error of iso sampling probe

8/9/2019 Error of Iso Sampling Probe

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EFFECT OF PROBE D IAM ETER ON ISOK INET ICSAM PLIN G ERROR SHideto YO SHID A , K enzou YA M A SHIT A ,Hiroaki M A S UD Aand K oichi I IN O YADep artment of C hem ical E ng ineering ,K yoto University, K yoto 606

T o e x a m in e t h e e f f e c t o f p r o b e d i a m e t e r o n i s o k i n e t i c s a m p l i n g e r r o r s , e x p e r im e n t a l s t u d i e sw e r e c o nd uc t e d u s i n g m e t h y le n e b l u e- u r a n in e a e r o so l g e n e r a t e d b y a s p in n in g d is k a n d ly co po d iu ms p o r e s i n t h e s m a l l a n d l a r g e i n e r t i a r e g io n s , r e s p e c t i v e l y . F r o m th e r e s u l t s , i t i s f o u n d t h a tt h e s t a n da rd d ev ia t i o n o f c o n c e n tr a t i o n r a t i o , d ef i n ed a s t h e r a t i o o f c o n c e n tr a t i o n m e a s u r e d b ya p r o b e o f a n y d i a m e t e r t o t h a t b y a o n e - c m d i a m e t e r p r o b e , i s l a r g e r a s t h e p r o b e d i a m e t e r d e -c r e a s e s . I t i s a l s o f o u n d i n t h e s m a ll i n er t i a r e g i o n t h a t t h e m e an v a l u e s o f c o n c e n t r a t i o n r a t i om e a s u re d b y s m a l l e r d ia m e t e r p ro b e s a re d if f e re n t f r o m o n e a n o th e r a n d d e v ia te s ig n i f i c an tl yfrom unity in some cases.

IntroductionI s o k i n e t i c s a m p l i n g s h o u l d b e conducted w henmeasuring th e c o n c e n t r a t i o n o f g a s - s o l i d flow ina d u c t . However, t h e r e a r e no t h e o r e t i c a l o r e x -

p e r i m e n t a l s t u d i e s o f t h e e f f e c t o f p ro b e d ia m e t e ron s a m p li n g e r r o r in i s o k i n e t i c s a m p l i n g . W a t s o n 3 }p o i n t e d o u t t h a t p r o b e d i a m e t e r s h o u ld b e l a r g eenough, because t h e i n l e t w a l l th ic k ne s s cannot b en e g l e c t e d and t h e a n i s o k i n e t i c s a m p l i n g e r r o r s b e -comel a r g e f o r a s m a ll - d ia m e te r p ro b e .In this work, experimental studies were conductedb y u s e o f a 3 - j u m a e r o s o l g e n e r a te d b y a s p in n in g d is ka n d o f a 2 4 - j u m a e r o s o l i n th e sm al l a n d l a r g e i n e r t ia lr eg io n s r es pe c t i v e ly .E f f e c t s o f p r o b e d i a m e t e r , m a i n f l o w c o n c e n t r a t i o na n d m a in f l o w v e lo c i t y o n i s o k i n e t i c s a m p li n g e r r o rsw ere examined.

E f f e c t s o f v e l o c i t y d i s t r i b u t i o n a t th e s a m p l in gp r o b e in le t a r e a l s o d i s c u s s e d .1 . E xperimental Apparatus and Me thodTwok i n d s o f e x p e r im e n ta l a p p a r a tu s w ere used .F i g u r e 1 s h o w s t h a t e m p l o y e d f o r th e l a rg e in er t i a lregion. Lycopodium spores w ere fed from a pow derf e e d e r t h r o u g h a mixer-type d i s p e r s e r to t h e t e s tsection. T he amount deposited on a prob e w all anda f i l t e r w as w e i g h e d g r a v i m e t r i c a l l y . A s o n i c j e ti o n i z e r w a s u s e d t o n e u t r a l i z e a e r o s o l c h a r g e s . F i g -ure 2 shows th e a p p a r a t u s u s e d f o r t h e s m a ll i n e rt i a lreg ion. I n this case methylene b lue-uranine aerosolsg e n e r a t e d b y a s p in n i n g d i s k w e r e u s e d . T o s t a b i l i z eR ec e i v ed o n J u l y 2 8 , 1 9 7 7 . C o r r e s p o n d e n c e c o n c e r n i n g t h i s a r t i c l e s h o u l db e a d d r e s s e d t o H . Y o s h id a .

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t h e m a in f l o w c o n c e n t r a t i o n , a l a r g e m i x i n g c h a m b e rw as s e t a f te r t h e a e r o s o l g e n e r a t o r . A s o n i c j e ti o n i z e r w as a l s o u s e d . P a r t i c l e s d e p o s i t e d on thef i l t e r a n d i n s i d e w al l o f t h e p r o b e w e r e r e m o v e d b yw a s h i n g w i t h a known volume o f d i s t i l l e d w a t e r ,

F i g . 1 S c h e m a t i c diagram o f e x p e r im e n t a l a p -p a r a t u s N o . 1 ( l y co po di u m s p o r e s )

F ig . 2 S c h e m a t i c d i a g r a m o f e x p e r im e n t a l a p -p a r a t u s N o. 2 ( m e t h y l e n e b lu e- u ra n in e a er o so lp ro du ce d b y s p in nin g d is k g en er a to r)

JOUR NA L O F C HEM IC AL ENG IN EER IN G O F JA PA N


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T a b l e 1 P re l i m in a r y e x p e r i m e n t a l r e s u l t s( u o = 7 [ m / s ] , D p = 2 4 |> m ] , n = 6 )Probe Mean Standarddiam e te r concentrati o n dev iati ond [cm ] c [g /m 3] [g /m 3]

0 . 1 9 4 0 . 2 4 8 0 . 1 2 10 . 3 0 8 0 . 2 3 7 0 . 1 2 50 . 3 6 7 0 . 2 4 7 0 . 1 3 30 . 4 0 9 0 .2 1 3 0 .1 1 80 . 4 4 6 0 . 2 3 6 0 . 1 4 2

0.504 0.256 0. 1090 . 5 9 0 0 .2 6 6 0 .1 3 00 . 7 1 5 0 . 3 4 9 0 . 0 2 9 50 .7 5 3 0 . 3 0 0 0 . 0 6 2 6

0. 804 0.258 0.04740 . 8 9 3 0 . 2 6 8 0 . 0 5 3 51 . 0 0 1 0 . 2 9 1 0 . 0 3 91 . 3 8 4 0 . 2 8 3 0 . 0 3 6

1 . 5 7 0 0 . 2 9 0 0 . 0 2 9

T ab le 2 P ro be dim e nsio ns*d [cm ] a [cm ] b [ cm ]0 . 1 3 3 4 . 4 0 . 0 0 8 20 . 1 9 4 4 .5 0 . 0 1 2 70 . 3 0 8 4 . 4 0 . 0 0 5 70 . 3 6 7 4 . 2 0 . 0 0 5 7

0 . 4 0 9 4 . 3 0 . 0 0 8 30 . 4 4 6 4 . 2 0 . 0 0 80 . 5 0 4 4 . 2 0 . 0 1 00 . 5 9 0 4 . 1 0 . 0 0 6 70 . 7 1 5 4 . 2 0 . 0 1 0

0 .7 5 3 4 . 3 0 . 0 0 8 30 . 8 0 4 4 . 2 0 . 0 1 00 . 8 9 3 4 . 1 0 . 0 1 01 . 0 0 1 4 . 2 0 . 0 0 7

* Se ealso Fig .4

and the amou ntwas measuredspectrophotome tr ical ly .I n b o th c a s e s , th e p a r t i c l e c o n c e n t r a t i o n c d e te r m in e din c lu d e d th e amoun t d e p o s i t e d on t h e in s id e w a l lso f th e p r o b e and th e s a m p l i n g l i n e . T e s t s e c t io n s o f

b o t h a p p a r a t u s e s w e re m a d e o f t r a n s p a r e n t p o l y v i n y lc h lo r i d e i n o r d er t o o b s e r v e p r o b e d ir e c t i o n p a r a l l e lt o w i n d d i r e c t i o n and d e p o s i t i o n o f a e r o s o l o n th ei n s i d e w a l l o f t h e d u c t . T o r e d u c e e r r o r s c a u s e d b ym is a l i g n m e n t o f s a m p l i n g p r o b e w i t h r e s p e c t t o f l o w ,t h e p r o b e c e n t e r i i n e w a s s e t t o c o i n c i d e w i t h a p r e -d e t e r m i n e d l i n e o f t h e t e s t s e c t i o n . T h e e r r o r s a s -s o c ia te d w i th t h i s p o in t a r e d i s c u s s e d b y W a t s o n 3 )a n d R a y n o r 2 ) . A p r e l i m i n a r y e x p e r i m e n t s h o w n i nT a b l e 1 r e v e a l e d t h a t th e c o n c e n tr a t i o n m e a s u re db y a p r o b e o f d i a m e t e r g r e a t e r t h a n 1 c m w a s n e a r l yc o n s t a n t. T h e r e f o re , th e c o n c e n t r a t i o n m e a s u r e d

b y th e p r o b e o f 1 cm i n d i a m e t e r w as taken a s t h eb a s i c main f low c o n c e n t r a t i o n . W i t h tw o p ro b e s( o n e r e f e r e n c e probe and one t e s t p r o b e ) s e t s id e

b y s id e in t h e t e s t s e c t io n , a s s h o w n i n F ig . 3 , e x p e r i -ments w e r e c a r r i e d o u t under t h e c o n d i t io n o f i s o -k i n e t i c s a m p l i n g . E x p e r i m e n t a l c o n c e n t r a t i o n r a t i ow as ob taine d fro m th e ratio o f co nce ntration m easu re db y t h e t e s t p r o b e t o th a t m e a s u r e d b y th e r e f e r e n c ep r o b e .

VOL ll N O . 1 J 9 7 8

F ig . 3 T e s t s e ct io n

F ig . 4 S a m p l i n g p r o b e

T o reduce a n i s o k i n e t i c s a m p l i n g e r r o r s , f l o w r a t ew as checked by a flow m eter and a w et gas m eter.S m a l l d e v ia t i o n s o f m e a s u re d c o n c e n tr a t i o n c a u s e db y a n i s o k i n e t i c s a m p l i n g we r e c o r r e c t e d b y u s e o fth e r e s u l t s o b t a i n e d p r e v i o u s l y 4 \ E x p e r i m e n t s w e r ec a r r i e d ou t u s i n g t h i r t e e n b r a s s p r o b e s o f d i a m et e rr a n g i n g f rom 0.1cm t o 1.0cm. F i g u r e 4 s h o w st h e p r o b e s u s e d , a n d th e s i z e o f e a c h p a r t i s s h o w n i nTbe2o reduce i n t e r f e r e n c e o f th e tw o p r o b e s , t h e yw e r e h e l d mo r e than t h r e e c e n t i m et e r s a p a r t a n de l e c t r i c a l l y e a r t h e d . Exper iments w e r e carried o ute i g h t t i m e s f o r each p r o b e , and c o n c e n t r a t i o n r a t i oc / c 0 a n d s t a n d a r d d e v i a t i o n a we r e c a l c u l a t e d . A sa n e x a m p l e , t h e r e l i a b i l i t y o f m e a n v a l u e a n d s t a n d a r dd e v i a t i o n f o r th e d a t a o b t a i n e d b y s m a l l e r d i a m e t e rp r o b e w e re c h e c k e d a n d a r e s h o w n i n A p p e n d e x 1 .S am p l i n g t i m e s e l e c t e d w as f rom 2 t o 1 5 m i n u t e s .The d i s t a n c e from th e p r o b e i n l e t to th e s a m p l in gf i l t e r w a s 1 5 c e n t im e te r s a n d s a m p l in g tu b e d ia m e te rw a s 1 c e n t im e te r . D e t a i l s o f e x p e r i m e n ta l c o n d it io n sa r e s h o w n i n T a b l e 3 .2 . E x p er i m e n t a l R e s u lt s a n d D i s c u s s i o n

F i g u r e 5 shows t h e e x p e ri m e n ta ll y d er i v ed r e la t io n49


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T a b l e 3 E x p ie rm e n t a l c o n d it i o n sP a r t i c l e D p | > m ] a g p p [ g / c m 3 ]

Lycopodium spores 24.0* 1.09 1.05M ethylene b lue-uran ine 3. 47 1. 07 1. 42G as velocity in duct u0=5-13 [m/s]Duct diameter D = S [cm]U p s t r e a m s t r a ig h t d u c t l e n g th B = 2 [m ]F l o w R ey n o l d s n u m b e r in d u c t R ed = ( 2 .6 7 - 6 .9 3 ) x 1 0 4 [ - ]* n o te : p a r t i c l e d i a m e te r m e a s u r e d b y m ic r o s c o p e i s 3 2 ^ m ,b u t S to k e s d ia m e te r m ea s u r e d b y s e d im e n ta t io n is 2 4 /u rn .

F ig . 5 E x p er im e n ta l r e la ti o n b e tw e en c o nc e nt r a -t io n r a tio a nd p ro b e d ia m ete r ( l y co p od iu m sp ore s)

F ig . 6 E x p e r im e n t a l r e la ti o n b e t w e e n c on ce n t r a -tio n ra t io a n d p ro b e d ia m e te r ( m e th y l e n e b l u e -uranine aerosol)

F ig . 7 Comparison o f e xp er im e n t a l and cal-c u la te d s ta n d a rd d ev ia tio n

5 0

b e tw e e n c o n c e n t r a t i o n r a t i o a n d p r o b e d i a m e t e r w h e nlycopodium spores were used. Though the st andardd e v i a t io n s f o r sm a l l e r d i a m e te r p r o b e s w e r e l a rg e , t h ec o n c e n tr a t i o n r a t io , ( c /c 0 ) , w a s n e a r l y e q ua l to u n i t y .F ig u r e 6 s h o w s t h e e x p e r im e n t a l r e s u l t s o n t h e c o n -c e n t r a t i o n r a t i o f o r m e th y l e n e b l u e - u r a n i n e a e r o s o l .I n t h i s c a s e , th e mean v a l u e s o f th e c on ce n t r a tio nra tio d e v ia te d s ig n if ic a n t ly f rom u n ity w he n th e p ro b ed i a m e t e r w as s m a l l e r . The s t a n d a r d d e v ia t io n s o fo n e - cm re f e r e n c e p ro b e , < 7 i ( c 0 ) , a r e a l s o p r e s e n t e d inF i g s . 5 a n d 6 . I n F i g s . 5 a n d 6 , t h e n i n e t y - f i v e p e r c e n tc o n f id e n c e in te r v al o f th e m e a n v alu e i s a l s o p re s e n te df o r e a c h p r o b e . T a b l e s 4 and 5 show t h e e x p e r i -mental d a t a f o r th e c a s e o f l y c o p o d i u m s p o r e s a n dm e t h y l e n e blue-uranine a e r o s o l , r e s p e c t i v e ly . T h ef o l l o w in g e m p i r i c a l e q u a t i o n s a r e o b t a i n e d b y u s e o fth e method o f l e a s t s q u a r e s , b e c a u s e th e s t a n d a rdd e v i a t i o n s h o u l d b e i n v e r s e l y p r o p o r t i o n a l to t h es q u a r e r o o t o f s a m p l i n g a m o u n t W .( 7 = 9 .1 9 X l0 - 3 W ~ 0 - 5 d - 'n ; f o r ly c o p o d iu m sp o re s ( 1 )a = 1 .2 5 x \ 0 ~ 4W ~ 0 '5 d ~ 0 - 2 8 ; f o r m e th y l e n e b lu e - u ra n in e

(2 )w h e r e W = ( tu /4 ) d 2 c u o t x 1 0 " 4 [g ]A c o m p a ri s o n o f e x p e rim e n t a l d a t a w i t h t h e r e su lt sc a l c u l a t e d b y E q s . ( 1 ) a n d ( 2 ) is shown in F ig . 7 .F r o m E q s . ( 1 ) a n d ( 2 ) , i t i s f o u n d t h a t t h e s t a n d a r dd e v ia t i o n o f c o n c e n t r a t i o n r a t io i s l a r g e r a s th e p r o b ed i a m e t e r d e c r e a s e s . T h e r e f o r e , t h e c o nc en tr a tio nmeasured b y i s o k i n e t i c s a m p l i n g i s n o t a l w a y s a c -curate when t h e i n l e t d i a m e t e r o f p r o b e i s s m a l l .T h e f o l l o w in g d is c u s s io n c o n c e rn s t h e e f f e c ts o f th i c k -n e s s o f i n l e t w a l l t i p a n d v e l o c i t y d i s t r i b u t i o n a tth e p ro b e in le t o n is o k in e t ic s a m p l in g e rro rs .I f one assumes t h a t h a l f o f th e p a r t ic l e s th a t a r ei m p a c t e d on t h e i n l e t w a l l t i p a r e s a m p l e d in to th ep ro b e , s a m p le d c o n c e n tr a t io n is a t m o s t 1 3 % h ig h e rth an th e ma in flow con cen tra tion for th e min imump r o b e d i a m e t e r 1 5 , b u t t h i s amount i s t o o sm a l l to e x -p l a i n th e d e v i a t i o n o f t h e mean value. ( S e e a ls oA pp e n d ix 2 .)T he effect o f v e l o c i t y d i s t r i b u t i o n a t th e p ro b ei n l e t on i s o k i n e t i c s a m p l i n g e r r o r s i s a n a l y z e d a sfo l lo w s. B ec a u s e o f f lu id v is c o s i ty , a v e lo c i ty d is t r i -b u t io n o f f lu id is f o rm ed a t th e p ro b e in l e t . O w in g tot h i s d i s t r i b u t i o n , t h e r e may be d i s t o r t i o n o f f l u ids t r e a m lin e s e v e n i f s a m p l in g is c a r r ie d o u t u n d e r i s o -k i n e t i c c o n d i t i o n s ( u = u 0 ) . I f d i s to r t ion e x i s t s , t h e ns a m p l i n g e r r o r m ig h t o c c u r u n d e r i s o k in e t i c s a m p l i n g .F i g u r e 8 shows v e l o c i t y d i s t r i b u t i o n s c a l c u l a t e d w ithth e N a v ie r - S to k e s e q u a t i o n f o r i s o k i n e t i c s a m p l i n g .I t is f o u n d th a t th e v e lo c i ty p ro f i l e a t th e p r o b e in l e ti s n e a r l y u n i f o rm a n d th a t th e b o u n d a r y l a y e r d e v e -l o p s r a p i d l y i n th e l o w R e y n o l d s nu mber reg ionb o th i n s id e a n d o u t s i d e t h e p r o b e . F ro m th e r e s u l t s

JO UR NAL OF C HEM IC AL ENG IN EERING OF JA PAN


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T ab le 4 E xp erim en tal resu lts (in case o f lyco pod iu m s po res)M ain flow Concentration P robe diam eter C oncentra tion S am pling tim e A mount of S tandardR un* velocity c0 [g /m3] d [cm ] c [g /m3] t [sec] sample dev iationo [m/s] W [g] a [-]T ~5 0^99 (K4O9 l7o4 180 12.3 x l0"3 0J282 5 1 . 0 6 0 . 1 3 3 1 . 0 5 1 0 3 2 7 . 5 0 . 1 9 3

3 5 1 . 1 3 0 . 1 9 4 1 . 0 4 6 4 2 9 . 9 0 . 0 9 44 5 1 . 0 3 0 . 3 0 8 0 . 9 2 3 38 2 1 3 . 1 0 . 0 7 45 5 1 . 1 4 0 . 3 6 7 1 . 1 6 6 24 0 1 4 . 8 0 . 0 7 96 5 0 . 9 8 0 . 4 4 6 0 . 9 6 2 1 8 0 1 3 . 5 0 . 0 9 07 5 0 . 9 9 0 . 5 0 4 0 . 9 8 5 1 8 0 1 7 . 6 0 . 0 8 08 5 0 . 8 1 0 .5 9 0 0 . 7 6 1 8 0 1 8 . 7 0 . 0 3 59 7 0 . 9 7 0 . 8 9 3 0 . 9 9 6 1 0 5 4 5 . 8 0 . 0 3 2

1 0 7 0 . 9 7 0 .8 0 4 0 .9 8 12 0 4 2 . 1 0 . 0 2 7ll 7 0 . 9 2 0 . 7 1 5 0 . 9 6 1 1 2 0 3 2 . 3 0 . 0 3 01 2 7 0 . 9 2 0 .5 9 0 0 . 9 2 1 3 5 2 3 .6 0 . 0 4 613 7 0 . 9 5 0 . 4 4 6 0 . 8 4 2 1 9 2 0 . 2 0 . 0 5 2 61 4 7 0 . 9 5 0 . 4 0 9 0 . 9 6 2 4 0 2 1 . 2 0 . 0 6 615 7 1 . 0 2 0 . 3 6 7 0 . 9 7 3 2 5 2 3 . 2 0 . 0 6 41 6 7 1 . 0 0 0 . 3 0 8 0 . 9 0 4 0 0 1 8 . 9 0 . 1 2 31 7 7 1 . 0 0 0 . 1 9 4 0 .9 3 6 0 0 l l . 5 0 . 0 9 818 7 1 . 0 2 0 . 1 3 3 0 . 8 8 71 2 6 . 0 7 0 . 2 1 219 7 0 . 2 9 0 . 8 9 3 0 . 2 7 1 7 3 2 0 . 2 0 . 1 0 22 0 7 0 . 2 9 0 . 8 0 4 0 . 2 6 2 6 0 2 3 . 8 0 . 0 6 82 1 7 0 . 3 2 0 . 7 5 3 0 . 3 0 3 1 5 2 9 . 4 0 . 1 3 22 2 7 0 .3 4 0 . 7 1 5 0 . 3 5 2 7 0 2 6 . 5 0 . 1 2 12 3 7 0 . 2 8 0 . 5 9 0 0 . 2 7 4 3 5 2 2 . 1 0 . 1 1 72 4 7 0 .2 8 0 . 5 0 4 0 . 2 6 5 7 6 2 0 . 6 0 . 1 5 925 7 0 .2 6 0 . 4 4 6 0 . 2 4 6 2 0 1 6 . 0 0 . 1 6 82 6 7 0 . 2 4 0 . 4 0 9 0 . 2 1 8 8 5 1 7 . 3 0 . 1 6 72 7 7 0 . 2 7 0 . 3 6 7 0 . 2 5 1 1 2 5 2 0 . 6 0 .2 0 22 8 7 0 . 2 5 0 . 3 0 8 0 . 2 4 1 2 0 0 1 4 . 8 0 . 2 2 829 7 0 . 2 4 0 . 1 9 4 0 . 2 5 2 1 7 5 l l . 1 0 . 1 5 23 0 7 0 . 9 6 0 . 5 0 4 0 . 8 9 1 8 0 2 2 . 4 0 . 1 0 33 1 7 0 .9 4 0 . 7 5 3 0 . 9 3 1 2 0 3 4 . 8 0 . 0 1 7

T ab le 5 E xp erim en tal re su lts (in c ase o f m eth yle ne b lu e-u ra nin e a ero so l)M ain flow C oncen tration P robe d iam eter C oncen tration Sam pling tim e A mount of S tandardR u n * v e lo c ity cQ d [ cm ] c t [ s e c ] s am p le d e v ia tio no [m /s ] [ g /m 3 ] [g /m 3 ] W [g ] a [ - ]1 5 0 . 4 6 X 1 0 " 3 0 . 8 9 3 O . 3 7 x l O ~ 3 2 0 0 2 3 . 2 x l 0 ~ 6 0 . 1 7 3

2 5 0 . 6 2 0 . 8 0 4 0 . 5 3 2 2 0 2 9 . 6 0 . 2 0 83 5 0 . 5 9 0 . 7 5 3 0 . 5 6 2 2 0 2 7 . 4 0 . 2 8 44 5 0 . 4 7 0 . 7 1 5 0 . 4 5 2 4 7 2 2 . 4 0 . 2 6 55 5 0 . 5 6 0 . 5 9 0 0 . 5 9 2 7 0 2 1 . 7 0 . 2 0 06 5 0 . 3 7 0 . 5 0 4 0 . 4 4 3 30 1 4 . 3 0 . 2 4 27 5 0 . 3 8 0 . 4 4 6 0 . 4 1 3 3 6 1 0 . 7 0 . 2 1 58 5 0 . 4 6 0 . 3 6 7 0 . 5 2 4 4 4 1 2 . 1 0 . 3 2 49 5 0 . 4 5 0 . 3 0 8 0 . 7 8 4 5 6 1 3 . 3 0 . 5 4 1

1 0 5 0 . 4 3 0 . 1 9 4 1 . 0 2 7 2 0 1 0 . 9 0 , 7 1 0H 5 0 . 3 3 0 . 4 0 9 0 . 4 6 3 4 5 1 0 . 5 0 . 6 8 71 2 1 0 0 . 2 5 0 . 8 0 4 0 . 2 7 2 2 5 3 0 . 5 0 . 1 4 21 3 10 0 . 2 8 0 . 7 1 5 0 . 2 8 2 4 0 2 6 .9 0 . 1 3 31 4 1 0 0 .2 8 0 . 5 9 0 0 . 2 4 3 4 5 2 2 .3 0 . 1 2 615 1 0 0 . 2 8 0 . 5 0 4 0 . 2 6 4 6 8 2 4 . 4 0 . 2 2 41 6 1 0 0 . 2 3 0 . 4 4 6 0 . 2 7 5 1 6 2 1 . 8 0 . 3 0 71 7 1 0 0 . 2 1 0 . 4 0 9 0 . 2 1 6 0 0 1 6 . 5 0 . 1 6 4

1 8 1 0 0 . 1 9 0 . 3 6 7 0 . 1 9 6 96 1 4 . 1 0 . 2 3 51 9 1 0 0 . 1 6 0 . 3 0 8 0 . 1 7 8 6 4 1 0 . 7 0 . 2 8 12 0 1 0 0 . 1 6 0 . 1 9 4 0 . 3 3 9 0 0 8 . 8 0 . 3 9 52 1 1 0 0 . 3 0 0 . 7 5 3 0 . 2 9 2 2 5 2 9 . 3 0 . 0 7 22 2 1 3 0 . 2 3 0 . 7 1 5 0 . 2 5 2 4 0 3 0 . 7 0 . 0 7 32 3 13 0 . 2 2 0 . 5 9 0 0 . 2 4 3 3 6 2 8 . 3 0 . 1 7 32 4 13 0 . 1 6 0 . 5 0 4 0 . 1 7 4 5 6 2 0 . 4 0 . 1 5 825 1 3 0 . 1 4 0 . 4 4 6 0 . 1 6 4 8 0 1 5 . 6 0 . 2 4 72 6 1 3 0 . 1 3 0 . 4 0 9 0 . 1 3 5 7 6 1 2 . 7 0 . 2 1 52 7 1 3 0 . 1 3 0 . 3 6 7 0 . 1 3 60 0 1 0 . 9 0 . 1 5 52 8 13 0 . 1 2 0 . 3 0 8 0 . l l 90 0 9 . 1 5 0 . 1 4 32 9 1 3 0 . 1 2 0 . 1 9 4 0 . 2 1 90 0 7 . 1 9 0 . 2 8 7

* E x p e r im e n t s w e r e c a r r i e d o u t 8 t im e s f o r e a c h p r o be .VOL . ll N O . 1 1 9 7 8 5 1


5/5

F i g . 8 V e l o c i t y p r o f i l e s o f f l u i d u n d e r i s o k i n e t i csam pling (u =uQ)o f n u m e r i c a l c a l c u l a t i o n o f p a r t i c l e t r a j e c t o r i e s , i t i sfound t h a t t h e o r d i n a t e o f c r i t i c a l t r a j e c t o r y e q ua l s

p r o b e r a d i u s . T h e measured concentration i s i n -d e p e n d e n t o f th e v e l o c i t y d i s t r i b u t i o n a t t h e p r o b ei n l e t a s l o n g a s s a m p l i n g i s c a r r i e d o u t und er iso -k i n e t i c c o n d i t i o n s ( u = u 0 ) .A s t h e above d i s c u s s i o n in d i c a t e s , e x pe r im e n t a l

r e s u l t s c a n n o t b e e x p l a i n e d a s t h e e f f e c t s o f t h e t h i c k -n e s s o f i n l e t w a l l t i p o r v e l o c i t y d i s t r i b u t i o n a t t h ep ro b e i n le t.A s E q s . ( 1 ) a n d ( 2 ) c o n t a i n th e t e r m s d~0 - 31 andd ~ 0 ' 2 8 , t h e v a r i a ti o n o f s t a n d a r d d e v i a t i o n canno t b e

e x p l a i n e d b y t h e t e r m W a l o n e : i t d e p e n d s u p o n b o t hp r o b e d i a m e t e r and sample amount .Conclusion

E x p e r im e n t a l s t u d y o f i s o k i n e t i c s a m p l i n g e r r o r swas c a r r i e d o u t , and t h e f o l l o w i n g c o n c l u s i o n s w e r eo b t a i n e d .

1 ) W it h r e s p e c t t o p r e c i s i o n , i t i s f o u n d t h a t s t a n d -a r d d e v i a t i o n s o f t h e c o n c e n t r a t i o n measured b yp r o b e s o f l e s s t h a n 5 m m in d i a m e t e r b e c o m e m o r et h a n 2 0 p e r c e n t o f t h e m e a n v a l u e s f o r 3 . 5 / u m m e t h -y l e n e b l u e - u r a n i n e a e r o s o l and 1 0 p e r c e n t f o r 2 4 j u ml y c o p o d i u m s p o r e s . T he e m p i ri c a l e q u a t i o n s , E q s .

( 1 ) a n d ( 2 ) , a r e r e s p e c t i v e l y o b t a i n e d .2 ) W i t h r e s p e c t t o a c c u r a c y , i t i s f o u n d t h a t m e a nv a l u e s o f th e c o n c e n t r a t i o n measured b y s m a l l e rd i a m e te r p r o be s a l s o d e v i a t e more than 5 0 p e r c e n tf rom t h e t r u e v a l u e s f o r a fine a er o so l . T h e r e f o r e ,

b o t h p r e c i s i o n a n d a c c u r a c y b e c o m e w o r s e i n t h e c a seo f s m a ll e r d i a m e t e r p r o b e .3 ) A s h a r p - e d g e d w a l l o f p r o b e in l e t i s p r e f e r a b l ef o r a c c u r a t e s a m p l in g , and th e f l u i d v e lo c i t y d i s t r i -b u t i o n a t t h e p r o b e i n l e t d o e s n o t a f f e c t t h e i s o k i n e t i csampling er ro r .

A ppe nd ix 1R e l i a b i l i t y o f t h e m e a n v a l u e i s c a lc u l a te d b y_ _ ) - , , 0 , ) " = < ( J L \ < ( J L ) + t i , ( j , > ( A - l )

c 0 I K * W n \ C o J o \ c o j ^ W nS u b s t i t u t i n g t h e d a t a o f R u n 2 0 i n T a b l e 5 i n t o E q . ( A r l )u=8, < j = 0 . 3 9 5 , / ? = 0 . 0 5 , c / c o = 2.O 63

$ 2

1.74 8 < (c /c o)o < 2 .378R e l i a b i l i t y o f t h e s t a n d a r d d e v i a t i o n i s c a l c u l a t e d b y

( n - \ ) o * 9 f o -IV 2 (A 2 ,-9 / . < o " o < -vr+ ; vA -4 )x A p ) xA\ -p)

S u b s t i t u t i n g / i = 8 , ( 7 - 0 . 3 9 5 , / 7 - 0 . 0 2 5 in t o E q . ( A - 2 )0 . 2 3 9 < ( 7 0 < 0 . 6 3 6

A ppend ix 2Assuming t h a t h a l f o f th e p a r t i c l e s t h a t a r e i m p a c t e d o ni n l e t w a l l ti p a r e s a m p l e d i n t o th e p r o b e , th e f o l lo w in g e q ua -

t i o n is o b t a i n e d 1 } :cod i+R +2 \R j

I n t h e c a s e o f t h e m i n i m u m p r o b e d i a m e t e r ( d = 0 . 1 3 3 c m )b 0 -0 0 8 2 0 , J r , _ _ _ 1 1 3

R -0 .0 6 6 5~ - 1 2 3 3 L J ' c , "

Nomenclature5 = u pst re am straigh t d uc t length [m]6 = th ic kness o f inlet w all tip [c m]c = meanmeasured concentration [g/m3]c 0 = mean me asured c o nc e ntrat io n fo r 1 c mre fe re nc e pro b e d iame te r [g/m3 ]cod = main flow concentration [g/m3]c /c o,(c /c o)o = c onc entratio n ratio o f sample andp o p u l a t i o n [ - ]D = inner d uc t d iame te r [c m]Dp = particle diameter |>m]d {=2 R ) = inner pro b e d iameter [c m]n = number of trial [-]p = lev e l o f signif ic anc e [- ]R = probe radius [cm]R e { = d u o p I i n ) = f l o w R e y n o l d s n u m be r i n p r o b e [ - ]R e d ( = D u 0 p l i ^ ) = ^ o w R e y n o l d s n u m b e r i n d u c t [ t - ] .r ( = r/ i ? ) , z ( = z / 7 ? ) = d im e n s i o n l e s s c y l i n d r i c a l c o - o r d i n a t e s [ - ]

t = sampling t i m e [ s e c ]t (p) = ^ -d istrib ut io n func t io n [-]w 0 = m ain flo w v elo c ity far ah ead o f pro b ea x i s [ m / s ]u, u ' = sampling v elo c ity and av erage sam plingvel oci ty [m/s]W = amount of sample [g]li = fluid viscosity [g/cm - sec]v(=n-1) = degree offreedom [-]Pp, P = part ic le and fluid d ensity [g/c m3 ]a, f fQ = no n-d imensio nal stand ard d ev iatio n o fsample and population [-]tfifco ) = standard dev iation o f 1 cm reference

pro b e d iame te r [g/m3 ]ag - geo metric stand ard d ev iatio n o f ae ro so l [-]X v (p) = ^-d istrib ution func tion [-]L i t e ra tu re C i t e d1 ) B e ly a e v , S . P . a n d L . M . L e v in : A e r . S c L , 3 , ( 1 9 7 2 ) .2 ) R a y n o r , G . S . : A m e r . I n d . H y g . A s s o c . / . , 3 1 , 2 9 4 ( 1 9 7 0 ) .

3 ) W atson, H.H. : A m e r . Ind. H y g . Assoc . Quart., 1 5 , 2 1( 1 9 5 4 ) .

4 ) Y o s h i d a , H ., T . O h s u g i , H . Masuda, S . Y uu and K .I i n o y a : K a g a k u K og a k u R o n b u n s h u , 2 , 3 3 6 ( 1 9 7 6 ) .

( P r e s e n t e d a t t h e 4 2 t h A n n u a l M e e t i n g o f T h e S o c . o f C h e m .E n g r s . , J a p a n a t H ir o s h im a , A p r i l 2 , 1 9 7 7 . )JO U R NA L O F C HE M IC AL EN GIN EE R IN G O F JA PA N

error of iso sampling probe

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