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Effects of exhaust inlet size on the fluid flow patterns created by an Aaberg exhaust hood
,17.Aerosol SoL, VoL 23, Suppl. 1, pp. S575-S578, 1992
0021-8502/92 $5.00 + 0.00
Printed in Great Britain.
Pergamon Press Ltd
EFFECTS OF EXHAI~'r INLEt SIZE ON THE FLUID FLOV PATI~IINS CRFATEDBYANAABEI~~IIOOD G.R.IRJNT and D.B. INGHAH Department of Applied H~thematlcal Studies, University of Leeds, l.kT~S LS2 9JT, Nest Yorkshire, England.
~ r r The alm of this paper is to Investigate the effects exhaust inlet on the fluid flow patterns created by an Streamlines and lines of constant speed modelling those hood are used to examine the effect of the inlet size on of the hood's effective suction area.
of the size of the Aaberg exhaust hood. created by an Aaberg the size and profile
EEYVORDS Aaberg; Capture; Exhaustion;
Injection;
Inlet; Hodelllng; Neutrally-buoyant.
IHTROI~'~I~ The introduction of a new local exhaust system, in 1965, by the Danish manufacturer C.P. Aaberg, has made it possible to create controlled air movement over greater distances than possible with traditional exhausts. By combining injection and exhaustion In a correctly balanced ratio the Aaberg exhaust hood concentrates the suction In a zone along the longitudinal axis of the hood, see Fig. l, thereby creating a selective hood with a greater range of influence than possible with traditional designs.
=
4
Fig. 1. The Aaberg P r i n c i p l e .
2S
I tx
~ y
Fig. 2. The g e o m e t r y and c o o r d i n a t e s used i n t h e model.
At p r e s e n t t h e hood i s n o t i m m e d i a t e l y a p p l i c a b l e t o i n d u s t r y s i n c e i t requires careful a d j u s t m e n t t o each o p e r a t i n g s i t u a t i o n and a l t h o u g h e x p e r i m e n t a l s t u d i e s have be e n c a r r i e d out on t h e hood (Hegsted, 1987, F l e t c h e r and Sa unde r s , 1992) a f u l l theoretical analysis of the fluid mechanics i n v o l v e d ha s y e t t o be p e r f o r m e d . O r i g i n a l l y s e e n i n d u c i n g a $575
$576
G.R. HUNTand D. B. INGHAM
three-dlmenslonal axlsymmetrIc flow t h e Aaberg principle has been implemented in a slot exhaust to produce a two-dlmenslonal flow. The fluid mechanics model of a two-dlmenslonal Aaberg flow obtained by Hunt and Ingham (1992) forms the basis of the following study. The only modification made to their model replaces the llne slnk of fluid modelling the exhaust inlet with an opening of finite size, see Flg. 2. Owing to the Introduction of a finite sized opening an analytical solution of the equations of motion (the Continuity and Laplace equations) as obtained by Hunt and Ingham is no longer possible and the governing equations are solved for the stream function using finlte-dlfference methods. Using the symmetry of the hood the flow need only be calculated In the region above the hood's centre-line. In t h e model all lengths of the exhaust flange, volumetric flow rate, quantities are therefore
a r e non-dlmenslonallsed with respect to the radius a, and the stream function with respect to the m, of the exhaust. The following dimensionless introduced: X = x/a , Y = y/a , S = s/a , @. = @/m.
RESULTS AND DISCUSSION
In an Industrial envlron~ent the alr speed In front of the hood must exceed a minimum speed, known as the capture speed, in order for the contaminated air to be sampled. The magnitude of the capture speed depends upon a number of factors Including the nature of the contaminant and background air dlsturbances, e.g. cross currents and temperature gradlents. Under normal conditions and for a neutrally-buoyant contaminant the capture speed is of t h e o r d e r o f 0 . 2 5 m s -1 ( H e g s t e d , 1987, F l e t c h e r a n d S a u n d e r s , 1992). A c a p t u r e s p e e d o f 0.25ms -I c o r r e s p o n d s to a n o n - d l m e n s i o n a l r e s u l t a n t s p e e d o f Qc=0.75 for the quantities g i v e n b y F l e t c h e r and S a u n d e r s . Thus, we c a n d e f i n e t h e effective suction area, from which the neutrally-buoyant contaminated alr w111 b e d r a w n I n t o t h e i n l e t a n d s u c c e s s f u l l y s a m p l e d , a s t h e a r e a b o u n d e d by t h e l l n e o f c o n s t a n t s p e e d Qc=0.75 a n d t h e d i v i d i n g s t r e a m l i n e @* = 0 . 5 . The dividing streamline separates the flow travelling t o w a r d s t h e i n l e t from t h a t travelling towards the ejector. The g e o m e t r y o f t h e A a b e r g hood m o d e l l e d ( F l e t c h e r a n d S a u n d e r s , 1992) l e a d s to the following approximate values of the physical quantities: a = 0.15m a n d s ~ 0.037m w h i c h r e s u l t I n a v a l u e o f S ffi I / 4 f o r t h e d l m e n s l o n l e s s s i z e o f the exhaust Inlet. For the purposes of this study the ratio o f momentum f l u x e s b e t w e e n t h e e x h a u s t i o n and I n j e c t i o n w l l l r e m a i n a f i x e d c o n s t a n t ; t h e r a t i o c h o s e n c o r r e s p o n d s t o G=2.0 I n t h e n o t a t i o n u s e d b y Hunt a n d Ingham, ( 1 9 9 2 ) . To p r e d i c t what e f f e c t v a r y i n g t h e s i z e o f t h e e x h a u s t i n l e t h a s on the air f l o w I n t o t h e A a b e r g hood t h r e e d i f f e r e n t sizes of Inlet are c o n s i d e r e d , n a m e l y S = I / 8 , 1 / 4 a n d 1 / 2 . F o r e a c h i n l e t s i z e s t r e a m l i n e s and l l n e s o f a i r c o n s t a n t s p e e d (and hence e f f e c t i v e suction areas) deduced from t h e model a r e e x a m i n e d f o r two i n l e t c o n d i t i o n s : a) a c o n s t a n t volume f l u x I n t o t h e I n l e t a n d b) a c o n s t a n t a i r s p e e d a c r o s s t h e I n l e t f a c e . a) Lines of constant speed modelling the air flow pattern created by an Aaberg exhaust hood are shown in Flgs. 3a, b and c for the Inlet sizes of S = 1/8, 1/4 and 1/2, respectively. By comparing Flgs. 3a, b and c It Is clear that the llne of constant speed, Qc=0.75, corresponding to the level of background alr disturbance is not affected by the size of the Inlet and Intersects the centre-line at a constant distance, of the order of 3a, from the Inlet. Sets of streamlines describing the flow for the Inlet sizes of S = 1/8, 1/4 and 1/2 are shown in Figs. 4a, b and c, respectively; the use of shading illustrates t h e e f f e c t i v e s u c t i o n a r e a . By c o m p a r i n g F l g s . 4a, b and c i t i s e v i d e n t t h a t , e x c e p t v e r y c l o s e t o t h e hood, v a r y i n g t h e s i z e o f t h e Inlet results I n no v I s l b l e c h a n g e i n t h e f o r m o f t h e s t r e a m l i n e s a n d h e n c e the effective s u c t i o n a r e a may b e c o n s i d e r e d t o b e i n d e p e n d e n t o f S f o r t h e
Fluid flow patterns created by an Aaberg exhaust hood
$577
(a). S=1/8
//
2.0 1.5 ~
2.0
1.5-
1.0
1.0 I~
0.5
0.5 I~ 0.0
0.0 [b]. S=1/4 2.0
1.5 1.0
1.0
2.0
3.0
4.0
!
2.0
3.0
4.0
2.0
3.0
4.0
1.5 1.0
7~~ 0.5
i.0
2.0
3.0
4.0
/
2.0"
1.5-
0.0 0.0
1.5
1.0
0.5-
0.5
0.0
1.0
2.0
t.0-
0.0
1.0
20
0.5 0.0 0.0 (c). S=1/2
0.0 0.0
75 /
o o
I ~0
2.0
3.0
4.0
Flg. 3. Lines of constant speed.
0.0
1
:o
- -
2.0
3.0
4.0
Flg. 4. Streamlines.
inlet sizes considered. Very close to the hood the effective suction area Is broadest for the largest inlet slze considered, thls Is most clearly lllustrated by comparing Flg. 4a wlth Flg. 4c. To further investigate the effects flow pattern the alr speed along model was examined for the inlet illustrates the variation in the
of the exhaust inlet slze on the Aaberg the hood's centre-llne deduced from the sizes of S = 1/8, 1/4 and 1/2. Flgure. 5 dimensionless resultant air speed as a
$578
G.R. HUNTand D. B. 1NGHAM
'.°/ ÷
s
1/2
z5
z0
1.5
0
. 0.0
5 0.5
~ 1.0
Y=y/ct
1.5
Fig. 5. Variation in the centre-line air speed with distance from the Inlet.
2.0
function of the distance, Y = y/a, from the inlet and indicates that although, for small values of Y, the air speed developed by the smaller of the inlet sizes is the greater the centre-line air speed for each inlet size considered rapidly approaches a common value as Y increases. The common a i r speed, reached a f t e r only a very s h o r t d i s t a n c e from t h e i n l e t (of the order of 1.5a), confirms that the suction has a very limited e f f e c t on t h e movement o f a i r . For larger distances the injection effect of the Aaberg hood almost totally dominates the fluid motion. This result is in agreement with the experimental observations (Fletcher and Saunders, 1992) and verifies the conclusions of the streamline and air speed plots.
b) A similar investigation of the constant inlet speed condition predicts that, as expected, the profile of the effective suction area grows longer and broader as the inlet size {and hence Inlet flux) is increased.
CONCLUSIONS In this simple mathematical model the fundamental air flow pattern modelling that created by an Aaberg exhaust hood for the case of a neutrally-buoyant contaminant, neglecting the effects of diffusion, has been considered. Under these assumptions the model predicts that varying the size of the exhaust inlet, whilst keeping the exhaust flow rate a constant, has no apparent effect on the air flow pattern created except very near to the hood. In practice owing to the random movement of the contaminant at the edge of the effective suction area, where the air speed is close to the capture speed, we expect the effects of diffusion to dominate the fluid motion. Therefore, in order to more accurately model the operating conditions, the effects of diffusion must be included in the model and this is at present under investigation.
ACKNO~E}~rrs
The authors would like to thank SERC and the Health and Safety Executive, Sheffield for their financial support of the project.
H~GSTED, P. (1987) Air Movements Controlled by Means of Exhaustion. PL}(MVENT'87. I n t e r n a t l o n a l C o n f e r e n c e On A i r D 1 s t r l b u t l o n I n V e n t l l a t e d Spaces, Stockholm. HUNT, G.R. and INGHAH, D.B. (1992) The F l u i d M e c h a n i c s Of A T w o - D i m e n s l o n a l A a b e r g E x h a u s t Hood. To be p u b l l s h e d i n The A n n a l s o f O c c u p a t l o n a l Hygiene. FLETCHER, B. and SAUNDERS, C.J. Private communlcatlon. Health and Safety Executive, Research Division, Sheffield, England, 1992.
0021-8502/92 $5.00 + 0.00
Printed in Great Britain.
Pergamon Press Ltd
EFFECTS OF EXHAI~'r INLEt SIZE ON THE FLUID FLOV PATI~IINS CRFATEDBYANAABEI~~IIOOD G.R.IRJNT and D.B. INGHAH Department of Applied H~thematlcal Studies, University of Leeds, l.kT~S LS2 9JT, Nest Yorkshire, England.
~ r r The alm of this paper is to Investigate the effects exhaust inlet on the fluid flow patterns created by an Streamlines and lines of constant speed modelling those hood are used to examine the effect of the inlet size on of the hood's effective suction area.
of the size of the Aaberg exhaust hood. created by an Aaberg the size and profile
EEYVORDS Aaberg; Capture; Exhaustion;
Injection;
Inlet; Hodelllng; Neutrally-buoyant.
IHTROI~'~I~ The introduction of a new local exhaust system, in 1965, by the Danish manufacturer C.P. Aaberg, has made it possible to create controlled air movement over greater distances than possible with traditional exhausts. By combining injection and exhaustion In a correctly balanced ratio the Aaberg exhaust hood concentrates the suction In a zone along the longitudinal axis of the hood, see Fig. l, thereby creating a selective hood with a greater range of influence than possible with traditional designs.
=
4
Fig. 1. The Aaberg P r i n c i p l e .
2S
I tx
~ y
Fig. 2. The g e o m e t r y and c o o r d i n a t e s used i n t h e model.
At p r e s e n t t h e hood i s n o t i m m e d i a t e l y a p p l i c a b l e t o i n d u s t r y s i n c e i t requires careful a d j u s t m e n t t o each o p e r a t i n g s i t u a t i o n and a l t h o u g h e x p e r i m e n t a l s t u d i e s have be e n c a r r i e d out on t h e hood (Hegsted, 1987, F l e t c h e r and Sa unde r s , 1992) a f u l l theoretical analysis of the fluid mechanics i n v o l v e d ha s y e t t o be p e r f o r m e d . O r i g i n a l l y s e e n i n d u c i n g a $575
$576
G.R. HUNTand D. B. INGHAM
three-dlmenslonal axlsymmetrIc flow t h e Aaberg principle has been implemented in a slot exhaust to produce a two-dlmenslonal flow. The fluid mechanics model of a two-dlmenslonal Aaberg flow obtained by Hunt and Ingham (1992) forms the basis of the following study. The only modification made to their model replaces the llne slnk of fluid modelling the exhaust inlet with an opening of finite size, see Flg. 2. Owing to the Introduction of a finite sized opening an analytical solution of the equations of motion (the Continuity and Laplace equations) as obtained by Hunt and Ingham is no longer possible and the governing equations are solved for the stream function using finlte-dlfference methods. Using the symmetry of the hood the flow need only be calculated In the region above the hood's centre-line. In t h e model all lengths of the exhaust flange, volumetric flow rate, quantities are therefore
a r e non-dlmenslonallsed with respect to the radius a, and the stream function with respect to the m, of the exhaust. The following dimensionless introduced: X = x/a , Y = y/a , S = s/a , @. = @/m.
RESULTS AND DISCUSSION
In an Industrial envlron~ent the alr speed In front of the hood must exceed a minimum speed, known as the capture speed, in order for the contaminated air to be sampled. The magnitude of the capture speed depends upon a number of factors Including the nature of the contaminant and background air dlsturbances, e.g. cross currents and temperature gradlents. Under normal conditions and for a neutrally-buoyant contaminant the capture speed is of t h e o r d e r o f 0 . 2 5 m s -1 ( H e g s t e d , 1987, F l e t c h e r a n d S a u n d e r s , 1992). A c a p t u r e s p e e d o f 0.25ms -I c o r r e s p o n d s to a n o n - d l m e n s i o n a l r e s u l t a n t s p e e d o f Qc=0.75 for the quantities g i v e n b y F l e t c h e r and S a u n d e r s . Thus, we c a n d e f i n e t h e effective suction area, from which the neutrally-buoyant contaminated alr w111 b e d r a w n I n t o t h e i n l e t a n d s u c c e s s f u l l y s a m p l e d , a s t h e a r e a b o u n d e d by t h e l l n e o f c o n s t a n t s p e e d Qc=0.75 a n d t h e d i v i d i n g s t r e a m l i n e @* = 0 . 5 . The dividing streamline separates the flow travelling t o w a r d s t h e i n l e t from t h a t travelling towards the ejector. The g e o m e t r y o f t h e A a b e r g hood m o d e l l e d ( F l e t c h e r a n d S a u n d e r s , 1992) l e a d s to the following approximate values of the physical quantities: a = 0.15m a n d s ~ 0.037m w h i c h r e s u l t I n a v a l u e o f S ffi I / 4 f o r t h e d l m e n s l o n l e s s s i z e o f the exhaust Inlet. For the purposes of this study the ratio o f momentum f l u x e s b e t w e e n t h e e x h a u s t i o n and I n j e c t i o n w l l l r e m a i n a f i x e d c o n s t a n t ; t h e r a t i o c h o s e n c o r r e s p o n d s t o G=2.0 I n t h e n o t a t i o n u s e d b y Hunt a n d Ingham, ( 1 9 9 2 ) . To p r e d i c t what e f f e c t v a r y i n g t h e s i z e o f t h e e x h a u s t i n l e t h a s on the air f l o w I n t o t h e A a b e r g hood t h r e e d i f f e r e n t sizes of Inlet are c o n s i d e r e d , n a m e l y S = I / 8 , 1 / 4 a n d 1 / 2 . F o r e a c h i n l e t s i z e s t r e a m l i n e s and l l n e s o f a i r c o n s t a n t s p e e d (and hence e f f e c t i v e suction areas) deduced from t h e model a r e e x a m i n e d f o r two i n l e t c o n d i t i o n s : a) a c o n s t a n t volume f l u x I n t o t h e I n l e t a n d b) a c o n s t a n t a i r s p e e d a c r o s s t h e I n l e t f a c e . a) Lines of constant speed modelling the air flow pattern created by an Aaberg exhaust hood are shown in Flgs. 3a, b and c for the Inlet sizes of S = 1/8, 1/4 and 1/2, respectively. By comparing Flgs. 3a, b and c It Is clear that the llne of constant speed, Qc=0.75, corresponding to the level of background alr disturbance is not affected by the size of the Inlet and Intersects the centre-line at a constant distance, of the order of 3a, from the Inlet. Sets of streamlines describing the flow for the Inlet sizes of S = 1/8, 1/4 and 1/2 are shown in Figs. 4a, b and c, respectively; the use of shading illustrates t h e e f f e c t i v e s u c t i o n a r e a . By c o m p a r i n g F l g s . 4a, b and c i t i s e v i d e n t t h a t , e x c e p t v e r y c l o s e t o t h e hood, v a r y i n g t h e s i z e o f t h e Inlet results I n no v I s l b l e c h a n g e i n t h e f o r m o f t h e s t r e a m l i n e s a n d h e n c e the effective s u c t i o n a r e a may b e c o n s i d e r e d t o b e i n d e p e n d e n t o f S f o r t h e
Fluid flow patterns created by an Aaberg exhaust hood
$577
(a). S=1/8
//
2.0 1.5 ~
2.0
1.5-
1.0
1.0 I~
0.5
0.5 I~ 0.0
0.0 [b]. S=1/4 2.0
1.5 1.0
1.0
2.0
3.0
4.0
!
2.0
3.0
4.0
2.0
3.0
4.0
1.5 1.0
7~~ 0.5
i.0
2.0
3.0
4.0
/
2.0"
1.5-
0.0 0.0
1.5
1.0
0.5-
0.5
0.0
1.0
2.0
t.0-
0.0
1.0
20
0.5 0.0 0.0 (c). S=1/2
0.0 0.0
75 /
o o
I ~0
2.0
3.0
4.0
Flg. 3. Lines of constant speed.
0.0
1
:o
- -
2.0
3.0
4.0
Flg. 4. Streamlines.
inlet sizes considered. Very close to the hood the effective suction area Is broadest for the largest inlet slze considered, thls Is most clearly lllustrated by comparing Flg. 4a wlth Flg. 4c. To further investigate the effects flow pattern the alr speed along model was examined for the inlet illustrates the variation in the
of the exhaust inlet slze on the Aaberg the hood's centre-llne deduced from the sizes of S = 1/8, 1/4 and 1/2. Flgure. 5 dimensionless resultant air speed as a
$578
G.R. HUNTand D. B. 1NGHAM
'.°/ ÷
s
1/2
z5
z0
1.5
0
. 0.0
5 0.5
~ 1.0
Y=y/ct
1.5
Fig. 5. Variation in the centre-line air speed with distance from the Inlet.
2.0
function of the distance, Y = y/a, from the inlet and indicates that although, for small values of Y, the air speed developed by the smaller of the inlet sizes is the greater the centre-line air speed for each inlet size considered rapidly approaches a common value as Y increases. The common a i r speed, reached a f t e r only a very s h o r t d i s t a n c e from t h e i n l e t (of the order of 1.5a), confirms that the suction has a very limited e f f e c t on t h e movement o f a i r . For larger distances the injection effect of the Aaberg hood almost totally dominates the fluid motion. This result is in agreement with the experimental observations (Fletcher and Saunders, 1992) and verifies the conclusions of the streamline and air speed plots.
b) A similar investigation of the constant inlet speed condition predicts that, as expected, the profile of the effective suction area grows longer and broader as the inlet size {and hence Inlet flux) is increased.
CONCLUSIONS In this simple mathematical model the fundamental air flow pattern modelling that created by an Aaberg exhaust hood for the case of a neutrally-buoyant contaminant, neglecting the effects of diffusion, has been considered. Under these assumptions the model predicts that varying the size of the exhaust inlet, whilst keeping the exhaust flow rate a constant, has no apparent effect on the air flow pattern created except very near to the hood. In practice owing to the random movement of the contaminant at the edge of the effective suction area, where the air speed is close to the capture speed, we expect the effects of diffusion to dominate the fluid motion. Therefore, in order to more accurately model the operating conditions, the effects of diffusion must be included in the model and this is at present under investigation.
ACKNO~E}~rrs
The authors would like to thank SERC and the Health and Safety Executive, Sheffield for their financial support of the project.
H~GSTED, P. (1987) Air Movements Controlled by Means of Exhaustion. PL}(MVENT'87. I n t e r n a t l o n a l C o n f e r e n c e On A i r D 1 s t r l b u t l o n I n V e n t l l a t e d Spaces, Stockholm. HUNT, G.R. and INGHAH, D.B. (1992) The F l u i d M e c h a n i c s Of A T w o - D i m e n s l o n a l A a b e r g E x h a u s t Hood. To be p u b l l s h e d i n The A n n a l s o f O c c u p a t l o n a l Hygiene. FLETCHER, B. and SAUNDERS, C.J. Private communlcatlon. Health and Safety Executive, Research Division, Sheffield, England, 1992.