Some characteristics of flow around a 90° open channel bend

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OF FLOW AROUND A 90° OPEN CHANNEL BEND

by B. s. THANDVESWARA

Research Scholar, Civil and Hydraulic Engineering Department, lndian Institute of Science, Bangalore-12 (India)

and K. SEETHARAMIAH

Professor, Civil and Hydraulic Engineering Department, lndian Institute of Science, Bangalore-12 (India)

Introduction

A knowledge of the flow characteristics in bends is necessary for designing the bend in open channels and is useful for the economical design of canals. Some of the important characteristics like energy loss, velocity distribution, superelevation have bcen studied in detail by Raju [1], Mockmore [2], Shukry [3] and many others [4, 5, 6 and 7]. But to the knowledge of the authors no lite- rature is available regarding the studies on separation characteristics, except the work of Shukry [3]. Shukry [3, 8]

has correlated the position of separation point with Rey- nolds N umbcr for bends of different central angle (8) and radius (r,). Occurrence of hydraulic jump was observed by Mostafa and Tinney [9] and Marris [10]. In the pre- sent investigation length of separation, coefficient of contraction, pressure distribution etc. were studied for subcritical flow for various Reynolds Number, Froude Number and Manning's roughness (n).

Experimental arrangements and experiments

The experiments were done in an one foot wide rectangular flume. The test section consisted of a 90" cir- cular bend with rjb ratio of 0.5 (b is the width of the flume). Good length of straight portion was provided be-

fore and after the bemi. Water entered the flume from a head box containing the stabilizing arrangements.

The water surface profile in the flume was measured using standard point gauges. The velocity distribution was measured by means of pitot tube with inclined mano- meter. The discharge was measured using a V-notch.

Length of separation, width of separation, etc., were measured using a scale in combination with dye, pieces of paper or 110ating material. The direction of flow was found using tufts.

Selected sand was used for varying the roughness, while fixing the sand, care was taken to avoid the formation of lumps or voids and it was distributed uniformly for the bcd and sides.

Experiments were conducted with different roughnesses and Froude number and Reynolds number was varied for cach experiments.

Results and discussion

Eddy delails.

The zone of separation al ways constitute a part of the source of the loss of energy. The fluctuations in the separation zone quantitatively increased as the Reynolds number increased for a given Froude number. However for the sa me discharge thc JIuctuations decrcased as the Fraude number dccreascd. Length of separation (L), the 43

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appeared at 90° section from the entrance. Figure 3 shows the details of separation zone in plan for various Reynolds numbers for different roughness.

.....0 ...J

1·0 ₁

1

0·50'15 0-20 0'25 0-40

Coefficient of contraction (Ccl.

11

Correlation of parameter Lib with Fraude num-

ber. Coefficient of contraction is defined as the ratio of the

width of main f10w at the maximum width of separation(a) to the width of the f1ume (b).

maximum width of zone (b'max) and coefficient of contraction (Cc) are discussed in the following paragraphs.

Length of separation is the distance from the point of separation to the point of reattachment. Graves and Renov [11] theoretically predicted by the method of hodograph that for a sharp bend with a sharp corner the maximum width of separation occurs at infinity and the length of separation would also be infinity. But the viscous force of real f1uids causes the reattachment and the length of separation reaches a finite value and the maximum width of separation occurs within a short reach. Nondimen- sional parameter Lib was correlated with Froude number.

Figure 1 shows that Lib decreases as the Froude number increases for ail roughnesses used in this investigation.

When the Froude number was increased keeping the discharge constant, the length of separation was found to be decreasing and slight increase in maximum width of separation was observed.

When the nondimensional length of separation was cor-

b - b'mllx

=

^{1 _} ^b'mux

b b

Graves and Renov [Il] found that the coefficient of contraction was equal to 0.674 for incompressible f10w f1uids (experiments conducted in wind tunnel).

Figures 4 and 5 represent the correlation of coefficient of contraction with Reynolds number and Froude number respectively. Coefficient of contraction is practically constant for the range of parameters considered for ail roughness. The mean value is 0.667.

Hydraulic jump and cross wave patern.

In bends when f10w separates in the downstream portion, it reaches supercritical f10w when the Froude number covered in the upstream is greater than 0.32. Then the

2'5~

..,

2.0 :; 1.5

1.0

3.0r--~,---'---'---"'---' n=0.01537

2.51--+---+---+---++~-

~

^2.0 ^... ^{- - - - -}

1.5 ~---=:3=-~:::±'A~=~+~"'~========~+"':===J=~ --~---__l

REYNOLDS NUMBER

5YM BOL: + li. fl 0 e v ~

F: 0.23 TO 0·295 0·275 TO 0.295 0·235 TO 0.25 0.31 TO c>37 0.24 TO 0.25 0;}.7 TO c>31 0-28 TO 0·30

21

Correlation of parameter Lib with Reynolds number.

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Q:::Q'18ct".

Rt=40310 RE:=S3840 F =0·2275 F =0-3395 OPr::20·S· Op=. 19"0"

0'1=4'0" CA'= B·d' C c =O'667 C c =Q'5411 b_max:=.4# b'max=.5'S/t

n=0'014S0

Q::::zO'7Scfs. R(=155445 OP=16'299'(414cm), F=0·3S33 OQ=6"J Cc=O·667.bmax=4"

n'0'0IS37

0=0·187 CFS Re~170574 Re=101000 F ~0·2157 F ~0.3073 OP: 14.89" OP':14·92"

Oq = 6" Oq'= 6"

WAVY SURFACE P

o _

~ ~-:.-~~

b.SECTION

b =^WIOTH ^OF ^THE ^FLUME

qQ=~max

=

^MAX· ^WIOTH ^OF ^EDDY

Op=L =LENGTH OF EDDY

oq =h=DI5TANCE AT WHICH M~~'c~~lH

C"=:OEFFICIENT OF CONTRACTION=a/b

Q=O·905cf5. F=û·3825 Re=180840 OPQI2.·S"(31·B cm.)

C_c::Q'667 Oq:::7" bmax=4'

n= 0·01450

Cc:: 0·5834

b_MAX::s"

Cc =0.6458

~MAX=4.25"

DEFINITION SKETCH

3/

Eddy details for different Reynolds number and Il.

n :.0·009634

~ $$ $

~IX '*'0

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.-

^~$0

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-

^A tf

•

^3)...^li'GA^_^..^,^_-_.--

• •

^• ^A ^.<LI

$ $ ^~

- ' " ^.... ... ---"'--~--".._-_._--

n

œ0'01450

<> 0·01537 âO'OO9834

1

0·9

0·7

0·5

0·3

50CXX> 100000 150000

4/

Variation of coefficient of contraction with Reynolds number.

<QQ ^$11)$

._,1./ •.dl.. 11) ~_ A

" ...

^~ ^'~ ''''- -o::r

"l!I"

'" _fil _•_fIl'

11)

.,

G) 0·01450

X 00·01537

_._-- A 0·009834_

0·8

0·6

0·4

0,2

010 0'15 0-20 0·25 0-30

F

0-35 0-40 0'45 0·50

5/

Variation of coefficient of contraction with Froude number.

45

(4)

6/

Hydraulic jump and crosswave pattern:

Q

=

^{0.18 cfs}

Re

=

⁵³⁸⁴⁰

F

=

^0.3395

Il

=

^0.01450

1. Length of separation increases with the increase in Reynolds number and decreases with the increase in Froude number for ail roughness.

4

Conclusions

~

ci . "'"

^----«-<

!?

( ⁰ ⁷ ^A

f

1

\

1 1

1 Q= \.IB7CF S

1 F=0'2457; R(l=17957

1 - - - - AT SURFACE

1 - - A T BED

1

1 CA, 7, 0, 15, 20, ETC.

1 STATIONS)

1

^\5

1

1 1

1 1 1

1 20

71

Streamlines.

6

Statie pressure distribution.

hydraulic jump occurs in the immediate downstream of the exit of the bend.

The separation zone causes the flow ta contract first upto throat (i.e. point of maximum width of eddy) and then ta expand within a short distance, causing the flow ta change from supercritical ta subcritical flow creating a favourabJe condition for the occurrence of hydraulic jump.

As the surface roughness increases jump will disappear.

The presence of jump caused the free surface to be fluc- tllating and a longer Jength would be needed for the flow ta revert to the uniform flow conditions. The occurrence of hydraulic jllmp has been citcd as an example of vortex hreakdown [10, 12]. Thus the flow in a 90" bend with relb

=

0.5 can aJso be cited as an example for vortex hreakdown.

Even though the flow was subcritical, the fluid particles reflected from the boundary form cross waves. The ins- tantaneOllS photo (Fig. 6) shows this pattern clearly.

Stream lin es.

Streamlines were traced along the water surface and bed.

The effect of secondary current can be seen in Figure 7.

Streamlines are three dimensional in nature. Figure 8 indicates the effect of centrifugaI force on the free surface.

The static pressure in the test section (bend) was measured at different depths and different points, along the radial planes. The static pressure recorded was found ta he 3% to 6% less than the hydrostatic pressure distribution neal' the bed. Thus it can be concluded that the presence of a bend in horizontal plane has the effect of convex bend in a vertical plane regarding pressure distribution.

,16

(5)

8/

Flow pattern:

Q

=

^{0.1390 cfs}

11

=

^0.01450

F

=

0.2382 Re

=

¹⁹³²⁰⁰

ur

Oy

,Iel 'l.R

n:

"O '. L:

Co:

F:

2. The coefficient of contraction is practically constant for Froude nUn1ber and Reynolds number for different roughness.

3. Hydraulic jump occurs in the downstream of the bend when the Froude number covered in the upstream of the bend is greater th an 0.32.

4. Flow in a 90° bend can be cited as an example of vortex breakdown.

5. Static pressure distribution is 3% to 6% less than hydrostatic pressure distribution, near the bed.

List of symbols

a: width of flow in contracted area;

b: width of flume;

maximum width of eddy zone;

coefficient of contraction = alb;

Froude number V

Iv

^gy;

acceleration due to gravity;

length of separation;

Manning's roughness "n";

Re: Reynolds number 4 VR/v;

1'0: radius of curvature of bene! along the centre line;

V: mean velocity of approach now;

y: depth of flow;

v: kinematic viscosity;

e:

central angle of the bend.

References

[1] RAJU (S.P.). - "Versuche uber den stromungs widerstand gekrimmten off-en-er kanalc", Mittelungen des Hydraulischen Institutes der Technischen Hochschule, Munchen, N° 6.

pp. 45-60, Munchen 1933. English translation by c.E.

Bradsley, Proc. A.S.C.E., vol. 63, pt. 2, p. ] 834, pp. 49, nov. ]937.

[2] MOCKMORE (C.E.). - "Flow around bends in stable channels", TI'. A.S.C.E., vol. ]09, pp. 593-618, 1944.

[3] SHUKRY (Ahmed). - "Flow around bends in an open flume", TI'. A.S.C.E., vol. ]15, pp. 751-779, ]959.

[4] IpPEN (A.T.) and DRINKER (P.A.). - "Boundary shear stresses in curved trapezoidal channels », Proc. A.S.C.E., JI. Hyd.

Dn. RY5, pt. I, vol 88, p. 3273, pp. 143-79, sept. 1962.

[5] THANDAVESWARA (B.S.). - "Characteristics of flow around a 90" open channel bend", A thesis submitted for the degree of Master of Science, Indian Institute of Science, Bangalore, India.

[6] MURAMOTO (Y.). - "Flow through curved open channeJs (pt I)", Bul. Disaster Prevention, Res. Inst. Annals, n" 8,1965.

[7] ROZOUSKII (l.L.). - "Flow of water in bends of open channels". Clearing house for Federal Scientific and Tech.

information, U.S.D.C. 5285, U.S.A. TT. 60-51133.

[8] CI-IOW VEN TE. - "Open Channel Hydraulics". McGrmv Hill Book Co. Inc, N.Y.

[9] MOSTAFA (M.), SOLIMAN and Roy TINNEY (E.). - "Flow around 180" bends in open rectangular channels". Proc.

A.S.C.E., Hy4, pp. 893-907, July 1968.

[10] MARRIS (A.W.). - "Free surface flow in a curved channel as an example of vortex breakdown". Symposium on fully separated flows, A.S.M.E. Fluids Eng. Philadelphia, pp. 53, May 18-20, 1964.

[Il] GRAVES (K.W.) and THEODOR RENOV. - "Separation of channel flow induced by a right angle bend". Ibid, pp. 10, 1964.

[12] BENJIMAN (TR). - "Theory of the vortex breakdown pheno- menon", JI. of Fluid Mech., vol. 14, pt. 4, pp. 593-629, 1962.

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48

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