4 p   {Mg

Equat ion 16 is int egrat ed num erically over th e soot layer th ickn ess 。

For norma l operat ing conditions, th e var iat ion of th e gas density due to press ur e loss thr ough th e wall is negligible 。 Moreover, th e Forchh eimer term an d th e slip corr ection can  be neglected。27

µvw

dur ing each steady-stat e point of th is tes t。 The sam e gra ph prese nt s th e comput ed evolut ion of soot ma ss in th e filter dur ing th e tes t。 There is no direct way to validat e th is res ult expe rimenta lly。 Howeve r, th e usua l practice is to compar e th e measur ed an d comput ed press ur e drops, which is a good indicat ion of th e soot ma ss evolut ion。 This compar ison is give n in th e middle gra ph of Figur e 5, togeth er with th e measur ed exhau st ma ss flow  rat e。

∆pwall )

ws (23)

s

The bottom gra ph prese nt s th e measur ed NOx an d NO2 emissions up- an d downstr eam of th e filter, to- geth er  with  th e  comput ed  NO2   concentrat ion down-

The checkered  face  of  th e  filter  cau ses  a  sudde n

contra ction of  th e  flow  at  th e  inlet  an d  a  sudde n exp an sion at th e out le t。 These press ur e losses can be assessed  with th e followi ng formu las respe ctively:28

str eam of th e filter。 The fraction of NO2/NOx at th e filter inlet depe nds on th e activity of th e (nonoptimized) oxidat ion cata lyst with respe ct to NO oxidat ion to NO2。

Our  measur ement s  indicat ed   that   th e   NO  to  NO

contra ction 

2

2Fvchan _in

2

conve rsion efficie ncy of th e cata lyst reached a maximum

concentrat ions at  th e filter inlet could be achiev able by

∆p )

(D - 2w)

1。1 - 0。4

s

 D2

1

21

2 (24)

2

of 30% betwee n 350 an d 400 °C。 Obviously, higher NO2

a  more selective  oxidat ion  cata lyst。 As  expected, NOx

emissions  ar e  equa l  before  an d  after  th e  filter。 The

production  of  CO   an d   is  a   clear  indicat ion  of NO2

∆pexp an sion )

1 -

2(D + ws)

2Fvchan _out

(25)

measur ed  consum ption  of  NO2   is  accompan ied  by a

reactivity with  soot in th e filter。

Initial and Bounda ry Conditions 。 The initial temperatur e an d soot  loading along th e  chann el wall ar e provided as initial conditions for th e model。 The boun dar y conditions, which need to be defined, include th e exhau st gas temperatur e, flow rat e, an d oxyge n cont ent as functions of time。 The govern ing equat ions prese nt ed above ar e solved num erically with finite difference techniques using an iterat ive proced ur e in th e sp at ial direction contr olled by th e requirement of zero axial velocity at th e end  of  th e  inlet  chann el  an d atm osp heric press ur e at th e end of th e exit chann el。 Time mar ching was effected with a fourth -orde r Runge- Kutta  techn ique。

Soot Accumu lation Mode l。 It is ass um ed that th e soot part icles in th e engine ar e homogeneously distr ib- ut ed in th e engine exhau st an d th ey follow th e str eam-

Ha ving fitt ed th e reaction rat e constant s (preexpo- nent ial factor an d activat ion  energy)  of  th e  NO2 + car bon reaction, it is possible to obtain a good corr elation betwee n measur ement an d model res ults over a rela- tively wide temperatur e ran ge, as shown in th e bottom gra ph of Figur e 5。 The activat ion energy used in th is simu lat ion is 40 k J/mol。