air-water flow in hydraulic structures' engineering ... · so mean air distribution function...

Attachment

"Air-Water Flow in Hydraulic Structures"Engineering Monograph No. 41

United States Department of the InteriorWater and Power Resources Service

A WATER RESOURCES TECHNICAL PUBLICATION

ENGINEERING MONOGRAPH NO. 41

AMR-WATER FLOW INHYDRAULIC STRUCTURES

UNITED STATES DEPARTMENTOF THE INTERIORWATER AND POWER RESOURCES SERVICE

MS 430 (8.78)Bairau of Reclanatton TECHNICAL REPORT STANDARD TITLE PAGE

E. REPORT NO. N * A 3. RECIPIENT'S CATALOG NO.

Engineering Monograph No. 4I'-- ,,; -'4. TITLE AND SUBTITLE S. REPORT DATE

Air-Water Flow in Hydraulic Structures December 19806. PERFORMING ORGANIZATION CODE

7. AUTHOR(S) S. PERFORMING ORGANIZATION

Henry T. Falvey REPORT NO.Engineering Monograph No. 4.

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. WORK UNIT NO.

Water and Power Resources ServiceEngineering and Research Center Il. CONTRACT OR GRANT NO.

PO Box 25007Denver, Colorado 80225 13. TYPE OF REPORT AND PERIOD

COVERnEC12. SPONSORING AGENCY NAME AND ADDRESS

Same

14. SPONSORING AGENCY CODE

IS. SUPPLEMENTARY NOTES

16. ABSTRACT

The purpose of this report is to summarize the work that has been completed on air-entrainment and air-demand in both open- and closed-conduit flows. The intent was toproduce a concise reference source from which design manuals, monographs, and chartsfor specific applications could be prepared. Areas that need additional research havebeen identified. The report was prepared from available reference material. In severalareas, data from several references have been combined to produce generalized curves.Includes 64 figs., 74 ref,. 3 app., and 155 pp.

17. KEY WORDS AND DOCUMENT ANALYSIS

a. DESCRIPTORS-- / *air demand/ *air entrainment/ *open channels/ *closed con-duits/ *design criteria! *air-water interfaces/ *shaft spillway/ air bubbles/ aeration/vents/ vacuum breakers/ relief valves/ jet aerodynamics

b. IDENTIFIERS--

c. COSATI Field/Group 1300 COWRR: 1407'5. DISTRIBUTION STATEMENT IS. SECURITY CLASS 1. NO. OF PAGES

Available from the Notional Technical Information Service. Operations (THIS REPORT} 155Division. Springfield. Virginia 22161. U CLASSIFIED 2. PRICE

(THIS PAGE)UNCLASSIFIED

A WATER RESOURCES TECHNICAL PUBLICATIONEngineering Monograph No. 41

AIR-WATER FLOW INHYDRAULICSTRUCTURES

By Henry T. FalveyEngineering and Research CenterDenver, Colorado 80225

United States Department of the InteriorWater and Power Resources Service

( � I'm

FRONTISPIECE.-High velocity jet from a slide gate. P801-D-79275

As the Nation's principal conservation agency, the Department of theInterior has the responsibility for most of our nationally owned publiclands and natural resources, protecting our fish and wildlife, preserving theenvironmental and cultural values of our national parks and historicalplaces, and providing for the enjoyment of life through outdoor recreation.T7ze Department assesses our energy and mineral interests of all ourpeople. The Department also has a major responsibility for AmericanIndian reservation communities and for people who live in IslandTerritories under U.S. administration.

ENGINEERING MONOGRAPHS are published in limited editions for thetechnical staff of the Water and Power Resources Service and interestedtechnical circles in Government and private agencies. Their purpose is torecord developments, innovations, and progress in the engineering and scien-tific techniques and practices which are used in the planning, design, con-struction, and operation of water and power structures and equipment.

First Printing 1980

H

U.S. GOVERNMENT PRINTING OFFICEDENVER, COLORADO

For Sulee by the SWelintendent ao Docurente. US. Government Printing Offce.Washington. D.C. JW02. or the Water and Power Resources Service, Attention 922,

P.O. Box 25007. Denver. Colorado 80225.

Preface

The material assembled in this report is the result of studies extending overmany years by a large number of engineers. Ellis Picket at the U.S. ArmyEngineer Waterways Experiment Station in Vicksburg, Mississippi, supplieda reference fist dealing with air-water problems. Personnel of the Water andPower Resources Service E&R Center, Water Conveyance Branch madetheir files and drawing on air design criteria in pipelines available for publica-tion in this report. Prior to publication, the report was reviewed by EllisPickett and Ted Albrecht with the U.S. Army Engineers; and by engineers inthe Dams, Mechanical, and Water Conveyance Branches, E&R Center,Water and Power Resources Service. The many constructive comments bythese individuals and the assistance of Richard Walters who provided con-tinuity and technical editing is greatly appreciated.

V

Letter Symbols and Quantities

Symbol Quantity Symbol Quantity

A Cross sectional area of water prismA . Cross sectional area of airflow

passageA, Cross sectional area of air core in a

vertical shaftAd Cross sectional area of conduitA, Orifice areaAP Cross sectional area of penstockAU Cross sectional area of vent

a Ratio of bubble terminal velocity inturbulent flow to terminal velocityin still water

so Mean air distribution functionaI Mean air distribution constantB Width of rectangular chuteb Width of flow channel

be Nappe widthb, Empirical coefficient accounting for

sand grain roughnessC Air concentration

C, Actual air concentrationCb Drag coefficient on a bubbleCd Discharge coefficient based on 100

percent gate openingCf Local loss coefficientCl Air concentration at dt/2

Cm Air concentration measured by apitot tube sampler

C. Orifice discharge coefficientC, Drag coefficient on a sphereC, Air concentration at the bottom of

the mixing zoneC Mean air concentration

c Waterhammer wave celerityD Conduit diameter

Db Smaller dimension of a rectangularconduit

Dd Diameter of water dropDe Equivalent bubble diameterD, Larger dimension of a rectangular

conduit

d Flow depthdb Bulked flow depthde Deflector heightd. Nappe thicknessdo Orifice diameterd, Total depth of underlying and air

free zonesds Bubble diameter for which 95

percent of the air, by volume, iscontained in bubbles of thisdiameter or smaller

E Relative width of the frequencyspectrum

exp Napierian logarithm equal to2.71828, approximately

f Darcy-Weisbach friction factorG Gate opening

Gg Mass velocity of gasG, Mass velocity of liquidg Gravitational constant (acceleration)

H Hydraulic radius of prototype airvent

Hf Fall height of a water jetH.,, Head across orificeH. Net head across turbineH. Distance from channel invert to

energy grade lineH, Total potential and kinetic energy

h Mean wave heighth. Height of airflow passagehf Distance from inlet to the water

level in the vertical shafth, Head loss per unit length

hm Head across manometerh,,, Allowable head rise in penstockK. Entrance lossK, Singular (form) loss

k Von Karman universal constantequal to 0.4

kr Coefficient of roughnessk, Sand grain roughness

vi

LETTER SYMBOLS and QUANTITIES-Continued


L Length of conduit or ventL, Distance to start of self-aerationL, Prototype to model scale ratioL, Distance between stiffener ringsM Unit mass

M 0 Maximum difference in elevationbetween a wave crest and themean water level

m Air concentration distributioncoefficient

N Safety factorn Manning's roughness coefficient

n, Velocity distribution power-lawcoefficient

P Energy dissipatedPg Normal distribution functionPh Probability that the wave height is

equal to given heightPw Probability that the water surface

is equal to or greater than thegiven elevation

p Pressure intensityps Allowable internal pressure

Pa m Atmospheric pressurePc Collapse pressure

pin Internal pressurepn Nappe perimeterQ Discharge

Q. Volume flowrate of airQ, Critical dischargeQr Discharge from reservoir

Q. Volume flowrate of waterq Unit discharge

q& Insufflation rate of air per unitsurface area

R Bubble radiusRb Equivalent bubble radiusR, Radius of curvature of the bubble

capR, Thickness of annular jet

r Water jet radius

r, Relative roughness of conduit(rugosity to diameter ratio)

S Submergence depthSO Pipe slopeSf Slope of energy grade lines Root-mean-square value of wave

height distributionSu, Root-mean-square value of water

surface distributionT Top width of flow passaget Pipe wall thickness

U Free stream velocityUd Velocity of water drop relative to

air velocityU, Water jet velocityu Local air velocityV Mean flow velocityVI Terminal velocity of bubbles

in turbulent flowV Nappe velocity at impact

Vm Minimum velocity required toentrain air

V. Maximum water surface velocityV Terminal velocity of bubbles in

slug flowV Terminal velocity of bubbles in

still waterW Wetted perimeterx Distance from start of boundary

layer growthy Distance normal to channel bottom

(flow depth)y, Distance from water surfaceye Conjugate depthye Effective depthYk Critical depthy' Normal distance to the bottom of

the mixing zonez Elevation

vii

LETTER SYMBOLS and QUANTITIES-Continued


alpha Angle chute invert makeswith horizontal

1 beta Ratio of volumetric airflowrate to waterflow rate

y gamma Specific force of waterd delta Boundary layer thicknessE epsilon Mass transfer coefficient

of bubbles. zeta Air concentration

distribution constantt eta Normalized wave height6 theta Void fraction

x kappa Gas constantA lambda Density ratioJ* mu Dynamic viscosityA Dynamic viscosity of air

Pu, Dynamic viscosity of waterv nu Kinematic viscosityVI Water viscosityw pi Ratio of the circumference

of any circle to itsradius, 3.14159...

Q rho DensityQa Air density

ewO Water densityQg Gas densityel Liquid density

em Density of manometer fluida sigma Interfacial surface tensionTo tau Wall shear stressTi Shear stress at water jet

t .,,m upsilon Specific volume of air atatmospheric pressure

Shear velocityW psi Multicomponent flow

parameterw omega Volume of gas bubbleCO& Volume of aircW Volume of water

E EdtvUs number

Et, Euler number

F Froude number

P Prandtl velocityratio

PIl Poiseuille number

R Reynolds number

fIt Distance Reynoldsnumber

W Weber number

- YD 2

a

(gDI"12

= ha2 (dp/dX)2tcV

- VDv

VxvI

- vla/eDJ"2

Infinity

viii

Contents

PagePr e f a ce...................................................... vLetter Symbols and Quantities ................................. viIntroduction .1....... ..... ... IPurpose and Applications . .................................... 3Summary and Conclusions .................................... 5,Open Channel Flow ........................................... 7

Introduction .............................................. 7Bubble Dynamics ......................................... 8

Terminal Velocity of a Single Bubble in Still Water ........ . 8Bubble Size in Shear Flows ........... .. ................ 10Terminal Velocity of Bubbles in Turbulent Flow ......... .. 12

Vertical and Longitudinal Flow Structure ......... ............ 14Design Parameters ........................................ 16

Location of Beginning of Aeration .......... .............. 16Location of Fully Aerated Flow ........... ............... 19Air Concentration Profiles ............. ................. 19

Definition of concentration ........... ............... 19Air distribution in the mixing zon3 ...... . . ........... 21Air distribution in the underlying zone ...... .......... 22Mean air concentration .......... ................... 24

Water Surface Location .............. .................. 28Effect of Air Entrainment Flow on Stilling Basin

Performance. . 36Closed Conduit Flow ........................................... 37

Classification of Flow ...................................... 37Flow in Partially Filled Conduits ............. ................ 41

Model Predictions ..................................... 41Air vent not designed .............. ................. 42Air vent designed ............... ................... 44

Analytic Estimates ..................................... 44Flow Having a Hydraulic Jump That Fills the Conduit ... ....... 48Flows From Control Devices .............. .................. 51

Flows From Valves .................................... 52Flows From Gates ..................................... 54

Falling Water Surface ...................................... 54Air Vent Design Criteria for Closed Conduits ................. .. 57

Purpose. . 57Location ............................................. 57Maximum Airflow Rate .............. .................. 57Structural Considerations ............................... 57Physiological Effects ................ ................... 57Safety of Personnel ..................................... 59

ix

CONTENTS-Continued

PageFreeze Protection ...................................... 59Cavitation Damage . ................................... 59Water Column Separation ............ .................. 59

Air Vent Design Criteria for Pipelines ......... ................ 60Introduction .......................................... 60Gravity Systems ....................................... 61

Vertical alinement criteria .......... ................ 61Horizontal alinement criteria ......... ............... 62Vent location ..................................... 62

Pumping Systems ..................................... 65Vent Structure Design Considerations ........ ............ 65

Evacuation of air during filling ............. ........ 65Removal of air during operation ........ ............. 66Prevent pipe collapse during draining ....... .......... 69

Flows in Vertical Shafts .................................... 77Classification of Airflows .............. ................. 77Region I Airflow Rates ............... .................. 79Region II Airflow Rates ............... ................. 80Reverse Airflow in a Vertical Shaft ........ ............... 80Submergence ......................................... 80

Free Failing Water Jets ....................................... 81Jet Characteristics ......................................... 81Airflow Around the Jet ..................................... 82Air Entraining Characteristics as a Falling Jet Enters a Pool ...... 83

Bibliography ................................................ 87Appedix .................................................. 93

I ProbabilityDepth Probe ............. .................. 95II Mean Air Concentration, Free Surface Flow,

Computer Program .............. .................. 97III Air Demand, Falling Water Surface, Computer Program... 113

Introduction...................................... 113junction Energy Equations ......................... 113Turbine Characteristics ............................ 115Geometry ................................. 118

x

CONTENTS-Continued

FIGURESNumber Page

1 Forms of air-entrainment on a spillway ....... .............. 92 Large gas bubble in a liquid .......... .................... 103 Terminal velocity of air bubbles in filtered or distilled water

as a function of bubble size, Haberman and Morton 126. 1 14 Terminal velocity of bubbles in turbulent flow ...... ......... 135 Structure of open channel flow, Killen and Anderson 142] ..... 146 Air entraining flow regimes in open channel flow ..... ........ 157 Experimentally determined local loss coefficient

Cf, Bormann [111 ............. ...................... 188 Location of inception of air entrainment ....... ............. 209 Cumulative Gaussian probability and measured air

concentration distributions in the mixing zone ..... ...... 2210 Actual air concentration distribution in mixing zone ..... ..... 2311 Air concentration distributions of channel flow on steep

slopes Straub and Anderson [661 ....................... 2412 Interfacial tension .................. ..................... 2613 Air entrainment coefficient .......... ..................... 2914 Air entrainment in open channel flow ....... ............... 3015 Examples of air entrainment in chutes ....................... 3116 Definitions of aerated flow depth ........ .................. 3217 Relation of aerated to nonaerated flow depth ...... .......... 3418 Probability density distribution for different values of the

width of the energy spectrum ......... ................ 3519 Probability description of water surface in a chute ..... ....... 3620 Flow patterns in horizontal pipes, Baker [7] ...... ........... 3821 Flow pattern sketches, Alves [I] ........................... 3922. Effect of conduit diameter on terminal velocity of a

bubble, Collins [161 ................................. 4023 Influence of air pressure in conduit on airflow rate, Sikora 1651. 4124 Model tests on a spillway, Sikora [651 ........ .............. 4325 Discharge coefficients for orifice at end of pipe ...... ......... 4526 Airflow above water surface ........... ................... 4727 Air entrainment with hydraulic jump closing conduit ..... .... 4928 Forces on a stationary bubble ........... .................. 5029 Bubble motion in closed conduits flowing full ...... .......... 5130 Slug flow in inclined pipes, Runge, and Wallis 1611 . .......... 5231 Valve and gate data, Kohler [441 ......... ................. 5332 Airflow rate for two 1375-nun fixed-cone

(Howell-Bunger) valves ............ .................. 5533 Falling water surface ............... ..................... 5634 Comparison of field data with computer prediction ..... ...... 5835 Air vent, Shadow Mountain Dam,

Colorado-Big Thompson Project, Colorado ..... ........ 60

xi

CONTENTS-Continued

FIGURES-ContinuedNumber Page

36 Pipeline configurations .................................. 6137 Plan and profile of a gravity pipeline ....... ................ 6238 Vent structure .......................................... 6339 Typical irrigation system air valve installation ...... ......... 6440 Vent location at changes in pipe slope ....... ............... 6541 Air binding in a pipeline ............. ..................... 6642 Large-orifice air valve ........... I ........................ 6743 Performance curves for large-orifice air release valves ..... .... 6844 Typical small-orifice air release valve ....... ................ 6945 Performance curves for smaD-orif ice air release valves ..... .... 7146 Typical frost protection installation ........ ................ 7247 Collapsing pressure of a steel pipe with stiffener rings ..... .... 7348 Performance curves for large-orifice vacuum relief valves ...... 7449 Specific volume and barometric pressure of air as a

function of elevation ............. .................... 7550 Required air relief orifice diameter to prevent collapse

of steel pipelines ................ .................... 7651 Observed air blowback in morning glory spillway at

Owyhee Dam, Oregon ........... .................... 7752 Typical types of vertical shaft inlet structures ...... .......... 7853 Vertical shaft spillway discharge characteristics ..... ......... 7854 Breakup of a water jet from a hollow-jet valve ...... ......... 8455 Water drop breakup ................. .................... 8556 Velocity distribution for flow over a flat plate, Bormann [111 ... 86

APPENDIXI-1 Electronics schematic ................. ................... 961-2 Probe schematic ........................................ 961-3 Controls in utility box ................. ................... 96

III-1 Definition sketch at penstock intake ....... ................ 114III-2 Typical turbine characteristics of runner specific speed 230 .... 116111-3 Turbine loss coefficient .............. .................... 117III-4 Air volume in penstock ............... .................... 118III-5 Water surface area . ...................................... 118

xii

Introduction

In many engineering projects a strong inter-action developes between the water flowingthrough a structure and the air which is adja-cent to the moving water. Sometimes the inter-action produces beneficial effects. However,more often than not, the effects are notbeneficial and the remedial action required toreduce the effects can be costly.

Cases in which air-water interaction developinclude:

• Open channels with fast flowing water thatrequire depths adequate to contain theair which is entrained within the water

* Morning-glory spillways that must have acapacity to convey the design flood andits entrained air

* Vertical shafts that entrain large quan-tit~es of air at small water discharges

* Measuring weirs that need adequate ven-tilation to prevent false readings and toeliminate surging

* Outlet gates that require adequate aerationto prevent the development of low pres-sures-which can lead to cavitationdamage

* Emergency gates at penstock entrancesthat require ventilation to prevent ex-cessive negative internal pressures duringdraining or emergency gate closures

* Sag pipes (inverted siphons)' that can bedamaged due to blowback of entrainedair

* Long pipelines that require air release andvacuum relief valves

From these cases it is noted that air-waterflows can be generalized into three basic flowtypes:

1. Air-water flows in open channels,2. Air-water flows in closed conduits, and3. Free-fall water flows.The first type usually is called air-entraining

flow because air is entrained into the watermass. The second basic flow type generally isreferred to as air-demand. The term air-demand is both misleading and technically in-correct, since an air vent does not demand airany more than an open valve demands water.However, since the term has been in commonuse for over 20 years, efforts to improve thenomenclature seem rather futile. The third typeis referred also to as air-entraining flow.

"'siphon, inverted-A pipe line crossing over a depressionor under a highway, railroad, canal, etc. The term is com-mon but inappropriate, as no siphonic action is involved.The suggested term, sag pipe, is very expressive and ap-propriate." Nomenclature for Hydraulics, Comm.on Hyd. Str., Hyd. Div., ASCE, 1962.

I

Purpose and Application

The purpose of this report is to summarize thework that has been done on air-entrainmentand air-demand regarding the most recenttheories and to suggest ways in which theresults can be applied to design. The intent wasto produce a concise reference of material fromwhich design manuals, nomographs, and chartsfor specific applications could be prepared.

Although many generalizations of the datacan be made, some types of flow conditions thatare encountered in practice can be treated onlyby individual studies with physical models.These cases are identified when they occur.

Additional studies are needed in many areas.Some of the most critical areas requiring fur-ther research include the following:

* Effects of turbulence and air concentrationon bubble dynamics

* Fluid dynamics in the developing aerationregime of free-surface flow

* Effects of hydraulic and conduit propertieson probabilistic description of water sur-face in free-surface, high-velocity flow

* Effect of pressure gradients on air flow inpartially-filled, closed conduits

* Bubble motion in closed-conduit flows forconduit slopes exceeding 45-degrees

* Effects of ambient pressure levels oncavitation characteristics of gates andvalves discharging into a closed conduit

* Interaction between the air and a free jet

3

Summary and Conclusions

Methods have been developed to predict themean air concentration and the concentrationdistribution with open channel flow. A newdescription of the free water surface in highvelocity flow is proposed which more accuratelyrepresents actual conditions in high velocityflow. The effect of air entrainment on the per-formance of a stilling basin can be estimatedusing a bulked flow concept. A computer pro-gram (app. II) is presented with which themean air concentration in steep chutes andspillways can be estimated.

With exception of a falling-water surface anddecreasing flow in pipelines, closed conduitflows require model studies. When properlyconducted and analyzed, model studies willyield accurate data for estimating air-flow

rates. Experimental methods are discussed. Acomputer program (app. III) is presentedwhich can be used to predict the airflow ratewith a falling-water surface. Design charts arepresented for sizing air relief valves andvacuum valves on pipelines.

The airflow rate in vertical shafts was foundto be extremely dependent upon the flow condi-tions at the shaft inlet. Equations are includedfor estimating the airflow rate having variousinlet conditions.

Factors influencing the airflow rate aroundfree falling jets are discussed. This area is iden-tified as one needing additional research. Equa-tions are presented from which the air entrain-ing characteristics of a jet entering a pool can beestimated.

5

Open Channel Flow

INTRODUCTION

In observing flow in a chute or on anoverflow spillway, one normally observes aregion of clear water where the water enters thechute or spillway. Then-at some distancedownstream-the water suddenly takes on amilky apperance. Lane 146] suggested that the"white water" begins when the turbulentboundary layer from the floor intersects thewater surface. The validity of this assumptionhas been verified by many researchers. Thecases in which the boundary layer creates theair entrainment are referred normally to as self-aerated flows. However, this is not the only wayin which air entrainment can begin on chutesand spillways. The American Society of CivilEngineers Task Committee on Air Entrain-ment in Open Channels 1512 has summarizedtests in which air entrainment is generated bythe boundary layer on the side walls of chutes.They also reported tests in which air entrain-ment was observed downstream of piers onoverflow spillways. This latter case is the resultof the flow rolling over on itself as it expandsafter passing through the opening between the

'Numbers in brackets refer to the bibliography.

piers. Levi [491 reported on longitudinal vor-tices on spillway faces. These vortices can en-train air if they intersect the water surface. Allof these forms of air entrainment are apparentin figure 1.

Air entrainment implies a process by whichair enters into a body of water. Normally, theappearance of "white water" is considered to besynonmous with entrainment. This is not al-ways true. For instance, if the water surface isrough enough and moving at a sufficiently highvelocity, the surface will appear to be whiteeven though the water volume contains no air.The whiteness of the water is caused by thelarge number of reflections coming from dif-ferent angles off the rapidly moving highly ir-regular surface (refer to frontispiece). For highwater velocities, one's eye does not respondrapidly enough to observe each individualreflection. Instead, these individual reflectionsblur into a fuzzy mass which appears white.High speed photography of "white water"demonstrates this effect very well. This leadsone to the obvious conclusion that a flow couldconceivably appear frothy but actually does notentrain any air! With air in the water, reflec-tions also come from the surface of the bubbles.These reflections produce the same impression

7

Closed Conduit Flow

CLASSIFICATION OF FLOW

The conventional term for the concurrentflow of air and water is two-phase flow. Here,phase refers to one of the states of matter (gas,liquid, or solid). Technically the term two-phase flow should be reserved to describe themotion of a substance which is present in two ofits phases, such as a flow of ice and water. Theword mukicomponent is a better description offlows which do not consist of the same chemicalsubstance, such as air and water. If both com-ponents move in the same direction, the flow istermed concurrent flow. If the componentsmove in opposite directions, the flow is counter-current.

Closed conduit flow can be classified accord-ing to the type of pattern that develops. Theflow patterns which develop depend upon theairflow rate relative to the waterflow rate andthe slope of the conduit. For example, the flow

patterns in horizontal conduits have been de-fined by Baker 171, (fig. 20). The correlationcan be applied to other gases and liquids bysubstituting appropriate quantities into thefollowing parameters:

Gg= mass velocity of gas, kg/(m2 s-)G.= mass velocity of liquid, kg/(m- s)

1=VeQg/QeAQie/Qw)1" 2

p=dynamic viscosity, Pa-sQg=gas density, kg/M3

Q8 =air density (at 101.3 kPa and20 OC)=1.20 kg/ms

e,=liquid density, kg/M3

Qe=water (at 101.3 kPa and20 C)=988 kg/m 3

o=interfacial surface tension, N/mo,,aw=air-water surface tension (at 101.3

kPa and 20 0 C)=0.0728 N/mwP = (Q e .Q' )Ij4Qz/Qe 21' 13, Pa's3 .8s/3

37

38 AIR-WATER FLOW IN HYDRAULIC STRUCTURES

100

I0

Spray

Wave Bubble

Strotified

Gel mass velocity of gasGL -mOss velocity of liquid Plugx -density ratio Plu*-multicomponent flow .poometer

l

n I0.01 0.1 lI to 100 1000

GL X\

Gg

FIGURE 20.-Flow pasterns in horizontal pipes, Baker (7).

These various flow patterns were describedby Alves [11 according to the physical ap-epearance of the flow as follows (fig. 21):

* Bubble flow.-The air forms in bubblesat the upper surface of the pipe. The bub-ble and water velocities are about equal. Ifthe bubbles are dispersed through thewater, the flow is called "froth flow."

* Plug flow.-For increased airflow ratesthe air bubbles coalesce with plugs of airand water alternately flowing along thetop of the pipe.

l Stratified flow.-A distinct horizontal in-terface separates the air and waterflows.

* Wave flow.-As the airflow rate is in-creased, surface waves appear on the strat-ified flow interface.

* Slug flow.-Wave amplitudes are largeenough to seal the conduit. The wave

forms a frothy slug where it touches theroof of the conduit. This slug travels witha higher velocity than the average liquidvelocity.

* Annular flow.-For greater airflow ratesthe water flows as a film on the wall of thepipe, while the air flows in a high-speedcore down the axis of the pipe.

* Spray flow.-For very great airflow ratesthe annular film is stripped from the pipewalls and is carried in the air as entraineddroplets.

A similar set of flow pattern descriptions ex-ist for vertical flows. They are:

* Bubble flow.-The air is distributed inthe water as spherical or spherical capbubbles which are small with respect tothe conduit diameter.

CLOSED CONDUIT FLOW3 39

* Slug flow.-As the air flow increases,alternate slugss of air and water move upthe pipe. The transition from bubble flowto slug flow is shown on figure 22. Thistransition occurs when the bubblediameter is about one-half the conduitdiameter.

If the vertical conduit is rectangular insteadof cylindrical, the appropriate relation for slugflow is given by Wallis 1731 as

-T(ot +. DbD. R 165)

whereD.=larger dimension of a rectangular

conduitDb=smaller dimension of a rectangular

conduitDe=bubble diameterV=terminal velocity of air bubbles in

slug flowt=terminal velocity of air bubbles in

still water

With respect to the flow quantities, Martin1521 found that the transition from bubbly toslug flow occurs at a void fraction somewherebetween 19 and 23 percent.

The void fraction 6 is the average volumetricconcentration in a length of pipe (assuminguniform flow) and expressed as

whereCow = volume of waterA= cross sectional area of conduitL =length of conduit over which the

volume cow is determined

Bubble

V -

Plug

Stratified

Wlave

- _, _ . _-

Slug

AnnularG= '-

AL(66)

'It is not clear whether the term slug refers to a slug of airor a dug of water. The air bubble could be called a slugdue to its bullet or slug shaped fonr. The water could becalled a slug due to its similarity in form to the terrestrialgastropod in horizontal flows or due to its impact proper-ties in vertical flow. The author prefers the reference toslugs of air. FIGURE 21.-Flow pattern sketches, Alves 1).

40 AIR-WATER FLOW IN HYDIIAULIC STRUCTURES

1.2

1.1

> 1.0

so

mU 0.8

o 0.7

0.6

0j 0.5

>0.4> OAILO

7- 0.3

-I 0.2

0.1

RELATIVE DIAMETER OF SLUG d/D

FIGURE 22.-Effect of conduit diameter on terminal velocity of a bubble, Collins 1161.

* Froth flow.-As the airflow increases,the slugs break up into a turbulentdisordered pattern of air and water.

The annular and spray flow patterns areidentical in both vertical and horizontal pipes.

In hydraulic structures, the conduits mayalso be placed on a slope. The additional com-plexities in the flow patterns caused by slopewill be discussed later.

From a designer's viewpoint, air-water flowsin closed conduits can be classified into fourgeneral categories. Each category may containonly one or a combination of the flow patternsenumerated previously. These categories are:

1. Flow in partially filled conduits,

2. Flow having a hydraulic jump that fills theconduit,

3. Flow from control devices, and4. Falling water surface.Each category listed above is considered in

detail in the following subsections.In addition to the four categories of flow, two

others are considered separately. These are:* Flow in pipelines and siphons* Flow in vertical shaftsThe pipelines and siphons require special

consideration because of their length. Verticalshafts present special problems because of thevarious types of flow which can exist in theshaft.

CLOSED CONDUIT FLOW 41

FLOW IN PARTIALLY FILLEDCONDUITS

Model Predictions

Flow in a partially filled conduit can bethought of as open-channel flow in a closed con-duit. The air flows through the passage which isformed above the water surface.

The total volume flow of air, which enters atthe upstream end of the air passage, equals thesum of the air that is insufflated into the flowand that which flows above the water surface asa result of the air-water shear forces. The quan-tity of air insufflated into the flow can beestimated from equation 59. The quantity of airthat flows above the water surface is a functionof the waterflow properties and the pressuredrop in the air vent. This can be expressed as

The interrelation between these parameterscan be found for a specific geometry throughthe use of model studies.

There are many literature references that in-dicate model predictions often underestimate inthe quantity of air which actually flows in pro-totype structures. However, very careful modeltests in which all air- and waterflow passageswere modeled in their entirety have shown goodagreement between model and prototypemeasurements.

For instance, Sikora [651 showed that the air-flow rates could be accurately predicted frommodel studies. His tests were with threegeometrically similar models having scales of1:1, 1:2, and 1:4 (fig. 23). The pressure valueson the figure refer to the difference between at-mospheric pressure and the air pressure at theupstream end of the waterflow passage.

QU=fL, V, g, p, ye, Qw) (67)

whereA = cross sectional area of water prismg=gravitional constant (acceleration)L =conduit lengthp=pressure intensity

Qa=total airflow rateT=top width of flow passageV=mean water velocity

y,=effective depth=A/TQe,=water density

Applying dimensional analysis to equation 67with ye, V, and ew as the repeating variablesgives

| a

aCYIt

I-

3:0

Iii

ki I

0:

o {(L 1 p/y X

Q. X F P/2g

FROUDE NUMBER OF FLOW F= V

0(68)

whereF=Froude number

Q= waterflow ratey =specific force of water

FIGURE 23.-Influence of air pressure in conduit in air-flow rate, Sikora 165).

Harshbarger, Vigander, and Hecker .1321conducted 1:20 scale model and prototype testsof a gated tunnel discharge. Free-surface flow


existed in the tunnel for all discharges. A scaleeffect was not detectable in their investigations.

These studies clearly indicate that forestimating airflow rates using models, it isnecessary to accurately reproduce the entireairflow passage above the water surface. Inthose cases where air enters the water conduitthrough a vent, two options are available formeasuring the airflow rates. The options de-pend upon whether or not the air vent has beendesigned.

Air vent not designed.-If the air vent designhas not been determined, it is necessary tomeasure the airflow rate while controlling theair pressure at the upstream end of the waterconduit. These tests must be performed for aseries of flow depths and flow rates in the waterconduit.

The upstream air pressures can be controlledby incorporating an air pump into the airflowmeasuring device. To be applicable for allpossible designs, the pressure should be variedover the maximum possible range. The lowestend of the range corresponds with the conditionof no airflow through the vent. The upper endof the range is achieved when the upstream airpressure is equal to the atmospheric pressure.

A good example of this procedure is the workby Sikora [651 who developed a set of curves forthe airflow in the horizontal leg of morning-glory spillway (fig. 24).

Once the family of curves for the airflow rateshas been experimentally determined it is possi-ble to investigate the effect of adding varioussize air vents to the structure. This is done byfirst developing an expression for the air ventcharacteristics in terms of the dimensionlessparameters on figure 24.

For air velocities less than 100 m/s andvalues of fL1/411 4, the volume flowrate Q.through a vent can be expressed as

Qa (69)'e ./weQa (patm/Y)-(Pi/y)+lz(QeaQ.ue

whereA,,=cross sectional area of vent

f=Darcy-Weisbach friction factorg=gravitational constant (acceleration)

H= hydraulic radius of prototype air ventK.=entrance lossK,= singular (form) loss in vent, the

greatest of which is the entrance lossK.=O.5

L =vent lengthpi= pressure at vent exit

Patm = atmospheric pressureAz=difference between vent intake and

vent exit elevationsy=specific force of water

Q.=air densityQ.= water density

Volume flowrate of water can be expressed as

Q,,v [2g (!! ] 1 (70)

whereA =cross sectional area of water prismV=mean waterflow velocity in conduit

Using these two expressions, the dimen-sionless airflow rate fl can be expressed as

R= Q-Q. (71)A, i Q./Q. r(Pstu/y1-(P3/y 11J2

= 7jyK4+fL/ HL P /2 Ja

when Az -is negligible.Qw

The first ratio inside the brackets is a func-tion of the fluid properties, the singular losses,and the flow geometry. The second ratio is inthe form of a pressure factor or Euler number.By using this equation, the characteristics of agiven vent can be plotted on the dimensionlessairflow curves (rig. 24). The intersection points

CLOSED CONDUIT FLOW4 43

AAd

deFUp

pApQo

OwVYe

=

cross sectional area of water prismcross sectional area of conduitdeflector heightFroude number- v--Yair densitygravitational constantpressure at end of air ventpressure drop across ventvolume flowrate of airvolume flowrate of watermean flow velocityeffective depth

Fydraulic jump withsubmerged flowS Outlet submerged

'-,.----Outlet submerged

8 9 10 11 12 13

FROUDE NUMBER OF FLOW F-I

FIGURE 24.-Model tests on a apllway, Sikora 1651.


of the two sets of curves gives the pressures andairflow rates for a given set of air ventparameters. If the resulting values are notsatisfactory, another set of vent characteristicsis chosen and the process repeated.

Air vent designed.-For some studies thedesign of the air vent is available. In these casesit is necessary to calculate the total loss for thevent and to simulate this loss in the model airvent. The loss for the prototype and the modelmust include both frictional and form losses.Normally, the air vent velocities are kept lowenough so that incompressible loss coefficientsare valid. The model air vent is simulated cor-rectly when the loss coefficients in the modeland prototype vents are made equal. If devicessuch as nozzles or orifices are installed into themodel air vent for flow measurement purposes,the loss across them must be included in com-puting the total model air vent loss coefficient.In the case of an orifice, its loss coefficient oftenconstitutes the entire loss for the model air vent.It is possible to express the required orifice sizeas

Analytic Estimates

In many instances, model tests for predictingthe airflow rates have not been performed. Forthese cases, the airflow rates often can beestimated closely enough by an approximatemethod. For this estimation three rather grossassumptions must be made, namely:

1. The amount of air flowing through thevent is a function of only the air insuf-flated into the flow and the air that is in-duced to flow by the moving water bound-ary,

2. The amount of air insufflated into theflow can be predicted by open channelflow equations, and

3. The air motion above the water surface isdetermined solely by the boundary layer dthickness at the most downstream conduitlocation.

These assumptions neglect the fact that airactually can enter from the downstream end ofthe conduit. Schlichting [631 showed that withCouette-Poiseufile6 flow in the larninar region,a flow reversal occurs when

AV172J Po= i o_-_ (73)

CaL43(1 +XK.+/L/4H) 11

whereA00=orifice areaAV= prototype air vent areaC.=orifice discharge coefficient

f=Darcy-Weisbach factor for prototypeair vent

H=hydraulic radius of prototype air ventK, =singular losses (including entrance,

bends, and changes in area)L=length of prototype air vent

L,=prototype to model scale ratio

If the orifice is placed on the end of themodel air vent pipe, its discharge coefficient isobtained from figure 25.

'The dimensionless parameter P. Is known as thePoisle number. Its primary use is in the laminar fluidfriction field. For example, in a round circular pipe, thePoiseuille number is equal to 32. In this ease the pipediameter is substituted for the height of the airflowpassage in equation 73. Couette flow exists between twoparallel walls when one wall is moving and the other isstationary. The motion is due solely to the shear fieldcreated by the relative movement of the two walls. Couetteflow has no pressure gradient In the direction of flow.Couette-Poiseulile flow describes a Couette type flow hav-ing a longitudinal pressure gradient. Turbulent Couette-Poiseuille flow should describe the air motion above amoving water surface in a closed conduit.


Ao=~

Hm=

conduit areaorifice areahead across orifice

Hm =hm(pm/po)

Q = volume flowrate of airPa = density of airpm= density of manometer fluid

Vena cont

Ad do

Ad D

racto --Hm

-F-

0

zw

ILw0

0

4%

kii

0

0 0.2 0.4 0.6 0.8 1.0

RELATIVE ORIFICE AREA °Ad

FIGURE 25.-Discharge coefficients for orifice at end of pipe.


whereha=height of airflow passage

dp/dx=pressure gradient in the airVO=maximum water surface velocityM=dynamic viscosity of air

Leutheusser and Chu [481 have investigatedCouette flow in the turbulent region. Insuf-ficient tests have been made to determine themagnitude of the dimensionless parameter P.for the turbulent Couette-Poiseuille flow.However, some laboratory tests indicate thatwith turbulence, reverse flow begins when

P.=-1000 (74)

The amount of air flowing above the watersurface can be visualized by considering aboundary layer which increases in thicknessfrom a value of zero at a gate, to a maximumvalue at the end of the conduit (fig. 26). Thegrowth of a turbulent boundary layer that is in-duced by a moving rough boundary has notbeen studied. As a first approximation it isassumed that

d=0.01x (75)

whered=boundary layer thicknessx=distance from gate

The velocity distribution within the bound-ary layer is assumed to obey a power law of theorder:

u=local air velocityV.=maximum water surface velocityya=distance from the water surfaced=boundary layer thickness

The value of the coefficient n,, varies between10 for flow over smooth surfaces to 5.4 for flowover rough surfaces when the Reynolds numberis about 106. Normally nR, is assumed to beequal to 7. This approach is similar to that usedby Campbell and Guyton 1121 except theyassumed the boundary layer always coincidedwith the roof of the conduit.

The boundary layer entrains the maximumamount of air at the extreme downstream loca-tion in the conduit. To maintain continuity,flow at upstream locations consists of boundarylayer flow plus some mean flow (fig. 26). Theair velocity at the water surface must be equalto the water velocity. Therefore, at theupstream locations, the air velocity above thewater surface may have a larger magnitudethan that at the water surface. Carefullaboratory experiments by Ghetti 1241 of theVaiont Dam (Italy) gated outlets show that themaximum air velocity near the water surface atthe vent can be as much as four times the watervelocity.

For some flow conditions the boundary layerwill reach the roof of the conduit. When thishappens the roof will begin to retard the flow.If the water surface and the roof of the conduithad equal roughness values, the maximum flowrate would be given by turbulent plane Couetteflow. For this case the maximum airflow rateQm is

U= V. (hi )

wheren,,=velocity distribution power law

coefficient

2(77)

(76)

whereA.= cross sectional area of airflow passage

(rectangular)V.= maximum water surface velocity


Volume flowrateof air, Qa

A. Profile sketch

Mean flow / u % I/rV

continuitySuperpositic

mean flow %boundary la,flow

t_ -

IBou.ndory A]layer flow -

in OT _ U( YaPvith iye X r

I Vo ..At ®

Boundary layer depth greaterthan f low passage depth

At (®

B. Velocity distribution

FIGURE 26.-Airkflow above water surface.

AIR-WATER FLOW IN HYDRAULIC STRUCTURES

Actually the roughness of the water surface isgreater than that of the conduit roof. This in-creased roughness will produce higher airvelocities near the water surface which result inairflow rates greater than those given by equa-tion 77. Sikora 1651 reasoned that the mean airvelocity could not exceed the mean watervelocity. This leads to the expression for themaximum possible airflow rate in a closed con-duit, which is

F= V(gy.1t /

480)

whereA = cross sectional area of water prismD=conduit diameterT=top width of flow

passage=2Jy1D-y)J l2

g=gravitational constant (acceleration)V=mean flow velocityy.=effective depth=A/Ty=flow depth(Q)0=Ad -1 (78)

whereAd= cross sectional area of conduitA = maximum cross sectional area of

water prism

Application of equation 78 without regard tothe boundary layer thickness will result in ex-cessively large values of the airflow rates.However, for design purposes, this approachmay be satisfactory since the resulting air ventwill be oversized.

FLOW HAVING A HYDRAULIC JUMPTHAT FILLS THE CONDUIT

Kalinske and Robertson 138J studied thespecial case of two-layer flow in which ahydraulic jump fills the conduit. From dimen-sional analysis and model studies, they deter-mined that the amount of air entrained by thejump is given by

Equation 79 is good only if all air entrained ispassed downstream. Prototype tests-for whicha hydraulic jump formed in the conduit and inwhich the conduit velocities were large enoughto convey all the entrained air out of the con-duit-confirm the experimentally derived curve(fig. 27).

If the conduit is horizontal or sloping upwardin the direction of flow then all the entrained airwill move with the flow. However, if the con-duit slopes downward in the direction of flowair bubbles can either move upstream or down-stream relative to the pipe wall.

The direction of movement taken by the bub-bles can be examined by considering therelative magnitudes of the buoyant and dragforces upon a stationary bubble in the flow (fig.28). For example, the bubble will move perpen-dicular to the pipe axis only when the upstreamcomponent of the buoyant force vector equalsthe drag force component. This can be writtenas

Q'=0.0066 (F-It )14Q C_,ne (79)(Qe, 6_. = Cb ' (R - (81)

where F=Froude number upstream of thehydraulic jump.

In a circular pipe the Froude number can becalculated conveniently from the flow depth yusig

whereCb=drag coefficient on bubbleD,=equivalent bubble diameter'S.=pipe slope=sin a

CLOSED CONDUIT FLOW 4'1

I I I lII II

/1.AInI1I

,v

- * Ikori Dam, Mura et al., [53) |- * Navajo Dam, WPRS, (not published)- A Pine Flat Dom, USCE, [71] (prototype)

*J.

/

If-

0I0

Ca

0qx

W.

0

-l

JUi.

hiI-

4-Iw

0.10

0.01

) _

%/ '

/ *SKalinske & Robertso n

/I

F-Froude numberV

V-meon velocityof water

g-gravitational constantye-effective depth

tests, [38] (model)

A#I - ________________________

7

I I I I II I_.___ | I I I I I IILaIs0 5.-...

10

FROUDE NUMBER OF FLOW, F-I

100

FIGURE 27.-Air entrainment uith hydraulic jump closing conduit.


diameter is a function of the interfacial surfacetension and the friction slope. In terms of di-mensionless parameters, the critical dischargerequired to move the bubbles can be expressedas

Q'2 =f ( r S1, S., cb) (84)

FIGURE 28.-Fortes on a atdonary bubble.

Rearranging terms and dividing by the con-duit diameter gives

D 4 D11-(egA RDCb) (82)gD 3 ~b

or

QDS -u D1-(eglew)] ReC; (831gD5 12 He)&

whereQ,=critical discharge needed to carry

bubbles with the flowD=conduit diameter

This relation shows that the critical dischargefor bubble motion is a function of the effectivebubble diameter D., the densities, Q, the dragcoefficient Cd of the bubble, and the pipe slopeS.. Unfortunately, the drag coefficient and ef-fective bubble diameter can not be predictedfor flow in a pipe. Therefore, the techniques ofdimensional analysis must be used to determinethe significant parameters for correlations.

As was shown under Design Parameters-Mean air concentration, the effective bubble

The parameter D is designated frequently0

as the Ebtvos number E.Kalinske and Bliss 137J found relatively good

correlations for the initiation of bubble move-ment by using only the pipe slope S. and theEbtvos number. Data by Colgate [151 also fitstheir curves relatively well (fig. 29).

Additional studies are required to define thebubble motion curve {fig. 29) for slopes greaterthan 45 degrees. Martin 1521 showed that a sta-tionary air pocket forms when the dimen-sionless discharge Q,,/gD5 is equal to 0.30 forvertically downward flow. Therefore, the in-creasing trend of the curve in, figure 29 pro-bably does not continue past the 45-degreeslope.

As the bubbles travel downstream in slopingconduits, they tend to rise to the top of the con-duit and form large pockets of air. Runge andWalis 1611 discovered that the rise velocity ofthese pockets is greater in sloping conduits thanit is in vertical conduits (fig. 30). For a specificrange of discharge, a flow condition can existwhereby bubbles will move downstream andform into pockets that move against the flow inan upstream direction.

Sailer 1621 investigated prototype cases inwhich large air pockets moved against the flowwith sufficient violence to completely destroyreinforced concrete platforms. The reverse flowregion has been delineated on figure 29 usingthe data of Colgate [15] and the dug-flow curveof figure 30. The five structures pointed out bySailer as having experienced blowbacks are in-dicated by crosses on figure 29. It Is noted that


wz110

ItWIIIL0-J0

DIMENSIONLESS FLOWRATE -Z9D

FIGURE 29.-Bubbe motion in closed conduits flaoing full.

two of these structures lie within the blowbackzone at design discharge. The other three mustpass through the blowback zone in coming upto the design discharge. For pipe slopes lessthan 0.1, the width of the blowback zone is sosmall that problems normally are not experi-enced.

FLOWS FROM CONTROL DEVICES

Flows from control devices refer to cases inwhich the primary cause of the air demand isdue to the waterflow conditions at a controldevice. Two types of flow control devices thatwill be considered are gates and valves. These

devices also induce air movement in open chan-nel flows. However, in unconfined flows thewater movement does not cause low pressureswhich must be relieved by air vents.

A distinction is made in the field of hydraulicmachinery between valves and gates eventhough both serve as flow control in a closedconduit. A valve is a device in which thecontrolling element is located within the flow(fig. 31). A gate is a device in which the con-trolling element is out of the flow when it is notcontrolling and which moves transverse to theflow when controlling (fig. 31). The jets fromgates are different than those from valves;therefore, the two cases are consideredseparately.


Air pocket or slug

Vt=terminal velocitin still water

I.-

>-S-

0 .

_j >r

4 U.

hi

75 60 45 30ANGLE OF CONDUIT WITH HORIZONTAL a

FIGURE 30.-Slug flow in iznled pipe, Runge and W'lli 1611.

Flows From Valves

Around the beginning of the 20th century,many outlet valves were placed on or near theupstream faces of the dams. Nearly all wereseverely damaged by cavitation erosion. Since asatisfactory method could not be found toreduce or eliminate the damage at all gate posi-tions, the operating ranges of these valves wereseverely restricted. Because of this limitation,the location of the throttling valves was shiftedto the downstream side of the dam. Presentpractice is to avoid placement of throttlingvalves within the conduit. Nevertheless, fromtime to time it is necessary to place the valveswithin the conduits. This is especially truewhen the downstream conduit is a tunnel-when spray could cause icing problems-and when a flow control station is placed in apipeline.

If stratified or wave flow exists downstreamof the valve, air is induced to move by arelatively low water velocity acting over a largesurface area. However, if the flow from thevalve impinges on the downstream conduitwalls, the airflow is induced by high velocitywaterjet acting over a relatively small surfacearea. In this case, the significant airflowparameters are the:

.

6

S

Kinetic energy of the waterflow,Gate opening, andAir pressure at some characteristic loca-tion.

Parameters such as length of conduitdownstream of the valve and the Froudenumbers of the downstream flows are obviouslyof lesser importance.


F1 I tFied cone- ' Hydrculic cylider-' r'Condut - Needle

FIXED-CONEVALVE HOLLOW-JETVALVE NEEDLE VALVE

I seot

SLEEVE VALVENAME TUBE VALVE

ISxinum head lappeoinstel 309m 399tn 300 m 90s 75. m

Dlschargecoefficient (C 085 0.70 04ST6O.60 O.SToO355 0.t0

Suhmeegrdoperation Yea 11 No III No Yes Yes 111

7weottling limitations None Avoid very unall discharge Nonw None None

Spray Veryheuvy 12) Moderate Sfatl Moderate III None

Leakage None None None None None

Nonuinal aberange diameter Ihb 200 to 2740-mm 760- to 2740-mm 250 to 244 0 -

nmm 910-to2440-Pnm 310- to6f10-mm

Availability Coimercial tandard 131 SpecIal dlaigin Speciaadlgo Speaideslgn Special dealgn

Masntenancereqsired Paint Paint Paint III Paint Paint

COMMENTS AND NOTES: Ill Air-ventingrequired. Illumergnce toenterlineI)Uwateroperation utd. IISprayinhevestat I ) Valve is designed fore121 Spray rating will change af Valvo il permianible. Diraaeembly a3to5y ear openings of le than 35%. only in fully subaerged

elt Coefficients are approximate to moderate if a down- intervals to, removing At the larger openings the onditiona.and may vary mon at with stream hood is added, scale deposits in imually rating would be better i21 Larger aim seem feasible

specificdesigna. 31V VaVesrenot stoecx aneceyAly. than moderate. andwillprobablybeIb) Sin ranges shown are represent. iten but standard oem- developed.

stive. sad are nt limiting. m ecialdeigs arevailable.

SERVICECLASSFICATION THROMTLING GATES

Air vent Identical guord ; Hostt Holot AirSCHEMATICMDAGRAM la qte veonntHoisttStem . - --- Airvent J-on ut. dut

FLOWDIRECTION Srome 44 Con tC ~ n d w t -~ L e a f-t* Leof- ~ _ t Conduit; Fr teef1t w e

UNBONNETED BONNETEDSLIDEGATES

NAME SLIDEGATE "HIGNPRESSURE"TYPE STREAMLINEDTYPE JETFLOCGATE TtPSEALRADIAIGATE

Maximum hed (apprmnlnatel 25m 60m 159 re 50 60-75rn

Discharge cflermnt Wa O6ToO.9 e9s 0.97 9.90To.4.9 0.95

Submerged operation No No Yea Qll Yes IIl NO

Throttling limitations Avoid very smll discharge AvoId very small discsarge Avoid very smnll dineharge None None

Spray Minimum Ytintum Minimum Small Minimum,

Leakage Small Sen Stmall None Small to moderate

Nominna ie rang libj 3660-wide a 3660-mm high 1830-wide 2740-mm high 303-to 6100-mm high 250- to 3054-mms dim. 4570-wide a 914-mm high

Availability Commercialstandsrd 11l Specisl design Special design Special desgn Specd ldeaigu

Maintenance raquired Paint Paint Point 421 Paint Paint-saab 11

COMMENTS AND NOTES: Ull Gates ra readily avalable IlI Air vente requited Ill Air vent required Il1 Seal rephacenseat in 5-13from several commercIal 121 Useofstainleea steel am- years is probable depend-

taP Coeficients are approximate uaces. They re net - faced fluldwoys, will r- hill on desvin and use.

and may vary somewhat with -off-the-diel' Item. due paInting require-wpectl'mdesigna. however. ments and cavitation

lbI Size rangea shown an represent- damage haard.tIes, and aem t limitn

FIGURE 31.-Valve and gate data, Kohler (44).


Colgate [141 made model studies of airflowsin valves having a fixed-cone." His results weregiven in terms of gate opening and discharge.Transforming these values into the appropriatedimensionless parameters results in good cor-relations for all conditions that were tested(fig. 32). In this case, the kinetic energy of theflow is proportional to the total upstream head'.Thus

Q.=/ (G "'y 1t)85)

whereG=gate opening in percent

Ht=total potential and kinetic energy(upstream)

hp/Y=differential between atmosphericpressure and air pressure at end ofvent

Y=specific force of water

Once curves like those presented in figure 32are developed, it is possible to determine theairflow rates through any air vent that is con-nected to the structure by using equation 1711.To perform the determination, equation 71 isplotted on figure 31. The intersections of thetwo sets of curves give the airflow rates for anyparticular vent.

Flows From Gates

At small gate openings, a considerableamount of spray is produced by flow whichimpinges in gate slots. This spray induces con-siderably more air movement than that pro-duced by stratified or wave flow. In a sense, theeffect of spray in producing air movement issimilar to that of flow from valves. However,with spray the jet does not impinge on the walls

'The fred-cone valve is also called a Howell-1unger valveafter its inventors.

of the downstream conduit; therefore, a sealdoes not form.

The significant parameters for flow withspray are the same as those for flow fromvalves; i.e.,

* Gate opening,* A reference air pressure, and* The total upstream energy.Model studies can be used to obtain

estimates of the airflow rates which can be ex-pected when spray is present.

As the gate opening increases, the amount ofspray decreases. Typically, spray is not signifi-cant for openings greater than 10 or 20 percent.The exact percentage depends upon the designof the gate. For the larger openings, the airflowrate is controlled by the two-layer flow rela-tions. That is, the significant parameters are:

* Length of conduit,* Froude number of the flow, and* Air pressure at some reference location.For jet-flow gates a point is reached-as the

gate opening increases above some value-where the flow impinges on the downstreamconduit. Typically this occurs at a 50- to60-percent opening. With impinging flow, theairflow rate is correlated with the parametersused for flow from fixed-cone valves. For thistype of flow, the length to diameter ratio of theconduit is significant only if the downstreamconduit length is less than the distance to theimpingement point or if the adverse pressuregradient is large.

FALLING WATER SURFACE

A falling water surface in a closed conduit in-duces airflow in the conduit. This flow is ana-logous to that induced by a piston in a cylinder;the water corresponds to the piston. A typicalexample of this type of flow occurs during anemergency closure of the intake gate to apenstock (fig. 33). As the gate closes, waterflowing into the penstock from the reservoir is

CLOSED CONDUIT FLOW

g - gravitational conHt - total potential chm = head across manp - pressure Intensii

,, pin - internal pressure_0 - volume flowrate

> Ow . volume flowrateV mean flow velocr = specific force o

3.0- -- ___ _

Air v(

-2- mm fixeo m l ';valves 3.7m

Work /Deflector¢ plotform.

I 120(3000 mm

7300r

-j 1.0-Ia

nstantond kinetic energyometer

of airof waterItyof water

ent, 10,675 mm diameter

I

RELATIVE AIR PRESSURE AT VALVE t (Pin

FIGURE 32.-Arflow rate for two 1375mm fixed-cone (Hoaell-Bunger) valves.


AirfLy2

, W

a

Gate

through

Penstock-

PowerplantDraft tube-

a. ENERGY AND PIEZOMETRIC GRADE LINESIN PENSTOCK AND DRAFT TUBE

Entranca- 1i i vent

Loss aeross eEnergy grade linegate Piezometric gradle

t .line

Loss due to flow .entering from T-gate chombar . °

Gate chamber(gate closing)

o

b. ENERGY AND PIEZOMETRIC GRADE LINESAT INTAKE STRUCTURE

FIGURE 33.-Failng water surface.

CLOSED CONDUIT FLOW

gradually stopped. However, water in the pen-stock continues to flow through the turbine inthe powerplant. Eventually the gate becomesfully closed. For water to continue flowing fromthe penstock, air must be allowed to enter thesystem through a vent located just downstreamfrom the intake gate.

The airflow and waterflow relations-through the penstock and gate chamber-canbe simulated analytically by the appropriatemathematical model, Falvey [221. This model,based upon momentum and continuity equa-tions, yields the airflow rates, etc., as a functionof time.

With relatively long penstocks; i.e., length todiameter ratios exceeding 30, the maximumairflow rate occurs slightly after the emergencygate closes completely. The magnitude of theairflow rate is equal approximately to thepenstock discharge prior to the start of the gateclosure. These observations provide "rules ofthumb" which can be used for the design of theair vent structures on dams. The computer pro-gram presented in appendix III should be run ifa time history of the air-water flow relation isrequired or if shorter penstocks are being ana-lyzed. This program is a generalized version ofthe original program and includes typical tur-bine characteristics.

Good correlations have been found betweenthe computer model calculations and prototypemeasurements (fig. 34).

and its possible attendant damage. Conversely,air vents can permit air to escape from a struc-ture. In this case the purpose is to bleed airfrom a conduit prior to operation.

Location

The next step is to locate the vent properly.General rules cannot be delineated for all casesother than the vent usually is placed where thepressure in the conduit is the lowest. For in-stance, in gates the appropriate location isimmediately downstream of the gate (fig. 31B).For valves the air vent is upstream from thepoint where the water jet impinges on the con-duit walls (fig. 32). In some cases the locationmust be determined by intuition or carefullyconducted model studies.

Maximum Airflow Rate

After the vent is located, the maximumairflow rate through the vent must beestimated. This estimate should be based upona consideration of the various types of flowwhich are possible in the water conduit. Theprevious sections have presented in detail somemethods of estimating the maximum airflowrates for specific types of closed conduit flows.

Structural Considerations

AIR VENT DESIGN CRITERIA FORCLOSED CONDUITS

Purpose

The design of air vents for closed conduits re-quires careful consideration. The preliminarystep is to decide the purpose that the vent is toperform. For instance, air vents can permit airto enter a structure to prevent collapse or toprevent the formation of low pressures withinthe flowing water which could lead to cavitation

The pressure drop across the air vent causesa reduced pressure in the penstock and gatestructure. Each part of the structure which issubjected to reduced pressure should be ana-lyzed to determine if it will withstand the im-posed loads.

Physiological Effects

The effects of noise produced by high airvelocities as well as the structural integrity must


E

TIME, seconds

Z4.a-.

xI-0

E

Ur4

40hiox

0

*-0q

,g-

0 0

0 C

a-

TIME, seconds

Izc- Beginning of free watersurface f low in penstock

Water surface below I - _

go - -Invert of emergency gate -_

Turbine speed-no bacf.20 3 40 10 e0 70 10 90 100 tO 120 IslNO

4

a;,

TIME, seconds

TIME, seconds

FIGURE 34.-Comparison of field daa with computer prediction.


be considered in the design of air vents. Thelimiting air velocity-with respect to noise-ina vent has been established Iby the Water andPower Resources Service) to be about 30 m/s.Above this velocity an objectionable whistlingsound occurs. The intensity of the sound andnot its mere presence is the governing factor.For instance, ear protection is required for ex-posure times greater than eight hours andpressure levels above 85 dB (decibels) Beranekand Miller [9].s For pressure levels above 135dB, ear protection is required for any exposuretime.

Field measurements 5 meters from an airvent having an 80-m/s velocity produced soundlevel intensities of 105 dB. With this sound in-tensity, ear protection is required for exposuretimes exceeding 7 minutes. Since sound level in-tensities increase by the 6th to 8th power ofvelocity Davies and Williams 1191, a 200-mr/air velocity would have produced a sound levelintensity between 128 and 136 dB which isdamaging to the ears for any exposure time.Based upon this limited result, a 90-m/s flowvelocity appears to be a good value to use as adesign criterion for air vents that operate for ashort duration. If the air will flow through thevent for extended periods, the upper limit onthe air velocity should be restricted to the30-m/s value.

'Construction Safety Standards, Water and PowerResources Services, pp. 27-28, rev. 1979. The standardstates * * *. Protection against the effects of noise ex.posure shall be provided when the sound levels exceedthose shown below when measured on the A-scale of astandard Type II sound level meter at a slow response.

Duration per day, Sound teveL dBA,hours slow response

8 906 924 953 972 1001.5 1021 1050.5 1100.25 or less 115

Safety of Personnel

Another design consideration concerns thesafety of personnel in the vicinity of the ventwhen it is operating. Generally, personnel bar-riers should be placed around vents at locationswhere the air velocities exceed 15 m/s. This willprevent personnel and loose objects from beingswept either through the air vent or held on theair vent louvers.

Freeze Protection

In areas where the vents operate in coldweather for prolonged periods, the vents shouldbe protected from freezing. Icing occurs whensupercooled air passes through the louvers andscreens at the vent intake. In some cases icebuildup was sufficient to completely block theflow area (fig. 351. Icing protection includesusing heating elements on the louvers,rerouting the vent to place the intake in a warmportion of the structure, or redesign of the in-take to eliminate ice buildup areas.

Cavitation Damage

The pressure downstream of gates discharg-ing into conduits should be prevented frombecoming too low. If the pressure does drop ex-cessively, cavitation damage may result duringprolonged periods of operation. Unfortunately,general guidelines concerning minimum accept-able pressures cannot be given. Each gate orvalve design has its own particular characteris-tics. Some designs are more susceptible tocavitation damage than others. Researchstudies are needed to define minimum pressurevalues for the different classes of gates andvalves.

Water Column Separation

If the pressure in the water column reachesvapor pressure of the water a possibility exists

(F AIR-WATER FLOW IN HYDRAULIC STRUCTURES

i, = that the column will separate. Depending uponthe geometry of the conduit, the separation canoccur at either one location or at several loca-tions. If water column separation is indicated,special waterhammer computations should beperformed to determine the overpressures whenthe water columns rejoin.

AIR VENT DESIGN CRITERIA FOR-Air vent PIELIN

Introduction

Flow in long pipelines presents a separateclass of considerations from those alreadydiscussed. One of the reasons for the new set of

A.-Vww of the vent pipe installed to provide ar for a considerations is the fact that the pipeline pro-square slide gate in an outlet works. Initial instal- file normally follows the ground surface topog-lation had a cap which required removal after raphy vary closely. This causes intermediatefrostplugged the screen. P801-D79278 high locations which provide an opportunity for

the collection of air pockets. To assure trouble-L _free pipeline operation, details of alinement,

- ; location, and sizing of vent structures must be_ considered.

There are essentially four main categories ofpipelines. They-are:

1. Gravity pipelines in which the water flows_ tfrom a higher elevation to a lower one

through the effect of gravity (fig. 36A).2. Sagpipes inverted siphons)' in which the

flow from one canal to another is passedunder a road or across a valley Ifig. 36B).

3. Pump lifts in which the water flows froma low elevation to a higher one throughpump action Ifig. 36C).

4. Siphons in which some portion of the pipeis designed to operate at subatmosphericpressures (fig. 36D). This type of struc-tare is used frequently to prevent waterfrom the upper reservoir from passingback through the pump if- a loss of elec-

B.-Closeup view of the screen for a vent pipe after re- tribac power occurs.moval of the cap. P801-D-79277t

FIGURE 35.-Air vent, Shadow Mountain Dam,Colorado-Big Thompson Project, Colorado. 9See footnote 1.


Gravity systems, figures 36A and B, normal-ly have different alinement problems thanpumping systems (fig. 36C and D}; therefore,the two are considered separately.

A.-Gravity pipeline B.-Sag-pipe

GRAVITY SYSTEMS

is below the downstream vent structure. There-fore, it is submerged by the pool which forms atthe no-flow condition.

To prevent difficulties during startup opera-tions, certain criteria should be followedregarding both the vertical and horizontalalinement at the upstream vent structure and atintermediate summits whose elevations lieabove the downstream open vent structure.

Vertical alinement criteria.-The pipe invertshould be placed on a uniform slope betweenthe vent or summit and the adjacent down-stream pool. If this cannot be achieved then thepipe should be placed on continuingly steeperslopes so that during filling the flow continuesto accelerate to the pool level. If the flow wereallowed to decelerate, the water depth in a cir-cular pipe could gradually increase until thepipe was about 82 percent full. At this depththe flow could become unstable, alternatingbetween full conduit flow and the 82-percentdepth.

At less than design discharge, the flow down-stream of nonsubmerged summits passes fromfree-surface to closed-conduit flow. An air-entraining hydraulic jump always forms whenthe flow makes this transition. The entrainedair can form large air pockets under certain cir-cumstances which move against the direction offlow. This condition is commonly referred to asblowback (refer to previous section-Flov%Having a Hydraulic Jump That Fills the Conduit).

If the alinement cannot be planned to avoideither- operating in or passing through theblowback region delineated in figure 29, thenthe pipe diameter should be altered to avoid theregion.

Some attempts have been made to collect thelarge air bubbles which form on the crown ofthe pipe and lead them away from the pipelineMfig. 38). In the example, the flow conditionsnever entered the blowback flow region.Therefore, the complicated air collection

C.-Pressure pipeline D. Siphon pipeline

PUMPING SYSTEMS

FIGURE 36.-Pipelne configurations.

Gravity Systems

A vertical section through a typical gravitysystem is shown on figure 37. The same type oflayout also applies to sag pipes if the open ventstructures are replaced by canal sections. Twotypes of summit configurations are depicted. Inone case the intermediate summit is above thedownstream vent structure. This forms a poolupstream of the summit at the no-flow condi-tion. In the other case, the intermediate summit


-Upstream open vent structure

-- m e d}

Downstream open vent struCture.

o vl =-w -tjUnifonn dope Pool level Ct_ _ __

I

PLAN

FIGURE 37.-Plan and profie aoa gravity pipehfne.

system was not needed. If flow had entered theblowback region, this structure probably wouldnot have worked. Colgate 1151 found that anunsteady flow condition develops when largeair bubbles are bled from a pipeline with toosmall a vent. To mininize the unsteady flow itis necessary for the vent diameter to equal thepipeline diameter. The design of antiblowbackstructures like the type shown on figure 38should not be attempted without hydraulicmodel studies.

Horizontal alinement criteria.-At the openvent structures and at the intermediate summits

higher than the downstream vent, the pipeshould not contain bends for 10 pipe diametersupstream of the location. In addition bendsshould be avoided in the section between thevent on the summit and the adjacent down-stream pool. These criteria prevent transversewaves from being formed on the free water sur-face which can exist downstream of the vent orsummit at partial flows. These transverse wavescould roll over with enough amplitude to inter-mittently seal the pipeline.

Vent location. -The type of air release struc-ture to be used at a summit is determined by the

~~~~~IJ. 6, .R -............ XS-._ 'lt' RbS be, -f~t);Sfw '

8 _~~O e his Rs"e - .f, Pon, M

be;,$RSA }ETO F X sFWcn A-A<* i #<jRt

WMf /5$t B t w%*in .iat:5.~~~~~~~~t _________ i 0C-i ...

. d4* C '.$ lZOr$nl0wS~~_*A

4, i~tf'1stcolp

n

cn

r3"Otpp

..jo.seno Ta

scro "-or o : .I - Hpm e

tot AdWI of1 prat we uOF mDIZZ

coreA"8 Ace ^."O inl Foof "O *¢@

F IGURE 38.-VentsJtructure. 2944D-799


distance from the pipe invert to the hydraulicgrade line at the summit. For summits higherthan the downstream vent, an open vent isdesirable. The maximum allowable vent heightis determined from topographic, aesthetic, andeconomic considerations. Normally, open ventsat intermediate summits are not feasible if thedistance to the hydraulic grade line HN exceeds6 to 10 meters.

For summits lower than the downstreamvent, the type of air release structure is moredifficult to determine. If the distance to thehydraulic grade line HI is less than about6 meters, an open vent should be used. How-ever, if the distance exceeds 6 meters an airvalve installation should be used (fig. 39). Sincemechanical air valves tend to chatter and spitwater if their operating pressures are too low,the top of the air valve should be set at least 3meters below the pool level.

To provide desirable operating characteris-tics at all discharges, vents also are required atlocations other than at the intermediate sum-mits. If the water velocities are of sufficientmagnitude to carry air bubbles with the flow,then vents are needed downstream of changesfrom negative to positive pipe slopes. Withoutthe vents the air slugs, which collect on thecrown of the pipe, will attain very highvelocities in areas with large positive slopes.These slugs can damage the vent structures atintermediate locations, at downstream connect-ing canals, and can cause slamming of airvalves. These vents should be located less than30 meters downstream from the negative topositive pipe slope change. If the distance fromthe intersection of the pool with the negativeslope and the proposed vent exceeds 20D,where D is the conduit diameter, then the ventshould be placed at the greater of the twodistances {fig. 40). The criterion for the venttype is the same as for vents placed at in-termediate summits below the downstream ventstructure. If the distance between the upstreamand downstream 'vent structures is very great,

_. **¶*AL * K

FIGURE 39.-Tycal irrigation astem air valve install-aton. P801-D-79279


VentI

20 Diameters

Pool levele

30 meters or less

I

jump

FIGURE 40.-Vent location at changes in pipe slope.

Lescovich 1471 recommends that air valves beplaced every 500 to 1000 meters along descen-ding, horizontal, or ascending stretches thathave no intermediate summits.

Pumping Systems

All intermediate summits are potential loca-tions for the collection of air pockets. If thesepockets begin to develop, the hydraulic gra-dient downstream of the summit will equal ap-proximately the pipe slope in the area where theair pocket has formed. For a pipe slope greaterthan the full-flow hydraulic gradient, the airpocket will require a greater head differential toproduce a given discharge. Conversely, for aconstant head differential, the presence of theair pocket will result in decreased discharges.The limiting condition is a complete blockageof flow. In pumping systems this blockage isknown as air binding [581. With air binding

the shutoff head of the pump will have beenreached (fig. 41). One obvious solution to theproblem of air collection at summits is to pro-vided air release valves or vent structures atthese locations. Another solution is to aline thepipeline so that all intermediate summits areeliminated.

Vent Structure Design Considerations

Vent structures have three primary purposes:1. Evacuation of air during filling,2. Removal of air during operation, and3. Prevent pipe collapse during draining.Each is considered in detail. The size of the

vent and the piping connecting the vent to thepipeline is determined by the purpose for whichthe vent is installed.

Evacuaton of air during filing. -The fillingrate of pipelines usually is set at 5 to 15 percent


Lescovich [471 indicated that large orificeair valves should be used to permit air escapeduring filling (fig. 42). In this case a largeorifice refers to diameters greater than 25millimeters. This type of air valve is designedto remain closed after the pipeline is filled.Thus, they cannot be used to release smallamounts of air that accumulate during opera-tion. These valves will open immediately whenthe pipeline pressure drops below atmospheric.This allows air to reenter the pipeline andprevents a vacuum from forming.

Normally, air velocities discharging from anair valve should not exceed 30 m/s. Theprimary reason for limiting the velocity is toprevent the air valve from being blown shut.Some air valves are designed to eliminate thisproblem.

With the 30-m/s velocity limitation, the aircan be considered to be incompressible. Theequation for the airflow rate is

FIGURE 41.-Air binding in a pipeline.Qa A 0C0Q1f2 (87)

of the design discharge. The actual rate isgoverned by the maximum waterhammer pres-sures that the pipeline and valves can with-stand. These pressures are generated when thewater column in the penstock reaches the airrelease valve. Based on waterhammer con-siderations the filling rate of pipelines can becomputed from

= gApAh (86)

whereQ, =penstock filling rate equals airflow

rate through ventAp=cross sectional area of penstock

c =celerity of waterhammer wave inpenstock

g=gravitational constant (acceleration)ha =allowable head rise in penstock due

to waterhammer pressures

whereA. orifice-area,- m'C0=orifice coefficient = 0.6Ap =pressure differential across the

orifice, kPaQa=air density (at 20 'C and a pressure

of 101.3 kPa, Q,=1.2 04 kg/n 3 )

From this equation, performance curves forlarge-orifice air valves can be derived (fig. 43).

If the desired capacity cannot be achievedwith a-single air valve, the-valves can-be placedin clusters-up to four valves-on a single ventpipe from the pipeline.

Removal of air during operation.-Twotypes of structures are used to remove air dur-ing operation. These are an open-vent structureand small-orifice air valves. In either case theconnection to the pipeline must be large enough

CLOSEDCONDUITl FUOW (7t

-Float

Water

A.-Lowered position - Float allows airto flow into or out of pipeline

B.-Raised position - Air cannotenter or leave pipeline

FIGURE 42.-Large-orfice air valve.

to collect the slugs and bubbles of air which aretraveling on the crown of the pipeline.

Colgate [151 investigated the sizing criteriafor open-vent structures. He found that if thecollection port was too small, portions of largeair slugs would pass by the vent. To trap all theair it was necessary for the diameter of the col-lection port to be equal to the pipe diameter.Additional tests were made to investigate thesize of the vent structure itself. It was foundthat if the air vent diameter was less than thepipeline diameter, an unsteady flow wasestablished in the vent as large air bubbles ex-ited from the vent. This unsteady flow pumpedair back into the pipeline. To minimize pump-ing it was necessary to make the vent diameterequal to the pipeline diameter.

Colgate [151 concluded that the collectionand evacuation of air from a pipeline can bebest accomplished by a vertical air vent whichis connected directly to the pipeline. Thediameter of the vent should be at least equal tothe diameter of the pipeline. From access con-siderations, the minimum vent diameter usu-ally is set at about 1 meter. Removal of air ispromoted if the pipe slope immediately down-stream of the vent is made steep enough tocause the air bubbles to return upstream.Figure 29 can be used to determine the requiredslope for a given discharge.

For the case in which the hydraulic grade lineis too far above the pipeline to economically in-stall an open vent, air valves are used to removethe air. Investigations concerning the design of


30

E

0-J

> 20

x

10

0

Iita:

hi

LItW

tocoea1:

M

J0LQ

AIR FLOW THROUGH VALVE m3/s

FIGURE 43.-Performance curves for large-orfice air release valves.

a collector have not been performed. Basedupon the design of open vents it can be assumedthat the diameter of the collector should be atleast equal to that of the pipeline. The height ofthe collector also should be one pipeline dia-meter. In many cases, manholes in the pipelinecan serve as collectors.

To release air from pipelines under highpressures, small-diameter orifice installationsare used (fig. 44). The smnal orifice assures thatthe opening force of the float is not exceeded bythe closing force whose magnitude is equal tothe internal gage pipe pressures times theorifice area. The volume flow of air relationthrough an orifice with a back pressure is givenby

Qa =460AoI(Pin"past,)e-2 85 - lJ 2 (88)

and

Q.= 11.8Ao.pin(pni/p.tm. 0 714 3112 (89)

for

pat HE 0.53pin

These equations are presented as perfor-mance curves (fig. 45).

To prevent the air valves from freezing, fre-quently they are placed in concrete structureslocated below the frost line fig. 46). In this caseit is necessary to provide adequate ventilationinto or out of the structure. The required ven-tilation area is based upon a 2.5-mis maximumair velocity through the gross area of a fixedlouver vent. If wire mesh screen is used, themaximum air velocity is 6.6 m/s through thegross area of the screen.

for

PaOm > 0.53pin

CLOSED CONDUIT FLOW (9

Orifice Prevent pipe collapse during draining. -The venting criteria discussed thus far arebased upon the need to remove air from thepipeline. In several instances above-groundsteel pipelines have collapsed because vacuumformed during rapid draining operations or be-cause of breaks in the pipeline. Parmakian [56]developed criteria for the size and location ofair valves to be placed in steel pipelines to pro-tect them against collapse.

Net On steel pipes, the collapse pressure can be

closing estimated from 1Parmakian [56]1

Connection =Patm (PinPabs (Pindgageto pipeline

whereD= conduit diameter, mm

A. High water level Patm =atmospheric pressure, kPap,=coliapse pressure, kPa

rrees Pi.= internal absolute or gagepressure, kPa

t=pipewall thickness, mm

With stiffener rings, the appropriate equa-tion is

L5.IXI0s(tID)2 5 (91)

PC= (L./D)

Floatlwhere L,=distance between stiffener rings.

openingforce

These two equations are presented graphi-cally in figure 47.

Applying a safety factor N to the internal col-lapse pressure Pc gives the allowable internalpressure P. as

P&=Pstmr Pn 192)B. Low water level

If the ratio of the internal to atmosphericIGURE44.-Typical small-orifice air release valve. pressure is greater than 0.53 then the volumeI

70 AIR-WATlER FLOW IN HYDRAULIC STRUCTURES

flow of air into the pipeline through an orifice isgiven by

Q.= Cd tA) 2pX (dOE (Ipi])\

If the ratio is equal to or less than 0.53 thenthe airflow rate into the pipeline through anorifice is given by

whereA.= orifice area, m2

Q. = airflow area, m3 /s

These equations are presented as perfor-mance curves for various size vacuum reliefvalves (fig. 48).

Parmakian presented an alternate method ofdetermining the required air vent size in termsof a dimensionless ratio. The ratio is in the formof an Euler number and is given by

Q (=CdA(+ 1) Qatm,am2 G\fI/J$ 494)

UsingCd= 0.6

putm=101. 3 kPaX= 1.4

Qetm=' 1.20 kg/M3

in equations 93 and 94 results in

0.715 0286 112

frPm t 95)

for

'&P 114

\ Q Pt. V'U7M)I

C."'~ Eu"'(97)

whereC,=orifice discharge coefficientE= Euler number=p.,m/Q, V

Patm =atmospheric pressureAYV=change in water velocity approaching

and leaving air ventQ. = density of air at standard

atmospheric pressureuatm=specific volume of air at

atmospheric pressure- > 0.53Patm

and

Q.=119A.

for

The pressure and specific volume of the at-(96) mosphere are both functions of elevation (fig.

49). This alternate method results in the re-quired air vent orifice diameter as a function ofthe pipeline diameter (fig. 501.

Normally, air valves are placed at the crestsin the pipeline profile and at locations wherethe pipeline begins a steep downward slope.

P_ 0.53Paum


a0.

w

0-'a5

z-j

a-

0.001 0.002 0.004 0.006 0.008 0.01 0

AIR FLOW THROUGH VALVE m%/s

D.02 0.04

FIGUHE 45.-Performance curves for smail-orifice air release valves.


Surface to _ - -Air vent, see Vent Detailbe horizontal- -Insulated cover not shown Short radius

FLOW return bendT. Conduit f. Air valve, Wire mesh S td. steel pipe

£Air valet Vent pipeqD Pipe well _ _ air vent

_______ and manhole Std. steelD i1pipe dia.

PLAN-AIR VALVE as domperPrecast concrete

21 cover requiredbut not shown damper

Origincl Insulated cover, VENT DETAILgrcund surface see Section E-E

- + Pipe well, reinf. concretepressure pipe

L ocate manhole on upslope* side of structure

CL ManholePipeipin Mitercut Pipe jointJoint,

!- .... *..... Bend sheet metalas shown

SECTION C-CCut insulation to fit

Short radius around vent piper 3 1 1G elbow :

Air vlve u1Adhere galvanized sheet metal to1 J i. one side of rigid styrofoom insulation

Se el ri ver for cover and drop in panelsSteel riser 5 !I F

Flexible foam insulation,adhere to concrete pipe

.____INSULATED COVER DETAILI ODSECTION E-E

(Valve not shown)

FIGURE 46.-Typical fiau protection installation.

73CLOSED CONDUIT FLOW

Shell ithicknessot__9

765

4

1&IN

C,

w

m 100a. 9

~, 8

( 6

4 5

-I 4

00

U 0r I

Stiffener ring

3 4 5 6 7 8 9100

L 8/D

FIGURE 47.-CoElapsing pressure of a steel pipe with stiffener rings.

-4 AIR-WATER FLOW IN HYDRAULIC STRUCTURES

Sonic velocity in orifice

10Itl

a.l 0. .4 06o

-L8w

wz

Ci-4ul

30

Sndrd c

0.1 0.2 0.4 0.6 0.8 I 2

AIR FLOW THROUGH VALVE, mS/s

FIGURE 48.-Performance curves for large-orifice vacuum relief valves.

4 6

CLOSED CONDUIT FLOW

E0 E

U Vx 2

> ..0

a- -U,

Cn

1100

100=

800

0O 1000 2000ELEVATION, meters

100

E4-0

o0Co aUs u0. 0xao 0

0

0 1000 2000ELEVATION, meters

FIGURE 49.-Specific volume and barometric pressure ofair as a function of elevation.

t6 AIR-WATER FLOW IN HYDRAULIC STRUCTURES

Pc - collapse pressure

POtm - atmospheric pressuredo do = orifice diameter in air valve.

Co = orifice discharge coefficient-0.5

[L2P = PatM -N

\N N= safety factorK= gas constantl1.4

I.X

0.6

IC02 Patmi

FIGURE 50.-Required air relief orifice diameter to prevent collapse of steel pipelines.

CLOSED CONDUIT FLOW

FLOWS IN VERTICAL SHAFTS

Classification of Airflows

Three types of hydraulic structures that use avertical shaft to convey water from one eleva-tion to another are:

* Spillways* Intakes* Drop shaftsThe air entrainment properties of these struc-

tures are important since at certain flowratesexplosive air blowbacks are possible (fig. 51).Often extensive studies are necessary to designvent structures to remove the air which is en-trained in the vertical shaft Anderson [31 andBabb 161.

The amount of air entrained in the shaft isstrongly dependent upon the type of flow intothe shaft and upon the water level in the shaft.The inlet flow can vary from radial to tangen-tial with flow entering around the circun-ference of the shaft. Typical types of inlet struc-tures (fig. 52) are:

* Circular weirs* Vortex inlets* Radius elbowsThe effect of water surface (reservoir eleva-

tion at the entrance to a shaft can be examinedby considering the discharge characteristics of avertical shaft spillway (fig. 53). For low watersurface levels the discharge is proportional tothe three-halves power of the total head on thecrest. The flow in the shaft clings to the walls in

FIGURE 51.-Observed air blowback in morning glory spiliway at Owyhee Dam, Oregon. P801-D-79280

M AIR-WATER FLOW IN HYDRAULIC S(TRUCTU RES

A

PLAN PLAN

SECTION A-A SECTION A-A SECTION A-A

A. Circular Weir B. Vortex C. Elbow

z0H4�

R095P.-9M

m

F1GURE52.-pical types of vertal shjtft inlet structures.

0 /Air

ion

) / ~equation ;R/11

// I SubmergedI |disharge P M

.1 isI Region Ia RegK

WATER DISCHARGE AIR DISCHARGE

FIGURE 53.-Vertical shaft spiliway discharge characteristics.


a relatively thin sheet. The volume flow rate ofair is determined primarily by the shear actionof the air-water interface and by entrainmentinto the mass of the water. This type of flow hasbeen designated as region I on figure 53. As thewater discharge increases with increasing reser-voir elevation, a point is reached when the sheetof water is sufficiently thick to completely fillthe upper end of the conduit. This waterdischarge separates region I from region II typeflows.

Region II type flows are characterized by anannular hydraulic jump. Further increases inreservoir elevation merely cause the location ofthe jump to move upward in the vertical shaft.When the jump reaches a point near the top ofthe shaft, the flow is said to become submerged.

For reservoir elevations in excess of that re-quired to produce the submerged water flow,all inflow of air to the shaft ceases. Thedischarge for this flow range is proportional tothe one-half power of total energy over thecrest.

If the bottom of the shaft is always sub-merged, then a region I type flow will notdevelop. Instead, the air motion will be de-scribed by a region II type flow up to the pointwhen the vertical shaft is submerged.

The airflow rates discussed above should notbe confused with those that are present in theportions of the structure downstream of the ver-tical shaft. The methods discussed in thischapter-Flow in Partially Filled Conduits-should be used to analyze the flow of air in thehorizontal sections of vertical shaft spillwaysand similar structures. Mussalli and Carstens155] studied surging problems that develop asthe horizontal conduit seals [fig. 21 15)1.However, they did not develop any air entrain-ment criteria for the vertical shaft.

a. The water flow on the shaft walls issimilar to open chanel flow, and

b. The lower end of the shaft is open to theatmosphere.

If the inlet is not designed to keep the waterflow attached to the wall, the airflow rate can-not be calculated.

Several methods are available to estimate theairflow rate when the water forms in a sheet onthe walls. For instance, the air insufflated intothe flow can be estimated from equation 59using open channel flow relations. The amountof air flowing on the core of the pipe can bedetermined from

Q.= V0 A, 498)

whereA,=cross sectional of air in coreV.=maximum water velocity in vertical

shaft

Hack [271 recommends that the total airflowbe determined from

Q=0.35+16.1 C2* a (99)

where C. =mean air concentrationThe mean air concentration is estimated from

C={ 1+1411 -ekr(F 4/3_F4/3))]-I)-I 4100)

whereD =conduit diameterF=Froude number at end of shaftF= Froude number at point where

boundary layer intersects water sur-face

k,= 1.8 r5+0.0108k. =equivalent sand grain roughnessr,= relative roughness=k,/D

Region I Airflow Rates

The airflow rate down the vertical shaft canbe calculated by assuming:

The point where the boundary layer in-tersects the water surface is found through theapplication of equations 27 through 30.

8( AIR-WATER FLOW IN HYDRAULIC STRUCTURES

Region II Airflow Rates

Various investigators have studied the en-trainment of air by an annular jet.

Haindl 1291 found that the air entrainmentobeys a law very similar to that found byKalinske and Robertson [381 for a hydraulicjump in a conduit. The relation is

Reverse Airflow in a Vertical Shaft

All the preceeding relations assume that thewaterflow rates are sufficient to remove all theentrained air from the system. Martin 1511showed that slug flow begins when the dimen-sionless airflow , exceeds 0.223. It was shownearlier that these slugs move up the shaft for

gD< 0 4104)

=Q'-=0.02 (F-l)0' 6

Qw

where F=Froude number

(101)

Therefore, for dimensionless water flowratios less than 0.3, the airflow quantities givenby equations 101 and 103 are too large. In addi-tion, it is possible that blowback will occur inthe shaft.

F= Q/ (102)

D =outside jet diameter (conduitdiameter)

g=gravitational constant (acceleration)Q,= volume flowrate of airQ., =volume flowrate of waterRj=thickness of annular jet

Kleinschroth [431 found a correlation forflows in vertical shafts having a vortex inlet.The relation is

Submergence

The water depth which causes a vertical shaftto flow submerged has been determined onlyfor the case of radial inflow. lain, Raju, andGarde 1361 determined that the submergence atwhich airflow down the shaft ceases is given by

= 0.47 F"'1 (105)

D=0.022 13 (103)

whereD=shaft diameterF= V/(gDl"2g=gravitational constant (accelerationsS=submergence depthV=mean water velocity in shaft flowing

full

For a vortex inlet or for approach flowhaving some circulation, the required submer-gence would be greater than that given byequation 105.

wherehf= distance from the inlet to the water

level in the vertical shaftD=shaft diameter

Bibliography

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On November 6, 1979, the Bureau of Reclamation wasrenamed the Water and Power Resources Service In theU.S. Department of the Interior.

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