1589

ASCE National Water Resources Engineering Meeting

January 24-28, 1972 • Atlanta, Georgia $0.50

HYDRAULICS BRANCH OFFICIAL FILE COPY

INFLUENCE OF

DRAFT TUBE SHAPE ON SURGING

CHARACTERISTICS

Uldis J. Palde, A. M. ASCE

BUREAU OF RECLAMATION HYDRAULIC LABORATORY

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WHEN BORROWED RETURN PROMPTLY

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R205563 72A DRAFT TUBE SHAPE INFLUENCES SURGING CHARACTERISTI CS Draft tube surges were noted in hydroelectric plants befo re th e sur ging was found to be caused by a flow phenomenon known as vortex breakdown. During 1940 , Rheingans s ummarized experiences and presented an eq uation for estimating th e expected . frequency of s urging. Invest i ga t or s now accept the fact t hat the dra ft t ube surge is a hvdrody nam ic 1..1stability occurring in the draft t ube as a result cf rct~ti cn r c~nining in t he fluid as i t leaves the turbine runner and ent ers the draf t tube throat. Experimental analysis and laborator y procedures are discussed. Dr af t tube shapes were studied and surge data obtained fo r over 50 distinc t · draft tube shapes. Conclusions are: (1) degr ee of dive r ge nce of a draft tub e is the mos t significant geomet ric feature affec t ing surging characteris tics; (2) surging can be minimized by using an equivalent expansion angle of about 15 deg through the entire length of t he draft tube; and ( 3) resonance with known natural frequencies of other feature s of the powerplant can be checked using results pres ented, Resonance can be avoided by se l ect ing proper geometric components in draft tube design .

Pa1de, U J R205563 72A

INFLUENCE OF DRAFT TUBE SHAPE ON SURGING CHARACTERI STICS

Prepr, ASCE Nat l Wa t er Resour Eng Mee t, Atlanta, Ga, Jan 1972. 25 p , 14 fig, 13 ref, 2 append

Bureau of Reclamation , Denver, Colo

DE.SCRIP'IDRS-~ *draft tubes/ *surges/ *geometry/ *shape/ hyd raulic turbines/ fri ction coefficient (hydraulic)/ experimental da t a/ analysis hydraulic structures/ model tests / resonance/ na tural fr eq uency/ fl~id mechanics/ hydraulic design/ vibr ation/ characteristics/ properties/ hydrodynamics/ fluid flow/ pulsating flow/ laboratory tests/ vortices IDENTIFIERS--

U.S. DEPARTMENT OF THE INTERIOR• BUREAU OF RECtAMATION • CURRENT AWARENESS PROGRAM• SELECTIVE DISSEMINATION OF INFORMATION

Document Requested _______ . Retain this card for your files.

INFLUENCE OF DRAFT TUBE SHAPE ON SURGING CHARACTERISTICS

By Uldis J. Palde, !/ A.M. ASCE

INTRODUCTION

Draft tube surges were noted in hydroelectric plants long before it was

determined that the surging could be attributed to the flow phenomenon

known as ''vortex breakdown." Rheingans (12) ~/ related and summarized the

experiences gained in several installations as early as 1940. He pre-

sented a plot of observed frequency versus turbine rotational speed and pro-

posed the equation f. n/60

3.6

for the expected frequency (hz) of the surge at the maximum pressure fluc­

tuation, where n is the rotational speed in revolutions per minute. The

Rheingans equation is frequently applied to obtain an estimate of expected

frequency of surging.

Although it can now be shown that surging flow will occur in every

reaction turbine installation over some range of partial load or overload

operation, this was not necessarily assumed at one time by designers.

Rather, the problem was hopefully expected not to occur in common operating

ranges, and as a result, little analytical or experimental model work was

reported in the literature.

In installations where the draft tube surging produced power swings

or penstock vibrations due to resonance, or simply objectionable vibration

and noise, remedial measures were taken in the field. These measures often

included the installation of vertical vanes in the draft tube throat. The

admission of air below the runner was also discovered to reduce the ampli­

tude of the surging. Both methods (particularly the vanes) can result in

reduced efficiencies.

1/ Hydraulic Engineer, Division of General Research, Bureau of Reclamation, Denver, Colorado. 2/Numerals in parentheses refer to corresponding items in Appendix I. -References.

1

Recently the vortex break.down phenomenon has attracted considerable

attention in the published work of Benjamin (1), Chenaud (4,5), Squire (13),

Harvey (10), and Gore and Rantz (9). Studies of vortex breakdown as related

specifically to draft tube surges have been reported by Deriaz (6), Dziallas

(7), and Hosoi (11). Investigators now generally accept that the draft tube

surge is a hydrodynamic instability which occurs in the draft tube as the

result of rotation remaining in the fluid as it leaves the turbine runner

and enters the draft tube throat.

The experimental work presented in this paper is a continuation and

expansion of the studies reported by Cassidy and Falvey (3,7). Analytical

studies, experimental equipment and technique development, and application

to prototype turbines were described in detail in a Bureau of Reclamation

report by Cassidy (2).

ANALYSIS

Dimensionless parameters were derived by Falvey and Cassidy (7) to help

generalize experimental results of surging flow in a draft tube. It was

assumed that for a particular draft tube· shape the frequency f and root-mean-,--

square (RMS) amplitude~~ of the surge are both functions of the den-

sity p and the viscosity v of the fluid, the diameter D and length L of the

draft tube, the discharge Q, and the flux of the moment of momentum (angular

momentum) o. Dimensional analysis yielded the following functional

relationships:

pressure parameter

and

frequency parameter s

f'D Q

where I is the Reynolds number

• ~2 (..@.. ' pQ,2

4Q/wDv.

L, R) ii

0D/pQ2 is referred to as the momentum parameter and is a ratio of angular

momentum flux to linear momentum flux. In applying it to the experimental

study, the assumption was made that regardless of the manner in which angular 2

momentum is introduced into the flow, the resulting surging characteristics

will be the same for a particular value of nD/pQ2• The frequency parameter

is a form of the Strauhal number fD/v (vis the axial velocity), written in

terms of discharge.

Based on his initial experimentation with a simplified model using air

as the fluid, Cassidy (2) concluded that

1. For a given draft tube shape there is a critical value of

nn/pQ2 above which surging flow exists.

2. The frequency and pressure parameters can be correlated with the

momentum parameter for a given draft tube shape.

3. Frequency and RMS pressure values of the surging flow are inde­

pendent of viscous effects for Reynolds numbers above approximately

80,000. (Prototype Reynolds numbers greatly exceed 80,000).

The momentum parameter nD/pQ2 can be computed for a turbine if the run­

ner diameter, wicket gate geometry, and the performance characteristics are

known. If we start with the basic expression for power,

p • wT (1)

where w is the angular velocity and Tis torque, and substitute

T • n1 - n2 (2)

where n1 - n2 is the rate of change of moment of momentum of the flow as it

passes through the runner, we obtain

! • n1 - n2 (II

Multiplying Equation (3) by D/pQ2 and rearranging terms,

PD pwQ2

(3)

(4)

The left side of Equation (4) is the momentum parameter associated with the

flow at the draft tube throat. The first term on the right of the same

equation is the momentum parameter of the flow leaving the wicket gates and

entering the turbine runner and can be computed by

3

'21D,. DR sinCI

pQ2 BNS (5)

Equation (5) shows that n1D/pQ2 is entirely a function of wicket gate geomet­

ric variables (defined in Fig. 1), and the draft tube throat diameter.

8 = depth of gate= t.65"

N = no. of gates= 24

I

\ \ Fig. 1. - Definition sketch of flov leaving wicket gates.

The second term of Equation (4) can be computed from performance character­

istics of the turbine. Combining Equations (4) and (5), we obtain

DR siM BNS

(6)

which can be evaluated for prototype or model turbines from data normally

obtained during performance tests.

LABORATORY MODEL

Laboratory experiments were conducted with air as the fluid and a model

(Fig. 2) consisting of some of the components of an actual model turbine. 4

Fig. 2. - Laboratory air model and instruments

The spiral case, stay vanes, and runner were removed. The wicket gates

remained and served to produce swirl in the flow as it passed from a symmet­

rical pressure chamber into the draft tube (Fig. 3). Radial inclination of

the gates could be set at any angle between 0° (radial) and 82° (closed).

SECTIONAL PLAN SECTION THROUGH

WICKET GATES

Fig. 3. - Schematic of laboratory air model.

The momentum parameter of the flow leaving the wicket gates and enter­

ing the draft tube could be computed by the same expression (Equation 5) used

to compute the momentum parameter of the flow entering the runner in a com­

plete turbine. In the simplified model the moment of momentum remains con­

stant and therefore also the momentum parameter at the draft tube throat

does not change from that existing at the wicket gate openings.

The computation of the pressure and frequency parameters required the

measurement of discharge and the frequency and RMS pressure of the draft tube

surges. The rate of discharge was controlled at the wicket gate openings

and varied as the gate opening area varied with changes in .the gate setting.

The discharge was measured by a differential orifice located in the inlet

pipe to the pressure box. Pressure differential across the orifice was t.i

measured with a pressure cell and conditioned by and recorded on one chan­

nel of a dual-channel recorder-amplifier. The various plastic draft tubes

had piezometer taps at several locations along the walls to which a pressure

cell with a short piece of flexible tubing could be attached for dynamic

pressure pickup. The signal was conditioned by the second channel of the

recorder-amplifier and fed through a band-pass filter to an oscilloscope and

RMS meter. Frequencies of the unsteady pressure were determined on the

retentive screen of the oscilloscope. The instrumentation is shown in

Fig. 2.

LABORATORY PROCEDURE

The values of R, S, and a defined in Figure 1 vary with the gate orien­

tation. The quantities were carefully measured or graphically determined

for numerous gate angle settings, and tables for use in computations were

prepared from the smoothed curves of R, S, and a versus gate angle. The

value of the momentum parameter for a particular gate setting could then be

readily computed using Equation (5).

For a particular draft tube, the range of gate settings for which surg­

ing flow could be detected was first noted, as well as the approximate maxi­

mum and minimum frequencies. If the frequency range was not too great, the

high- and low-pass circuits on the band-pass filter were set somewhat out­

side this range. Occasionally the frequencies varied greatly and the band­

pass was set to include most of the frequencies encountered and then later

adjusted as required.

For a particular gate setting, a given draft tube surges at the same

frequency throughout the entire tube (with a few notable exceptions). The

amplitude, however, varies at different locations along the tube wall.

Data were generally taken at a location where amplitude was maximum, since

the frequency was best defined at that location.

During one complete run the gate setting was repeatedly changed by

small increments. Values of the discharge and RMS pressure signals were

7

recorded and the frequency read from the oscilloscope for each gate setting.

The data, along with amplifier attenuation factors, air density, and descrip­

tive information were recorded on data sheets suitable for ADP card keypunch

use. The dimensionless parameters and other flow variables were computed by

computer. Frequency and pressure parameter versus momentum parameter curves

were plotted on an on-line cathode-ray tube and photographed on 35-mm micro­

film for later copying and convenient storage •. The graphs used in Fig, 4

through 13 are computer generated.

DRAFT TUBE SHAPES STUDIED

Surge data were obtained for over 50 dis~inct draft tube shapes. A few

were actual models of draft tubes with minor modifications. The greater

majority, however, were simple geometrical shapes or combinations thereof

consisting of straight circular cylinders, truncated diverging cones, and

circular cross-section elbows. These shapes are representative of the shape

components found in most draft tubes. The diameter, length, and angle of

divergence were varied.

A minor limitation on the draft tube shapes studied was imposed by the

model itself. The downstream face of the pressure chamber had a thickness

of 1.93 inches (see Fig. 3) in which a circular opening of 6.13 inches in

diameter was provided for the outflow. A short, circular cylinder thus

existed as a geometrical component upstream of any shapes tested (which were

attached by means of a flange to the outer face of the pressure box). To

eliminate the cylindrical section, a machined plastic insert of the required

inside dimensions had to be positioned in the opening. In many instances,

however, the 1.93-inch length of constant diameter opening was included as

the upstream component of the total draft tube shape.

RESULTS

Some of the more significant results are included as plots of the

dimensionless parameters in Fig. 4 through 13. In most cases the surging

characteristics of several shapes are compared in the same figure. The 8

presence of an asterisk(*) in the legend below the graphs indicates that

the described shape was downstream of a short, circular cylinder either

6.13 inches (see Fig. 4, Run 62) or 3.50 inches in diameter (see Fig. 8).

Fig. 4 shows the surging characteristics of three draft tubes. The

throats of both variations of the Fontenelle draft tube were modified from

the actual prototype geometry, The Grand Coulee pump-turbine draft tube is

geometrically similar to the prototype. Its cross-section is circular for

the entire length. For all three draft tubes the frequency and pressure

parameters initially increase with an increase of the momentum parameter.

This was typical of all tubes tesoed. For some tubes the pressure parameter

continues increasing monotonously while for others one or more peaks occur.

Most tubes surge over a finite range of moment parameter, as is the case

with the two variations of the Fontenelle draft tube . Others, like the

Grand Coulee pump-turbine draft tube, surge continuously up to the point of

complete wicket gate closure, where the momentum parameter approaches

infinity. A slight variation of the Fontenelle throat geometry produces

significant changes in the surge parameter values, but does not change the

range of surging. Removal of the piers and progressively sections of the

downstream end of the draft tube has little effect on the surge parameters .

A short tube including only the first 30 degrees of the elbow has only

slightly different characteristics than the entire draft tube (see Fig. 5).

Simple sections of truncated 15 degree-cones surge over a smaller

range of momentum parameter and display lower frequencies and amplitudes

than the draft tubes (see Fig . 6). The frequencies measured from the

cones were far less well defined than those from any other shape. Differ­

ent inlet diameters and L/D ratios have only slight effect on the dimen­

sionless surge parameters. Fig. 6 also verifies the validity of the

dimensional analysis.

Straight cylindrical tubes display surging characteristics quite

different from those of expanding cones (see Fig, 7). Short sections 9

GRAND COULEE P/T DRAFT TUBE

0 Cylindrical Throat

A

ELEVATION

0 Piers

PLAN FONTENELLE TURBINE DRAFT TUBE

a:: w I-w L <(

a:: <(

a.. w a:: ::::, lf) lf)

w a:: a..

a:: w I-w L <(

a:: <(

a.. >-u z w ::::, 0 w a:: u..

2

·:

I

0 s 000

(.,

2

00 1 2

MOMENTUM PARAMETER INLET DIA . LID DRArT TUBE DESCRIPTION POS. RUN

0 , . 24ltl. t 15. ,CHJ °w roNTE~LLE 0. T. 1 1 '2 A 5. 251to. 1: , . ,CHJ , . 25 rotH[N. 0. l , ffVLL LI 0/S or 12. 25 oc,.c. I :,i: ~ 5.25!t,. :!5. ,CHJ 5. 50 , .c. PUMP/Tl/RB. 0. T. !100 OE,. ElBO•l !Sl 145

Fig. 4. - Surging characteristics of three model draft tubes.

10

El

0

V 6 .13"

ELEVATION

Piers

PLAN

a:: w I-w L <(

a:: <(

a.. w a:: ::> l/) l/)

w a:: a..

a:: w 1-w L <(

a:: <(

a.. >­u z w ::> C)

w a:: LL

2

J J ~' r.CJ:l y

,, .

Q" Q i· 0 0 ~ i hf.J !i El El

-r.!~ Ii jW••·

1

MOMENTUM PARAMETER INLET D~ LID DRAFT TUBE DESCRIPTION

0 , 2, :1. : :5. 9(1'\ ; 5. " r o1. ~[t4: .. LE C ~ . • L , . N :t,. : :5. 9CP" ; 5" r Jt.~ [t4: .... ( : • . 1 11: P:£~S GI o u :• . . :5 9C t"" : 2 u r :1.·c14: .... £: · 1 ::0 21 :•, '. 5 9( " : :5 r :1,"['I( .... [: • I

Fig. 5. - Effect of pier elimination and draft tube shortening on surging characteristics of Fontenelle draft tube.

11

2

2

0

0 on -

0 d

a:: w 1-w I: <( a:: <( a..

2

w a:: ::,

01Jb 0 0

Vl Vl w a:: a..

a:: w 1-w I: <( a:: <( a.. >­u z w ::, C, w a:: L,_

&l1

0 A ~A0

0 A !. 0

"'A -

~i""

1

MOMENTUM PARAMETER INLET DIA. LID DRAFT TUBE DESCRIPTION

05.5Alli. llA . ICNl 1.A& 15 . 00E• . CONE !.5.5AI1,.1 1A . 1CN J 2.58 15 .0 OE•. COIIE G 2. 8A II,. : ~. 2CNI 2. 58 15.0 OE•. COIIE D 2. u:• .. : • 2ce : •. 52 15 . : OE,. ccP,E

Fig. 6. - Surging characteristics of 15 degree truncated cones.

12

2

2

PCS. RUN 98 9"

15: 129

A

[J 0 []

D x+

• 1

-~

b lq_ - 3 a::

w 1-w I: < ~ 2 Q_

w a:: ::, U1 U1 1 w a:: Q_

a:: 3 w 1-w I: < a:: cf. 2

>­u z w iS 1 w a:: u..

INLET 0 , . :,:, •. L , . :,:, •. " ,. :,:,, . a,.:,:, .. X , . :1:, .. +' :5:,.

0

0

V

8 8 X X

0 8 ) 8 ~ ~ i~. ~

X ; A 0 r 8 X & A

li A 0 & AA A Ap 1 A y \ ,A

E1' X /" AA+ + 0 ~~& •'* + I++ ·.-.+++

T

t 8 -

+ t 8 tJ 8 A A

A

+ 0 AA A ~

0 '

b~ A" X fPrJ)rJ) i X

A

0 + 0 + X

+ .,,, X

+ * l / I

•• y~

,,t"

1 2 3 4

MOMENTUM PARAMETER,~

DIA . LID DRAf'T TUBE DESCRIPTION !5 . ""' l. !I t40 ORArT Tvl[ lHOOEL. J\.:T;.[T CP<.L.1 1

15 . ""! i. ,. STAIJ/iMT C1L. . T•J9£

!5 . ""' C. 9' S'!R1!""1 c,;. . T•M : • . r : :5 . ,c., : . 9' S'!AAJl,,MT (, .. . T•JI[ :" .r .:

. :5. ,c•: ! .58 S'!Rl!r.,,.T c, .. . ! ·JI[ ... . r .:

. ,5 ,c•: , . 58 STAA!(.HT c, .. . T•JI[ :,,. . r .:

Fig. 7. - Surging characteristics of circular cylinders.

13

~

T

ffi X

A

A

5

"

5

POS.RUN ! l" ::8 ! l9 !!:

19 99 !9 !H

(L/D <1) produce high frequency curves, while longer sections have two dis­

tinct frequencies - the higher being exactly double the lower. In a tube hav­

ing an L/D of 0.96 the lower frequency predominates up to a momentum param­

eter value of about 2.0, while beyond this point only the higher frequency is

apparent (Runs 109 and 110). Several other intermediate lengths between

L/D ~ 0.96 and L/D • 3.58 were tested. The tubes all had surge characteris­

tics similar to the tube with L/D • 3.58. It should be noted that both high

and low frequency parameter curves of all cylinders show considerably higher

values than those of draft tubes with expanding sections.

Adding a short or a long cylinder section upstream of a long cone sig­

nificantly increases the frequency and extends the range of surging (see

Fig. 8). Adding a cylinder to the downstream end of a long cone has no

effect on the frequency, but does decrease the surge amplitude significantly

throughout the whole draft tube (Fig. 8, Run 123).

7.5-degree cones with short cylinder inlets display somewhat varying

surging characteristics with variation of cone L/D (Fig. 9). The longest

tube (L/D • 4.10) displays a surging range and frequency and pressure param­

eter curves quite similar to those of the Fontenelle draft tube. The surging

ranges of the shorter tubes, however, are far greater than the ranges of the

shortened lengths of the Fontenelle draft tube (see Fig, 5, Run 64).

The surge amplitude decreases with respect to distance from the inlet

in an expanding cone, but generally increases in a long cylinder (Fig. 10).

A 100-degree elbow produces lower frequencies than a cylinder of the

same length (Fig. 11)'. The range of surging is also reduced. In pipe

elbows of different lengths the highest pressure fluctuations were measured

near the outlet. The fluctuations were always higher at the inside of the

bend than at the outside, both in pipe elbows and expanding cross-section

elbows of draft tubes.

Substitution of a straight cylinder of equal length for the elbow

in the Grand Coulee pump-turbine draft tube does not alter the surge

14

0 ~ LE__iJ

a:: w 1-w L < a:: < a.. w a:: ::> V) V)

w a:: a..

a:: w 1-w L < a:: < a.. >­u z w ::> 0 w a:: u...

2

G

A A

A

i A

G G G G ~G L:J

Ai

A' ~a

00° -·~

0G l '·

G 0

~ ~ G ~ i!I ~

<l!j)G",1 " -G 111111 G~

G( 00

00G 000 ~0

rfi.~

1

MOMENTUM PARAMETER

A

A A

G G G

2

~

r,

~ l!l l!l

2

INLET DIA. LID DRAFT TUBE DESCRIPTION POS. RUN 0 2. u:, .. " . 2Ct'IJ 2. 58 ,s. o or,. COl,E A s.,c:, .. 8. , CH: 2. ,. IS. C or,. COt.lEt ~ !., c:, .. 8. ""': 2. , . IS. : DE•. COU[ CIS ; r ! . 5: ·12 .5 .. : , ... G s., : :1. 8. "t': 2T 1s : or,. c;11t1 • ,c- !C~ C , ... .

Fig. 8. - Surging characteristics of 15 degree cones in combination with circular cylinders.

15

:s: :22 :2e :25

0 w.11 l:E_jJ

4

D .

"'

'':. - 3 0: w r w l: < ~ 2 0..

w ~ Vl Vl I w &:

0: w r ~ < 0: t 2

>-~ w 5 I w 0: u.

e e •

'iA

~:

1• A

A

A A

0

A 0A

e!A ,I A

• 'i,

.-,'--. A

eel? 'i/Pe A A .A A

.A!AAAAAAA A AA

,,ee . e "..ftll.1111

:1•

I 2 3 4

MOMENTUM PARAMETER,~

INLET DIA. LID DRAF'T TUBE DESCRIPTION POS.RUN 0 , .o,!tt 1~5. !CMI 1.0l ' · 5 OE•. COt,(I la , .0,:1 .. : 1S. ,CI'! ; 2.05 , .s OE•. COt,(I $ ,.c,:, .. :1s . ,ori1 , . 10 ,.s OE•. COf..£1

Fig. 9. - Surging characteristics of 7.5 degree truncated cones with short cylinder inlets.

16

'Z

.,

a: w I-

~ < a: < 0..

w ~ l/) l/) w 8:

O!-O----J'----.1.1----J'-----J.2

MOMENTUM PARAMETER !>I.ET DIA LID DRArT TUBE DESCRIPTION

0 , . 0.4!lj, LIS. SC") ;-;; 15. D oc,. COt,(I ,,. 0,11,. 1!5. SC"l 2. 05 15. oDE,. CHI " ' ' ':1,.: :5. SCMl 2. 0S 15. 00C,. CH• ::J , . :,:1. ::s. sc10 2. os 1s.o ou •. CH• )( ' ~,1:1. : :5. ,CM! 2. 05 15. 0 D[fo. (~I

!'.Qi AVN l ... .,

" 0: 12

,~ . ' Q:

w

i < ~ 2 Q..

w ~ V) V> I

~

',

• i· •:,

" 8 .~ • • • • b • • • '' • e e

l!ee 8

. • • • •

• I I

• 8 • • • • • •

• • . •

•!-, ---.1.,---+.---.l,,---.J.-----!

MOMENTUM PARAMETER.~

!>I.ET CIA. LID DRAFT TUBE DESCRIPTION E) ~ 1 'i:Hs1u1"4T(TL, ll.W: IL. r .1 It. , . m,j, ns. ''"l , . ,. STU.Jli,Ml ( TL, ll.t( IL. r. I t' :,it, :1s. ,cM1 , .st Sl11.I-"' (tL. , ,.. IL. r . 1 0, : s :1, :15 ,c,11 S. 5t S1U.!t;t!T (IL: Tl.fl( IL. f .)

0 A

POS. AUN

"' IO I IA 100 l9 H

Fig. 10. - Variation of surge &11plitude with respect to distance from inlet.

17

00

C

,~ - 3

Cl'.: w 1-w :1::: <C

~ 2 a.. w Cl'.: ::) lfl lfl I w Cl'.: a..

Cl'.: 3 w 1-w :1::: <C Cl'.: ~ 2

>­u z w ~I w Cl'.: u.

0 ~ i< &

/ "o x & t¥+

& i ~ A X A A A [l

t0 [l :~~· C [l

~ - [l

V 0

[l

[l

[l X [l X

[l X

x:+ i +

iii + ~· 0 0 r A

+ 0 A i• AG &

·"'~ &&

&

~·

X

X

X

e 0 0

V

t [l

A [l & [l

2

[l [l [l

X

X X

0 0

0 • A A &

& G

i

(

[

3

[l

'

A

0

0

A

I

3

0 s

A

e

I 2 3 •

MOMENTUM PARAMETER.ft,

INLET DIA . L/0 ORArT TUBE DESCRIPTIOI'-< 0 6. : 5:1, . : :5 . 6CM I 2. 28 STRA!(,HT CIL. TUBE tL . r . : b 6. ! l:1,. : :5 . 6CM : 2 . 28 •5 OEr. . ELB . I 55 OEr. . ELB . •E·, . : • . r " 6. : i:1. _ . :5. &C"' 2 . 28 :oo OEr. . ELBOW I II • . r . I 8 o : ,: ,. :! 5. 6CM : 2. 28 STRAlltHT C,L . TuBE !HJ .)

X • :,:·. :5 ""·

2. 28 •5 :,rr. . ELB . 1 55 OEr. . [LB . RE, ·" r + • :1:·.

:5 ""' 2. 28 :ci :,rr. . [LBOWI '" r :

Fig. 11. - Effect of bends on surging characteristics.

18

3

5

5

;>OS . RUN :1 :,:

.:1: !54 .. . 1'2

1 l2 : 1: : 155 ... :,,

characteristics to a great extent (see Fig. 12). The maximum amplitude is

typically higher in the elbow tube. An interesting phenomenon in the

straight tube is the presence of a second frequency equal to about two­

thirds of the predominant one. The predominant frequency parameter curve

varies only slightly from the frequency parameter curve of the elbow draft

tube. Parameter plots for the 12.25-degree cone, elbow, and straight cyl­

inder have been included in Fig. 12 for comparison. The frequencies of the

individual components are all higher than the two complete draft tubes.

The downstream section of the 7.5-degree cone apparently helps reduce the

frequency and also the amplitudes. The influence of straight cylinder sec­

tions inserted between cone sections can be seen in Fig. 13.

Two lengths of 30-degree expanding cones were also tested. No peri­

odic pressure fluctuations could be detected with the instrument and meas­

uring techniques used in the other tests.

COMPARISON WITH '!URBINE MODEL

A 1:9.S scale model of the Grand Coulee Pumping Plant pump-turbine

units was tested by the manufacturer (NOHAB, Trollhlittan, Sweden). Included

in the contract were requirements for pressure pulsation measurements on the

model. The manufacturer furnished the Bureau of Reclamation complete model

operating data and draft tube pressure pulsation oscillograms and magnetic

recording tapes. From these data it was possible to compute the dimension­

less parameters for comparison with the results of the air model studies of

the Grand Couleepump-turbine draft tube. The frequency parameter compari­

son is quite satisfactory (see Fig. 14). Pressure parameter values were not

comparable because data were not obtained at the same location, and differ­

ent band-pass ranges had to be used in the two studies. The computed

values were of the same order of magnitude, however.

19

~]

,~ 3

0:: w ..... w l: .,:

~ 2 Cl.

w 0:: ::, V1 V1 I w 0:: Cl.

0:: w ..... ~ .,: 0:: .,: Cl.

.>­u z w ?51 w 0:: u..

e e

] Q Q ( Q 6

Q Q Q ~ Q

0

X <XQ - . • X ' X Q 0 I A

] X A A

e'fflt o 0 A A

• 0 t 'le Q ~,.., AACI .. A

jQQ.'

e A A AA A

rri &A

2

I 0

0 Q I

Q Q

Q C

Q X X e

';fl X X X • 6

~1 xX A A l

X A 0 0 A

~ e•TI 0 A A A •

6 AA AA A AA

I 2 3 4

MOMENTUM PARAMETER.ft,

INLET DIA. L/0 ORArT TUBE DESCRIPTION Pos.~·, 0 5 25:1 •. '.!. !CHJ 5. lC • · C. P~/TUR8. 0. T. 11cc OE • . Ec80o: L 5.25:, •. ''· ""' 5.2, • · C. '""""""'· 0. T. !STH l l.ttT C1~ . : ~ 5. 25:, •. : , . ,Cff; e.·a 12. 25 oc,. co~ 0' :, :, .. :5.""' 2.28 STRA?(.t4T C•L . Tt.9[ IL. r .1 X; :,:, .. . :5. ,ctt; 2.2e : Cl OE•. ELIOWt I~ . r. :

Fig. 12. - Comparison of surging. characteristics of tvo draft tubes and their geometric components.

20

IS.. 145 ll "' ! .. 1: t l : ll~ !42

A

EJ X

0:: w 1-­w I: .,:

•

3

~ 2 0..

w 0:: ::, l/1 l/1 w 0:: 0..

0:: w 1-­w I: .,: 0::

I

cf. 2

>­u z w 151 w 0:: Lo..

;J

~ ' .

~ -

• • ~

• • I+ +

• * • X + ~ +

• X X

• ~ A A

• I X • + " ~ja x++.,. +

+ ¥ + + ,Ii~+

5

I

I I

~ A 0

A + 00 A +

A A + + • • •

A A A + ~ +

ii~ t+i+i I 1 I +

I 2 3 A 5

MOMENTUM PARAMETER,f}.

+ INLET DIA. LID DRAFT TUBE DESCRIPTION POS . RUN

~ 0 5 . 25!1, . :5 . !Cl'IJ 0.78 12.25 OE• . CO>.£ I L 5. 25:1 •. '. !.!Ct' : l.o" 12. 21j 0£1i . . • . IL r.of.£ • '°· 12L C1:,. !l G, '5 2i;:1 .. :5 !CM ; 5. C! 12 . 25 OE• .. ,.lL, " . 5 OE• .. 15. 81. C0>.£5 ' 8 s.2s: 1• " lCM:

, ., !2 25 OE• . CO"i • 41L c,1. . , ". 5 0£•. C. ' X 5 25:1 . . :, l C• : ,. ,, 12 . 2'5 0£C. . COti: • 4L (11,. . • ". 5 0£•. C I + 5 25:•. :, ,,,.: 5. 29 • C PVH9n:JRB :l . T.! STU:(,Hl ( , .. : "

Fig. 13. - Comparison of surging characteristics of truncated cone and cyl­

inder combinations,

21

"' !51 :, .. 151 159 :,,

~la rr LU I­LU :::;: <l ll: <l c..

>-0 2 LU ::::> a LU ll: u.

-~-Ai

0 0

0

WA O ~JAo A ~ A

1 AO Cl' -

JtA9 -6,f;:A ~

~ At!,AA

0

A

2

MOMENTUM PARAMETER, .Q.D2 pQ

AIR MODEL

MODEL TURBINE

Fig. 14. - Comparison of frequency parameter for Grand Coulee pump­turbine draft tube computed from air model and 1:9.5 scale model turbine.

':i-A

3

The favorable comparison of results of the air model with the turbine

model verifies a major assumption in applying the results of the dimensional

analysis to experimental studies. That is, that regardless of the manner in

which angular momentum is introduced into the flow the resulting dimension­

less surging characteristics in geometrically similar draft tubes will be

the same for a particular value of m>/pQ2• This says nothing about the accu­

racy of determining the correct value of OD/pQ2• The methods used to deter­

mine the value of the moment parameter in the two studies are not as exact

as could be desired, and possibly can be improved in future experiments and

analyses.

CONCLUSIONS

1. A model of the type described in this paper can successfully be

used to determine the surging characteristics of draft tubes. The equipment

need have no more mechanical components than the minimum required to

22

precisely introduce, control, and measure swirling flow at the draft tube

inlet.

2. The degree of divergence of a draft tube is the most significant

geometric feature affecting surging characteristics. Bends and relative

length have lesser influence.

3. Surging can be minimized by using an equivalent expansion angle of

about 15 degrees through the whole length of the draft tube, and probably

eliminated entirely with even greater (approximately 30-degree) angles.

4. The use of straight cylinder sections (any L/D) in the draft tube

throat will increase the range of surging and increase the frequency and

amplitude of the surge.

5. The possibility of resonance with known natural frequencies of

other features of the hydroelectric plant can be checked with fair accuracy

using the results presented. Resonance can be avoided by proper choice of

geometric components in the draft tube design.

APPENDIX I. - REFERENCES

1. Benjamin, T. B., "Theory of the Vortex Breakdown Phenomenon,"

Journal of Fluid Mechanics, Vol. 14, pp 493-629, 1962

2. Cassidy, J. J., "Experimental Study and Analysis of Draft-Tube

Surging," Report No. REC-OCE-69-5, U.S. Bureau of Reclamation,

Denver, Colorado, October 1969

3. Cassidy, J. J., and Falvey, H. T., "Observations of Unsteady Flow

Arising After Vortex Breakdown," Journal of Fluid Mechanics,

Vol. 41, Part 4, pp 727-736, 1970

4. Chanaud, R. C., "Experiments Concerning the Vortex Whistle,"

Journal of the Acoustical Society of America, Vol. 35, No. 7

pp 953-960

23

5. Chanaud, R. C., "Observations of Oscillatory Motion in Certain

Swirling Flows," Journal of Fluid Mechanics, Vol. 21, Part 1,

pp 111-127, 1965

6. Deriaz, P., "A Contribution to the Understanding of Flow in Draft

Tubes of Francis Turbines," Hydraulic Machinery and Equipment

Symposium, International Association for Hydraulic Research,

Nice, France, 1960

7. Dziallas, R., "Francis Turbines under Partial and Overload," (Trans­

lated from German by Wunderlich, W. O., and Vigander, S.,

Tennessee Valley Authority, Norris, Tennessee, 1966), VDI Berichte,

No. 75, pp 53-64, J.M. Voith, Heidenheim, Germany, 1964

8. Falvey, H. T., and Cassidy, J. J., "Frequency and Amplitude of

Pressure Surges Generated by Swirling Flow," Transactions of

Symposium Stockholm 1970, International Association for Hydraulic

Research, Part 1, Paper El, Stockholm, Sweden, 1970

9. Gore, R. W., and Rantz, W. E., "Backflows in Rotating Fluids Moving

Axially through Expanding Cross Sections," Journal, American

Institute of Chemical Engineers, Vol. 10 , No. 1, pp 84-88, 1964

10. Harvey, J. K., "Some Observations of the Vortex Breakdown Phenomenon,"

Journal of Fluid Mechanics, Vol. 14, pp 585-594, 1962

11. Hosoi, Y., "Experimental Investigations of Pressure Surge in Draft

Tubes of Francis Water Turbines," Hitachi Review, Vol. 14, No. 12,

1965

12. Rheingans, W. J., "Power Swings in Hydroelectric Power Plants,"

Transactions, American Society of Mechanical Engineers, Vol. 62,

pp 171-184, 1940

13. Squire, H.B., "Analysis of Vortex Breakdown Phenomenon, Part l,"

Report No. 102, Aeronautics Department Imperial College of Science

and Technology, Great Britain, 1960

24

APPENDIX II. - NOTATION

The following symbols are used in this paper:

B • height of wicket gates

D • diameter of draft tube throat

f "' frequency (hz)

L • length of draft tube

N • number of wicket gates

n = rotational speed (rev/min)

p • power

p' • pressure surge amplitude fluctuation from mean

Q • discharge

R = radial distance to center of flow through wicket gates

S • width of opening between wicket gates

T • torque

V • axial velocity

a= radial inclination of flow through wicket gates

+1, +2 = functions

v .. kinematic viscosity

,r = 3.1416

p • fluid density

0 • flux of moment of momentum

w • angular velocity (rad/sec)

25