I Water Act - IDEALS

transcript

WRC RESEARCH RJ3PORT No. 155

MEASUREMENTS I N MERGING FLOW

W. Ha l l C. Maxwell

Arni Snorrason

Department of C i v i l Engineering

Universi ty of I l l i n o i s a t Urbana-Champaign

Urbana, I l l i n o i s 61801

FINAL REPORT

Pro jec t No. A-103-ILL

This p r o j e c t was p a r t i a l l y supported by t h e U . S . Department o f t h e I n t e r i o r i n accordance with T i t l e I o f t h e Water Research and Development Act o f 1978,

i P.L. 95-467, Agreement No. 14-34-0001-0115.

UlJIVER3ITY OF ILLINOIS WATER RESOURCES CENTER

2535 Hydrosystems Laboratory Urbana, I l l i n o i s 61801

January 1981

Contents o f t h i s p u b l i c a t i o n do not necessar i ly ' r e f l e c t the views and p o l i c i e s o f the O f f i c e o f Water Research and Technology, U.S. Department o f the I n t e r i o r , nor does rnentlon o f t rade names o r conmerclal products c o n s t i t u t e t h e i r endorsement o r reconmendation f o r use by the U . S . Government.

ABSTRACT

Previous measurements of t h e v e l o c i t y f i e l d i n t h e v i c i n i t y of two i n t e r s e c t i n g submerged tu rbu len t j e t s provided evidence t h a t , cont rary t o t h e usual assumptions, i n t e r s e c t i n g flows may no t n e c e s s a r i l y be combined using vec tor add i t ion of v e l o c i t i e s o r momentum f l u x d e n s i t i e s .

To ga ther add i t iona l experimental evidence on t h e d e t a i l s of t h e v e l o c i t y f i e l d nea r t h e i n t e r s e c t i o n of two submerged tu rbu len t j e t s , t h i s s tudy measured time average v e l o c i t y magnitudes and d i r e c t i o n s of two perpendicular i n t e r s e c t i n g axisymmetricsubrnerged tu rbu len t incompressible a i r j e t s of approximately equal s t r eng th . Because o f t h e need t o d e t e c t r eve r se flows, a three-dimensional p i t o t - t y p e probe was used. This could sense yaw and p i t c h angles a s wel l a s v e l o c i t y magnitudes. Two s e t s o f measurements were taken. The more d e t a i l e d s e t was confined t o t h e p lane o f t h e nozzles , t h e l e s s d e t a i l e d s e t obtained c ross - sec t iona l d a t a a t four s t a t i o n s , t h r e e o f t hese being i n t h e observed r eve r se flow.

The da ta show t h a t t h e r eve r se flow spreads much more r a p i d l y perpendicular t o t h e nozzle plane than i n t h e nozzle plane, whereas t h e forward flow i s f a i r l y symmetric. , S i m i l a r i t y p r o f i l e s were found i n both t h e forward and r eve r se flows. In t h e forward flow t h e d i s t r i b u t i o n was e s s e n t i a l l y Gaussian. This was a l s o t r u e i n t h e backward flow i n t h e d i r e c t i o n normal t o t h e plane of t h e nozzles . In the p lane of t h e nozzles the backward flow p r o f i l e s were c l o s e t o s e m i - e l l i p t i c a l o r semi-c i rcu lar , depending on the s c a l e s f o r p l o t t i n g .

Maxwell, W. Hal l C . , and Arni Snorrason MEASUREMENTS I N MERGING FLOW Final r e p o r t t o t h e Off ice o f Water Research and Technology, Department of I n t e r i o r P ro jec t A-103-ILL, January 1981.

KEYWORDS: *Diffusion-flow/flow cha rac te r i s t i c s /* f low p r o f i l e s / f l u i d mechanics/* j e t s / *mixing

TABLE OF CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF TABLES

. . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF FIGURES

. . . . . . . . . . . . . . . . . . . . . . . . . . LISTOFSYMBOLS

1 . INTRODUCTION AND OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . VELOCITY DISTRIBUTION IN A SINGLE JET

3 . EXPERIMENTAL MEASUREMENTS IN CROSSING FLOWS . . . . . . . . . 3.1 P u r p o s e a n d S c o p e . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . 3.2 E x p e r i m e n t a l A p p a r a t u s

. . . . . . . . . . . . . . . 3.3 E x p e r i m e n t a l M e a s u r e m e n t s

. . . . . . . . . . . . . . . . . . . . . 3.4 D a t a R e d u c t i o n

3.5 E x p e r i m e n t a l D a t a . . . . . . . . . . . . . . . . . . . 4 . DATA ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . 5 . CONCLUSIONS AND P3COMMENDATIONS

. . . . . . . . . . . . . . . . . . . . . . 5.1 C o n c l u s i o n s

. . . . . . . . . 5.2 Recommenda t ions o n F u t u r e A p p l i c a t i o n s

. . . . . . . . . . . . . . . . . . . . . . . . . LISTOFREFERENCES

P a g e

v i i i

LIST OF TABLES

Table Page

1 Measured Two-dimensional Spreading Coefficients . . . . 3

2 Measured Axi-symmetrical Spreading Coefficients . . . . 5

LIST OF FIGURES

Page Figure

Def in i t i on ske tch . . . . . . . . . . . . . . . . . . 8

Schematic r ep resen ta t ion of c ross ing a i r j e t a p p a r a t u s . . . . . . . . . . . . . . . . . . . . 9

Veloci ty vec to r s i n t h e p lane of t h e jets . . . . . . 15

Veloci ty i n the forward flow i n t h e p lane o f t h e n o z z l e s . . . . . . . . . . . . . . . . . . . 16

Veloci ty t r a v e r s e i n t h e backflow i n t h e p lane of t h e nozzles . . . . . . . . . . . . . . . . 17

Contours of equal v e l o c i t y i n t h e backflow a t x = 25.2 cm . . . . . . . . . . . . . . . . . . . 19

Contours of equal v e l o c i t y i n fbrward flow a t x = 26.2 cm . . . . . . . . . . . . . . . . . . . 2 2

Isometr ic p ro jec t ion of su r face represent ing backflow v e l o c i t i e s a t x = 25.2 cm . . . . . . . . . 2 3

Isometr ic p ro jec t ion of s u r f a c e r ep resen t ing backflow v e l o c i t i e s a t x = 25.5 cm . . . . . . . . . 2 4

I sometr ic p ro jec t ion of su r face r ep resen t ing v e l o c i t i e s a t x = 25.8 cm . . . . . . . . . . . . . . 25

Isometr ic p ro jec t ion of s u r f a c e represent ing forward v e l o c i t i t e s a t x = 26.2 cm . . . . . . . . . 26

Forward flow p r o f i l e s compared wi th Gaussian d i s t r i b u t i o n . . . . . . . . . . . . . . . . 28

Veloci ty p r o f i l e s i n t h e p lane of t h e nozzles i n the backflow . . . . . . . . . . . . . . . 2 9

Veloci ty p r o f i l e s normal t o t h e p lane of t h e nozzles i n t h e backflow . . . . . . . . . . . . . 3 1

P r o f i l e widths i n the forward and backflows . . . . . 32

LIST OF SYMBOLS

A incoming j e t nozz le , s e e Fig. 1

A. o u t l e t a r e a (per u n i t length f o r s l o t )

B incoming j e t nozzle, s e e Fig. 1

b ha l f width of v e l o c i t y p r o f i l e i n xy p lane Y

b ha l f width of v e l o c i t y p r o f i l e i n xz plane Z

C spreading c o e f f i c i e n t

j = 0 f o r p lane symmetry, = 1 f o r a x i a l symmetry

t o t a l p re s su re

p res su res sensed by l a t e r a l p o r t s

= P2 - P3

pressures sensed by upper and lower p o r t s

= P4 - P5

t r u e s t a t i c pressure

t r u e t o t a l pressure

time average ve loc i ty i n t h e x d i r e c t i o n , o r v e l o c i t y magnitude

average v e l o c i t y a t o u t l e t

average v e l o c i t y a t nozz le A o u t l e t

average v e l o c i t y a t nozz le B o u t l e t

maximum o r c e n t e r l i n e v e l o c i t y

or thogonal co-ordinate axes

ang le of p i t c h

y dev ia t ion from loca t ion of maximum v e l o c i t y

z dev ia t ion from loca t ion of maximum v e l o c i t y

angle of yaw

s tandard dev ia t ion of v e l o c i t y p r o f i l e i n xy plane

s tandard dev ia t ion of v e l o c i t y p r o f i l e i n xz p lane

2. VELOCITY DISTRIBUTION IN A SINGLE JET

The v e l o c i t y d i s t r i b u t i o n i n a submerged tu rbu len t j e t had been

considered by many i n v e s t i g a t o r s t o be adequately descri 'bed by a normal

d i s t r i b u t i o n . For both plane-symmetric and axisymmetric j e t s , t he

v e l o c i t y d i s t r i b u t i o n may be descr ibed by t h e fol lowing equat ion:

i n which u = t ime average v e l o c i t y i n t h e a x i a l , x, d i r e c t i o n ; u = average 0

v e l o c i t y a t t h e o u t l e t ; A. = o u t l e t a r e a (per u n i t l eng th f o r plane-symmetry);

C = spreading c o e f f i c i e n t ; y = a x i s normal t o x ( r a d i a l a x i s f o r a x i a l

symmetry); j = 0 f o r p lane symmetry, and j = 1 f o r a x i a l symmetry.

D i f f e ren t i n v e s t i g a t o r s have obtained d i f f e r e n t experimental

va lues f o r C, t h e spreading c o e f f i c i e n t , i n t h e case of both t h e plane-

symmetric j e t and t h e axisymmetric j e t . These r e s u l t s a r e d e a l t with i n

d e t a i l i n t h e fol lowing sec t ion .

2.2 Spreading Coef f i c i en t s f o r Plane- and Axi-Symmetric J e t s .

Table 1 summarizes spreading c o e f f i c i e n t s measured by a number of

i n v e s t i g a t o r s f o r two-dimensional t u rbu len t j e t s . The information has

been c o l l e c t e d from Refs. 1, 10 , 27 and 33. Where p o s s i b l e t h e o r i g i n a l

source of d a t a has been l i s t e d i n t h e References. The t a b l e r e f l e c t s t he

f a c t t h a t t h r e e d i f f e r e n t sources (1, 26, 33) gave t h r e e d i f f e r e n t va lues

of C from f i t t i n g F8rthmann1s data . Round-off e r r o r i n convert ing from t h e

no ta t ion of Refs. 1, 2 7 and 33 t o t h e p re sen t n o t a t i o n may account f o r p a r t

TABLE 1. Measured Two-dimensional Spreading Coef f i c i en t s

Experimenter

F'br t hmann

Reichard t

van d e r Hegge Zijnen

Albertson e t a l .

Reichard t

Mi l l e r & Comings

van d e r Hegge Zijnen

Nakaguchi

Bradbury

Heskestad

Knystautas

Gartshore

Heskest ad

Goldschmidt & Eskinazi

F lora & Goldschmidt

Mih & Hoopes

Jenkins & Goldschmidt

Kotsovinos

Se lec ted Average by:

Newman

Abraham

Fischer e t a l . 0.097+0.003 0.082+0.001

Axial C

- 0.114

- 0.093

0.098(?)

L a t e r a l C

0.082,0.084,0.086

of t h e d i f f e r ences . The t a b l e shows va lues ob ta ined by f i t t i n g t h e d a t a f o r

decay of t h e maximum v e l o c i t y a long t h e a x i s and va lues ob ta ined by f i t t i n g

t h e d i s t r i b u t i o n s normal t o t h e a x i s . Depending on one ' s ob j ec t i ve s ,one

may o b t a i n a "best" f i t t o e i t h e r of t h e s e d a t a sets o r , by compromising

s l i g h t l y on t h e goodness of f i t i n both cases, s e l e c t a s i n g l e spreading

c o e f f i c i e n t which a p p l i e s reasonably w e l l t o both ca se s e. g. t h e r e s u l t

ob ta ined by Albertson e t a l . (2 ) . This may then be used wi th Eq. 1. A

f u r t h e r oppor tun i ty f o r some compromise a r i s e s i n t h e s e l e c t i o n of a zero

c o r r e c t i o n o r s l i g h t s h i f t i n t h e o r i g i n of t h e co-ordinate system from t h e

phys i ca l l o c a t i o n of t h e s l o t o u t l e t .

Newman (33) concluded t h a t v a r i a t i o n s i n l a t e r a l spreading

c o e f f i c i e n t s ev ident from an examination of t h e work of e a r l i e r i n v e s t i g a t o r s

was appa ren t ly l a r g e l y due t o end e f f e c t s . E a r l i e r measurements were made

wi th low a s p e c t - r a t i o s l o t s , and i n s u f f i c i e n t c a r e was taken t o provide

f a i r i n g s on t h e end p l a t e s o r t o make them adequately l a r g e . This l e a d s

t o va lues of spreading c o e f f i c i e n t which a r e too low. H e pos tu l a t ed t h a t

v o r t i c e s forming a t t h e edge of t h e end p l a t e s induce spanwise f lows which

u s u a l l y t h i n t h e s h e a r flow. S ince t h i s problem does n o t a r i s e f o r

axisymmetric j e t s , v a r i a t i o n s i n measurements of t h e i r r a t e of growth a r e

much less. Based on a neg lec t of doub t fu l measurements Newman recommended

a l a t e r a l spreading c o e f f i c i e n t of 0.088 + 2%.

Albertson e t a l . (2) s t a t e d " . . . . c lose agreement i n t h e l i m i t e d

zone of es tab l i shment i s considered l e s s s i g n i f i c a n t than eva lua t ion of

both zones ( a s i n t h e two-dimensional case) i n terms of t h e same c o e f f i c i e n t . . . . ' I

Abraham (1) s e l e c t e d average va lues of 0.101 f o r a x i a l decay and

0.100 f o r l a t e r a l spreading a t l a r g e d i s t a n c e s from t h e o u t l e t i n h i s

TABLE 2. Measured h i - symmet r i ca l Spreading Coef f i c i en t s

Experimenter

Triipel

Reichardt

Corrs in

Corrs in and Uberoi

Hinze and v. d. Hegge Zijnen

Keagy and Weller

Keagy, Weller, Reed & Reid

Alber t son ,Dai , J ensen& Rouse

Becher

Corrs in and Uberoi

Reichardt

Taylor , Grirnrnett, &Comings

~ l e x a n d e r , Baron & Comings

F o r s t a l l and Gaylord

Poreh and Cermak

Ricou and Spalding

Rosenweig, H o t t e l b Williams

Johannesen

Wilson and Danckwerts

0.075+0.006

Average L a t e r a l C

0.076+0.002

Axia l C

- - - - - -

Average + s t . dev.

Se lec ted Average by:

Newman

Abraham

F i sche r e t a l .

L a t e r a l C

0.073, 0.076

- 0.081, 0.092

0.076, 0.078

0.085, 0.081

0.064, 0.071 pp

0.077+0.005

Average Axial C

- 0.081

0.081+0.001

study. H e remarked t h a t t h e d a t a of Alber t son e t a l . i n d i c a t e t h a t t h e

l a t e r a l spreading c o e f f i c i e n t a c t u a l l y t ends t o i n c r e a s e wi th i nc reas ing

d i s t a n c e from t h e o u t l e t . H e i n d i c a t e d t h a t o t h e r experimental work

showed s i m i l a r t r e n d s , which agrees wi th obse rva t ions t h a t l a t e r a l d i s t r i -

bu t ions of t u r b u l e n t s t r e s s e s i n axisymmetric j e t s (7) and i n two-

dimensional jets (31) do no t e x h i b i t s i m i l a r i t y f o r d i s t a n c e l e s s than

40 diameters o r 40 s l o t h e i g h t s downstream from t h e o u t l e t .

Kotsovinos (27) a l s o advanced t h e hypothes i s t h a t t h e b a s i c

reason f o r v a r i a t i o n s i n spreading c o e f f i c i e n t s f o r p lane t u r b u l e n t jets

is t h a t growth is not exac t ly l i n e a r on a l a r g e s ca l e . Data from s e v e r a l

sources i n d i c a t e d t h a t t h e j e t width is a 'weak' non- l inear f u n c t i o n of x.

No explana t ion was advanced f o r t h e observed behavior .

F i s che r e t a l . (10) summarized va lues of l a t e r a l and a x i a l

spreading c o e f f i c i e n t s bu t d i d n o t d e t a i l t h e o r i g i n a l sources incorpora ted

i n t h e averages.

Clear ly , then , t h e r e i s no consensus on " c o r r e c t " va lues f o r

e i t h e r a x i a l o r l a t e r a l c o e f f i c i e n t s f o r two-dimensional jets.

Table 2 summarizes a x i a l and l a t e r a l spreading c o e f f i c i e n t s f o r

axisymmetr ical jets, aga in taken from Refs. 1, 10 , and 33. I n some c a s e s

where two v a l u e s a r e l i s t e d f o r t h e same t e s t , e.g. Ruden, 1933, t h e t a b l e

r e f l e c t s t h e f a c t t h a t Abraham (1) and F ischer e t a l . (10) ob ta ined

d i f f e r e n t v a l u e s of C from f i t t i n g t h e da t a . The d i f f e r e n c e aga in a l s o

i nc ludes e f f e c t s of round-off e r r o r when conver t ing from t h e n o t a t i o n used

by Abraham and by F ischer e t a l . t o t h e n o t a t i o n used h e r e i n . Table 2

i l l u s t r a t e s t h a t t h e r e is a l s o no consensus on "cor rec t" va lues of a x i a l

o r l a t e r a l c o e f f i c i e n t s f o r axi-symmetrical j e t s .

3. EmERIMENTAL MEASUREMENTS I N CROSSING FLOWS

3.1 Purpose and Scope

Measurements of v e l o c i t y time average magnitude and d i r e c t i o n

were aimed a t d e t a i l e d mapping of t h e v e l o c i t y f i e l d i n t h e v i c i n i t y of two

i n t e r s e c t i n g incompressible a i r j e t f lows. I n p a r t i c u l a r , t h e r e was an

i n t e r e s t i n t h e three-dimensional cha rac te r of t h e r e s u l t i n g j e t - l i k e

flows. Figure 1 shows a d e f i n i t i o n ske tch of the va r ious elements of t h e

flow p a t t e r n . Measurements were made holding a a t 90° and the quot ien t

u /ub i n t h e narrow range 1.015 i- 0.001. The discharge through tubes a

A and B was he ld cons tant by monitoring t h e pressure a t and ac ross the

o r i f i c e meters i n t h e i r supply l i n e s (Fig. 2) . The co-ordinate system was

a l igned with t h e x-axis approximately p a r a l l e l t o CD, t h e a x i s of maximum

v e l o c i t y f o r t h e r e s u l t a n t flow, and t h e y-axis p a r a l l e l t o a l i n e through

t h e tube o u t l e t s .

3.2 Experimental Apparatus

The apparatus used t o s tudy the v e l o c i t y d i s t r i b u t i o n i n t h e flow

f i e l d c rea t ed by two cross ing a i r j e t s is i l l u s t r a t e d i n F ig . 2. Two

i d e n t i c a l 3/16 in . (0.475 cm) i n t e r n a l diameter copper tubes were used

a s nozzles and were mounted perpendicular t o each o t h e r on a h o r i z o n t a l

board. Each copper tube was connected t o a 1 112 i n . (3.8 cm) diameter

pipe by means of tygon tubes. I n order t o maintain and monitor cons tant

pressure , a pressure r egu la to r and gauge were i n s t a l l e d i n t h e a i r supply

upstream from the 1 112-in. pipe. A d i f f e r e n t i a l water manometer was used

t o measure t h e p res su re drop ac ross t h e o r i f i c e . The p res su re on t h e

upstream s i d e of t h e p l a t e was measured using a mercury manometer. The

ho r i zon ta l board was l e v e l l e d on a t a b l e top,and a probe t r a v e r s i n g mechanism

LOCATION OF OUTLET

CENTERS

! I I TUBE x , c m y , f t z , i n

A 23.68 0.956 18.77

B 23.68 1.119 18.77

Fig. 1 Defin i t ion sketch

3/16" x 1 1 / 2 " ORFICE METER -', TYGON TUBE

a 1 - I 1 1 1 / 2 " I D P I P E

NEEDLE VALVE

\ - PRESSURE GAUGE

PRESSURE REGULATOR

3/16" I D COPPER

TYGON TUBE

Fig. 2 - Schematic representation of crossing air j et apparatus

was mounted on a r i g i d framework independent ly mounted on t h e f l o o r .

Time average v e l o c i t y magnitudes and d i r e c t i o n s were measured

us ing a United Sensor and Control Corporat ion Type DC three-dimensional

d i r e c t i o n a l probe. This had a s ens ing head diameter of 1/8-in. (0.318 cm)

and a l e n g t h of 36-in. (91.4 cm) . It was mounted on a United 'Sensor and

Control Corporat ion manual t r a v e r s e u n i t . This has b 0 t h . a l i n e a r v e r n i e r

t r a v e r s i n g s c a l e f o r d i s t a n c e read ings and a r o t a r y v e r n i e r s c a l e f o r

angle of yaw readings. The read ings p r e c i s i o n on t h e l i n e a r s c a l e was

0.01 i n . (0.025 cm) and 0 . 1 degrees on t h e angu la r v e r n i e r s c a l e .

The manual t r a v e r s e u n i t was mounted on a s t u r d y h o r i z o n t a l

c a r r i a g e running on a l a r g e r h o r i z o n t a l c a r r i a g e . This i n t u r n r a n

pe rpend icu l a r ly on h o r i z o n t a l r a i l s incorpora ted i n a heavy s t e e l frame

and was moved us ing a p o i n t gage set h o r i z o n t a l l y . The v e l o c i t y probe,

thus mounted, could be moved i n t h r e e mutual ly or thogonal d i r e c t i o n s and

r o t a t e d wi thout a l t e r i n g t h e l o c a t i o n of t h e sens ing head. Co-ordinates

w e r e recorded t o 0.01 i n . (0.025 cm), 0.001 f t (0.030 cm) and 0 .1 cm

(0.039 i n . ) , us ing t h e manual t r a v e r s e , po in t gage read ing and main

c a r r i a g e l o c a t i o n s c a l e s r e spec t ive ly .

The three-dimensional d i r e c t i o n a l probe measures t h e yaw and

p i t c h ang le of t h e v e l o c i t y vec to r a s w e l l a s t o t a l and s t a t i c p r e s su re s .

Five sens ing p o r t s a r e l oca t ed on t h e t i p of t h e probe. The c e n t r a l l y

l o c a t e d p o r t senses t h e t o t a l p r e s su re P The two l a t e r a l p o r t s sense 1'

p re s su re s P and P The probe is r o t a t e d us ing t h e manual t r a v e r s e u n i t 2 3'

u n t i l P = P a s i n d i c a t e d on a d i f f e r e n t i a l manometer. The v e r n i e r on 2 3

t h e c i r c u l a r s c a l e of t h e manual t r a v e r s e u n i t then i n d i c a t e s t h e yaw angle .

With t h e probe a l igned along t h e d i r e c t i o n f o r which P = P -P = 0 t h e 23 2 3

d i f f e r e n t i a l p re s su re P = P -P sensed by t h e two p o r t s above and below 45 4 5

t h e t o t a l p re s su re p o r t is read on a d i f f e r e n t i a l manometer. The

c a l i b r a t i o n curve f o r t h e probe can then be used t o determine t h e angle of

p i t ch . This is a func t ion of P /P i n which P = pl-112 (P2 + P3). 45 12' 12

For any p a r t i c u l a r p i t c h angle , B , t h e c a l i b r a t i o n curve of (Pt-P )/.P s 12

may be used t o determine t h e v e l o c i t y . Pt = t r u e t o t a l p re s su re and

P = t r u e s t a t i c pressure . The f l u i d v e l o c i t y is S

= [2(Pt - Ps)/pI 112 (2)

The d i f f e r e n t i a l manometers f l u i d was Meriam 827 Red O i l which

has a s p e c i f i c g r a v i t y of 0.827. The P12 manometer was t i l t e d a t 45'; t h e

'23 and P manometerswere t i l t e d a t 20.5'. For d a t a r educ t ion t h e

c a l i b r a t i o n curve f o r p i t c h ang le was approximated by two l i n e a r func t ions ,

one f o r p i t c h ang le s i n t h e range + 10' w i th maximum e r r o r of lo, t h e

o t h e r f o r 2 40' wi th maximum e r r o r of + 2.5'. The p i t c h ang le measurements

wereunreliablewhenvelocities, a n d h e n c e p were low. A l o w e r l i m i t 12'

of 0.8 l b s per square f o o t was t h e r e f o r e s e t on measurements of P12. A

good approximation t o t h e c a l i b r a t i o n curve f o r p i t c h ang le s i n t h e

range + 10' i s t h e cons tan t va lue 0.87 f o r (P -P )/p12. Since t h e v a s t t s

ma jo r i ty of r e l i a b l e readings f e l l w i th in t h i s range t h i s cons tan t va lue

was used f o r d a t a reduct ion .

3 .3 Experimental Measurements

For each measurement s e t t h e atmospheric temperature and p re s su re

were recorded. For t h e mapping of t h e v e l o c i t y v e c t o r f i e l d i n t h e p lane

of t h e nozz les ( z = 18.77 cm) t r a v e r s e s were made a t constant va lues of x ,

wi th y being var ied . The z - se t t i ng w a s found by t r a v e r s i n g t h e p i t o t u n t i l

maximum v e l o c i t y was found. Traverses were repea ted a t x i n t e r v a l s ranging

from 0 .1 cm up t o 0.5 cm, s o a s t o cover t h e incoming j e t s , t h e forward

j e t and t h e back flow j e t . The va lues of P 12 ' Pt , yaw angle and P a s

45 ' w e l l a s t h e coord ina tes (x, y , z ) of t h e probe t i p were recorded a t each

po in t of t h e t r a v e r s e . I n t h e zone nea r t h e s t agna t ion p o i n t , v e l o c i t i e s i n

t h e back f low j e t were very smal l and t h e r e was i n t e r f e r e n c e between t h e

probe and t h e incoming j e t s . The back flow j e t measurements were t h e r e f o r e

conducted wi th cons t an t yaw angle . The yaw ang le was s e t by moving back

i n t o a r eg ion of h ighe r v e l o c i t y back flow. The a p p l i c a b i l i t y of ho ld ing

t h e yaw a n g l e cons tan t i n t h e e n t i r e back flow region was checked from

t i m e t o t i m e where t h e back flow v e l o c i t y was s u f f i c i e n t l y h igh t o permit

it, and proved t o be adequate. S imi l a r d i f f i c u l t i e s were found near t h e

edges of t h e incoming j e t s ad jacent t o t h e backflow j e t and were again

reso lved by s e t t i n g t h e yaw ang le t o i t s va lue i n t h e ad j acen t reg ion of

h ighe r incoming v e l o c i t y . I n a l l o t h e r p o r t i o n s of t h e f low f i e l d t h e

p i t o t was set a t t h e yaw ang le determined by P = 0. 2 3

Because adjustment of t h e yaw ang le was very time-consuming

and considerably more d a t a p o i n t s had t o be c o l l e c t e d f o r mapping of t h e

c ros s - sec t iona l v e l o c i t y f i e l d , t h e yaw ang le was s e t a t a cons t an t va lue

determined i n t h e reg ion of maximum v e l o c i t y f o r t h e forward j e t . Traverses

were made a t cons t an t yaw angle and cons t an t x. For each c ross -sec t ion

t r a v e r s e s were made i n t h e y d i r e c t i o n f o r va r ious va lues of z . Three

c r o s s s e c t i o n s were measured f o r t h e back flow j e t and one f o r t h e

forward j e t . The va lues of P 12' Pt ' P45 and x , y and z were recorded f o r

each p o i n t whi le holding t h e yaw ang le cons tan t .

3.4 Data Reduction

Computer programs were developed t o analyze and present t h e da t a .

Three s e t s of programs were u t i l i z e d : one f o r handl ing raw d a t a ; one f o r

g raph ica l p re sen ta t ion of t h e v e l o c i t y v e c t o r f i e l d i n t h e p lane of t h e

nozz les ; and one f o r g raph ica l p re sen ta t ion of t h e c ros s - sec t iona l da t a .

The program f o r handl ing of raw da ta c a l c u l a t e d p i t c h ang le s

and v e l o c i t y p re s su re c o e f f i c i e n t s by l i n e a r i n t e r p o l a t i o n of t h e

c a l i b r a t i o n curves f o r t he probe. The o u t l e t average v e l o c i t i e s were

ca l cu la t ed using the c a l i b r a t i o n s f o r t h e o r i f i c e meters used i n t h e

supply l i n e s t o determine t h e a i r discharge.

The second program non-dimensionalized t h e raw d a t a and

p l o t t e d t h e v a r i a t i o n of t h e v e l o c i t y , yaw angle , 8 , and p i t c h ang le ,

6 % f o r each t r a v e r s e . A subrout ine was used t o p l o t t h e vec to r f i e l d ,

showing t h e ang le of yaw and t h e length of t h e v e l o c i t y vec to r . The

i n t e r f a c e between t h e back flow j e t and t h e incoming j e t s A and B was no t

w e l l def ined. The most probable explana t ion i s t h a t t h e incoming j e t s

i n t e r f e r e wi th t h e p i t o t tube when t h e backflow j e t i s measured and

the backflow j e t i n t e r f e r e s wi th t h e p i t o t tube when t h e incoming j e t s

a r e measured. Two s e t s of p l o t s were prepared, one g iv ing t h e forward

v e l o c i t i e s readings p r i o r i t y , t h e o t h e r g iv ing p r i o r i t y t o t h e backward

v e l o c i t i e s . The zone where t h e p l o t s d i sag ree i n d i c a t e s t h e reg ion of

i n t e r f e r e n c e .

The program f o r t h e c ros s - sec t iona l d a t a was used t o p l o t contour

o r i s o v e l o c i t y p l o t s and t o i l l u s t r a t e t h r e e dimensional s u r f a c e s viewed

from d i f f e r e n t vantage po in t s .

3.5 Experimental Data

F i g u r e 3 shows a p l o t of t h e v e l o c i t y v e c t o r f i e l d i n t h e p l ane

of t h e j e t nozz l e s . Th i s p l o t is a composite of t h e p l o t s de sc r i bed i n t h e

last s e c t i o n . The p l o t g iv ing backward v e l o c i t i e s p r i o r i t y was l a i d over

t h e p l o t g i v i n g t h e forward v e l o c i t i e s p r i o r i t y . The r e g i o n of disagreement

between t h e s e two is hatched i n F igu re 3, which is b a s i c a l l y t h e backward

p r i o r i t y p l o t . There may b e some c o r r e l a t i o n between t h e f a c t t h a t more

c o n f l i c t i s observed on one s i d e of t h e flow p a t t e r n and t h e f a c t t h a t t h e

probe always p rogressed i n t o t h e f low f i e l d from t h a t s i d e . Note a l s o t h a t

t h e l i n e a r s c a l e is i n d i c a t e d a t t h e t o p of t h e f i g u r e . Some of t h e

measurements were t aken a t a l a t e r t i m e than o the r s , and i t w a s no ted

t h a t t h e maxima of t h e later and earlier p r o f i l e s d i d n o t q u i t e l i n e

up. Th i s w a s a t t r i b u t e d t o s l o p i n t h e c a r r i a g e r a i l system, and an

i n d i c a t i o n of i t s o r d e r of magnitude is no ted on t h e f i g u r e . T h i s problem

d i d no t p r e s e n t i t s e l f dur ing any con t inuous set of measurements and on ly

became e v i d e n t n e a r t h e end of t h e exper imenta l program when some

measurements were made t o f i l l i n gaps i n t h e v e c t o r f i e l d p l o t . It would

appear t o be r ea sonab l e t o s h i f t t h e p r o f i l e s t o a l i g n t h e maxima; however \

t h e d a t a a r e p r e sen t ed a s recorded . F i g u r e 3 is u s e f u l i n a s s e s s i n g t h e

o v e r a l l c h a r a c t e r of t h e flow. However t h e d e t a i l e d t r a v e r s e s upon which

it is based a r e more u s e f u l i n a n a l y s i n g t h e e x i s t e n c e o r no t of

s i m i l a r i t y p r o f i l e s w i t h i n t h e f low and t h e i r d e t a i l e d c h a r a c t e r . Two

c r o s s - s e c t i o n a l l o c a t i o n s are f l agged on Fig. 3 a t x v a l u e s of 25.4 cm and

26.0 cm. The d e t a i l e d t r a v e r s e s f o r t h e s e two l o c a t i o n s a r e p r e sen t ed i n

F ig s . 4 and 5 . Figure 4 shows t h e v a r i a t i o n of v e l o c i t y magnitude, yaw

MAXIMUM VELOCITY 2 2 9 . 3 f p s OUTLES AT X = 2 3 . 6 8 cm

SHIFT DUE TO CARRIAGE SLOP

REGION OF CONFLICTING DATA

TRAVERSE STARTED FROM THIS SIDE

F i g . 3. V e l o c i t y v e c t o r s i n t h e p l a n e o f t h e j e t s .

THE REFERENCE VELOCITY I F 229.3 FBS THE REFERENCE ANGLE I S 180' OUTLET CENTERS AT X a 23.68 CM, Z = 1.564 FT

- YAW ANGLE, 0 +-+ -At

'n 4--+ +-- ' ,,A'-. -3-

- j++ -.+ - +-A jh+-?c -

I - -+ -Y -F- ,/ \ . ~ x -- +

\ ./,/ '/ / PITCH ANGLE, B

Fig. 4. Veloc i ty i n the forward f low i n the plane of the nozz les .

5 - . 2 5 +

I : M , E N 1 :S - . 5 * I I

0 ' N , : L - - 7 5 -.- E

S Iv I I I -1 .

-- ---- - -- - - -- - - - -- - - - -

THE X - L g C IS 26.0 CM 1 I T H E Z-LCiC I S 1 . 5 6 4 ~ ~ ! TWE 3,I"E I S 3 i 1 1 9 G 3 i

I I t -- 1- - ----+---.-I 0 . 1 . 2 . 3 . 4 .

- 5 1. 5 2 . 5 3 . 5

r-- .i-. . - . - . ,- " .- . .-.----.--...--z.-----.u.-.--.m....

: J . . . / C.

-r ! .THE REFERENCE VELOCITY I S 229.3 FPS

I :.- j r- / , J

THE REFERENCE ANGLE I S 180' , C 1 OUTLET CENTERS AT X - 23.68 CM, Z = 1.564 FT

;I , r i 7-

i ;r . 5 -!- i

> -? > , 1

i I I i A ---6 VELOCITY

L' .+ -{ ',

.1 PITCH ANGLE, B a A.

't" - i3 2 pi t:' C T 13 N (NOZZLE DIMTERS)

Fig. 5. Velocity traverse in the backflow in the plane of the nozzles.

a n g l e and p i t c h a n g l e i n t h e forward f low r e g i o n as t h e two incoming jets

merge. I ts g e n e r a l form sugges t s t h e con junc t i on of two e s s e n t i a l l y

Gaussian p r o f i l e s . F igu re 5, on t h e o t h e r hand, shows t h e same parameters

i n t h e reg ion of backflow. C l e a r l y t h e v e l o c i t y p r o f i l e i n t h a t reg ion i s

non-Gaussian i n c h a r a c t e r .

F igs . 6 through 9 show contours of equa l v e l o c i t y a t f o u r

l o c a t i o n s i n t h e f low f i e l d . Figs . 6 through 8 are l o c a t e d i n t h e r eg ion

of backflow. These i l l u s t r a t e t h a t t h e backflow sp reads much more r a p i d l y

i n t h e z - d i r e c t i o n than i n t h e y -d i r ec t i on . Fig. 9 is i n t h e forward

flow. Note t h a t it i s p l o t t e d t o a d i f f e r e n t l i n e a r s c a l e t h a n t h e t h r e e

p reced ing f i g u r e s . F ig s . 1 0 through 1 3 show t h r e e dimensional s u r f a c e

p r o j e c t i o n s of t h e same d a t a viewed from a p o i n t on a l i n e p a r a l l e l t o

t h e x-axis , w i th t h e l i n e of s i g h t depressed 15' towards t h e yz p l ane and

a t an a n g l e of 45' t o bo th t h e x and y d i r e c t i o n s .

I n o r d e r t o c r e a t e F ig s . 6 through 1 3 m a t r i c e s were formed t o

ho ld d a t a from t r a v e r s e s t aken a t i n t e r v a l s of z . S ince t h e z i n t e r v a l s

were less i n some f low r eg ions t han o t h e r s , i n t e r m e d i a t e p r o f i l e s were

c r e a t e d by l i n e a r i n t e r p o l a t i o n where d a t a d i d n o t e x i s t . Then, t o

c o r r e c t f o r t h a t f a c t t h a t u n i t s and i n t e r v a l s of measurements were

d i f f e r e n t i n t h e y and z d i r e c t i o n s , a new m a t r i x was c r e a t e d u s ing a f o u r

p o i n t i n t e r p o l a t i o n scheme. This l a t te r ma t r i x i s t h a t upon which t h e

p l o t s a r e based. The e lements of t h e ma t r i x are t h u s n o t n e c e s s a r i l y

p h y s i c a l d a t a , b u t a r t i f i c i a l d a t a c r e a t e d by i n t e r p o l a t i o n .

(interva

r I-'.

R 0 z V1

9 . P 0 0 I-'.

.c" G- l-t 3 n,

'3 PI D 7; M P

2 s X (I

P\) Cn

!- 7 y (interval 0.01 in.)

-r- y (interval 0.01 in.)

Fig. 9. Contours of equal v e l o c i t y i n forward flow a t x = 26.2 cm.

k! rt 1 I-'. n 'd 1 0 LI. (D n rt I-'. 0 3

9 P 0 n P. rt I-'. (D M

4. DATA ANALYSIS

I n o rde r t o develop assumptions as t o t h e cha rac te r of s i m i l a r i t y

p r o f i l e s i n t h e flow, which could b e used as t h e b a s i s f o r development of

a so lu t ion , t h e forward and backward flow p r o f i l e s were examined f o r

s i m i l a r i t y .

Figure 14 shows t h e p r o f i l e s measured i n t h e forward flow

compared wi th a normal d i s t r i b u t i o n . Clear ly they a r e e s s e n t i a l l y

Gaussian i n charac ter . Figure 15, on t h e o t h e r hand,shows t h e v e l o c i t y

p r o f i l e s i n t h e plane of t h e nozzle i n t h e back flow. Since t h e r e is

r e v e r s a l of flow a t t h e edge of t h e j e t , t h e j e t width f o r zero v e l o c i t y

may be c l e a r l y defined. However, s i n c e i n most circumstances such a

d i s t i n c t p r o f i l e edge does not e x i s t , i t has become customary t o work wi th

t h e half-width of t h e veloc2ty p ro f i l e , i . e . t h e width of t he p r o f i l e

when t h e v e l o c i t y is equal t o ha l f t h e maximum value . I n t h i s case

b = half-width i n t h e xy plane and bZ = half-width i n t h e xz plane. Y

Because t h e r e is a d i s t i n c t edge t o t h e j e t a Gaussian p r o f i l e would

not be appropr ia te . F igure 15 has p l o t t e d on i t a cubic curve and

an e l l i p s e a s poss ib l e simple funct2ons. The e l l i p s e f i t s t h e d a t a we l l

i n t h e reg ion of higher v e l o c i t i e s and l e s s we l l i n the region where

v e l o c i t i e s a r e l e s s r e l i a b l e . It i s of course poss ib l e t o a l t e r t h e absc i s sa

s c a l e t o make t h e dimensionless base width of t h e p r o f i l e equal t o one,

i n which case t h e semi-e l l ipse becomes a semi-circle. The equat ion f o r

t h e e l l i p s e i s

The cubic equat ion is given by

'a r-( 0 Ill P. I-' ID m

'a I-' !3 3 (D

3 0 N N I-' (D m

Figure 16 shows t h e corresponding p l o t f o r t h e v e r t i c a l d i s t r i b u t i o n of

v e l o c i t i e s i n t h e back flow. I n t h i s case t h e d a t a is w e l l f i t by a

simple cos ine funct ion

2 8 Az u/um = cos (- -)

Since t h e r e is no c l e a r r e v e r s a l of d i r e c t i o n a t t h e upper and lower edges

of t h i s p r o f i l e i t may a l s o be q u i t e w e l l f i t by the Gaussian d i s t r i b u t i o n

u/u, = exp [-2.77 ( ~ z l b ~ ) ' ]

Thus, t h e p r o f i l e i n t h e reverse flow may be represented by a combination

of Eq. 3 o r 4 w i th Eq. 5 o r 6.

Figure 17 shows t h e measured va lues of b and bZ i n t h e r eve r se Y

flow, and t h e observed va lues of a i n t h e forward flow.

The s t agna t ion poin t obtained by l i n e a r i n t e r p o l a t i o n from t h e

p r o f i l e s shown on Fig. 3, i s indica ted on Fig. 17 f o r re ference . The

da ta suggests t h a t , a f t e r some i n i t i a l d i s t ance back from t h e s t agna t ion

poin t , t h e r e i s n e g l i g i b l e spreading i n t h e plane of t h e nozzles and

approximately l i n e a r spreading normal t o t h i s plane.

b bZ, a o r a Y' Y z

5. CONCLUSIONS AND RECOMMENDATIONS

5.1. Conclusions

I n t e r s e c t i n g flow may no t n e c e s s a r i l y be combined us ing vec to r add i t i on

of v e l o c i t i e s o r momentum f l u x d e n s i t i e s . When two perpendicular i n t e r s e c t i n g

axisymmetric submerged tu rbu len t j e t flows of approximately equal s t r e n g t h

combine, a reg ion of backflow i s observed. The backflow spreads much more r a -

p i d l y i n t h e d i r e c t i o n perpendicular t o t h e p l ane o f t h e nozz les than i t does

i n t h e p lane of t h e nozz les . In t h e reg ion of forward flow t h e p r o f i l e s were

e s s e n t i a l l y Gaussian. In t h e reg ion of backflow t h e p r o f i l e s were approximately

e l l i p t i c o r cubic i n t h e p lane of t h e nozz le , and approximately Gaussian o r

c o s i n a l normal t o t h i s p lane . A f t e r some i n i t i a l d i s t a n c e back from t h e s t a g -

n a t i o n p o i n t observed i n t h e flow, spreading i n t h e backflow i n t h e p lane of t h e

nozz les appeared t o be n e g l i g i b l e and approximately l i n e a r normal t o t h i s p lane .

Attempts t o develop an a n a l y t i c s o l u t i o n f o r t h e flow f i e l d have so f a r proved

unsuccessfu l . The s i m i l a r i t y p r o f i l e s may, however, provide t h e b a s i s f o r

u s e f u l assumptions i n developing such a s o l u t i o n . Because o f t h e l i m i t e d amount

of d a t a which could be c o l l e c t e d i n t h i s i n v e s t i g a t i o n , it would be unwise t o

at tempt t o draw any genera l conclusions about t h e magnitudes of empir ica l

c o e f f i c i e n t s used t o f i t mathematical formulat ions t o t h e observed d a t a .

5 .2 . Recommendations on Future Appl ica t ions

The work descr ibed i n t h i s r e p o r t r ep re sen t s an i n i t i a l i n v e s t i g a t i o n

of a phenomenon t h a t , when more f u l l y understood, can lead t o an improvement

i n t h e q u a l i t y of p r e d i c t i v e computational models f o r t h e flow f i e l d s involv ing

zones of chemical, sedimentary o r thermal ly a l t e r e d d ischarges i n t o moving

c u r r e n t s . Present methods a r e gene ra l ly based on t h e no t ion t h a t an accu ra t e

gene ra l d e s c r i p t i o n of t h e flow f i e l d may r e s u l t from v e c t o r combinations of

v e l o c i t i e s o r momentum f luxes on an elementary l e v e l . Such models then have t o

be modified t o t a k e i n t o account wake e f f e c t s by t h e in t roduc t ion of drag coef-

f i c i e n t s . Extension of t h e p re sen t work which might l ead t o improved modeling

of t h e elementary process used t o syn thes i ze t h e o v e r a l l f low p a t t e r n would inc lude

numerical a n a l y t i c i n v e s t i g a t i o n of t h e p re s su re f i e l d t h a t develops when a s imple

j e t i s d i r e c t e d a t an angle toward a f l a t su r f ace , and t h e ex tens ion of t h i s

i n v e s t i g a t i o n t o t h e p re s su re f i e l d wi th in t h e flow c rea t ed by two merging s t reams.

F i n a l l y , a t h e o r e t i c a l b a s i s should be sought t o j u s t i f y t h e combination of small

elements of l a r g e flow f i e l d s , t a k i n g i n t o account backflows (which may be over-

r idden by t h e forward flow i n a proximate element). This would provide t h e

p o s s i b i l i t y of p r e d i c t i n g a flow p a t t e r n involving backflows i n some reg ions

without t h e n e c e s s i t y of in t roducing a r t i f i c i a l concepts such as drag c o e f f i c i e n t s

accounting f o r t h e blockage e f f e c t of t h e i n j e c t e d flow.

LIST OF REFERENCES

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