Inlet Cone Effect on Diesel Particulate Filter Regeneration upon a

Article pubs.acs.org/IECR

Inlet Cone Effect on Diesel Particulate Filter Regeneration upon a Rapid Shift to Idle Mengting Yu and Dan Luss* Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas 77204, United States ABSTRACT: The particulate matter (PM) emitted by a diesel engine is collected and then burned in a diesel particulate filter (DPF). A major technological challenge in the operation of the ceramic, often cordierite, filter is that a rapid shift to idle may create a local hot region with a temperature much higher than under stationary feed conditions. This excessive transient temperature rise may cause local melting or cracking of the ceramic filter. Almost all previous studies of temperature excursions during the DPF regeneration (combustion of the deposited PM) were of cases in which equal exhaust flow rate was fed to all the parallel inlet channels. The diesel engine exhaust pipe is sometimes connected to the DPF by a wide-angled cone (diffuser). This leads to a mal-distribution of the flow rate to the inlet channels and of the deposited PM. Simulations revealed that following a rapid shift to idle the highest regeneration temperature in a DPF fed by a cone exceeded that in one not fed by a cone and it may exceed the cordierite DPF melting temperature (1200 °C). Moreover, it may generate transient radial and axial temperature gradients several times higher than under stationary regeneration that may crack the cordierite DPF. The increase in the temperature gradient is especially large in the axial direction. One of the surprising findings is that the highest temperature attained following a step change to idle is not a monotonic function of the initial PM loading.

1. INTRODUCTION A diesel particulate filter (DPF) is used to remove particulate matter (PM) from automotive diesel engine exhaust. It consists of thousands of parallel square channels, with the opposite ends of adjacent inlet and outlet channels being plugged. The exhaust gas passes through the filter porous walls from the inlet to the adjacent outlet channels. A schematic of the flow through a pair of inlet and outlet channels is shown in Figure 1a. The

undesirable formation of the high temperature excursions in a DPF.1−41 Experiments showed that under stationary exhaust feed high regeneration temperatures occur under operation with either low inlet gas flow rate, high feed gas temperature and/or oxygen concentration, or high initial PM loading.1,2 Bissett developed the first single DPF channel model.3 Konstandopoulos et al.4 extended the Bissett’s model to a two layer model that took into account the incomplete contact between the particulate layer and catalyst coating. Haralampous and Koltsakis5,6 studied the impact of oxygen diffusion and NO2 back-diffusion on DPF regeneration in a one-dimensional model. Various multichannel models have been developed. Miyairi et al.7 used a two-dimensional model to study the impact of DPF structure and material properties on DPF regeneration temperature and thermal stress. Konstandopoulos et al.8 used multichannel DPF regeneration simulations to study the impact of the PM loading and impregnated catalyst nonuniformities on the highest regeneration temperature and efficiency. This was followed by a study of the impacts of DPF heat losses, local hot spots and nonuniform inlet velocity on the regeneration efficiency.9 Koltsakis et al. used both 2-D10 and 3D11 regeneration models to study the dependence of the highest regeneration temperature on nonuniform PM deposition and the adhesive cement layers inside a SiC filter. The predicted temperature rise under stationary operation is usually too low to explain the reported damage of commercial DPFs. Recent studies pointed out that the observed DPF damage can be explained by formation of high transient temperature

Figure 1. (a) Schematic of the flow in an inlet and adjacent outlet channels. (Reproduced with permission. Copyright Corning Inc., 2002). (b) Schematic of a DPF with an inlet cone in the front.

deposited PM is periodically combusted to prevent excessive pressure drop buildup. Experience has shown that transient local temperature excursions may destruct the DPF either by local melting or by cracking caused by thermal stresses. Circumventing these occasional local temperature excursions is still a major technological challenge in the design, operation, and control of a DPF. Numerous experimental and theoretical studies have attempted to understand and predict the © 2012 American Chemical Society

Received: Revised: Accepted: Published: 11355

April 10, 2012 August 2, 2012 August 10, 2012 August 10, 2012 dx.doi.org/10.1021/ie300948c | Ind. Eng. Chem. Res. 2012, 51, 11355−11366

Industrial & Engineering Chemistry Research

Article

inlet pressure to all the channels was equal to one atmosphere (P1i,0 = 1atm). COMSOL 3.5a standard k−ε model was used to calculate the incompressible turbulent flow inside the cone for a specified flow rate. The flow in the cone cannot enter into areas occupied by either exit channels or DPF walls. The flow hitting a blocked area flows into the adjacent inlet channels. The model predicted the temporal inlet velocity to channels located at different radial positions. The model is described in Appendix 1. A laminar flow model was used to determine the ith outlet channel exit pressure corresponding to the jth iteration (Pji,L). The inlet pressure profile was iterated and the calculations repeated until the exit pressure of all the outlet channels was equal to the assumed exit value of one atmosphere. The (j+1)th j assumed inlet vector (Pj+1 i,0 ) was updated from (Pi,L) by the relation:

excursions following a rapid change in the driving mode, such as a rapid shift to idle.5,10−16 These transient temperature excursions can be sufficiently high to explain the observed damage of the DPFs. Their occurrence is similar to the wrongway behavior of packed bed reactors.17−23 Recently, catalytic DPFs have been developed, which simultaneously remove the PM and oxidize any emitted organic compounds.24−30 Also, new DPF systems for simultaneous NOx and PM reduction are under intense development.31−35 In these cases the exhaust pipe is connected to the larger diameter DPF by a wide-angled cone (diffuser). Stratakis and Stamatelos36,37 experiments revealed that the cone caused mal-distribution of the inlet velocity to the various channels. The highest inlet velocity was at the DPF center. Experiments by several research groups38−40 also revealed that an inlet cone led to mal-distribution of the deposited PM, with the maximum deposited at the DPF center. Luss et al.41 developed a twodimensional model and studied under stationary feed conditions the impact of the inlet cone on the deposition rate and the regeneration temperature as well as on the transient inlet velocity distribution among the various DPF channels. Those simulations predicted that the PM deposition in a DPF fed by a cone is highly nonuniform with the maximum PM thickness in the center and a second maximum formed close to the wall. The corresponding maximum regeneration temperatures are much higher than those in a DPF with no cone. The maximum regeneration temperature in a DPF with a cone can exceed 1200 °C (the melting temperature of cordierite DPF) under stationary operation of oxygen concentration exceeding 15% and exhaust gas flow rate lower than 100 kg/h.41 These high oxygen concentration and low exhaust gas flow rate conditions are unlikely to be encountered under common driving conditions. However, rapid changes in the driving mode may lead to exhaust conditions exceeding those obtained under stationary driving mode, for example following a rapid deceleration of a car or a shift to idle. The goal of this study was to determine the impact of the inlet cone on the highest temperature rise following a rapid shift to idle.

Pij,0+ 1 = Pij,0 + (0.5) j − 1(1 − Pij,L)

i = 1, 2..., N (1)

Experience showed that less than 10 iterations led to convergence. After determining the inlet velocities, we calculated the relative flow resistance change among the various channels during the PM deposition and regeneration. This required repeated iterative adjustments of the radial inlet velocities throughout both the filtration and regeneration. PM Regeneration Model. Several PM deposition and regeneration models have been described in the literature.3−11,41,42 Most assumed that the feed velocity in all the inlet channels was uniform or just affected by the temperature (physical properties) difference among the channels. When a wide-angled cone (diffuser) connects the upstream exhaust pipe to the DPF, the feed is mal-distributed among the various inlet channels. This leads to variations in the deposition and regeneration among the channels, which, in turn, affects the velocity. We modified the assumption of constant inlet velocity to each channel to one in which the total flow rate to the cone was specified. Using the iterative calculations of the channel inlet pressure described above, we determined the transient radial inlet velocity distribution. These transient pressure calculations were adjusted as the nonuniform PM deposition or regeneration changed the relative resistance to flow among the channels. The flow was assumed to be axi-symmetric, that is, no azimuthal dependence existed. A 2-D PM deposition model described previously41 was used in the present work. The detailed single channel PM deposition model presented by Konstandopoulos et al.42 was adapted to determine the deposit layer thickness in each inlet channel. The deposited PM layer thickness was nonuniform with the highest in the center of the DPF. When the specified PM loading limit was reached, regeneration was started by increasing the feed temperature to a value exceeding the PM ignition temperature. We assumed that the PM regeneration proceeded by the overall reaction:

2. MODEL DEVELOPMENT Radial Inlet Velocity Distribution. We used a 2-D mathematical model to simulate the flow, PM deposition and regeneration in a cylindrical DPF fed by a wide-angled cone. The axi-symmetric model assumes that the same flow exists in all the channels at any radial position; that is, no azimuthal dependence exists. The simulations of this 2-D model are significantly faster and easier than those of a 3-D one. A schematic of the filter shape and dimension is presented in Figure 1b. Preliminary simulations revealed that the exit nozzle had only a minor impact on the DPF behavior. Thus, to minimize the computational effort, the impact of the exit cone was not accounted for, i.e., we assumed that the exit pressure of all the outlet channels was the same, one atmosphere. The first step in the numerical procedure was calculating the inlet velocity to each channel. The flow nonuniformity among the inlet channels is due to the difference in the inlet pressure to the inlet channels caused by the cone. The flow in the cone is turbulent while the flow in each channel is laminar due to their small hydraulic diameter. The numerical procedure consisted of repeated iterative steps. At the jth iteration we assumed the inlet pressure at each ith inlet channel (Pji,0), where i = 1 and N denote the inlet channel at the DPF center and that adjacent to the wall, respectively. Initially, we assumed that the

C + αO2 → 2(α − 0.5)CO2 + 2(1 − α)CO

(2)

where α is an oxidation reaction index. We used in our simulations α = 0.85, which is within the range of reported values.10 The corresponding heat of the reaction is 10

ΔH = 2(α − 0.5)ΔHco2 + 2(1 − α)Hco

(3)

The oxygen reaction rate consumption through the PM layer is 11356

dx.doi.org/10.1021/ie300948c | Ind. Eng. Chem. Res. 2012, 51, 11355−11366

Industrial & Engineering Chemistry Research ro2 = αko2(Ts)

Article

ρw (Ts)y

Hreac = −ΔH × ρP

M o2

(4)

V1 = Vin ;

(5)

∂ 2 (d ρβ Vβ) = ( −1)β 4dρw Vw ∂z +

Cpgρ1V1|z

∂T1 4 = h1 (Ts − T1) ∂z d

Cpgρ2 V2|z

∂T2 4 = (h2 + Cpgρw Vw) (Ts − T2) ∂z d

P2 = Pa ;

∂Ts =0 ∂r

at r = 0

he =

2 ⎡ (d − 2W )2 ⎤ Ma(ρ1V1 )z = 0 ⎥ ΔPen + ΔPex = ⎢1.1 − 0.4 29T1 2(d + Ws)2 ⎦ ⎣

ρp

2

The total pressure drop for each pair of the channels across the DPF is predicted by the above two equations and the frictional pressure drop (eq 7). We used a 2-D transient solid energy balance to account for the axial and radial heat conduction, heat convection in the channels, heat convection by flow through the filter wall, and heat generated by the exothermic PM oxidation. Specifically,

at z = L

at r = R

ws w d−w λs + λp + λa ws + d ws + d ws + d

(14)

1 1 ha

+

wins λ ins

(15)

⎡ ⎛M ⎞ ⎛ αko (Ts)w ⎞⎤ dw 1 2 ⎟⎟⎥ = −⎜⎜ P ⎟⎟ρw Vwy ⎢1 − exp⎜⎜ − dt Vw α ⎢⎣ ⎝ ⎠⎥⎦ ⎝ M o2 ⎠

(16)

Tin = T (0) × H(ts − t ) + T (s) × (t − ts)

(17)

Fin = F(0) × H(ts − t ) + F(s) × (t − ts)

(18)

O2,in = O2 (0) × H(ts − t ) + O2 (s) × (t − ts)

(19)

The transient energy balance equation was solved by the explicit finite difference method and the method of lines. The gas phase equations were solved using the shooting method, the Runge−Kutta method, and also the finite difference method. The iterative procedure described above (eq 1) was periodically used to determine the inlet velocity (Vji,0) and pressure (Pji,0) of each inlet channel i, as these are affected by the relative flow resistances in the various channels.

∂ (ρ wCppTs + ρs wC s psTs) = Hcond + Hconv + H wall + Hreac ∂t p (12)

Hcond = λp

3. RESULTS AND DISCUSSION The maximum temperature rise following a sudden step change in the feed is affected by the rate of the change and by the time when the change occurs. The largest temperature excursion occurs when the shift is rapid, that is, a step change rather than

(13a)

(13c)

∂Ts =0 ∂z

After the PM was ignited and the peak of the temperature wave reached the middle of the DPF at time ts, the feed conditions (Tin, Fin, O2,in) were step changed from the initial values (T(0), F(0), O2(0)) to new ones (T(s), F(s), O2(s)) as follows:

(11)

H wall = CpgVwρw (T1 − Ts)

∂Ts =0 ∂z

Accounting for the relation between the PM layer consumption and oxygen depletion (eq 2), the transient local PM layer thickness satisfies the relation

The channel entrance and exit pressure drop were calculated as below:10,45

(13b)

T2 = Ts ;

An effective heat transfer coefficient was used to account for the conductive heat loss through the insulation and the convective heat loss to the ambient at the DPF boundary wall:

(9)

Hconv = −h1(Ts − T1) − h2(Ts − T2)

∂Ts = he(Ts − Ta) ∂r

λe =

(8)

The pressure drop across the PM layer and filter wall is computed by Darcy’s Law: μ μ ΔPPM + ΔPwall = Vww + Vwws Kp Ks (10)

∂ 2T ∂ ⎛ ∂Ts ⎞ ⎜w ⎟ + λsws 2s ∂z ⎝ ∂z ⎠ ∂z ∂T ⎞ 1 ∂⎛ ⎜r(ws + w) s ⎟ + λe ⎝ r ∂r ∂r ⎠

T1 = Tin ;

All gas and filter properties were calculated as functions of the local temperature. The effective radial heat conductivity depends on the heat conductivity of the filter wall, PM layer, and gas in the channels and the volume fraction that each occupies:

(7)

⎤ Ma(ρ V2 )z = L ⎡ d2 2 ⎥ + ⎢1 − 2 29T2 2(d + Ws) ⎦ ⎣

V1 = 0;

λe

(6)

∂ (ρ Vβ2) = −α1μVβ /d 2 ∂z β

V2 = 0;

at z = 0

where E is the apparent activation energy, ko is a preexponential factor, and y is the oxygen mass fraction. In the simulation, the apparent activation energy of 137 kg/mol43 and pre-exponential factor of 6.0 m/s K44 are used. We used a one-dimensional model that has been extensively described in the literatures3−11 to predict the PM regeneration in each set of inlet−outlet channels based on its inlet flow. The mass, momentum, and energy balances of the exhaust gas in the inlet (β=1) and outlet (β=2) channels are

∂z

(13d)

The corresponding boundary conditions are

⎛ E ⎞ ko2(Ts) = koTs exp⎜ − ⎟s p ⎝ RTs ⎠

∂Pβ

dw /M p dt

11357



Article

a ramp. The magnitude of the temperature rise decreases if the change in the feed conditions is reversed before the transient temperature excursion reaches its maximum, which is of the order of 2−3 min in the examples we considered. The maximum temperature depends on the time when the feed conditions are changed, the largest occurring when the peak of the temperature wave is in the middle of the DPF length (z/L = 0.5).15 The goal of our simulations was to determine the impact of using a cone to feed the DPF on the amplitude of the transient temperature rise following a rapid shift to idle and of the conditions affecting its amplitude. Thus, the simulations were conducted assuming that after the step change occurred the feed conditions remained unchanged until the maximum temperature excursion occurred. Moreover, the step change occurred when the peak of the temperature wave was in the middle of the DPF. Thus, the reported temperature excursions provide a conservative estimate of the largest amplitude of the temperature rise following a rapid shift to idle drive conditions. The simulations were conducted assuming that a 50 mm long inlet cone connected the DPF to the exhaust pipe, the radius of which was 25 mm (i.e., L′/R′ = 2). A schematic of the filter shape and dimension is presented in Figure 1b. We assumed that the DPF was surrounded by a 6 mm insulation layer with a heat conductivity of 0.1 W/(m·K).46 The ambient air temperature was assumed to be constant at 25 °C. Therefore its heat transfer coefficient was 20 W/(m2 K). Simulations were conducted to determine the impact of using a cone to feed a commercial cordierite DPF. The PM deposit was generated by filtration of exhaust gases containing 0.02 g PM/kg fed at the rate of 250 kg/h through the inlet cone. The 2-D filtration model used previously41 was used in the present simulations. This model was validated with laboratory experiments by Fino et al.38,47 Details of the model validation were presented in our previous work.41 We assumed that the initial cordierite filter porosity was 48% and filter mean pore diameter was 12.5 μm. The Ergun’s equation48 predicted that the corresponding filter initial permeability was 4.3 × 10−13 m2. According to the Konstandopoulos et al.42 the PM deposition inside the filter wall continued until its permeability decreased to 1.4 × 10−13 m2, causing a shift to cake filtration. Konstandopoulos et al.49 reported that the PM packing density and permeability remain constant if the Peclet number exceeds 1. In all our simulations the minimum filtration velocity was 2.2 cm/s so that the Peclet number exceeded 1.4. Therefore, we assumed that the PM permeability and density did not change during the filtration step. On the basis of the reported PM deposition in commercial DPFs we assumed that the PM permeability was 1 × 10−14 m2 and its density was 100 kg/m3. The properties of the PM deposit are reported in Table 1. The thickness of the deposited PM layer depended on the radial position of the inlet channel. The largest load was at the DPF center inlet channel. These predicted features closely agree with experimental results reported by Harvelet al.40 In all our simulations, unless otherwise stated, the regeneration was started after an average PM deposition of 6 g/L. The PM load was periodically removed by combustion (regeneration) that generated a moving temperature wave. Initially the PM regeneration was conducted under the initial inlet conditions: T (0) = 550 °C,

F(0) = 250 kg/h,

Table 1. Properties of Cordierite DPF and PM Deposit DPF length DPF diameter cell density wall thickness porosity of clean filter mean pore size of clean filter filter wall permeability

clean fully loaded

bulk density of pm deposit permeability of pm deposit

0.254 m 0.144 m 200 cpsi 12 mil (0.3 mm) 48% 12.5 μm 4.3 × 10−13 m2 1.4 × 10−13 m2 100 kg/m3 1 × 10−14 m2

After the peak of the temperature wave reached the middle of the DPF, we simulated a rapid shift to idle by a step change of the inlet conditions to T (s) = 300 °C,

F(s) = 50 kg/h,

O2 (s) = 15% (21)

Typical axial and radial variations of the temperature and deposited PM during the regeneration are shown in Figure 2.

Figure 2. Spatial (a) temperature and (b) PM deposit at four times in a DPF fed with a cone following a step change in the feed conditions 22.5 s after the start of the regeneration.

The PM combustion proceeded by a moving temperature wave (Figure 2a) that formed close to the upstream. Its peak temperature increased as it moved downstream. The inlet conditions were step changed 22.5 s after the start of the regeneration. At that time the temperature wave reached the middle of the DPF (z = L/2). The PM profiles in Figure 2b show that initially the regeneration consumed the PM in the upstream of the DPF and propagated downstream. After the step change of the inlet conditions, the PM combustion slowed

O2 (0) = 7% (20) 11358



Article

down. The highest peak temperature was attained at the end of the DPF at t = 140 s. Subsequently the hot region slowly exited the reactor due to the cooling of the filter by the exhaust gas. At t = 140 s, some unburned PM remained in the DPF front and rear part. The remaining PM near the DPF exit eventually was combusted during the DPF cooling. However, unburned PM at the DPF front was not combusted by the end of the regeneration. During the next PM filtration the small amount of residual PM increased the flow resistance in these flow channels. This increased the filtration velocity and PM deposition in the channels in which all the PM was burned during the previous regeneration. This caused the axial and radial deposited PM profiles at the end of the filtration step to be indistinguishable from those in a clean DPF. Temporal radial inlet velocity profiles are shown in Figure 3 at 0, 22.5, 100, and 150 s after the start of the regeneration. The

Figure 4. (a) Temporal maximum regeneration temperatures by a stationary feed (defined by eq 20) in a DPF fed by a cone (solid line) and one without a cone (dashed line). (b) Temporal maximum regeneration temperatures following a step change to idle operation (from eq 20 to eq 21) at t = 22.5 s in the two types of DPF configurations. (c) Radial position at which the temporal maximum temperature occurs following a step change to idle in a DPF fed by a cone.

The shift to idle operation increased the peak regeneration temperatures from 958 °C (stationary feed) to 1274 °C (transient feed) for a DPF with a cone and from 927 °C (stationary feed) to 1140 °C (transient feed) for a DPF without a cone. The peak temperature increase following the step change in a DPF fed by a cone exceeded by 134 °C that in one not fed by a cone. The highest regeneration temperatures following a step change in a DPF not fed by cone were usually lower than the cordierite DPF melting temperature of 1200 °C. In contrast, the highest predicted temperature in a DPF fed with cone following a step change exceeded 1200 °C. The shift to idle operation increased the regeneration time. In the case shown in Figure 4, the DPF regeneration was completed in about 75 s under stationary feed, while it took 200 s following the step change to idle. The radial positions at which the temporal maximum temperatures were reached in a DPF fed by a cone following a shift to idle are shown in Figure 4c. This maximum temperature was initially reached at the DPF center. It shifted for t > 59 s to inlet channels at other radial positions. The maximum temperature reached its peak at t = 140 s in channel no. 5 (r/R ≈ 0.25). In contrast, the highest temperatures in DPF not fed by a cone were always at its center and the maximum was reached at t = 113 s. A DPF filter may be damaged by a local high transient temperature rise either by melting or by cracking.7,10,16,51,52 The temperature gradients for DPF with a cone were always higher than those in DPF not fed by a cone. The highest temporal radial and axial temperature gradients generated during regeneration of a DPF fed by a cone following a shift to idle operation were much higher than those under stationary operation. This was expected as the highest temperature following a shift to idle was higher than that under stationary operation. In the case shown in Figure 4a,b, the temperature excursions following a shift to idle increased at most by 30%. Figure 5 shows that this shift can more than double the corresponding temperature gradients. The radial temperature gradients were larger than the axial ones under stationary feed. However, the axial temperature gradients were almost as large

Figure 3. Radial inlet velocity at different times after start of PM regeneration in a DPF fed by a cone.

average remaining PM load at these times was 100, 49, 2.2, and 0.5% of the initial deposit. The entry velocity into the DPF channels at the start of the regeneration (t = 0 s) was nonuniform with the highest at the DPF center (Figure 3a). The velocity into the inlet channels decreased with distance from the axis, reaching a local minimum at r/R ≈ 0.7 and then increased close to the wall. This velocity increase next to the wall was caused by the radial pressure increase next to the wall that pushed the fluid through the exterior inlet channels. A similar behavior was observed experimentally by Stratakis and Stamatelos.37 Similar features were also observed in experiments and simulations of the flow through a monolith fed by a high-angle diffuser.50 The locus of the velocity into the inlet channels are shown as a continuous line in Figure 3a. For simplicity, we show just the velocity locus in the other figures. Following a step change in the inlet conditions at t = 22.5 s, the average velocity decreased as the inlet flow rate and inlet temperature decreased. A velocity drop near the wall, shown by Figure 3b at t = 22.5 s, was caused by the radial heat loss that decreased the PM regeneration rate near the DPF wall. By the end of the regeneration, the inlet velocity became identical to that in a clean DPF with a lower average inlet velocity. Figure 4b shows by a solid (dashed) line the temporal variation of the maximum regeneration temperature at any location in a DPF fed by a cone (without a cone) following a rapid change in the inlet conditions at t = 22.5 s. For comparison, the transient maximum regeneration temperature under stationary feed defined by eq 20 is shown in Figure 4a. 11359



Article

Figure 7. Comparison of the inlet velocity into central channel no. 1 during the regeneration under a feed with a cone (solid line) to that without one (dashed line).

increased flow resistance in the center decreased the inlet velocity in channel no. 1. Meanwhile, as the temperature increased faster in channel no. 1, the deposited PM in it started to burn first and at a higher rate. Eventually the flow resistance decreased as the PM burning became dominant, and the inlet velocity in channel no. 1 started to increase. In contrast in a DPF not fed by a cone (dashed line), the inlet velocity to the center channel no. 1 remained essentially constant before shifting to idle. After the step change (at t = 22.5 s in Figure 7) the two inlet velocities (V1) became identical and V1 in the DPF fed by a cone gradually became slightly higher toward the end of the regeneration. Figure 8 compares the PM thickness profiles during the DPF regeneration in channel no. 1 fed by a cone (solid line) with the

Figure 5. Comparison of the temporal maximum radial (solid line) and axial (dashed line) temperature gradients in a DPF fed by a cone under stationary feed and that following a shift to idle.

as the radial gradients following a shift to idle. The largest axial and radial temperature gradients were generated near the end of the DPF, so that a thermal crack is mostly expected to occur there. The amplitude of the temperature gradient depends on the maximum regeneration temperature which is affected by the inlet cone, the heat loss through the insulation mat, and the initial PM distribution. Figure 6 compares the temporal axial temperature profiles in channel no. 1 in a DPF fed by a cone (solid line) with that in

Figure 8. Comparison of temporal PM layer thickness in the central channel no. 1 during regeneration of a DPF fed with a cone (solid line) to that not fed by a cone (dashed line).

Figure 6. Comparison of the axial temperature profiles in channel no. 1 at several times during PM regeneration between a DPF fed with a cone (solid line) and without one (dashed line).

one not fed by a cone (dashed line). At the start of the regeneration (t = 0 s) the PM layer thickness in channel no. 1 fed by a cone is higher than in the one not fed by a cone due to the higher inlet velocity during the filtration step. Comparison of the PM profiles in channel no. 1 at t = 10 and 20 s, that is, before the step change to idle, indicates that the PM combustion in the DPF fed by a cone was faster than the one not fed by a cone. By t = 20 s, the upstream PM (z < 40 mm) in the DPF fed by a cone was thinner than that in the one not fed by a cone even though the initial PM load was higher in the DPF fed by a cone. However, the PM in the downstream of channel no. 1 in the DPF fed by a cone was still higher than that in the DPF not fed by a cone before the shift to idle at t = 22.5 s. After the step change the PM burned at a similar rate in both cases. The above simulations were conducted for a DPF with an initial PM load of 6 g/L. Additional simulations were

one not fed by a cone (dashed line). The maximum regeneration temperature in channel no. 1 fed by a cone always exceeded that in channel no. 1 which is not fed by a cone. As the temperature waves propagated downstream, the temperature differences between the two cases increased. The highest temperature difference between the two cases shown in Figure 6 was 122 °C attained at the end of the DPF. This difference was affected by the difference in the inlet velocities and of the PM deposit thickness following the filtration step. We compare in Figure 7 the temporal inlet velocity to the central channel of the two cases. Before the shift to idle the inlet velocity to channel no. 1 in a DPF fed by a cone exceeds that in the one not fed by a cone. As the DPF heats up at the beginning of the regeneration, channel no. 1 in a DPF fed by a cone (solid line) heats up faster than the surrounding channels because of the higher inlet gas flow rate. Therefore, initially the 11360



Article

difference of 204 °C occurred for an initial PM loading of 4 g/L. The highest regeneration temperature depends on the initial average PM deposit as well of the values of the simultaneous step changes in the feed temperature, flow rate, and oxygen concentration. In all the previous simulations the original inlet conditions were T(0) = 550 °C, F(0) = 250 kg/h, O2(0) = 7%. Additional simulations (Figures 10−12) were conducted to

conducted to determine the dependence of the initial PM loading and the form of DPF feed on the maximum regeneration temperature rise following a step change to idle. As we predicted, a DPF fed by a cone led to higher peak regeneration temperatures than the one not fed by a cone following a shift to idle under all PM loadings. Obviously, when PM = 0 g/L no regeneration occurs and the temperatures in both cases are equal. When some PM load exists at a low PM loading the flow distribution among the inlet channels for a DPF fed with a cone is rather nonuniform with the highest flow and PM deposition occurring in the center. This causes the highest temperature in a DPF with a cone to exceed that in one without a cone. The highest regeneration temperature following a step change to idle reached a maximum at an intermediate PM loading of about 6 g/L for a DPF fed by a cone and 8 g/L for one not fed by a cone (Figure 9). At a low

Figure 10. Peak regeneration temperature dependence on the initial inlet temperature following a step change to idle in a DPF fed by a cone (solid line) and one without it (dashed line). Other properties are F(0) = 250 kg/h, O2(0) = 7% and T(s) = 300 °C, F(s) = 50 kg/h, O2(s) = 15% and PM = 6 g/L.

determine which of the initial feed conditions T(0), F(0) and O2(0) had the most dominant effect on the temperature excursions. In all these simulations the initial PM loading was 6 g/L and the step change shifted the feed to T(s) = 300 °C, F(s) = 50 kg/h, O2(s) = 15%. Figure 10 shows that the highest regeneration temperature is a monotonically increasing function of the initial inlet gas temperature in a DPF fed either with or without a cone. However, unlike the case of a stationary feed, the temperature rise in the DPF was not a linear function of the feed temperature. The highest temperature attained in a DPF fed by a cone always exceeded that attained in one not fed by a cone. The highest temperature difference of 236 °C occurred when the initial inlet temperature was 500 °C. The lowest temperature difference of 134 °C occurred when the initial inlet temperature was 550 °C. A decrease of the initial inlet temperature decreases the maximum regeneration temperature, and this may avoid local DPF melting. However, a large decrease in the feed temperature may significantly decrease the combustion rate so that the regeneration will not consume all the PM. Figure 11 indicates that the maximum regeneration temperature attained in a DPF fed either with or without a cone are rather insensitive to variations in the initial inlet flow rate, F(0). The reason is that the increase in the heat generation upon an increase in F(0) is almost the same as the increase in the heat removal by convection from the DPF. For example, the maximum regeneration temperature obtained inside the DPF with an inlet cone before the shift to idle was 860, 869, and 878 °C for F(0) equals to 250, 150, and 50 kg/h, respectively. Hence, upon a shift to idle to the same flow rate F(s), oxygen concentration O2(s) and feed temperature T(s), the final maximum regeneration temperatures are almost the same. The regeneration temperature following the shift to idle is however sensitive to the new decreased feed flow rate, F(s). The simulations showed that in a DPF fed by a cone following a step change to idle the highest regeneration

Figure 9. Dependence of the peak regeneration temperature on the initial PM loading for a DPF fed by a cone (solid line) and one with no cone (dashed line) following a step change to idle from T(0) = 550 °C, F(0) = 250 kg/h, O2(0) = 7% to T(s) = 300 °C, F(s) = 50 kg/h, O2(s) = 15%.

initial PM loading, as abundant oxygen was available for the PM oxidation, the limiting reactant was the PM. Increasing the PM loading increased the oxidation rate and hence the heat generation. Therefore, the highest regeneration temperature following a step change to idle was a monotonic increasing function of the initial PM loading at low PM loadings. At a PM loading above 6 g/L for a DPF fed by a cone and 8 g/L for one not fed by a cone, the highest regeneration temperature monotonically decreased following a shift to idle. This decrease in the highest regeneration temperature upon an increase in the PM loading occurred only following a step change to idle. It is due to the large decrease in the flow rate and feed temperature upon the step change to idle. When the shift to idle operation started, most PM in the upstream was combusted leaving a large amount of PM in the downstream (see Figure 2b). Higher initial PM loading led to a higher residual PM amount and hence higher downstream flow resistance. This pushed more flow to the upstream decreasing the availability of oxygen and reaction rate. The PM combustion in the downstream was incomplete in these cases, even though the feed oxygen concentration increased following the step change. The resulting incomplete downstream combustion decreased the highest regeneration temperature with increasing PM loading following a step change to idle. Because of the decrease in the maximum regeneration temperature between the two cases at high PM loading, the maximum difference between the two cases following a rapid shift to idle was at some intermediate initial PM loading. For the simulations shown in Figure 9 this 11361



Article

cone did not occur in a DPF not fed by a cone. The reason is that in a DPF fed by a cone the velocity to inlet channels depends on the radial position and is time dependent. However, in a DPF not fed by a cone, the inlet velocity and the PM layer in all the channels are identical. Hence, when the heat generation increased with the increased oxygen concentration, the change in the rate of the heat removal was rather small. Hence, the maximum regeneration temperature for DPF without an inlet cone always increased as the oxygen concentration increased. However, the rate at which this peak temperature increased was initially increased then decreased upon an increase in the oxygen concentration. It is because the reaction rate depends mainly on the oxygen concentration under low initial oxygen concentrations.1 When the oxygen concentration is high, the PM loading became another major effect on reaction rate. The highest regeneration temperature in a DPF fed by a cone exceeded that of one fed without a cone including under 0% initial oxygen concentration. When the initial oxygen concentration is 0%, no reaction occurs. Following a shift to idle, the inlet gas temperature was lowered to 300 °C while the oxygen concentration was increased to 15%. Because the oxygen concentration wave travels faster than the temperature wave, a reaction occurs in the still hot DPF regions. Since the initial PM loading in the center inlet channel in a DPF fed with cone is higher than that in a DPF not fed by a cone, it attains a higher PM regeneration temperature. The highest temperature following a step change to idle for a feed containing initially more than 4% oxygen was sufficiently high to cause cordierite filter local melting in a DPF fed by a cone. Normally the oxygen concentration is around 7%. It is difficult to control the diesel engine initial oxygen concentration to be around 4% to avoid the filter melting in such an extreme case. Simulations examined how the idle state (T(s), F(s), O2(s)) affects the maximum regeneration temperatures when the initial feed is described by eq 20. Table 2 reports the results of

Figure 11. Peak regeneration temperature dependence on the initial inlet flow rate following a step change to idle of a DPF fed by a cone (solid line) and one without it (dashed line). Other properties are T(0) = 550 °C, O2(0) = 7% and T(s) = 300 °C, F(s) = 50 kg/h, O2(s) = 15% and PM = 6 g/L.

temperatures always occurred in the DPF central region where r < 0.5R. Under our specific cone geometry and regeneration conditions, an increase in the initial oxygen concentration from 0% to 8% following a shift to idle in a DPF fed by a cone increased the maximum regeneration temperature. However, increasing the initial inlet oxygen concentration from 8% to 15% caused a small decrease in the maximum regeneration temperature. This behavior was caused by the opposing impact of the increase in the heat generated by the PM combustion and the increase in the heat convected by the exhaust gases. As the oxygen concentration was increased, more heat was generated, especially in the DPF central region because of the higher flow rate there when the DPF is fed by a cone. The PM combustion in the central region decreased the flow resistance, which, in turn, increased the flow through the central channels. When the oxygen concentration was increased from 0% to 8%, the increase in the combustion heat was higher than the increase in heat removal by convection. However, at oxygen concentration exceeding 8%, the increase in the heat removal exceeded the increase in the heat generated by the PM combustion. This caused a slight decrease in the maximum regeneration temperature with increasing oxygen concentration. However, in a DPF fed without an inlet cone (dashed line in Figure 12) a higher initial oxygen concentration always increases the peak regeneration temperatures. The opposing impact of the change in the oxygen concentration on the heat generation and heat removal which occurred in a DPF fed with

Table 2. The Maximum Regeneration Temperature Dependence Following a Change from the Initial Inlet Conditions Described by eq 20 to a New Feed State (T(s), F(s), O2(s)) with Initial PM = 6 g/L

case case case case

no. no. no. no.

1 2 3 4

T(s) [°C]

F(s) [kg/h]

O2(s) [%]

max T with cone [°C]

max T with no cone [°C]

550 300 300 300

50 50 250 50

15 15 15 7

1320 1274 1127 1022

1131 1140 1077 983

simulations in which two of the three idle states were changed leaving the third unchanged. The table reports the highest regeneration temperatures in a DPF fed with and without a cone. The highest regeneration temperature in a DPF fed by a cone occurred in case no. 1, in which the inlet temperature remained constant following the shift to idle operation, while the inlet flow rate and oxygen concentration were step changed. The second highest temperature occurred when all three inlet conditions step changed. The lowest maximum regeneration temperature was obtained when the oxygen concentration remained constant after the step change. Therefore, avoiding an increase in the oxygen concentration following a shift to idle is the most effective means to minimize the temperature excursion during the PM combustion. Reggie Zhan et al.12

Figure 12. Peak regeneration temperature dependence on the initial oxygen concentration following a step change to idle of a DPF fed by a cone (solid line) and one without it (dashed line). Other properties are T(0) = 550 °C, F(0) = 250 kg/h and T(s) = 300 °C, F(s) = 50 kg/ h, O2(s) = 15% and PM = 6 g/L. 11362



Article

prediction of the magnitude of this difference and its dependence on the operating conditions. The major impact of the cone on the DPF is that it leads to a difference in the entry velocity between inlet channels located at different radial positions. The highest velocity is to the channel at the DPF center. The inlet velocity attains a local minimum close to r/R ≈ 0.7 and becomes more uniform following the PM deposition. Owing to the different entry velocities, following the PM deposition the thickest PM layer is at the center of the DPF. Another local maximum in the deposited layer thickness forms close to the DPF boundary wall. In contrast, when a DPF is not fed by a cone, the same PM deposit thickness forms in almost all inlet channels. A slightly thicker layer forms next to the wall due to the wall heat loss which decreases the gas viscosity, which, in turn, increases its velocity. The impact of the connection of the exhaust pipe to the DPF on the highest regeneration temperature is higher following a rapid step change to idle than under stationary feed conditions. In the example shown in Figure 4, the shift to idle increased the peak regeneration temperatures from 958 °C (stationary feed) to 1274 °C in a DPF fed by a cone and from 927 °C (stationary feed) to 1140 °C in a DPF not fed by a cone. The peak regeneration temperature in a DPF fed by a cone exceeded the cordierite DPF melting temperature (1200 °C) following a step change to idle. Similarly, a step change to idle led to transient radial and axial temperature gradients several times higher than under stationary regeneration (Figure 5). The increase in the thermal gradient is especially large in the axial direction, causing it become almost as large as the radial one. An interesting finding is that the maximal radial and axial temperature gradients are both encountered in the downstream of the DPF. A thermal crack is mostly expected to occur at that location. The highest regeneration temperature in a DPF is strongly affected by the initial PM load, and the exhaust oxygen concentration, temperature, and flow rate both before and after the step change to idle. The highest temperature in a DPF fed with a cone always exceeds that in one not fed by a cone. The most effective strategy to bind the regeneration temperature is to control the oxygen concentration after the step change to idle, to start the regeneration when the PM load is relatively low, and to have a gradual shift rather than a step change to idle. The nonuniformity of the inlet velocities, which causes temperature rise in a DPF fed by cone to exceed that in DPF not fed by cone, depends on the ratio between the pressure drop in the cone to that in the DPF. The larger this ratio is (which depends among others on the cone geometry, feed flow rate, DPF dimension and PM loading) the less uniform is the velocity among the inlet channels and the higher is the temperature increase following a shift to idle. In the cone used in our simulation (L′/R′ = 2) the maximum excess temperature rise following a shift to idle was 1274 − 1140 = 134 °C. Using a longer cone (L′/R′ = 10) led to a much smaller temperature rise of 1214 − 1140 = 74 °C. In the limit of a very long cone the maximum temperature rise is equal to that of a DPF not fed by a cone. Simulations showed that following a shift to idle the flow distributions at the inlet channels and maximum DPF regeneration temperatures were insensitive to the channel entrance and exit pressure drop. The simulations revealed some nonobvious dependence on the operation conditions. First, in a DPF fed either with or without a cone, the highest regeneration temperature following

described an effective method to maintain a constant oxygen concentration during transient regenerations. The highest regeneration temperature in a DPF not fed by a cone occurred following a step change of all three inlet gas properties. The lowest was again obtained when the oxygen concentration was kept constant following the shift to idle. Table 2 shows another surprising impact of feeding the DPF by a cone on the temperature excursion following a step change. A comparison of the temperature rise in cases no. 1 and no. 2 indicates that a decrease in the feed temperature following a step change from 550 to 300 °C lowered the maximum regeneration temperature of DPF with cone by 46 °C from 1320 to 1274 °C. However, in a DPF not fed by a cone the maximum regeneration temperature increased by 9 °C from 1131 to 1140 °C. This difference in the response to the same step change is rather surprising and counterintuitive. It is of interest to determine the impact of the entrance and exit pressure drop effects on the temperature rise in a DPF fed by a cone following a shift to idle. Simulations using the experimentally validated eq 1110,45 revealed that at the beginning of the filtration accounting for the entrance and exit effects increased the pressure drop at the center of the cone fed DPF by 2.0% and decreased the entry velocity into the center channel no. 1 by 7%. However, the velocity difference quickly dissipated after the start of the filtration. When the average PM loading was 6 g/L, the average PM thickness in the DPF center channel no. 1 accounting for the end effects was smaller by 0.72 μm from that when the end effects were not accounted for. This difference is very small relative to the average PM layer thickness in channel no. 1 at that instant (=85.85 μm). We simulated the regeneration of a DPF containing 6 g/L PM by a feed with an inlet temperature of 550 °C. When the temperature wave peak reached the middle of the DPF, we step changed the inlet conditions from T(0) = 550 °C, F(0) = 250 kg/h, O2(0) = 7% to T(s) = 300 °C, F(s) = 50 kg/h and O2(s) = 15%. The flow distribution and maximum regeneration temperatures were practically the same for these two cases. Accounting for the entrance and exit effects throughout the whole regeneration process increased the entry velocity to channel no. 1 by less than 0.5% and the maximum regeneration temperature by 0.2 °C. Additional simulations conducted accounting and not accounting for the entrance and exit pressure drop revealed that the flow distributions at the DPF inlet and maximum regeneration temperatures were essentially the same following a sudden shift to idle.

4. CONCLUDING REMARKS In various cases a DPF is connected by a wide-angled cone to the engine exhaust pipe. Examples are the recently developed catalytic DPFs24−30 that simultaneously remove the PM and oxidize the effluent organic compounds, and the new DPFs31−35 that reduce both the PM and NOx emissions. A potentially dangerous temperature excursion occurs following a rapid deceleration of the diesel engine or a sudden shift to idle. In these cases the increase in the oxygen concentration increases the rate of the heat generation, while the decrease in the flow rate decreases the rate of heat removal from the DPF. This may lead to a transient local excessive temperature rise. This study points out that the highest transient temperature rise following a step change to idle in a DPF depends on the way it is connected to the exhaust pipe and is higher when the connection is by a cone. Simulations of our model enable 11363



Article

wall boundary condition, which is a standard option in COMSOL. The DPF channel inlet pressures were used as the cone outlet conditions. Unstructured mesh was applied, the number of which depends on the shape of the cone and predefined mesh parameters. Additional edge mesh is placed near the cone boundaries to better capture the turbulent flow features near the wall. The axi-symmetry model calculates the behavior on one radius of the circular cone. The flow at the end of the cone (DPF face) cannot enter into the areas occupied by the exit channels and the DPF walls. The flow hitting a solid area flows radially and enters into the adjacent inlet channels. The flow distributions coming out of the cone at several regeneration times were shown in Figure 3. Values of the turbulent flow model parameters are determined in experiments54,55 and are included in the COMSOL turbulent model (eq A9). Using the standard k−ε model, values of three parameters need to be adjusted in any specific application: the turbulent intensity, the dissipation length scale at the inlet and the distance from the wall in the logarithmic wall function. We checked the sensitivity of the peak DPF inlet velocity to a ± 10% change in the value of each of these parameters. The perturbation in the value of the inlet turbulent intensity of the inlet dissipation length scale and of the distance from the wall in the logarithmic wall function changed the peak DPF inlet velocity by less than ±0.04%, ∓0.04%, and ∓0.7%, respectively. These calculations show that the velocity distributions are insensitive to changes in the values of these three parameters. This implies that the peak regeneration temperatures are insensitive to the values of these turbulent model parameters.

a step change to idle increases monotonically with the initial PM loading for loading up to a critical value, but decreases upon a further increase. Second, as Figure 12 shows in a DPF fed by a cone the highest regeneration temperature following a step change to idle increases with the initial oxygen concentration up to a critical concentration but decreases upon a further increase of the initial oxygen concentration. This behavior was not observed in a DPF not fed by a cone. Last, when the inlet temperature was decreased from 550 to 300 °C, the maximum regeneration temperature for DPF with no cone increased 9 °C compared with that from constant inlet temperature of 550 °C, but this counterintuitive response did not occur in a DPF fed with cone.

■

APPENDIX COMSOL 3.5a standard k-ε model was used to calculate the incompressible turbulent flow inside the cone.53−55 The governing mass and momentum conservation equations are: ∇·U⃗ = 0

(A1)

ρU⃗ ·∇U⃗ = −∇P⃗ + ∇·τ

(A2)

where U⃗ is the local (time-averaged) velocity vector, ρ and P⃗ are the local (time-averaged) fluid density and pressure, and τ is the shear stress tensor accounting for both the viscous and turbulent contributions:

τ = μeff ∇U⃗

(A3)

μeff = μ + μt

(A4)

■

Here μeff is the effective viscosity, μ is the intrinsic flow viscosity and μt is the turbulent eddy viscosity. According to the k-ε model: k2 μt = ρCμ ε′

*E-mail: [email protected]. Notes

(A5)

The authors declare no competing financial interest.

■ ■

where k is the turbulent kinetic energy and ε′ is the turbulent dissipation. The turbulent kinetic energy and dissipation are predicted by the equations: ⎛μ ⎞ ⃗ = ∇·⎜ t ∇k ⎟ + G k − ρε′ ∇·(ρU) ⎝ σk ⎠

(A6)

⎛μ ⎞ ε′ ∇·(ρU⃗ ε′) = ∇·⎜ t ∇ε′⎟ + (C1G k − C2ρε′) k ⎝ σε′ ⎠

(A7)

ACKNOWLEDGMENTS We thank the NSF and the BSF for partial financial support of this research.

where Gk is the generation term for k, G k = τ: ∇U⃗

(A8)

We use the commonly reported values for the dimensionless k−ε model parameters:53−55 Cμ = 0.09, σε ′ = 1.3

C1 = 1.44,

C2 = 1.92,

AUTHOR INFORMATION

Corresponding Author

σk = 1, (A9)

The properties of the fully developed turbulent flow in the circular pipe are used to specify the velocity profile at the cone inlet. Besides, the turbulent intensity and dissipation length scale at the inlet as well as the inlet temperature are defined. According to the guidelines for specifying these two numbers, 5% is used for the intensity and 0.0035 for the dissipation length scale.54 We use a logarithmic wall function as the cone 11364

NOMENCLATURE: cpsi = cell density, cells/in2 Cp = heat capacity, J/(kg·K) d = hydraulic diameter of clean channel, m dpore = filter wall mean pore diameter, μm D = filter diameter, m E = activation energy, J/mol F = flow rate, kg/h h = heat transfer coefficient, W/(m2 K) k = turbulent kinetic energy ko = pre-exponential factor, m/(s·K) ko2 = oxygen reaction rate constant, s−1 Kp = particulate layer permeability, m2 Ks = ceramic wall permeability, m2 L = filter length, m Ma = air molecular weight, 29 × 10−3 kg/mol Mp = particulate molecular weight, 12 × 10−3 kg/mol Mo2 = oxygen molecular weight, 32 × 10−3 kg/mol P = pressure, Pa r = coordinate/radial direction, m ro2 = oxygen reaction rate, mol/(m3 s) dx.doi.org/10.1021/ie300948c | Ind. Eng. Chem. Res. 2012, 51, 11355−11366


Article

(9) Kostoglou, M.; Housiada, P.; Konstandopoulos, A. G. Mutichannel Simulation of Regeneration in Honeycomb Monolithic Diesel Particulate Filters. Chem. Eng. Sci. 2003, 58, 3273−3283. (10) Haralampous, O. C.; Koltsakis, G. C.; Samaras, Z. C. Partial Regenerations in Diesel Particulate Filters. Soc. Automot. Eng. 2003 No. 2003-01-1881. (11) Koltsakis, G. C.; Haralampous, O. A.; Margaritis, N. K.; Samaras, Z. C.; Vogt, C. −D.; Ohara, E.; Watanabe, Y.; Mizutani, T. 3Dimensional Modeling of the Regeneration in SiC Particulate Filters. Soc. Automot. Eng. 2005 No. 2005-01-0953. (12) Zhan, R.; Huang, Y.; Khair, M. Methodologies to Control DPF Uncontrolled Regenerations. Soc. Automot. Eng. 2006 No. 2006-011090. (13) Koltsakis, G. C.; Haralampous, O. A.; Samaras, Z. C.; Kraemer, L.; Heimlich, F.; Behnk, K. Control Strategies for Peak Temperature Limitation in DPF Regeneration Supported by Validated Modeling. Soc. Automot. Eng. 2007 No. 2007-01-1127. (14) Chen, K.; Martirosyan, K. S.; Luss, D. Wrong-Way Behavior of Soot Combustion in a Planar Diesel Particulate Filter. Ind. Eng. Chem. Res. 2009, 48, 8451−8456. (15) Chen, K.; Martirosyan, K. S.; Luss, D. Hot Zones Formation during Regeneration of Diesel Particulate Filters. AIChE J. 2011, 57, 497−506. (16) Boger, T.; Tilgner, I.-C.; Shen, M.; Jiang, Y. Oxide Based Particulate Filters for Light-Duty Diesel ApplicationsImpact of the Filter Length on the Regeneration and Pressure Drop Behavior. Soc. Automot. Eng. 2008 2008-01-0485. (17) Boreskov, G. K.; Slinko, M. G. Modeling of Chemical Reactors. Pure Appl. Chem. 1964, 4, 611−624. (18) Chen, Y. C.; Luss, D. Wrong-Way Behavior of Packed-Bed Reactors: Influence of Interphase Transport. AIChE J. 1989, 35, 1148−1156. (19) Crider, J. E.; Foss, A. S. Computational Studies of Transients in Packed Tubular Chemical Reactors. AIChE J. 1966, 12, 514−522. (20) Hoiberg, J. A.; Lyche, B. C.; Foss, A. S. Experimental Evaluation of Dynamic Models for a Fixed-Bed Catalytic Reactor. AIChE J. 1971, 17, 1434−1447. (21) Mehta, P. S.; Sams, W. N.; Luss, D. Wrong-Way Behavior of Packed-Bed Reactors: I. the Pseudo-homogeneous Model. AIChE J. 1981, 27, 234−246. (22) Pinjala, V.; Chen, Y. C.; Luss, D. Wrong-Way Behavior of Packed-Bed Reactors: II. Impact of Thermal Dispersion. AIChE J. 1988, 34, 1663−1672. (23) Sharma, C. S.; Hughes, R. The Behavior of an Adiabatic Fixed Bed Reactor for the Oxidation of Carbon Monoxide: 2. Effect of Perturbations. Chem. Eng. Sci. 1979, 34, 625−534. (24) Koltsakis, G. C.; Haralampous, O. A.; Dardiotis, C. K.; Samaras, Z. C.; Vogt, C.-D.; Ohara, E.; Watanabe, Y.; Mizutani, T. Performance of Catalyzed Particulate Filters without Upstream Oxidation Catalyst. Soc. Automot. Eng. 2005 No. 2005-01-0952. (25) Mizutani, T.; Watanabe, Y.; Yuuki, K.; Hashimoto, S.; Hamanaka, T.; Kawashima, J. Soot Regeneration Model for SiCDPF System Design. Soc. Automot. Eng. 2004 No. 2004-01-0159. (26) Maly, M.; Claussen, M.; Carlowitz, O.; Kroner, P.; Ranalli, M.; Schmidt, S. Influence of the Nitrogen Dioxide Based Regeneration on Soot Distribution. Soc. Automot. Eng. 2004 No. 2004-01-0823. (27) Dardiotis, C. K.; Haralampous, O. A.; Koltsakis, G. C. Catalytic Oxidation in Wall-Flow Reactors with Zoned Coating. Chem. Eng. Sci. 2008, 63, 1142−1153. (28) Cutler, W. A.; Boger, T.; Chiffey, A. F.; Phillips, P. R.; Swallow, D.; Twigg, M. V. Performance Aspects of New Catalyzed Diesel Soot Filters Based on Advanced Oxide Filter Materials. Soc. Automot. Eng. 2007 2007-01-1268. (29) Peck, R.; Becker, C. Experimental Investigations and Dynamic Simulation of Diesel Particulate Filter Systems. Chem. Eng. Technol. 2009, 32, 1411−1422. (30) York A. P. E.; Watling, T. C.; Ahmadinejad, M.; Bergeal, D.; Phillips, P. R.; Swallow, D. Modeling the Emissions Control Performance of a Catalyzed Diesel Particulate Filter (CDPF) System

R = radius, m 9 = gas constant, 8.3145 J/(mol·K) sp = specific area of PM deposit layer, m−1 t = time, s T = temperature, K U⃗ = local (time-averaged) velocity vector inside cone, m/s V = velocity, m/s Vw = filtration velocity through solid layer, m/s w = particulate layer thickness, m ws = substrate layer thickness, m y = oxygen concentration of the exhaust gas (mass fraction) z = coordinate/axial direction, m Greek Letters: α = oxidation reaction index α1 = constant in square channel pressure drop correlation -ΔH = reaction heat, J/mol ΔP = backpressure, Pa λ = thermal conductivity, W/(m·K) ε = filter porosity ε′ = turbulent dissipation rate μ = exhaust gas viscosity, kg/(m·s) μt = turbulent eddy viscosity, kg/(m·s) ρ = density, kg/m3 ρw = gas density inside solid layer, kg/m3 τ = shear stress tensor Subscripts: 1 = inlet channel 2 = outlet channel a = ambient air e = effective variable en = channel entrance ex = channel exit g = exhaust gas p = particulate layer s = substrate layer in = DPF inlet ins = insulation mat

■

REFERENCES

(1) Higuchi, N.; Mochida, S.; Kojima, M. Optimized Regeneration Conditions of Ceramic Honeycomb Diesel Particulate Filters. Soc. Automot. Eng. 1983, 830078. (2) Chen, K.; Martirosyan, K. S.; Luss, D. Soot Combustion Dynamics in a Planar Diesel Particulate Filter. Ind. Eng. Chem. Res. 2009, 48, 3323−3330. (3) Bissett, E. J. Mathematical Model of the Thermal Regeneration of a Wall-Flow Monolith Diesel Particulate Filter. Chem. Eng. Sci. 1984, 39, Nos. 7/8, 1233-1244. (4) Konstandopoulos, A. G.; Kostoglou, M. Periodically Reversed Flow Regeneration of Diesel Particulate Traps. Soc. Automot. Eng. 1999 No. 1999-01-0469. (5) Haralampous, O. A.; Koltsakis, G. C. Oxygen Diffusion Modeling in Diesel Particulate Filter Regeneration. AIChE J. 2004, 50, 2008− 2019. (6) Haralampous, O. A.; Koltsakis, G. C. Back-Difussion Modeling of NO2 in Catalyzed Diesel Particulate Filters. Ind. Eng. Chem. Res. 2004, 43, 875−883. (7) Miyairi, Y.; Miwa, S.; Abe, F.; Xu, Z.; Nakasuji, Y. Numerical Study on Forced Regeneration of Wall-Flow Diesel Particulate Filters. Soc. Automot. Eng. 2001 No. 2001-01-0912. (8) Konstandopoulos, A. G.; Kostoglou, M.; Housiada, P. Spatial Non-uniformities in Diesel Particulate Trap Regeneration. Soc. Automot. Eng. 2001 2001-01-0908. 11365



Article

for Light Duty Diesel Applications. Soc. Automot. Eng. 2009 2009-011266. (31) Czerwinski, J.; Zimmerli, Y.; Mayer, A.; Heeb, N.; D’Urbano, G. Diesel Emission with DPF+SCR in VERTdePNTesting & Potentials. Soc. Automot. Eng. 2011 No. 2011-01-1139. (32) Tan, J.; Solbrig, C.; Schmieg, S. J. The Development of Advanced 2-Way SCR/DPF Systems to Meet Future Heavy-Duty Diesel Emissions. Soc. Automot. Eng. 2011 No. 2011-01-1140. (33) Hug, H. T.; Mayer, A.; Hartenstein, A. Off-Highway Exhaust Gas After-Treatment: Combining Urea-SCR, Oxidation Catalysis and Traps. Soc. Automot. Eng. 1993, 930363. (34) Rusch, K.; Kaiser, R.; Hackenberg, S. DPF SCR Combinations Integrated Systems to Meet Future LDV Emission Limits. Soc. Automot. Eng. 2006 No. 2006-01-0637. (35) Pischinger, S.; Körfer, T.; Wiartalla, A.; Schnitzler, J.et al. Combined Particulate Matter and NOx Aftertreatment Systems for Stringent Emission Standards. Soc. Automot. Eng. 2007 No. 2007-011128. (36) Stratakis, G. A.; Stamatelos, A. M. Flow Distribution Effects in the Loading and Catalytic Regeneration of Wall-Flow Diesel Particulate Filters. Proc. Inst. Mech. Eng., Part D 2004, 218 (D2), 203−216. (37) Stratakis, G. A.; Stamatelos, A. M. Flow Maldistribution Measurements in Wall-Flow Diesel Filters. Proc. Inst. Mech. Eng., Part D 2004, 218 (D), 995−1009. (38) Bensaid, S.; Marchisio, D. L.; Russo, N.; Fino, D. Experimental Investigation of Soot Deposition in Diesel Particulate Filters. Catal. Today 2009, 147s, s295−s300. (39) Ranalli, M.; Hossfeld, C.; Kaiser, R.; Schmidt, S; Elfinger, G. Soot Loading Distribution as a Key Factor for a Reliable DPF System: An Innovative Development Methodology. Soc. Automot. Eng. 2002 No. 2002−01−2158. (40) Harvel, G. D.; Chang, J.-S.; Tung, A.; Fanson, P.; Watanabe, M. Three-Dimension Deposited Soot Distribution Measurement in Silicon Carbide Diesel Particulate Filters by Dynamic Neutron Radiography. Soc. Automot. Eng. 2011 No. 2011-01-0599. (41) Yu, M.; Luss, D. Inlet Cone Effect on Particulate Matter Deposition and Regeneration Temperature in a Diesel Particulate Filter. Ind. Eng. Chem. Res. 2012, 51, 3791−3800. (42) Konstandopoulos, A. G.; Kostoglou, M.; Skaperdas, E.; Papaioannou, E.; Zarvails, D.; Kladopoulou, E. Fundamental Studies of Diesel Particulate Filters: Transient Loading, Regeneration and Aging. Soc. Automot. Eng. 2000 No. 2000-01-1016. (43) Yezerets, A.; Currier, N. W.; Kim, D. H.; Eadler, H. A.; Epling, W. S.; Peden, C. H. F. Differential Kinetic Analysis of Diesel Particulate Matter (Soot) Oxidation by Oxygen Using a StepResponse Technique. Appl. Catal., B 2005, 61, 120−129. (44) Koltsakis, G. C.; Stamatelos, A. M. Modeling Thermal Regeneration of Wall-Flow Diesel Particulate Traps. AIChE J. 1996, 42, 1662−1672. (45) VDI-Waermeatlas; VDI-Verlag: Duesseldorf, Germany, 1992; Vol. 6. (46) Bauman, J. L.; Brunner, N. R.; Fairbanks, M. A.; Hornback, L. R.; Lindeman, D. D. Relationship Between Substrate Mounting Materials and Diesel Substrate and Shell Surface Temperatures: OnEngine Experimental Testing and Thermal Modeling. Soc. Automot. Eng. 2007 No. 2007-01-1119. (47) Bensaid, S.; Marchisio, D. L.; Fino, D.; Saracco, G.; Specchia, V. Modelling of Diesel Particulate Filtration in Wall-Flow Traps. Chem. Eng. J. 2009, 154, 211−218. (48) Adler, J. Ceramic Diesel Particulate Filters. Int. J. Appl. Ceram. Technol. 2005, 2, 429−439. (49) Konstandopoulos, A. G.; Skaperdas, E.; Masoudi, M. Microstructural Properties of Soot Deposits in Diesel Particulate Traps. Soc. Automot. Eng. 2002 No. 2002-01-1015. (50) Benjamin, S. F.; Haimad, N.; Roberts, C. A.; Wollin, J. Modeling the Flow Distribution through Automotive Catalytic Converters. Proc. Inst. Mech. Eng., Part C 2001, 215 (4), 379−383.

(51) Murtagh, M. J.; Sherwood, D. L.; Socha, L. S., Jr. Development of a Diesel Particulate Filter Composition and Its Effect on Thermal Durability and Filtration Performance. Soc. Automot. Eng. 1994, 940235. (52) Guo, Z.; Zhang, Z.; Sheng, B.; Peng, W. Three-Dimensional Transient Elastic Thermal Stress Field during Diesel Particulate Filter Regeneration. J. Eng. Gas Turbines Power 2009, 131, 012802−1. (53) Karvounis, E.; Assanis, D. N. The Effect of Inlet Flow Distribution on Catalytic Conversion Efficiency. Int. J. Heat Mass Transfer 1993, 36, 1495−1504. (54) COMSOL 3.5 Manual; COMSOL. AB.: Burlington, MA, 1997. (55) Wilcox, D. C. Turbulence Modeling for CFD; DCW Industries, Inc., 1998.

11366


Inlet Cone Effect on Diesel Particulate Filter Regeneration upon a

Recommend Documents