Trajectories of raindrops in a jet issuing into a normal crosswind

ISSUING INTO ANORMAL CROSSWIND

,

-fO,

Jtli'r'

t9r't'

_ .... r-T.I

HOGESCHOOL

ti

LI"

••

UOTJlEEIC

TRAJECTORIES OF RAINDROPS IN A JET

by

G. A. S. Allen and R. T. Lake

Page No: 2 2

3

5

6.

ERRATA FOR TECHNICAL NarE NO. 165 by

G.A.S. Allen

&

R. T. Lake

Equation (5) reads: ?Tl = 2 ?Tl

=

_Tg/VT 2 Tg/V J should read:

Line following equation (8) reads:

••••• where the focal length p

=

t [

~JJ2

should read:

••••• where the focal length p

In all lines following equation (15) all variables x, X, z, Z should have hats 'A'. e.g., equation (17) should read:

" 1\ " 2

A"

2 1/2

n

=

sgn (x-X) ((2-x) + (z-Z) ) also last line should read:

dZ

" A

dx 2z

Line preceding equation (22) reads:

••• The zero of the integral of this equation equated to zero .. o • o •

should read:

•••••• The zero of the integral of this equation .•••••• Equation (23) should read:

5V 5N 7Td3

TRAJECTORIES OF RAINDROPS IN A JET ISSUING INTO ANORMAL CROSSWIND

by

G.A.S. Allen and R. T. Lake

Submitted September, 1971.

•

ACKNOWLEDGEMENT

This project was concieved and supervised by Prof. B. Etkin. The authors wish to thank him for his suggestions and encouragement.

The research was supported by the National Research C0uncil under operating grant

A-1894 .

SUMMARY

Numerieal solutions are presented to the motion equations of solid spheres simulating raindrops fal11ng into a plane jet issuing into anormal

erosswind. The results of these eomputations are diseussed in terms of their

signifieanee for 'air eurtain' type deviees. This ineludes a diseussion of

basie sealing laws and some order of magnitude estimates of the power require

-ments. It is stressed that this is prineipaliy a qualitative investigation of

sealing effeets and is not to be taken as an exaet simulation of the partiele

TABLE OF CONTENTS

Notation

1. INTRODUCTION

Ir.

EQUATIONS OF MOTIGN

III.

FLOW FIELD

IV.

COMPUTATION

V.

ANALYSIS OF COMPUTATION

1. Trajectories

2. Power/Area Plots

VI.

SPATIAL DISTRIBUTION OF RAINFALL DOWNSTREAM OF JET EXIT

VII.

CONCLUDING REMARKS REFERENCES APPENDIX FIGURES PAGE 1 1 2

4

4

4

5

6 6

8

A d g

N

D

n p p s V V J V T v 0 (ut,

w?

(u,

w)

W

(x,

z) X s T 1T 5 TJ

NOTATION

protected area drop diameter gravitational acceleration number density fupction

normal distance power

parabola focal length arc length

volume

jet exit speed drop terminal speed jet boundary speed jet velocity

partiele velocity

wind speed

partiele location protected span

jet thickness (initial) dimensionless parameter

jet thickness

I. INTRODUCTION

Although the concept of using air jets as screens or shields is not

new~ it is only recently that the comprehensive notion of a 'dynamic structure' has arisen l ,2 Previously interest tended to be centered on some particular devicej and consequently the research wuich was carried out tended to be empirical and fragmented. The current approach aims at acquiring an accurate picture of the particle flow field interactions on which to base the design phase of a 'dynamic structure' technology.

Of particular current interest is the annular air curtain or 'air dome' .

An experimental projec~ has bee~carried out which indicated that the power requi

re-ments for such a device in an architectural context were not out of the question3 . It was noted in that investigation that there was considerable uncertainty involved in the sealing of the experimental results up to some 'architectual' full scale. Although dimensional analysis yields the necessary sealing invariants it cannot determine the relative importance of these invariants. Since it is not possible

to satisfy all the sealing conditions, dimensional analysis alone is of limited

usefulness. It is known for example, that the power/area requirements for the air structures discussed herein is independent of the system area for sufficiently

large systems

4.

We do not know however what constitutes 'sufficiently large'. In

order to obtain this, and other information regarding the relative importance of the non-dimensional parameters it is necessary to examine the non-dimensional motion

equations for the partiele flow system. In most cases of interest~ analytical treatment is restricted to consideration of particular limiting cases so that

numerical solution becomes necessary. By constructing a simulation of the partiele flow system and systematically varying model parameters a complete picture of the

sealing laws can be obtained. The principal aim of this research is to obtain such

information for a particular, relatively simple flow field, as well as to give order

of magnitude estimates of the power requirements. In the previous experimental investigation the effect of horizontal sidewind was not considered. As this is ob-viously an important factor it was decided to include it in this current investiga-tion. Since there is relatively little data available on the flow fields of annular

jets, especially in crosswinds it was decided to replace the annular jet by a plane solid jet. Such a jet was earlier proposed as a windscreen by G. I. Taylor

who gave an empirical expression for the form of the jet5. An experimental pro-ject investigating

6

the use of such a jet as a screen for salt spray has also been recently completed •

A collection of data relevant to the modelling of rainfall appears in the appendix.

II. EQ,UATIONS OF MOTION

In these computations the phenomena of drop breakup and deformation were completely neglected. The water drop was considered as a rigid sphere whose

aerodynamics could be entirely described by specifying its terminal velocity in

still air. While these approximations naturally limit the 'quantitative reality'

of the computed results (a purely secondary consideration in this work) they should not drastically effect the sealing laws, which is the primary item of interest.

The non-dimensional motion equations are from Etkin

4.

dd

A A

da - 7T (~

",

) v 7T 2

di

= 1 - w

"

u

-

ft

(2) d~ W 11 dj; =

_û:

( 3) v = ( (" u-u 1\,)2 +

(~_~,)2

)1/2 (4 ) where the 'A' denotes a non-dimensional quantity, lengths being non-dimensionalized with respect to the jet thickness Tand velocities with respect to the jet velocity V J. The non-dimensional parameters 7T

l ,7T2 are given by 7T l = Tg

_,

2

,

V

J 7T 2 = Tg

2

V J (6)

lIL THE FLOW FIELD

The flow field as stated earlier is that of a plane jet issuing into a uniform crosswind of constant velocity W. The velocity field was constructed by first determining the shape of the jet centerline and then the velocity profiles along this curve.

Let the jet centerline be given by a curve

~

=

f(~)

(see Fig.

1)

.

At any point on this curve we can errect anormal and describe the velocity profile by some function of the distance ~ measured along this normal.

v

V

max

= g(n)

The physical function

f(~)

was obtained from Vizel and Mostinskii

7 who~

employing a simple momentum analysis obtained:

A ;;

fw

l2

A

2

x =

4"

V J z (8)

which is a parabola of farm

~2

=

p~

where the facal length p

=

t

[~J

]

2

Since no empirical information was available glvlng the velocity o~ the jet boundary a rather arbitrary assumption was made, namely

The velocity the velocity velocity g • o v o v o

"

WSin(xlp) W 11

xlp

<

0.5

A

xlp

>

0.5

8

profile was determined from Bradbury. He gives an expression for profile for a turbulent jet immersed in a co-flowing stream of

v - g /

max 0 2.5 (T/s)l 2

(V (V _ _{J J go} )1/2

( 10)

In the case under eonsideration there is no single g as the co-flowing stream

has velocity g

=

v on the outside and g

=

0 on th~ inside. As an approximation

g was chosen !€.o beOthe average v /2. Th~n the maximum veloeity is given by

o 0 \

1/2

v _max

=

2.5 (vJ(vJ-v /2'(T/s» + v /2

0 { 0

The jet width is given by

on the outer side and s T 1

+

1 s 5₂

=

0.109 T {l1) (12) ( 13) on the inner side of the jet. Taking ~

=

n/5 where n is the distanee along the

normal from the jet centerline, we have for the outer side of the jet

v

=

(v - v )exp(-.675

~2(1

+ .0269

~4»

max 0

and on the inner side of the jet

2

4

v

=

v _max exp(-.675~ (1 + .o269~

».

+ v

o (14 )

(15 )

The direetion of the veloeity kS ~arallel to the jet axis. To eompute the flow

veloeity (u', w') at a point (x, 2) inside the jet we first need to transform the

eoordinates

(~, ~)Ato~n,s).

This is done simply by determining for eaeh point

(~,

2)

the point

(X,

z)

whieh lies on the line through the given point that is

perpendicular to the jet axis at

(~, ~).

The are length s and the normal distance

nare then easily eomputed. We ean obtain (X, Z) from

((~)1/2)3

+

(~)1/2 (p/2-~) _ pj2 ~

=

0 A2 " Z

=

pX then _{2 2 1/2} sgn (x-X) (x-X) + (z-Z) ) n

Th e s 1 ope 0 f th e Je een er 1ne lS . t t l' . glven . b y dz dx

=

-

1

=

tan8 pz

( 16)

Then the flow field is given by

u'

=

v cose w'

=

v sine

It must again be emphasized that the aim in this research has been to obtain a qualitative understanding of the interaction between particles and a particular flow field which in a rough sense only corresponds to the flow field for a jet issuing into anormal crosswind. The flow field just described is not considered to be a faithful model of the latter.

IV • CQMPUTATION

Calculations were carried out on an IBM 1130 and an IBM 360-65 and were displayed on an IBM 1627 plotter. The motion equations were solved using a

standard Runge-Kutta integration routine employing a variable step size. A final value error check was used to ensure a computational accuracy of 1%. In view of the nature of the computation this was felt to be sufficient. The parameters varied in the computations and the range of values employed are given below in Table 1.

TABLE 1. Ranges of Parameters in Computation

PARAMETER VALUES

Jet velocity V

J 20, 40~ 60, 80 ft./sec. Wind velocity W 10, 20, 30 ft./sec.

Jet thickness T 0.5--144. ft. (depended on the V

J, W combination)

Drop diameter d Except in a single computation the values of d were 1.35 mm and 3~0 mm corresponding to drop

terminal velocities of 5.0 and 8.0 meters/sec. respectively.

All drops were injected at the same non~dimensional location near the jet exit. This location was chosen by trial and error to be the 'worst' entry point. The effect of different ejection points was investigated by computing trajectories for a range of different entry points x. This is shown in Fig. 3.

o V. ANALYSIS OF COMPurATION

1. Trajectories

A representative sample of the computed trajectories plotted in non-dimensional coordinates appears in Fig. 2a to 2h. It is apparent from this sample that the trajectories fall roughly into two categories which can be denoted

'ballistic' and 'in~jet'. In the former case the effect of the jet on the drop path is confined to a very small region near the jet exit. The jet provides a brief impulse which launches the drop into the calm wake region downstream of the jet exit. These trajectories are thus simply 'ballistic' • In Fig. 2a, 2b,

a given (V,J/W, d) the trajectories become flatter with pronounced vertical descents a!ter the drop has left the jet. For these drops the jet influences the drop path for a substantial portion of its travel. The limiting case for this category occurs as T ~oo. This fact can be seen very graphically in Fig. 2d, the trajec-tories of increasing T converging together.

We can examine the two limiting cases more closely as follows. Consider first the case of ballistic trajectories. Let us assume that the drop crosses the jet at constant velocity independent of the jet thickness T. In doing so the drop acquires an impulse

ff

dt where f is the drag force on the drop which we will further assume to be constant with respect to T. Then the drops initial velocity on leaving the jet will be proportional to the transit time and hence to the jet thickness T. If we neglect air resistance the range of the drop X is given by

s so that X s V 8 X ex T2 s initial velocity initial angle (20) (21) We see for T < 5.0, W

=

20.0, V

J

=

80.0 in Fig. 8 that this is a

reason-able approximation. Referring to Fig. 2g it is evident that T

=

500 is about yhe upper limit of the ballistic class of trajectories.

In the limit of very large systems X /T is a constant as it is cne of the dimensionless parameters of the system. T~e particle's velocity is then just a superposition of the local wind velocity components and the drop terminal velo-city.

Although this yields a differential equation of motion which is formally simple, the complexity of the flow field makes solution exceedingly difficult. Evidence of the a~ymp~otic behaviour can be seen in Fig. 8. (V_J = 8?0,

w

= 1?~0

V

T

=

16.4p), and 1n Flg. 5.

(V

J

=

80.0,

W

=

10.0, VT

=

16.40). It lS also eVl -dent from Fig. 8 that the approach to the asymptote may be very complex, as for example, the behaviour of (V

J

=

80.0, W

=

3(}.0, VT

=

-26.24). 2. Power/Area Plots

It A A ft

The differential equation of motion is of the form dz/dx

=

f(x,z). The zero of the integral of this equation equated to zero, namely

f(x, z) dx =

°

J

A"

(22) is the protected span X. In these computations the reported X is X - 0.5 to

allow for the jet thick3ess. s s ·

In Figs. 5, 6, 7 the power requirements per sq. ft. of protected area are shown as functions of the protected span X. It is apparent that V

J, W, T

inter-act in a very complicated manner as is eviaent fr om the ~s' portion of Figs. 6,7. The most significant feature of these plots is the existence of the power asymptote for large T. (This is clearly evident only for Fig. 5). This is a

consequence of the proportionality of X with T for large T. The existenc€ of

this asymptote means that for large T the power/area is independent of the size

of the system. The value of this fact for practical systems is obvious. We

should also note that the span at whieh the system effectively asymptotes is

strongly dependent on V

J

'

W, d. It would have been yery convenient from an

experimental point of Vlew if the P/A had been independent of the system size X • s

This would certainly simplify the sealing of the experimental results.

Unfortu-nately the situation is far more complex in that the span at whieh the system

con-figuration asymptotes is very large being much in exeess of 400'. This mea~s that

in practically all situations uhe detailed sealing picture must be known before any

sealing of the experimental results ean be attempted.

VI. SPATIAL DISTRIBUTION OF RAINFALL DOWNSTREAM OF THE JET EXIT

In addition to knowing the size of the protected span X , it would be s

of some interest to know how the rainfall is distributed by the jet downstream

of the j ei:; exit.

Let the rainfall with the jet off (or at some large distance above the

jet) be described by a number density function ND(x,d) where x_is the horizontal

coordinate and d the drop diameter sueh that the )number of drops with diameters

(d, d + 5d) in the ~nterval (x, x + 5x) is given by 5N

=

N

D (x,d) 5x5d (22)

Such a function appears in Fig.

A7.

We can derive a normalized volume distribution

functions by taking 5V

Vi

5N 1T d3 ~..,-:..:..,....;..;- - V' V'

6

5d5x (23)

Downstream of the jet exit we will have a new distribution V*(x,d)/Vr*(x,à).

In the appendix data appears giving V(d)/V'(d) Fig.A6. It was not practiçal in

this investigation to eompute V*(x,d)/V'*(x,d). Instead, for a single injection

point a~d three jet cOflfigurations (V

J' W, T) trajectories were computed for a

range of drop sizes. A plot of X vs. V appears in Fig. 10. Using this plot

s T

and Fig. A6 we can compute for this single injection point the downstream

distri-bution function. This appears in Fig. 11. A qualitative idea of the effect of

different injeçtion points for a single drop size is shown in Fig.

3.

It is not

however possible to compute the actual drop distribution from these two figures

as the dispersion of drops of different diameters will be different at each successive

injection point owing to the increase in jet thickness.

VII. CONCLUDING REMARKS

It fu apparent that for large systems the power/area is independent of

the system dimensions, although 'large' may be considerably beyond 'architectually'

feasi91e dimensions. The interaction of partieles and flow fields, even for so

simple a case as that of rigid spheres in the flow field considered, is exceed

-ingly complex. It seems doubtful then that techniques other than experime~tation

of this investigation indieate power requirements in the 0.1 h.p./ft2• range for spans of 100 - 150 feet, whieh is more or less in agreement with the results for the annular jet obtained experimentally3. The eomplexity of the sealing laws defies any simple statement beyond the funetions presented in Figs. 5-10. An idea of the eomplexity ean be obtained by eonsidering that from a 50' model

(V

J = 80. VT = 26.24.

w

= 30.0) we would prediet smaller power/area

require-ments at a 250' full seale whereas for

(V

J

=

80.0. VT

=

16.40. W

=

10.0) just

the opposite situation prevails.

Until full seale experimental projeets have been earried out, it would seem prudent based on the ealeulations herein, to aecompany eaeh small seale experimental investigation by an approximate numerieal simulation so that some idea of the sealing behaviour will be had.

l . Etkin, B. Korbacher, G. K. 2. Etkin, B. Goering, P. 3. .Lake, R. Etkin, B. 4. Etkin, B.

5.

Taylor, G. I. 6. Allen, G. 7. Vizel, M. Mostinskii, I. L. 8. Bradbury, L. 9. Mason, T. 10. Caton, P. G. 11. Finkelman, L. Holtz, Co D. REFERENCES

"Towards Dynamic Structures - Thoughts About Feasi-bility". Architecture Canada, March 1969, No,3 46. "Air Curtain Walls and Roof~, 'Dynamic' Structurestl

0 Roy. Soc. of London, Proceedings of Conference on Architectural Aerodynamics 1970.

"The Penetration of Rain Through An Annular Air-Curtain Dometl

• Univ. of Toronto, UTIAS Report No.163.

"Interaction of Precipitation wi th Complex Flows" • Proc. of the 3rd International Conference on Wind Effects on Structures, Tokyo, August 1971.

IIThe Use of a Vertical Air Jet. as a Windscreen" • In Collected Scientific Papers of G. I. Taylor, Vol.3, p.537. Also in Memoires sur la Mechaniques des Fluides (M.D. Riabouchinsky Anniversary Volume). Publications Scientifiques et Techniques du Ministere de l'A~r, Paris (1954), ppo313-7o

IIExperimental Investigation of

An

Air-Curtain For Protection of an qutdoor Power Installation from Salt Spray, Univ. of Toronto, UTIAS T. N. No. 171. IIDeflection of a Jet Injected into a Stream"o Inzhenerno-Fizicheskii Zhurnal, VOl.8, No,2

pp.238-242, 1965.

IISimple Expressions for the Spread of Turbulent Jets".

Aero~utical Quarterly, May 1967, pp.133-142o "The Physics of Cloudsll

• Appendix B. 'The Physical

Properties of Freely Falling Raindrops'.

"A Study of Raindrop-Size Distributions in the Free Atmosphere". Royal Met. Soc. Quarto Journal, 1966,

92, pp.15-30o

"Rainfall Distribution of Amount and Durationll

0 Dept. of Trfnsport, Meteorology Branch, Toronto, Ont.

APPENDIX

This appendix contains information necessary for constructing a model of rainfall. The following notes provide explanations for this material.

Figures Al to A3 present Reynolds number, terminal velocity and drag coefficient as a function of drop diameter. This data was used in the trajec-tory calculations

9 .

Figures A4 to A7 present data on the distribution of volume and drop numbers as functions of drop diameter. These are empirical curve fits

(A4-A6) produced by Best

9.

A sample of the variation in the measured results for a single rainfall rate appears in Fig. A4. In Fig. A5 the derivative of the function is plotted against drop diameter for a number of rainfall rates. Using the data of Fig. Al, Fig. A6 was obtained which is a cumulative volume distribution function for a number of rainfall rates. In Fig. A7 the Marshall-Palmer number density function is presented with a rainfall rate parameter~O It should be noted that this is not a true density function in that discrete drop class intervals are employed. In Figs. A8, A9 the distribution of duration and amount with rainfall rate are presented for the month of July 1968 in Southern

Ontario1~ In principle one could use this latter data in conjunction with the

earlier computed data to derive a distribution of duration with power required

U> LO

_v

É

E

... Cl:: wrt) ~ W ~

«

ON

a.

o

Cl::

o

..

WATER DROPS FALLING IN STILL AIR

GUNN and KINZER (1949)

FIG. Al

2

3

4

5

6

7

8

9

10

0:: _C\I

-

ct

~ ~

-

~

-(/)

en

•

z

en

-(!) 0:: Z lIJ ~ N ~ ~ Z Z

~

~ lIJ (/)

"

0 CL c: 0 LL C\I

.

0 LL < 0:: Z lIJ ~ Q Z 0

g

::l 0 0:: <!) H lIJ <!) rz. ~ <X

~

a::

0 ("WW) ~3.13W"IO dO~O

0 0 0 ~ Cl: <t ...J ...J

-~

en

0:: Cl)

•

_{lAJ M} Z

en

Om tC1!

-

0

2

~ (!)

a:

0::J ::J Z _LIJ N Z t9 H ...J _N Cl) r... ...J _Z 0

«

-

_...J LL ~ 0 Cl) ." _Z

a..

c

_>

0 0

_w

Cl:

z

_a:

c

_z

Q:: ::l 0 w (!) 0 ~ 0

~

~~I ~I~I~I-+I~I~I-+I~I~I~I~I-+I~I ~I~I~I-+I~I~I ~ _ _ ~-+~+-~~

9

ç

~ ~ ~

1.0

..,

2.8

~ ..J

~

I: lIJ

.6

;

~ 11.

o .'

z

o

~

u

.2

ct Cl: 11. O~S I~O

CUMULATIVE VOLUME DISTRIBUTION FOR A NUMBER OF OBSERVERS

RAINFALL RATE=2.0 mm./hr .

BEST FUNCTION F(x)=1.0-exp(-Jx/a)n)

LENARD (1904 ) GERMANY À

LAWS & PARSONS(1943) USA V

MARSHALL et a1(1947) CANADA

•

ANDERSON (1948) HAWAII

•

BEST(GT. BRT.)(1950) YNYSLAS 0 SHOEBURYNESS

...

EAST HILL

..

MEAN(exc1uding HAWAII) I~S 2~0 2~5

3:0

3:S

DROP DIAMETER

(mm.)

PIGURF. AL.

Z '

o

C

_x

'·0 ·8

....

...:... OC Z

~

.6 ::::>

x

LL_ I

)-0.

.... x

- Cl» Cl) • ~

cl-&

.4

o •

-

₎₍

....

-Cl) LL LLJ

m

.2

RAINFALL VOLUME DENSITY FUNCTION

(ADAPTED FROM BEST 1950) Mean of Pub1ished Results

Parameter is Rainfa11 Rate

1.0 _{2.0 2.·~ 3.0}

3.5

t.O UJ ~ .8 ::> ...J

o

>

Cl:: UJ ~ .6

~

1.1.

o

Z ·

o

.-~

a::

1.1. .2

CUMULATIVE VOLUME DISTRIBUTION PLOTTED AGAINST TERMINAL VELOCITY (ADAPTED FROM BEST 1950) Mean of Pub1ished resu1ts

Parameter is Rainfa11 Rate

FIGURE A6

.ol~~

2 3 4 5 6 7 8 MIS I --. --- I I I ~ 10 I~ 20 25 FT./S

TERMINAL

VELOCITY

IC)

a:

UJ

....

UJ 2

"

iloO~----~---4~~~~--~~----~~--~ ~

•

N

..

~

IJ) N °10-1~---r---r---~~~----~--~~r---~

--Parameter is Rainfall Rate

V)

0-e

a:

o u.

e

a: K)-2~---~---~---+---~~~----~~----~ UJ m ~ ~

z

10-

3

RAINFALL SIZE DISTRIBUTION MARSHALL AND PALMER

4

-.21 -1

1-_ _ ND=· 08 exp( -xD) x= l.p cm

where p=rainfall rate D=drop diameter

and ND~D=number of drops/unit vol. with

diameters D to D+~D

10~~---'---r---,---~---4~----~~

O.S 1.0 I.S 2.0 2.5 3.0

DROP DIAMETER (mm.)

DISTRIBUTION OF RAINFALL DURATION

from 26 stations in Southern Ontario Ju1y 1968

"""'-u

₇₅

'a

.,

U

•

'a ~ ~

/

total time=8223 minutes

~

•

Q. ~

50

-

u

e

;:

.,

•

₀

25

•

"--

IX

.,.

.2

..,

-~

10°

-

lOl

10 103

..,

-

RAINFALL RATE (mm/hr)

FIGURE A8.

•

W

'0

o

U QJ '0 ~

60

QJ Q. ~

.t..

...

_c

à

E

o

'6 40

Ö

,

-

et: Ol o

~

~20

"

-DISTRIBUTION OF RAINFALL AMOUNT

from 26 stations in Southern Ontario Ju1y 1968

~

/

_\

total amount=740 mm /

\

/

_\

/

1

\

/

\

/

~

----10°

10'

10

2

10

3

RAINFALL RATE (mm/hr)

FIGURE A9.

--•

--i

c~ , /

-,,".,:.~

~

/V"., \

(X

17) " - - - JET CENTER L

",,"

b

fo __ - INE

""

w

rOL - -

~

""

\.

"WI,.-/ ;,.. ... /

""

, /

~

,/ JET / / ",..

~

NORMAL / " " D R O P JET 80UNDARY / "., / / / / / TRAJECTDRY

'1

1/

1

1 /

I . I

w

~t

,.

X ..

axis

I-... N ~.

ëS

f--1 W I ---.J «:

b

f--1 !..>'l Z-W L I----! 0 I

§

C? ru LJ"'! ,-I C? <rl ~1 0 o o 0·0 Q,S ~T=24.0ft. T=16.o ft. T=12.0 ft. T=4.o ft. T=2.0 ft. T=l.O ft. 1·0 1 cc ' . .J 2·5 3·0 NON-DIMENSIDNAL 5PAN X/T

JET VELOCITY - 20 -00 WIND VELOCITY

=

10,00 TERMINAL VELOCITY - 15,40

I-... N ~. I L.J f--1 W I ---.J «: z 0 f--1 ~ W 2 I----! 0 I

§

C? al 0 u:; C? <;t 0 ru o o FIGURE 2a.

----+--- -.. -.-.-+--/-/ '

~ROP

TRAJECTORIES (Jet thickness T

a~

'

a

~arameter)

.-/ JET CE:~!lLlNE /~// ..• /~.~_ ... _---~

/

'\

/ ,/ T=24.o ft. T=4.0 ft.

---\ T=12.0 ft. T=2.0 ft. T=l.O ft. +-____ ~-. __ --~~L-~---~---~---+---+ 0·0 4·0 5·0 8·0 12·0 NDN-DI~I\5IONAL 5PAN X/T

JET VELOCITY - 40·00 WINJ VELOCITY

=

10-00 TERMINAL VELOCITY - 15·40

a

R:J DROP TRAJECTORIES (Jet thickness T as a parame __ te_rl _ _ _

a a 0·0

S·S

_ _ '1'=2.0 ft. '1'=24.0 ft. '1'=16.0 ft. '1'=12.0 ft. _ _ _ _ _ '1'=4.0 ft. 11·0

15·S

22·0 27,5 33·Q

N(}J-OHJENSIONAL SPAN

x/r

JET VELDCITY

-

50·00

WIND VELDCITY

=

10·00

TERMINAL

VELDCITY -

15·40

.-.

... N a a (Tl a a ru a a ..--l a a 0,0 Figure 2c

DROP TRAJECTORIES (Jet thickness T as a parameterl

~~

~ JEf/CENTERLlNE ~ '1'=1.0 ft . ~'1'=2.0 ft. '1'=12.0 ft. '1'=16.0 ft. '1'=4.0 ft. '1'=24.0 ft.

..,----10·0- 20·0 ]0·0 40-0 50·0 50·0

f'rn-DIrvfNSIDNAL

SPAN

x/r

LT VELCCITY

- 80

·00

WIND VELOCITY

=

10·00

TERMINAL

VELOCITY

-

15.40

c:

/

@ JET CENTERLlNE I- '-N

_c:

1-. III

êJ

-rl _{T=32.0 ft.} I--i ~ T=24.0 ft. -1 ~

c:

0 CJ I--i -rl ~

I:!i

I--i 0 T=4.0 ft. I

§

c:

T=2.0 ft. III

DROP TRAJECTORIES (Jet thickness T as a parameter)

5·Q 10·0 15·0 20·0 (5·0 30,0

N)\J-DItvfJtJICNAL SPAN

X /

T

JET VELOCITY

-

50·00

WIND

VELOCITY

=

10·00 TERMINAL VELOCITY - 25·24

0·0

FIGURE 2e.

---DROP TRAJl;;CTORIES (Jet thickness T as a p a r //"

""--JET CENTERLlNE

~T=20.0ft.

T=18.0 ft.

T=12.0 ft.

2·5 5·0 10,0 _12·5

t\ON

-DIM

Er'tJIONAL SPAN

X /

T

15·0

I-... Cl N in f _. "-~ H ~ o (1·0

DROP TRAJECTORIES (Jet thickness T as a parameter)

JET CENTERLlNE 1'=32.0 ft. 1'=16.0 ft.

__

'--:~---t-\-tt----T=l.O ft. 5·0 NO~-mME!f~IONAL 5Fm X/T 1 ,-.n -~

-ST

VEUIITY - 50,1:;0 wmc VELOCITY

=

30,00

TfRMINAL VELOCITY - 25,i:?4

I-... Cl CD ~-I N :n o m Cl 6 0·0 FIGURE 2h. ._. - +1- - - - -+ -- - --+-- - -- -+--- - --+-- -._=-,-- --+

DROP TRAJECTORIES (Jet thickness T as a parameter)

JET CENTERLINE

1'=16.0 ft.

_ _ _ _ T=8.0 ft.

4·5

g·o

13·5 18·0 22·5 27·0

f'il\J-DIMENSIDNAL SPAN X/T

JET VELOCITY - 80-00 WIND VELOCITY

=

20·00 TERMINAL VELOCITY - 25·24

.~

~

<~

IC') I'--"

0.

10

o

0.0

WIND VELOCITY W=20.0 ft./sec. JET VELOCITY V

j=60.0 ft./sec.

JET THICKNESS T=lO.O ft.

2.5

5.0

JET BOUNDARY " .... , ; . / , ;

7.5

A •

X-axis

"

, ;

"

"

. /

"

10.0

....

....

....

. /

DROP TRAJECTORIES (Point of injection X

_o

as a parameter)

FIGURE 3.

12.5

JE'I' C.è.~I'l';';~:.:,::::m Initial drop x-coordinate X

_o

0-

X O=O.12 1-X O=O.34 2-

_xo

=O.81 3 -Xo=l. 78 4-X

_o

=3. 73 5 - X

_o

=5. 71 15~0

.sa

) ( 0

<N

10

,...:

q

10

lel

N

0.0

WIND VELOCITY W=20.0 ft./sec.

JET VELOCITY V

j=60.0 ft./sec.

JET THICKNESS T=lO.O ft.

V T=17·5

ff/

v =?C; ()

2.5

5.0

"-X-axis

\ ~VT=22.5

7.5

10.0

DROP TRAJECTORIES(Terminal velocity V

T as a parameter) . < V T=15.0

12.5

15.0

.J

-

.,;

-~

. " , ~d

i

•

~

•

Q. D:

:z:

-~"f

a:

0 ct

"

a: lIJ

~

ó'

POWER/AREA VS. PROTECTED SPAN (Parameter is Jet Velocity V J)

WIND VELOCITY W=lO.O ft./sec. DROP TERMINAL VELOCITY V

T=16.40 ft./sec. • V J=40.0 ft./sec. • V =60.0 ft./sec . J [] V J=80.0 ft ./sec. 50 100 150 200 2.50 300 350 400

450

PROTECTED SPAN (ft,) FIGURE 5

-::

o

of;

o

ia

_~

•

Q. Q: ~

-~~

et:

~

o

B.

o

•

POWER/AREA VS. PROTECTED SPAN (Parameter is Jet Velocity V

J)

50

WIND VELOCITY W=20.0 ft./sec. DROP TERMINAL VELOCITY V

T=26.24 ft./sec. 100 A V J=40 . 0 ft. / sec. <lil V J=60 ,0 ft. /sec, ~ V J=80.0 ft./sec. 150

200

250

300

PROTECTED SPAN

(ft.) 350

400

POWER/AREA VS. PROTECTED SPAN (Parameter is Jet Velocity VJ )

~

WIND VELOCITY W=30.0 ft./sec.

DROP TERMINAL VELOCITY V_T=26.24 ft./sec.

Á V J=40.0 ft./sec •

• v

_J=60.0 ft./sec . • V J=80.0 tt./sec.

a

50 100 150 200 250 300 350 400 PROTECTED SPAN (ft.) FIGURE 7 .

•

-.:

--

zO

~~

Cl) Q

'"

~

~8

~N

o

a::

G.

o

2

' }

•

~

PROTECTED SPAN VS. JET THICKNESS (Parameter is Wind Velocity W)

10

20

V J=80.0 tt./sec. V T

a26.24

tt./sec. W=lO.O tt./sec.

~

V_J=80.0 tt./sec.

~

V_T=16.40 tt./sec . W=30.0 tt. / sec.

~

~

_W=20.0 tt./sec. W=lO.O tt./sec. 30 40 50

60

70 80

JET THICKNESS

(ft.)

~

-

.--

-~~

Cl) Q

~

b8

fN

8

10

PROTECTED SPAN VS. JET THICKNESS (Parameter is Jet Velocity VJ )

W=lO.O ft./sec. V_T=16.40 ft./sec. V J=80.0 rt./sec. V J=60.0 ft./sec. V J=40.0 ft./sec. 2-0 _{30 4"0 50}

₆₀

₈₀

JET THICKNESS (ft) FIGURE 9 .

•

o

PROTECTED SPAN VS. TERMINAL VELOCITY

!!

o

~

o

_ 0

::--

z

~

C 1&10 ~CI) U

~

o

Cl: Q.

o

CD

o

N W=20.0 ft./sec. T=10.0 ft. V_J=80.0 ft./sec. V J=60.0 ft./sec. v J=40.0 ft. /sec 5 10 15 20 25

TERMINAL VELOCITY VT(ft.IseC.)

FIGURE 10.

LIJ ~

3

g

~

~

o

0:", lIJ

~

~ ~ .

•

_o

""

o

o

10

DISTRIBUTION OF WATER VOLUME

FOR A SINGLE INJECTION POINT (X

O=O.12) RAINFALL RATE=5. 0 mm/hr. V J=40.0 tt./sec. W=20.0 ft./sec. T=lO.O ft.

I

I I I 20

30

40

50

DIST ANCE FROM JET EDGE

(ft.)

FIGURE 11 .

Balance of water (30%)

distributed beyond this po int

----.

~

I I