sp k1,k(Tw)w



k ) 1, 2 (12)

Conse rvation of Ene rgy of the Channe l Gas。 The following term s ar e tak en into account : convective heat exchan ge with th e chann el wall an d th e entha lpy flowing into or from th e  elementar y  contr ol  volum e thr ough th e filter wall。 For th e inlet chann el, th e gas leaves th e contr ol volum e  at  temperatur e T1:

exp - Rk

vw

Ene rgy Ba lance in the Wall。 The energy balance equat ion for th e wall should tak e into  account  th e contr ibut ion of convective heat tran sfer from th e chan - nel flow an d from th e flow thr ough th e wall, th e    heat

2 2 released  by  exoth erm ic soot combustion, an d  th e con-

Cp,g[D F1v1 T1|z+∆z - D F1v1 T1|z + 4D∆zFwvw T1|z] )

h14D∆z(Tw - T1) (7)

ductive heat  tran sfer along th e chann el  wall:

 ∂ (F wC

T   +F w C

T ) ) h (T

- T ) +

On th e oth er han d, for th e outlet chann el, th e gas ent ers

∂t p

p,p   w

s     s    p,s    w

1 1 w

th e contr ol volum e at  temperatur e Tw:

h2(T2 - Tw) + FwvwCp,g(T1 - Tw) + H react + Hcond

(13)

2 2

Cp,g[D F2v2 T2|z+∆z - D F2v2 T2|z - 4D∆zFwvw Tw|z] )

h24D∆z(Tw - T2) (8)

Mass  Ba lance  for the  Deposit   Laye r。 Ass um ing

From th e equat ion for th e consum ption rat e of th e deposit (eq 12), th e heat released by th e overall reaction exp ressed  per un it time is comput ed:

that both reactions (1) an d (2) ar e first order in th e oxidant s (O2 an d NO2, respe ctively) an d that diffu sion is negligible  compar ed  to convection, th e oxidant s bal-

2

H react ) -

k)1

∆Hk

Mk

1

Fwvwy

Rk

1 - exp-

sp k1(Tw)w

vw

ance equat ion in th e exhau st gas  is

 ∂

∂x(Fgvyk) ) -sjkj,kFgykRk j ) 1, 2 an d k ) 1, 2 (9)

where th e subscript j ident ifies regions 1 (deposit) an d 2 (porous wall) an d th e subscript k identifies th e gaseous

k ) 1, 2 (14)

∆Hk indicat es a combined reaction entha lpy res ulting from th e complete an d incomplete oxidat ion of car bon in th e two cases of soot-O2 an d soot-NO2 reactions, which is linked  to R according to th e  relat ions

reactant s of th e reactions (1) an d (2) (O2 an d NO2, respe ctively)。 Becau se th ere is no reaction in th e porous

∆H1 ) 2(R1 - 0。5)∆HCO

+ 2(1 - R1)∆HCO (15)

wall, k2 ) 0。 The coefficie nt k1 for th e deposit is assum ed to be an Arrh enius-type function of temperatur e, an d th e following rat e exp ression is used for th ese reactions:

∆H2 ) (1 - R2)∆HCO

+ (R2 - 0。5)∆HCO - R2∆H NO

(16)

k1,k

) k  T e-Ek/RT (10)

The contr ibut ion of  heat conduction is

As far as th e reaction with O2 is concern ed, th e values of th e kinetic rat e param eters can be tak en from previous expe rience (Table 5)。25 Any minor ina ccura cies

Hcond  ) -λp

∂  w