pressure drop characteristics of the CR-DPF based on NO2 assisted regeneration are rarely reported in related literatures. In order to improve the regeneration performance of the CRDPF and ensure dynamic equilibrium point between the DOC and the DPF, it is necessary to study the effects of the physical parameters of exhaust gas and the structure parameters of the DPF on pressure drop characteristics of the CR-DPF based on NO2 assisted regeneration and reduce the fine particle emissions from the diesel engines. In this work, a novel pressure drop model of the CR-DPF based on NO2 assisted regeneration is established and tested by experimental data. This work provides theoretical basis on optimizing design of the CR-DPF and reducing particular emissions from the diesel engines into the atmospheric environment. 2. Mathematic model of the CR-DPF 2.1. Governing equations Fig. 2 presents the working principle and the flow model of inside channel in the CR-DPF. As shown in Fig. 2, the exhaust gas from the diesel engine flows into a channel and goes through the ceramic wall, so the soot in the exhaust gas is captured and deposited on the porous wall surface in the CR-DPF. According to the research results of Kandylas et al. [32], some assumptions are made as follows: (a) the thermal radiation loss in the CR-DPF is neglected; (b) the particulate matter (PM) from the exhaust gas is pure soot; (c) the inlet size of channel in the CR-DPF is not affected by particle’s deposition and regeneration reaction on wall surface; (d) the effects of the air temperature inside channel and concentration parameters in the CR-DPF at the radial
DO C
DPF
Exhaust gas from the diesel engine HC, Coal(C) NO x
inlet of the channel y wp
It is well known that diesel engines have been widely used as the vehicle power in the world [1,2] due to their good performance such as low fuel consumption, reliable performance and strong power performance. Unfortunately, the particulate matter (PM) has been always an issue in diffusion flames under compression ignition engines and the development of the diesel engine is challenged seriously for their particulate emissions. Currently, some new combustion modes (PPCI (partially premixed compression ignition) [3,4], RCCI (reactivity controlled compression ignition) [5–7], HCCI (homogeneous charge compression ignition) [8,9], etc.) have been proposed and studied to solve the particulate emissions. However, the diesel particulate filter (DPF) is considered to be one of the most effective and simplest methods for reducing particulate emissions [10,11] and its regeneration technology [12,13] is the key process for actual application of the DPF. At present, the continuous regeneration technology [14–17] including a diesel oxidation catalyst (DOC) and a diesel particulate filter (DPF) (as shown in Fig. 1) has been investigated by lots of researchers. In continuous regeneration process of the DPF [18], the NO from the exhaust gas in the DOC is cataleptically oxidized to the NO2 that is a stronger oxidizer than O2 so that it is more useful for the low temperature combustion of the soot in the DPF without control system or heat sources under the exhaust temperature of 623 K [19]. Moreover, the CO and the HC from the exhaust gas in the DOC are cataleptically oxidized to the CO2 and H2O, and the soluble organic fractions (SOF) in the DOC can be removed from the soot. As a result, the continuous regeneration-diesel particulate filter (CR-DPF) is considered as an after-treatment device with low-cost, simple structure and good performances for reducing carbon emission [20]. In order to reveal the thermodynamic and kinetic mechanism [21–25] for the low temperature combustion of the soot by the NO2, some researches had investigated some factors such as space velocity, temperature, catalyst component and exhaust gas component. For example, Schejbal et al. [21] established a two-dimensional soot oxidation by the NO2 based on detailed kinetics of soot combustion, and the soot conversion and other properties of the systems during the passive regeneration are compared successfully. Azambre et al. [22] investigated the effects of the NO2 on the kinetics of diesel soot oxidation by the thermogravimetric analysis. Tighe et al. [23] investigated the kinetics of oxidation soots by the NO2 at various temperatures (300–550 °C) and [NO2] (20–880 ppm) relevant to regenerating a DPF was analyzed; the results revealed that the regeneration window of the CR-DPF was wider than that of other DPF. Müller et al. [24] investigated the oxidation of soot particulate in the presence of NO2; the results revealed that the NO2 accelerated the oxidation of soot in the low temperature region (250–400 °C) due to an increased surface functionalization with oxygen groups and a subsequent decomposition thereof. Serrano et al. [25] predicted pressure drop in wall-flow DPFs under soot loading conditions by the packed bed of spherical particles. The above results reveal that the CR-DPF based on NO2 assisted regeneration has become an advanced regeneration technique
D
1. Introduction
357
Filter body Fig. 1. Representative CR-DPF.
Filtered exhaust emissions
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direction are both neglected; (e) no chemical reactions happen on wall surface in the CR-DPF filter. Based on the above assumptions, the governing equations of a one-dimensional mathematic model of the single channel are expressed as follows:
Table 1 Main parameters of the DOC.
DOC
1. Mass conservation equation of the exhaust gas
⎧ ∂ ( ρ1v 1 ) ρ1v 1 ∂A 4 ⎪⎪ ∂z + A ∂z + D ρwv w = 0 for inlet channels ⎨ ⎪ ∂ ( ρ2v 2 ) + ρ2v 2 ∂A − 4 ρwv w = 0 ⎪⎩ ∂z for outlet channels A ∂z D
(2)
∂T ⎧ ⎛ 2 ⎞ ⎪⎪c p ⎜⎝ D ρ1v 1 ∂z + 4D ρwv wT1 ⎟⎠ + 4h1D (T C − T1 ) = 0 for inlet channels ⎨ ⎪c p ⎛⎜ D 2ρ2v 2 ∂T + 4D ρwv wT 2 ⎞⎟ − h2D (T C − T 2 ) = 0 ⎠ ⎪⎩ ⎝ for outlet channels ∂z (3) 4. Energy conservation equation of the soot
∂T w = h1 (T1 − T w ) + h2 (T 2 − T w ) ∂t ΔH 2 ⎞ ⎛ ΔH 1 + ρwv wc pw (T1 − T w ) + ⎜ R + R ⎝ M 1 1 M 2 2 ⎟⎠ + λp
∂ ⎛ ∂ 2T ⎞ ∂ ⎛ ∂T w ⎞ ws 2 w ⎟ ⎜⎝ w p ⎟⎠ + λ w ⎜ ∂z ⎝ ∂z ⎠ ∂z ∂z (4)
Reaction rate R1 of the oxygen and reaction rate R2 of the NO2 are expressed by Equations (5) and (6), respectively.
R1 = ρwv wY1 {1 − exp[S pk 1 (1 − α1 2)w s ]}
(5)
R 2 = ρwv wY 2 {1 − exp[S pk 2 (2 − α 2 )w s ]}
(6)
Based on the Arrhenius law, reaction rate constant k1 between the soot and the oxygen is described by Equation (7):
⎛ E ⎞ k 1 = A1T w exp ⎜ − 1 ⎟ ⎝ R 0T w ⎠
(7)
Based on the Arrhenius law, reaction rate constant k2 between the soot and the NO2 is described by Equation (8):
⎛ E ⎞ k 2 = A 2T w exp ⎜ − 2 ⎟ ⎝ R 0T w ⎠
(8)
5. Mass conservation equation of soot on filter wall According to assumption (e), the mass conservation equation of soot on filter wall is described by Equation (9):
⎧ ∂ ( ρwv 1Y1 ) = −k 1S pv 1ρwY1α1 ⎪⎪ ∂w s for inlet channels ⎨ ⎪ ∂ ( ρwv 2Y 2 ) = −k 2S pv 2ρwY 2α 2 ⎪⎩ ∂w s for outlet channels
266 150 0.19 49.1 1.5 1.8
According to the research results [33,34], the deposition layer of soot and inside-wall of the CR-DPF are considered as two connected porous media. Darcy law is applied to calculate the pressure drop between inlet channel and outlet channel [35]; as a result, a novel model of the total pressure drop Δp between inlet channel and outlet channel, including the pressure drop Δpwall through the wall, the pressure drop Δpcarbon through the soot deposition layer, the local pressure loss ΔpL and the friction pressure loss Δpf, is defined by Equation (10):
Δp = Δp wall + Δp carbon + Δp L + Δp f
3. Energy conservation equation of the exhaust gas
(ρpw pc pp + ρww sc pw )
Value
Diameter/mm Length/mm Channel wall thickness/mm Channel diameter/μm Channel width/mm Catalyst amount/(g/L)
(1)
According to assumption (c), it is obvious that cross sectional area of square channels A is a constant. 2. Momentum conservation equation of the exhaust gas
⎧ ∂p 1 ∂ ( ρ1v 12 ) μ1 (T1 )v 1 =0 ⎪⎪ ∂z + ∂z + k D 2 for inlet channels ⎨ 2 ρ ∂ v ( ) T v μ ∂ p ( ) 2 2 ⎪ 2+ + k 2 22 2 = 0 ⎪⎩ ∂z for outlet channels D ∂z
Parameter
(9)
=
(10) μ1v p ρgv 12 ρgv 22 μv μv μ1v w ws + wp +ξ +ξ + F γ 1 21 L + F γ 2 2 2 L ks kp 2 2 D D
2.2. Initial and boundary conditions The initial conditions of this model are defined as follows: the thickness wp of the soot on the deposition layer is equal to initial thickness wb of the particle layer at initial time, and the temperature Tw of filter wall is equal to the temperature Tb of the exhaust gas in inlet channel and outlet channel, as presented in Equation (11).
w p = w b, T w = T b ( when t = 0)
(11)
The boundary conditions of the inlet channel are defined by Equation (12):
⎧T1 = T 0 ⎪v = v ⎪ 1 0 ⎨ v = 0 1 ⎪ ⎪⎩Y1 = Y 0
(when (when (when (when
t t t t
> 0, z > 0, z > 0, z > 0, z
= 0) = 0) = L) = 0)
(12)
The boundary conditions of the outlet channel are defined by Equation (13):
⎧v 2 = 0 ⎪ ⎨p 2 = p 0 ⎪T = T w ⎩ 2
(when t , z = 0) (when t , z = 0) (when t , z = 0)
(13)
3. Results and discussions The key parameters of regeneration performance of the CRDPF are the exhaust gas parameters and structural parameters of the DPF. The exhaust parameters include the exhaust flow rate, the exhaust temperature, the NO2 concentration, the O2 concentration and m(NO2)/m(soot), while structural parameters of filter mainly include length, pore density and channel wall thickness. The cordierite is employed as the filter material of the DOC and its main parameters as well as main parameters of the four DPFs (namely 1#DPF, 2#DPF, 3#DPF and 4#DPF) are given in Table 1. The effects of the exhaust gas parameters and structural parameters on pressure drop characteristics in the CR-DPF are investigated.
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Pressure gauge
Electric dynamometer
Valve 1
Flowmeter 1 Diesel engine
Valve 2 DOC
Gas analyzer
Flowmeter 3
Flowmeter 2
Valve 5 Valve 4
Valve 3
NO2
DPF
Valve 6 Data acquisition card
O2 PC display
(a) Schematic diagram of the test bench
(b) Main equipments in the test bench Fig. 3. Test system of the CR-DPF.
3.1. Experimental verification The test bench is composed of the diesel engine, the CR-DPF, the flowmeter, the pressure gauge, the gas analyzer (AVL AMAi60) and the electric dynamometer (Schenck DYNAS HT350), etc. Continuous regeneration of the DPF test system is shown in Fig. 3(a) and main equipments in the test bench are shown in Fig. 3(b). The direction injection diesel engine YC4A following Chinese emission standard III is used in the experiment and its main parameters are given in Table 2. The electric dynamometer is used in the DPF test system.
Table 2 Technique parameters of the diesel engineYC4A. SN
Parameter
Value
1 2 3 4 5 6 7
Cylinder number Compression ratio ε Air induction Displacement V/L Max velocity n/r·min−1 Max power Pmax/kW Max peak torque T/N·m
4 17.5 Turbocharged/after cooling 4.84 2300 85 450
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Table 3 Test matrix of the CR-DPF.
Engine speed/rpm Engine load/% Exhaust gas recycling rate/% Injection pressure/MPa Initial soot mass/g Exhaust temperature/K Exhaust flow rate/kg·s−1 Volume fraction of the NO2/10−6 m(NO2)/m(soot) Volume fraction of the O2/% Length of the filter/mm Channel diameter/μm Thickness of the channel wall/mm
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Case 8
1#DPF
2#DPF
3#DPF
4#DPF
1#DPF
2#DPF
3#DPF
4#DPF
2000 20.0 5 65 19.1 545 0.40 300 21 20 250 75 0.21
2000 40.0 15 65 19.2 575 0.50 235 15 15.0 300 58 0.31
2000 55.0 20 65 19.2 600 0.60 200 10.5 10.0 350 48 0.41
2000 70.0 25 65 19.1 660 0.70 100 5.0 5.0 400 38 0.51
2000 20.0 5 65 25.5 545 0.40 300 21 20 250 75 0.21
2000 40.0 15 65 25.5 575 0.50 235 15 15 300 58 0.31
2000 55.0 20 65 25.5 600 0.60 200 10.5 10 350 48 0.41
2000 70.0 25 65 25.5 660 0.70 100 5.0 5 400 38 0.51
In order to verify the reliability of experimental device, a test matrix of the CR-DPF is selected as shown in Table 3. The main test steps are as follows: Step 1: Pretreatment for the DPF Step 1.1: Insulation pretreatment for the DPF In order to obtain steady and accurate experimental temperature, glass wool is adopted for insulation treatment of pipeline before starting experiment. Step 1.2: Clean pretreatment for the DPF Apart from the initial use of the new DPF, the DPF must be placed into the oven with the environmental temperature of 600 °C to bake for 10 minutes before each test experiment, ensuring that the residual soot deposition of the DPF is completely oxidized and the catalyst in the DPF does not fail at the environmental temperature of 600 °C. Then, mass Δm1 of the clean DPF is weighted by microgram level balance and placed on the test bench for experiments. Step 2: Soot capture process for the DPF Firstly, the valve 2 is closed and then the valve 1 is opened. When the work case of the diesel engine is stable, the valve 2 is opened firstly and then the valve 1 is closed and soot is captured by the DPF. When the total pressure drop between inlet channel and outlet channel is kept a constant which is greater than 7 kPa, the soot capture process for the DPF is over. Then the mass Δm2 of the DPF with the captured soot is weighed under the temperature 150 °C by microgram level balance. Step 3: NO2 assisted regeneration process for the DPF The inlet flow of the DPF is adjusted by valve 2 and flowmeter 1 and detection parameters are obtained through gas analyzer controlled by the valve 3 and the valve 4. The data about total pressure drop between inlet channel and outlet channel is collected. When the total pressure drop between inlet channel and outlet channel is kept a constant which is less than 2 kPa, the NO2 assisted regeneration process for the DPF ends. Then the mass Δm3 of the regenerated DPF is weighed by microgram level balance under the temperature 150 °C. If |Δm3 − Δm1|/Δm1 is greater than 0.02, the NO2 assisted regeneration process for the DPF must be continued. As depicted in Fig. 4, the regeneration time t0 in the CR-DPF from case 1 to case 8 is 3556 s, 3667 s, 3764 s, 3929 s, 4438 s, 4547 s, 4663 s, and 4834 s respectively. With the increase of the engine load and exhaust gas recycling rate, the NO2 concentration decreased and regeneration time is extended. Moreover, the increase of initial soot mass is another reason resulting in extended regeneration time. Fig. 5(a) depicts the comparison of pressure drop in the CRDPF at the end of soot capture process by simulations and
experiments. As shown in Fig. 5(a), the maximal relative error between the simulation value and measurement value from case 1 to case 8 are 2.56%, 3.53%, 3.06%, 2.75%, 2.88%, 3.48%, 2.38% and 3.52%, respectively. Fig. 5(b) shows the pressure drop comparison between simulation values and measurement values in the CRDPF in the process of NO2 assisted regeneration. It can be seen in Fig. 5(b) that the change trends of the simulation values are consistent with the measurement values in the CR-DPF in the process of NO2 assisted regeneration. The relative error of the simulation value and measurement value of the pressure drop in the CR-DPF probably derives from the following reasons: (1) The permeability kp of soot on deposition layer in computed model is treated as a constant due to nominal value of factory, but the actual permeability kp is a random variable varying from 1.0 × 10−15 m2 to 1.0 × 10−13 m2, which will have a greater impact on the calculation of the pressure drop. (2) The thickness wp of soot deposition layer is treated as an uniform thickness, but it is true that the thickness wp of soot deposition layer gradually increases along the axial direction. (3) There are some unavoidable errors from measuring instrument and testing process. Obviously, simulation results of the one-dimensional mathematic model based on the NO2 assisted thermal-regeneration developed match with experimental results, which proves that the mathematic model can be used to analyze the influence of the different parameters in the CR-DPF on the pressure drop characteristics based on the NO2 assisted regeneration process.
5000
Regeneration time t0/s
Parameters
4000
3000
2000
1000
0
1
2
3
4
5
6
Case Fig. 4. Measurement value of regeneration time.
7
8
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361
Simulation value Measurement value
14 12
p/kPa
10 8 6 4 2 0
1
2
3
4
5
6
7
8
Case
(a) The pressure drop at the end of soot capture process 15 Measurement value in case 1 Measurement value in case 2 Measurement value in case 3 Measurement value in case 4 Measurement value in case 5 Measurement value in case 6 Measurement value in case 7 Measurement value in case 8
14 13
8 7
12
p/kPa
11 6
10 9
4 5
8 7 6
3 2 1
5 4 0.0
0.2
0.4
t/t0
0.6
0.8
1.0
1- Simulation value in case 1; 2- Simulation value in case 2; 3- Simulation value in case 3; 4- Simulation value in case 4; 5- Simulation value in case 5; 6- Simulation value in case 6; 7- Simulation value in case 7; 8- Simulation value in case 8 (b) Simulation value and measurement value of the pressure drop in the DPF Fig. 5. Comparison between experiment and simulation.
3.2. Effects of exhaust gas parameters on pressure drop characteristics based on the NO2 assisted regeneration process Based on the case 2 shown in the Table 3, the effects of some exhaust parameter on pressure drop characteristics are investigated on condition that the other exhaust gas parameters and the structural parameters of the CR-DPF are kept at a constant. 3.2.1. Exhaust flow rate As shown in Fig. 6(a), the change trend of the pressure drop Δp in the CR-DPF is obtained when the exhaust flow rate is 0.4 kg/s, 0.5 kg/s, 0.6 kg/s and 0.7 kg/s, respectively. With the increase of the exhaust flow rate G, the pressure drop in the DPF is increased. The regeneration endpoint for the CR-DPF appears when the regeneration time is about 4000 s. It is very obvious that the pressure drop Δp1 in the regeneration endpoint is 10.4 kPa at the exhaust flow rate of 0.7 kg/s, while the pressure drop Δp2 in the regeneration endpoint is 4.3 kPa at the exhaust flow rate of 0.4 kg/s. This is due to that the increase of the exhaust flow rate leads to the increase of the frictional pressure loss and the local pressure loss. 3.2.2. Exhaust temperature As shown in Fig. 6(b), the change trend of pressure drop Δp in the CR-DPF is obtained when the exhaust temperature is 545 K,
575 K, 600 K and 660 K, respectively. It can be seen that the initial backpressure of the exhaust gas is higher when the exhaust temperature is increased at initial point of the NO2 assisted regeneration process. When the temperature of the exhaust gas is higher than 600 K, the NO2 is of stronger oxidizing property and its activity and oxidation capacity are gradually enhanced with the increase of the exhaust temperature. As a result, NO2 plays a major role on the main regeneration reaction of the carbon particles and there is a larger decrease of pressure drop. While the exhaust temperature is lower than 600 K, activity and oxidation capacity of the O2 are stronger than that of the NO2, that is to say, O2 plays a major role on the main regeneration reaction of the carbon particles and there is a slight decrease of pressure drop. 3.2.3. NO2 concentration As shown in Fig. 6(c), the change trend of pressure drop Δp in the CR-DPF is obtained by changing the NO2 concentration. In order to gain various NO2 concentrations, the NO2 is added as diluents in the test system as shown in Fig. 3. The results show that the NO2 concentration has a great impact on the pressure drop in the CRDPF. With the increase of the NO2 concentration, the pressure drop of the CR-DPF is reduced. It suggests that the NO2 has great effects on the decrease of the pressure drop in the process of continuous regeneration. The working performance and the service life of the
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14 1 - 100 2 - 200 3 - 235 4 - 300
16
p/kPa
12 2 10
8
2
6
3
4
8
3
4 2
4
6 4
1
10
p/kPa
14
12
1 - 0.70kg/s 2 - 0.60kg/s 3 - 0.50kg/s 4 - 0.40kg/s
1
0
0
-6
10 -6 10 -6 10 -6 10
1000
2000 3000 Regeneration time/s
4000
0
1000
2000
3000
4000
Regeneration time/s
(c) NO2 concentration
(a) Exhaust flow rate 12
1
12
1
3
10
6 4 2
0
8 3 1 - m(NO2)/m(PM)=5.0
1000
2 - m(NO2)/m(PM)=10.5
2000 3000 Regeneration time/s
4 - m(NO2)/m(PM)=21.0 0
4000
4
3 - m(NO2)/m(PM)=15.5
4
2 0
2
6
4
1000
2000 3000 Regeneration time/s
(d) m(NO2)/m(SOOT)
(b) Exhaust temperature 14
1 - 5% 2 - 10% 3 - 15% 4 - 20%
13 12
p/KPa
p/kPa
8
1 - 660K 2 - 600K 3 - 575K 4 - 545K
p/kPa
10
11 2 10
3
9
1 4
8 7
0
1000
2000 3000 Regeneration time/s
4000
(e) Oxygen concentration Fig. 6. Effects of various parameters of exhaust gas on pressure drop of the CR-DPF based on NO2 assisted regeneration.
4000
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CR-DPF can be improved and extended with the increase of the NO2 concentration.
3.2.4. m(NO2)/m(soot) As shown in Fig. 6(d), the change trend of the pressure drop in the CR-DPF is obtained by changing the m(NO2)/m(soot). The higher the ratio of the m(NO2)/m(soot) is, the faster regeneration rate of the CR-DPF is. When the ratio of the m(NO2)/m(soot) reaches a critical value, it appears a net decrease for the soot. With the increase of the regeneration time, the regeneration process and deposition process of the CR-DPF appear to be in dynamic balance, i.e. the deposition rate is equal to oxidation rate of the soot and the pressure fluctuates in a small range. If the m(NO2)/m(soot) is too low, it appears as a net increase for the soot in the CR-DPF and the pressure drop becomes larger and larger; finally, the CR-DPF cannot work properly. When the CRDPF works in such operating condition for a long time, the power and the fuel economy of the diesel engine are greatly affected. As a result, the pressure drop of CR-DPF will be decreased with the increase of the m(NO2)/m(soot). When the range of ratio m(NO2)/ m(soot) is from 20 to 25, there is a smaller pressure drop in the CR-DPF.
3.2.5. O2 concentration As shown in Fig. 6(e), the change trend of pressure drop Δp in the CR-DPF is obtained by changing the O2 concentration. It can be seen that the pressure drop of the CR-DPF is decreased with the increase of the O2 concentration. It suggests that the O2 has small effects on the decrease of the pressure drop in the process of continuous regeneration. The working performance and the service life of the CR-DPF can barely be improved and extended with the increase of the O2 concentration. Therefore, the decrease of pressure drop of the CR-DPF is limited.
3.3. Effects of filter structural parameters on pressure drop characteristics in NO2 assisted regeneration process Based on the case 2 shown in the Table 3, the effects of some structural parameter on pressure drop characteristics are investigated on condition that the exhaust gas parameters and the other structural parameters of the CR-DPF are kept at a constant.
3.3.1. Filter length As shown in Fig. 7(a), the change trend of the pressure drop in the CR-DPF is obtained by changing the CR-DPF filter length. It is well known that the end of the inlet channel is blocked, so the exhaust gas can only seep from the particle deposition layer and the filter wall to the outlet channel. When the CR-DPF filter length is shortened, the exhaust gas flowing into the channels of the CRDPF filter is blocked alternately and the initial pressure drop is increased. Therefore, the shorter the CR-DPF filter length is and the faster the seepage velocity of the exhaust gas is, the larger the seepage resistance of the CR-DPF is. Furthermore, Fig. 7(a) reveals that the total pressure drop is decreased at a period of equal regeneration time with the increase of the CR-DPF filter length. Moreover, the change of the CR-DPF filter length leads to the change of the total DPF’s volume and affects the regeneration capacity of the filter soot in unit time. Therefore, the two factors such as regeneration capacity and trapping capacity should be both considered when the CR-DPF filter length is determined. When the range of the CR-DPF filter length is from 200 mm to 250 mm, there is the optimal regeneration speed and smaller pressure drop in the CR-DPF.
363
3.3.2. Channel diameter The change trend of the pressure drop in the CR-DPF is obtained by changing the channel diameter in the CR-DPF filter. As shown in Fig. 7(b), with the increase of the channel diameter in the CR-DPF filter, the velocity of exhaust gas inside the channel is increased and the frictional resistance from the filter wall will be reduced so that the pressure drop is decreased when the channel wall thickness is kept at a constant. Moreover, when the diameter of the CR-DPF and the thickness of the CR-DPF filter wall are unchanged, the decrease of the channel diameter in the CR-DPF filter will increase the local pressure loss if the exhaust flow rate is kept at a constant. As a result, in the case of the same soot mass concentration, the smaller the channel diameter in the CR-DPF filter is, the higher the blockage probability of the channel in the CR-DPF filter is. 3.3.3. Channel wall thickness Fig. 7(c) presents the effects of the channel wall thickness on the pressure drop of the CR-DPF. As shown in Fig. 7(c), the change of the channel wall thickness has great effects on the pressure drop of the CR-DPF. It is due to the fact that the increased channel wall thickness will cause the increase of seepage resistance of the exhaust flow rate going through soot deposition layer and filter wall in the CR-DPF. The trapping efficiency is affected by the channel wall thickness so that the increase of the channel wall thickness is useful for improving the trapping efficiency of the CR-DPF and prolonging its service life. However, small channel wall thickness will lead to the some difficulties on design and manufacture of the CR-DPF. As a result, two factors such as trapping efficiency and pressure loss are considered to determine the channel wall thickness in the CRDPF. When channel wall thickness is less than 0.31 mm, there is a smaller pressure drop in the CR-DPF. According to above analysis results, the range of some key parameters such as the m(NO2)/m(soot), the filter length and the channel wall thickness are determined for reducing pressure drop of the CR-DPF: (1) When the range of ratio m(NO2)/m(soot) is from 20 to 25, there is a smaller pressure drop in the CR-DPF. (2) When the range of the filter length in the CR-DPF is from 200 mm to 250 mm, there is a smaller pressure drop in the CR-DPF. (3) When channel wall thickness is less than 0.31 mm, there is a smaller pressure drop in the CR-DPF. Obviously, the smaller pressure drop is very useful for preventing particulate matter into the atmosphere. 4. Conclusions 1. In the case of the small flow rate of exhaust gas, the appropriate increase of exhaust flow rate in the CR-PDF is favorable for increasing amount of strong oxidizing agent NO2 and decreasing the pressure drop, and the larger exhaust flow rate leads to the increase of the pressure drop in the CR-DPF. 2. The increase of the exhaust temperature increases the initial pressure drop of the CR-DPF, and it appears the net cost or net increase in the CR-DPF. 3. The increase of the O2 concentration is useful for the decrease of the pressure drop, but the decreasing range is limited. But the oxidant NO2 has great effects on the decrease of the pressure drop in the process of continuous regeneration, and the increase of the NO2 concentration is useful for enhancing the working performance and prolonging the service life. 4. When the exhaust temperature is below 673 K and M(NO2)/ m(soot) is too low, a net increase of the soot inside the channel leads to the increase of the pressure drop and the decrease of the economy and the power of diesel engine fuel.
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22
14
8
3
6
18 4 16
p/kPa
p/kPa
10
1 - 75 2 - 58 3 - 48 4 - 38
20
1 - 250mm 2 - 300mm 3 - 350mm 4 - 400mm
12
4
m m m m
3
14 12
1
1
2
2
10
4
8
2
0
1000
2000
3000
0
4000
1000
Regeneration time/s
2000 3000 Regeneration time/s
4000
(b) Channel diameter
(a) Filter length 20
1 - 0.21mm 2 - 0.31mm 3 - 0.41mm 4 - 0.51mm
16 4
p/kPa
12
1
4
0
3
2
8
0
1000
2000 3000 Regeneration time/s
4000
(c) Channel wall thickness Fig. 7. Effects of filter structural parameters on pressure drop of the CR-DPF based on NO2 assisted regeneration.
5. The change of the filter length leads to the change of the total DPF’s volume, and the two factors such as regeneration capacity and trapping capacity should be both considered after the filter length is determined. 6. The increase of the channel diameter in the CR-DPF filter is useful for decreasing the pressure drop when the channel wall thickness is kept at a constant. 7. The trapping efficiency is affected by the channel wall thickness so that the increase of the channel wall thickness will improve the trapping efficiency of the CR-DPF and prolong its service life. 8. The proper range of some key parameters such as the m(NO2)/ m(soot), the filter length, and the channel thickness is determined for reducing pressure drop of the CR-DPF.
Acknowledgements The authors would like to acknowledge the project (51176045) supported by the National Natural Science Foundation of China
and the National Studying Abroad Foundation Project (No. 201208430262) supported by the China Scholarship Council. Nomenclature A A1 A2 cp cpp cpw D E1 E2 F h1
Cross-sectional area of the square channel [m2] Pre-exponential factor of the O2, A1 = 2.8 × 10−2 mol·K/(m2·s) Pre-exponential factor of the NO2, A2 = 5.0 × 10−1 mol·K/(m2·s) Specific heat capacity of exhaust gas [J/(kg·K)] Specific heat capacity of deposition carbon particle layer [J/(kg·K)] Specific heat capacity of filter [J/(kg·K)] Side-length of square channel [m] Activation energy of the oxygen, E1 = 125 kJ/mol The activation energy of the NO2, E2 = 40 kJ/mol Friction factor of wall surface for channel, F = 28.454 Heat transfer coefficient between airflow and filter wall in inlet channels, h1 = 1.419cpρ1v1Re1−0.717 W/(m2·K)
J. E et al./Applied Thermal Engineering 100 (2016) 356–366
h2 k k1 k2 kp
ks
M1 M2 L p0 p1 p2 R0 R1 R2 Re1 Re2 Sp T0 T1 T2 Tb TC Tw v0 v1 v2 wb wp ws vw Y0 Y1 Y2 z α1 α2 ρ1 ρ2 ρp ρw μ1 μ2 λp λw ξ γ ΔH1
Heat transfer coefficient between airflow and filter wall in outlet channels, h2 = 1.419cpρ2v2Re2−0.717 W/(m2·K) Pressure coefficient of the channel, k = 28.45 Reaction rate constant between the carbon particles and the oxygen inside channel Reaction rate constant between the carbon particles and the nitrogen dioxide inside channel Permeability of carbon particles on deposition layer, kp = 1.0 × 10−15 m2~1.0 × 10−13 m2 (in this work, kp = 1.0 × 10−14 m2) Permeability of inside wall of filter, ks = 1.8 × 10−14 m2~1.8 × 10−11 m2 (in this work, ks = 1.8 × 10−13 m2) Molar mass of the oxygen [kg/kmol] Molar mass of NO2 [kg/kmol] Length of the filter [m] Atmospheric pressure [Pa] Exhaust pressure in inlet channels [Pa] Exhaust pressure in outlet channels [Pa] Universal gas constant, R0 = 8.314 J/(mol·K) Reaction rate of the oxygen inside channel Reaction rate of the nitrogen dioxide inside channel Reynolds number in inlet channel, Re1 = ρ1v1D/μ1 Reynolds number in outlet channel, Re2 = ρ2v2D/μ2 Specific surface area of carbon particle layer [1/m] Inlet temperature in the channel [K] Exhaust temperature in inlet channels [K] Exhaust temperature in outlet channels [K] Initial temperature at initial time (namely t = 0) [K] Exhaust temperature on particle deposition layer in filter wall [K] Exhaust temperature inside the filter [K] Initial velocity of the exhaust gas in the diesel [m/s] Inlet velocity of the exhaust gas in the channels [m/s] Outlet velocity of the exhaust gas in the channels [m/s] The initial thickness of carbon particle layer at initial time(namely t = 0) [m] Thickness of carbon particle deposition layer [m] The channel wall thickness [m] Exhaust velocity inside the filter [m/s] The oxygen content of the inlet in channel [mol/m3] Mass fraction of the oxygen inside channel Mass fraction of the nitrogen dioxide inside channel Axial direction of channels Selectivity coefficient for completely reaction between O2 and carbon particle, with a range from 0.55 to 0.9 Selectivity coefficient for completely reaction between NO2 and carbon particle, with a range from 1.2 to 1.8 Exhaust density in inlet channels [kg/m3] Exhaust density in outlet channels [kg/m3] Particle density of deposition carbon particle layer [kg/m3] Airflow density inside the filter [kg/m3] Dynamic viscosity of the exhaust gas in the inlet channels [Pa·s], μ1 = 1.364T10.5 Dynamic viscosity of the exhaust gas in the outlet channels [Pa·s], μ2 = 1.364T20.5 Thermal conductivity of carbon particles on deposition layer [W/(m·K)] Thermal conductivity of the filter [W/(m·K)] Partial loss coefficient sum of inlet and outlet’s, ξ = 0.82 Modified coefficient, and modified coefficient γ is equal to 1/3 Enthalpy reacting from the carbon particles and the oxygen [J]
ΔH2 Δp
365
Enthalpy reacting from the carbon particles and the NO2 [J] Total pressure drop [Pa]
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