.. ..

"'-nentFile Cop, It. ....., FaUt Hydraulic Laboratory

UNIVERSITY OF MINNESOTA

ST. ANTHONY FALLS HYDRAULIC LABORATORY

~toject Report No~ 175

HEADLOSS CHARACTERISTICS OF SIX PROFILE~WIRE SCREEN PANELS.

by

a~in~ Stefan . and

Alec Fu

Prepared unQer contract with

Johnson Division UO~, Inc. St. paul, Minnesota

for

Consumer Power Company Jaokson, Miohigan .

and

Commonweal thA$$O~taees, . tn:o. Jaokacm, Michigan

Septembe~, 19'78 Minneapolis, Minnesota

!n

'., I" I , ,.

,~

:-.

". I

Unive~sity of Minnesota St. Anthony. Falls Hydraulic La.borato~

Projeot Repo~t No. 17,

HEADLOSS CBARACT.ERISTICS OF

SIX PROFILE-W!RE SCBEElN PANELS

by

Heinz Stefan

and

Alec Fu.

Prepared unde~ cont~act with

Johnson Division UOP, Inc. St. Paul, Minnesota

fo~

Consumer Powe~ Co. Jackson, Miohigan

and

Commonwealth ~ssociates, Inc, Jaokson, Michigan

September 1978 Minneapolis, Minnesota

.\)

,",0

~

Screen Panels (15" x 24") Wire Spacings are 3/8" (Screens No.1. 3, 4, and 5),

1/2" (Screen No.2) and 2 rnm (Screen No.6)

" .. .. .,

(i

CONTENTS

Photo of Screen Panels • • • • • • • • • • • • • •• i

I.

II.

.AJ3STRACT • . . . . . . . . . . . · . . . . . . . . . Listing of Studies for the James H. Campbell

Unit No. 3 Cooling Water Intake ••••• • • • •

List of Figures • • • • • • • • • • • • • • • • • •

List of Tables • • • • • • • 8 • • • • • • • • • • •

Introduction • · . . . . . . . . . . . . . . . . . . Description of Screen Panels · . . . . . . • • • • •

III. Literature Review on Headloss Coefficients of Screens . . . . . . . . . . . . . . . . . . . . . .

IV. Experimental Apparatus • · . . . . . . . . . . . . . V. Experimental Procedures · . . . . . . . . . . . . .

VI. Data Reduction • • • • • • • · . . . . . . . . . . . VII. Experimental Screen Headloss • • • · · · • · • • · •

VIII. Fundamental and Theoretical Considerations for Flow Through Screens · . • • · • • · · • · • • • • · • •

IX. Headlosses at Low Approach Flow Velocities • • · • •

X. Conclusions • • • • • . • • • • · • • • • • • • • •

REFERENCES • • • • • • • • '0' •••••••••••

ii-

iii

iv

v

viii

1

1

4

7

9

16

22

31

62

67

71

ABSTRACT

Headloss coefficients for six screen panels manufactured by the

Johnson Division UOP, Inc., Minnesota were determined experimentally.

The screens are considered for use at the cooling water intake of

Consumers Power Company's James H. Campbell Unit No.3. The plant

is located on the east shore of Lake Michigan near Grand Rapids,

Michigan. The flat screen panels, 24 x 15 inches in size and of

differing wire and rod assembly, were tested in a laboratory flume

at approach velocities ranging from 0.9 to 2.6 ft/sec. The angle of

approach relative to the screen surface was varied from 900 to 450 in

intervals of 150 • In the range of velocities and angles tested the

headlosses were found to be less than 0.3 ft of water. Headloss coefficients

(using approa04 velocity head as a reference) ranged from 0.5 to 2.8 at

900 angle of: ·approach., The experimental data led to the conclusion that

the screens tested. would not produce an appreciable'headloss when used

in low veloci.ty surface water intakes.

- iii -

<,

Listing of Studies

for the James H. Campbell

Uni t No. 3 Cooling water Intake

1. H. Stefan and A. Fu., "Headloss Characteristios of Six Profile-Wire Screen Panels," University- of Minnesota, St. Anthony Falls J:!;y'draulic Laboratory-, Minneapolis, Minnesota, Projeot Report No. 175, September 1978, 71' pages.

2, H. Stefan and A. Fu., "Colleotor Well study for the Cooling Water Intake Sy-stem of the James H. Campbell Eleotrio Power Generating Plant, Unit No.3," University- of Minnesota, St. Anthony Falls HYdrau1io Laboratory-, Minneapolis, Minnesota, Projeot Report No. 176, November 1978, 46 pages.

3. H. Stefan, W. Q. Dahlin, J. F. Ripken, A. Wood. and T. Winterstein, "Experimental Flow Studies with the Dual-Soreen Cooling Water Intake Assembly- ("Riser") for the James H. Canpbell Electrio Power Generating Plant, Unit No.3," University- of Minnesota, St. Anthony Falls Hydrau1io Laboratory-, Projeot Report No. 177, Deoember 1978, 130 pages.

4. H. Stefan, C. Sha.:nmugha.m, and S. Dhamotharan, "Cooling Water Manifold Intake (Header) Study for the James H. Campbell Eleotrio Power Generating Plant, Unit No.3," University of Minnesota, St. Anthony Falls Hydraulic Laboratory-, Minneapolis, Minnesota, Projeot Report No. 178, January-1979, 59 pages.

5. John M. Killen and 'H, Stefan, "J:!;y'draulio Analysis of Alternative Cooling Water Intake Designs for the James H. Campbell Eleotric Powe~ Generating Plant, Unit No.3," University of Minnesota, St. Anthony Falls HYdraulio Laboratory-, Minneapolis, Minnesota, External Memorandum No. 161, Deoember 1978, 22 pages.

- iv -

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

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6(a).

Fig. 6(b).

Fig. 6(0).

Fig. 7.

Fig. 8(a).

Fig. 8"(b).

Fig. 8.(.0).

Fig. 8(d).

Fig. 9(a).

Fig. -9(b) •

Fig. 10.

Fig. 11.

Fig. 12.

Fig. 13.

Fig. 14.

LIST OF FIGURES

Schematic View of Screen Panel

Profiles of Wire and Rods.

50-ft Glass-Walled Flume (Schematic).

Screen Panel Oriented at a and {3 angl9sf itl. F!Lu.me.V5ei,. (0)

Contractions Used for Different Screen .Angles f3 •

Screen Igstallatign in Laboratory Flume. Screen No.1, {3 ~ 90 , a = 90 •

Screen Igstallatiog in Laboratory Flume. Screen No.1, {3 = 90 , a = 60 •

Screen Installation in Laborato:,g Flume Screen No.4, f3 = 450 , a = 90 ; Screen No.1, f3 = 600 , a' == 900 •

06 0 Flow Through Screens. 0 Screen Ng. 1, f3 == 90 , a = 0 ; Screen No.1, f3 = 60 , a = 90 •

Chart of Headloss Coefficient Correotion.

Headloss Coefficient Correotion - 12.5" Water Depth.

Headloss Coeffioient Correotion - 12.5" Water Depth.

Headloss Coeffioient CorJ:.'ection - 9.5" WateJ:.' Depth.

HeadlossoCoefficient of Screen Panels at Angle of Approach a = 90 •

HeadloSSoCoefficient of Screen Panel at Angle of Approach a == 90 •

Headloss Coefficient of Screen Panel at Angle. of Approach a "" 75°.

Headloss Coeffioient of Soreen Panels at Angle of Approach a = 60°.

Headloss Coeffioient of Screen Panels at Angle of Approach a ~ 45°.

Headloss Coeffioient of Screen Panels at Angle of Approach f3 ;::: 75° ..

HeadlossoCoeffioient of Screen Panels at Angle of Approach {3 = 60 •

- v-

Fig. 15·

Fig. 16(a).

Fig. 16(b) •

Fig. 16(c).

Fig. 17·

Fig. 18(a).

Fig. 18 (b).

Fig. 18{ c).

Fig. 19(a)..

Fig. 19(b).

Fig. 19 (c).

Fig. 20(a) •

Fig. 20 (b).

Fig. 20(0) •

Fig. 21 (a).

\l Fig. 21 (b).

Fig. 21 (c).

Fig. 21(d).

LIST OF FIGURES (cont'd)

Headloss Coefficient of Screen Panels at .Angle of Approach {:3 := 450 •

Headloss of Screen Panels No.1, 3, and 5 (15/16 11 x 3/8" opening) at .Angle of Approach a:= 900 •

Headloss of Screen Panel No. 4 (3/8" x 3/811 opening) at Angle o of Approach a := 90 •

Headloss of Screen Panel No.6 (2 rom opening) at .Angle of o Approach a := 90 •

Headless of Scree:g Panel No. 6 (2rom opening) at.Angle of Approach a:= 75 •

Headloss of Screen Panels Nos. 1, 3 ,a.:gd 5 (7/811 x 3/8" opening) at .Angle of Approach a := 60 •

.. Headloss of Screen Panel No. 4 (3/8 11 x 3/8" opening) at Angle of Approach a := 60°.

Headloss of Screen Panel No. 6 (2rom opening) at Angle of Approach a := 600 ,

Headloss of Screen Panels Nos. 1, 3, and 5. ( 7/8" x 3/811 opening) at Angle of Approach a =450 •

Headloss of Screen P~el No. 4 (3/811 X 3/811 opening) at Angle of, Approach a:= 4.5 •

HeadlosS of SCreen Panel No. 6 (2rorn opening) at Angle of Approach a := 4.50 •

Headloss of Screen Panel No. 1 (15/16 11 x 3/8" 9pening) at Angle of Approach {:3:= 7.50 •

Headi~ss of Screen Panels Nos. 3 and 5 (7/8" x 3/8" opening) at .Ang-Ie of App:t'oach{:3 := 750 • . '

Headloss of Screen No. ~- (3/8" x 3/8" opening)atAngle of Approach {:3:= 750 • .

Headloss of Screen Panel No. 1 (15/16 11 x .3/8" opening) at Angle of Approach {3:= 600 •

Headloss of Screen Panel No. 3 (1.5/16" x 3/8" opening) at Angle of Approach {3:= 60 0 • ' I

HE3adloss of Screen P~el No. 4 (3/8" x 3/8" opening) at .Angle of Approach{3 := 60 •

Headloss of Screen Panel No.5 (7/8" x 3/8" opening) at Angle of .Approach 13:= 60°.

- vi-

LIST OF FIGURES (cont'd)

Fig • 22(a). Headloss of Screen Panel Ng. 1 (1.5/16" x 3/8" opening) at .. lingle of Approaoh f3 = 4.5 •

Fig. 22 (b). Headloss of Screen Panel No. lingle of Approach f3 = 4.50 •

3 (1.5/16" x 3/8" opening) at

Fig". 22(c) • Headloss of Screen Panel No. 4 (3/8" X 3/811 opening) at .Angle 0

of Approach f3 = 4.5 •

Fig. 22(d) • Headloss of Screen Panel ~o. .5 ( 7/8" x 3/8" opening) at .Angle of Approach f3 = 4.5 •

Fig. 22.(e) • BSadloss of Screen Panel No. Approach f3 ~ 4.50 •

6 (2mm opening) at .Angle of

Fig. 23·" Flow Through Single Screen Opening

Fig. 24· Flow Through Inclined Screen - Schematic.

"

- -v.ti -

Table No.

1

2

;3

4 , 6

7

8

9

LIST OF TABliES

Dimensions of Screen Panels.

Coefficients of Jet Contraction at a = ~= 900 •

Coefficients of Jet Contraction for Rods.

Coefficients of Jet Contraction for Wire.

Theoretical Headloss Coefficient of Screen ~els at a = 900 (without Reynolds number effect).

Theoretical Headloss Coefficients of Screen Panels at a = 600 (without Reynolds number effect).

Theoretical Headloss Coefficients of Screen ~els at ~= 7,0 (without Reynolds number effect).

Theoretical Headloss Coefficients of Screen Panels at ~= 600 (without Reynolds number effect).

Upper Bound for Screen Headloss at a Through-Screen Velocity of 0., ft/sec at 7,oF Water Temperature.

- viii -

EEADLOSS CHARACTERISTICS OF SIX SCREEN PANELS

1. Introduction

Screens are used in surface water intakes to prevent entrainment

of debris and aquatic life when supplying cooling water to power generating

plants. At high intake velocities, screens may cause injury or death

to aquatic life, particularly fish. At elevated velocities, small fish

may be entrained and fish too large to pass through the opening slots

may be impinged on the screen surface. Design for low withdrawal velocities

and use of fine mesh screens are expected to minimize both entrainment and

impingement conditions.

A screen may be defined as a regular assemblage of elements forming

a pervious sheet which is relatively thin in the direction of flow.

Examples are woven round-wire screens, perforated thin sheets, grids of

bars of rectangular cross section, screens composed of streamlined wire,

etc. A screen is characterized geometrically by element type (round­

wire, etc.), by element arrangement (square mesh, etc.), and by screen

shape (plane, etc).

The losses in surface intake screens are determined by screen geometry,

scale effects (Reynolds number), and the orientation of the screen with

respect to the flow direction.

This report describes experiments and associated analysis to deter­

mine the headloss characteristics of welded profile wire fine-meshed 3/8", 1/2" and 2 mm slot opening screens over a range of flow velocities. The

headloss coefficients of six screens of different geometry at various

orientations with respect to the flow direction were determined.

The screens described herein are manufactured by Johnson Divison

UOP Inc, St. Paul, Minnesota. The study was conducted under contract

with Johnson Division for Consumer Power Company and for Commonwealth

Associates, Inc., both in Jackson, Michigan.

II. Description of Screen Panels

A schematic view showing the general features of the six screen

panels tested is given in Fig. 1. The dimensions identified by letters

'a' through Ie', 'r', and 'WI in Fig. 1 are specified in Table 1.

- 2 -

" ,

TABLE 1. Dimensions of Screen Panels*

Screen Panel Open Spacing Widths Rod Center Lengths Per cent** Number Rods Wires Wire Rod Spacing ~ Wire open area

(a) (b) (c) (d) (e) (r) (w)

1 .930n (15/16" approx.) 3/8" (.37511 ) .128" .070" 1" 1" 1/4" 74.5 2 .930"( 15/16" approx.) 1/2"(.50011 ) .128" .070" 1" 1" 1/4" 79.6 3 .930"(15/16" approx.) 3/8"( .375") .128" .070" 1" 1/2" 1/4" 74.5 \.AJ

4 .348(5/16"-3/8") 3/8"( .375") .128" .1,52" 1/2" 3/16" 1/411 74.5 5 .848(13/16"-7/8") 3/8"(.375") .12811 .152" 1" 3/16" 1/4" 74.5 6 .930(15/16" approx.) 2mm (.079") .075" .070" 1" 111 3/16" 51.3

* specified by Johnson Division UOP.

** b!C ' rods not taken into consideration.

- 4 -

The screens are made of stainless steel and welded at all orossings

of the profile wire a.n.d the rods.

The profiles of wires and rods used for all six screens are given in

Fig. 2. The wires for screens 1 through 5 were identical in shape. The

rods for screens 1, 2, and 3 were rectangular but differed in length.

III. Literature Review on Headloss Coefficients of Screens

Headloss coefficients of the type of screens being tested could not

be found in the literature. Most of the available literature deals with

screens made of round wires and with woven screens.

The flow through a screen can be considered as flow through a number

* of orifices or nozzles in parallel (see e.g. Ref. 1). The head10ss across

a screen is often expressed in terms of a headloss coefficient and the vel­

ocity head just upstream of the screen. The head10ss coefficient is a

function of the open area fraction of a screen and a dimensionless discharge

coefficient which is a function of Reynolds number. The Reynolds number

can be based on aperture width, upstream velocity and the fractional free

projected area of screen. For plain rectangular mesh screens, a plot of

discharge coefficients versus Reynolds numbers is given in Reference 1.

For closed conduit flow and for screens made of circular metal wire,

Ide1'Chik (Ref. 2) expressed the Reynolds number in terms of the wire dia­

meter and the upstream velocity. The head10ss coefficient was expressed as

the ratio of head10ss to upstream velocity head. The loss coefficient was

related to the ratio of open flow area in the screen to the area of the

cross-section before the obstruction. At Re ~400, the loss coefficient

could be determined from a simple mathematical expression. At Re < 400, a

correction factor given in a graph in Ref. (2) had to be used.

In a manual published by the British Hydromechanics Research Associa­

tion (Ref. 3), a solidity factor was defined as the ratio of the area

occupied by bars to the total cross-sectional area. The Reynolds number

was calculated using mean approach velocity, wire or bar diameter and

the solidity factor in accounting for the obstruction. For a woven round­

wire screen and round-bar screen, and for Reynolds numbers greater than 300,

* Biographical references are given on page 71.

- 5 -

SCREEN PANEL NUMBER

6

Cross Sections Ro d Cross Sections

I

I

Fioure 2 PROFILES OF WIRES AND RODS (APPROXIMATE FULL SCALE)

SEE TABLE I for actual dimensions of

a, b, c, d, I, r, and w

I

I

"

- 6 -

the headloss coefficient was solely a function of solidity factor. It was

indicated that if the thickness of the bars in the stream direction was

greater than half the gap between the bars, flow re-attachment would occur

and loss coefficients would be reduced. By using streamlined bars, loss

coefficients might be halved.

In the case of duct flow, Monson and McDonald (Ref. 4) obtained an

expression for the loss coefficient by first determining the drag on the

front and rear rods and then converting the drag to loss coefficients.

The loss coefficient is a measure of total pressure loss across the screen.

For woven screens, Monson and McDonald made use of the approach vel­

ocity, wire diameter, and open area fraction to calculate the Reynolds

number of the wire. The loss coefficient was related to open area fraction (a

function of wire diameter and orthogonal bar spacings) and the drag coef­

ficient on the Reynolds number of the wire.

For cross-bar matrices screens, Monson and McDonald (Ref. 4) used the

approach velocity and the hydraulic diameter of the opening in calculating

the Reynolds numbers. The.loss coefficient was related to open area fraction

of the front row, the drag coefficients of front rods and rear rods. In

determining the drag coefficients, th~ effective Reynolds number of front

rods (in terms of approach velocity, front rod diameter and open area fraction

of front row) and the effective Reynolds number of rear rods (in terms of

approach velocity, rear rod diameter and open area fraction) were used. The

. corresponding drag coefficients were read from graphs prepared by Cornell

(Ref. 5).

Wieghardt (Ref. 6), as quoted in Ref. 5, visualized the flow through

round-wire screen as similar to the flow over single infinite cylinders

bathed in a uniform flow of velocity V1(1 - S), due to the constriction

imposed by the screen. VI was the upstream velocity and 8 the ratio of

blocked area to total area. He expressed th~ loss coefficient (h) as the

ratio of total pressure loss in a screen (L\ PT). to the upstream dynamic

pressure (~PV12). Thus Wieghardt correlated h(l - S)2/8 with

Re = V1d(1 - 8)v, anticipating a curve similar in trend to the drag coef­

ficient. d was the diameter of the round wire. Wieghardt's correlation

covered the range 60 < Re < 1,000 and is represented by the relation

- 7 -

(1)

MacDougall (Ref. 4) correlated data in the range 0.006 < Re < 20 and

obtained the relation

A _ 33.93 8(1 _ 8)-1.27

- Re 1 + (1 - 8)~ (2)

For low Mach number flow normal to plane sharp-edged screens, Weinig1)

used a two dimensional model of the flow around one-half of a screen ele­

ment for the flow in ribbon parachutes and compared the results success­

ful~y with experimental data for losses in strip screens. The loss

coefficient was given by

(3)

under the assctmptionof incompressible, perfect fluid flow, the wake vel­

ocity being taken as zero. Weinig used the theoretical results of Von Mises

for contraction coefficient C, based on a free streamline potential theory .c .

model of flow in .a sharp edged orifice.

IV. Experimental Apparatus

Experiments were conducted in a 50 ft long glass walled laborator~

flume of 24" width and 15" depth. The screen panels were also 2411 X 15".

The water level in the channel could be controlled by an adjustable gate

at the downstream end of the channel (Fig. 3),. Water from the Mississippi

river was fed intotheheadbox of the channel through a 12" line in which an

orifice flow meter is installed. A calibration curve for the flow meter

was prepared prior to the screen panel experiments.· The laboratory weighing

tanks were used for the calibration.

The screen panels were installed in the flUme at a distance of about

15 ft from the upstream gate. Disturbances from the upstream gate and

from the header box were quite small at that distance.

Travelling point-gauges were installed upstream and downstream from

the screen panel to measure water surface elevations.

1) Quoted in Ref. (5).

Orifice Fl.ow Meter

~_J---..-..

Head :Sox

II II II tl II II II

!1 11 fl 11 fl-I II

.Gate

";

-Screen

2

15n

Screen Panel

Control Gate

_-.", \ \

I " .(.._.)1

I I f I~now . ~ J

• 50 ft

Tail :Sox

Fig. 3 - 50-ft Glass-Walled Flume (Schematic).

I 00

- 9 -

The orientation of a screen panel relative to the channel axis was

variable. Six different orientations were investigated, as shown in

Fig. 4.

Flow in the channel was maintained at subcritical conditions at all

times. The upstream depth was maintained at 12-1/2" for all runs except

a = 450 , when a depth of 9" had to be maintained, because of the lim! ted

height of the panel in the tilted position,

Standing waves were generated downstream from the screen panel. At

high discharges the amplitudes of the waves were large enough to induce

significant errors in measurements. Ae a remedy, a wooden board was

placed on the water surface at a distance of about one foot downstream

from the screen panel. The board was taken out whenever the standing

waves were insignificant.

Rather than manufacturing panels of different length, a contraction

was installed in the channel to fill the gap between the end of the screen

panel and the sidewall when the angle ~ was different from 900 , as shown

in Fig. 4c. The ~hape of the contractions used is shown in Fig,S. Each

was 15" high (equal to the maximum depth of the flume).

Photographs of several installed screens are shown in Fig. 6 and Fig.

7.

V. Experimental Procedures

The following procedure was followed in the experiments.

(1) Install desired screen panel at Proper angle.

(2) Set waximum discharge through channel.

(3) Adjust control gate at downstream end to maintain subcritical

flow in channel and to keep water depth upstream from screen

panel at 12~". Decrease discharge, if necessary, until sub­

critical flow is achieved downstream from the screen panel.

(4) SeCUre board on downstream water surface at a distance of

about one foot from the screen panel to suppress any possible

standing waves generated. Take out the board whenever the

waves and surface disturbance created by the screen becomes

insignif icant.

(5) Read manometer deflection of orifice meter and determine the

corresponding discharge from the calibration curve.

Flow Direction

Wire

- 10 -

'---- Screen Panel

-k---Rod

o a = 90·

Channel :Bottom

Flow, ......... ~>-Direction

/ Side-walls ~ of C~ el

Wire

Flow Direction

(a) Vertical Section

Screen. Panel

Channel :Bottom

(b) Vertical Section

. Obstruction

-~-

Screen Panel

(0) Plan View

Fig. 4 - Soreen Panels Oriented at a a.nd B Angles in Flume.

------------- -----_ .. _---------------- ----------"

(a)

- 11 -

7"

0.82"

Flow =t:::>

27.15"

3.22"

55.4"

7"

\4--- Screen Panel

Screen Panel

Screen Panel

Glass Wall

Glass Wall

Glass \~all

Fig. 5 - Contractiorg; Used for Di:t;lerent ScreenJ.ngles {3. (a) f3 = 75 , (b) {3 = 60 , (c) f3 = 45

- 12 -

a . 0 0 Soreen No. 1, ~ ~ 90, a =:; 90 • Side View

Soreen No.1, f3:.;: 900 , a =:; 900 •

OveJ::'bead View

F~g. 6(a) - S9reen Installation in LaboJ::'atory Flume.

- 1.3 -

(3 ° ° Sc~een No.1, = 90, a = 60 • ..

Side View

Sc~een No.1, (3 = 90°, a = 60°. Overhead View

Fig. 6(b) - Screen Installation in Laboratory Flume.

- 14 -

Soreen No.4, {3 = 45°, a = 90° Side View

So:t'een No.4. (3;::; 450 , . a = 90° Overhea.d View

Fig. 6(0) - Sore en Installation in Laboratory Flume.

- 1$ -

Sore en No.1, f3;::: 900 , a = 600

Side View

,Soreen No.1, 8;::: 600 , a ::;: 900

Overhead view

Fig. 7 - Flow Through Soreens.

- 16 -

(6) Record water temperature.

(7) Record upstream water surface levels at five locations, each

6" apart, with the travelling point gauge 1. Start measurement

about 4 ft upstream from the screen panel to avoid any back­

water effect created by the screen.

(8) Using the average channel bottom elevation with respect to the

upstream point gauge, determine the average water depth upstream.

(9) Record downstream water surface levels with the travelling point

gauge 2 at ten locations, each 611 apart. Start measurement at

approximately 3 ft downstream from screen.

(10) Using the average channel bottom elevation with respect to the

downstream point gauge, determine the average water depth down­

stream.

(11) R~peat (1) through (10) for smaller and smaller discharges until

the water surface level drop at the screen is no longer detectable.

(12) Repeat (1) through (11) for a different screen.

(13) Repeat (1) through (12) for a different orientation of screen

. panels. Determine the headloss coefficient following the pro­

cedure outlined in the next section.

(14) Determine headloss and headloss coefficient of channel without

screen panel, following the above procedure.

(15) Calculate screen headloss coefficient by subtracting channel

loss coefficient from bulk headloss coefficient.

VI. Data Reduction

(1) Calculation of average reference velocity

Velocity (V) is calculated using the relationship

where

V=9. A

Q = discharge in cfs

A = wetted cross sectional area of experimental 2 channel in ft •

(4)

, . !

- 17 -(2) Calculation of Reynolds number

Reynolds number (Re) is calculated using the relationship

where a,b = dimensions of opening of a grid in ft

v = kinematic viscosity in ft 2/sec.

(3) Calcuiation of headloss coefficient

Writing the energy equation for an upstream and a

downstream cross~section, we have

V :2 I

2g

V 2 2

+ YI = 2g + Y2 + ~

where VI' V2 = average velocities upstream and downstream

from screen, respectively,

YI ' Y2 = average depths upstream and downstream from

screen, respectively,

~ = friction loss due' to screen, channel walls

and obstruction, if applicable.

Rearranging the above equation, we have

The headloss ooefficient is exp~essed as the ~atio of headloss

to upstream velocity head, i.e. K ~ hL(V12/2g)-1.

(5)

(6)

Headloss coeffioients to acoount for the friotion loss in the ohannel,

the wave suppressing board, and the oonstriotion were determined separately

and are shown in Figs. 8a to 8d. The friction loas due to the obstruction

at R;::. 750 was found to be almost undetectable. For practioal purposes, the

same oa~ibration ourve (Fig. 8a) has been used fo~ oases at a= 900 and

P = 750 • In Figs. 8a to 8d the ooeffioient inoreases as disoharge deo~eases. (The one and only deviation is shown in Fig. 80 and is attributed to inoreased

surfaoe wave formation and the impaot of the flow downstream from the oon­

traotion on the channel walls.) This indioates the presenoe of a Reynolds

number effect and agrees with the findings of Cornell (Ref. 5) who stated

.6 -r \. o Flume, plus board 0

0 "\ G Flume,plus board plus obstruction for ~ = 750

0 8. Flume

.5 t .~

'" o FI~e, plus obstruction for f3 = 75 0

-I"' s:1 Q)

-r-! 0

-r-! ~ ~ OJ a .4 0

m m a

r--l

.3 1 ~ , ~I rd III Q) co .Q

~ I I a r:I s:1 a

-r-! -I"' Cl Q)

~ &.~ ~~ 0 1 a 0

.2 .........,.., @

0

~ Jr...-

.1 I

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Flow rate Eers)

Fig. 8(a) - Headloss coefficient correction - 12.5" water depth.

+'

&i .,-! C)

.,-! '4-l ~ .(I) o o til fI) o

...-I "'CI

<1l ~ ::r:

4-1 o I=l o

.,-! +' C) ~ 1-1 l-I o o

.5

.4

.3

.2

.1

o 1.0 1.5

~ Flume plus wooden board plus obstruction for ~= 600

, 0 ~ Flume plus obstruction for ~= 60

o .......

'" o

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Flow rate (cfs)

Fig. 8(bJ - Headloss coefficient correction - 12.SIf water depth.

~-----!

~

o Flume plus board plus obstructiol1 for f3 = 45°

A Flume plus obstruction for 13 = 450

·7

+" .6 ~ 4D

..-I 0 • .-1 fH fH ., 0

0

m .5 m 0

~ 8- f\) M 0 ~ ~ fH 0

s:: .4 ~ 8-0

• .-1 .p 0 ., ~ 0

0

·3 1.0 2.0 3·0 4.0 5.0

Flow rate (cfs )

Fig. 8(e)'" - Headloss coefficient correction - 12.5" water depth.

~. <, j .·'cce; ":1..1

-5_ 4 0 Flume p'lus board

A Flume

\ ~ .4 ()

-r-! 0

-r-! Co-! Co-! () 0 0

tll .3 tll 0

r-l to

r ~ Q i'v m

~ -"

0 Co-! 8. 0

~ .2 0 "r"/ .p 0 ~ F-I F-I 0

0

.1 _L __ . __ ___ ~.J

1.0 2.0 3.0 4.0 Flow rate (era)

Fig. B(d) .- Headloss coefficient correction- 9.5ft water depth.

- 22 -

"The effect of Reynolds number on loss is found to be small, except at

very low Reynolds number". The headloss coefficient of the soreen is

obtained by subtraoting the correction due to the flume (the board and

the obstruction, where applioable) from the bulk headloss ooeffioient.

VII. E~perimental Screen Headloss

Headloss coefficients determined for individual screens have been plotted

vs. Reynolds number (defined by Eq. 5) in Fig. 9 (for a= 90°), Fig. 10 (for

(l = 75°), Fig. 11 (a = 60°), Fig. 12 «(l = 45°>, Fig. 13 (f3 = 75°), Fig. 14

( (3 I::; 60°), and Fig. 15 ({3 = 45°).

Upon comparing the results shown in Figs. 9 thru, 12, i.e. for cases with

o == 90°, a =75°, a I::; 600 , and a = 45°, it can be concluded (i) that the

value of the loss coefficient k at the same Reynolds number increases as

the angle of approach a decreases, and (ii) that the loss coefficient in­

creases as the open area fraction of the, screen decreases. 'Both results can

be explained by the fact that headloss is directly proportional to the blocked

area imposed, as will be shown in the next section.

For flow perpendicular to the screen, headloss coefficients for screens

No.1, 3, and 5 can practically be represented by the same curve. This is

to be expected since the three screens have identical opening sizes and the

same shapes of wires and rods. If a screen is tilted at an angle 'l3 , the

length of the rod begins to play an important role. In Fig. 13, it can be

seen that only the headloss coefficients of screens No. 3 and 5 (but not

No.1) can be represented by the same curve. Screen No. 1 has a longer rod

than screens No. 3 and No. 5 and is therefore more effective in deflecting

the jets formed in passing through the screen openings. This deflection of

the flow leads to an additional loss. As velocity increases (Reynolds

number increases), the rods become more and more effective in deflecting

the flow. This is illustrated by the curve representing screen No. 1 in

Fig. 13 ( ~ == 75 0 ) and further emphasized by the curves representing screens

No. 1 and 3 in Fig. 14 ( ~ = 600 ). As ~ increases to 600 , dat~ points

for screens 3 and 5 no longer fallon the same curve

In Fig. 13, for (3 = 75 0 , screen No.4 generally has a higher headloss

coefficient than screen No.1, since screen No. 4 has a smaller area of , 0

screen opening. As (3 decreases to 60 (Fig. 14), the effect of rod length

has already overridden the contraction eHect around 'the wires. The impact

...... I

----f()

~ C\II>

---,il II

~

~ ~ 0 til

Ct-t 0

~ III • ..-1 0 'M tI I) 0 0 III III 0

~ ~

" ',j

~.'''''''''''~'''~"'-.".'.

',' ,

'I

.. "23-

• Screen No. Opening

2.0 0 3/8 inch 1

<> 2 1.f2inch

0 3 3/8 inch

~ 4 3/8' inch

III , 3/B 'inch

8. ~ 1.0 & 8.

.9 6, ~ 6

0 .8 0 00

0 8 0

.7 0

.6 ~ I;) <> I;) . .....,,-.--"' . ~ ........... "",,' ., ,.... .... 1;" ...

0 ., ...... / . .,..

0 ...... '",.

// / 0

·4 .

·3

2,000 3 4 6 7 8

Re;yn.olds Nwnber :::: v\fa.b7J1 Fig.' ~(a~; - Headloss CoefficieBt of Screen Panels at Angle

of Approach' t!X::::' 90 •

0 0

9 10,000

10

9

8

7

6

5 ,-,

,..."

~ C\I

...........

~ 4 '--'"

~ II

.!.4

s:I 3 .,

Gl

~ ro fH 0

11 ., .r! 0 .r! fH

2 fH ., 0 0

III III 0

~ ~

1

1000

- ,.24-

Sore en No.

I

2

Opening

2mm

- I

Reynolds Number = V

\fl

I I .

'3 4 ~ab/V

Fig. 9'b) - Headloss Coefficient of Screen Panel at Angle of Approach a = 900 •

5000

B.o

7.0

6.0 ..--

I ..-... 1:10

~ ,.0 e rtf \I

,ltl 4.0

s:l tl

~ t)

U,)

Ct-t 3·0 0

~ tl 'M t)

'M Ct-t Ct-t tl 0 0

m m 2.0 0

~ !!l

1.0

- 25 -

Soreen No. Opening

'0/ 6 2>.mm

1000 2 3 4

Reynolds Number = V ~/"

Fig. 10 - He~dloss Coefficien~ of Soreen Panel at Angle of Approach a = 75 •

,000

II ,.¥I

10.0 9.0 8.0

7.0 6.0

5·0

4.0

3·0

2.0

1.0 ·9 .8 .7 .6

·3

· 26-

Soreen No. Opening

0 1 3/8 inch

0 3 3/8 inch

b 4 3/8·a.ncl1

EJ 5 3/8 Jinch

V 6 l.2nim

1,000 2 3 4 5 6 7 8 9 10, 000 2 30,000

Reynolds Number ~ V~v

Fig. 11 - 'Headloss Coefficient of Screen Panels' at Angle of Approach a '"' 600,

o 1. 0 I--__ -..I......,...,..,_......J-~_L ~ ~ I , .• -L-....L.~_,,~,.J_._L....I-_L..JI-.J.J --L-I .,.J.I ~_--I

2,000 3 4 5 6 7 8 9 10

Reynolds Number:::: V ..Jab/v

Fig. 12 _. ;Headloss Co~fficie;nE of Screen Panels at Angle of Approach a ~ 45 .

12,000

or-I .........

. ttl

~ (:\,I\>

.........

rtf 1\

.14

~ I). F-I 0

tf.l

4-1 0

~ Il • .-1 0

'.-1 4-1 4-1 I> 0

I:.)

m m a

~ ~

1.0

·9

.8

.7

.6

.5

.4 r l I

·3

.2 2,000

- 28 -

tr 6 -f:::,. ~.6. k· 't:s-

8 r::J

EJ

Soreen No. Opening

0 1 3/8 inch

0 3 3/8 inch

£::. 4 3/8 inch

m 5 3/8 inch

3 4 5 6 7 8 9 10,000

Reynolds Number ~ V ~/v

Fig. 13 - Headloss Coefficient of Screen Pane~s at Angle of Approach {3=75°,

,... I 2.0 ........

~ ~ o ' ~ 0 ~ .,. 0,0 0 ....., .cf

, II

1>4

~ 1.0

I) ·9 ~ .8 0 fI.l

Crt .7 0

~ .6

I) ., ·ri 0 'r! Crt Crt .4 I) 0 0

m m ·3 0

~ ~

.2

.1 ~~ __ ~ __ -L __ ~~~ __ ~ __ ~~_._.~I~~~ ____ ~~ __ ~ ____ ~

1000 2 3 4 5 6 7 8 9 10 ,000 2 3

Reynolds Number = vvablv

Fig. 14 - Headloss" COeffi.cient of S'C'reen, :i'aneits tat,,- Angle of Approach /3 = 60Q. .

10.0

9·0

8.0

7.0

6.0

,... I

5.0 ,-.... I?{)

~ 'i> ~

.rf 4.0 II

,.!4

I=l I> G)

F-l C)

t1.l 3·0 !t; 0

~ CI)

'r-! C)

'r-! !t; !t; I> 0

0 2.0

In In 0

~ ~

1.0

- 30-

Screen No. Opening

0 1 3/8 inch'

0 3 3/8 inch

8. 4 "'3'/8 inch'. t:

l!l 5 3/8 inch

\fl 6 2mm

0

b b A-zi~

8. - 6 8 A

0

G --8- -8 -EI- -G

0 G-

O

'--__ ..l..-...._--'-,_.,...,......JL...... __ ll-.....-L __ .J_l.. .. _ .. i._....J,_..L1 ........+.1 --L.I --I...-I--..L-.l-_---I

2,000 3 4 5 678

Reynolds Number~ V ~ab/v

Fig. 15· - Headloss Coefficien~ of Screen Pa;t'l.els at Angle of Approach ~ = 45 .

9 10 12,000

- 31 -

of the flow on the sidewalls of the experimental flume becomes significant

and a limitation to the accuracy of the data. At f3 == 60°, screen No. 1

has the largest headloss coefficient among screens No.1, 3, 4, and 5, and

the headloss coefficient for screen No. 3 (rod length == 0.5") now comes

closer to that of screen No. 4 (rod length == 0.2") as compared to the dif~

ference at {3 == 75° (Fig. 13).

(:j ° ' At ~ == 75 , all the screens have headloss coefficients slightly

higher than those at a == 90°, At f3 = 60°, the differences are even larger.

Design ourves fo~ all so~een panels have been p~epared. These ourves

are in the form of headloss as a funotion of ~efe~enoe app~oaoh velooity

and are shown in Figs. 16 tb,:rough 22. Curves at 320 F water tempe~ature ~ep~esent winte~ conditions, while curves at 75°F wate~ temperature represent

approximate summer oondition!? In the velooity range f~om 0.5 to 2.5 ft/seo

summe~ losses a~e generally shown slightly highe~ than winte~ losses beoause

lower water visoosity in summer gives ,higher Reynolds numbers whioh in turn

gives higher loss ooeffioients in FigS. 9 through 14. Graphs are provided

for diffe~ent angles of app~oaoh a and~. The reference approaoh velooity

is defined as the flow rate divided by screen panel area. Its value is

independent of the orientation of the soreen.

VIII. Fundamental and Theoretical Considerations for Flow Through Soreens

TIle literature referred to in an earlier seotion and other studies

not specifically referred to herein oontain theoretical attempts to predict

headloss ooefficients by application of fund~ental hydrodynamio principles.

Prereq,uisites for such efforts include some,lmowledge of the q,ualitative

features and kinetics of flow through a screen, and the acoeptanoe of

simplifioations and hypothesis regarding the geometry and the flow field.

Theoretical analysis may not be carried through without introduction of

some ex.perimental ooefficients foJ;:' many types of screens. Despite this \

obvious deficiency, it would appear of value to a designer or manufacturer

at one time or anothe;r to engage :Ln some more fundamental analysis of a

SOreen design.

(1 ) Mechanism of Screen Flow , \

The flow is accelerated when it passes through the screen due

to the oonstriotion imposed by the soreen, and for.ms jets of higher than

approaoh velooity behind the openings, interspersed with wakes of relatively

T .... · ............. ·· .. -'-";"-.:,',-.'

,--..,. +' It-! "-'

U,I m 0

r-! rg ~

.08

.06

.04

.02

o

- 32- -

Water Temperature

o 32°F

!1l 75°F

'---a::::::.;:::;;--+----"_ ... _....,-.--t-____ -+~ _._

o 1 1.5

ApprQaoh Veloc.ity (fps)

"

2

Fig .. · .. t6(a) ':,'~ Headloss of Screen Panels Nos.l~ ,3, and 5 ~15/16" x 3/8" opening) at Angle of Approach a = 90 .

r--.

~ '-.-/.

11.l 11.l

° ~ ~

, • l!

.08

.06

.O~ .

• 02

I .

o

Water ~emperatuxe

o 32°F

875°F

1

Approach Velooity (fps)

2

Fig. 16('b)~1'1.''' Headioss of Screen Panel No.4 (3/8". x 3/8 II" opening) at .A~~,~.:Le of Approach a;:: 90°.

" .,- ,

m m o

~ ~

-J4 -

Water Temperature

. CD .32oF

0·3

0.2

0.1

o . _____ 1 ...... __ , __ . __ --" ____ --1

o 1 1.5 2

Approaoh Ve.locity (fps)

. Fig. 16(0)'- Headloss of Screen Pane~ No.6 (2 rom opening) at Angle " 0 \.

of Approach a = 90 •

.1

.05

o o

-3, -

w~ter Temperature

Q) 320F

1 1.5

Appro~h Velooity (ips) 2

.••• r"

F;ig. 17 .... Headloss of Screen Panel No. 6 (2mm opening) at Angle of Approach a =75°,

,.

.12

.10

.08

,-..

~ .06 ""-"

[Q [Q 0

~ ~

.04

.'()2

o

Water Tempe~ature

o 32°F

(II 7!5°F

~==~ ____ L-__ -L __ .• _._ .. J~~~ ___ "_.L~ __ ,---L __ , __ ~ __ ~ __ ~

e , 1 1.5 2

Appro~h Velooity (fps)

Fig. 18(a) -. Headl-oss of :SCl:een Panels Nos. 1, 3, and 50 (7/8", X

.3/8" op~nil1.g) at Angle of Approach, a = 60 •

.16

.14

~ 12

.10

"""' ~

"'--" .08 [Q [Q 0

i ~

.06

.02

o

I f

o

- 37 -

Water Temperature o 32°F

-'-_"_~.l...-_.J...~ .. ~ . .-L,...._~....L.. __ ~J...._" _ .. ....,.1.,.1,.... _.-..1..1 __ .1--_--'

1 2

Ap~roaob V~looity (f~s)

Fig·. 18 (b) - Headloss of Sc;reen Panel NQ. ,~ (3/8" :x '3/8" opening) at Augle of Approach a = 60 ,

.1

.0,

o

- 38-

Water Temperature

o 32°F

I] 7,oF

J .••

1

Approach Velocity (ips)

Fig., 1,8 (c) '-,. lWaQ.losEi of ,Screen ~anel No. 6 (2nnn opening) at Angle - of Approach a = 60 •

·02

o 0

- 39 -

Water Temperatu:t'e

o 32°F

r.n 75°F

Approacb Velocity (fps) 2

F~g. 19(a).- Headloss of Screen,Panels No~~ 1, 3~. and 5 ~ 7/8 .. 11 X

. 3/8" opening) at Angle of Approach ct JIll 45 •

- 40-

Water ~emperature

.2

o ~-=~~~------~------~------~----~ 0.$ 1 1.$ 2 2.$ Approach Velocity (fps)

Fig. 19(b) - Headloss of Screen Panel No. 4 (3/8" X 3/8" opening) , ,. .' at Angle of Approach t% 1= 45°.

l r- .. -. , .

, ":

.4

·3

.2

- 41 -

Water ~emperature

o 32°F

o 0 2

Approaoh Velooity (fps)

Fig. 19(c) - Headloss of Scre~n Panel ~o, 6 .(2mm opening) at Angle of -Approach a ~ 45 .'

0.08

,-....

~ "Y' 0.06

0.04

C.02

o o

- 42 -

Water Temperature

1.0 2.0

Approaoh Velooity (fpa)

Fig. 20(a) - Ileadlos's of :S~reen Panel No. '1' (15/16": x"'3l8n v- ~ 'opeWing)"'at Angle of Approach {:J = 75°.

1

0.10

0.08

,-... 0.06 ~

'-'"

m m 0

r-I

~ ~

0.04

0.02

o o

- 43-

Wate~ ~empe~ature

o 32°]'

IZl 75°w

--" -,.,.". II----,·~·,·-+__·-·----+------.1

1 2

App~oaoh Velooi ty (ips)

Fig~20(b)-'Headloss of Screen Panels No. '3 and' 5 C7/86~ x 3/8" 'opening) 'at "Angle of Approach f3 = 75°.

0.10

0.08

0.04

0.02

o

~ 44-

Water Temperature

------~I .. ·------,--4_--------~--------~1 0·5 2.0 2.5

Approaoh Velooity (rps)

Fig. 20(c) - Headloss of Screen Panel No: 4 (3/8" :k 3/8" opening at ~ngle of Approach ~ = 75° • .

Ii }i

~

~ II i I ,......., }i ~ ,Ii

I '--"

!Xl

I !Xl 0

~ C\!

I!l

.16

.14

.12

.10

.08

.06

.04

.02

o

Water Temperature

o 32°F

~-"""J".,;_J_,_.L.~"_.,I..,L_....,.....I.J ....... _" _'--_ ........ _--"-__ '-_ ..... "

o ., 1 1.5 2

Approach Velocity (fps)

Fig. 21'(a) - Headloss" of Screen :Panel No. 1 (15/16""x 3/8" . opening)' at Angle of " Appr.oach {3::;: 60°.

I

! I

,,-....

~ '-"

tn tn 0

~ Gl

IJ;I

.16

.14

,10

.08

.06

o o

Water Temperature

o 32°F

1

- 46>-

1.5

Approaoh Velocity (fps)

2

Fig. '21'(b)' - , Headli()ss . of Screett'Panel No. 3 (15/16" JC.' :3/8" \ opening) at Angl~, of <Approac'h 1:~fJ 0:: 60°.

3

......... ~ --III III 0 g ro

.~

- 47. -

.1~. w~ter Temperature

o 320 F

.12

.10

.08

.06.

.04

.02

o .. ~-=~ ____ ~ __ ~ ____ ~ __ ~ ____ L-__ ~ ____ ~ __ ~ __ ~

o 1 2

Approach Velocity (fps)

Fig. 21(c) - Headloss of Screen. Panel No.4 (3/8" x 3/8" opening) at Ang;1e of Appro'acu,r {3 = -600 •

.12

.10

.08

r--.

~ .....,....

m .06 m 0 r-l

'al ~

.04-

.02

o o

- 48 -

Water Temperature

.5 1 1.5 2

Approach Velocity (fps)

Fig. 2I(d") - Headloss of Screen Panel No. 5 (7/8 " x 3/8" opening) at Angle of Approach /3 = 60°.

0

2.5

.4

.1

o

J

o

-49 -

Water Temperature

o .32oF

f3 75°F

1

I,

1., Approach Velocity (ips)

2

Fig. 22(a)- - Headloss of Screen P:mel No. 1 (15/16" x 3/8' opening) at Angle of Approach f3 = 45°.

! j

I I. !

I

.20

.15

.05

- so -

Water Temperature

o 32°F

° Q 75 F

o ~~ ______ ~ ________ ~ ________ ~ ________ ~ ______ ~ o 1 2

Approach Velocity (fps)

Fig. 22(b) - Headlo's's of Sere'en Panel No.' 3 (1,5/16 11 X 3/8" " opening) kt Angle of Approach f3 == 45°.

I

m m o

~ t!l

- 51 -

Water Temperature

o 32°F

G 75°F

.2

.1

o ~==~ ____ ~ ________ ~ ________ ~ ________ ~ ________ ~ o 1 2

Approaoh Velocity (ips)

Fig. 22(c) ..a;l He.adlosp ·of Screen'PaIiel No.4 (3/S''?,:&: 318" opening) at Angle:6f Apptoach ~ = 45°

1 !

I I I I l i' t

,.-...

~ ..........

m m 0

~ ~

.2

.15

.10

.05

o

o

- 52 -

Water Temperature

o 32°F

[:!l 75°F

1 1·5 Approaoh Velooity (fps)

2

Fig. 22(d) - Headloss of Screen Panel No.5 (7/8 " 'X 3/8" opening) at Angle ef Approach '(3 := 45°.

".......

~ ....."

r:n r:n 0

~ ~

.6

.4

.3

.2

.1

- 53 -

Water TemperatUre

o 32°F

o ~=....-__ "--~ ____ I.,.I __ • _..;., ___ , ._ll--. ____ ""-"' _____ .... J

o .5 1 1.5 2 2.5

Approach Velocity (ips)

Fig. 22 (e)- Headlo!?s ,of Screen Panel No.~ 6 (2~. openi~g) at I ' Angie of '''Approach .{B = '450 • I •.

r·'·l······.,.·~·.···· '1, ;.~ ~;,: :,0".

~

- 54. -

low velocity behind the elements. As the flow passes downstream, the jets

and wakes mix to yield finally a uniform flow. Most of the energy loss

(head1oss) occurs in the mixing process, although some loss also occurs in

the flow within the screen passages.

The use of screens in fluid mechanic experimentation to produce >

turbulence of specific characteristic (grid turbulence) is wide-spread.

Eddy scales, frequencies and turbulence intensities are related to screen

dimensions and flow Reynolds numbers.

The headloss across a screen is a function of the velocity differ­

ence between the jet at the vena contracta and the downstream flow, the

geometry of the screen, the viscosity of the fluid, the density of the

fluid, and the inclination of screen to the flow direction. Since the bulk

of the head10ss is due to the interaction of the turbulent shear stress

developed at the interface between jets and the ambient fluid, the head­

loss does not occur right at the screen but over a distance downstream

from the screen.

(2) Derivation of Head10ss Coefficient in Flow through Screen

Let V == velocity at vena contracta of jet s

V == upstream or downstream velocity and

a,b,c,e == dimensions of screen elements as defined in Fig. 1

The flow between two wires and that between two rods is depicted

in Fig. 23(15) and (0). The flow through a screen opening can be visualized

as a' combina6onof (b) ahd (6)iri a three dimensional sense. The flow

wO'\lld be a non-axisymmetric jet. Note that in Fig. 23(0), the velocity

at the vena contracta is only approximately equal to Vs' This is because

the location of the vena contracta between the wires does not necessarily

coincide with that between the rods. Consequently, the following equation

of continuity holds approximately true, i.e.

V ab C C ~ V(b+c)e s cw cr (8)

- 55 -

Vena: Contracta

(a) Mean Velocity Distribution in Jet

c

Wire Rod

Cb) Flow Through Wires (c) Flow Through Rods

Fig. 23 - Flow Through Single Screen Opening.

where

- 56 -

Ccw ~ contraction coefficient of wire

C := contraction coefficient of rod cr

Re-arranging the above equation gives

:::: V (b+c)e Vs abC C

cw cX' (9)

The headloss (l\,) across the screen is similar to that in an expansion and

is given in first approximation by

(V - V)2 s

(10)

Substituting Eq. (9) into Eq. (10) gives

1 := V2 [ (b+c) e _ ~ 2g abC C cw cr

(11)

To account for any Reynolds ~umber effect and for simplifying

assumptions, a correction factor YJ has to be incorporated in Eq. (11).

Thus Eq. (11) becomes

Expressing the headloss coefficient k as

k :=

we have, from Eq. (12)

(b+c)e abC C cw cr

(3) Effect of Inclination of Screen

(12)

(13)

(14)

The flow through an inclined screen is illustrated in Fig. 24. The

ratio of the obstructed area to the unobstructed flow area remains unchanged.

The contraction coefficients, however, have to be modified. ;Conseql,lently,

Eq. (13) can still be applied with a modification of contraction coefficients.

-------------------------------~~

~ I ~l ~~~~*~F8~ '.5ZV -~~:~·t~~~~~4-~~-~~~~~~~~·~-~~~~~~-- -~~

I

Fr-ee Surface

Flow

==t>

Channel Bottom

Rod

Wire

b cos :a

(b+c)cos a ~Separation Streamline

Fig. 24 - Flow Through Inclined Screen - Schematic.

\J1. -:J

When the screen is inclined at an angle a (as defined in Fig. 4(a)

and 4(b», the contraction coefficient of the wire has to be modified while

that of the rods remains unchanged. When the screen is inclined at an angle

{3 (as defined in Fig. 4(C»J the contraction coefficient of the rod has to

be modified, while that of the wires remains unchanged.

Values of the contraction coefficients for the wires and rods in

the current investigation are not found in the literature. However) values

of the contraction coefficients for 2-D sharp edged slots are available

(e.g. in Ref. 7). These values can be used to specify the lower limits of the

contraction coefficients of the wires and the rods. More accurate estimates

of contraction coefficients can be made from experimental headloss data. A tabulation of contraction coefficients, using linear interpolation between

values given in Ref. 7 is shown in Tables 2, 3, and 4. It is important to

bear in mind that the values in Tables 2, 3, and 4 indicate only the limiting

values, and not the actual values of contraction coefficients of the wires

and the rods.

{ll') Theoretical Headloss Coefficients

Calculation of theoretical headloss coefficients from Eq. 14 requires

estimation of ry(Reynolds number effect) and the contraction coefficients of

wires (C ) and rods (C ). The effect of Reynolds number can be determined cw cr

from experimental data. Exact contraction coefficients C . and cw

the screens considered herein cannot be found in the literature.

C for cr

However,

lower limits of C and C can be estimated and have been given in Tables cw cr

2, 3, and 4.

As shoWl1 in Fig. 10, for a = 900 , the contraction coefficients

are almost independent of Reynolds number except at low Reynolds numbers.

For {3:=: 600 , C cw would have the· same values at;; for a ;" 900 •

Ccw ' however, has to be modified. The product i

from experimental data with the aid of Eq. 14.

C C cw cr

can be estimated

c C cw cr' values of C cr

Using the known

can be estimated for different screens.

C cw

and

For {3 == 750 and 600 , C cw o would have the same value as for a ==

90 , as explained earlier. Using the same process as described above,

can be estimated for different screens.

C cr

I

b * ¢ = 4~ b+o

0.0 0.746

0.1 0.747

Oc2 0.747

0.3 0.748

0.4 0.749

0.50.752

0.6 0.758

0.7 0.768

0.8

0.9

1.0

0.789

0.829

1.000

¢= 60°

0.701

0.702

0.703

0.706

0.710

0.716

0.726

0.741

0.767

0.813

1.000

* See Fig. 1 for definition.

COEFFICIENTS OF JET CONTRACTION AT q: e {3 = 90° (By Interpolation from Reference 7)

¢ = 75° ¢ = 90°

0.656

0.657

0.660

0.664

0.671

0.680

0.694

0.714

0.745

0.797

1.000

0.611

0.612

0.616

0.622

0.631

0.644

0.662

0.687

0.722

0.781

1.000

Definition sketoh for slots 2-D

~ = 12d'. ¢ = 13s<'

0.562 0.537

0 .. 568· 0.546

0.575 0.555

0.585 0.566

0.597 0.580

0.614 0.599

0.634

0.664

0.706

0.768

1.000

'if>

0.620

0.652

0.698

0.761

1.000

¢ = 1500

0.525

0.5J5

0.546

0.559

0.575

0.595

0.618

0.65.0

0.696

0.761

1.000

B . b -t -f-- ,- • ] c, b

~ = 165" ~ = 1800

0.513 0.500

0.524 0.513

0.537' 0.528

0.552 0.544

0.570 0.564

0.591 0.586

0.616

0.648

0.694

0.761

1.000

0.613

0.646

0.691

0.760

1.000

__ ---.J

I

vl. '-0

- 60 -

TABLE :5 .

Coefficients of Jet Contraction for Rods

* f3 :;: 75° f3 :::: 60° f3 == 4~ ale mean of( 16f , 7f) l11ean of( 600 , 1500 ) mean o£(4S>, 135°)

0.0 .0.58 0.61 . 0.64

o~ 1 0.59 0.62 0.65

0.2 0.60 0.62 0.65

0.3 0.61 0.63 0.66

0.4 0,.62 0.64 0.67

0.5 0.64 0.65 0.68

0.6 0.65 0.67 0.69

0.7 0.68 0.70 0.71

0.8 0.72 0.73 0.74

0.9 0.78 0.79 0.80

1.0 1.00 1.00 : 1.00

Angle f3 defined in Fig. 4(c).

*See Fig. 1 foJ:' definition •.

, --co',-

b * b+O

0.0

0.1

0.2

0 • .3

0.4

0.,5

0.6 .

0.7

0.8

0.9

1.0

- 6:1. -

TABLE 4

Coeffioients of Jet Contraction for Wire

a ;:: 60° a ;:: 45" mean of( 600 , 120°) mean of(4,O,

0.63 0.64

0.6.3 0.6,

0.64 0.6,

0.6, 0.66

0.6, 0.67

0.67 0.68

0.68 0.69

0.70 0.71

0.74 0.74

0.79 0.80

1.00 1.00

a defined in Fig. 4 (b).

* See Fig. 1 for definition.

135")

- 62 -

Headloss ooefficients calculated from the estimated contraction

coefficients are shown in Tables, through 8.

Theoretical prediction of headloss coefficients hinges essen­

tially on proper estimates of contraction ooefficients. Such estimates

are difficult when separatio,n points are not clearly identified, as in the

case for round~wire screens. E~uation (14) is ver,y sensitive with respect

to contraction coefficients. In addition to jet dissipation losses, wall

:f.':riction of the screen elements can rn.ake an important oontribution to

headlosses at very low Reynolds number.

IX. Headlosses at Low Approach Flow Velocities

The experimental soreen headloss data reported in Section VII were

obtained at approach flow velooities from 0.9 to 2.6 ft/sec. The maximum

through-screen design velooity for the Campbell intake is 0., ft/sec. The

purpose of the headloss measurements in the laboratory was to detexmine

whether screen losses were significant when compared to other losses"

specifically those in the risers and headers. Very early in the experi­

ments it was found that at velooities of 0., ft/sec and less, the soreen

losses could not be measured in the channel without resorting to micromano­

metry. Therefore, higher approach flow velocities were used.

In the experimental flume the approach flow'was always turbulent.

The flow around the wires and rods was a separated flow producing a wake

downstream from each rod or wire. Had the velocities been decreased

separation would have become less pronounced as is well known from the

fundamentals of fluid mechanics. At extremely low velocity the flow

would have even remained attached. It is well known that in the case of

a cylinder complete attachment of' the flow requires a cylinder Reynolds

number on the order ,of about 1.0. That Reynolds number is defined as

vn/ v , where V is the approach flow veloai ty, ]) is the cylinder diameter

and v is the kinematic viscosity. The Reynolds numbers for the flow

around the wires and rods of a Johnson screen at through-screen velooities

from 0.1 to 0., ft/sec would be on the order of 2, to ,00, well above

the range of fully attached flows. The flow regime through a Johnson

screen in the velocity range from 0.1 to 0., ft/sec can therefore be

Screen No. a b

(in) (in)

1 0.930 3/8

2 0·930 1/2

3 0.930 3/8

4 0.348 3/8

5 0.848 3/8

6 0.930 2nnn

TABLE 5. Theoretical Headloss Coefficient of Screen Panels at 0<. = 900 (without Reynolds number effect).

Estimated Values b a C C 0 e -

b+o e ow cr

(in) (in)

(

0.128 1 0.746 0.930 0.85 0.92

0.128 1 0.796 0.930 0.85 0.92

0.128 1 0.746 0.930 0.85 0.92

0.128 0.5 0.746 0.696 0.95 1.00

0.128 1 0.746 0.848 0.85 1.00

0.075 1 0·513 0.930 0.80 0.92

k' = [ .. be8b+cb -1J cw cr

d-. \N

0.7 I·',

0.5

0.7

1 .. 0

0.7

2.8

'Screen No. a b

(in) (in)

1 0·930 3/8

3 0.930 3/8

4 0.348 3/8

5 0.848 3/8

6 0.930 2mm

I .

TABLE 6. Theoretical Headloss Coefficients of Screen Panels at 0<: = 600 (without Reynolds number effect)

Estimated Values b a C Cor c e -b+o e cw

(in) (in)

0.128 1 0.746 0·930 0.75 0.92

0.128 1 0.746 0.930 0.75 0 .. 92

0.128 0·5 0.746 0.696 0.85 1.00

0.128 1 0.746 0.848 0.75 1.00

0.075 1 0.513 0.930 0.78 0·92

k' ~ [ e(b+c) -f ab C C cwcr

1.2 .0'\ +:-I·'

1.2

1.6

1.2

3·7

Screen No •. a

(in) ,

1 0.930

3 0.930

4 0.348

5 0.848

TABLE 7. Theoretical Headloss Coefficients of Screen Panels at fJ = 750 (without Reynolds number effect.

Estimated Values

b b a °ow °or 0 e - -b+o e

(in) (in) (in)

3/8 0.128 1 0.746 0·930 0.85 0·90

3/8 0.128 1 0.746 0.930 0.85 0.90

3/8 0.128 0.5 0.746 0.696 0.95 1.00 .

3/8 0.128 1 0.746 0.848 0.85 1.00

[ e{lH-o) -1Y kT = ab O. O' ow or

'0 .• 8

0.8

1.1 ~

\.n.

1

0.7

Li; ...... ., t_ ",1? ' .. '-- W.;;;"" ., •.. ! ..... 'O' ".' "'!' .:.~""'~~;"C".-.: ... ,:',.,-.,' .,"'.".,,-.,.,,,,,..~~._,',":.,"~""'7;_.:-:·~:'~ .. :' .. ,,..r;.............,~~.':' . .. ,.... ,_ ... ,~= ..... C.--=-.~"',.,., .. '" •. ,H._:~

T.AJ3LE 8. Theoretioal. Headloss Coeffioients of Soreen Panels at (3 = 60 0 (without Reynolds number effeot).

~

- 67 -

expeoted to be in the transition range between :fully attaohed and :fully

turbulent. In t~t range the headloss ooeffioients'are likely to var,y

with Reynolds number. An indioation of suoh variations is already shown

in Figs. 9 through 15. As the Reynolds numbers in those figures are . ', .. ,' .. lowered by a .faotor of 'two or more, the variations are likely to oontinue.

Headlosses through the Johnson soreens at low approaoh flow velooities

are small. For oomparison with other losses in the Campbell intake system

an upper bound for the soreen headlosses oan be speoified using Figs. 16 through

22. Sinoe the maximum through-soreen velooity is 0.5 ft/seo, headloss t~unds will be given for that velooity only. The approaoh flow velooity will be

oaloulated by multiplioation of the through-screen velooity (0.5 ft/seo) with

the open area peroentage given in Table 1. The upper bound of the headloss

will be estimated as the arithmetio mean of the following two values; one

deterndned from the ourve shown on Figs. 16 through 22(b) and the other read

on a straight-line oonneotion from the o;t'igin of eaoh graph to the nearest

data pOint. Eaoh value is read at the approach flow velooity shown in Table 9. The first reading is the best graphioal extrapolation from the given data, and

. ,

the seoond reading would be obtained if the flow were fully laminar between

~ero velooity and the last data point.

x. Conolusions

Readlosses experienoed by the flow of water through six Johnson

soreens of different geomet~~es (see Table 1 and Figs. 1 and 2) have been

measured and'analy~ed. Measurements were made at approaoh flow velooities

from 0.9 to 2.5 ft/sec. The measurements were made in a 24 inch wide

laboratory c~el. The soreens were plaoed at angles of 90°, 75°, 600

and45() relative to theohannelaxis. The objeotive of the experiments

was to establish the order of magnitude of the headless to determine if

it could be ignored in the design of the James Ro' Campbell oooling water

intake risers. The flow rates in the ol~el were varied to ohange the approach flow velooity.

The headloss data were reduoed to headloss ooeffioients, using the

approaoh flow velooity head as a referenoe and plotted versus a mesh,Reynolds

l"\ - 68 -

T.AJ3LE 9 I ,

~ ,

t Upper Bound for Soreen Headloss at a Through-Soreen Velooity f of 0.5 ft/seo at 75°F Water Temperature I, I: Upper' p

Panel Opening Approaoh Orientation Bound (,

Ii No. Ratio Velooity a {3 Headloaa

r (%) (ft/seo) (ft) t ~:.

90° 900 I' 1,3,5 74.5 .37 .002 r 4 74.5 .37 90° 90° .003 Ii 6 $1.3 .26 90° 90° .008 t 6 $1.3 .26 7$° 90° .008 r f

1,,3,$ 74.5 .37 60° 90° .004 " 4 74.5 .37 60° 900 .006 ",

r 6 $1.3 .26 60° 90° .008 1;;: 1,,3,5 74.$ ·37 4$° 90° .006 1"

4 74.$ 4$° 90° .008 .37 6 $1.3 .26 4$° 90° .008

1 74.$ • 37 90° 7$° .003 3,5 74.5 .37 90° 7$° .003 4 74.5 .37 90° 75° .004

1 74.5 .37 90° 60° .006 I;, 3 74.$ • .37 90° 60° .00$ ~" 4 74.$ .37 90° 60° .00$ I}

$ 74.5 .37 90° 60° .004

f ~ 74.$ .37 90° 4$° .016 3 74.5 .37 90° 45° .008

:\ 4 74.5 .37 90° 45° .013 5 74.5 .37 90° 45° .007 6 51.3 .26 ' 90° 45° .015

L ~ .

. t 1 , t I 1 I f··.·····.···.·.·.··."·,,.··· .'

- 69

number (Figs. 9a,through 15). The dependenoe of the ooefficients on

Reynolds number in the data range is not verJr strong. The coeffioients

.tend to deorease somewhat as the B.eynolds numbers are lowered suggesting

that the flow regime through the soreen may be in the transition to

fully develop turbulent flow. The trend of lowered headloss ooeffioients

at lower Reynolds numbers is oonsistent for all angles of .. a1nvestigated,

(a is the angle between the ohannel bottom and the soreen faoes, see

Fig. 4), but not for all angles of f3 (f3 is the angle between the ohannel wall and the screen faoe, see Fig. 4).

When ~ is less than 900 it was observed that the flow is deflected

by the rods and reoriented towards the ohannel wall. The resulting impaot

. (momentum loss) probably affeots the measured headloss. It appears also

that at ~ = poo, the effeot of flow oonoentration between wires beoomes

less important than the length of the rod in determining the headloss.

Because the design flow velooity in the James H. Campbell oooling

water intake is muoh less than the velocity used in the experiments desoribed

herein, a set of oharts was prepared (Figs. 16a through 22e) in which head­

loss is plotted versus approaoh flow velooity for water temperatures of

320 F &1d 75°F. Between the last data point and the origin (zero headloss

at zero velooity) the ourves are interpolated. These graphs show that at

low approaoh flow velocities the headloss through the Johnson soreens is

verJr small. Upper limits for soreen headloss at 0.5ft/seo through screen

velooity have been estimated in Table 9. Summarizing the results in Table 9, it oan be stated. that at ,0.5 ft/seo through-soreen velooity and at angles

of approaoh from 600 to 900 (for both a or (3) the headloss through a clean

screen will not exoeed 0.008 ft or one-tenth of an inch of water for all

six soreens investigated,inoluding one with a 2 rom. opening between wires.

At an angle of approach of 450 it oould be up to two-tenths of an inch of

water. It should be pointed out, however, that the measurements at f3 = 450

screen inolination are prob~bly the least reliable beoause of the wall

effects in the laboratorJr flume.

A oomparison of the experimental results with separated flow theorJr

over blunt objeots shows that headloss ooefficients increased as open

area fraction of the screen decreased, pretty much as predicted by theorJr.

Purely theoretical headloss prediction for screens is, however, not advisable

because it requires verJr precise estimates of flowoontraotion ooefficients.

Such ooeffioients are usually pot available in the literature for the

,

t I

t f

I t ~ I I l. I I

I I

f , t v • r f

t I l X

l I

·I··~.· .. ~ .... -. .

- 70 -

variety of geometrioal oonfigurations and flow oonditions enoountered

for oommercial sc~eens.

All results presented are for olean soreens only. Debris aooumulated

on a soreen panel was removed prior to every measurement.

I t I !

t

-71 -

REFERENCES

(1) ph~1Uical Engineers Handbook, Section 5, by John Perry, Robert H. Perry, Cecil H. Chilton, and Sidney D. Kirkpatrick, McGraw­Hill Book Co., Inc., 1963.

(2) Handbook of Hydraulic Resistance! Coefficients of Local Resistance and of Friction,Section 8, by i. E. Idel'Chik, translation from Russian. Published for the U.S. Atomic Energy Commission and the National Science Foundation, available from National Technical Information Service, AEC-TR-6630.

(3) Internal Flow: A Guide to Losses in Pipe and Duct Systems, by Donald s. Miller, published by British Hydromechanics Research Association, Cranfield, Bedford, England, 1971, 329 pp.

(4) MacDougall, "Loss Coefficients of Duct Geometries, Nozzles, Orifices, Perforations, Grids, and Screens", Program 5014, Project 1-2104A, Donaldson Co., Inc., Dec. 1974.

(5) Cornell, W. G., "Losses in Flow Normal to Plane Screens", Transactions of the American Society of Mechanical Engineers, Vol. 80, May 1978, pp. 791-799.

(6) Wieghardt, K. E. G., liOn the Resistance of Screens", The Aeronautical Quarterly, Vol. 4, Feb. 1953, pp. 186-192.

(7) Engineering Hydraulics, Chapt. I, 'Section C, edited by H. Rouse, John Wiley and Sons, 1949, 1039 pp.