Experimental simulation of the interaction of wind driven precipitation with an annular air curtain dome

EXPERIMENrAL SIMULATION OF THE INTERACTION OF WIND DRIVEN PRECIPITATION WITH AN ANNULAR

AIR CURTAIN DOME

by 1 4 SEP.

lil!

R. Lake and B. Etkin

EXPERIMENTAL SIMULATION OF THE INTERACTION OF WIND DRIVEN PRECIPITATION WITH AN ANNULAR

AIR CURTAIN DOME

by

R. Lake and B. Etkin

Submitted: March 1973

I •

Acknowledgement

This work was supporteà under NRC grant No. A-1894.

I would like to thank Mr. A.Harting anp' Dr. H. Teunissen for their he lp-ful discussio~s anà suggestions during this p roj ect.

Further I shoulà like to thank Mr.S • Brinton for his assistance in the set up and running of this experiment.

Finally I shoulà like to express a considerable debt to Prof. B. Etkin not only for his assistance and supervision on this project, but as weil for his interesteà friendship over the several years that I have had the pleasure to work

with him. , .

Summary

A simulation of the interaction of wind-driven rain with an annular air curtain dome was conducted in which small glass spheres were employed as the simulating material. Non-dimensional collection functions were obtained for a range of winà speeàs at two values of the particle quasi-Froude number ~l • . In addition, data was obtained for the shape of the jet centerline and fer the up-stream wallof the dome. A simple rigid-body, uniform laminar flow model of

the drop-plume interaction suggests a àependence of the non-dimensional collectien function on V

l opposite to what was obtained in these experiments and in UTIAS Report

163.

It is apparent that the simulation of precipitation-air flow inter-actions is quite complex and may involve such phenomena as turbulent diffusion and the action of shear-induced lift forces. The analysis given in Part B indi-cates that turbulent diffusion may be responsible for the above discrepancy.

There is however still a degree of uncertainty in projecting the re-ported .results to full scale. The basic result that power requirements are greater than reported in UTIAS R~port

163,

is, however, substantiated.

1 .. 2.

3.

4.

5.

6.

7.

8.

9.

Table of Contents

I NTR ODUC TI ON (Part A by R. Lake) EXPERD1ENTAL APPARATUS

MOTION EQUATIONS

StMULATION-DISCUSSION OF NEGLECTED PARAMETERS WIND FLOW FIELD

RESULTS

a) ~he Jet Flow Field

b) Non-dimensional Collection Functions

DISCUSSION OF RESULTS ••• FULL SCALE IMPLICATIONS THE FUTURE OF AIR CURTAIN DOMES

REFERENCES

APPENDIX I: Properties (Pqysical anà Aeroàynamic) of theCGlas'S Beads

APPENDIX 11: Lift Forces on Rigià and Deformable Particles in Shear Flows

APPENDIX 111: The Relationship Between Trajectory Computa-tioJ;ls and Non-Dimensional Collection Functions

(Part Bby

B.

Etkin)

APPROXIMATE ANALYSIS OF THE EFFECT OF 'I'URBULENT DIFFUSION

iv Page .1 1 3

4

6

7 7

7

9 10 12

15

c d D g m N(x,d) RN T u,v,w u',v',w'

u

v

x,y,z

w

5

,

,

A

d B Q. k

v

K List of Symbols mass of penetrating contaminant

(6C/6C

_a) particle diameter

annulus diameter

gravitational constant particle mass

particle number density function Reynolds number

jet thickness

particle velocity vector fluid velocity vector mean tunnel velocity particle velocity

particle terminal velocity in still air jet exit veloci~y

particle position vector wi;nd velocity

non-dimensional scaling parameter

angular velocity of a particle particle, fluid viscosity particle, fluid density

denotes a non-dimensional quantity lengths are non-dimensionalized with respect to ~and velocities with respect te V

J

The following pertain ,only to Appendix II particle radius, drop radius

tube diameter Volume flow

velocity gradient kinematic viscosity l6Q./B

4

Page No'.

3

I I . l

.E' R R fiT Pi.

Technical Note No. 182 by

R. L~e & B. Etkin

3rdline from bottom delete '=' in 'a,= lift force'

2nd paragraph, 4th line shouJ.d read:

'migrates to the axis, i.e., towaràs the·velocity maximum'

All references to Tables 1, 2 in Appendix II, .pg. 11.1 sheuld be replaced by Tables AlI.l, AlI.2 respectively.

Readings of Tables currently labelled Al,2 'should read AI1.l, AII.2

respectively.

In Table Al a.ll references to 'unflowing' sheuld be replaced by downflowing •

The final column· of T~ble Al should xead:

settling velocity/fluid velocity All areas. in Table I are in square feet.

PART A - by R. Lake 1. INTRODUCTION

The pra&matic function of any architectural structure is to maintain certain environmental variables such as temperature, humidity or contami~ant concentration within some prespecified ranges in a prescribed space. Ordinarily this is accomplished by enclosing the region of interest by means of asolid structure, the form of such a structure being dictated at least in part by its protective function. The dynamic structure l accomplishes this 'protective func-tion' by means of air walls and roofs; that is without any solid structure.

Recent studies2 have indicated that it may be feasible to protect a given space by an 'annular curtain dome'. In such a device, the region to be protected is surrounded by an annul~r jet nozzle. Due to entrainment the annu-lar air sheet issuing from the nozzle folds in upon itself to completely enclose the region within the annulus.

The present work extends the initial studies2 in two ways. Firstly the effect of side wind is considered and secondly the simulation material, formerly actual water drops is in this case replaced with fine glass beads in order to achieve proper dynamic scaling.

In the course of this work it became apparent that the scaling of the annular air dome-rain interaction was much more complex than had been anticipated. Hence considerable space is devoted herein to consideration of those parameters which were not included explicitly in the si~ulation.

2. EXPERIMENTAL APPARATUS Precipitation Wind tunnel

The experiments were carried out in the UTIAS Precipitation Wind Tunne13 • This tunnel has a test section

42"

x

42"

and can operate at wind speeds of O-lOft. per seconde It is equipped with a simple vibrating sieve mechanism via which the simulating material enters the tunnel. This bead feed system can be placed at apy of

5

locatiol1s in the tunnel roof depending on the value of W/V

t employed. The system as reported previously3 required some modification before repeatable results could be obtained. This consisted of adding a clamp to prevent the motion of the honeycomb relative to the sieve andaguide to aid in loading the sieve.(see Fig.

5).

An inherent disadvantage of the technique employed is that i t -is.; im-possible to maintain the same distribution of particle velocity over the model region for all the positions of the bead feed. Locations nearest the model exhibit the greatest variation in terminal veloeities (fast partieles at the leading edge; slow ones at the do~nstream edge) than locations farther upstream. This varia-bility c9ll1d be removed by 'rai~ing' over a large area of the tunnel or by using a bead sample having a very narrow diameter range.

The Annular Jet Nozzle

The annular jet nozzle was supplied via a ~uct assembly (see Fig. 1) from a Buffalo Forge 2LEH variabie speed centrifugal" blower; controlled by a variabie transformer in conjunction with a sliding valve on the blower intake.

The blower can deliver up to 200 CFM at .95" SP or 50 CFM at 3.65" SP.

Primary flow volume~ was determined fromanlorifice plate in the delivery pipe upstream of the diffuser. The orifice plate was designed according to speci-fications in the ASME Flowmeter Computation Handbook (1961). Attention

4

was paid to the length of pipe both ~pstream and downstream of the orifice plate. The pressure drop across the plate was measured with a standard Betz manometer. The mean velocity in the nozzle exit was then computed from the measured volume flow through the orifice by means of the equation of continuity.

The contraction upstream of the jet exit in the case T/D

=

.051 was approximately 6:1. The T/D ratio was variable: two hemispherical plugs could be threaded onto the steel center shaftto give T/D

=

.05 and T/D

=

.01. (see Fig.2).

In order to collect the particulate matter that penetrated the dome, shallow removable pans (1" de~p) w.ere mated to the drums such that the edge of the jet exit was flush with the tunnel floor. Af ter a run the pan could be removed for weighing. This was accomplished on a Metler B4clOOO beam balance.

Run Technique

A typical run consisted of first weighing a set of samples of the beads then setting the tunnel and jet speeds and then loading the beam feed system. Finally af ter the beads had all run out,the pan was removed from the tunnel and

the accumulated material was weighed. Boundary Layer Generation

To obtain arealistic velocity profile it would be necessary to simulate the earth~s surface layer 5 • At the expected scale (1:100) this would require a model boundary layer thickness of at least 2 ft. Sinçe it was not particularly germane to the present investigation, ~he time investment necessary to produce a logarithmic profile using m10cks or spires in the available distance was con

-sidered excessive, and a more modest program was followed. Various combinations of barrier plates and roughness blocks were employed. The flow field was examined downstream of the barrier plate to ensure that the blocks were placed downstream of the point of reattachment, and in the test section to get a qualitative idea of the flow field, i.e" existence of pronounced flow reversals etc. Reasonable results were obtained for the configuration shown i~ Fig. 3. This set up was employed in all of the tests reported herein. Using a hot wire system (DISA55DOl anemometer and DISA55D10 linearizer-see Fig. 6) profiles of the mea~velocity Ü and the longitudinal turbulence intensity u'/Ü were measured on the tunnel centerline a few inches upstream of the jet exit. Since the RMS voltmeter em-ployed in the u' measurement had a lower cutoff frequency of 2 Hz. an analogue

computer (PACE TR-20) was employed to compute u' at low speeds. The computer was also used to obtain the mean velocity (see Fig.

7).

Photographs of the turbulence signal were taken via a Tektronix Polaroid Scope camera in conjunction with a Hewlett Packard Storage Oscilloscope.

Photograpl]y

To eliminate reflections from the,tunnel windows a small portable room was bgilt which could be positioned at any point along the work section and which was large enough to accomodate a photographer and his equipment. Black burtains were used to cover the open window space on either side of the room.

To illuminate the jet a standard slide projector was found to give ade-quate results when placed 2-3 ft downstream of the annular jet maiel.

Smoke was produced from cigarettes and fed into the dome interior at velocities which were sufficiently low that they did not influence the dome flow. All photographs were taken with a Polaroid Land camera using 3000 type

47

film.

In addition to the smoke photographs of the jet flow, photographs were taken of the simulated rain shower.

The use of video tape (SONY PORTAPAK) was also experimented with briefly. This appears to be a promising technique as it allows the entire dynaroics of the flow to be studied. Not only can the flow be repeatedly examined but as weil the video tape can be stopped at any time and still photographs taken of the TV image. Measurement of the W

=

0 Case

To determine the collectiop function with the wind off it was necessary to remove the bead feed system and the annular jet model from the wind tunnel and arrange then as shown in Fig.

4.

The cloth shroud was necessary to limit the influence of small air currents present in the room. Although no measurements o~

the jet velocity were made at the point of bead release, observations of beads released by hand indicated th at the jet velocity over at least the first couple of feet from the bead feed system was not very large. Consequently it was felt safe to assume that the beads entered the jet at terminal velocity.

The test procedure followed in the W

=

0 case was identical to that in all the other cases.

3.

T,.HE MOTION EQUATIONS

The particle motion equations for the vertical xz plane are in tne simple 'drag form' from Etkin

6

1\ A du V

_{(''I, ")}

=

$1 u -u

d~

A U 1\ j. A 1\ 7r₂ dw V ( l)

~

7rl Ä (w'-w)

-"

u u

d~

A W

d~

_"

u

In the event we wish to consider the presence of a

=

lift force of the Magnus type the motion equations for 2-D flow in the xz plane

(g

=

(o,n,o»

are:

n -

angu~ar rotation rate k

=

constant

1\

"

7T8 du

v

_(",

_") (, .!,\) 7T_l u -u + - - w'''''W 1\

"

1\ dx u u ( 2)

d~

1\ 7T 8 7T2 V _{1\ " (11, 11)}

-

7T l (w'-w) + - u -u

-,;-~

_"

1\ u u U 11 _i ' 7T l

~

7T2

!L

_{V 2} V t J knT 7T8 _mV J

4.

SIMULATION-DISCUSSION OF NEGLECTED PARAMETERS

In this section many of the significant phenomena not included in the

simulation are discussed.

(a) Problems iQ Scaling

From dimensional analysis the non-dimensional parameters are

7T

₅

""'=

_.

-T/D 7T

₇

=

~ /~.

p 1 '

(4)

Clearly in any experimental situation it is not possible to maintain all of these parameters at their full scale values. In the experiments herein only 7T

17T27T

₅

were considered. Hence the results may be affected by ~he neglected para-meters.

In order to deal with particulate clouds we must add further restric-tions. In a full scale rain we will have a distribution of 7T

l (due to the distribution of V

t) and hence it will be necessary that we have the same distri-bution for the experiment. This implies that the distridistri-bution functions for V

t in the model and in the full sca~e must be 'similar' in the mathematical sense.

I~ the particle number density is higher than same minumum the partic\es interact in such a way that the terminal veloc{ties exceed that of an individuàl particle falling by itself7 • In order to simul~te this effect (i.e., to obtain the same fractional change in V~) it would be necessary to replicate the full scale number densities in the model. Even this may n§t be sufficient as the particle interaction law is Reynolds number dependent. Since in thie"majbyity of cases it will not be possible to simulate both the individual particle V

t and the correct i~teraction effects it would be advantageous to know which is tfie more important. Owing to the great dispersion that occurs af ter contacting fhe

jet it seems likely that at least in the post-jet portion of the trajectory that

particle co~centrations will be low. Hence the dominant parameter in this region

would bIe the indiviq,ual V t. Upstream and up to the region of interaction the

reverse will be true. Unfortunately there seems to be no simple general reso~ution

of these contradictory requirements.

We wish now to consider some of the important phenomena associated with the particle-flow interaction with the hope of getting a better understanding of the effect of omitting certain parameters from the simulation.

(b) Particle Deceleration in the Jet Plume

We consider here the effects of the patameter

~l

=

TgjV t

2

by eXamlnlng the equations of motion for a particglar flow case. (The limiting case of

~l ~~ was treated earlier by Etkin ).

Coniider ~ow the motion of a single fluid drop falling in the plume region of an annular air dome when there is no sidewind i.e., W

=

0. Even if the velocities in the plume exceed the terminal velocity of the particle it still may penetrate to the dome interior due to its inertia. There exists some decleration length in which the drop is brought to rest, which will of course depend on the drop, its initial velocity, and on the nature and dimensions of the flow field. To compute this we wi~l consider a particle with initial velo-city

(0, -V

t), moving in an unbounded jet field u'

=

0,

w'

=

w'(z). The typical case of w'

=

kzb leads to a rather complex Abel's equation and hence we treat the simple case w'

=

w'(z)

=

constant.

which

"

z where

The motion equations

"

w on integration yields _1 ln

r

27r 1

l

5 1\2 1\ 2 w -2w-5 + 1 25 + 1

d~

cfz

are from (1)

=

('" ")2 w -w _~1-~2

1

1

+

5

-w)

l

t

A

J

2;15

1991_5_~)(1+

f5)

I ~,

=

w'/V J

=

1

then setting ~

=

°

we obtain the non-dimensionat decleration length

~*

=

l

l-5 2

J

1 ln 1+25 +

~~i5

ln (1-5)(1+25)

l

l+5

J

(6) (7)

A plot of

~*

vs. 5

with~]

as a parameter appears in Fig.

8.

Tne values of' ~l shown are those employed in tne experime~s herein and in Ref. 2. We can expect these computations to be of practical importance if we can determine a

suit-a~le effective jet velocity. Using the exit velocity will clearly give decleration

lengths much shorter than would be found in the plume of a real jet with axially varying flow velocity in the plume.

the 'Tr l and 'Tr

l

The main point of interest in Fig.

8

is the very clear dichotomy between

.0023 case (the earlier experiment with water drops) and the cases 'Tr

l

=

.267

1.67 (the present experiments with glass beads). (c) Lift Forces and Drop Deformation

In Appendix 11 a survey of some of the available literature on the lift

forces on small particles is presented. In general these forces depend on the

local wind shear (and aence on d/T)and 0)1 ot her parameters such as nd/V (rigid

particles) or ~p/~f9,1 ,15 (liquid drops),

ppl

~ and the particle Reynolds number.

It is important t.o realize here that the lift forces on the liquid drops and the

rigid particles employed in this simulation are of quite different origin, and hence the difference between the two cases is much more than just a difference of

Reynolds number. In this respect one could reaso~ably consider as a non-dimensional

parameter the ratio of the 'structural integrity' forces (such as surface tension in the liquid drop case) to the aerodynamic forces. Clearly such a parameter would have a very different value in this simulation than for the case of fuIl scale liquid drops. Two critical cases exist namely when the aerodynamic forces cause such drop deformation that the aerodynamics of the drop is altered (e.g.

the generation of lift) and when·the aerodynamic forces cause the drop to

dis-integrate. Since drops can be expected to encounter relative winds much larger than their terminal velocity, for short periods, such deformation effects are

likely to be large. The data of Lane, Prewett and Edwardsl~i yes a critical

break-up velocity of only 60 fps for a drop of 1 mm diameter. Hence rigid particles

can be considered satisfactory models in this sense only for very small drops. Of course whether or not the drop breakup occurs depends on the relative scale of the particle (relative to the dome dimensions) and hence the suitability of a particular simulation material depends as well on diT.

(d) Turbulent Mass Transport

All of the flow fields to be encountered in these Bxperiments are clearly turbulent. Hence one can expect that turbulent mass transport may play a role in the motion of particulate matter into the dome interior. The complexity of t4e flow field and the non-linear character of the drag law makes the analytical investigation of the process very difficult. A general method exists ll which

allows one to compute the mean square deviation about a mean particle trajectory. This mean square deviation cao be expected to dep end on the particle Froude number.

A solution for t~e above at least for the case of a linearized drag law appears

to be tractable at least for the case of an unbounded homogeneous turbulent field.

~f however there are lift forces present (in addition to the drag non-linearities)

which depe~ on the local wind shear, such a . linear analysis could be grossly in

error.

Recently the above problem has received related experimenta~ treatment.

The autocorrelation function for small spherical beads in grid generated

turbu-lence was investigated by Snyder

&

Lumley12. Further the diffusion of large

particles in turbulent pipe flow has received treatment 13 •

5.

WIND FLOW FIELD

As was mentioned earlier, the aim of the boundary layer generation was simply to obtain a boundary layer of reasonable thickness, with profiles of known mean velocity and turbulence intensity.

---~--~~--~--- - - - -

-The reslilts of the flow field survey described earlier are presented in Figs. 9a, 9b. The kink in the velocity profile is most probably due to the super-position of two boundary layers, one due to the barrier plate ~~d one due to the roughness blocks.

In addi tion to the measurements of the turbulence intensi ty some photo-graphs of the transduced signal were obtained (Fig. 10). Figures lOc, lOd clearly show the intermitt~cy phenomena at the edge of the boundary layer.

6. RESULTS

(a) The Jet Flow Field

To indicate the boundaries of the jet flow field, a series of smoke photographs were taken for various values of VJ/W. A selection of these appears

in Fig. ll. The jet plume centerlines and the dome walls were digitized fr om projector enlargements yie

₆

ding the curves of Figs. 12,13. A theoretical model based.on plane jet theoryl was constructed but proved unsatisfactory.

The flow in the region outside the jet bcundaries was investigated with a smoke 'wind' which could be placed at B1lY point in the flow. This indicated the presence of vort ex shedding behind the dome much as in the case of solid bodies. Such vortex shedding has also been observed in the wake of circular jets in crosswinds17•

In some of the observations the vortex tubes were inclined at large angles to the horizontal so that they resembled small tornados.

The existence of strong vortex action inthe jet wake was also indicated by the deposition patterns outside the collection p~~. (see Fig. 14). It would be interesting to be able to correlate the flow structures associated with different values of (VJ/W,

VJ/V

t ) to these accumulation patterns. (b) Non-Dimensional Collection Functions

The principal results of this section are expressed in terms of the non-dimensional collection function 6c/6c

O

=

f(W/VJ,vJ/v

t

).

These are presented in

partially dimensionless form (i.e., vs.

W,

V

J) in Figs. 15, 16. To present the results in complete dimensianless form offers some problems due to the difficulty in selecting (see discussion in Section 4) a suitable

V

t • Using the

V

t determined from streak photographs (see Appendix I) we obt&in the curves in Fig. 17. It is of interest to co~are the W= 0 case in Fig. 17 with the results from the water-shower experiments • This is done in Fig. 18.

It is evident from the last figure that the 6c/6c

_o

= f(~l' 5) with

o =

constant do not tend in the direction predicted by the analysis of section4 (for increasing ~l ~ decreases; i.e., consider W

=

0 case for the different values of ~l)' Of course the para,meter 5 is not constant for all three cases but it is nearly so for the two glass bead cases. In any event the analysis in Section 4 indicates a great difference between the glass bead and watershower cases over a very great r~nge of 5.

It is reasonable to assume that some other phenomena are involved which mayor may not depend on ~l. For example we might consider the partiele Reynolds

numbers: certainly they are di~~erent for the three cases (we note that the drag dependence on RN has already been taken care of in the parameter vt/v). In addition one of the experiments involves liquid drops. In Appendix It and in Section.4 we discussed the existence of lateral migration forces on particles in shear flows. A particle falling down the jet plume or entering the side wall will de fini tely be irmnersed in a shear flow and hence can be expected to experience a lift force.

A related problem in meteorology offers some insight. Rain squglls are known to be sharply delineated laterally and recently Mollo-Christiensenl of~ered the following explanation of the fact, making use of Alexander and Hultgrens data

(unpublished) for the settling of spheres. This data indicates that a rigid sphere ·falling in an upward moving shear flow migrates in the direction of the minimum flow velocity. Mollo-Christiensen argued that this data could be expected

to hold for raindrops. Applying this argument to the raindrop-dome interaction, it would appear that particles falling parallel to the plume axis (W = 0 case) would be deflected away from the plume centerline, that is away from the region

to be protected. The data of Alexander - Hultgren also indicated no migration for RN

<

50.

Of the results (W

=

0) for Fl .0023, .267, 1.67 (henceforth referred to as cases 1,2,3) only case 1 occurs for a RN

>

50. Certainly this argument gives us results compatible with what was experimentally obtained.

Closer examination of the data on the lateral migration (see Appendix 11) of rigid spheres and liquid drops indicates that the straight forward applica-tion of the Alexander-Holtgren data to the raindrop situaapplica-tion is naive. Most other results in the literature (Appendix 11) give lateral migration results which do

not even agree in sign with the Alexander-Hultgren data even in the same Reynolds number range.

Further the critical RN = 50 does not appear elsewhere in the literature, although one must admit it is indeed reasonable in that spheres begin to develop wakes around a Reynolds number of 40. 20 Finally the phenomena responsible for the migration of large drops (i.e., drops do not remain spherical in the flow), is clearly of a different character from that of the rigid spheres. Hencewe are not warranted in assuming that these results hold in the case of liquid drops at Reynolds numbers of 1000-3000.

Nonetheless we can sal vage something of the above argument. From rough observations 2 and from Mollo-Christiensen's example it appears that some sort of lift forces, akin at least in sign to the Alexander-Holtgren data are experienced by drops in shear flows at the high Reynolds numbers above. Furthermore we are

justified in applying the lateral migration data for rigid spheres19 to the glass bead experiments (cases 2,3). This data shows that a rigid sphere falling in an upward moving shear flow migrates to the jet axis (i.e., toward the velocity maximum). Thus a simulation employing rigid spheres could be expected to yield conservative results with respect to a simulation employing liquid drops at higher

RN.

Thi sargument has one apparent weakness. important parameter (see Fig. 8) and thus it seems essentially secondary effect like lateral migration expect to be a countering tendency due to Fl' .

It is clear that Fl is an difficult to believe that an

should swamp what one would

The explanation may lie in the existence of another phenomenon, also dependent on Fl but whose derivative with respect to Fl is opposite in sign

~- ~~~---.

from the deeeleration length. Sueh aphenomenon may be turbulent mass transfer

(see earlier remarks in Section 4, and discussion in Part B). Unfortunately the

nature of the dependence of turbulent mass ~ransport on ~l' is unknown for the

complex turbulence·fields involved in jet iIiteraction. One Vlould expect this

phenomenon to be significant tor small particles in large systems (i.e., for

small diT.) and for particles with small relaxation times. In a range of ?Tl where

turbulent mass transport is ef importance, diop breakup mll interact wi th the turbulent mass transport by converting dróps wi'th large relaxation times into many, more diffusable drops.

Whether or not the above discussed discrepancy can be accounted for in terms of particle diffusion remains a problem for future experimentation.

Even in the absence of diffusion, drop breakup may play all in;;>ort~t

role. This would be especially true of systems with large diT, where the rela~

tive shear ~velocities would be large. Drap disintegration would not account for

the qifference between the two bead cases 2,3.

From Fig.19 it is apparent th at substantial increases in

vJc/vJc'w

= 0

(for case 2) begin around

w/v

J

=

.14 but that they reach a peak around

w/v

_J

=

.24 and then decline. I t àJ..so is apparent that small values of 6C/6C

O may

not be obtainable for large

W

without going to excessively large values of

V

Jc• We consider a simple explana,tion of Fig. 19. It appears toot at large

values of

w/v

J (see photographs in Fig. lld) the protective portionof the dome

is confined to a segment of the upstream walL Let us assume that this seg:rrent

acts as asolid fence of hight 1. Then from the geometry, the fence casts a

shadow oflength

L "" (8)

rf L

<

D we ean assume proportionality of 6C/6C with L-D so that we have

o

Fig.

19.

This gives 6C/6C as a decreasing function of W approximately as in o

We note that the performance for cases 2 with (Fig.

19)

is radically

different from case 3, although the previous explanation should apply in both

cases at large values of

wjv

J• At present ne explanation is offered for the

difference between cases 2, 3.

7.

,FULL

seALE

INTERPRETATION

To give the results a more practical flavour 3 illustrative examples

o~ full scale systems were computed. The relevant parameters were obtained for

various values of the full scale V

t ' corresponding to heavy and light rain and

to heavy and light snowfall. These appear in Table 1. The double rows corres-pond to the two values of ?Tl employed in these experiments. The raindrop terminal velocities were obtained from Gunn and Kinser2l and the snowflake terminal velocities

from Mellor22 • Distribution data for raindrop ·terminal velocity and diameter can be

The tabled data .is presented for W = 0 only. One can obtain the requi-sitepower required at given W by multiplying the results in Table 1 by p3 where p

=

p(W) is obtained from Fig. 20 with 6C/6C

=

.05.

o

It is evident that the HP/Sq.Ft. reported here greatly exceeds that re-ported previously2. Further it exceeds, eSPÎc~~lly in the presence of a .side wind the power requirements of a .linear jet sheet' • This latter fact is due in part to ~ inherent geometric inefficiency of the annular device. In the W

=

0 case the particle velocity vector and the jet velocity vector are of opposite sign and parallel. Hence one could expect for W = 0 superior performance from the annular

device with respect to the linear one. When W

f

0 the annular device acts more like a linearone. The annular jet is now however wasteful of power in that the downstream wall serves no protective function at all. This means that a.linear device of width D and span also D protects an area greater than an annular device of effective width

nD,

although the jet exit area of the linear device is smaller than that of the annular device by a .factor of 7T. At con:q:>arable values of V the powerrequirements would also be in the ratio 7T:l. In actual practice

t~e

linear sheet would perform somewhat more poorly than stated here owing to the folding up of the jet sheet downstream of the jet exit. Nonetheless it is clear that in the presence of a .side wind, it would be advisable in the interest of economy to alter the flow from the annular nozzle such that anly as much curtain as is actually required is operating at any one time.

THE FUTURE OF AIR CURTAIN DOMES

The results herein prompt some speculation as to the future of the still nascent annular jet device. Can it be made economically feasible? What will constitute the field of application? What is the most likely size domain?

Answers to these questions are still indefinite owing to the uncertain-ties surrounding small scale simulation. Nonetheless we are certainly able to makesome tentative statements.

Air domes to cover very large areas such as cities or towns are likely to remain in the realm of Swiftian fantasy. The power requirements for such applications are astronomical and even the most optimistic projections using the most exotic technology are not likely to make them less so.

Even

the case of public stadia must be viewed with considerable skepticism. Here, the power requirementslie in the physically obtainable range and hence, given individual willing to make the expenditure fall also within the economically obtainable. However such a project is at best one of those technological monstrosities whose consumption of resources and technical endeavour cannot be justified in terms of any reasonable social goals. Rather they come into existence in their own right, as if propelled by the shear magnitude of their realized form.

Smaller structures with diameters of 100' or less especially for snow-like environments appear to offer considerable promise. Not only are the power requirements more reasonable but the volume of accessory machinery such as fans, blowers, motors and ducting is also reduced. This of course leads to a much better balance between operating cost and capital cost than can be achieved

wi th the much larger units.

The nature of the applications for smaller air domes will be varied. To date the protection of hydroelectric switching stations, of radio transmitters, and of small construction yards have been considered. It can be expected that the field of application will widen as the technology becomes more sophisticated and as the device becomes known more widèly.

In spite of the difficulties encountered in the investigation of the

annular device and in spite of the pessimistic results for large sizes it appears

that such research should continue. A clear field of application is now de-veloping, which if less glamorous than 'bubbled' cities is no less technically demanding and considerably more in line with its role as a device for environmental control.

~---~ 1. Etkin, B. Goering, P. ~J 2. Etkin, B. Lake, R. 3. Harting, A. 4. Sprenkle, R. E. 5. Teunissen, H. 6. Etkin, B. 7. Lapple, C. E. 8. Jayaweera,

K.

o.

9. Savic, P. 10. Lane, W. R. Green, H. L. 11. Etkin, B. 12. Snyder, W. H. LuniLey, J. L. 13. Sharp, B. B. 14. Taylor, G. I. 15. McDonald, J. 16. Vizel, M. Mostinskii, I. L. REFERENCES

"Air Curtain Wal1s and Roofs - Dynamic Structures". Proceedings of Conference on Architectural Aerodynamics, Roy. Soc. of London, 1970.

"The Penetration of Rain Through an Annular Air Curtain Dome" • UTIAS Report No. 163.

"The UTIAS Precipi tation Tunnel". UTIAS Technical Note No. 181.

'Piping Arrangements for Acceptable Flow Meter Accuracy', Trans. ASME, Vol. 67, 1945, p. 345.

"Characteristics of the Mean Wind ~d Turbulence in the

Planetary Boundary Layer". Review No. 32 .lnst. for Aerospace Studies, Univ. of Toronto.

"Interaction of Precipitation with Co~lex Flows". Proc. of the 3rd International Conference on Wind Effects on Structures, Tokyo, August 1971.

"Partiele Dynamies" in Flud.d and Partiele Mechanies , Lapple, C. E. Ed., University of Delaware, Newark, Delaware, March 1954.

"The Behaviour of Clusters of Spheres Falling in a Viscous Fluid", Part 1. JFM,52., 121 (1964).

"Circulation and Distortion of Liquid Drops Falling Through a Viscous Medium", NRC Mr-22, July 1953.

'The Mechanics of Drops ~d Bubbles' in Surveys in Mechanies, G. 1. Taylor 70th Anniversary,

Batchelor, G.

K.

(Ed)., Carnbridge University Press, 1956. "Theory of the Flight of Airplanes in Isotropie Turbu-lence-Review ~d Extension", AGARD Report 372,-1961. "Some Measurements of Partiele Velocity Auto-correlation Functions . in. Turbulent Flow", JFM 48, 41 (1971).

"La.teral Diffusion of Large Partieles in Turbulent Pipe Flow". JFM 45, 575 (1971).

"The Shape and Acceleration of a Drop in a High Speed Air Stream". Collected works of G. 1. Taylor, Vol. 3.

"The Shape ~d Aerodynamic s of Large Raindrops". Journal of Meteorology 11, 478 (1965).

"Deflection of a Jet lnjected into a Stream". Inzhenerno-Fizicheskii Zhurnal, ~, No.2, 238 (1965).

17. McMahon, H. M. Hester, D. D. Palfery, J. G. 18. Mo1lo-Christiensen,E. 19. Jeffrey, R. C. Pearson, J. R.

A.

20. Dennis, S. C. R. Walker, J. D. A. 2l. Mason, T. 22. Meiler, M. 23. Graham, B. 24. Oli ver, R. 25. Small, S. Eichorn, R. 26. Goldsmith, H. L. Mason, S. G. 27. Denson, G. D. Salt, D. L. Chri stiensen, E. B. 28. Day, J. T. Genetti, W. E. 29· Segre, G. Silverberg, A. 30. Segre, G. Silverberg, A. 31. Brenner, H. 32. Bretherton, F. P.

"Vortex Shedding from a .Turbulent Jet in a Cross WindH, JFM 48, 73 (1971).

"The Distribution of Raindrops and Gusts in Showe.rs and Squalls". Journal of the Atmospheric Sciences 19; 191

(1962).

-'Particle Motion in Laminar Tube Flow'. JFM (1965). 22, pp.72l-735.

"Calculati on of the Steady Flow Past a Sphere at Low and Moderate Reynolds Numbers". JFM

!:.ê"

771 (1971).

:The Physics of Clouds' • Appendix B. The Physica1 Properties of Freely Falling Raindrops (contains Gunn

& Kinser data).

"Blowing Sn ow" • CRREL - Cold Regions Science and Engineering. Part 111, Section A3C.

"Jet Stream Umbere11a". B.A.Sc. Thesis, Engineering SCience, University of Toronto, 1970 (unpublished). "Influence of Particle Rotation on Radial Migrat ion in the Poiseuille Flow of Suspensions". Nature 194, 1269, (1962).

"Experiments on the Lift and Drag of Smal1 Spheres Suspended in a Poiseulle Flow". JF,M~, 513 (1964). "The Flow of Suspensions Through Tubes". Journalof Colloid Science 17, 448 (1962).

'Partic1e Migration in Shear Field'. IACHE Journal 12 (1966). pp.589-595.

"The Motion of Spinning Particles in Shear Fields". B. Sc. Thesis, University of Utah, Salt Lake City, Utah, 1964.

'Annulus Formation: A Possible Explanation', Nature 203, (1964), p.1436.

"Behaviour of Macroscopic Rigid Spheres in Poiseuille Flow Part 2. Experimental Results and Interpretation." JFM 14, 115 (1962).

"Hydrodynamic Resistance of Particles of Smal1 Reynolds Number". in Advances in Chemical Eng. 6. Academic Press, N.Y. 287 (1966).

'The Motion of Rigid Particles in a Shear Flow at Low Reynolds Number'. JFM 14, 284 (1962).

33. Rubinow, S. I. Keller, J. R. 34. Saffman, P. G. 35. Haber, S. Hetsroni, G. 36. Allen, G.

p,..

Lake,

R.

"The Transverse Force on a Spinning Sphere Moving in a Viscous Fluid". JFM 11, 447 (1961).

"The Lift on a Small Sphere in a Shear Flow". JF.M,gg, 385 (1965).

"The Dynamics of a Deformab1e Drop Suspended in an Un-bounded Stokes Flow". JFM~, 257 (1971).

"Trajectories of Raindrops in a Jet Issuing into a Normal Crosswind" , urIAS Technica1 Note No. 165, _ 1971.

PART B - B. Etkin

APPROXIMATE ANALYSIS OF t'HE EFFECT OF TURBULENT DIFFUSION

In Part

A,

Lake has presented an analysis that expresses the fact that heavier drops (larger

V

t and smaller TIl) are more able to penetrate a laminar jet

curtain than light ones. This is illustrated on Fig.

8,

in which

TI

=

.oq23

corresponds to the experiments with water drops,and the ot her two cbrves

l

correspqnd to the experiments with glass beads. The ordinate is a measure of the distance it takes to bring apartiele to rest from its terminal velocity when it falls into a vertically-rising jet, and it is seen that there is a ratio of the order of 50 be-tween the penetration distances correspondin~ to TIl of

.0023

and

.267.

One might therefore expect ;tha~ larger va lues of TIl would lead to better protection by the annular jet and smaller values of the colleetion function. Exactly the reverse is seen to be the case in Figs.

17

and 18~ The larger the value of TI , the more precipitation penetrates the dome. Since large TIL cor.r.esponds to fult scale, this is a matter of great eonsequence. Among the possfble reasons for the discrepaney

is the action of turbulent diffusion of the partieles aeross the mean streamlines

of the flow. In order to asses this possibility quantitatively we present the

following approximate analysis. We assume that we have a homogeneous turbulent

flow at mean speed

V.,

in which partieles of mass m are released from the origin and are eonvected do~nstream. We eompute the cross-stream dispersion of these partieles for the appropriate values of the non-dimensional parameters, and from this infer the significanee of this phenomenon for the experiments earried out.

In the interests of obtaining a simple result we assume a linear drag law, such as holds in the Stokes flow regime for very small partieles. Although this assUID-ption limits the validity of the results to very sma~l partieles, nevertheless

it is believed that the main qualitative conclusion would not be invalidated by i t .

Let the drag law for the partiele be

D

=

kV

w~ere D

=

drag and

V

=

relative velocity. T~en k

equations of motion are

k 1 u (u -À!) m k {v vl) v _m k 1 w (w - w ) - g m

mgjv

t and the dimensional

(B .1)

Sinee these equations are uncoupled, we may derive the results of interest from any one of them (the third caR be put into the same form as the

firs~ two by the substitution w

=

w +

V

t). We choose the second, and write it as

where

(B.2)

The y displacement of the particle is then given by the differential equation

« , 1

Y + Ày = Àv (B.3)

1

The impulse response function obtained fr om B.3 (for v (t)

=

5{t) ) is

h(

t)

=

(l-e -Àt) (B.4)

The lateral displacement of the particle in time t in response to the turbulence (y

=

0 at t

=

0) is then given by

t

y(t)

=

,

1

vl(t-CX)h(CX)da {B.5)

and its square by

cx=o

t

y2(t) =

~~ vl(t-cx)vl(t_~)h(CX)h(~)dCX~

p

The ensemble mean is then

where t < y2(t)

>

=

~

~ <vl(t-cx)vl(t-~»h(CX)h(~)dCX~

0, t

=~

1

R(CX-~)h(CX)h(~)da~

0 -1 1

R(T)

=

< v (t)v (t +

T)

>

(B .6)

(B.8)

is the Lagrangian correlation of the y component of the turbulence. On sub-stituting (B.4) into

(B.7)

we get the mean-square dispersion:

t

rJ/

=

< y2(t)

>

=

~

J

R(CX_~)(l_e-ÀCX)(l_e-f$)dQ:~

(B.9)

o

In order to evaluate

(B.9)

we need an expression for the correlation function. The details of R would not be expected to be very important since it occurs inside the integrale As a reasonable approximation we assume the exponential form

(B

.10)

where

rJ

2 is the mean square vaLue of vl. When (B.10) is substituted into (B.9) th~ re sult is

rJ

ç

..L

= 2

rJ

V

16

r where t I1

=J

J

e -11

1Ck-~

I

dad~

0 t I 2

-J

J

e -/.$ e

~1l1Ck-~

I

dad.t3 (B.n) 0 t

I3

-

.

J Je-ra

e -Il

1Ck-~

I

dad.t3

P

:t

I4 =

fJ

e -À(O:

+

~)

e

-1l1Ck-~

I

dad.t3

()

Beeause (B.10) is symmetrie w.r.t. T, 0: a~d ~ ean be interchanged without changing

the value of the integra1 in (B.9). It fo1lows that the integra1 in the 0:, ~ p1ane

can be eva1uated as indieated be10w (see Fig. B.l):

Fig. B-1 t

in which o:-~ ~

O.

When the four integra1s of (B.11) are eva1uated, the resu1t is

(B

.12)

~

r

11 (-Àt -(À+Il)tj 112 ( -Àt 1)] 2

Lil

+ À e -e ~ + À(À + Il} e -11 2 (-2Àt - (À+Il)t) 1 (-2Àt 1) ~ e -e - -

À(À+}

e -À ~ 11

17

We now introduce the non-dimensional variables " , , " 2 v v /N j '. y = y /T, t = Il t, TIl = T g/V t

"

a-y 1\

.

() =

v

The ratio À/Il is an important parameter, being the ratio of the characteristic correlation time to the time constant of particle response. Now the turbrtence correlation parameter ~ (dimension time- l ) must scale with the jet speed and size as

v .

....J. or T c

v.

....J. T where c is a constant. Whence (see

B.2)

À Il = gT CVtVj V

t

- - TI = TI ' cV. 1 1 J

T~e main resu1t can th en be expressed in non-dimensional form as

" 2 where a-"Y2

=~l

+ J

₂

+ J 3 + J4 a-v. A A . ~

1

[2 (-2IT

l ' t _ - (TIl L+ 1) t ) __ 1_ ( -2IT1 ' t ) ]

--:::2---1 TI '-1 e e

TI'

e -1

c (TI1'+1) 1 1

(B.13)

(B.14)

To obtain numerical resul}s, it now remains to assign a va~ue to the constant c, to the parameters TIl and Vt/V_j , and to the range of~. If we assume that the length scale of the turbulence is roughly equal to the jet exit thickness, and convert the 1ength scale to a time scale by the convection speed V., we get

J 1 1.1 T

V.

J

18

~---,

or c

=

1, and TIl'

=

TI1Vt/V_j• The non-dimensional time is then t

=

Ilt

=

Vjt/T, which

is equal to the downstream convection distance measured in units of jet exit thick-neSSe Figure (B.2) gives results for the range of TIl associated with the experiments, and for Vt/V_j

=

1/4. It is quite clear that there is virtyally zero dispersion for

the value of TIl corresponding to the experiment with water drops, and very substantial

dispersion for the two cases with glass beads. For etample, consider a turbulence

intensityof 10%, which is a reasonable value, i.e., ~

=

.1, ~ 2

=

.Dl, and a

v v

downstream distance of 10 jet thickness, Le., t

=

10. Then for the smaller glass

beads, TIl

=

1.67, the graph yields '

~

2 11.7

A

~ 2 .117 y v Ä .34 or ~ = .y or ~ .34T y

Thus the rms lateral dispersioB of the particles would be about 1/3 of the jet exit thickness. This amount of dispersion in the annular jet experiment would be expected to bring many more P8fticles into the region of the flow field where they

would subsequently fall out into the center than would be case for a laminar flow.

The numerical re sult is of course only rough because of the approxima-tions made -- the linear drag law, the form of R, the value of c. In particular the value of c chosen is probably on the large side, and refereBce to (B.14) shows

that ;this would lead to an underestimate of the dispersion. It does allpear:,that

we may tentatively conclude that the phenomenon of turbulent spread of the

part-icles is a significant one, and offers a possible explanation of the anomalous

results.

APPENDIX I: . THE PHYSICAL AND AERODYNAMIC PROPERTIES OF 'TIHE GLASS BEAU SIMULATION MATERIAL

~he simulation material employed in these experiments consisted of 2 sizes of glass spheres supplied by MICRO-BEAD CORF. ·having nominal diameter ranges of 38-5~ and 74-105~.

T~e coarse beads tended to flow very readily while the finer beads had apronounced te~dency to stick to each other and to a wide variety of sur-faces. This tendency to agglomerate places a ·lower bound on the useable bead diameter; in fact the small beads employed in these experiments must be said .to about the smallest size that is practical.

A particle size analysis was carried out by the Ontario Research Foundation using a Quantimet

70

Image analyzer. The distribution functiops obtained for the two beaä sizes appear in Figs. 21,22. Assuming the beads to be spherical (microscopie examination reveals that this is so for the majority) and using the empirical data of Ref.

7

we obtain the distribution functions in Figs.

23,24.

Terminal velocities were measured by taking streak photographs of the bead shower with the wind on and measuring the slant angles. Photographs of the bead shover for a variety of wind-jet conditions is shown in Fig~ .

25.

The

terminal velocity was computed from the slant angles from the local wind velo-city. Such a method is clearly approximate in that it assumes that the local partiele direction depends only on the local wind vector. Earlier computations using the free stream velocity W in place of the local wind velocity yielded

higher values of the terminal velocities than had been expected and the difference had been attributed to the existence of wake iPferaction effects. Although the present calculations using the local velocities yield terminal ~elocities nearer to the standard values for spheres there is still sufficient reason to expect that collective effects are present in the bead shower. The mean term~al veloeities obtained from the streak photographs are:

d = 74-105~

v

= 1.69

fps and

t d

=

38-56~ V t =

.68

fps

A further attempt was made to measure the particle terminal veloeities by dropping the particles down a long tube onto a sticky rotating drum. No re

-sults were obtained wit~ this method for the smallest beads owing to the presence of quite obvious interaction effects being present. The results obtained for the larger beads were also not very satisfactory owing in all probability to inter-action effects.

APPENDIX II: LIFT FORCES ON RIGID AND DEFORMABLE PARTICLES IN SHEAR FLOWS

Studies in the flow of dilute suspensions in tubes have indicated that particles of a wide variety of shapes in low Reynolds n~ber shear flows experience a lift force which depending on the relative density of the particle, is dir~ct.ed

toward or away from the jet axis. It can be shown theoretically32 that no lift force can arise in creeping flow and hence the forces are due to inertia. Although the evidence is not conclusive .it is generally believed th at the lift force has two causes. When immersed in a shear flow a rigid spherical particle experiences both a torque and a lift force due to shearing stress es and the pressure assymetry. The torque will in turn cause the sphere to rotate and thus give rise to a further lift force. (RubinowKeller force). It is difficult however to obtain a clear picture of the influence of Reynolds number from the literature owing to the ~arge

number of other parameters. involved in the experiments.

In Table 1 a summary is given of the main result-s for rigid particles in shear flows. It is evident that the data is not free from c ontradiction. However the bulk of it indicates that a bouyant sphere in a downward flowingfluid mi-grates to the wall, ,Le., tqwardsl : the velocity maximum.

Several investigators have attempted to derive theoretical expressions for the lateral force. These expressions appear in Table 2. Unfortunately the correlation of the data with any of these expressions is not very good. Lateral migration in shear flows occurs also for particles such as liquid drops. Not only

ao

the drops deform in a viscous shear but as weil t~ey take up particular orientations in the flow. The mechanics of the generation of lift forces is in-deed complex and thus we restrict ourselves here to a brief statement of some of the lift laws that appear in the literature.

Goldsmith and Mason26 have maintained that migration in a poiseuille flow and only for deformable bodies. Starting theory for small deformations of liquid drops, they derive the

= 6m-tfbf2(P)f3(P) where f₂(p) p + 2/3 F

r p + 1

is possible only with the Taylor lateral force F • r (2) -771-L l{2_b3 3(19p + 2 I-lp/I-l f and f3(P) f 16)(8p + 99pL5+ 6_L p =

48')'

(16p + 16)(3p + 2)

Far more general tr~atments of the existence of lateral forces on de-formable bodies can be found3~ but they are largely of theoretical interest.

In the case where the Reynolds pumber is high and there is significant shear the aerodynamic pressure forces will serve to distort the drop as did the viscous,shear farces above. Whether or not one can expect lift forces to arise as a result of this deformation is at the moment a matter of conjecture. However in the previous experiment with the water shower2 lateral deflections of the drops were in fa ct observed.

APPENDIX 111: THE RELATIONSHIP BETWEEN TRAJECTORY COMPUTATIDNS AND NON-DIMENSIONAL COLLEC~ION FUNCTIONS

Experimenta12 and numerical-theoretica1

36

efforts generally aim at two different but related results. In this section the relation between computed tra-jectories and experimentally determined collection functions is explicitly stated.

It is possible to describe a rainfield by a distribution function N(x,d); where x is the horizontal coordinate a~d d the drop diameter. (N(x,d)

=

nö. of drops with diameters (d, d+ 5d) in the interval (x,x + 5x».

We ~estrict our attention here to a l-dimensional case for simplicity although one could formally replace x with

x

(and a few changes). Af ter interactipg with the ~dynamic structure' the rainfield is described by a new function N*(x*,d*).

We can obtain this function by realizing that the particle trajectories constitute a mapping

x*

=

x*(x,d) d*

=

d*(x,d) ( 1)

where x* is the coordinate of the drop af ter interacting with the jet and contacting the ground. Since we will not consider drop disintegration in this formalism, we have d* = d. Now given the inverse function (assuming that it exists), we have

x

=

x (x*,d*) d ::: d* (2) then N*(x*,d*) ::: N(x(x*,d*),d*)(J(x*,d*» where J(x*,d*)

o

1 then N*(x*,d*) ::: N(x(x*,d*),d*) . oxjdx* (4) This gives the ground distribution of rainfall downstream of the jet. Now consider a target defined by the interval [x

l,x2

J.

fhe vol~e of water in this interval is then given by

\

x

*

d

*

J

:2

J

2 _N*(x*,d*)

~

_{d*3 5x*5d} x ₁

*

d ₁

*

Now the function N*(x*,d*) depends on V

J, W. Then denoting the dis-tribution function with V~ ::: 0 by ~O*(x*,d*), the non-dimensional collection function can be written

JI

N( (x(x* ,d*) ,d*)

I

~

/

~

d*35x* 5d*

11

No((x(x*,d*) ,d*)

I

~~*

,/

~

d*35x*5d*

(6)

In some cases it wi11 be'possible to treat d,x as statistically indepen

-dent and so write ~(x,d)

=

N

1(x)N2(d). In this case N2(d) cou1d be specified by

a Marsha1l-Palmer distribution for example.

From numerical computation of the drop trajectories we can easily determine the functions in equations (1),(2) and hence proceed to compute the above integrals.

EXPERIMENTER

ALEXANDER

+ 18

HULTGREN

OLIVER

24

SMALL

+25

HICHORN

GOLDSMITH

+26

MASON

DENSON,SALT

27

CHRISTIANSEN

JEFFEREY

+

19

PEARSON

TABLE Al. SHEAR nmUCED LIFT FORCES**

FLOW SETUP

downward flowing glycerine in vertical tubes. glass spheres

p/P

f

<

1 1

>

1 downward flow of

<

1

lead nitrate solu- 1

tion methyl methacrylate

>

1 spheres unf;owing water in

>

1 inclined tube.glass spheres ? downward flow downward flowing fluid downward flowing fluid 'Unflowing fluid 1

<

1

>

1 1

>

1

FLOW.RN

? ? ? 100-500 860-2400 .8-16 x 10-

6

208 809

22.7-116 11.2-76.8 - 22-180

PART.RN

DIRECTION

OF

}1IGRATION

ROTATION

REMARKS

SETTLING VELOCITY

FLUID VEI.OCITY

effects wall none

occur for none

RN 50 axis 1-13. -80 247 2.5x 10-

6

6-120 .37-1.3

.01-.n

.28-1.6 axis wall wall axis non-rotating spheres moved to axis;rotating ones to wall none no migration none axis(RN 6-10) none

axis but osci-llates for RN 15-J.20 wall axis+wal-l stable at t3

=

.68 axis none notie none continued ••••.• ? ? 1.7-21.8 .003- .0077 .22-5.5 .028-0.43

.0025- • .040

.020-.42

continued •••••. TABLE Al. SHEAR INDUCED LIFT FORCES**

EXPERIMENTER FLOW SET-UP

_p/~f

fi'LQW.RN PART .RN DIRECTION OF ROTATION SETTLING VELQCITY

MIGRATION - "REMARKS _{FLUtD VELOCITY}

DAY +28 _{unflowing fluid}

_>

_{1 see}

_<

_{120 axis none} see Renson 27

GENETTI Denson 27 550 undamped radial

osci lla tion

REPETTI +29 downflowing

>

1 500 lO waU none .26

fluid

.

< 1 500 27 axis none .38

r

=

1 500 ? ? none ?

SEGRE +30 downflowing

=

1 2-30 <.01 .63 radii none ?

SILBERBERG from axis

,

**

This table is adapted from a table in 31. This is a very comprehensive review of lift and drag forces on small particles and should be consulted~

'I'ABLE I

FULL SCALE SYSTEMS

D T EXIT HP

HP/AREA

AREA

V

J

ft.

ft.

AREA

PRarECTED

PRO-TECTED

fps

V

t

=

25 fps

l85

9.4

5763

85,5DO

3.l8

26,900

190

heavy rain

458

23.4 35,320 l,960,000

l1.90

l65,000

295

V = l5 fps

t

66.8

3.4

751.4

2407

.69

3505

l14

light rain

l65

8.4

4584

54,000

2.57

2l,400 l77

V

t

=

6.6 fps l2.7

.65

27.2

7.26

.057

l26.7

49.8

heavy snow

31.5

1.6

l67.l

l68.2

.216

779.3

77.5

V

_t

=

1.64 fps 7.96

.4l

10.7

.04

.00090

49.8

l2.4

light snow

19.7

l.0

65.4

1.02

.0033

3p4.8

19.3

• I'

- - - -

- - - .

RESEARCHER

33

RUBINOW, S.

I.

KELLER,

J.

B.

SAFFMAN, p.G.

34

EICHORN, R.25

SMALL, S.

TABLE 2

EXPRESSIONS FOR THE LIFT ON A SMALL

PARTICLE IN A SHEAR FLOW

nd

3

pn

x V(l

+

O(RN))

COLLECTlNG PAN

\

NOZZLE PLUG

SPIDER MOUNTING BRACKET

NOZZLE.OUTER SHELL

E

•

-

•

~ ti)

i

~

---

--

-

-

-

---

--JOOI.:l leuun.l

lepow

Ier JDlnuu\t

S)lOOIB

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c

c

~

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•

•

8

0

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...

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~

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::l

§

-

ti)

•

'"

~

-

0

-

c

•

_E

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!.

.n

MODI FI EO BEAD FEED

SYSTEM

LOAD GUlDE

RING

INSERT--

- - - l

:a~9

HONEYCOMB

---

~~

SIEVE

- - - " 1

VIBRATING

BOARD

(VIBRATOR NOT SHOWN)

BFS BODY

/

FIGURE 5. MODIFIED BEAD FEED SYSTEM

,-leope

I

_Xl

l?

I

d.e.

I

voltmet.r

I

I

ij

L

~

rml

voltmet.r

ANALOGUE COMPUTER

55010

55001

llneariz.r

anemometer

hot wlre

9 70'

•

eN Z

...

•

Z 1&1 ..J Z 0

-~

~

eo'

1&1 ..J 1&1 Co) lil

a

..J C

!

ëi

m

:w

a

z

0 50'

z

10-0.1 0.2 0.5 0.4 0.5 0.8 0.7 0.8 0.1 1.0 '.Vt/~

32

30

28

N

-

26

=

.s::.

g

24

-

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o

o

ti:

.,

c C ::J ~

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f

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.,

CJ C

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16

U ref. (tunnel U)

1.0

(ft./aec.)

•

2.0

0

4.0

0

6.0

Á

8.0

0

Non - Dimensional Vel. vs

Z

(in.)

95% B.L.

thickness

8

=

12

11

1----4

Error Bar

D

0.1

0.2 0.3 0.4 0.5 0.6

0.7 0.8 0.9

1.0

1.1

Non - Dimensional Velocity

U

I

U_max