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`
`SAE TECHNICAL
`PAPER SERIES
`
`2001-01-0912
`
`Numerical Study on Forced Regeneration _of
`Wall-flow Diesel Particulate Filters
`
`Y. Miyairi, S. Miwa, F. Abe, Z. Xu and Y. Nakasuji
`NGK Insulators, Ltd.
`
`Reprinted From: Diesel Exhaust Emission Control:
`Diesel Particulate Filters
`(SP-1582)
`
`400 Commonwealth Drive, Warrendale, PA 15096·0001 U.S.A.
`
`Tel: (724) 776-4841 Fax: (724) 776-5760
`
`SAE 2001 World Congress
`Detroit, Michigan
`March 5-8, 2001
`
`BASF-2039.001
`
`

`
`Downloaded from SAE International by BASF SE, Thursday, January 28, 2016
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`ISSN 0148-7191
`Copyright 2001 Society of Automotive Engineers, Inc.
`
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`BASF-2039.002
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`
`2001-01-0912
`
`Numerical Study on Forced Regeneration
`of Wall-Flow Diesel Particulate Filters
`
`Y. Miyairi, S. Miwa, F. Abe, Z. Xu and Y. Nakasuji
`NGK Insulators, Ltd.
`
`Copyright© 2001 Society of Automotive Engineers, Inc.
`
`ABSTRACT
`
`A computational model which describes the combustion
`and heat
`transfer
`that
`takes place during
`forced
`regeneration of honeycomb structured wall flow type
`diesel particulate filter was developed. In this model, heat
`released by the soot- oxygen reaction, convection heat
`transfer in the gas phase, conductive heat transfer in solid
`walls, and heat transfer between the gas and wall of each
`honeycomb cell at various radial positions in a filter are
`calculated. Each honeycomb cell was modeled as one
`solid phase and two gas phases and these three phases
`were divided in the axial direction into small elements.
`Conductive heat
`transfer between
`the small solid
`elements and convection heat transfer between the small
`gas elements were calculated
`for each small time
`increment. Conductive radial heat transfer between
`honeycomb cells was also calculated. By comparison
`this model and
`between calculated
`results with
`experimental results under available limited conditions
`the accuracy of the calculation model was verified. Filte;
`temperature distributions were calculated for a wide
`range of material
`thermal properties, various cell
`structures and various filter shapes.
`Using the
`calculated
`temperature distributions,
`thermal stress
`analyses were performed for various filter designs and
`materials to discuss the relative merits of materials and
`structur~.s. As conclusions, effects of material properties
`and structural design on filter durability in respect to
`thermal stress during forced regeneration are presented
`and favorable material selection and an example of
`stress relief design are proposed.
`
`INTRODUCTION
`
`While the diesel engine is more favorable for the
`purpose of environmental protection than a spark-
`
`Numbers in brackets designate references at the
`end of paper
`
`1
`
`ignition engine in terms of its higher thermal efficiency and
`reduced volume of C02 emissions, it has the disadvantage
`of emitting particulates, and the reduction of this emission
`is strongly desired. As information on the influences that
`this substance exerts on human health has been reported,
`the societal demands to promote a reduction of particulate
`emissions are thought to further strengthen the regulations
`in this area.
`The most effective method for responding to these
`demands is to install a filter in the exhaust system, and
`the type of filter that currently excels in collecting diesel
`particulates is the wall-flow type made of a ceramic
`material. Currently, there are ·several issues that the
`diesel particulate
`filter
`(DPF) confronts. The most
`important issue among them is the prevention of the
`breakage of the filter due to the thermal load that is
`applied to
`it during regeneration. Breakage occurs
`primarily in two forms. One is damage through melting, as
`the material is exposed to high temperatures that exceed
`its thermal resistance threshold. The other are the cracks
`created
`through
`thermal stress.
`Therefore,
`it
`is
`desirable for the material to have a higher thermal
`resistance and a characteristic that resists the creation of
`thermal stress. Meanwhile, it is also necessary to devise
`a system that will not apply a high thermal load to the
`DPF, with one of the solutions being the continuous
`regeneration system. However, it is difficult to effect
`continuous generation with all operating conditions. Soot
`loads the DPF during low exhaust temperature operating
`conditions, during which regeneration is impossible. Thus,
`the removal of soot through some form of forced
`combustion is considered impossible except on certain
`heavy-duty vehicles (HDVs) that operate constantly with
`high-load conditions.
`The purpose of our reserach is to analyze, through
`numerical calculation, the characteristics that are needed
`in the material used for the wall-flow type DPF, with the
`premise of forced regeneration. Numerous studies have
`already been
`reported concerning
`the simulation
`calculation of the combustion and regeneration of soot
`that loads the wall-flow type DPF.[1-10]1. These reports
`were used as references in this research, and the heat
`
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`transfer coefficient at the peripheral surface of the DPF
`and activation energy of the soot oxidation reaction were
`tuned through comparison with the actual test results. In
`the reference papers[1-2], a quasi one-dimensional
`model and the reaction equation are reported. Basically
`the quasi one-dimensional model. and Arrhenius reaction
`parameters in these references were used. Another
`paper [1 O] presented a 2-D thermal conduction model in
`which quasi one-dimensional models are connected
`axisymmetrically with the thermal conductance between
`them. This method is thought to be useful for estimating
`the temperature distribution and thermal stress of DPFs .
`More detailed 2-D models for one set of an inlet cell and
`an outlet cell of a DPF are presented in other papers [8,9].
`These models can predict the flow and the reaction more
`precisely than the quasi one-dimensional model, however,
`it takes more computational time to estimate the whole
`DPF temperature distribution. Then, in the research here,
`the quasi one- dimensional model was selected for the
`description of one set of an inlet cell and an outlet cell.
`These quasi one-dimensional models are put side by side
`with the thermal conductance between them. Through
`this model, the temperature distribution was estimated by
`varying the materials, cell structures, and DPF sizes. We
`used this temperature distribution to carry out stress
`analyses in order to research the material characteristics
`and structure that are needed.
`
`ANALYSIS MODEL
`
`MODEL - Fig. 1-a and Fig. 1-b show type specimen
`diagrams of the model. The quasi one-dimensional
`model shown in Fig. 1-a has been placed in the radial
`direction as shown in Fig. 1-b to create a two-dimensional
`thermal conduction model in which the flow of heat in the
`radial direction through solid wall is taken into account. As
`shown in Fig. 1-a, the basic one-dimensional model
`consists of the gas in the inlet cell, filter solid wall, and the
`gas in the outlet cell. The single solid wall that separates
`the inlet and outlet cells and 1/4 of the gas in the cells
`that sandwiches the wall have been rendered into a
`model. Independent quasi one-dimensional models for
`the gas flows were created, and, in terms of their
`combination in the radial direction, only the thermal
`conductance through the solid wall was taken
`into
`account. The volume of soot and its heat capacity were
`ignored, and it is assumed that the combustion heat is
`created in the solid wall. Furthermore, it is assumed that
`the gas that flows
`into the wall attains the same
`temperature as the solid wall. Because the surface area
`in the porous wall material is adequately large, the gas
`and the solid material have an extremely efficient heat
`transfer, and
`this assumption
`is considered
`to be
`justifiable. Based on the results of the observation of the
`experiments, it is assumed that soot evenly loads on one
`side of the filter wall.
`
`for
`this paper, equations
`in
`research presented
`momentum conservation are not solved. Instead of that,
`assuming the constant gas density, mass flow rates at
`each position are calculated as mentioned
`later. A
`calculation of pressure is not performed .
`
`Continuity
`aptat. + a(p9u)tax + a(p9v)ta~ = o
`
`Momentum Conservation
`
`a(p9u)/at. + a(p9uu)tax + a(p9 uv)ta~
`
`=aptax + µa2u1c;;-
`
`a(p9v)/at. + a(p9uv)tax + a(p9w}ta~
`= - ap1a~ + µa2v1ae - µvtkeq
`
`Energy Balance
`
`(Gas)
`
`a(p9Cp T)/at. + a(p9uCp T)tax + a(p9VCp T)ta~
`
`= hS(Ts -T)
`
`(Solid Wall)
`
`a(psCs Ts)/at. - a2(J..s Ts)/c;j- - a2(~ Ts)/af
`
`The last term in the equation for solid wall corresponds to
`the enthalpy transfer by the wall-flow gas. h is the heat
`transfer coefficient between the gas and wall. S is wall
`surface area per unit volume of the gas. qr is the heat
`release rate from soot oxidation reaction.
`
`Here, [mp] is the soot mass in a unit volume. HL is
`calorific value of soot combustion. The value of HL
`=33000 kJ/kg was used. The formula below has been
`applied to calculate the oxidation reaction rate of the
`soot[1,2,3].
`
`dmp/dt =a mp[02]exp(-Ea!RT)
`
`The values of the frequency factor a=300000m3/kgs, and
`the activation energy Ea= 1 OSOOOkJ/kmol were used.
`As an experimental result, pressure drop through
`the wall with a uniformly distributed soot layer had been
`expressed by following equation:
`
`EQUATIONS - The general equations for the gas and the
`solid wall, respectively, are given below, neglecting the
`energy of gas compression, the thermal diffusivity of gas,
`and the radiation heat transfer. [1 O]
`However, in the
`
`2
`
`tp: apparent soot layer thickness [m]
`µ:viscosity of gas [Pas]
`v: gas velocity [m/s]
`c,: constant= 1.06x109 [1 /m2]
`
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`< ~----r--...,.C<-ontr-ol-Vo-lu~me 1
`r;; i _
`
`Control Volume 2
`
`Inlet Channe~
`
`WaU Flow
`
`Fig.1 -a Quasi one-dimensional model
`
`Wall Flow
`
`j=l
`
`J=l
`
`y
`
`·....::__..,...,,....~~=--,,.....Le_. . / x
`.··
`.
`/dx /
`.
`: -· --~V-
`~~
`iv
`·r~·~_k dy
`1--m_
`J=3-~··-1
`--. r-· ~ l
`
`Thermal Conductance
`-~P.,'
`__ v
`·--.. ("
`!
`:
`
`Inlet . : ,.......
`s_L i
`
`:
`
`C2: constant= 0.7x10·5 [m]
`
`This means the flow resistance through the wall with a
`soot layer is a linear function of the soot layer thickness.
`This relationship has been used to calculate the flow .
`rates at each position of the DPF during regeneration
`where the soot distribution is uneven.
`Wall flow resistance Rt (i, j) at each position is:
`
`Rt(i,j) = feqQ,j) lkeq(i,j)
`
`=1.06x109(0.7x10..s + fpQ,j))
`
`[1/m]
`
`keq(i,j): apparent permeability of wall with soot [m2]
`feqQ,j): thickness of wall with soot [m]
`
`For the purpose of simplifying the calculation, it is
`assumed that the density of the gas is not affected by the
`temperature in calculating the inner axial gas flow speed
`in the inlet cell at each position in the DPF, the wall flow
`speed, and the inner axial gas flow speed in the outlet cell.
`Furthermore, it is assumed that the flow direction of the
`wall gas flow to be perpendicular to the wall.
`Furthermore, because the pressure loss in the flow
`path direction in the cell is very small as compared with
`the wall flow pressure loss when soot has been loaded,
`this can be ignored in determining the flow rate of each
`area through the distribution of the wall flow resistance.
`Rendering the total flow rate of the two-dimensional
`thermal conduction model to be Q'm, the wall flow rate at
`the position Q,j) is:
`
`qm(i,j) = O'm/RQ,j)/(!(1/RQj)))
`
`The apparent wall flow speed v Q, j) is:
`
`v(i,j) = qm(i,j) I (Spgillc}
`
`The inner axial flow speed at each position in inlet cells
`and outlet cells, respectively, are as follows:
`
`Inlet cell
`
`k=n
`
`U;n(i,j) = [ I:qm(k,j)] I (pg s2/4)
`
`k=i+1
`
`Outlet cell
`
`k=i
`UoutQ,j) = [ I:qm(k,j)] I (pg s2/4)
`k=1
`
`j l b
`
`Peripheral Swface
`
`Fig.1-b 2-D thermal conduction model
`
`Based on the aforementioned assumptions, solving
`the momentum equations is not necessary and the
`energy balance is simplified to the equations given below.
`The up wind difference of first order precision is
`used
`to discretize the space-differencial
`terms for
`convection in the x direction, and a central difference of
`first order precision is used to discretize the space(cid:173)
`differencial terms for thermal conduction in the solid wall.
`Each term on the right side of the equations for gas
`correspond to the enthalpy that flows into a control
`volume, the enthalpy that flows out from a control volume ·
`and the heat transfer between the gas and wall during the
`time increment dt.
`In the equation for the solid wall, the first term on
`the right side corresponds to the enthalpy that flows into
`the wall with the gas that flows through the wall. The
`second term and the third term are the heat transfer
`The
`forth
`term
`the wall.
`between
`the gas and
`corresponds to the enthalpy that flows out from the wall
`with the gas that flows through the wall. The temperature
`of the gas that flows out from the wall is assumed to be
`the same as the wall temperature. The fifth and the sixth
`correspond to axial and radial heat flows of the thermal
`
`3
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`conductance of the solid wall. The last term corresponds
`to the heat of the soot combustion mentioned before.
`
`Inlet gas (Control volume 1)
`
`d[M1 Cp Tin(i .il]/dt
`
`+ h(Tw(· ·i - T (. ·i}sdx
`l,J
`tn l,J
`
`Wall (Control volume 2)
`
`d[M2Cs T W(i,j))/dt
`
`= V;p9CpAT;n (i,j) + h(T w (i,j)- T;n (i,j)}sdx
`
`+ h(T out (i,iJ- T w c;.n}sdx - V;p9CpA T w Ci.il
`
`+ hsbs(T w (i+1 ,j) + Tw (i-1 .il - 2T w (i.n)/dx
`
`+ hsbs(T W (i ,j+1) + Tw (i ,j-1) - 2T w (i, i)}/dy
`
`+ HL(dmp(i.il/dt)
`
`M2 = Psbsdx , h = Nuhg/dh, A= s2/4
`
`Outlet gas (Control volume 3)
`
`d[M3Cp Tout (i,j) )/dt
`
`= Uout (i-1,j)pgCpATout (i-1,j) -Uout (i,j) pgCpATout (i,j)
`
`+vipgAT out (i,j) + h(T w (i,j) - Tout (i.i))sdx
`
`The h is the heat transfer coefficient between the wall
`and channel flow gas. The nusselt number of laminar
`flow through a tube; Nu=3.657 has been used to calculate
`the h. The material value of the gas was assumed to be
`constant without being temperature-dependent. Although
`in the preliminary research, a comparison was made by
`taking the temperature dependence of the material
`property of the gas into account, its influence on the
`resulting temperature distribution was very small, thus
`making the assumption permissible.
`In terms of the
`thermal material property of the solid wall material,
`namely the thermal conductivity and heat capacity,
`temperature dependence has been taken into account.
`The discretized equations were numerically
`integrated with respect to elapsed time.
`The time
`increment was set to 2x10-4 seconds.
`The spatial
`increment for the y direction has been set to the real cell
`pitch. The spatial increment for the axial (x) direction has
`been set to dx=8x1 o-3m which corresponds to 20 divisions
`of DPF length for the DPF of a 6 inch (152mm) length. In
`
`4
`
`the preliminary research, the effect of the number of
`divisions in the x direction had been examined for the DPF
`of a 6 inch (152mm) length. With the number of divisions
`more than 20, convergence of the variation in the
`maximum regeneration temperature and
`the energy
`balance error within the range less than 0.5% had been
`confirmed.
`The computational time for a DPF with D =144mm
`and L=152mm and for a regeneration duration of 600
`seconds was approximately 1 hour using a personal
`computer with a clock frequency of 500 MHz.
`
`VLIDATION OF THE MODEL - First, the regeneration test
`results were compared to the calculation results in order
`to calculate the soot oxidation reaction speed constant
`and the peripheral thermal conductance coefficient in
`reference to the following DPF dimensions: D=5.66"
`(144mm), L=6" (152mm). The regeneration conditions
`consisted of a gas temperature of 600°C and a flow rate
`of 0.7Nm3/min (0.014kg/s). In the experiment, the soot
`created by a diesel fuel burner was collected, followed by
`introducing the combustion gas from a propane fuel
`burner
`into
`the DPF. At
`that
`time,
`sheathed
`in diameter were
`thermocouples measuring 0.5mm
`inserted into 20 locations to measure the temperature
`distribution in the DPF. The DPF is exposed to the most
`stringent condition when the inlet gas temperature at the
`start of the regeneration is raised in increments over an
`inadequate amount of time. To approximate this condition,
`we provided a bypass and a switching valve immediately
`preceding the DPF of the regeneration test burner.
`Combustion gas was introduced into the bypass in
`advance to warm up the entire piping system of the test
`equipment, in order to introduce high-temperature gas
`In the simulation
`into the DPF by switching the valve.
`time change pattern of the gas
`calculation,
`the
`temperature that is measured in the experiments was
`used as the inlet gas temperature condition. Furthermore,
`the radial
`temperature distribution of the
`inlet gas
`temperature was measured in the experiments, and this
`distribution was used as the boundary condition for the
`calculation.
`Fig.2-a and Fig.2-b show the measured value of the
`temperature time changes at the 5 points on the DPF
`center axis, and the calculated value of the filter materials,
`The wall
`namely cordierite and SiC, respectively.
`thickness of the SiC DPF is 12 mil (0.305mm) and wall
`thickness of the cordierite DPF is 14 mil (0.356mm). The
`cell density of the SiC DPF is 300 cpsi (46.5/cm2) and the
`cell density of the cordierite DPF is 200 cpsi (31/cm2) and
`the soot loading rate is 1 Og per liter of DPF volume.
`Table1 shows the thermal property values of cordierite
`and SiC, respectively. As shown in Fig.2-a and Fig.2-b,
`the calculated and measured values match in terms of
`the correlation of the temperatures of the areas, the
`in
`the maximum
`temperature between
`difference
`materials, and the relationship of the times elapsed until
`is attained. Both
`the
`the maximum
`temperature
`calculations and measurement exhibit
`increased
`maximum temperatures the closer they are to the outlet
`end. Compared to SiC, cordierite requires a shorter
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`length of time to attain the maximum temperature, and
`completes regeneration quicker.
`Fig. 3 compares the temperature distribution at the
`is
`reached. The
`time
`the maximum
`temperature
`calculation results exhibit the simula·tion of a greater
`temperature gradient between the center and peripheral
`areas with cordierite than with SiC. Even when the model
`in which soot combustion and gas flow have been
`simplified is used, 'the test results and the calculation
`results match relatively well.
`Fig.4 shows the respective maximum temperatures
`of cordierite and SiC, with varying soot loading rates. The
`maximum temperature of cordierite is higher than SiC,
`and the result of the actual measurement in which the
`maximum temperature becomes higher with the increase
`in the soot loading rate has also been simulated in the
`calculation.
`
`Table1 Thermal properties of material
`
`Property
`
`NGK-SiC
`
`Cordierite
`
`Specific Heat Capacity Cs
`[kJ/(kgK)l
`
`Thermal Conductivity A.
`[kJ/(msK)]
`
`RT
`800 °C
`1200°c
`RT
`800 °C
`1200°c
`
`Density
`[kg/m3]
`
`Ps
`
`0.7
`1.1
`1.3
`O.D15
`0.01
`0.01
`
`1700
`
`0.7
`1.7
`1.7
`0.0008
`0.001
`0.002
`
`--
`1200
`
`1200 . . . - - - - - - - - - - - - - - -
`Measured
`
`1200 - - - - - - - - - - - - - - -
`Measured
`
`800
`
`0
`Cll
`Cll ...
`"O .
`.... ~ 400
`
`OI
`Cll
`
`• -+-·2'""3"'1!'""~--
`
`2
`
`5
`
`800
`
`0
`Cll
`Cll ...
`
`OI
`Cll
`"O
`
`.... ~ 400
`
`5
`
`• -+-2'""3"'1!'"}·-
`
`Gas temperature: 600 degree C
`Gas flow rate: 0.014 kg/s
`02 concentration: 10%
`
`Gas temperature: 600 degree C
`Gas flow rate: 0.014 kg/s
`02 concentration: 10%
`
`0
`
`200
`
`400
`
`600
`
`0
`
`200
`
`400
`
`600
`
`t ,S
`
`t ,s
`
`Simulation
`
`1200 r---------------
`• -+-2'""3"'1!'""~--
`
`800
`
`0
`Cll
`Cll ...
`"O .
`.... ~ 400
`
`OI
`Cll
`
`1200 . - - - - - - - - - - - - - - - - - .
`Simulation
`
`-+-2'""3"'1!'""~--
`
`4
`
`•
`
`5
`
`800
`
`0
`Cll
`Cll ...
`
`OI
`Cll
`"O
`
`....~ 400
`
`Gas temperature: 600 degree C
`Gas flow rate: 0.014 kg/s
`02 concentration: 10%
`
`Gas temperature: 600 degree C
`Gas flow rate: 0.014 kg/s
`02 concentration: 10%
`
`0
`
`200
`
`400
`
`600
`
`0
`
`200
`
`400
`
`600
`
`t ,S
`
`t ,s
`
`Fig.2-a Clculated and measured temperature
`OfSiC DPF
`D=144mm, L=152mm (12mil/300cpsi)
`Ls=10g/I
`
`Fig.2-b Clculated and measured temperature
`of Cordierite DPF
`D=144mm,L=152mm(14mil/200cpsQ
`Ls=10g/I
`
`5
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`E
`
`)(
`
`0. 12
`
`0. 10
`
`0.08
`
`0. 06
`
`0.04
`
`0.02
`
`0.00
`
`0. 14
`
`0. 12
`
`0. 10
`
`E 0.08
`x
`
`0.06
`
`0.04
`
`0.02
`
`r;;
`.J
`
`LO
`M
`
`-40
`
`40x10-3
`
`0
`Y . m
`
`-40
`
`0
`
`40x10-3
`
`v,m
`
`[a] Experimentally measured result for Cordierite
`Cell density: 200 cpsi, Wall thickness:14 mil
`
`[b] Model calculation result for Cordierite
`Cell density:200 cpsi, Wall thickness: 14mil
`
`0
`0
`Ct:>
`
`.
`
`0
`LO
`LO
`
`0. 12 :,'o\~¥~ \
`\ ~\750
`\
`
`0 ~ 0
`0
`Ct:>
`
`800
`
`700
`
`0. 10
`
`0.08
`
`E
`-
`
`)(
`
`0. 06
`
`0
`LO
`LO
`
`0
`0
`Ct:>
`
`0.04 \
`
`\
`
`0
`LO
`LO
`
`-
`
`0.02
`
`0.00
`
`-40
`
`0
`Y , m
`
`0. 14
`
`0. 12
`
`0. 10
`
`~I ~~ 16lJ
`
`700 ,
`750
`(C 700
`~ 100-- /
`650 650
`
`I
`
`E
`
`)(
`
`0.08 \
`
`0.06
`
`I
`
`0
`0
`LO
`
`0
`LO
`LO
`
`. 0
`
`I
`600
`I
`' LO '
`
`0
`LO
`
`0
`LO
`
`20
`
`60x10-3
`
`0.04
`
`0.02
`
`40x10-3
`
`0
`0
`LO
`
`0
`LO
`LO
`
`600
`
`J J l
`
`-60 -40-·-20 0
`y,m
`
`[c] Experimentally measured result for SiC
`Cell density: 300 cpsi, Wall thickness:12 mil
`
`[d] Model calculation result for SiC
`Cell density:300 cpsi, Wall thickness: 12mil
`
`Fig.3 Maesured and calculated
`Soot loading rate Ls=10g/I
`Inlet gas temperature : 600 degree C
`Gas flow rate: 0.7 Nm3/min (0.014kg/s)
`02 concentration : 10%
`
`temperature distributions
`
`6
`
`BASF-2039.008
`
`

`
`Downloaded from SAE International by BASF SE, Thursday, January 28, 2016
`
`•
`
`Conlierilll(14mil/Zl0Cpsi)-Elcperlmantal rest&
`
`-Cordierile(14mil/ZlOCpsi)-MDdel results
`o SiC(12miU300cpsi)-E>cperimantal results
`
`..,._SiC(12miU300cpsi}Model results
`
`1200
`
`1100
`
`()
`~ 1CXXJ
`Cl
`Cl)
`"C_
`
`OOJ
`
`Im
`1.1
`~
`700
`
`Em
`
`5
`
`•
`
`15
`10
`Sect Loacing Ls , gll
`
`20
`
`Fig.4 Maximum temperature with various soot
`loading rate
`D=144mm, L=152mm
`
`ANALYSIS RES UL T-1 (TEMPERATURE)
`
`EFEECTS OF MATERIAL PROPERTIES - The material
`properties that influence the transient heat transfer i~ a
`solid material are thermal conductivity and heat capacity.
`Fig. 5 and Fig. 6 show the maximum regeneration
`temperatures when · these properties are varied
`that measures 0=5.66"
`parametrically on a DPF
`(144mm) in diameter, L=6" (152mm) in length, a cell
`density of 300 cpsi (46.5/cm2), and a wall thickness of 12
`mil (0.305mm). The soot loading rate has been set to _1 Og
`per liter of DPF volume in order to make a comparison
`under the following conditions: 600°C gas temperature,
`10%
`oxygen
`concentration,
`and
`0.7Nm3/min
`(Qm=0.014kg/s) gas flow rate. In Fig. 5 and Fig. 6, the
`calculations do not take the temperature dependence of
`the material properties into account.
`As Fig. 5 shows, the thermal conductivity of the
`material influences the maximum temperature in the
`region below 0.01kJ/(msK)(=10W/(mK)), while
`its
`influences above 0.01 kJ/(msK) are small. Meanwhile,
`the thermal capacity in the range normally expected of a
`DPF material influences the maximum temperature in a
`practically linear relationship: the smaller the thermal
`capacity, the greater the maximum temperature will be.
`A volume of 1/(psCs"5) 112 is generally given as being
`proportionate to the temperature amplitude of a solid with
`a transient local heating. However, within the realistic
`range of material properties for DPF, heat capacity and
`thermal conductivity are exerting different influences as
`shown in Fig.5 and Fig.6.
`It is presumed that in the
`research on the material properties shown in the Fig.6,
`the influence of heat capacity seem to be exerted linearly
`because the variable range of the heat capacity of the
`material is small. With an even smaller heat capacity
`range, it is presumed that the influences exhibit a non-
`
`linear relationship in which the maximum temperature
`increases more suddenly
`in accordance with
`the
`reduction in the heat capacity.
`Based on these results, it becomes effective to
`increase the. thermal conductivity
`to a minimum of
`0.01 kJ/(msK)(=1 OW/(mK)) in order to lower the maximum
`temperature during the forced regeneration of the DPF
`and to select a material with a greater heat capacity.
`Wrth a given cell construction, increasing its wall
`thickness
`is considered equivalent to
`increasing
`its
`material thermal conductivity and heat capacity, which is
`estimated to be effective in reducing the maximum
`regeneration temperature.
`
`1300 ~--------------,
`
`p5 C s =1350 kJ/(ni3K)
`
`1200
`
`0 1100
`.,
`;, 1000
`-8
`= 900
`i! 800
`
`Gas temperabn :600 degree C
`Gos tk>N note: 0.014 kg.'s
`02 concertration: 10%
`
`700
`600 L_ _ _ _ _._ _ _ _ __._ _ _ _ ___.
`
`0
`
`0.04
`0.02
`Therrral Conductivity /1. 0 ,
`k.J/(1T6K)
`
`0.06
`
`Fig .5
`
`Influence of thermal conductivity
`on maximum temperature
`D=155mm,L=144mm,Ls=1 Og/I
`
`1200
`
`1100
`
`/l. 5=0.025 kJ/(IT6K)
`
`0
`" 1000
`" to
`-8
`.. ..
`i!
`
`800
`
`900
`
`700
`
`600
`
`0
`
`Gas temperat"e :600 degree C
`Ga. tk>N rate: 0.014 legs
`02 conceriration: 10%
`
`500
`Heat Capacity p 5 C • , k.J/(m'.31<)
`
`1000
`
`1500
`
`Fig .6
`
`Influence of heat capacity
`on maximum temperature
`D=144mm,L=144mm,Ls=1 Og/I
`
`Fig. 7 and Fig. 8 show the time-dependent changes of
`each heat values; axial thermal conductance , radial
`thermal conductance, gas heat transfer, and heat release
`from oxidation of the soot at outlet center of cordierite
`DPF and SiC DPF, respectively. Initially, the solid wall is
`heated with 600°C gas, then, after the heating reaction of
`the soot begins, a portion of the heat that is generated is
`taken away by the gas, and another portion is released
`through thermal conductance to another area via the wall.
`
`7
`
`BASF-2039.009
`
`

`
`Downloaded from SAE International by BASF SE, Thursday, January 28, 2016
`
`Thus, the temperature of the wall changes through the
`balance of these actions.
`
`SiC
`
`1.50E-04
`
`1.00E-04
`
`.,
`' ..,
`.x.
`ti 5.00E-05
`~ c:
`" 0.00E+OO
`~
`f< c: -5.00E-05
`" ~
`~ -1.00E-04
`~
`-1.50E-04
`
`0
`
`100
`
`200
`
`400
`
`500
`
`600
`
`300
`t 's
`
`Fig.7 Time-dependent changes of transfered heat
`values at outlet center of SiC DPF
`12mil/300cpsi,D=144mm,L=152mm,Ls=1 Og/I
`
`the activation
`length suddenly increases when
`time
`energy exceeds a certain value. In a range of activation
`energy lower than this value, the maximum temperature
`slightly decreases by lowering the activation energy.
`Fig. 10 shows the regeneration efficiency of SiC and
`cordierite by varying the activation energy undec the soot
`loading conditions of 1 Og/L. Here, regeneration efficiency
`indicates the ratio of the amount of soot that is burned off
`through regeneration in proportion to the total amount of
`soot
`that was
`loaded prior
`to
`regeneration. The
`regeneration time is 900 seconds. The regeneration
`efficiency suddenly worsens when the activation energy
`exceeds a certain value.
`
`1200
`
`1000
`
`Cordei.i.rite:::::.----._
`
`700
`
`600
`
`(.) 800
`
`600
`
`" " Iii
`-8
`~
`..! 400
`
`500
`
`.,
`400 • -~
`..
`
`300
`
`I!..
`
`200
`
`Cordierite
`
`200
`
`0
`O.E+OO
`
`100
`
`0
`2.E+OS
`
`1.E+OS
`5.E+04
`Activation Energy Ea , kJ/kmol
`
`Fig.9
`
`Influence of activation energy on maximum
`temperature,
`12mil/300cpsi,D=144mm,L=152mm,Ls=10g/I
`
`1.50E-04
`
`1.00E-04
`
`.,
`' ..,
`.x.
`ti 5.00E-05
`~
`§ O.OOE+OO
`~
`f< c: -5.00E-05
`" ~
`~ -1.00E-04
`~
`-1.50E-04
`
`0
`
`100
`
`200
`
`400
`
`500
`
`600
`
`300
`t,s
`
`Fig.8 Time-dependent changes of transfered heat
`values at outlet center of Cordierite DPF
`12mil/300cpsi, D=144mm,L=152mm,Ls=10g/I
`
`At the time the heating reaction through soot oxidation
`favorable
`thermal
`occurs with SiC, which provides
`conductivity, the level of thermal conductivity in the
`material in the radial directions is comparable to that of
`gas. In contrast, it is evident that cordierite provides less
`thermal conductivity and relies on the convection of gas to
`take the heat of soot combustion away.
`
`INFLUENCES OF ACTIVATION ENERGY - Fig. 9 shows
`the maximum
`regeneration
`temperatures and
`the
`maximum temperature time by varying the activation
`energy of the soot oxidation reaction on SiC and cordierite,
`respectively. Reducing the activation energy is equivalent
`to using a fuel additive or using a catalyst with a coat
`applied to the DPF. An activation energy value in which
`the maximum temperature becomes the highest exists.
`The maximum temperature suddenly decreases and the
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`SiC
`
`0:
`
`.!!
`
`"'
`"" "' " c:
`" IE
`w
`c:
`.!2
`f ..
`.. .. .. 0::
`
`c:
`
`0.00
`O.E+OO
`
`1.E+OS
`5.E+04
`Activation Energy Ea , kJ/kmol
`
`2.E+OS
`
`Fig.10 Influence of activation energy on regeneration
`efficiency,
`12mil/300cpsi,D=144mm,L=152mm,Ls=10g/I
`
`INFLUENCE OF CELL STRUCTURE - Fig. 11 shows the
`respective maximum temperatures of cordierite and SiC,
`by varying their cell structure (wall thickness and cell
`density). The comparison was made by setting the
`following values: DPF dimensions D=S.66" (144mm ) and
`L=6" (152mm); soot loading rate of 14g per liter of DPF
`volume; gas flow rate of 0.7 Nm3/min (Qm=0.014kg/s);
`gas temperature of 600°C and oxygen concentration of
`10%. As shown in the Fig.11, the maximum regeneration
`
`8
`
`BASF-2039.010
`
`

`
`Downloaded from SAE International by BASF SE, Thursday, January 28, 2016
`
`temperature generally depends on the specific filtration
`area (GFSA) because the soot loading rate per specific
`area and wall flow speed change due to the change in
`GFSA. Greater GFSA brings smaller wall flow velocity
`and lower rate of soot loading per specific area. These
`lower the cooling efficiency of gas conduction and make
`heat release rate from soot combustion higher. Then
`increasing GFSA brings about a higher maximum
`temperature. Therefore, decreasing the GFSA is one
`way to lower the maximum temperature. However,
`decreasing the GFSA brings about a higher pressure loss.
`The results for