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26
\ ( \· ' - H 0 - 9'2. HYDRAULICS BRANCH OFFICIAL FILE COPY HYDRAULIC LABORATORY . -- - - --- -.. - . . ·- ICE EION BY A-LI G CO by Thos G. an

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Page 1: H 0-9'2. - usbr.gov

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HYDRAULICS BRANCH OFFICIAL FILE COPY

HYDRAULIC LABORATORY . --=- - - --=---- - .. =-- . . ·-

ICE PREVENI'ION BY THE AIR-LIFT SYsrEM Kr GRAND COULEE

by Thomas G. OWan

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ICE PRETurJTION BY THE AIR-LIFT SYSTEM AT GRAND COULEE

Laboratory· Investi�ations Disclose Problems Encountered in Desi�ning Orifices for the Air-Lift Ioe�Prevention

System for the Grand Coulee Dam, Colum.bia Basin Project, Washingyon

by Thomas G. Owen Assistant Hydraulic Engineer, Bureau of Reclamation, Denver, Colo.

ABSTRACT

A laboratory study of the orifices for the air-lift de-icing

system at Grand Coulee Dam was made which embraces testing of sin­

gle- and multiple-hole arrangements of orifices of the short-tube

type, the diverging-tube type, and various combinations of both.

Flow patterns were studied with these various orifices discharg­

ing upward, horizontally, and drnmward. Special attention was de­

voted to the freezing phenomenon and rules for designing a satis­

factory nonfreezing orifiqe have been proposed. An orifice was

developed which gave a satisfactory balance between flow pattern,

economy of operation, and nonfreezing characteristics.

The formation of ice in front of the trashracks and drum

gates of Grand Coulee Dam will be both detrimental to good opera­

tion and dangerous to the structure. Temperatures of -28° F. and

of several days duration have been recorded at the dam site. The

problem confronting the designing engineers was to develop a sys­

tem whereby the reservoir surface immediately adjacent to the up­

stream face of the dam could be maintained free of ice. Many

methods of aooomplishing this result were studied but discarded

Page 3: H 0-9'2. - usbr.gov

in favor of the air-lift system because of its simplicity. In

the air-lift system compressed air is forced into the reservoir

adjacent to the structure at a depth at which the water temper­

ature is at or near that corresponding to maximum density. The

stirring and mixing action of the rising air induces the upward

flow of relatively warm currents of water., which either melt the

ice or prevents its formation.

A typical plan and section of the proposed location of the

orifices in front of one trashrack and in front of one drum gate

is shovm in figure 1. Provision is made to introduce air at

three different elevations in front of the trashracks and at two

separate levels in front of the drum gates. This feature allovrn

air to be introduced at a depth equal to or greater than 10 feet,

which has been found to be the minimum depth for best results.,

regardless of the reservoir elevation.

The problems of determining the best size., shape., and direc­

tion of discharge of the orifice and the cooling effect due to

expansion of the air at the orifice exit were studied in a 1 to 1

scale model in the hydraulic laboratory of the Bureau of Reclama­

tion in Denver., Colorado. The laboratory investigation was di­

vided into two parts: First, a preliminary examination of several

orifice designs; second., a detailed study concerning the cooling

effect due to expansion.

In the preliminary tests the equipment consisted of a glass-

2

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PART PLAN• MAIN UNIT TRASHRACK STRUCTURES

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TYPICAL SICl'l0NAL EL.£VATl0N-MAIN UNl1' TRASHRACK STRUCTURES � .,, . (I

TYPICAL SECTlc»IAL ELEVATION THROUGH DRUM-GATE SPILLWAY

Fla. 1 TRIOAL OBll'ICII LoOATioxa IN Faoin OI' TBABB-RAOK AND Da1JK-G.A.T11 SPILLWAY STBuOTUBBa

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Page 5: H 0-9'2. - usbr.gov

sided tankj noar the bottom of which was located the orifice to

be tested. The orifice was connected with a high-pressure air

line and a throttling valve was placed in the line to control

the pressure. Air-line pressure at the orifice and static water

pressure at the orifice elevation were measured by mercury U­

tubes, and the difference between these two observed pressures

gave the differential pressure across the orifice.

In the experiments on orifices A, B, and c, the tests were

purely visual. The general details of these orifices are shown

in figure 2 and a typical flow pattern in figure 3. From these

tests it was determined that discharge directed vertically down­

ward gave the best flow pattern, the criterion being the largest

cross-sectional area of the rising air current and the fineness

of division of the air bubbles, It was observed further that an

orifice of type C gave a better pattern than type B, which had

the same cross-sectional area.

After these initial tests, a gas meter of the displacement

type was installed to obtain the discharge characteristics of the

various orifices. The flow pattern of orifice D was found to be

good but its discharge was too low to establish a strong upward

water current. Orifice F produced a good flow pattern and also

a good upward circulation of water. The orifices thus far tested

had only one hole. The multiple-hole nozzles were then examined.

This group embraces orifices F1, H, I, and J (figure 2). The

4

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DISCHARGE IN CUBIC FEET OF FREE AIR PER MINUTE AT GALLERY CONDITIONS: 50"F., 28.811 IN.

A. PRESSURE-DISCHARGE CURVES BASED ON AVERAGE STATIC WATER HEAO ON ORIFICE OF 1.987 POUNDS PER SQUARE INCH ANO AVERAGE LABORATORY BAROMETER OF 12.142 POUNDS PER SQUARE INCH

,

GRAND COULEE DE-ICING EXPERIMENTS

PRESSURE-DISCHARGE CURVES AND ORIFICE DETAILS

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T.G.O. 10·17·39

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I ANDJ Note: For orifice I, D=o.100•

For orifice J, D=0.081"

B. ORIFICE DETAILS

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Page 7: H 0-9'2. - usbr.gov

Figure 3 - Typical vertical discharge flow pattern at 3 pounds per square inch differential pressure (orifice c).

6

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flow pattern from nozzle H was no better than F, and the water

current it established was inferior. Nozzles F1, I, and J all

gave excellent flow patterns and induced strong water currents

but the discharge capacity of each was excessive. It was thought

that if the diameters of the holes in these three nozzles were

reduced to lower their discharge capacity, the holes would then

be so small that they might easily become fouled or plugged by

foreign matter.

For the detailed investigation a special tan.1<: was construct­

ed and equipped with instruments. The tank was made 12 feet deep

so that at least 10 feet of static waterhead could be imposed on

the orifice. Inside the tank about 54 feet of 3/4-inch copper

pipe was placed in coils at the end of which was located the ori­

fice to be tested. In one side of the tank and at the elevation

of the orifice a piezometer opening and a resistance thermometer

bulb were located. Located in the same side of the tank at two­

foot intervals vertically above the thermometer bulb at the ori­

fice level were five other thermometer bulbs to determine the

temperature gradient during testing. These details are shown in

figure 4-A. The resistance thermometers were connected through

a selector switch to a Wheatstone bridge and the resistance bal­

ance was indicated by a very sensitive light-beam galvanometer.

The temperature of the air before entering the copper coils was

·measured by resistance thermometer No. 9, and the air temperature

7

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TG.0. 10-12-39

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A. DETAILS OF DE-ICING EQUIPMENT

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EXPLANATION

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TEMPERATURE IN DEGREES F.

B. TEMPERATURE GRADIENT CURVES, TEST: GIC·II

GRAND COULEE DE· ICING E)5PERIMENTS

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32 34 36 38 40 TEMPERATURE IN DEGREES F.

C. TEMPERATURE GRADIENT CURVES, TEST: GIC-12

DETAILS OF APPARATUS AND TEMPERATURE GRADIENT CURVES

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Page 10: H 0-9'2. - usbr.gov

before expansion through the orifice, by thermometer bulb No. s.

Attempts were made to measure the temperature of the air stream

issuing from the orifice by using a small resistance thermometer

bulb and also by a thermocouple. However, because of the oscil­

lation of the air jet and the vibration of the thermocouple it

was thought that neither the resistance thermometer nor the ther­

mocouple was continuously surrounded by air alone and hence the

indicated temperatures were unreliable.

Insulating material was placed between the inner and outer

tank walls which were separated by 2- by 6-inch studding. The

bottom of the tank was insulated and the top was equipped with a

close-fitting removable cover, also insulated. The air pressure

was controlled by a system of three valves (figure 5) so arranged

that variations in the supply-line pressure would be minimized.

The humidity of the air from the supply line was increased by pass­

ing the air through the humidifier, consisting of two atomizers

which sprayed water on two porous baffles. Mechanically entrained

water was removed by a system of three solid baffles (figure 5),

From the humidifier the air passed through the air rotameter, a

device for measuring rate of flow. The air rotameter (figure 5)

consists of an accurately machined glass tube tapered to increase

in bore from bottom to top. A spinning metal rotor floats in the

air stream and its position, read on a scale on the glass tube,

indicates the amount of air flowing. Just above the rotameter, a

9

Page 11: H 0-9'2. - usbr.gov

Figure 5 - Humidifying and air-metering apparatus.

10

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Bourdon-type pressure gage was located• For more accurate air­

pressure measurements, a mercury manometer was used. For visual

observation and photographic recording, two 9¼- by 9¼-inch glass

windows were located on opposite sides of the tank at the orifice

level.

Before starting a test, the tank was charged with about

11200 pounds of ice in pieces of about 25 pounds each. The ini­

tial temperature gradient as indicated by thermometer bulbs Nos.

1 to 6, inclusive (figure 4-A) was recorded. Figure 4-B shows

typical temperature gradient curves. The static waterhead on

the orifice was recorded and then the air flow was started.

Water and air temperatures.,

air pressure, and the quantity of

air discharged was observed• The differential pressure across

the orifice was progressively increased by increments of about

one pound per square inch until the orifice froze or until the

pressure limit of the apparatus was attained•

The preliminary tests indicated that orifice F had the most

desirable properties. A check calibration was !fl.D.de on this ori­

fice in the new model as sho�m on the pressure-discharge curve

plotted in figure 6. Tests on the cooling effect due to expan­

sion of the air indicated that the orifice would freeze solidly,

forming a cone of ice in the tapered exit when the air tempera­

ture before expansion was 32.38 ° F. and the differential pressure

was 5.4 pounds per square inch.

11

Page 13: H 0-9'2. - usbr.gov

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ORIFICE F

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ORIFICE T1

,· i 0-.. r-f I I �ft ORIFICE T2

3" u 0·,-, re-f II -t�r ORIFICE T3

EXPLANATION o Orifice F 6 Orifice T,

x------- Orifice T,, &------e Orifice r, * o-----� Orifice 7j* Air-line humidity unchanged in these tests. In all others the air was artificially saturated.

I 2 3 4 5 6 7 8 9 DISCHARGE IN CUBIC FEET OF FREE AIR PER MINUTE AT GALLERY CONDITIONS: !5O °,28.6!5 IN.

GRAND COULEE DE-ICING EXPERIMENTS

PRESSURE-DISCHARGE CURVES

,.,,

Page 14: H 0-9'2. - usbr.gov

As an alternative design ., orifice T1 was built. It is the

same in every detail as orifice F except that its initial diam­

eter is 3/32 inch instead of 1/8 inch, which makes its area rough­

ly half that of orifice F. The calibration curve for this ori­

fice is shown in figure 6. Temperature tests were made but the

range of air temperature before expansion was too high to cause

freezing. The highest differential pressure during the test was

17. 54 pounds per square inch., and the air temperature before ex­

pansion was 35. 39° F. No further temperature tests were made on

this orifioe.

Orifice T2 was tested because it was believed it would have

a lesser tendency to freez� than an orifice having a tapered exit,

such as F or T1• The general dimensions and calibration curve

are shovm in figure 6., and figure 8 shows orifice T2 during a

freezing cycle.

Orifice T3 is a short tube similar to T2, having its length

equal to three diameters (figure 6). Its area., however, is ap.­

proxiroately half that of T2• The calibration curve for this ori­

fice is shovm in figure 6. At this point in the test program it

was decided to adopt orifice T2 so no further temperature inves­

tigations were conducted on T3•

From data on the freezing tharacteristics of orifice T2 a

"critical freezing curve" was constructed by plotting air temper­

ature before expansion against differential pressure (figure 7-A).

13

Page 15: H 0-9'2. - usbr.gov

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DIFFERENTIAL PRESSURE ACROSS ORIFICE, POUNDS PER SQUARE INCH

A. CRITICAL FREEZING CURVE FOR ORIFICE "Ti"

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B. SECTION ON l OF ORIFICE "Ti"

GRAND COULEE DE-ICING EXPERIMENTS

CRITICAL FREEZING CURVE AND FLOW DIAGRAM FOR ORIFICE ·�·

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Page 16: H 0-9'2. - usbr.gov

This curve passes through the points which lie furthermost to

the left and upwards. Thus, it divides the temperature-pressure

plane into two regions : one region lying upward and to the left

of the curve, in which no combination of initial air temperature

and differential pressure will cause freezing; the other lying

dovmward and to the right of the curve, in which all combinations

of initial temperature and pressure result in ice formation in

the orifice . Ice formation in the orifice is a function of at

least the differential pressure across the orifice, the air tem­

perature before expansion, and temperature of the surrounding

water; but since the air temperature before expansion is, in

turn, a function of the temperature of the surrounding water,

the initial air temperature was chosen as one of the coordinates

for the freezing curve. In one test the air temperature before

entering the cooling coils was purposely raised about 90 degrees

(F. ) higher than in other tests, but the temperature before ex­

pansion was found to be about the same as in other tests. This

indicates that the air temperature before expansion will be sen­

sibly the same as that of the surrounding medium, regardless of

its initial temperature.

The critical freezing curve ( figure 7-A) does not give all

the data in regard to the freezing of orifice T2• While it gives

the combinations of initial air tem:r:;e rature and differential pres­

sure at which freezing starts, it doos not indicate the degree or

15

Page 17: H 0-9'2. - usbr.gov

seriousness of freezing. In the range of initial air tempera­

tures up to about 33° F • ., it was observed that it was possible

to have the orifice freeze solidly at points lying on the criti­

cal freezing curve. However, these instances were exceptions

rather than the usual result; generally ice would start to form

in the orifice, partially fill it, and then be removed by the

passing air. In order to obtain quick freezing and ice cones

( such as shown in figure 8 ) the differential pressure was in­

creased to 19. 25 pounds per square inch. In the range of initial

air temperature lying above 33° F., freezing of the orifice was

not such a serious factor within the differential pressure range

tested• The start of freezing in the range above 33° F. became

progressively more and more difficult to detect by visual obser­

vation of the jet as the differential pressure necessary to pro­

duce freezing increased, until in the vicinity of 10 or 11 pounds

per square inch it could only be detected by the instruments.

When the mercury manometer., indicating the air-line gage pres­

sure., showed an increase in pressure , and when the rota.meter

showed concurrently a decrease in discharge, it was definitely

established that freezing had started. In the region of tempera­

ture lying above 33° F. , it was observed that the duration of the

decreased discharge due to ice formation in the orifice became

shorter as the values of temperature and differential pressure

necessary to cause freezing became greater. Clearing of the ori-

16

Page 18: H 0-9'2. - usbr.gov

I-' -.:J A. Unobstructed flow prior

to ice formation. B. Deflected and r estricted

�low due to ice formation. c. Large dense i ce oone com­

pletely restricts flow.

Figure 8 - Orifice Tz discharging at 1 9 . 2 5 pounds per square inch differential pressure; air temperature before expansion was 32.37° Fe Thermocouple is seen immediately below orifice .

Page 19: H 0-9'2. - usbr.gov

fice was manifested by a sudden increase in di scharge and decrease

in differential pressure.

In attempting to explain the phenomenon of ice formation in

the orifices, the f ollowing interpretation is offered. A theoret­

ical analysis was made for expansion of saturated air through ori­

fice T2, taking the actual values of initial and final pressure

and initial air temperature found in one test. The expansion was

considered adiabatic and account was taken of the variation of the

specific heat o f the saturated air with temperature, and of the

heat of vaporization and heat of fusion given to the mixture by

the moisture which condensed and froze. Thus, by approximation,

the final temperature of the gas mixture was obtained, and found

to be about 2. 34° F. This analysis has taken no c onsideration of

heat transfer from the orifice to the gas mixture although there

must have been some. It will be remembered that this set of

values of pressure and initial temperature constituted one point

on the critical freezing curve, which means that freezing of the

orifice just started under these conditions. The theoretical

final temperature of 2.34° F. is far below the freezing point

and it is difficult to conceive that the orifice whose tempera-

ture cannot be greater than that of the surrounding water (32.48 ° F. )

could raise the air temperature to such a point that freezing just

starts under these conditions. Another question rising from a

study of the freezing phenomenon is how frozen moisture particles

18

Page 20: H 0-9'2. - usbr.gov

can stick to the walls of the o rifice when moving at such a high

velocity, approximately 525 feet per second or 358 miles per hour

for orifice T2 at a differential pressure of 6e 01 pounds per

square inch• A solution which would satisfactorily explain both

of these points is proposed and reference will be made to figure

7-B. The mixture of air and water vapor at pressure P1 expands

through the orifice to pressure P2 following the approximate

streamlines as shown in the figure. From point "a" to point "b"

the jet contracts, passes through the vena contracta, and then ex­

pands a gain following the walls of the orifice between points "b"

and "c" . The cold air cools the wall s of the orifice between

points "b " and "c" to some temperature ·which is higher than that

of the air and lower than that of the water surrounding the ori­

fice. As the saturated air expands the temperature drops, result­

ing in moisture being removed from the air by condensation. The

resulting fluid is then a mixture of moisture particles and satu­

rated air, the air temperature being below freezing. It is c on­

ceivable that the particles of moisture do not freeze instantly

because there must be a heat transfer before freezing can occur,

and therefore, because of the high velocity through the orifice,

it could be possible that unfrozen moisture particles could come

in contact with the walls of the orifice between points 11b 11 and

"c" • It will be remembered from studies of refrigeration that a

moist finger will stick instantly to a metal surface when that

19

Page 21: H 0-9'2. - usbr.gov

surface is at a temperature of 15 degrees F. or lower. (This is

known as the "stick test. 11 ) If the walls of the orifice were at

15° F. , then the moisture particles would stick instantly upon

contact and freezing of the orifice would start. This hypothesis

would satisfy both the question of low air temperature and that

of the high air velocity. It is of interest to note that for the

one point on the critical freezing curve for which the theoretical

final air temperature was computed and found to be 2 . 34° F • ., the

average of this final air temperature and that of the surrounding

water is exactly 15° F., which is the highest temperature at which

the "stick test 11 will occur•

By extending this reasoning further it can be explained why

freezing is more serious (that is, the orifice may freeze solid­

ly) when it occurs with the temperature of the surrounding water

in the region of 320 to 330 F. The orifices tested in the labo­

ratory were made of wrought iron and lead. The thermal conduc­

tivity at 64° Fe is 20.1 for lead., and 34. 9 for wrought iron. 1

For ice, the thermal conductivity1 is given as l e 26. This means

1 Marks ' Handbook, Third Edition., First Printing, Tables 1 and 3 .,

PP• 396- 39 71 McGraw-Hill Co • ., N. Ye

that a temperature gradient plotted from the surrounding water ,

through the metal forming the orifioe and to the inside wall can

be of a relatively flat slope, but from the inside wall through

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the ice to the cold air stream the temperature gradient has rela­

tively a very steep slope. Therefore, when freezing of the ori­

fice starts with the temperature of the surrounding water in the

region of 32° to 33° F. , the temperature of the inside wall of

the orifice can conceivably remain below the melting point, the

bond betvreen metal and ice remain unbroken, and the freezing proc­

ess continue on to ultimate restriction of air flow. VVhereas,

with a higher temperature of the surrounding water the freezing

of the orifice may start, but as the ice deposit increases in

thickness the temperature of the inside wall of the orifice rises

until the melting point is reached, the bond between th e ice and

metal is broken, the flow-restricting ice deposit is removed, and

complete freezing of the orifice is prevented.

From this investigation it was concluded that :

( a) The direction of discharge vertically downward from the

orifice gave a superior flow pattern.

(b) An orifice with an 18-degree tapered exit similar to type

F gave the best flow pattern of al l single-hole ·cypes tested.

The multiple-hole types were at once abandoned because of the

high discharge capacity or because of danger of becoming plugged

if the diameter of the holes were decreased so that the discharge

would be equ ivalent to the single-hole type.

( c) A discharge of two cubic feet of free air per minute at a

differential pressure of two pounds per square inch is sufficient

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to induce a strong upward water current. This value for discharge

is also consistent with practical limits of compressor size re ...

quired for the Grand Coulee air de-icing system.

(d ) An orifice of the short-tube type (T2 ) was found to be

somewhat superior to the type represented by orifice F as far as

freezing is concerned; its flov1r pattern was not materially worse,

and its discharge characteristics about the same. Therefore, this

orifice was adopted for use in the Grand Coulee de-icing system.

(e ) v1/hen freezing in the orifice occurs with the initial air

temperature and surrounding water temperature in the range of 32 °

to 33° F. , the orifi ce may freeze completely thus stopping the

air flow. lfo complete freezing was observed in the tests when

the temperatures of the air end surrounding water were above 33°

Fe and the differential pressure was ��thin the range available

with the laboratory apparatus. Hovrever., complete freezing may be

possible at higher differential pressures.

(f ) Freezing of the orifice is a function of the initial air

temperature., the differential pressure1 the type of orifice., the

temperature of the surrounding water., the thickness of the ori­

fi ce walls, and the thermal conductivity of the material of which

the orifice is �ade• ( It is presupposed that the air used has a

sufficiently high initial humidity that moisture will be condensed

during expansion. )

1Nhere the danger of freezing is imminent, a sharp-edged ori-

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fice should be used. If1 however, an orifice of the short-tube

type is used because of its superior flow pattern, the freezing

hazard may be decreased by making the operating differential pres­

sure small, the walls of the tube as thin as possible and of a ma­

terial of high thermal conductivity such as copper .

The hydraulic laboratory in which these studies were made is

directed by J. E. Warnock, Engineer, and is a section of the mate­

rials, testing, and control division, supervised by R. F. Blanks

and Arthur Ruettgers, Senior Engineers, in the Denver office of

the Bureau of Reclamation. Design studies and investigations are

made under the direction of J. L. Savage, Chief Designing Engineer ,

s . O, Harper is Chief Engineer for the Bureau, and J. c . Page is

Commissioner of Reclamation.

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(

(

the results were very so.ti sfac tory and materially s trengthen the case

for the reliabili ty of model tests . Tho results arc shown in de tai l

on Figs . 49 to 60 .

Comparisonn of the water levols for tho vari ous flows wi th

the crest gates down arc shown on Fi6s . 49 and 50 . Thoso show very

closo acroo�onts of tho wator surface levels , oxcept for a rise in

' tho surface whi ch s0oms to exis t in tho 1 : 20 modol noar the downstream

and . The caune of this is not apparent and un1'ortunatoly time was not

avai lable :tm:r to study i t in more detai l .

Loil[:;i tudinal profilos of coIIl!)arable condi tions on the 1 : 20 and 1 : 60

codols wi th crest gatos rai sed to various hoights is shown on Figs . 51

and 53 . Cross soctiona of t!1O water pri sm in tho channel for tho same

condi tions aro shown on Figs . 52 , 54 and 55 . T:ho 1 : 100 modol had no

movable gatos , and thoroforo i t .-,as not inc luded in this s tudy . Tho

agreement in th".3so ca ses , was also �ood . Tho riso previously montionod

appoars in these also .

On Fig . 56 i a shown a compari son of tho '7ator surface for the

same di schargo �1 th catos at vari ous e lovationa , on each model acparato­

ly. As previ ously explained , the a&;roomcnt of tho lines on a gi von modol

indicates tho reliabi li ty of tho assumption usually used in side channol

spillnay design that the entire energy of tho ovori'a.lling wator is dis­

sipntod wi thout causi � lonei tudinal flow in tho spi llw�y channel.

Tho pressures actill€ on tho weir and in tho aide channel , as

shown by tho piozomctric observations on tho 1 : 20 and 1 : 60 models aro

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shown on Figs . 57 to 60 . Considerine the difficulties of obtaining

consistent piezometric readincs where high veloc i ties and impacts are

involved , the results are very consistent and comparable . In general

they show the same pressure concentrations and reductions as the

observations previously described on tho M-3 model . The pressures on

the weir and on the drum gates will be discussed in moro dotail in

Book 4 , of this report .

J'inal Gate Operating Program

A comparison of the action of the three gate operating pro­

grams studied in dotail is shown on Platos 117 and 122 . Tho simi larity

of action i s shown by tho closo agromnont of tho water surfaces in all

cases , both in tho longi tudinal profiles of mean water surface shown

on Figure 61 and tho croso sections shown on Figure 62 . Tho only point

at which the surface lovols differ approciably is at Statio� 4 + 25 for

the 90 ,000 soc . ft . di schargo . In this caso tho �tor surface for tho

program adopted rises somewhat higher than wi th tho two other schemes .

This is not bel ieved to be inportant or cspocially Wldosirable .

Flow in tho Spillway Transition Secti ons

Tho soction of tho oido channel spillways in which the change

was mado from tho trapezoidal sec tion of tho s ide channel to tho c ircu­

lar section of tho tunnel , roforrod to in . this roport as tho " transi­

tion , " was a transition sec tion not only from tho standpoint of tho

shapo � tho channel but also from tho standpoi nt of diroc tion of flow ,

30