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A Differential-pressure Probe for Velocity Measurements
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5/19/2018 A Differential-pressure Probe for Velocity Measurements in Swirling Air Flo...
http:///reader/full/a-differential-pressure-probe-for-velocity-measurements-in-swir
Tihon l ; Sobo l ik V (1993) Dynam ics o f e lec t rod if fus ion p robes in
wavy f ilm f low. Proceed ings o f the 3 rd In te rna t iona l W orkshop on
Electrodiffusion Diagnostics of Flows, Dou rdan, F rance,
pp
397 404
Wan g DM; Tarbe l l JM (1993) An a pprox im ate so lu t ion fo r the
dynamic response o f wa ll t r ans fe r p robes . In t I Hea t Mass Trans fe r
36:4341 4349
Wein O (1981) On the t r ans ien t Leveque s p rob lem w i th an app l ica -
t ion in electroche mistry. Collect Czech Chem C omm un 46:
3209-3220
134
A d i f f e r e n t i a l p r e s s u r e
U S ch m id t
Experiments n Fluids
0 1 9 9 5 )
134 135 Sp ring er-V erlag995
p r o b e f o r v e l o c i t y m e a s u r e m e n t s in s w i r l i n g a i r f l o w s
Ab s t r a c t
F o r m e a s u r i n g a i r v e l o c i t ie s i n s w i r l i n g f lo w s a
d i f f e r e n t i a l p r e s s u r e p r o b e o f s m a l l a x i a l l e n g t h w a s d e v e l -
o p e d . T h e d e t e r m i n a t i o n o f t he v e l o c i t y i s b a s e d o n m e a -
s u r i n g t h e d i f f e r e n c e b e t w e e n t h e s t a g n a t i o n p r e s s u r e a n d t h e
b a s e p r e s s u r e o f a c i r c u l a r d i s k w h o s e s u r f a c e i s p e r p e n d i -
c u l a r t o t h e m a i n f l o w d i r e c t i o n .
1
Int roduct ion
I n s i t u a t io n s w h e n l a s e r - D o p p l e r o r h o t - w i r e a n e m o m e t e r s a r e
n o t a v a i l a b l e o r d i f f i c u lt t o a p p l y , a i r f l o w v e l o c i t ie s a r e o f t e n
m e a s u r e d w i t h d i f f e r e n t i a l - p r e s s u r e p r o b e s , e .g . th e c l a s s i c a l
P r a n d t l tu b e o r , w i t h a m u c h h i g h e r d e g r e e o f d i r e c t i o n a l
r e s o l u t i o n , f i ve - a n d s e v e n - h o l e p r o b e s ( e .g . O s t o w a r i a n d
W e n t z 1 9 83 ; Z i l l i a c 1 9 93 ). I t s r e l a t i v e l y l a r g e l e n g t h m a k e s
t h e P r a n d t l p r o b e i n a p p r o p r i a t e f o r b e i n g u s e d i n s w i r li n g
f lo w s w h e r e t h e r a d i u s o f c u r v a t u r e o f t h e s t r e a m l i n e s i s o f t h e
s a m e o r d e r o f m a g n i t u d e o r e v e n s m a l l e r t h a n t h e a x i al
d i m e n s i o n o f t h e p r o b e . F o r m e a s u r i n g a i r v e l o c it i es in s u c h
f lo w s w i t h s w i r l a p r e s s u r e p r o b e o f s m a l l a x i al l e n g t h h a s b e e n
d e v e l o p e d t h a t i s d e s c r i b e d i n t h is N o t e . T h e p r o b e i s b a s e d o n
m e a s u r i n g t h e d i f f e r e n c e b e t w e e n t h e s t a g n a t i o n ( t o t a l ) p r e s -
s u r e a n d t h e b a s e p r e s s u e o f a c i rc u l a r d i s k w h o s e s u r f a c e i s
p e r p e n d i c u l a r t o t h e m a i n f l o w d i r e c t i o n . T h e p r o b e h a s b e e n
f o u n d t o b e u s e f u l f o r m e a s u r i n g t h e a i r v e l o c i t i e s i n a c y c l o n e
s e p a r a t o r .
Received: 13 Dece mber 1994~Accepted: 4 July 995
U. Schmid t
Lehrstuhl ff i r Appara tebau, Universit~t Essen,
D-45117 Essen, Germany
D e s i g n o f t h e p r o b e
T h e p r o b e c o n s i s t s o f t w o p a r a l l e l t u b e s o f o u t e r d i a m e t e r d
a n d a c i r c u la r p l a n e d i s k o f d i a m e t e r D = 2 d m o u n t e d b e t w e e n
t h e t w o t u b e s a t t h e i r e n d s ( F i g . 1 ) . T h e p r o b e s h o u l d b e
o r i e n t e d s u c h t h a t t h e d i s k is p e r p e n d i c u l a r t o t h e m a i n f l o w
d i r e c ti o n . T he l o n g e r t u b e, m o u n t e d o n t h e u p s t r e a m s i d e o
t h e d i s k , h a s i n i t s w a l l a h o l e o f d i a m e t e r d o =
D / 6
p o s i -
t i o n e d i n t h e a x i s o f th e d i s k a n d f a c i n g a g a i n s t t h e f lo w
d i r e c t i o n , s o t h a t t h e t o t a l p r e s s u r e c a n b e s e n s e d b e c a u s e t h e
l o w e r e n d o f t h i s t u b e , a t t h e r i m o f th e d i s k , is c l o s e d . T h e
o p e n e n d o f th e s e c o n d s h o r t e r t u b e o n t h e d o w n s t r e a m s i de o
t h e d i s k i s e x p o s e d t o t h e b a s e p r e s s u r e i n t h e s e p a r a t e d f l o w
( F ig . 1 ). T h e t w o t u b e s o f i n n e r d i a m e t e r 4 5 d a r e c o n n e c t e d t o
a d i f f e r e n t i a l p r e s s u r e g a u g e w h o s e r e a d i n g c a n b e c a l i b r a t e d i n
t e r m s o f t h e a i r f l o w v e l o c it y .
B e c a u s e o f i ts s m a l l e x t e n t i n f l o w d i r e c t i o n t h e p r o b e i s
a p p r o p r i a t e f o r b e i n g u s e d i n t h e a f o r e - m e n t i o n e d s w i r l i n g
f l ow s e x i s t i n g , e. g ., i n a c y c l o n e s e p a r a t o r . A p r o b e h a s b e e n
b u i l t w i t h b r a s s t u b e s o f o u t e r d i a m e t e r d - - 2 m m . T h i s a l l o w e d
t o i n t r o d u c e t h e p r o b e i n t o t h e f l o w t h r o u g h 4 m m h o l e s
d r i l l e d i n t h e w a l l o f th e c y c l o n e .
3
C al ib r a t io n o f t h e p r o b e
T h e m e a s u r e d p r e s s u r e d i f f e re n c e
A p ~ -
(Plolal --P base )
i s se t p r o p o r t i o n a l t o t h e d y n a m i c p r e s s u r e :
1 w 2
w i t h p b e i n g t h e f l u i d d e n s i t y a n d w t h e f l o w v e l o c i ty . F o r
a P r a n d t l t u b e o n e h a s K = 1 . S i n c e th e b a s e p r e s s u r e i s u s u a l l
l o w e r t h a n t h e s t a t i c p r e s s u r e i n t h e f r e e s tr e a m , t h e K - v a l u e f o
t h i s p r o b e s h o u l d b e s m a l l e r t h a n o n e . T h e v a l u e s o f K t h a t
5/19/2018 A Differential-pressure Probe for Velocity Measurements in Swirling Air Flo...
http:///reader/full/a-differential-pressure-probe-for-velocity-measurements-in-swir
i
NI -
\
r o = D / 8 r s = 0 , 1 s / ( s / 2 )
I D - - ,
Fig. 1. Design of disk prob e
- - - - - - - @ - -
~ - - - - - D - . - _ . ~
0 . 8 5
0 . 8 0 -
K = 0 . 7 6
/
9 & A / 9 & 9
v . 0 . 7 5 - 9
0 . 7 0
0 .6 5 ~.~ ~ ~ ', . . . . ', , . : , , i . . . . . . . . . . . . . .
l x l 0 4 3 x 1 0 ' * 5 x i 0 4 ' 7 x 1 0 4
R e
Fig. 2. C alibration of factor K versus R eynolds num ber
m u s t b e d e t e r m i n e d b y c a l i b ra t io n a r e e x p e c t e d t o d e p e n d o n
t h e R e y n o l d s n u m b e r ,
R e .
A s t r o n g d e p e n d e n c e o n
R e
h o w -
e v e r, w o u l d b e o f g re a t i n c o n v e n i e n c e ( O w e r a n d P a n k h u r s t
1 9 7 7 ) . A n i n d i c a t i o n t h a t K m i g h t b e i n d e p e n d e n t o f R e
f o r c e r t a in r a n g e s o f t h e R e y n o l d s n u m b e r i s g i v e n b y t h e
o b s e r v a t i o n t h a t t h e d r a g o f a d is k e x p o s e d n o r m a l l y t o t h e
f lo w is a l m o s t c o n s t a n t f o r R e - n u m b e r s a r o u n d 1 0 4 t o 1 0 5 (see,
e .g ., De b l e r 1990) a n d b y t he f a c t t ha t t he d r a g o f s uc h a d i s k i s
a l m o s t t o t a l l y it s b a s e d r a g .
K - n u m b e r s h a v e b e e n d e t e r m i n e d b y t a k i n g m e a s u r e m e n t s
i n t h e f u l l y d e v e l o p e d a i r f lo w i n a p i p e a t R e y n o l d s n u m b e r s
1 . 1 . 1 0 4
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