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Annular air-curtain domes for sports stadia
Journal o f Wind Engineering and Industrial Aerodynamics, 25 ( 1 9 8 6 ) 7 5 - - 9 2 Elsevier Science P u b l i s h e r s B.V., A m s t e r d a m - - P r i n t e d in T h e N e t h e r l a n d s
75
A N N U L A R AIR-CURTAIN DOMES F O R SPORTS STADIA
A.A. H A A S Z
and B. K A M E N
University of Toronto Institutefor Aerospace Studies, 4925 Dufferin Street,Downsview, Ontario M 3 H 5T6 (Canada) (Received March 10, 1985)
Summary T h e p e r f o r m a n c e o f a n n u l a r a i r - c u r t a i n s as p r o t e c t i v e barriers against p r e c i p i t a t i o n was i n v e s t i g a t e d e x p e r i m e n t a l l y using a 60 c m d i a m e t e r l a b o r a t o r y m o d e l a n d a 6 m d i a m e t e r o u t d o o r t e s t facility. P r e c i p i t a t i o n was s i m u l a t e d b y small size glass b e a d s a n d w a t e r d r o p lets. T h e scaling r e q u i r e m e n t s for t h e particle--air j e t i n t e r a c t i o n d y n a m i c s were reviewed a n d m o d i f i e d t o explicitly include t h e effects o f t h e s i m u l a t i o n material. T h e e f f e c t s of R e y n o l d s n u m b e r , h o w e v e r , are o n l y implicitly i n c l u d e d . Based o n t h e results o f this s t u d y a set o f criteria for f u t u r e t e s t s t h a t c o u l d lead t o reliable p r o j e c t i o n s for larger-scale i n s t a l l a t i o n s is p r e s e n t e d in t h e f o r m o f d i m e n s i o n l e s s p a r a m e t e r s .
1. Introduction
The basic air-curtain principle is the utilization of rapidly moving air jets to separate t w o potentially different environments. Possible applications of this concept include protection against rain and snow for malls, sports stadia and construction sites. Our research programme at the University of T o r o n t o over the last decade [1--10] has concentrated on the development of both theoretical and experimental models for the dynamics of the precipitating particles as they interact with the complex flows of the air-curtain jets. Extensive work on both of these fronts has been performed for the horizontal air,curtain jet configuration [5--7]. Research on annular jet aircurtains, on the other hand, has only involved small-scale experimentation. Theoretical treatment of particle dynamics in annular jets is comparatively more difficult due to the complexity of the annular jet flow field. The major objective of our research with air,curtains is to establish the scaling laws for particle--jet interactions and to determine the feasibility of using air-jets for full-scale applications. The emphasis in this report is on the annular jet configuration. Previous studies with such a system were performed with models ranging in size from about 15 to 86 cm in diameter [8--10]. The simulation of rain was performed with either water drops [8,10] or glass beads [ 9 , 1 0 ] . The results presented here for the 6 m diameter o u t d o o r model provide a very important extension of physical size for studying the scaling laws. 0167-6105/86/$03.50
© 1 9 8 6 Elsevier Science P u b l i s h e r s B.V.
76 Another important aspect of the present work is the revision of the scaling laws, which was necessary in order to achieve consistency among previous and present results. Proper scaling is extremely important for the projection of small-scale results to full-scale installations. 2. Annular jet structure and scaling laws
2.1. Annular jet structure As previously mentioned, an air-curtain is just a jet of air formed and oriented for a special purpose. In the case of the annular jet configuration, air is discharged straight up through an annular nozzle to form a hemispherically shaped enclosure -- hence the name "air-curtain d o m e " . Protection against rain and snow within the enclosure is achieved via the interaction of the jet curtain and the precipitating particles. Falling rain and snow encountering the upward moving jet is slowed down, stopped and eventually accelerated up and away from the covered area. The annular jet has been studied for its uses in air cushion vehicles [ 11,12 ] and in oil burners and combustion facilities [13]. There are four basic regions associated with an annular air-curtain dome: ( 1 ) t h e exiting primary annular jet, (2) the entrainment regions, (3) the recirculation zone within the dome, and (4) the combined jet. The processes involved in creating these regions are excellently described by Chigier and Beer [13] and are paraphrased in the following paragraph for completeness. "As the jet exits the annular nozzle, a potential core {first region) with essentially constant velocity is established in the centre, with mixing zones forming (second region) on the inner and outer edges due to the shearing action of the jet and the stagnant air. On the outside of the annular nozzle there is an endless supply of air for the entrainment but on the inner side of the jet there is only a limited, fixed a m o u n t of air to meet the entrainm e n t requirements of the jet. This results in an internal vortex being set up (third region) which is toroidal in shape. The vortex creates a low pressure region and the resulting pressure gradient across the annular jet causes the jet to bend towards the axis of the jet. As the converging streamlines approach the axis, a stagnation region is set up and the resulting high pressure redirects the flow away from the axis until the combined jet expands in the same manner as a single jet (fourth region)." (See Fig. 1.) Chaplin [12], by making several assumptions about the flow pattern and the entrainment, as well as using the limiting case of infinitely thin nozzles, derived an equation for the height of the stagnation point above the floor. Adapted to the models studied at UTIAS [8], the result yields a stagnation point occurring at a height equal to the radius of the annulus. However, this height {which also represents the length of the internal vortex) is a function of the nozzle thickness-to-annulus diameter ratio (t/D) as well as the exit speed of the jet [13]. For a constant t/D, as the exit speed of the jet increases, the internal circulation increases causing a greater pressure gradient
77
let boundary~
~..
entrainment region /# /
/
/
//i
/ / " / /.~jet
ill
/ / ~ /I /
ll[
X
entrainment region
|/stagnation ~=/ point boundary-~,~,. \ \
i
i /~ .
~lit<
.___J
Ir
"\
\,, \',\
\,\
',kll I
vj
t
floor
et nozz e
vj
Fig. 1. Cross-sectional view of an annular jet. across the jet which would t e nd to force it towards the axis sooner. However, the increased inertia of the faster jet resists the increased force and the height o f the stagnation p o i n t remains essentially a constant. T he height o f the stagnation poi nt and the internal recirculation are o f prime i m p o r t a n c e when applications of the annular jet are considered. In all previous studies the nozzles were positioned at what would be field level in a full-scale stadium case. However, in the case of a baseball or football stadium the nozzle would be m o u n t e d above the stands in some manner and the resulting v o r te x and recirculation m ay be considerably different. Fut ure research must be directed t o studying, and if necessary, reducing the effects of the internal recirculation on the activities and people shielded by the d o me.
2.2. Scaling laws If the air d o me is to be used to p r o t e c t large areas (typically 100 m diameter) th en the c o n c e p t must be d e m o n s t r a t e d with the use of small-scale l a b o r ato r y and o u t d o o r models. In order to confidently compare models of various sizes and predict p e r f o r m a n c e for full-scale facilities, the cases in question must all be dynamically similar. Formal dimensional analyses have been d o n e [ 8 ,9 ] which led to t he dimensionless parameters t hat must be m a t c h e d f r o m case to case for dynamic similarity. The first approach is based on a formal dimensional analysis involving the nine physical variables associated with particle--jet interactions [8] : Vj, t , D , W,d, p p , p , l ~ , g
78 where Vj is the jet exit velocity, t the thickness of the jet nozzle, D the annulus diameter, W the wind velocity, d the rain drop diameter, pp and p the drop and air densities, respectively,/~ the air viscosity, and g the acceleration due to gravity. These variables are thus reduced to the following six non
Vj t
d
pp' W ' D ' D '
Vjtp
V}
p ' Dg
The fact that it is impossible to simulate all of these parameters simultaneously in air is clearly demonstrated if we consider the following three: t/D, Vjtp/p and V 2/Dg. As model size D increases, in order to keep t/D and Vj2/Dg constant, it is obvious that both t and Vj must increase; however, this conflicts with the requirement for Vjtp/p to be constant. This argument then leads to the conclusion that total dynamic similarity for the complete set of parameters considered is essentially impossible to achieve. An alternative approach suggested by Lake and Etkin [8] emphasizes the particle dynamics as the particle encounters an arbitrary flow field. This approach yields the following non
dt
-
~r1(ti - - ~ ' ) ~
(la)
rr~ (/~ -- b')~
(lb)
It I (dJ - - t b ' ) ~ - - 7r 2
(Ic)
where t~, b, tb are the non,dimensional drop velocity components after normalizing with respect to Vj. Similarly, t2', b', tb' are the non-dimensional components of the jet fluid velocity. The quantity fi is defined as /) ~__ [(/~ __ /~')2
.~_ (/) __ {)')2 _~_ (/~ __ i~)')2 ] 1/2
(2)
and 7rI and 7r2 are defined as follows: 1 7rI = -~ CDpd2 D / m
(3)
~2 = Dg/Vj 2
(4)
To reduce the complexity of the n~ parameter, previous analyses involved the use of a simplifying assumption, namely that the particle was falling in still air at its terminal velocity Vt. This resulted in n l being simplified to 7rl = g D / V 2
(5)
79 so that the third equation of m o t i o n (lc) became
d~) dt
[
-
(ytt2 1
7rl (~ -- tb')fi + \-~j]
(6)
Two seemingly important facts follow from such an analysis: ( 1 ) t e r m i n a l velocity is scaled with jet exit velocity (i.e., Vt/Vj is a constant); and (2) nl has the form of a Froude number and hence is an important scaling parameter. This "Froude-like" number allowed for the determination of the precipitation material and drop/particle size for any model based on a full-scale rainfall. Lake and Etkin [8] originally used water from a shower head to simulate rain. This was done mainly for convenience with the implications of the decision being made after the tests. In their later tests [9], they used glass beads as the simulation material in order to achieve proper dynamic scaling of the Froude number. Proper Froude number scaling was t h o u g h t to be more important than other factors such as particle Reynolds number scaling and raindrop deformation and breakup (which cannot be obtained using solid particles). However, later work by Raimondo and Haasz [5--7] on numerical simulations of particle dynamics in linear jet air-curtains showed a significant Reynolds number dependence. In particular, they f o u n d that under the influence of the jet a particle may experience a relative velocity much greater than its terminal velocity and therefore the drag must be evaluated for the Reynolds number based on particle velocity. Consequently, the drag and resulting trajectories are different from those expected from the simplified equations (5) and (6). Hence, the m e t h o d of scaling and the selection of the simulation material requires further consideration, which has been undertaken in the present study. Going back to the complete non-dimensional equations of motion, the two dimensionless parameters ~rj and 7T2 need to be conserved for dynamic similarity. For a spherical particle, ~ can be written as 3
p D
T(l : 4- CD --pp--d
(7)
Clearly the problem of maintaining 7r~ constant for different scales will arise through the drag coefficient CD. There is no one analytic function expressing CD t h a t will simplify the analysis. However, since most of the important previous experiments as well as the present tests involve low Reynolds numbers, Re, we shall consider CD = CD (Re) in such a flow regime. For R e ~ 1000 the CD curve can be expressed as a series of piecewise functions of the form
CD = k l / R en
(8)
where k 1 and n are constants. Of course the particle in the presence of a jet will experience a changing relative velocity, Vp, and hence a changing Reynolds number which will alter the drag coefficient over time. The Reynolds number for substitution into eqn. (8) is therefore R e , which is based on Vp, i.e.,
80
Rep = p V p d / #
(9)
Thus 7r~ becomes
7r~ -
3 k I p D VLVt d t 4 Re~ pp d Vt Vj t d
(10)
The Vt/Vj term was i nt r oduc e d here to allow for direct comparisons with the simplified analysis (eqns. 5 and 6). Equation (10) can be rewritten as:
p Vj Vtt
rrl =
k, Ret Re~, Rej -~
(11)
where
Re t = p Y t d / p
(12a)
and
Rej = p V j t / #
(12b)
or
lr 1 = ~r3 • F(Rep, Ret, Rej, D, t, d)
(13)
where
vj ~3
-
p
Vt Pp
(14)
The new dimensionless parameter ~3 is i m p o r t a n t because it contains the relationship generated f r om the simplified analysis with an additional t erm which can acco u n t for different materials used to simulate rain. Also important to n o te is that the f unc t i on F implicitly contains the jet Reynolds n u m b e r as well as the particle Reynolds numbers based on actual particle velocity and terminal velocity. Thus the non
3. Experiment 3.1. Description o f 6 m outdoor air-dome model The air for the 6 m diameter annular air-curtain model was provided by a 50 m 3 s -1 capacity fan driven by a 100 MW m o t o r . The facility consisted of a plenum chamber which was c o n n e c t e d to the fan via various transition sections (see Fig. 2). Air f r om the plenum, flowing radially outward from the centre region, exited through an annular nozzle vertically upward resulting in an " air - d o me" . U ni f or m i t y of the circumferential velocity profile was
81
Fig. 2. Top view of 6m diameter annular air-curtain test facility. (1) Circular-square transition piece, (2) angular transition piece, (3) diffuser section, (4) plenum, (5) annular nozzle.
achieved by appropriately positioning baffles in the plenum chamber. A jet thickness of 18 cm, corresponding to t / d = 0.03, was selected in order to allow for comparisons to be made with previous results [8--10]. Variable-pitch blades on the fan enabled the jet exit velocity to be varied in the 3.5--11 m s -1 range. Velocity measurements of the jet at the nozzle exit were made with the use of hot-wire anemometry and pitot probes. The circumferential velocity variation was f o u n d to be within ~15%. The radial velocity profiles across the nozzle exit were reasonably flat from the inner edge to the nozzle centre followed by a gradual increase toward the outer edge, with the outer edge velocity being about 1.5--2 times higher than the plateau level. This is most likely caused by the fact that the flow upon entering the nozzle must turn from an essentially horizontal direction to a vertical one in the nozzle. Although a flat radial velocity profile is desirable, we do not expect the integrity of the air dome and its protection capability to be drastically affected by radial flow non-uniformities.
82 The integrity of the annular jet was investigated in the following ways. First, sawdust was t h r o w n into the jet at various locations and the particle trajectories were observed. In all cases the sawdust was entrained by the jet, carried upwards and curved towards the axis, just as would be expected from the pattern of Fig. 1. The second m e t h o d involved flow visualization with the use of wool tufts attached to wires strung across the dome at various heights in a plane through the centre of the annulus and perpendicular to the floor. It was clearly evident that when the jet was turned on the tufts above the nozzle exit were pointing straight up, and started to bend inwards with increasing height, providing visual evidence of the formation and expected behaviour of the dome. A further study was done by measuring the jet speed at several locations in the curtain jet using a pitot tube. The pitot tube was placed at the approximate centre-line of the inwardly curving jet by noting the t u f t deflections and then oriented to record the maximum pressure difference on the manometer so that the direction at the m a x i m u m speed of the jet could be determined. A plot consisting of four points is shown in Fig. 3.
/.~
[ 5 9 , 30 °)
o
o c~
L (10 O, 9 0 ° )
'I\ 3
I 2 Radiol
I ) Position
(m)
Fig. 3. S p e e d and d i r e c t i o n o f t h e 6 m annular jet for t/h = 1/3 a n d blade setting 3. The o r d e r e d pair at t h e tip o f each a r r o w r e p r e s e n t s t h e velocity in m s -1 and t h e angle relative to t h e h o r i z o n t a l . Velocities w e r e m e a s u r e d w i t h p i t o t tubes.
3.2. Precipitation e x p e r i m e n t s w i t h 6 m o u t d o o r m o d e l
In the first instance we must determine the type of rainfall (as rainfall rate controls the water drop size distribution) to be simulated and then the model characteristics and requirements. It was shown above that among various non-dimensional groups of parameters associated with air jet--water drop interactions, the most important ones appear to be:
t/D ~1 = 7r3 " F ( R e p , R e t, R e j , D , t, d)
83 where ~3 = (Vj/Vt)(p/pp). Since one o f the objectives of this investigation is t o assess the ef f ect of t he f u n c t i o n F on the air dome, we shall, for the purposes o f selecting t he simulation material, assume F to be a constant. This results in Ir 3 replacing 7rl as one of t he three scaling parameters. Maintaining t/D cons t a nt in t he model and f, ill-scale cases results in similar jet flow configurations for the t w o cases. The const ancy of ~2 establishes the relationship b etwe en linear and velocity sc ~ling ratios. For example, if a fullscale installation is 16 times the size of the model, as is the case in this e x p e r i m e n t (i.e., Dfs = 16Din ), t he n the jet velocity for the full-scale will be 4 times t h a t f o r the m ode l (i.e., Vj~s = 4Vim ). The param et er 7r3 in t urn establishes the relationship between the jet velocity and the particle terminal velocity. F o r model experiments using-water as the simulation material, the r e q u i r e m e n t f o r Ir3 to be c ons t ant simply reduces to Vj/Vt being a constant in b o t h full-scale and m ode l situations. Simulation of a m e d i u m rainfall rate (~1 m m h -1) with a characteristic water d r o p diameter of a b o u t 2 m m (corresponding t o Vt = 6.5 m s -1 ), and using a linear scaling ratio o f D~s/Dm = 16, requires a Vt of a b o u t 1.6 m s -1 for the simulating water drops. The corresponding characteristic water drop diameter required f or model testing is a b o u t 400 t~m. T he p r o d u c t i o n of this d ro p size was achieved with the use of a SPRACO full cone cluster nozzle (15151014). Analysis o f the dr op size distribution (using m i c r o p h o t o g r a p h s o f drops falling on an oil film) yielded an average diameter of ~- 380 pm with a' standard deviation o f 140ttm. The corresponding mean Vt was a b o u t 1 . 5 m s -1 . The choice o f water drops t o simulate rainfall seemed appropriate for at least t w o reasons: (1) it is the same substance and (2) there are a variety of atomizing nozzles which are commercially available to produce almost any desired size range of drops. However, the choice of water drops does introduce some difficulties as well. Full-scale raindrops of the order of 1--3 m m diameter d e f o r m and m ay experience breakup in the presence of an air jet. Such events are n o t only difficult to model experimentally but also present difficulties in the analysis of the full-scale case. The 380-um drops used in this investigation do def or m , albeit less than full-size drops, but t hey do n o t break up. The breakup of large raindrops into smaller drops with smaller terminal velocities reduces the workload of the lower port i on of the jet, leading to the r e q u i r e m e n t o f a reduced jet exit velocity. On the o t h e r hand, with no drop breakup in the case of the model, t he jet must handle the simulated large drops requiring higher velocities than would be necessary in the presence o f p r o p e r simulation o f dr op breakup. F o r modelling purposes i n order to p r o d u c e a fine spray of the desired small size, a pressurized waterline is needed as the degree of atomization is, in part, a f u n c t i o n of the pressure. T he finer the mist, the higher the pressure and hence a greater water flow for a given nozzle. This means t hat t h e simulated rainfall rate f r om a particular nozzle increases with decreasing size o f drops p r o d u c e d , which is exactly the opposite o f what happens in nature.
84 T h e s t e a d y , all d a y , low r a t e t y p e o f rain is a s s o c i a t e d with small d r o p s while t h e h e a v y d o w n p o u r s with large rates are c o m p r i s e d o f large drops. This a f f e c t s t h e d r o p c o n c e n t r a t i o n p e r u n i t v o l u m e o f air w h i c h c o u l d result in d i f f e r e n t d r o p i n t e r a c t i o n effects. T h e q u a n t i t a t i v e e f f e c t s associated w i t h the full-scale a n d t h e m o d e l c o n c e n t r a t i o n s are e x t r e m e l y c o m p l e x a n d r e q u i r e statistical i n f o r m a t i o n w h i c h is n o t c u r r e n t l y o b t a i n a b l e f o r t h e e x p e r i m e n t a l m o d e l s . H e n c e , t h e e f f e c t s o f d i f f e r e n t and changing c o n c e n t r a t i o n s are n o t explicitly k n o w n . N o w w e c o n s i d e r t h e s o u r c e o f t h e d r o p s used in this e x p e r i m e n t . By o b s e r v a t i o n it c o u l d be seen t h a t t h e exit speeds o f t h e d r o p s at t h e w a t e r n o z z l e w e r e g r e a t e r t h a n t h e i r t e r m i n a l velocities d u e to t h e w a t e r l i n e pressure. T h u s the air j e t v e l o c i t y r e q u i r e d to s t o p the p e n e t r a t i o n of t h e s e " f a s t e r " d r o p s is b o u n d to be " t o o h i g h " , leading to s o m e w h a t c o n s e r v a t i v e results. A n o t h e r e f f e c t t h a t c o u l d lead to c o n s e r v a t i v e results is a s s o c i a t e d w i t h t h e f a c t t h a t t h e w a t e r d r o p s in t h e m o d e l tests w e r e i n t r o d u c e d at a height o f 6 m a b o v e t h e floor. Since t h e jet rises well a b o v e this p o i n t , a p o r t i o n o f t h e j e t is n o t utilized f o r t h e slowing d o w n p r o c e s s o f t h e d r o p s as w o u l d be t h e case in a full-scale facility. In o r d e r to achieve a w i d e s p r a y p a t t e r n f o r t h e tests, t h r e e nozzles were e m p l o y e d . T h e y w e r e p o s i t i o n e d along a d i a m e t e r o f t h e a n n u l u s such t h a t o n e n o z z l e was d i r e c t l y o n the axis o f t h e a n n u l a r j e t and o n e o n either side at a distance o f 1.8 m f r o m t h e axis. T h e height o f t h e nozzles a b o v e t h e f l o o r was a b o u t 6 m. Water was supplied t o t h e nozzles t h r o u g h o r d i n a r y 1.3 c m d i a m e t e r garden hoses w h i c h w e r e h o o k e d u p t o a s t a n d a r d waterline w i t h n o m i n a l pressure o f a b o u t 5 5 0 k P a (80 psi). T h e c o r r e s p o n d i n g f l o w t h r o u g h t h e n o z z l e s was a b o u t 3.41 m i n -~ . T h e n o r m a l m e t h o d o f testing involved t h e d e t e r m i n a t i o n o f the q u a n t i t y o f w a t e r r e a c h i n g t h e f l o o r in a given t i m e w i t h t h e j e t o f f and t h e n w i t h t h e j e t o n t o see h o w m u c h p r o t e c t i o n was achieved. With the o u t d o o r facility this was n o t an easy task. First o f all, side winds w e r e a p r o b l e m . Since t h e t e r m i n a l v e l o c i t y o f t h e 3 8 0 - ~ m d r o p s is o f t h e o r d e r o f 1.5 m s -~ , a side wind o f t h a t m a g n i t u d e (3.5 m p h = 3 k n o t s ) is e n o u g h to cause t h e s p r a y f r o m t h e n o z z l e t o fall at a 45 ° angle so t h a t m o s t o f t h e s p r a y d o e s n o t even land w i t h i n t h e area b o u n d e d b y the annulus. T h e s e c o n d p r o b l e m was t h e efficient c o l l e c t i o n o f t h e s p r a y t h a t did r e a c h t h e floor. A t a w a t e r f l o w r a t e o f 3.41 m i n -~ , assuming a u n i f o r m c o v e r a g e o f t h e area b o u n d e d b y t h e nozzle ( ~ 25 m 2 ), t h e e x p e c t e d d e p t h o f w a t e r a f t e r 1 m i n is o n l y a b o u t 150 p m . C o n s e q u e n t l y , f o r m e a s u r a b l e q u a n t i t i e s o f w a t e r o n the f l o o r long c o l l e c t i o n t i m e s are n e e d e d . In a d d i t i o n to t h e d i f f i c u l t y o f m a i n t a i n i n g stable e x p e r i m e n t a l c o n d i t i o n s f o r long times, long c o l l e c t i o n t i m e s also p o s e an e v a p o r a t i o n p r o b l e m , especially f o r small drops. This p r o b l e m is w o r s e w i t h t h e jet t u r n e d o n since d r o p s w h i c h r e a c h t h e f l o o r are subject t o a g r e a t e r r a t e o f e v a p o r a t i o n c a u s e d b y t h e r e c i r c u l a t i o n flow.
85 Another problem, caused by the presence of side winds, is the wind interaction with the annular jet itself, causing the jet to bend in the direction of the wind. As has been shown by Lake and Etkin [ 9 ] , this bending of the jet results in a significant loss in the ability to stop precipitation, and if the wind is strong enough, the annular jet can completely collapse, Both of these cases were at one time or another observed for our 6 m model. As the m a x i m u m exit velocity of the jet was only 11 m s - ' , the presence of steady side winds and the inevitable gusts made it nearly impossible to study fully quantitatively the performance of this air roof. Fortunately there is a daily period when one can expect little or no side winds. This occurs in the early morning, so all tests were therefore carried out during the period from just before sunrise until about an hour and a half after. Even though the tests were performed in the near absence of winds when the water drops from the spray nozzle were falling nearly straight down, quantitative measurements were still not possible. Instead a "qualitatively quantitative" estimate was made in the following manner. With the jet off, an observer could " d e t e r m i n e " the quantity of water falling on an exposed arm and eye glasses over a brief period of time. This was then repeated with the jet on so that comparisons could be made. Photography was also used to d o c u m e n t the protection. Many photographs from different vantage points were taken. Good photographs were obtained by standing on either side of the annular nozzle and looking straight up; the pictures show the upward-moving spray. The best photographs were the sequence shots, taken with a 2.5 frames per second m o t o r drive, showing the spray first coming d o w n with the jet off, then being blown upward when the jet is turned on. Figure 4 shows such a typical sequence for the case when the jet exit velocity was 7.5 m s -1 (time between photographs is 5 s). At the lowest speed setting (Vj -- 3.5 m s -1 ) with the presence of even the smallest of wind speeds, there was at least 50% penetration. On one brief occasion when there was absolutely no side wind present, almost 100% protection efficiency was achieved. This confirmed Lake and Etkin's results [9] regarding the possible catastrophic effects of a relatively high side wind. At V~ = 5.5 m s -~ , the no-wind case yielded a protection efficiency of about 90--95%. With slight side winds, the upstream area was completely protected but the downstream end suffered 20--30% penetration. For jet exit velocities of 7.5 and 11 m s-~ there was very little difference in protection efficiencies. The only time t h a t penetration was noticed coincided with a gust of side wind. Essentially complete no-wind protection was achieved and only minimal penetration occurred (5--10%) in the presence of slight side winds. The only real difference of course was that for the higher speed setting the side winds h a d t o be somewhat stronger to cause the same a m o u n t of performance deterioration as observed in the lower-speed case. Regarding the effect of side winds, it is important to note that the winds were due to real full-scale atmospheric air movements, while the annular model jet velocities were scaled down by a factor of four (the velocity scale
86
Fig, 4. S e q u e n c e o f p h o t o g r a p h s s h o w i n g w a t e r d r o p trajectories a f t e r t u r n - o n o f air jet w i t h t h e 6 m air-curtain test facility. Vj ----7.5 m s -1 . Time b e t w e e n p h o t o g r a p h s : 5 s.
87 factor). Thus, for full-scale installations, where the jet velocities will be considerably higher than in the model, the effect of side winds is expected to be less significant. One of the goals of this experiment was to find the critical jet velocity needed to " s t o p " precipitation from penetrating the air-curtain dome. For the purpose of this study, we have defined the critical velocity, Vc, to be the jet velocity t h a t results in about 95% protection efficiency (i.e., 95% of the precipitation is prevented from penetrating the air dome). A discussion of the present results and comparisons with previous experiments will follow. 3.3. Precipitation experiments with 60 cm laboratory model The 60 cm model was a small-scale version (1:10 linear scale) of the 6 m o u t d o o r facility and it was originally built to study the pressure losses associated with the 6 m system. Attempts were made to use this small model for precipitation simulation experiments with water drops. Due to difficulties encountered in the production and control of the small water drops needed these experiments were unsuccessful. Although glass beads were f o u n d to have limitations for particle trajectory simulations associated with linear jets [5--7 ], their applicability for annular jet simulations has not been ruled out so far. Therefore, glass bead tests were undertaken with the following three objectives: (1) to test the reproducibility of earlier experiments [9] with glass beads, (2) to show whether or not particles with a terminal velocity of about 0.5 m s -1 (the desired value based on V j / V t being constant) could be stopped by a 60 cm annular air-curtain whose highest jet exit speed was 7.5 m s -l , and (3) most importantly, since the parameter 7r3 contains a term to account for the density of the simulation material, this test could provide useful information regarding the validity of 7r3 as a scaling parameter. We have proposed t h a t 7r3 should replace the Vj/V t parameter widely used in previous annular air-curtain studies. The glass beads were in the size range 74--105 ~m and had a specific gravity of 2.39. A feed system was improvised that neither ensured that the beads would slow d o w n to terminal velocity before encountering the jet nor that the beads were adequately separated to prevent wake interaction. Thus any results would be conservative. The experiments performed with these beads, at a jet exit velocity of 7.5 m s -1 , yielded an average penetration of only about 2% which was consistent with previous results [9]. Thus, the first two objectives of the test were met with positive results. The final matter of checking the validity of ~3 as the relevant scaling parameter will be discussed below.
4. Comparison of present and previous results This section summarizes all the important results from the present and previous experiments in order that comparisons and conclusions may be made based on the new general scaling laws. Table 1 lists the important
(ram) 5.1 7.7 10.6 14.3 6.9 6.9 18.0 17.2 25.8 34.4 180.0
18.0
t
D
(m)
0.300 0.297 0.294 0.291
0.150 0.150
0.600 0.860 0.860 0.860
6.00
0.600
Lake a n d E t k i n [ 8 ] , water drops
Lake a n d E t k i n [ 9 ] , glass beads
Baines and Wong (see ref. 10), water drops
K a m e n a n d Haasz, water drops
K a m e n a n d Haasz, glass beads
3.0
3.0
3.0 2.0 3.0 4.0
4.6 4.6
1.7 2.6 3.6 4.6
(%)
t/D
7.5
7.5
22.7 22.7 21.5 13.3
6.10 2.74
24.4 21.3 21.0 15.2
( m s -1 )
Ve
Vt
1.5
0.380
0.515
2.95 2.95 2.95 2.95
0.728 0.728 0.728 0.728
0.098
0.515 0.207
7.62 7.62 7.62 7.62
( m s -1 )
0.098 0.050
2.6 2.6 2.6 2.6
(mm)
d
S u m m a r y of present results a n d previous results for a n n u l a r air-curtains
TABLE 1
14.6
5.0
7.7 7.7 7.3 4.5
11.8 13.2
3.2 2.8 2.8 2.0
vdvt
PVtd ----
3.46
39.3
5.0
6.1
147.1 147.1 147.1 147.1
3.46 0.71
1356 1356 1356 1356
Re t :
7.7 7.7 7.3 4.5
4.9 5.5
3.2 2.8 2.8 2.0
Yc yt" SG
O0 O0
89
parameters and results from Lake and Etkin's water drop [8] and glass bead [9] experiments, Baines and Wong's water drop tests (see ref. 10) and t he current wo r k for b o t h water and glass beads. For ease o f com pari son all results have been converted t o SI units. The numbers from t h e previous works, if n o t directly stated a nyw her e in the respective reports, were either inferred from graphs or calculated from parameters that were explicitly stated. Th e drop or particle R e ynol ds n u m b e r in Table 1 is based on the terminal velocity Vt. This R e t was calculated in order to determine the R e y n o l d s n u m b e r f o r the drop as it first encounters the jet. Thus, R e t was c o m p u t e d as pVtd Ret
-
(15)
#
where p = 1.225kgm-3 and p --~ 1.8 x 10 -s kg m "1 s-' The q u an tity ~3 was defined as ~3 =
(16)
Since p is essentially a constant for simulation in air and pp can be expressed as the particle specific gravity (SG) times the density of water, 7r3 can be rewritten as: ~r3 =
(17)
This lr~ is p lo tted as a f unc t i on of the particle Reynolds n u m b e r in Fig. 5. Neglecting the Lake and Etkin [8] water tests because o f the high Reynol ds numbers, a horizontal straight line m a y be drawn through the data indicating t h a t 7r~ is essentially i n d e p e n d e n t of Reynolds n u m b e r based on particle
8 n 6
*
+
÷
D
4
o Loke ond Etkin D ~alnes and wono & Kemen ond Itoasz
Woter Drops
2
o o0 o
Gloss Beaes { e+ L.oke ond E f k i n Kamen and Haosz
0; 10 -~
I
I
I
10 0
101
10 a
Particle
Reynolds
Number
10 3
(Re i) F
Fig. 5. Non-dimensional parameter ~3 versus particle Reynolds number R e t.
90
terminal velocity. This has the very important implication that the function F(Rep, Ret, Rej, D, t, d) in eqn. (13) has remained essentially constant for the various simulations. This confirms the significance of ~ as the controlling scaling parameter, replacing ~ ] . Figure 6 shows ~ as a function of annulus diameter and again it appears that ~ is independent of model size, at least for the size range tested so far (i.e., Dr, < 6 m). This can be tied in with the Reynolds number independence. The model sizes used so far have necessarily demanded small water drops and hence low Reynolds numbers. This leads to a plot of Re as a function of annulus diameter as shown in Fig. 7. Intuitively it is clear that a largerdiameter model would require a larger jet velocity to maintain dynamic similarity, and in fact from the equations of motion arose the parameter n2 = Dg/V~h which dictates how jet speed varies with model size. This greater jet velocity would then be able to deflect larger drops which have greater Reynolds numbers. Hence, the Re--D curve should start near the origin and rise up and to the right, asymptotically approaching the real rain's Reynolds numbers as model size increases. Figure 7 shows that this has not occurred, which indicates that the individual tests simulate different raindrop sizes. In fact Lake and Etkin's water tests [8] used drops of the size of real rain but on a very small model. Therefore, one must exercise caution in interpreting such a mixed variety of results. These results from all sources not only have not simulated the same rainfall, but also have not had dynamically similar annular jets due to various t/D ratios. However, the trends noted in Figs. 5 and 6 indicate that the performance (namely, the ~ needed to achieve ~ 9 5 % protection
10 !
o =L
10 z
8 10' t~
6 > o
4
10 o
F o Lake and Etki~ Water Drops ~ 0 8olnel ond Wonq L& Komln and HOOIZ
2
f o Lake and Etkin woler Orops~a Barnes and Won~ L A Komen
÷
Gloss 8eod$~ + Lake and Elk[n l * Komln and Hoosz
0 01
Ol
2
I
0.4
r
I
0 . 6 0.8
Annulus
I
1
Diameter
Gloss Beads { +e
J
L
I
2
4
6
(rn)
D
I
I0 q
Fig. 6. Non-dimensional parameter ~'3 versus annulus diameter D . Fig. 7. Particle R e t versus annulus diameter D .
I
01 Annulus
t
and Efkin Komen and HOOSZ Lok#
Diameter
(m)
91
efficiency) of the air-curtain d o m e is n o t seriously affected by the disparities among the various simulations. 5. Conclusions
The major objective of the present investigation was to verify the validity of the air-curtain scaling laws by extending previous small-scale laboratory simulations to the testing of a 6 m diameter o u t d o o r air-curtain d o m e facility. In addition to the successful testing of the 6 m model with the use of water drops, tests were performed with a 60 cm diameter small-scale version of the 6 m model. Analysis of the current experimental results as well as all previous aircurtain d o m e results led to the identification of a new scaling parameter, ~ = V c / ( V t " SG), which plays an important role in determining the critical jet velocity needed to provide a certain level of protection efficiency. Thus ~r~, together with t / D and 7r~ = Dg/V~j, are the parameters t h a t need to be kept constant in model and full-scale situations. The ratio t / D assures kinematic similarity for the jets, ~r: establishes the relationship between linear and velocity scaling, and ~r~ determines protection efficiency. Direct comparisons of our results for the 6 m model using water drops and the 60 cm model using glass beads yielded excellent agreement for ~ . Further comparisons with previously published results also yielded good agreement for ~ even though case-to-case variations of t/D, particle R e , etc., were present. This implies that, at least for the particle Reynolds number and annulus diameter ranges considered, the effect of such variations does not significantly affect air-curtain performance. With a major assumption that the validity of the three scaling parameters (t/D, 7r2 and 7r~ ) could be extended to full-scale air-curtain installations, we shall now a t t e m p t to make certain projections for a 100 m diameter air dome. Maintaining t/D = 3%, as was the case in the present experiments, leads to a jet thickness of 3 m. For our 6 m model experiments with water (SG = 1) Vc, Vt and ~'3 were 7.5 m s-1, 1.5 m s-1 and 5.0, respectively. Assuming a characteristic raindrop diameter of about 2 mm with Vt = 6.5 m s-1 (this corresponds to a medium rainfall rate of about 1 m m h-~), we obtain a critical jet velocity of about 33 m s-1. The corresponding air flow (Q) and power (P) requirements are 3 1 0 0 0 m a s -1 (66 Mcfm) and 10 000kW (113 000 hp), respectively. Similar calculations for a heavy rainfall, with drops of about 3 m m diameter, yield the following projections: Vt = 8 m s -1 , Vc = 40 m s -1 , Q = 38 000 m a s -1 (80 Mcfm), and P = 36 000 kW (48 000 hp). Acknowledgements The authors wish to acknowledge the financial support provided by Air Roofs Canada for the construction of the 6 m diameter facility, and the University of Toronto Institute for Aerospace Studies for providing the site
92 for the facility. The research programme was performed with the help of an N S E R C g r a n t . D i s c u s s i o n s w i t h Dr. B. E t k i n a r e a l s o g r a t e f u l l y a c k n o w l edged.
References 1 G.A.S. Allen, Experimental investigation of an air-curtain for protection of an outdoor power installation from salt spray, UTIAS Tech. Note No. 171, University of Toronto, Toronto, Canada, 1971. 2 G.A.S. Allen and R.T. Lake, Trajectories of raindrops in a jet issuing into a normal crosswind, UTIAS Tech. Note No. 165, University of Toronto, Toronto, Canada, 1971. 3 A.A. Haasz, B. Etkin, R.T. Lake and P.L.E. Goering, Laboratory simulation of an aircurtain roof for the Ontario Science Centre, UTIAS Tech. Note No. 192, University of Toronto, Toronto, Canada, 1975. 4 A.A. Haasz and P.L.E. Goering, Intermittent enclosures -- air-curtain walls and roofs, Proc. IASS World Congress on Space Enclosures, July 1976, Montreal, Quebec, Canada, WCOSE-76, Vol. 1, pp. 151--163. 5 S. Raimondo and A.A. Haasz, Single and dual air-curtain jets used as protection against precipitation, UTIAS Rep. No. 227, University of Toronto, Toronto, Canada, 1978. 6 A.A. Haasz and S. Raimondo, Effectiveness of an air-curtain canopy against precipitation, J. Wind Eng. Ind. Aerodyn., 6 (1980) 273--290. 7 A.A. Haasz and S. Raimondo, Performance of adjacent dual-jet air-curtain roofs, J. Wind Eng. Ind. Aerodyn., 10 (1982) 79--87. 8 R.T. Lake and B. Etkin, The penetration of rain through an annular air-curtain dome, UTIAS Rep. No. 163, University of Toronto, Toronto, Canada, 1971. 9 R.T. Lake and B. Etkin, Experimental simulation of the interaction of wind-driven precipitation with an annular air-curtain dome, UTIAS Tech. Note No. 182, University of Toronto, Toronto, Canada, 1973. 10 B. Kamen and A.A. Haasz, Experimental investigation of annular air-curtain domes, UTIAS Rep. No. 288, University of Toronto, Toronto, Canada, 1984. 11 G.D. Boehler, Aerodynamic theory of the annular jet, IAS Rep. No. 59-77, Institute of the Aeronautical Sciences, New York, 1959. 12 H.R. Chaplin, Effect of jet mixing on the annular jet, Navy Department David W. Taylor Model Basin Aerodynamics Laboratory, Washington, DC, Aero Rep. 953, 1959. 13 N.A. Chigier and J.M. Bedr, The flow region near the nozzle in double concentric jets, Trans. ASME, J. Basic Eng., 86 (1964) 797--804.
75
A N N U L A R AIR-CURTAIN DOMES F O R SPORTS STADIA
A.A. H A A S Z
and B. K A M E N
University of Toronto Institutefor Aerospace Studies, 4925 Dufferin Street,Downsview, Ontario M 3 H 5T6 (Canada) (Received March 10, 1985)
Summary T h e p e r f o r m a n c e o f a n n u l a r a i r - c u r t a i n s as p r o t e c t i v e barriers against p r e c i p i t a t i o n was i n v e s t i g a t e d e x p e r i m e n t a l l y using a 60 c m d i a m e t e r l a b o r a t o r y m o d e l a n d a 6 m d i a m e t e r o u t d o o r t e s t facility. P r e c i p i t a t i o n was s i m u l a t e d b y small size glass b e a d s a n d w a t e r d r o p lets. T h e scaling r e q u i r e m e n t s for t h e particle--air j e t i n t e r a c t i o n d y n a m i c s were reviewed a n d m o d i f i e d t o explicitly include t h e effects o f t h e s i m u l a t i o n material. T h e e f f e c t s of R e y n o l d s n u m b e r , h o w e v e r , are o n l y implicitly i n c l u d e d . Based o n t h e results o f this s t u d y a set o f criteria for f u t u r e t e s t s t h a t c o u l d lead t o reliable p r o j e c t i o n s for larger-scale i n s t a l l a t i o n s is p r e s e n t e d in t h e f o r m o f d i m e n s i o n l e s s p a r a m e t e r s .
1. Introduction
The basic air-curtain principle is the utilization of rapidly moving air jets to separate t w o potentially different environments. Possible applications of this concept include protection against rain and snow for malls, sports stadia and construction sites. Our research programme at the University of T o r o n t o over the last decade [1--10] has concentrated on the development of both theoretical and experimental models for the dynamics of the precipitating particles as they interact with the complex flows of the air-curtain jets. Extensive work on both of these fronts has been performed for the horizontal air,curtain jet configuration [5--7]. Research on annular jet aircurtains, on the other hand, has only involved small-scale experimentation. Theoretical treatment of particle dynamics in annular jets is comparatively more difficult due to the complexity of the annular jet flow field. The major objective of our research with air,curtains is to establish the scaling laws for particle--jet interactions and to determine the feasibility of using air-jets for full-scale applications. The emphasis in this report is on the annular jet configuration. Previous studies with such a system were performed with models ranging in size from about 15 to 86 cm in diameter [8--10]. The simulation of rain was performed with either water drops [8,10] or glass beads [ 9 , 1 0 ] . The results presented here for the 6 m diameter o u t d o o r model provide a very important extension of physical size for studying the scaling laws. 0167-6105/86/$03.50
© 1 9 8 6 Elsevier Science P u b l i s h e r s B.V.
76 Another important aspect of the present work is the revision of the scaling laws, which was necessary in order to achieve consistency among previous and present results. Proper scaling is extremely important for the projection of small-scale results to full-scale installations. 2. Annular jet structure and scaling laws
2.1. Annular jet structure As previously mentioned, an air-curtain is just a jet of air formed and oriented for a special purpose. In the case of the annular jet configuration, air is discharged straight up through an annular nozzle to form a hemispherically shaped enclosure -- hence the name "air-curtain d o m e " . Protection against rain and snow within the enclosure is achieved via the interaction of the jet curtain and the precipitating particles. Falling rain and snow encountering the upward moving jet is slowed down, stopped and eventually accelerated up and away from the covered area. The annular jet has been studied for its uses in air cushion vehicles [ 11,12 ] and in oil burners and combustion facilities [13]. There are four basic regions associated with an annular air-curtain dome: ( 1 ) t h e exiting primary annular jet, (2) the entrainment regions, (3) the recirculation zone within the dome, and (4) the combined jet. The processes involved in creating these regions are excellently described by Chigier and Beer [13] and are paraphrased in the following paragraph for completeness. "As the jet exits the annular nozzle, a potential core {first region) with essentially constant velocity is established in the centre, with mixing zones forming (second region) on the inner and outer edges due to the shearing action of the jet and the stagnant air. On the outside of the annular nozzle there is an endless supply of air for the entrainment but on the inner side of the jet there is only a limited, fixed a m o u n t of air to meet the entrainm e n t requirements of the jet. This results in an internal vortex being set up (third region) which is toroidal in shape. The vortex creates a low pressure region and the resulting pressure gradient across the annular jet causes the jet to bend towards the axis of the jet. As the converging streamlines approach the axis, a stagnation region is set up and the resulting high pressure redirects the flow away from the axis until the combined jet expands in the same manner as a single jet (fourth region)." (See Fig. 1.) Chaplin [12], by making several assumptions about the flow pattern and the entrainment, as well as using the limiting case of infinitely thin nozzles, derived an equation for the height of the stagnation point above the floor. Adapted to the models studied at UTIAS [8], the result yields a stagnation point occurring at a height equal to the radius of the annulus. However, this height {which also represents the length of the internal vortex) is a function of the nozzle thickness-to-annulus diameter ratio (t/D) as well as the exit speed of the jet [13]. For a constant t/D, as the exit speed of the jet increases, the internal circulation increases causing a greater pressure gradient
77
let boundary~
~..
entrainment region /# /
/
/
//i
/ / " / /.~jet
ill
/ / ~ /I /
ll[
X
entrainment region
|/stagnation ~=/ point boundary-~,~,. \ \
i
i /~ .
~lit<
.___J
Ir
"\
\,, \',\
\,\
',kll I
vj
t
floor
et nozz e
vj
Fig. 1. Cross-sectional view of an annular jet. across the jet which would t e nd to force it towards the axis sooner. However, the increased inertia of the faster jet resists the increased force and the height o f the stagnation p o i n t remains essentially a constant. T he height o f the stagnation poi nt and the internal recirculation are o f prime i m p o r t a n c e when applications of the annular jet are considered. In all previous studies the nozzles were positioned at what would be field level in a full-scale stadium case. However, in the case of a baseball or football stadium the nozzle would be m o u n t e d above the stands in some manner and the resulting v o r te x and recirculation m ay be considerably different. Fut ure research must be directed t o studying, and if necessary, reducing the effects of the internal recirculation on the activities and people shielded by the d o me.
2.2. Scaling laws If the air d o me is to be used to p r o t e c t large areas (typically 100 m diameter) th en the c o n c e p t must be d e m o n s t r a t e d with the use of small-scale l a b o r ato r y and o u t d o o r models. In order to confidently compare models of various sizes and predict p e r f o r m a n c e for full-scale facilities, the cases in question must all be dynamically similar. Formal dimensional analyses have been d o n e [ 8 ,9 ] which led to t he dimensionless parameters t hat must be m a t c h e d f r o m case to case for dynamic similarity. The first approach is based on a formal dimensional analysis involving the nine physical variables associated with particle--jet interactions [8] : Vj, t , D , W,d, p p , p , l ~ , g
78 where Vj is the jet exit velocity, t the thickness of the jet nozzle, D the annulus diameter, W the wind velocity, d the rain drop diameter, pp and p the drop and air densities, respectively,/~ the air viscosity, and g the acceleration due to gravity. These variables are thus reduced to the following six non
Vj t
d
pp' W ' D ' D '
Vjtp
V}
p ' Dg
The fact that it is impossible to simulate all of these parameters simultaneously in air is clearly demonstrated if we consider the following three: t/D, Vjtp/p and V 2/Dg. As model size D increases, in order to keep t/D and Vj2/Dg constant, it is obvious that both t and Vj must increase; however, this conflicts with the requirement for Vjtp/p to be constant. This argument then leads to the conclusion that total dynamic similarity for the complete set of parameters considered is essentially impossible to achieve. An alternative approach suggested by Lake and Etkin [8] emphasizes the particle dynamics as the particle encounters an arbitrary flow field. This approach yields the following non
dt
-
~r1(ti - - ~ ' ) ~
(la)
rr~ (/~ -- b')~
(lb)
It I (dJ - - t b ' ) ~ - - 7r 2
(Ic)
where t~, b, tb are the non,dimensional drop velocity components after normalizing with respect to Vj. Similarly, t2', b', tb' are the non-dimensional components of the jet fluid velocity. The quantity fi is defined as /) ~__ [(/~ __ /~')2
.~_ (/) __ {)')2 _~_ (/~ __ i~)')2 ] 1/2
(2)
and 7rI and 7r2 are defined as follows: 1 7rI = -~ CDpd2 D / m
(3)
~2 = Dg/Vj 2
(4)
To reduce the complexity of the n~ parameter, previous analyses involved the use of a simplifying assumption, namely that the particle was falling in still air at its terminal velocity Vt. This resulted in n l being simplified to 7rl = g D / V 2
(5)
79 so that the third equation of m o t i o n (lc) became
d~) dt
[
-
(ytt2 1
7rl (~ -- tb')fi + \-~j]
(6)
Two seemingly important facts follow from such an analysis: ( 1 ) t e r m i n a l velocity is scaled with jet exit velocity (i.e., Vt/Vj is a constant); and (2) nl has the form of a Froude number and hence is an important scaling parameter. This "Froude-like" number allowed for the determination of the precipitation material and drop/particle size for any model based on a full-scale rainfall. Lake and Etkin [8] originally used water from a shower head to simulate rain. This was done mainly for convenience with the implications of the decision being made after the tests. In their later tests [9], they used glass beads as the simulation material in order to achieve proper dynamic scaling of the Froude number. Proper Froude number scaling was t h o u g h t to be more important than other factors such as particle Reynolds number scaling and raindrop deformation and breakup (which cannot be obtained using solid particles). However, later work by Raimondo and Haasz [5--7] on numerical simulations of particle dynamics in linear jet air-curtains showed a significant Reynolds number dependence. In particular, they f o u n d that under the influence of the jet a particle may experience a relative velocity much greater than its terminal velocity and therefore the drag must be evaluated for the Reynolds number based on particle velocity. Consequently, the drag and resulting trajectories are different from those expected from the simplified equations (5) and (6). Hence, the m e t h o d of scaling and the selection of the simulation material requires further consideration, which has been undertaken in the present study. Going back to the complete non-dimensional equations of motion, the two dimensionless parameters ~rj and 7T2 need to be conserved for dynamic similarity. For a spherical particle, ~ can be written as 3
p D
T(l : 4- CD --pp--d
(7)
Clearly the problem of maintaining 7r~ constant for different scales will arise through the drag coefficient CD. There is no one analytic function expressing CD t h a t will simplify the analysis. However, since most of the important previous experiments as well as the present tests involve low Reynolds numbers, Re, we shall consider CD = CD (Re) in such a flow regime. For R e ~ 1000 the CD curve can be expressed as a series of piecewise functions of the form
CD = k l / R en
(8)
where k 1 and n are constants. Of course the particle in the presence of a jet will experience a changing relative velocity, Vp, and hence a changing Reynolds number which will alter the drag coefficient over time. The Reynolds number for substitution into eqn. (8) is therefore R e , which is based on Vp, i.e.,
80
Rep = p V p d / #
(9)
Thus 7r~ becomes
7r~ -
3 k I p D VLVt d t 4 Re~ pp d Vt Vj t d
(10)
The Vt/Vj term was i nt r oduc e d here to allow for direct comparisons with the simplified analysis (eqns. 5 and 6). Equation (10) can be rewritten as:
p Vj Vtt
rrl =
k, Ret Re~, Rej -~
(11)
where
Re t = p Y t d / p
(12a)
and
Rej = p V j t / #
(12b)
or
lr 1 = ~r3 • F(Rep, Ret, Rej, D, t, d)
(13)
where
vj ~3
-
p
Vt Pp
(14)
The new dimensionless parameter ~3 is i m p o r t a n t because it contains the relationship generated f r om the simplified analysis with an additional t erm which can acco u n t for different materials used to simulate rain. Also important to n o te is that the f unc t i on F implicitly contains the jet Reynolds n u m b e r as well as the particle Reynolds numbers based on actual particle velocity and terminal velocity. Thus the non
3. Experiment 3.1. Description o f 6 m outdoor air-dome model The air for the 6 m diameter annular air-curtain model was provided by a 50 m 3 s -1 capacity fan driven by a 100 MW m o t o r . The facility consisted of a plenum chamber which was c o n n e c t e d to the fan via various transition sections (see Fig. 2). Air f r om the plenum, flowing radially outward from the centre region, exited through an annular nozzle vertically upward resulting in an " air - d o me" . U ni f or m i t y of the circumferential velocity profile was
81
Fig. 2. Top view of 6m diameter annular air-curtain test facility. (1) Circular-square transition piece, (2) angular transition piece, (3) diffuser section, (4) plenum, (5) annular nozzle.
achieved by appropriately positioning baffles in the plenum chamber. A jet thickness of 18 cm, corresponding to t / d = 0.03, was selected in order to allow for comparisons to be made with previous results [8--10]. Variable-pitch blades on the fan enabled the jet exit velocity to be varied in the 3.5--11 m s -1 range. Velocity measurements of the jet at the nozzle exit were made with the use of hot-wire anemometry and pitot probes. The circumferential velocity variation was f o u n d to be within ~15%. The radial velocity profiles across the nozzle exit were reasonably flat from the inner edge to the nozzle centre followed by a gradual increase toward the outer edge, with the outer edge velocity being about 1.5--2 times higher than the plateau level. This is most likely caused by the fact that the flow upon entering the nozzle must turn from an essentially horizontal direction to a vertical one in the nozzle. Although a flat radial velocity profile is desirable, we do not expect the integrity of the air dome and its protection capability to be drastically affected by radial flow non-uniformities.
82 The integrity of the annular jet was investigated in the following ways. First, sawdust was t h r o w n into the jet at various locations and the particle trajectories were observed. In all cases the sawdust was entrained by the jet, carried upwards and curved towards the axis, just as would be expected from the pattern of Fig. 1. The second m e t h o d involved flow visualization with the use of wool tufts attached to wires strung across the dome at various heights in a plane through the centre of the annulus and perpendicular to the floor. It was clearly evident that when the jet was turned on the tufts above the nozzle exit were pointing straight up, and started to bend inwards with increasing height, providing visual evidence of the formation and expected behaviour of the dome. A further study was done by measuring the jet speed at several locations in the curtain jet using a pitot tube. The pitot tube was placed at the approximate centre-line of the inwardly curving jet by noting the t u f t deflections and then oriented to record the maximum pressure difference on the manometer so that the direction at the m a x i m u m speed of the jet could be determined. A plot consisting of four points is shown in Fig. 3.
/.~
[ 5 9 , 30 °)
o
o c~
L (10 O, 9 0 ° )
'I\ 3
I 2 Radiol
I ) Position
(m)
Fig. 3. S p e e d and d i r e c t i o n o f t h e 6 m annular jet for t/h = 1/3 a n d blade setting 3. The o r d e r e d pair at t h e tip o f each a r r o w r e p r e s e n t s t h e velocity in m s -1 and t h e angle relative to t h e h o r i z o n t a l . Velocities w e r e m e a s u r e d w i t h p i t o t tubes.
3.2. Precipitation e x p e r i m e n t s w i t h 6 m o u t d o o r m o d e l
In the first instance we must determine the type of rainfall (as rainfall rate controls the water drop size distribution) to be simulated and then the model characteristics and requirements. It was shown above that among various non-dimensional groups of parameters associated with air jet--water drop interactions, the most important ones appear to be:
t/D ~1 = 7r3 " F ( R e p , R e t, R e j , D , t, d)
83 where ~3 = (Vj/Vt)(p/pp). Since one o f the objectives of this investigation is t o assess the ef f ect of t he f u n c t i o n F on the air dome, we shall, for the purposes o f selecting t he simulation material, assume F to be a constant. This results in Ir 3 replacing 7rl as one of t he three scaling parameters. Maintaining t/D cons t a nt in t he model and f, ill-scale cases results in similar jet flow configurations for the t w o cases. The const ancy of ~2 establishes the relationship b etwe en linear and velocity sc ~ling ratios. For example, if a fullscale installation is 16 times the size of the model, as is the case in this e x p e r i m e n t (i.e., Dfs = 16Din ), t he n the jet velocity for the full-scale will be 4 times t h a t f o r the m ode l (i.e., Vj~s = 4Vim ). The param et er 7r3 in t urn establishes the relationship between the jet velocity and the particle terminal velocity. F o r model experiments using-water as the simulation material, the r e q u i r e m e n t f o r Ir3 to be c ons t ant simply reduces to Vj/Vt being a constant in b o t h full-scale and m ode l situations. Simulation of a m e d i u m rainfall rate (~1 m m h -1) with a characteristic water d r o p diameter of a b o u t 2 m m (corresponding t o Vt = 6.5 m s -1 ), and using a linear scaling ratio o f D~s/Dm = 16, requires a Vt of a b o u t 1.6 m s -1 for the simulating water drops. The corresponding characteristic water drop diameter required f or model testing is a b o u t 400 t~m. T he p r o d u c t i o n of this d ro p size was achieved with the use of a SPRACO full cone cluster nozzle (15151014). Analysis o f the dr op size distribution (using m i c r o p h o t o g r a p h s o f drops falling on an oil film) yielded an average diameter of ~- 380 pm with a' standard deviation o f 140ttm. The corresponding mean Vt was a b o u t 1 . 5 m s -1 . The choice o f water drops t o simulate rainfall seemed appropriate for at least t w o reasons: (1) it is the same substance and (2) there are a variety of atomizing nozzles which are commercially available to produce almost any desired size range of drops. However, the choice of water drops does introduce some difficulties as well. Full-scale raindrops of the order of 1--3 m m diameter d e f o r m and m ay experience breakup in the presence of an air jet. Such events are n o t only difficult to model experimentally but also present difficulties in the analysis of the full-scale case. The 380-um drops used in this investigation do def or m , albeit less than full-size drops, but t hey do n o t break up. The breakup of large raindrops into smaller drops with smaller terminal velocities reduces the workload of the lower port i on of the jet, leading to the r e q u i r e m e n t o f a reduced jet exit velocity. On the o t h e r hand, with no drop breakup in the case of the model, t he jet must handle the simulated large drops requiring higher velocities than would be necessary in the presence o f p r o p e r simulation o f dr op breakup. F o r modelling purposes i n order to p r o d u c e a fine spray of the desired small size, a pressurized waterline is needed as the degree of atomization is, in part, a f u n c t i o n of the pressure. T he finer the mist, the higher the pressure and hence a greater water flow for a given nozzle. This means t hat t h e simulated rainfall rate f r om a particular nozzle increases with decreasing size o f drops p r o d u c e d , which is exactly the opposite o f what happens in nature.
84 T h e s t e a d y , all d a y , low r a t e t y p e o f rain is a s s o c i a t e d with small d r o p s while t h e h e a v y d o w n p o u r s with large rates are c o m p r i s e d o f large drops. This a f f e c t s t h e d r o p c o n c e n t r a t i o n p e r u n i t v o l u m e o f air w h i c h c o u l d result in d i f f e r e n t d r o p i n t e r a c t i o n effects. T h e q u a n t i t a t i v e e f f e c t s associated w i t h the full-scale a n d t h e m o d e l c o n c e n t r a t i o n s are e x t r e m e l y c o m p l e x a n d r e q u i r e statistical i n f o r m a t i o n w h i c h is n o t c u r r e n t l y o b t a i n a b l e f o r t h e e x p e r i m e n t a l m o d e l s . H e n c e , t h e e f f e c t s o f d i f f e r e n t and changing c o n c e n t r a t i o n s are n o t explicitly k n o w n . N o w w e c o n s i d e r t h e s o u r c e o f t h e d r o p s used in this e x p e r i m e n t . By o b s e r v a t i o n it c o u l d be seen t h a t t h e exit speeds o f t h e d r o p s at t h e w a t e r n o z z l e w e r e g r e a t e r t h a n t h e i r t e r m i n a l velocities d u e to t h e w a t e r l i n e pressure. T h u s the air j e t v e l o c i t y r e q u i r e d to s t o p the p e n e t r a t i o n of t h e s e " f a s t e r " d r o p s is b o u n d to be " t o o h i g h " , leading to s o m e w h a t c o n s e r v a t i v e results. A n o t h e r e f f e c t t h a t c o u l d lead to c o n s e r v a t i v e results is a s s o c i a t e d w i t h t h e f a c t t h a t t h e w a t e r d r o p s in t h e m o d e l tests w e r e i n t r o d u c e d at a height o f 6 m a b o v e t h e floor. Since t h e jet rises well a b o v e this p o i n t , a p o r t i o n o f t h e j e t is n o t utilized f o r t h e slowing d o w n p r o c e s s o f t h e d r o p s as w o u l d be t h e case in a full-scale facility. In o r d e r to achieve a w i d e s p r a y p a t t e r n f o r t h e tests, t h r e e nozzles were e m p l o y e d . T h e y w e r e p o s i t i o n e d along a d i a m e t e r o f t h e a n n u l u s such t h a t o n e n o z z l e was d i r e c t l y o n the axis o f t h e a n n u l a r j e t and o n e o n either side at a distance o f 1.8 m f r o m t h e axis. T h e height o f t h e nozzles a b o v e t h e f l o o r was a b o u t 6 m. Water was supplied t o t h e nozzles t h r o u g h o r d i n a r y 1.3 c m d i a m e t e r garden hoses w h i c h w e r e h o o k e d u p t o a s t a n d a r d waterline w i t h n o m i n a l pressure o f a b o u t 5 5 0 k P a (80 psi). T h e c o r r e s p o n d i n g f l o w t h r o u g h t h e n o z z l e s was a b o u t 3.41 m i n -~ . T h e n o r m a l m e t h o d o f testing involved t h e d e t e r m i n a t i o n o f the q u a n t i t y o f w a t e r r e a c h i n g t h e f l o o r in a given t i m e w i t h t h e j e t o f f and t h e n w i t h t h e j e t o n t o see h o w m u c h p r o t e c t i o n was achieved. With the o u t d o o r facility this was n o t an easy task. First o f all, side winds w e r e a p r o b l e m . Since t h e t e r m i n a l v e l o c i t y o f t h e 3 8 0 - ~ m d r o p s is o f t h e o r d e r o f 1.5 m s -~ , a side wind o f t h a t m a g n i t u d e (3.5 m p h = 3 k n o t s ) is e n o u g h to cause t h e s p r a y f r o m t h e n o z z l e t o fall at a 45 ° angle so t h a t m o s t o f t h e s p r a y d o e s n o t even land w i t h i n t h e area b o u n d e d b y the annulus. T h e s e c o n d p r o b l e m was t h e efficient c o l l e c t i o n o f t h e s p r a y t h a t did r e a c h t h e floor. A t a w a t e r f l o w r a t e o f 3.41 m i n -~ , assuming a u n i f o r m c o v e r a g e o f t h e area b o u n d e d b y t h e nozzle ( ~ 25 m 2 ), t h e e x p e c t e d d e p t h o f w a t e r a f t e r 1 m i n is o n l y a b o u t 150 p m . C o n s e q u e n t l y , f o r m e a s u r a b l e q u a n t i t i e s o f w a t e r o n the f l o o r long c o l l e c t i o n t i m e s are n e e d e d . In a d d i t i o n to t h e d i f f i c u l t y o f m a i n t a i n i n g stable e x p e r i m e n t a l c o n d i t i o n s f o r long times, long c o l l e c t i o n t i m e s also p o s e an e v a p o r a t i o n p r o b l e m , especially f o r small drops. This p r o b l e m is w o r s e w i t h t h e jet t u r n e d o n since d r o p s w h i c h r e a c h t h e f l o o r are subject t o a g r e a t e r r a t e o f e v a p o r a t i o n c a u s e d b y t h e r e c i r c u l a t i o n flow.
85 Another problem, caused by the presence of side winds, is the wind interaction with the annular jet itself, causing the jet to bend in the direction of the wind. As has been shown by Lake and Etkin [ 9 ] , this bending of the jet results in a significant loss in the ability to stop precipitation, and if the wind is strong enough, the annular jet can completely collapse, Both of these cases were at one time or another observed for our 6 m model. As the m a x i m u m exit velocity of the jet was only 11 m s - ' , the presence of steady side winds and the inevitable gusts made it nearly impossible to study fully quantitatively the performance of this air roof. Fortunately there is a daily period when one can expect little or no side winds. This occurs in the early morning, so all tests were therefore carried out during the period from just before sunrise until about an hour and a half after. Even though the tests were performed in the near absence of winds when the water drops from the spray nozzle were falling nearly straight down, quantitative measurements were still not possible. Instead a "qualitatively quantitative" estimate was made in the following manner. With the jet off, an observer could " d e t e r m i n e " the quantity of water falling on an exposed arm and eye glasses over a brief period of time. This was then repeated with the jet on so that comparisons could be made. Photography was also used to d o c u m e n t the protection. Many photographs from different vantage points were taken. Good photographs were obtained by standing on either side of the annular nozzle and looking straight up; the pictures show the upward-moving spray. The best photographs were the sequence shots, taken with a 2.5 frames per second m o t o r drive, showing the spray first coming d o w n with the jet off, then being blown upward when the jet is turned on. Figure 4 shows such a typical sequence for the case when the jet exit velocity was 7.5 m s -1 (time between photographs is 5 s). At the lowest speed setting (Vj -- 3.5 m s -1 ) with the presence of even the smallest of wind speeds, there was at least 50% penetration. On one brief occasion when there was absolutely no side wind present, almost 100% protection efficiency was achieved. This confirmed Lake and Etkin's results [9] regarding the possible catastrophic effects of a relatively high side wind. At V~ = 5.5 m s -~ , the no-wind case yielded a protection efficiency of about 90--95%. With slight side winds, the upstream area was completely protected but the downstream end suffered 20--30% penetration. For jet exit velocities of 7.5 and 11 m s-~ there was very little difference in protection efficiencies. The only time t h a t penetration was noticed coincided with a gust of side wind. Essentially complete no-wind protection was achieved and only minimal penetration occurred (5--10%) in the presence of slight side winds. The only real difference of course was that for the higher speed setting the side winds h a d t o be somewhat stronger to cause the same a m o u n t of performance deterioration as observed in the lower-speed case. Regarding the effect of side winds, it is important to note that the winds were due to real full-scale atmospheric air movements, while the annular model jet velocities were scaled down by a factor of four (the velocity scale
86
Fig, 4. S e q u e n c e o f p h o t o g r a p h s s h o w i n g w a t e r d r o p trajectories a f t e r t u r n - o n o f air jet w i t h t h e 6 m air-curtain test facility. Vj ----7.5 m s -1 . Time b e t w e e n p h o t o g r a p h s : 5 s.
87 factor). Thus, for full-scale installations, where the jet velocities will be considerably higher than in the model, the effect of side winds is expected to be less significant. One of the goals of this experiment was to find the critical jet velocity needed to " s t o p " precipitation from penetrating the air-curtain dome. For the purpose of this study, we have defined the critical velocity, Vc, to be the jet velocity t h a t results in about 95% protection efficiency (i.e., 95% of the precipitation is prevented from penetrating the air dome). A discussion of the present results and comparisons with previous experiments will follow. 3.3. Precipitation experiments with 60 cm laboratory model The 60 cm model was a small-scale version (1:10 linear scale) of the 6 m o u t d o o r facility and it was originally built to study the pressure losses associated with the 6 m system. Attempts were made to use this small model for precipitation simulation experiments with water drops. Due to difficulties encountered in the production and control of the small water drops needed these experiments were unsuccessful. Although glass beads were f o u n d to have limitations for particle trajectory simulations associated with linear jets [5--7 ], their applicability for annular jet simulations has not been ruled out so far. Therefore, glass bead tests were undertaken with the following three objectives: (1) to test the reproducibility of earlier experiments [9] with glass beads, (2) to show whether or not particles with a terminal velocity of about 0.5 m s -1 (the desired value based on V j / V t being constant) could be stopped by a 60 cm annular air-curtain whose highest jet exit speed was 7.5 m s -l , and (3) most importantly, since the parameter 7r3 contains a term to account for the density of the simulation material, this test could provide useful information regarding the validity of 7r3 as a scaling parameter. We have proposed t h a t 7r3 should replace the Vj/V t parameter widely used in previous annular air-curtain studies. The glass beads were in the size range 74--105 ~m and had a specific gravity of 2.39. A feed system was improvised that neither ensured that the beads would slow d o w n to terminal velocity before encountering the jet nor that the beads were adequately separated to prevent wake interaction. Thus any results would be conservative. The experiments performed with these beads, at a jet exit velocity of 7.5 m s -1 , yielded an average penetration of only about 2% which was consistent with previous results [9]. Thus, the first two objectives of the test were met with positive results. The final matter of checking the validity of ~3 as the relevant scaling parameter will be discussed below.
4. Comparison of present and previous results This section summarizes all the important results from the present and previous experiments in order that comparisons and conclusions may be made based on the new general scaling laws. Table 1 lists the important
(ram) 5.1 7.7 10.6 14.3 6.9 6.9 18.0 17.2 25.8 34.4 180.0
18.0
t
D
(m)
0.300 0.297 0.294 0.291
0.150 0.150
0.600 0.860 0.860 0.860
6.00
0.600
Lake a n d E t k i n [ 8 ] , water drops
Lake a n d E t k i n [ 9 ] , glass beads
Baines and Wong (see ref. 10), water drops
K a m e n a n d Haasz, water drops
K a m e n a n d Haasz, glass beads
3.0
3.0
3.0 2.0 3.0 4.0
4.6 4.6
1.7 2.6 3.6 4.6
(%)
t/D
7.5
7.5
22.7 22.7 21.5 13.3
6.10 2.74
24.4 21.3 21.0 15.2
( m s -1 )
Ve
Vt
1.5
0.380
0.515
2.95 2.95 2.95 2.95
0.728 0.728 0.728 0.728
0.098
0.515 0.207
7.62 7.62 7.62 7.62
( m s -1 )
0.098 0.050
2.6 2.6 2.6 2.6
(mm)
d
S u m m a r y of present results a n d previous results for a n n u l a r air-curtains
TABLE 1
14.6
5.0
7.7 7.7 7.3 4.5
11.8 13.2
3.2 2.8 2.8 2.0
vdvt
PVtd ----
3.46
39.3
5.0
6.1
147.1 147.1 147.1 147.1
3.46 0.71
1356 1356 1356 1356
Re t :
7.7 7.7 7.3 4.5
4.9 5.5
3.2 2.8 2.8 2.0
Yc yt" SG
O0 O0
89
parameters and results from Lake and Etkin's water drop [8] and glass bead [9] experiments, Baines and Wong's water drop tests (see ref. 10) and t he current wo r k for b o t h water and glass beads. For ease o f com pari son all results have been converted t o SI units. The numbers from t h e previous works, if n o t directly stated a nyw her e in the respective reports, were either inferred from graphs or calculated from parameters that were explicitly stated. Th e drop or particle R e ynol ds n u m b e r in Table 1 is based on the terminal velocity Vt. This R e t was calculated in order to determine the R e y n o l d s n u m b e r f o r the drop as it first encounters the jet. Thus, R e t was c o m p u t e d as pVtd Ret
-
(15)
#
where p = 1.225kgm-3 and p --~ 1.8 x 10 -s kg m "1 s-' The q u an tity ~3 was defined as ~3 =
(16)
Since p is essentially a constant for simulation in air and pp can be expressed as the particle specific gravity (SG) times the density of water, 7r3 can be rewritten as: ~r3 =
(17)
This lr~ is p lo tted as a f unc t i on of the particle Reynolds n u m b e r in Fig. 5. Neglecting the Lake and Etkin [8] water tests because o f the high Reynol ds numbers, a horizontal straight line m a y be drawn through the data indicating t h a t 7r~ is essentially i n d e p e n d e n t of Reynolds n u m b e r based on particle
8 n 6
*
+
÷
D
4
o Loke ond Etkin D ~alnes and wono & Kemen ond Itoasz
Woter Drops
2
o o0 o
Gloss Beaes { e+ L.oke ond E f k i n Kamen and Haosz
0; 10 -~
I
I
I
10 0
101
10 a
Particle
Reynolds
Number
10 3
(Re i) F
Fig. 5. Non-dimensional parameter ~3 versus particle Reynolds number R e t.
90
terminal velocity. This has the very important implication that the function F(Rep, Ret, Rej, D, t, d) in eqn. (13) has remained essentially constant for the various simulations. This confirms the significance of ~ as the controlling scaling parameter, replacing ~ ] . Figure 6 shows ~ as a function of annulus diameter and again it appears that ~ is independent of model size, at least for the size range tested so far (i.e., Dr, < 6 m). This can be tied in with the Reynolds number independence. The model sizes used so far have necessarily demanded small water drops and hence low Reynolds numbers. This leads to a plot of Re as a function of annulus diameter as shown in Fig. 7. Intuitively it is clear that a largerdiameter model would require a larger jet velocity to maintain dynamic similarity, and in fact from the equations of motion arose the parameter n2 = Dg/V~h which dictates how jet speed varies with model size. This greater jet velocity would then be able to deflect larger drops which have greater Reynolds numbers. Hence, the Re--D curve should start near the origin and rise up and to the right, asymptotically approaching the real rain's Reynolds numbers as model size increases. Figure 7 shows that this has not occurred, which indicates that the individual tests simulate different raindrop sizes. In fact Lake and Etkin's water tests [8] used drops of the size of real rain but on a very small model. Therefore, one must exercise caution in interpreting such a mixed variety of results. These results from all sources not only have not simulated the same rainfall, but also have not had dynamically similar annular jets due to various t/D ratios. However, the trends noted in Figs. 5 and 6 indicate that the performance (namely, the ~ needed to achieve ~ 9 5 % protection
10 !
o =L
10 z
8 10' t~
6 > o
4
10 o
F o Lake and Etki~ Water Drops ~ 0 8olnel ond Wonq L& Komln and HOOIZ
2
f o Lake and Etkin woler Orops~a Barnes and Won~ L A Komen
÷
Gloss 8eod$~ + Lake and Elk[n l * Komln and Hoosz
0 01
Ol
2
I
0.4
r
I
0 . 6 0.8
Annulus
I
1
Diameter
Gloss Beads { +e
J
L
I
2
4
6
(rn)
D
I
I0 q
Fig. 6. Non-dimensional parameter ~'3 versus annulus diameter D . Fig. 7. Particle R e t versus annulus diameter D .
I
01 Annulus
t
and Efkin Komen and HOOSZ Lok#
Diameter
(m)
91
efficiency) of the air-curtain d o m e is n o t seriously affected by the disparities among the various simulations. 5. Conclusions
The major objective of the present investigation was to verify the validity of the air-curtain scaling laws by extending previous small-scale laboratory simulations to the testing of a 6 m diameter o u t d o o r air-curtain d o m e facility. In addition to the successful testing of the 6 m model with the use of water drops, tests were performed with a 60 cm diameter small-scale version of the 6 m model. Analysis of the current experimental results as well as all previous aircurtain d o m e results led to the identification of a new scaling parameter, ~ = V c / ( V t " SG), which plays an important role in determining the critical jet velocity needed to provide a certain level of protection efficiency. Thus ~r~, together with t / D and 7r~ = Dg/V~j, are the parameters t h a t need to be kept constant in model and full-scale situations. The ratio t / D assures kinematic similarity for the jets, ~r: establishes the relationship between linear and velocity scaling, and ~r~ determines protection efficiency. Direct comparisons of our results for the 6 m model using water drops and the 60 cm model using glass beads yielded excellent agreement for ~ . Further comparisons with previously published results also yielded good agreement for ~ even though case-to-case variations of t/D, particle R e , etc., were present. This implies that, at least for the particle Reynolds number and annulus diameter ranges considered, the effect of such variations does not significantly affect air-curtain performance. With a major assumption that the validity of the three scaling parameters (t/D, 7r2 and 7r~ ) could be extended to full-scale air-curtain installations, we shall now a t t e m p t to make certain projections for a 100 m diameter air dome. Maintaining t/D = 3%, as was the case in the present experiments, leads to a jet thickness of 3 m. For our 6 m model experiments with water (SG = 1) Vc, Vt and ~'3 were 7.5 m s-1, 1.5 m s-1 and 5.0, respectively. Assuming a characteristic raindrop diameter of about 2 mm with Vt = 6.5 m s-1 (this corresponds to a medium rainfall rate of about 1 m m h-~), we obtain a critical jet velocity of about 33 m s-1. The corresponding air flow (Q) and power (P) requirements are 3 1 0 0 0 m a s -1 (66 Mcfm) and 10 000kW (113 000 hp), respectively. Similar calculations for a heavy rainfall, with drops of about 3 m m diameter, yield the following projections: Vt = 8 m s -1 , Vc = 40 m s -1 , Q = 38 000 m a s -1 (80 Mcfm), and P = 36 000 kW (48 000 hp). Acknowledgements The authors wish to acknowledge the financial support provided by Air Roofs Canada for the construction of the 6 m diameter facility, and the University of Toronto Institute for Aerospace Studies for providing the site
92 for the facility. The research programme was performed with the help of an N S E R C g r a n t . D i s c u s s i o n s w i t h Dr. B. E t k i n a r e a l s o g r a t e f u l l y a c k n o w l edged.
References 1 G.A.S. Allen, Experimental investigation of an air-curtain for protection of an outdoor power installation from salt spray, UTIAS Tech. Note No. 171, University of Toronto, Toronto, Canada, 1971. 2 G.A.S. Allen and R.T. Lake, Trajectories of raindrops in a jet issuing into a normal crosswind, UTIAS Tech. Note No. 165, University of Toronto, Toronto, Canada, 1971. 3 A.A. Haasz, B. Etkin, R.T. Lake and P.L.E. Goering, Laboratory simulation of an aircurtain roof for the Ontario Science Centre, UTIAS Tech. Note No. 192, University of Toronto, Toronto, Canada, 1975. 4 A.A. Haasz and P.L.E. Goering, Intermittent enclosures -- air-curtain walls and roofs, Proc. IASS World Congress on Space Enclosures, July 1976, Montreal, Quebec, Canada, WCOSE-76, Vol. 1, pp. 151--163. 5 S. Raimondo and A.A. Haasz, Single and dual air-curtain jets used as protection against precipitation, UTIAS Rep. No. 227, University of Toronto, Toronto, Canada, 1978. 6 A.A. Haasz and S. Raimondo, Effectiveness of an air-curtain canopy against precipitation, J. Wind Eng. Ind. Aerodyn., 6 (1980) 273--290. 7 A.A. Haasz and S. Raimondo, Performance of adjacent dual-jet air-curtain roofs, J. Wind Eng. Ind. Aerodyn., 10 (1982) 79--87. 8 R.T. Lake and B. Etkin, The penetration of rain through an annular air-curtain dome, UTIAS Rep. No. 163, University of Toronto, Toronto, Canada, 1971. 9 R.T. Lake and B. Etkin, Experimental simulation of the interaction of wind-driven precipitation with an annular air-curtain dome, UTIAS Tech. Note No. 182, University of Toronto, Toronto, Canada, 1973. 10 B. Kamen and A.A. Haasz, Experimental investigation of annular air-curtain domes, UTIAS Rep. No. 288, University of Toronto, Toronto, Canada, 1984. 11 G.D. Boehler, Aerodynamic theory of the annular jet, IAS Rep. No. 59-77, Institute of the Aeronautical Sciences, New York, 1959. 12 H.R. Chaplin, Effect of jet mixing on the annular jet, Navy Department David W. Taylor Model Basin Aerodynamics Laboratory, Washington, DC, Aero Rep. 953, 1959. 13 N.A. Chigier and J.M. Bedr, The flow region near the nozzle in double concentric jets, Trans. ASME, J. Basic Eng., 86 (1964) 797--804.