Influence of structural and operating factors on performance degradation of the diesel particulate filter based on composite regeneration

Applied Thermal Engineering 121 (2017) 838–852

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Research Paper

Influence of structural and operating factors on performance degradation of the diesel particulate filter based on composite regeneration Bin Zhang a,b, Jiaqiang E a,⇑, Jinke Gong a,⇑, Wenhua Yuan b, Xiaohuan Zhao a, Wenyu Hu a a b

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China Department of Mechanical and Energy Engineering, Shaoyang University, Shaoyang 422004, China

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


An efficient method combining OED Maximum wall temperature (K)

and FGRA for evaluating impacts is presented.
Pressure drop and maximum wall temperature under various conditions are obtained.
Fuzzy grey relational grades are employed for comprehensive evaluation.
The primary influence factors of the DPF’s performance degradation are obtained.

1200

1000 Case 1 Measured Case 2 Measured Case 2 Simulation Case 3 Measured Case 3 Simulation Case 4 Measured Case 4 Simulation

800

600

0.0

0.2

0.4 0.6 Axial location

0.8

1.0

1.0 Fuzzy membership grades Euclidean grey relational grades Fuzzy grey relational grades

0.9 0.8 0.7

R3

0.6 0.5 0.4 0.3 0.2 0.1 0.0

a r t i c l e

i n f o

Article history: Received 17 November 2016 Revised 29 March 2017 Accepted 30 April 2017 Available online 2 May 2017 Keywords: Diesel particulate filter Composite regeneration Performance degradation Influence factor Fuzzy grey relational analysis

x1

x2

x3 Factors

x4

x5

a b s t r a c t In order to effectively investigate the effects of various factors on the DPF’s performance deterioration, and obtain the primary influence factor, an efficient evaluation method is proposed in this work. Firstly, the maximum wall temperature and the pressure drop are taken as the evaluation indexes of DPF’s performance deterioration (thermal aging and filter clogging) respectively, and the orthogonal experimental design is used for obtaining the simulation conditions of test cases. Then, the impacts of four structural factors (wall thickness, mean pore size, porosity and channel width) and five operating factors (exhaust flow rate, exhaust oxygen concentration, microwave power, catalytic additive mass concentration and deposited ash mass) on DPF’s performance deterioration are evaluated by fuzzy membership grades and Euclidean grey relational grades, respectively. Finally, fuzzy grey relational analysis is employed to make a comprehensive evaluation. The results show that the wall thickness and the channel width have the most noticeable effect on filter clogging and thermal aging among all structural factors, respectively. Moreover, the deposited ash mass and the microwave power are the most important operating factors for filter clogging and thermal aging, respectively. This work offers us great reference value for optimizing DPF performances and improving its degradation resistance. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction

⇑ Corresponding authors. E-mail addresses: [email protected] (J. E), [email protected] (J. Gong). http://dx.doi.org/10.1016/j.applthermaleng.2017.04.155 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.

With the rapid increase of car ownership, the impact of automobile emission pollutants on the environment become more and more serious [1,2]. At present, various emission control methods

B. Zhang et al. / Applied Thermal Engineering 121 (2017) 838–852

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Nomenclature cross-sectional area of the inlet channel [m2] cross-sectional area of the outlet channel [m2] area of the soot layer [m2] area of the ash layer [m2] area of the substrate wall [m2] filter length [mm] filter diameter [mm] activation energy [J mol1] friction coefficient of the filter wall, F = 28.45 exhaust flow rate [g s1] universal gas constant, R = 8.314 J (mol K)1 oxygen consumption rate by catalytic soot oxidation oxygen consumption rate by thermal soot oxidation filter volume [m3] specific heat capacity of the exhaust gas [J (kg K)1] specific heat capacity of soot [J (kg K)1] specific heat capacity of ash [J (kg K)1] specific heat capacity of the substrate wall [J (kg K)1] molar mass of carbon particles [kg/mol] molar mass of oxygen [kg/mol] oxygen concentration in the inlet channel (%) oxygen concentration of the exhaust gas (%) the amount of energy for solid phase [J] convection heat [J] transfer heat [J] heat of reaction for catalytic oxidation [J] heat of reaction for thermal oxidation [J] reaction heat of soot oxidation [J] specific surface area of carbon particle layer [m1] exhaust temperature in inlet channels [K] exhaust temperature in outlet channels [K] exhaust temperature inside the substrate wall [K] maximum wall temperature [K] initial exhaust temperature [K] Reynolds number in the inlet channel Reynolds number in the outlet channel total pressure drop of the DPF [Pa] local pressure drop of the inlet with variable crosssection in filter channels [Pa] Dpexp local pressure drop of the outlet with variable crosssection in filter channels [Pa] Dpinlet_channel pressure drop along the inlet channel [Pa] Dpoutlet_channel pressure drop along the outlet channel [Pa] Dpwall pressure drop of the filter wall [Pa] Dpash_layer pressure drop of the ash layer [Pa] Dpsoot_layer pressure drop of the soot layer [Pa] Dp1 pressure drop of the DPF with PM [Pa] Dpc pressure drop of the clean DPF [Pa] Dpr pressure drop of the DPF after regeneration [Pa] p0 atmospheric pressure [Pa]

A1 A2 Asoot Aash Aw L D E F Q R Rcat O2 Rth O2 V Cg Csoot Cash Cw MC MOX Y1 Y0 Hacc Hcon Htran 4Hcat 4Hth Qreaction Sp T1 T2 Tw Tw_max T0 Re1 Re2 Dp Dpcont

and electric vehicle technologies are used to solve environmental pollution and to comply with the increasingly stringent emission standards [3–5]. It is well known that diesel engines have been widely used as the vehicle power in the world due to their low fuel consumption, strong power performance and better reliability [6–9]. Unfortunately, diesel powered vehicles produce a considerable amount of particulate matter (PM) [10], which is thought to be the main source of air pollution. Currently, the wall-flow diesel particulate filter (DPF) is considered to be one of the most effective aftertreatment device for PM abatement in diesel powered vehicles [11,12], and the regeneration technology [13,14] is the key process for its actual application. However, widely application of the DPF in automobiles is restricted due to its deterioration after multiple

p1 p2 Pmw a a1 a2 d kwall kash ksoot kO2_0 w wash wsoot ws_0 msoot mash Y0 ca

e

b

l1 l2 ncont nexp

q1 q2 qw qsoot qash qwall qcell

v1 v2

h1 h2 ksoot kash kw

a1 a2

exhaust pressure in inlet channels [Pa] exhaust pressure in outlet channels [Pa] microwave power [kW] channel width of the filter [mm] channel width for inlet channels considering soot and ash deposition channel width for outlet channels mean pore size [mm] permeability of the filter wall, kwall = 1.8  1013 m2 permeability of the ash layer, kash = 3.08  1014 m2 permeability of the soot layer, ksoot = 1.0  1014 m2 pre-exponential factor of oxidation reaction rate, kO2_0 = 5.96  102 m s1 wall thickness [mm] thickness of the ash layer [mm] thickness of the soot layer [mm] the initial thickness of soot layer at initial time [mm] the mass of PM deposition [g L1] the mass of ash deposition [g L1] exhaust oxygen concentration [%] catalytic additive mass concentration [mg L1] porosity [%] complete coefficient of the soot oxidation reaction, b = 0.8 dynamic viscosity of the exhaust gas in the inlet channels [Pa s] dynamic viscosity of the exhaust gas in the outlet channels [Pa s] contraction coefficient of the inlet channel, ncont = 0.4 expansion coefficient of the outlet channel, nexp = 0.4 exhaust gas density in inlet channels [kg m3] exhaust gas density in outlet channels [kg m3] exhaust gas density inside the substrate wall [kg m3] packing density of the soot layer, qsoot = 1500 kg m3 packing density of the ash layer, qash = 450 kg m3 density of the filter wall [kg m3] cell density of the filter [cells in2] inlet velocity of the exhaust gas in the channels [m s1] outlet velocity of the exhaust gas in the channels [m s1] heat transfer coefficient between exhaust flow and filter wall in inlet channels [W (m2 K)1] heat transfer coefficient between exhaust flow and filter wall in outlet channels [W(m2 K)1] thermal conductivity of the soot layer [W (m K)1] thermal conductivity of the ash layer [W (m K)1] thermal conductivity of the filter wall [W(m K)1] thermal carbon monoxide selectivity catalytic carbon monoxide selectivity

regenerations in the porous media filter [15,16], and DPF degradation can inevitably result in the increase of pressure drop as well as the decrease of filtration efficiency and regeneration efficiency, limiting the DPF’s in use service life, so that the DPF requires removal for periodic cleaning or replacement. Therefore, it is quite necessary to investigate the performance degradation or durability of the DPF to improve its service life. Over the years, the material of the filter, the regeneration strategy, the filter structural parameters, and the operating condition have been investigated to guarantee best performances, such as high filtration efficiency and regeneration efficiency as well as low pressure drop during standard operations, but also reliability and durability in the long run.

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Essential properties of candidate materials for use in the DPF are low coefficient of thermal expansion, high thermal shock resistance, and thermal stability. Adler et al. [17] listed suitable materials which possess these properties as cordierite, aluminum titanate, silicon carbide (SiC), silicon nitride, mullite, etc. Cordierite and silicon carbide have long been used as substrate material for the DPF, on account of their combination of good thermal shock resistance, filtration efficiency, and durability under most operating conditions. However, under certain circumstances cordierite filters are susceptible to damage and some have even failed catastrophically. Kim [18] verified that Al2TiO5 ceramics with different inorganic materials have a low thermal expansion and high thermal shock resistance, which is suitable for high temperature applications with all the advantages of cordierite but without the disadvantages. Since the durability of the DPF may be limited by the high transient thermomechanical stresses created during severe regeneration, Benaqqa et al. [19] focused on the determination of the microstructural, thermal and mechanical properties of the constitutive materials of a DPF, and found that the grout with higher porosity is prone to important thermal transformations with no further consequences on filtration and durability. In the regard of the regeneration method, a composite regeneration technology that combines active regeneration [20–23](thermal regeneration with methods to raise the exhaust temperature by the supply of external energy from electricity, microwave and fuel that includes post fuel injection and additional fuel burners) and passive regeneration [24–27](catalyst mixed in fuel or deposited on filter substrate to reduce regeneration temperature from 823 K to 673 K) has been reported in the literature to improve DPF performances and delay its degradation. However, it is known that fuel post-injections for active regeneration causes oil dilution that could damage the engine. In order to investigate this important issue, Fasolo et al. [28] provided three solutions to reduce oil dilution. Song et al. [29] investigated the effects of oil diluted by post-injected fuel for CDPF regeneration on engine wear and found out the characteristic variation of diluted oil according to operating conditions. Yoon et al. [30] presented correlations between the fuel injection strategy and exhaust gas temperature for DPF regeneration, and revealed that double post-injection can reduce the amount of oil dilution. Nowadays, the representative composite regeneration technologies have been studied, for example, Ma et al. [31] demonstrated a microwave-assisted catalytic DPF, using microwave energy to increase exhaust temperature and accelerate soot combustion, and employing iron and copper catalysts to lower the soot ignition temperature, which can lead to less energy consumption and lower peak filter temperature, thus prolong the filter life. Zi et al. [32] has designed a compound regeneration system realized by reducing the PM burning temperature by use of fuel borne catalyst and increasing exhaust temperature by use of burner and Diesel Oxidation Catalyst (DOC). Palma et al. [33] proposed a regeneration method combining microwave heating and Copper Ferrite (CuFe2O4) deposited on filter substrate, reducing the temperature and minimizing the microwave energy required for the regeneration. E et al. [34] also presented a new composite regeneration mode by coupling microwave and ceriamanganese base catalytic additive (MnOx-CeO2) in diesel fuel, which can improve regeneration performance and durability of the DPF. These results point out that composite regeneration technology has shown potential in the DPF manufacture. Despite the efforts for the development of materials and regeneration strategies, lots of numerical and experimental studies about investigating the effect of structural and operating parameters on DPF performance deterioration have been conducted for obtaining a better service life of the DPF. For example, Sappok et al. [35,36] not only demonstrated that ash accumulation alters both the filter geometry, decreasing the DPF’s soot storage capac-

ity, as well as the exhaust flow conditions within the DPF, and the observed increase in DPF pressure drop sensitivity due to ash accumulation, which limits filter service life, is primarily attributed to geometric effects, but also illustrated important effects of ash composition and exhaust conditions on ash properties (packing density, porosity and permeability) affecting DPF flow restriction and pressure drop. O’Sullivan et al. [37] conducted a series of experiments to investigate chemical interactions between silicon carbide (SiC) and synthetic ash compositions expected to be deposited on the surfaces and within the pore structure of a DPF. The results showed that neither a fluxing type degradation of the SiC filter element or pore blockage via appreciable ash sintering is likely to occur with the baseline ash unless temperature excursions above 1173 K arise, and significant degradation in filter behavior is unlikely to occur at temperatures below 1373 K if iron or cerium based additives are used in the diesel fuel. Pomeroy et al. [38] investigated the thermochemical degradation resistance of a typical cordierite DPF by synthetic ashes. The results indicated that thermochemical degradation of cordierite by ashes under conditions representative of typical diesel engine systems is highly unlikely at temperatures of 1100 °C and below. Das et al. [39] presented a comparative study on thermal shock resistance (TSR) of extruded cordierite honeycombs used for automobile pollution control as a DPF. It was observed that TSR was generally represented as maximum temperature gradient that the material can resist, and the influence of design parameters such as cell density, wall thickness and open frontal area was found to be significant for TSR values. Lee et al. [40] carried out numerical design of a DPF for optimum thermal performances during regeneration, and investigated the effect of the ratio of the length to diameter, cell density, the amount of soot loading on the temporal thermal response in order to enhance DPF thermal durability. Haralampous and Kontzias [41] presented the development of approximate analytical expressions for the estimation of pressure drop and filtration efficiency of semi-open channels, and these expressions were validated with one dimensional model simulations, which covered various design parameters and operational conditions, i.e. filter permeability, length, mass flow rate and soot loading. Finally, the failure effect on filtration and pressure drop performance was estimated. Lupše et al. [42] established a semi-analytical, one dimensional model to predict variations of DPF performances under different channel size, and the impact of channel number and size, filter hydraulic permeability and thermal capacity on backpressure, regeneration efficiency and risk of thermal failure were discussed to improve the design of automotive DPFs. Chen et al. [43] described the effects of ash deposits on exhaust condition and heat transfer, and the results indicated that the deposited ash layer can reduce the exhaust flow rate and increase the heat conduction resistance during DPF regeneration, thus leading to high wall temperature and thermal aging. To sum up, the above studies reveal that pressure drop and wall temperature of the DPF are the most related parameters with the performance deterioration, partial influential factors of DPF degradation were investigated, providing a significant theoretical basis for the improvement of DPF durability, but the comprehensive evaluation on influencing factors of DPF degradation as well as primary structural and operating factors have not been presented. However, the factors affecting DPF performance degradation are too many to make a comprehensive investigation, and they could influence with each other. In addition, grey relational analysis (GRA) is an useful method to evaluate the impacts of various effectors without knowing the mathematical relationship among the investigated factors and performance deterioration, and it has become increasingly popular and successful in many research fields such as energy, environment, buildings and power plants [44–47]. As a result, the objective of this work is finding out the

B. Zhang et al. / Applied Thermal Engineering 121 (2017) 838–852

primary factor influencing performance deterioration of the DPF by combining fuzzy grey relational analysis (FGRA) and orthogonal experimental design (OED) [48] to investigate the impacts of various factors on the DPF degradation for reducing the number of cases and saving computational time, providing us great reference value for further improving the degradation resistance or service life of the DPF. 2. Evaluation index and influencing factors of the DPF degradation The DPF using a new composite regeneration mode by coupling microwave and ceria-manganese base catalytic additive (MnOx-CeO2) in diesel fuel is verified as an effective way to reduce the PM emission in our previous works [34], so it is continually studied in this work to evaluate the influencing factors of performance deterioration. This DPF has a wall-flow honeycomb ceramic filter, and its material is cordierite. Basic parameters of this DPF are shown in Table 1. In the composite regeneration process, soot combustion and external heating result in rapidly increasing wall temperature of the porous media filter, and filter crack will occur under period thermal shock with the increase of vehicle mileage. As a result of multiple regenerations, a residual incombustible ash composed of the contaminant oxides from the lubricating oil, iron from engine abrasion, and oxides from catalytic fuel additives will gradually accumulate on and in the walls of the filter over time, which eventually leads to irreversible plugging of the DPF if the structure design of the DPF is not reasonable or the operating parameters are not adjusted properly. Moreover, excessive DPF pressure drop due to this irreversible plugging will greatly affect exhaust backpressure, power performance and fuel economy of the diesel engine. PM oxidation is a highly exothermic reaction and, if uncontrolled, can cause local temperature increases well above 1273 K. At these elevated temperatures, the residual ash may react with the ceramic substrate, which cause premature chemomechanical failure through formation of low eutectic surface liquids as well as crystalline and vitreous phases of incompatible thermal expansion with the DPF [37]. In addition, ash deposition in inlet channels also decreases the soot carrying capacity of the DPF, thus increases the regeneration frequency and thermal shock frequency, which accelerates performance deterioration of the DPF. Therefore, the main deterioration modes or direct factors of the DPF are thermal aging (thermal failure) and filter clogging. Generally, since the maximum peak temperature occurs in the rear part of the DPF (DPF Rear-Bed) [14], and actually the ash deposition is not uniform on the wall (usually the DPF Rear-Bed has more deposited ash), the rear part of the DPF appears the blocking and thermal aging more easily. In addition, wall temperature in other fields of the DPF RearBed is lower than that of the centre line, and the maximum tem-

841

perature gradient increases along the radial direction of the DPF Rear-Bed [49]. Pressure drop and trapping efficiency both are relative to the blocking of DPF. Structural parameters such as wall thickness, mean pore size, porosity and cell density can influence the trapping efficiency of the DPF. Mean pore size and porosity have a direct effect on the trapping efficiency, and the trapping efficiency increases with the decrease of the porosity or/and the mean pore size. It also increases with increase of the cell density or the wall thickness, but the wall thickness has the more important effect on the trapping efficiency than the cell density. Since the pressure drop of the DPF is easy to measure, and with the increase of the vehicle mileage, the change of pressure drop is much more obvious than that of trapping efficiency, the pressure drop was often used as evaluating index of the DPF blocking, and it was used to detect the DPF failure [50]. In this work, the maximum wall temperature and the pressure drop are taken as the evaluation indexes of thermal aging and filter clogging of the DPF, respectively. In addition, the influencing factors of thermal aging and filter clogging can be divided into two categories, i.e. structural parameters (wall thickness, mean pore size, porosity and channel width) and operating parameters (exhaust flow rate, exhaust oxygen concentration, microwave power, catalytic additive mass concentration and the mass of ash deposition). Hierarchy structure of influence factors of the DPF’s performance deterioration is shown in Fig. 1. For the structure parameters, channel width and wall thickness determines the number of channels (cell density) of the filter, while the porosity and pore size determines wall permeability. For the operating parameters, the mass of ash deposition can reflect the vehicle mileage [51]. 3. Mathematical-physical model of the DPF 3.1. Physical model Generally, the DPF is divided into five parts: inlet tube, inlet cone, porous medium filter (core part), outlet cone and outlet tube. The schematic diagram of the DPF structure is presented in Fig. 2. Schematic physical model of the DPF as shown in Fig. 3 has two adjacent channels called inlet channel and outlet channel respectively. When the diesel engine exhaust gas flows from the inlet channel into the outlet channel through the porous ceramic wall (filter wall), the PM including soot and soluble organic matter (SOF) is trapped by the porous medium filter of the DPF, and deposited on the filter wall in the inlet channel, eventually the cleaned exhaust gas is discharged from the exhaust pipe into the

Table 1 Basic parameters of the DPF. Basic parameters

Parameter values

Filter length L/mm Filter diameter D/mm Cone angle of inlet and outlet cones h/deg Density of the filter /kg m3 Melting point /K Poisson’s ratio Young’s modulus /GPa Coefficient of thermal expansion /107 K1 Compressive strength /MPa Modulus of rupture /kg cm2 Thermal conductivity /(W (m K)1) Friction coefficient of the filter wall F

260 190 45 1400 1733 0.21 17 4 13.4 79 0.85 28.454

Fig. 1. Hierarchy structure of influence factors of the DPF’s performance deterioration.

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B. Zhang et al. / Applied Thermal Engineering 121 (2017) 838–852

Fig. 2. Schematic diagram of the DPF structure.

L ρ1 , v1 , p 1 ,T1

Inlet channel

wash

Exhaust gas from

wsoot

Wall Plug

the diesel engine

x

a

w

z

y

Δ p wall

ρ 2 , v2 , p 2 ,T2

Outlet channel

ρw, vw,Tw

Filtered exhaust gas

(a) Side view of adjacent channels Ash layer

Wall Soot layer

(b) Front view of the inlet channel Fig. 3. Schematic physical model of adjacent channels of the DPF.

atmosphere. Through regeneration, the accumulated PM is burnt off, and a portion of incombustible material (ash) in PM is deposited on the surface of the filter wall, so the sediment on the filter wall should consist of the ash layer and the soot layer. In order to establish the mathematical model, the effect of deposited ash layer on exhaust flow characteristics and the following assumptions are considered: (a) The thermal radiation loss in the DPF is neglected; (b) The particulate matter (PM) from the exhaust gas is pure soot; (c) Radial changes of gas velocity, temperature, and concentration in the inlet channel as well as axial dispersion are insignificant; (d) The temperature gradient in the radial direction is neglected; (e) The distributions of soot and ash along all inlet channels are the same, and the model assumes uniform flow distribution at the filter front face and an adiabatic operation. Based on the above assumptions, the governing equations of the single channel are expressed as follows: (1) Mass conservation equation of the exhaust gas

@ðqi v i Þ qi v i @Ai 4ðqw v w Þ þ ¼ ð1Þi @z ai Ai @z

ði ¼ 1; 2Þ

ð1Þ

where i = 1, 2 for the inlet and outlet channels, respectively. Since the size of inlet channels in the DPF is affected by particles deposition and ash deposition, a1 and cross-sectional area of the inlet channel A1 can be described as follows:

a1 ¼ a  2ðwsoot þ wash Þ

ð2Þ

A1 ¼ ða  2ðwsoot þ wash ÞÞ2

ð3Þ

(2) Momentum conservation equation of the exhaust gas

@pi @ðqi v 2i Þ F li v i þ þ 2 ¼ 0 ði ¼ 1; 2Þ @z @z ai

ð4Þ

(3) Energy conservation equation of the exhaust gas

C g qi v i

@T i 4 þ ðhi þ ð1Þi C g qw v w ÞðT w  T i Þ ¼ 0 ði ¼ 1; 2Þ @z ai

ð5Þ

where Cg is the specific heat capacity of the exhaust gas, and its value is 1090 J/(kg K); hi is the convective heat transfer coefficient between exhaust flow in the inlet channel and the outlet channel and the filter wall, and hi ¼ 1:419C g qi v i Re0:717 ; Rei is Reynolds i number of the inlet channel and the outlet channel, and Rei ¼ qi v i a=li . (4) Soot oxidation reaction To simplify calculations, diesel particulate is assumed as carbon particulate. A previous study [52] that considers carbon oxidation reaction as non-complete oxidation reaction has been shown to be in better accordance with the soot regeneration process in the

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B. Zhang et al. / Applied Thermal Engineering 121 (2017) 838–852

DPF. Thus, the non-complete oxidation reaction of carbon is assumed in this study:

C þ bO2 ! 2ðb  0:5ÞCO2 þ 2ð1  bÞCO

ð6Þ

where b is the complete coefficient of the soot oxidation reaction. For this study, an experience value of 0.8 is used, which is taken from Refs. [43,52]. (5) Mass conservation equation of soot on the filter wall

@wsoot MC þ @t bM O2 

  Sp kO2 0 T w E  wsoot ¼0  qw v w Y 0  1  exp   exp  RT w vw

qsoot

ð7Þ (6) Energy conservation equation of the solid phase (soot, ash and filter wall) Ash layer not only changes the flow resistance but also affects the heat transfer resistance of the filter. Ash layer, as a part of the solid computational domain, absorbs heat during regeneration and raises the wall temperature. The accumulated energy for solid phase is expressed as:

Hacc ¼ ðqsoot C soot Asoot þ qash C ash Aash þ qwall C w Aw Þ

@T w @t

ð8Þ

The accumulated energy in the solid phase is originated from soot oxidation, and delivered through heat convection and conduction during DPF regeneration. Assuming that the catalytic oxidation path occurs over certain fraction a of the soot specific area, while the thermal oxidation path occurs over the rest, i.e. 1  a, the heat released by the soot oxidation reaction can be written as [53]:

Q reaction ¼


 DHth MC 1 Rth O2 M C M OX 1  a1 =2
 DHcat M C 1 þ Rcat M C M OX 1  a2 =2 O2

ð9Þ

ð10Þ

The transfer heat for solid phase includes the contributions of heat transfer between soot/ash layer and substrate wall.

Htran



 @ @T w @ @T w ¼ ksoot Asoot Aash þ kash @z @z @z @z
 @ @T w Aw þ kw @z @z

ð11Þ

The energy conservation equations for substrate wall, ash layer, and soot layer are described as follows:

Hacc ¼ Q reaction þ Hcon þ Htran

(7) Pressure drop of the DPF The substrate wall, deposited ash, and soot layer on the filter could be regarded as three different porous media in series. Considering the effect of ash deposition and assuming that the ash is uniformly deposited on the filter wall, the total pressure drop of the DPF can be described as follows [54,55]:

Dp ¼ Dpinlet

channel

þ Dpoutlet

channel

þ Dpwall þ Dpash

layer

þ Dpsoot

layer

þ Dpcont þ Dpexp " lQ 4FL2 4FL2 w 2 ¼ þ þ ða þ wÞ 4 2V 3a4 kwall a 3ða  2wash  2wsoot Þ

 1 a 1 a  2wash þ þ ln ln 2kash a  2wash 2ksoot a  2wash  2wsoot þ

32qg ncont Q 2

p2 D4 ða  2wash Þ4 q2cell

þ

32qg nexp Q 2

p2 D4 a4 q2cell

ð16Þ

where Dpcont and Dpexp are local pressure drop of the inlet and outlet with variable cross-section in filter channels, respectively, Dpinlet_channel and Dpoutlet_channel are pressure drop along the inlet and outlet channel, respectively, Dpwall is pressure drop of the filter wall, Dpash_layer is pressure drop of the ash layer, Dpsoot_layer is pressure drop of the soot layer, l is dynamic viscosity of exhaust gas, Q is exhaust flow rate, V is filter volume, kash is permeability of the ash layer, w is thickness of the filter wall, wash is thickness of the ash layer, a is channel width, F is friction coefficient of the filter wall, L is filter length, ncont and nexp are contraction coefficient and expansion coefficient of the inlet and outlet channel, respectively, and their value is 0.4, qg is exhaust gas density, qcell is cell density of the filter, and D is filter diameter. (8) Initial and boundary conditions

The convection heat term can be described as follows:

Hcon ¼ h1 ðT 1  T w Þa1 þ h2 ðT 2  T w Þa2

conduction and rise the temperature at the solid-gas interface during DPF regeneration.

ð12Þ

The area of soot/ash layer and substrate wall in the computation domain is related to the thickness of soot and ash layer.

Asoot ¼ ða  2wash Þwsoot  w2soot

ð13Þ

Aash ¼ awash  w2ash

ð14Þ

Aw ¼ aw  w2

ð15Þ

As can be seen from Eqs. (8)–(11), the heat capacity and transport properties of solid phase are changed due to the existence of ash layer. The heat convection between solid and gas is affected by the inlet channel narrowing. These increase the resistance of heat

The initial conditions of this model are defined as follows: the soot layer thickness wsoot is equal to initial thickness ws_0 of the particle layer at initial time, and the temperature of filter wall Tw is equal to the exhaust gas temperature in the inlet channel and the outlet channel, as presented in Eq. (17).

T 1 ¼ T 2 ¼ T w ; wsoot ¼ ws

0

ðwhen t ¼ 0Þ

ð17Þ

The boundary conditions of the inlet channel are defined by Eq. (18). In the front of the inlet channel, exhaust gas temperature is equal to that of the upstream exhaust gas and exhaust flow rate is equal to that of the upstream exhaust gas.

8 T1 ¼ T0 > > > < q1 v 1 ¼ Q > > q1 v 1 ¼ 0 > : Y1 ¼ Y0

ðwhen t > 0; z ¼ 0Þ ðwhen t > 0; z ¼ 0Þ ðwhen t > 0; z ¼ LÞ

ð18Þ

ðwhen t > 0; z ¼ 0Þ

The boundary conditions of the outlet channel are defined by Eq. (19). The rear of the inlet channel and the front of outlet channel are clogged. Therefore, the exhaust flow rate would always be zero.

8 ðwhen t; z ¼ 0Þ > < T2 ¼ Tw p2 ¼ p0 ðwhen t; z ¼ 0Þ > : q2 v 2 ¼ 0 ðwhen t; z ¼ 0Þ

ð19Þ

3.2. Model verification In order to verify the mathematical model, four identical DPFs (namely 1#DPF, 2#DPF, 3#DPF and 4#DPF) are installed in the test

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Fig. 4. Test system of the DPF.

Table 2 Experimental cases. Parameters

Case1 (1#DPF)

Case2 (2#DPF)

Case3 (3#DPF)

Case4 (4#DPF)

Microwave power /kW Initial exhaust temperature /K Exhaust flow rate /g s1 Soot mass /g L1 Deposited ash mass /g L1 Oxygen content in the exhaust gas /% Catalytic additive mass concentration /mg L1

0.6 500 100 6 10 15 20

0.6 500 100 6 20 15 20

0.6 500 100 6 30 15 20

0.6 500 100 6 40 15 20

system as shown in Fig. 4, and they are tested respectively under 4 working cases that are selected as shown in Table 2. Parameters of the DPF are shown in Table 1. The test bench is composed of the lubricant injection system, the diesel engine, the DPF, the flowmeter, the pressure gauge, the gas analyzer (AVL AMAi60) and the electric dynamometer (Schenck DYNAS HT350), etc. The engine used in this study is Cummins ISB 300 (a 6 cylinder, 5.9 L, turbocharged, direct injection diesel engine). It is rated at 224 kW at 2500 rpm and 890 N m at 1600 rpm. Diesel fuel type is 0#, and the model of magnetron which was made by Panasonic is 2M236 (the fluctuant range of output power is from 500 W to 1000 W and frequency is 2455 ± 30 MHz). Since the mathematical model is established based on some assumptions such as ‘‘radial temperature change in the inlet channel is insignificant and the temperature gradient in the radial direction is neglected”, the radial temperature of the DPF is unnecessary to be measured (it has been experimentally investigated in our previous study [14], and the

axis of the DPF has higher temperature than corresponding radial locations perpendicular to the axis), and the K-type thermocouples are located according to the axis of exhaust only in order to record the internal temperature along the axis of the DPF which are used to compare with numerical simulation results. The thermocouple locations in the axial direction are shown in Fig. 5. The main experimental 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 min before each test experiment, ensuring

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Pointt 1

Experimental results Simulation results

z x

1/2

0

Point 2

1 3/4

Point 3

Point 5

Fig. 5. Thermocouple locations in the DPF.

that the residual soot deposition of the DPF is completely oxidized. Then, mass Dm1 of the clean DPF is weighed by microgram level balance and placed on the test bench for experiments. Step 1.3: Catalytic additive pretreatment for the diesel fuel A certain concentration of catalytic additive is added in diesel fuel before the composite regeneration experiment. Step 2: Accelerating ash deposition process for the DPF Spraying lubricating oil into the engine intake manifold by a lubricant injection system is selected as the accelerating ash deposition experimental scheme. In this lubricant injection system, a heat exchanger is used to increase the temperature of lubricating oil for a better atomization effect of the lubricating oil after its spraying out from injector. In the accelerating ash deposition process, the valve 2 and valve 3 are opened, but the other ones are closed. When the mass of the ash deposition in four DPFs are arrived at 10 g/L, 20 g/L, 30 g/L and 40 g/L, respectively, the accelerating ash deposition process is over, and the mass Dm2 of the DPF with the deposited ash is weighed. Step 3: Soot capture process for the DPF Firstly, the valve 2 is closed and the valve 1 is opened. When the work case of the diesel engine is stable, the valve 2 is opened and then the valve 1 is closed so that the exhaust gas can flow through the DPF and soot is captured by the DPF. When the captured soot mass meets the experimental cases, the soot capture process for the DPF is over. Then the mass Dm3 of the DPF with the captured soot and the deposited ash is weighed under the temperature 150 °C by microgram level balance. Step 4: Composite regeneration process for the DPF The inlet flow of the DPF is adjusted by the valve 2, the valve 3, flowmeter 1 and flowmeter 2 and detection parameters are obtained through gas analyzer controlled by the valve 5 and the valve 6. Thermocouple 1 shows the exhaust temperature from the engine. If this temperature is up to the experimental requirements, the experiments can be started with opening the microwave source. During composite regeneration, the data about total pressure drop between inlet channel and outlet channel is collected by the pressure gauge and internal temperature of the DPF is measured by the thermocouple. When the total pressure drop between inlet channel and outlet channel is kept a constant, the composite regeneration process for the DPF ends. Then the mass Dm4 of the regenerated DPF is weighed by microgram level balance under the temperature 150 °C. If |Dm4  Dm2|/Dm2 is greater than 0.02, the composite regeneration process for the DPF must be continued. Fig. 6(a) depicts the comparison of pressure drop in the DPF at the end of soot capture process by simulations and experiments. As shown in Fig. 6(a), the relative error between the simulation value and measurement value from case 1 to case 4 are 6.67%, 8.82%, 5.92% and 8.07%, respectively. Fig. 6(b) shows the thermal response (maximum wall temperature of the filter) comparison between simulation values and measurement values of the DPF in the process of composite regeneration. It can be seen in Fig. 6(b) that

Pressure drop (kPa)

1/4

y

20

Point 4

15

10

5

0

1

2

3

4

Case

(a) The pressure drop at the end of soot capture process Maximum wall temperature (K)

Therm mocouple

1200

0 1/4 3/4 1/2 1 DPF

1000 Case 1 Measured Case 1 Simulation Case 2 Measured Case 2 Simulation Case 3 Measured Case 3 Simulation Case 4 Measured Case 4 Simulation

800

600

0.0

0.2

0.4

0.6

0.8

1.0

Axial location

(b) Thermal response of the DPF in the composite regeneration process Fig. 6. Comparison between simulation results and experimental results.

the change trends of the simulation results are consistent with the experimental results in each case. Obviously, the above figures show a good agreement between experimental results and simulation results, but there is still a smaller difference between these results. The major reason for the difference is the errors of experimental equipments and operation and the assumptions for building the mathematical model. However, the difference is acceptable and bearable, so the mathematical model can be used to predict the evaluation index value of performance degradation, such as pressure drop and maximum wall temperature, and investigate the influence of various factors on the performance degradation of the DPF. 4. Evaluating method 4.1. Orthogonal experimental design Orthogonal experimental design is a popular method to deal with the test, including multiple factors and levels. It has been successfully applied to many fields and saving a large amount of time for acquiring the optimum level group [48,56]. The key of this method is making an orthogonal design table based on the reasonable and representative levels of the investigated factors. This method can help us to select the representative cases for lowering the number of test cases. In this work, investigated factors include four structure parameters and five operating parameters, and orthogonal design tables L9(34) and L16(45) are needed, reducing

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the number of test cases from 81 to 9 and from 1024 to 16, respectively.

 =Dmax , the resolution coefficient is (2) Based on the ratio c ¼ D determined as follows:

4.2. Fuzzy grey relational analysis

l2

Grey relational analysis (GRA) is an effective statistical method for measuring the degree of approximation among the sequences using a grey relational grade. It was developed by Deng [57] and has been successfully applied in other fields. In this work, this method is improved and employed to evaluate the impact of various factors on the performance deterioration of the DPF. The steps are as follows: Step 1: Determine reference matrix and comparison matrix. The reference matrix is expressed as follows:

in this work, if c < 1/3, l = 1.25c, else if c  1/3, l = 1.75c. Step 5: Calculate the Euclidean grey relational grade. In order to improve the evaluation accuracy, the Euclidean distance in the Fuzzy Mathematics is applied to show the difference between the reference matrix and the comparison matrix. So the weight vector of different factors in the reference matrix is defined as follows:



Y i ¼ ½yi ð1Þ yi ð2Þ    yi ðnÞ ði ¼ 1; 2Þ

ð20Þ

where Y1 represents the reference sequence of pressure drop, Y2 represents the reference sequence of maximum wall temperature and n is the number of test cases. If the number of investigated factors is m and these factors are investigated under n various conditions, so the comparison matrix is expressed as follows:

2

3

2 x1 ð1Þ 6 7 6 x2 7 6 6 7 6 x2 ð1Þ 6. 7 X ¼ 6 .. 7 ¼ 6 .. 6 7 6 6 7 4. 4 xm 5 xm ð1Þ x1

x1 ð2Þ

   x1 ðnÞ

x2 ð2Þ .. .

   x2 ðnÞ .. .. . .

3 7 7 7 7 5

ð21Þ

Step 2: Nondimensionalize original sequences. As the investigated factors and the reference variable have various dimensions, they must be nondimensionalized by the following equation: 0

xj ðkÞ ¼

xj ðkÞ  min xj ðkÞ max xj ðkÞ  min xj ðkÞ

ðj ¼ 1; 2; . . . ; m; k ¼ 1; 2; . . . ; nÞ ð22Þ

Step 3: Calculate the cosine value of fuzzy membership (fuzzy membership grade). In this work, the included-angle cosine method is adopted, which is not affected by the linear proportional relationship of the data. The similarity of the two factors is determined by the included-angle cosine of the two factors. It is expressed as follows:

Pn k¼1 yi ðkÞxj ðkÞ ffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ij ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn Pn 2 2 k¼1 yi ðkÞ k¼1 xj ðkÞ

ð23Þ

Step 4: Calculate the grey relational coefficient.

fij ðkÞ ¼

Dmin þ lDmax Dij ðkÞ þ lDmax

ð24Þ

where Dmin is the minimum absolute difference, Dmin ¼ min jyi ðkÞ  xj ðkÞj, Dmax is maximum absolute difference, Dmax ¼ Dij ðkÞ is the absolute difference, max jyi ðkÞ  xj ðkÞj, Dij ðkÞ ¼ jyi ðkÞ xj ðkÞj, and l is the resolution coefficient. The nature of the resolution coefficient l means the weight of the maximum absolute difference. The requirements for deciding the resolution coefficient is to satisfy the integrity and antiinterference of the relational grade due to that a large or small resolution coefficient cannot correctly reflect the relationship of the investigated factors. The method to determine the resolution coefficient is expressed as follows: : (1) Calculate the mean value of all absolute difference D m X n X ¼ 1 D jy ðkÞ  xj ðkÞj m  n j¼1 k¼1 i

ð26Þ

ð27Þ

The fuzzy analytic hierarchy process (FAHP) methodology is applied to solve the weight of different factors. Then, the Euclidean grey relational grades r 0ij are calculated by the following formula:

r0ij ¼ 1  2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Xn 2 ½w ð1  f ðkÞÞ ij ij k¼1

ð28Þ

Step 6: Calculate the fuzzy grey relational grades. Based on the fuzzy membership grades and the European grey relational grades, the fuzzy grey relational grades of the investigated factors are computed by the following formula:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 2ij þ ðr 0ij Þ2 2

ð29Þ

where Rij is the fuzzy grey relational grade between xj and yi. It represents the level of correlation between the reference sequence and the comparability sequence. Step 7: Rank. Based on the magnitude of the fuzzy grey relational grade, impacts of the investigated factors are ranked. 4.3. FAHP methodology and weight determination Grey relational analysis uses the grey relational grade to describe the influence degree and ranking of each factor to evaluation indexes, and average distribution of the weight between all factors cannot show their importance difference. It is necessary to determine the weight of each factor as the comprehensive evaluation system has a multilevel factors and each factor has a different impact on the performance degradation. The AHP was developed by Saaty in 1971 [58]. It is considered as a systematic analysis method for quantitatively treating complex and multicriteria systems, and can decompose a complex problem into multi-layers and multi-factors, as well as expediently compare and calculate weights [46]. Essentially, AHP is a subjective weighting method. The element value of the judgment matrix reflects the relative importance between two comparative factors. Generally,

Table 3 Judgment matrix scale and its meaning. Scale

Meaning

1 3

Two factors have the same importance One of the two factors is slightly important compared with the other One of the two factors is obviously important compared with the other One of the two factors is very important compared with the other One of the two factors is extremely important compared with the other Intermediate values of the adjacent judgment above If the ratio of the importance of factor A to the importance of factor B is c, then the ratio of the importance of factor B to the importance of factor A is 1/c

5 7 9 2, 4, 6, 8 Reciprocal

ð25Þ

c < 1=3

ð1:5c; 2c c P 1=3

W ¼ ðw1 ; w2 ;    ; wj Þ j ¼ 1; 2; . . . ; m

Rij ¼

xm ð2Þ    xm ðnÞ

½c; 1:5c

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the measurement scale of 1–9 is used to represent such relative importance, as shown in Table 3 [45,59]. However, FAHP introduced the fuzzy consistent matrix based on the AHP to reduce subjective effects, thus can obtain an objective comprehensive evaluation result. In this paper, the FAHP is used for deciding the weight of each index or factor, and paired comparison method in FAHP is used to establish fuzzy evaluation matrix conforming to consistency. The analytic process of FAHP should comply with the following steps: Step 1: The pairwise comparison matrix (also called the judgment matrix) is constructed according to the above-mentioned method and Table 3.

2 A ¼ ðaji Þmm

a11

a12

6 6 a21 6 ¼6 6. 6 .. 4

.. . am2

   amm

ðj ¼ 1; 2; . . . ; mÞ

> > > > : ai ¼

ði ¼ 1; 2; . . . ; mÞ

i¼1 m X

aji

ð30Þ

ð31Þ

j¼1

Step 3: Transform matrix A into a fuzzy consistent matrix by the following formula:

ðaj  ai Þ þ 0:5 2m

a0ji ¼

ð32Þ

According to the fuzzy consistent matrix, the weight wj of element aj can be solved. The weight vector W = (w1, w2,. . ., wm) of fuzzy judgment matrix should satisfy the normalization condition: Pm j¼1 wj ¼ 1. Step 4: Consistency check of the fuzzy judgment matrix. The consistency check steps are as follows: (1) The maximum value kmax is calculated as follows:

kmax

m ðAWÞj 1X ¼ m j wj

ð33Þ

(2) A consistency check is carried out by calculating the consistency ratio (CR).

CR ¼

CI RI

ð34Þ

where RI is the random index. The values of RI, which change with variations of the dimension m, are shown in Table 4 [46]. CI is the consistency index, and can be calculated by the following equation.

CI ¼

m 1 1 1 X  þ a0 m 2a ma i¼1 ji

ðj ¼ 1; 2; . . . ; mÞ

ð36Þ

5. Results and discussion

where aji is the importance intensity of the jth factor compared with the ith factor. The determination of aji is according to Table 3. The importance intensity of 1–9 is used to represent the relative importance between two factors. While for the ith factor compared with the jth factor, the importance intensity can take the reciprocal of that of aji. Step 2: Add the elements of the same line/row of matrix A, following equation can be obtained.

8 m X > > a ¼ aji > j > <

wj ¼

3

7    a2m 7 7 7 7 .. .. 7 . . 5

a22

am1

   a1m

Generally, if the CR < 0.1, the judgment matrix passes through the consistency check, else if CR  0.1, it is advisable to adjust the judgment matrix until it passes through the consistency check. Step 5: When the fuzzy judgment matrix is a complete consistent judgment matrix, the element a0ji of the fuzzy consistent judgment matrix can satisfy: a0ji ¼ aðwj  wi Þ þ 0:5, and a  (m  1)/2. By substitution of it into the normalization condition, the weight wj can be deduced as follows:

kmax  m m1

5.1. Results based on orthogonal experimental design According to the previous studies, the investigated factors and their levels are determined. The investigated factors can be divided into two categories, i.e. structure parameters and operating parameters. Structure parameters include wall thickness w, mean pore size d, porosity e and channel width a, which have three levels, as presented in Table 5, while operating parameters consist of exhaust flow rate Q, exhaust oxygen concentration Y0, microwave power Pmw, catalytic additive mass concentration ca and the mass of ash deposition mash, which have four levels, as depicted in Table 6. Furthermore, with the help of the orthogonal design table L9(34) and L16(45), the simulation conditions of testing cases are obtained, as shown in Tables 7and 8, respectively. Through various investigations, the evaluation indices of filter clogging and thermal aging (i.e. pressure drop Dp and maximum wall temperature Tw_max) are calculated by numerical simulation as shown in Tables 7 and 8. According to Table 7, it can be clearly observed that Case 9 owns the pressure drop above 16 kPa, Case 3, Case 4, and Case 8 own the maximum wall temperature above 1350 K, while Case 5 has a relative lower pressure drop about 12 kPa, and Case 9 has a relative lower maximum wall temperature below 1200 K, which means that a larger wall thickness and channel width (i.e. lower cell density) has an easy access to reaching

Table 5 Structure factors and levels. Levels

Factors

1 2 3

w (mm)

d (mm)

e (%)

a (mm)

0.30 0.43 0.50

13 23 34

40 45 50

1.3 1.7 2.1

Table 6 Operating factors and levels. Levels

1 2 3 4

Factors Q (kg/s)

Y0 (%)

Pmw (kW)

ca (mg/L)

mash (g/L)

0.05 0.10 0.15 0.20

5 10 15 20

0.4 0.6 0.8 1.0

10 20 30 40

0 15 30 45

ð35Þ

Table 4 RI values. Dimension

1

2

3

4

5

6

7

8

9

RI

0.00

0.00

0.58

0.90

1.12

1.24

1.32

1.41

1.45

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Table 7 Simulation test cases of structure factors and results (Q = 100 g/s, Y0 = 15%, Pmw = 0.6 kW, ca = 20 mg/L, mash = 15 g/L, msoot = 6 g/L and T0 = 500 K). Case

w (mm)

d (mm)

e (%)

a (mm)

Dp (kPa)

Tw_max (K)

1 2 3 4 5 6 7 8 9

0.30 0.30 0.30 0.43 0.43 0.43 0.50 0.50 0.50

13 23 34 13 23 34 13 23 34

40 45 50 45 50 40 50 40 45

1.3 1.7 2.1 2.1 1.3 1.7 1.7 2.1 1.3

13.1 13.6 14.7 14.9 12.2 13.4 15.3 15.1 16.2

1240 1315 1362 1380 1204 1298 1286 1365 1183

higher pressure drop, while a higher wall thickness and a lower channel width (i.e. higher cell density) lead to lower maximum wall temperature. This is due to that the larger wall thickness can increase thermal inertia, speeding up the heat loss. From Table 8, it can be seen that Case 5, Case 11, Case 12, Case 13, Case 14 and Case 16 have the pressure drop above 20 kPa, Case 13 and

2

y1 ðkÞ

3

2

½y1 ðkÞ  y1 ð5Þ=½y1 ð9Þ  y1 ð5Þ

pressure drop, and larger microwave power has an easy access to reaching higher maximum wall temperature. This can be attributed to that higher mass of ash deposition can block up the inlet channel and pores, and the increase of microwave power can contribute to increase the exhaust temperature or internal temperature of the DPF. 5.2. Results of structure parameters effect based on FGRA The above results have shown that the investigated factors have various impacts on performance degradation (filter clogging and thermal aging) of the DPF. As a result, fuzzy grey relational analysis, an improved method based on the grey relational theory, is adopted in this work. Firstly, the pressure drop and maximum wall temperature under various conditions are considered as the reference matrix Y1(k) and Y2(k), respectively. Wall thickness, mean pore size, porosity and channel width are taken to be the element x1(k), x2(k), x3(k) and x4(k) in comparison matrix, respectively. The reference matrix and comparison matrix are processed by Eq. (22):

3

6 y ðkÞ 7 6 ½y ðkÞ  y ð9Þ=½y ð4Þ  y ð9Þ 7 7 6 2 7 6 2 2 2 2 7 6 7 6 6 x1 ðkÞ 7 6 ½x1 ðkÞ  x1 ð1Þ=½x1 ð9Þ  x1 ð1Þ 7 7¼6 7 6 6 x ðkÞ 7 6 ½x ðkÞ  x ð1Þ=½x ð9Þ  x ð1Þ 7 2 2 2 7 6 2 7 6 2 7 6 7 6 4 x3 ðkÞ 5 4 ½x3 ðkÞ  x3 ð1Þ=½x3 ð7Þ  x3 ð1Þ 5 x4 ðkÞ 2 0:2250 6 0:2893 6 6 6 0:0000 6 6 ¼ 6 0:0000 6 6 0:0000 6 6 4 0:0000

½x4 ðkÞ  x4 ð1Þ=½x4 ð3Þ  x4 ð1Þ 0:3500 0:6250 0:6750 0:0000 0:6701 0:9086 1:0000 0:0000 0:0000 0:6500 0:4762 1:0000

0:0000

0:5000

1:0000

0:5000

0:5000

1:0000

1:0000

0:3000

0:7750 0:7250 1:0000

3

0:1066 0:5838 0:5228 0:9239 0:0000 7 7 7 0:6500 0:6500 1:0000 1:0000 1:0000 7 7 7 0:4762 1:0000 0:0000 0:4762 1:0000 7 7 1:0000 0:0000 1:0000 0:0000 0:5000 7 7 7 0:0000 0:5000 0:5000 1:0000 0:0000 5

Case 14 have the higher maximum wall temperature above 1400 K, while Case 1 and Case 2 own a relative lower pressure drop below 10 kPa, and Case 1 Case 2 and Case 3 have a relative lower maximum wall temperature below 1150 K, it means that a larger mass of ash deposition and exhaust flow rate can easily lead to higher

Secondly, the cosine value of fuzzy membership is calculated by Eq. (23). Thirdly, the Euclidean grey relational grades are computed by Eqs. (24)–(28). In Eq. (27), the weight of a factor determined by

Table 8 Simulation test cases of operating factors and results (w = 0.4 mm, d = 23 mm, e = 45%, a = 1.7 mm, msoot = 6 g/L and T0 = 500 K). Case

Q (kg/s)

Y0 (%)

Pmw (kW)

ca (mg/L)

mash (g/L)

Dp (kPa)

Tw_max (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.05 0.05 0.05 0.05 0.10 0.10 0.10 0.10 0.15 0.15 0.15 0.15 0.20 0.20 0.20 0.20

5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20

0.4 0.6 0.8 1.0 0.6 0.4 1.0 0.8 0.8 1.0 0.4 0.6 1.0 0.8 0.6 0.4

10 20 30 40 30 40 10 20 40 30 20 10 20 10 40 30

0 15 30 45 45 30 15 0 15 0 45 30 30 45 0 15

7.8 9.7 12.1 15.4 21.5 19.7 16.8 13.2 18.9 15.4 25.2 22.4 24.7 28.3 19.2 21.4

1098 1125 1137 1154 1186 1169 1210 1183 1195 1204 1216 1238 1422 1413 1287 1255

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1.0 Fuzzy membership grades Euclidean grey relational grades Fuzzy grey relational grades

0.9 0.8 0.7

R1

0.6 0.5 0.4 0.3 0.2 0.1 0.0

x

1

x

x

2

3

x

4

Factors

(a) Relational grades R1 of four structure factors to the pressure drop 1.0 0.9 0.8

Fuzzy membership grades Euclidean grey relational grades Fuzzy grey relational grades

0.7 0.6

R2

FAHP methodology is considered to be equal in different cases due to the mutual independence of the cases. Finally, the fuzzy grey relational grades of four structure factors to the pressure drop (i.e. filter clogging) and the maximum wall temperature (i.e. filter thermal aging) are calculated by Eq. (29). Fig. 7 illustrates the fuzzy membership grades, the Euclidean grey relational grades and the fuzzy grey relational grades of four structure factors to the pressure drop and the maximum wall temperature. It indicates that the fuzzy membership grades of the four structure factors have a big difference. As shown in Fig. 7(a), the wall thickness owns the highest fuzzy membership grade, while the fuzzy membership grades of mean pore size and porosity are nearly the same, which are smaller than that of the wall thickness and the channel width. As presented in Fig. 7(b), the channel width owns the highest fuzzy membership grade, while the fuzzy membership grades of mean pore size, porosity and wall thickness are nearly the same, which are smaller than that of the channel width. Based on the analysis of Eq. (23), the higher the fuzzy membership grade is, the better the similarity of the changing trends between the investigated factors and two performance degradation evaluation indices (pressure drop and maximum wall temperature) is. However, it also can be seen that the Euclidean grey relational grades of the four structure factors have a small difference. As shown in Fig. 7(a), the Euclidean grey relational grades of the wall thickness and the channel width to the pressure drop are higher than that of the mean pore size and the porosity, which are nearly the same. As presented in Fig. 7(b), the Euclidean grey relational grade of the channel width to the maximum wall temperature is the highest, while that of the porosity and the wall thickness are the lowest. Based on the analysis of Eqs. (24)–(28), it still can be shown that the similarity of the changing trends of wall thickness and pressure drop is better than that of the changing trends of mean pore size and pressure drop, however, the similarity of the changing trends of channel width and maximum wall temperature is better than that of the changing trends of porosity and maximum wall temperature. It is also known that the fuzzy grey relational grades in Fig. 7 offers us comprehensive consideration for evaluating impacts of the four structure factors. Fig. 7(a) shows that the fuzzy grey relational grades of four structure factors (wall thickness, mean pore size, porosity and channel width) to the pressure drop are 0.8224, 0.7227, 0.7175 and 0.7816, respectively, meaning that the impacts of the four structure factors on the pressure drop (i.e. filter clogging) are ranked from the most important to the least important as wall thickness, channel width, mean pore size and porosity. Fig. 7(b) depicts that the fuzzy grey relational grades of four structure factors (wall thickness, mean pore size, porosity and channel width) to the maximum wall temperature are 0.6677, 0.6765, 0.6767 and 0.9434, respectively, meaning that the effect of the four factors on the maximum wall temperature (i.e. filter thermal aging) are ranked as: channel width > porosity > mean pore size > wall thickness. Therefore, mean pore size and porosity which determine the permeability of the filter wall show a similar effect on the pressure drop (i.e. filter clogging) and the maximum wall temperature (i.e. filter thermal aging), and the four structure parameters are all main influence factors of performance degradation, but the wall thickness and the channel width which determine the cell density of the filter have the most noticeable effect on the pressure drop and the maximum wall temperature, respectively. Consequently, in order to prevent the performance degradation and improve durability and service life of the DPF, wall thickness and channel width of the filter must be firstly optimized for lower pressure drop and maximum wall temperature during the design stage of the DPF.

0.5 0.4 0.3 0.2 0.1 0.0

x

1

x

x

2

3

x

4

Factors

(b) Relational grades R2 of four structure factors to the maximum wall temperature

x1- Wall thickness; x2- Mean pore size; x3- Porosity; x4- Channel width Fig. 7. Impacts of four structure factors on the pressure drop and the maximum wall temperature.

5.3. Results of operating parameters effect based on FGRA Similarly, the pressure drop and maximum wall temperature under various conditions are considered as the reference matrix Y1(k) and Y2(k), respectively, and exhaust flow rate, exhaust oxygen concentration, microwave power, catalytic additive mass concentration and the mass of ash deposition are taken to be the element x1(k), x2(k), x3(k), x4(k) and x5(k) in comparison matrix, respectively. The cosine value of fuzzy membership, the Euclidean grey relational grades and the fuzzy grey relational grades can also be solved by Eqs. (22)–(29) based on above method in the of 5.2, and they can be shown in Fig. 8. Fig. 8 shows impacts of the five operating factors on the pressure drop (i.e. filter clogging) and the maximum wall temperature (i.e. filter thermal aging), respectively. As depicted in Fig. 8(a), the mass of ash deposition owns the highest fuzzy membership grade, while the exhaust oxygen concentration has the lowest fuzzy member-

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1.0 Fuzzy membership grades Euclidean grey relational grades Fuzzy grey relational grades

0.9 0.8 0.7

R3

0.6 0.5 0.4 0.3 0.2 0.1 0.0

x1

x2

x3

x4

x5

Factors

(a) Relational grades R3 of five operating factors to the pressure drop 1.1 1.0

Fuzzy membership grades Euclidean grey relational grades Fuzzy grey relational grades

0.9 0.8 0.7

R4

0.6 0.5 0.4

concentration to the maximum wall temperature is nearly the same as that of the mass of ash deposition. It is also known that the fuzzy grey relational grades of five operating factors (exhaust flow rate, exhaust oxygen concentration, microwave power, catalytic additive mass concentration and the mass of ash deposition) to the maximum wall temperature are 0.7134, 0.7437, 0.9117, 0.7791 and 0.7751, respectively, meaning that the effect of the five operating factors on the maximum wall temperature (i.e. filter thermal aging) are ranked as: microwave power > catalytic additive mass concentration > the mass of ash deposition > exhaust oxygen concentration > exhaust flow rate. Obviously, the mass of ash deposition which is determined by automobile travel mileage is the most important factor for filter clogging, which has the most noticeable effect on the pressure drop, accelerating the DPF failure, catalytic additive mass concentration and the mass of ash deposition nearly show a same effect on the maximum wall temperature, and the microwave power which can rapidly increase the internal temperature of the DPF during regeneration period has the most significant impact on the maximum wall temperature, which can result in higher thermal stress on the substrate wall. In addition, the catalytic additive mass concentration which can reduce the ignition temperature of soot also has noticeable effect on the maximum wall temperature. As a result, appropriate microwave power and catalytic additive mass concentration should be chosen to prevent the thermal aging, and effective measures are necessary to clean the ash on the filter wall, reducing the pressure drop of the DPF.

0.3 0.2

6. Conclusions

0.1 0.0

x1

x2

x3

x4

x5

Factors

(b) Relational grades R4 of five operating factors to the maximum wall temperature x1- Exhaust flow rate; x2- Exhaust oxygen concentration; x3- Microwave power; x4- Catalytic additive mass concentration; x5- The mass of ash deposition Fig. 8. Impacts of five operating factors on the pressure drop and the maximum wall temperature.

ship grade, and the fuzzy membership grades of microwave power and catalytic additive mass concentration are nearly the same, which are lower than that of the exhaust flow rate. It also can be seen that the Euclidean grey relational grades of the mass of ash deposition and exhaust flow rate to the pressure drop are higher than that of other factors, and the Euclidean grey relational grade of the exhaust oxygen concentration is the lowest, which is nearly the same as that of the catalytic additive mass concentration. Moreover, the fuzzy grey relational grades of five operating factors (exhaust flow rate, exhaust oxygen concentration, microwave power, catalytic additive mass concentration and the mass of ash deposition) to the pressure drop are 0.8566, 0.5538, 0.6466, 0.6025 and 0.8981, respectively, meaning that the impacts of the five operating factors on the pressure drop (i.e. filter clogging) are ranked from the most important to the least important as the mass of ash deposition, exhaust flow rate, microwave power, catalytic additive mass concentration and exhaust oxygen concentration. As presented in Fig. 8(b), the microwave power owns the highest fuzzy membership grade, while the fuzzy membership grade of exhaust flow rate is lowest; the Euclidean grey relational grades of the microwave power to the maximum wall temperature is the highest, while that of the exhaust flow rate and the exhaust oxygen concentration are the lowest, which are nearly the same. Moreover, the Euclidean grey relational grade of the catalytic additive mass

In this work, orthogonal experimental design (OED), fuzzy grey relational analysis (FGRA) and fuzzy analytic hierarchy process (FAHP) are employed to evaluate the impacts of various factors on performance deterioration of the DPF. As a result, the major conclusions are summarized as follows: (1) For structural factors, the fuzzy grey relational grades of the four structural factors (wall thickness, mean pore size, porosity and channel width) to the filter clogging are 0.8224, 0.7227, 0.7175 and 0.7816, respectively, meaning that the impacts of the four structural factors are ranked from the most important to the least important as wall thickness, channel width, mean pore size and porosity. Moreover, the fuzzy grey relational grades of the four structural factors to the thermal aging are 0.6677, 0.6765, 0.6767 and 0.9434, respectively, meaning that the impacts of the four factors on the filter thermal aging are ranked as: channel width > porosity > mean pore size > wall thickness. (2) For operating factors, the fuzzy grey relational grades of the five operating factors (exhaust flow rate, exhaust oxygen concentration, microwave power, catalytic additive mass concentration and the mass of ash deposition) to the filter clogging are 0.8566, 0.5538, 0.6466, 0.6025 and 0.8981, respectively, meaning that the impacts of the five operating factors are ranked from the most important to the least important as the mass of ash deposition, exhaust flow rate, microwave power, catalytic additive mass concentration and exhaust oxygen concentration. Moreover, the fuzzy grey relational grades of the five operating factors to the thermal aging are 0.7134, 0.7437, 0.9117, 0.7791 and 0.7751, respectively, meaning that the impacts of the five factors on the filter thermal aging are ranked as: microwave power > catalytic additive mass concentration > the mass of ash deposition > exhaust oxygen concentration > exhaust flow rate.

B. Zhang et al. / Applied Thermal Engineering 121 (2017) 838–852

(3) For all influencing factors, wall thickness and the mass of ash deposition have the most noticeable effect on filter clogging, while porosity and exhaust oxygen concentration have the lowest effect on filter clogging. In addition, channel width and microwave power have the most noticeable effect on filter thermal aging, while wall thickness and exhaust flow rate have the lowest effect on filter thermal aging.

7. Conflict of interests The authors declare that they have no conflict of interests regarding the publication of this paper.

Acknowledgements The authors thank the financial support of National Natural Science Foundation of China (Nos. 51676066, 51276056 and 91541121) and General Project of Hunan Provincial Department of Education in China (No. 16C1432).

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