WRC RESEARCH RJ3PORT No. 155 MEASUREMENTS IN MERGING FLOW by W. Hall C. Maxwell and Arni Snorrason Department of Civil Engineering University of Illinois at Urbana-Champaign Urbana, Illinois 61801 FINAL REPORT P r o j e c t No. A-103-ILL This project was partially supported by the U. S. Department of the Interior in accordance with Title I of the Water Research and Development Act of 1978, i P.L. 95-467, Agreement No. 14-34-0001-0115. UlJIVER3ITY OF ILLINOIS WATER RESOURCES CENTER 2535 Hydrosystems Laboratory Urbana, Illinois 61801 January 1981 Contents of this publication do not necessarily' reflect the views and policies of the Office of Water Research and Technology, U.S. Department o f the Interior, nor does rnentlon of trade names or conmerclal products constitute their endorsement or reconmendation for use by the U.S. Government.
Transcript
WRC RESEARCH RJ3PORT No. 155
MEASUREMENTS I N MERGING FLOW
by
W. Ha l l C. Maxwell
and
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
THE REFERENCE ANGLE I S 180' , C 1 OUTLET CENTERS AT X - 23.68 CM, Z = 1.564 FT
;I , r i 7-
I j I
/ I T
/ f-:
i ;r . 5 -!- i
> -? > , 1
i I I i A ---6 VELOCITY
4 f
L' .+ -{ ',
-. 2
I i
.1 PITCH ANGLE, B a 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 .
~ i i
(interva
I l l
r I-'.
OP Y
n 0
R 0 z V1
0 M
n, 9
E . P
9 . P 0 0 I-'.
.c" G- l-t 3 n,
'3 PI D 7; M P
2 s X (I
P\) Cn
Cn
p
!- 7 y (interval 0.01 in.)
-r- y (interval 0.01 in.)
'- N
Fig. 9. Contours of equal v e l o c i t y i n forward flow a t x = 26.2 cm.
H M 0
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 (- -)
3 b Z
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
44
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.
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