Novak P. Developments in hydraulic engineering

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163. GRANT, E.L. and GRANT, I. Principles of Engineering Economy, 5th edn, Ronald Press,

New York, 1970.

164. JAMES, L.D. and LEE, R.R. Economics of Water Resources Planning, MCGraw-Hill, New

York, 1971.

165. Reference 72, Chapter 12.

166. Reference 89, Section 2.2.4.

167. HUNTER, J.K. The cost of hydroelectric power, Reference 84, Vol. 3.

168. MOSONYI, E. Vizeröhasznositás (Water Power Utilization), Vol. 2, university textbook,

Budapest (Hungary), 1953.

169. Reference 154, Chapter 8, Section 20.

170. KRUTILLA, J.V. and ECKSTEIN, O. Multiple Purpose River Development, Johns Hopkins

Press, Baltimore, 1958.

171. MCINTOSH, P.T. and LA TOUCHE, M.C.D. Cost sharing in a multipurpose project, Int.

Water Power Dam Constr., January 1985.

172. GORDON, J.L. Hydropower cost estimates, Int. Water Power Dam Constr., November 1983.

173. BINGLI, DENG. Small hydro in China: progress and prospects, Int. Water Power Dam

Constr., February 1985.

Water power development: low-head Hydropower utilization 99

Chapter 2

INTAKE DESIGN FOR ICE

CONDITIONS

G.D.ASHTON

US Army Cold Regions Research and Engineering Laboratory, Hanover,

New Hampshire 03755, USA

NOTATION

A area of water surface (m

)

C Chezy coefficient (m

1/2

−1

)

C volumetric frazil concentration (dimensionless)

specific heat of water (J kg

−1

°C

−1

)

D flow depth (m)

e porosity

g acceleration due to gravity (ms

−2

)

h ice thickness (m)

H total depth (m)

depth to top of a submerged intake (m)

heat transfer coefficient, ice to air (Wm

−2

°C

−1

)

head loss (m)

distance from bottom of intake to stream bottom (m)

thermal conductivity of ice (Wm

−1

°C

−1

)

r radius (m)

radius of bar (m)

t time (s)

air temperature (°C)

flow temperature (°C)

melting temperature of ice (°C)

max

time to complete blockage (s)

surface temperature (°C)

water temperature (°C)

V mean velocity (ms

−1

)

critical velocity for ice block underturning (ms

−1

)

volume of frazil per unit area (m)

collection efficiency (dimensionless)

heat loss rate (Wm

−2

)

heat flux through ice (Wm

−2

)

heat loss from ice to air (Wm

−2

)

heat flux from water to ice (Wm

−2

)

λ heat of fusion of ice (J kg

−1

)

density of ice (kg m

−3

)

density of water (kg m

−3

)

1 INTRODUCTION

The design of water intakes is almost always based on a combined consideration of the

water supply needs and the characteristics of the source water body. The water supply

requirements generally consist of a required withdrawal or passage rate, some measure of

reliability, and some measure of quality ranging from temperature in the case of selective

withdrawal structures to the exclusion of debris or trash. The source water body may be a

lake, a reservoir, the ocean, or a river. It is not surprising therefore that there is a wide

range of types, sizes, arrangements, and concepts for specific intake designs. Where ice

forms in or on the source water body, consideration must also be given either to

preventing its ingestion into the intake or ingesting it in such a condition that it does not

interfere with the water usage. At first glance one is tempted to treat ice at intakes simply

as a debris problem. This is generally a naive approach because the quantities of ice are

orders of magnitude larger than those of debris, and the nature of ice, other than its slight

buoyancy, is often very different. Because of the diversity of intakes, the approach taken

in this text is to characterize ice conditions that occur in the vicinity of intakes and then

describe the principles behind various counter measures that have been used both

successfully and unsuccessfully to avoid or mitigate ice problems. Finally some case

studies will help demonstrate the large measure of engineering judgment that must be

used to effectively accommodate ice conditions at intakes.

Developments in hydraulic engineering–5 102

A number of reviews have been published putting the particular ice problems of

intakes in the overall context of river and lake ice behavior.

3,5,6,30,41

Others

14,25

surveyed

ice problems at intakes in some detail.

2 ICE CONDITIONS IN RIVERS

2.1 Freeze-up

The nature of initial ice formation in rivers depends largely on the flow velocity. At very

low velocities a sheet of ice forms over the entire surface, interlocks with the banks, and

forms an intact ice cover. At low velocities shore ice also rapidly grows out from the

banks and covers the river, again forming an intact ice cover. For such rivers, ice

generally does not cause problems at intakes unless the ice is broken up and carried

downstream because of higher discharges and hence increased velocities. This condition

of a low velocity and an intact ice cover is the aim of some schemes to prevent ice

problems at intakes. Unfortunately it is often difficult to attain without expensive

impounding structures.

At intermediate velocities the initial ice formation is in the form of thin plates on the

surface that move with the flow; this ice is termed skim ice. In this case there is sufficient

turbulence to prevent an intact cover from forming but not sufficient to entrain the initial

crystals of ice into the flow. The total production of ice over a reach under these

conditions may pose a problem at intakes downstream; it must be either passed or

accumulated in an ice cover that progresses upstream, forming an initial cover that

subsequently thickens by thermal growth.

At some higher velocity turbulence is sufficient to entrain the initial crystals, and a

form of ice termed ‘frazil’ is produced. Frazil ice consists of very small crystals that are

suspended in the flow initially throughout the depth but subsequently cluster together,

flocculate, and rise to the surface, often in the form of loosely organized ‘pans’ of frazil.

Gosink and Osterkamp

termed this regime ‘layered flow’ of frazil. Since this type of ice

causes most of the river ice intake problems, we will discuss it later in more detail. At

even higher velocities the turbulent mixing prevents the flocculation and formation of

pans, and the frazil is distributed throughout the flow without organized structure of pans

on the surface. Figure 1 distinguishes these regimes of initial ice formation on the basis of

the

Intake design for ice conditions 103

FIG. 1. Regimes of initial formation of

ice in rivers (after Matousek

velocity V and the heat loss rate . The division between skim ice run and layered frazil

runs depends on the roughness coefficient, here characterized by the Chezy coefficient

(defined by V=CR

1/2

where R is the hydraulic radius); the lines for C=30 and 40

1/2

−1

are shown. The vertical line distinguishing layered frazil runs and well mixed runs

is based on Gosink and Osterkamp’s suggestion that the transition is described by

(1)

These threshold boundaries should not be taken as exact, but they do correspond

reasonably well with field data from various rivers.

Frazil can also form anchor ice, which is the deposit, growth, and accretion of frazil on

bed materials. The crystals interlock somewhat and they may grow larger than those of

frazil moving with the flow. Anchor ice forms only in areas of open water. Its importance

to intakes is that it often rises to the surface during warmer periods. It then appears much

like frazil slush masses, with the added danger that it may bring rocks and stones with it.

2.2 Frazil Ice

Frazil ice consists of small particles of ice that form in water that has been supercooled

below the melting point. While often associated with rapids in rivers, it also forms in

rapidly moving open areas of rivers once the water has been cooled to 0°C, on the surface

of lakes and reservoirs when the wind conditions prevent a stable ice cover from

remaining intact, and in the ocean in open areas subject to wind mixing. It is predictable

in the sense that if the water surface is open to the atmosphere and the rate of cooling

through the 0°C point is known, then the production rate can be calculated using a simple

energy balance. Since all the heat loss must result in ice production once the water is at

0°C, the rate of frazil production per unit area is given by

Developments in hydraulic engineering–5 104

(2)

where V

is the volume of frazil per unit area, t is time, is the heat loss to the

atmosphere from the water surface, A is the area of open water, ρ

is the density of ice,

and λ is the heat of fusion. Frazil generally forms as tiny discs with diameters typically a

millimeter or less and thicknesses 1/5 to 1/10 of the diameter. The initial nucleation is at

the surface, but the number of particles multiplies rapidly and they are easily entrained to

great depths in river flows. As water containing the frazil particles moves downstream,

the particles flocculate together, and the flocs rise to the surface, eventually forming a

loose cover consisting of pans or floes that may be characterized as floating slush masses.

With further heat loss the surface may freeze, pans of ice are formed and eventually may

attain sufficient structural integrity to bridge the river and initiate a stable ice cover. The

ice cover on the river then protects the water below from further heat loss to the

atmosphere. As a consequence frazil does not form beneath solid ice covers, although it

may be transported and deposited at considerable distances beneath the cover.

Frazil ice forms in nearly all rivers. The amount that forms depends on the extent of

open water, the rate of heat loss to the atmosphere, and the duration of the heat losses.

During the frazil formation period the matrix water is supercooled to between 0°C and

−0·05°C; in these conditions the particles grow actively and tend to attach to any cold

object they contact. When the water temperature returns to 0°C and the ice and water are

in equilibrium with each other, or when the water is slightly above 0°C, the particles no

longer grow and the frazil is termed ‘passive’. Passive frazil, when dispersed throughout

the flow, is generally not a problem to intakes.

A typical time-temperature curve of a body of water undergoing super-cooling and

frazil formation is presented in Fig. 2. From A to B the water is cooling at a rate

(3)

FIG. 2. Water temperature during frazil

formation.

Intake design for ice conditions 105

where T

is the water temperature, ρ

is the water density, C

is the specific heat, and D

is the depth of the flow. As the temperature passes below 0°C it supercools, and at point

C ice begins to form; the water continues to cool until the ice production is in balance

with the heat loss and the temperature gradually returns toward 0°C at D. As long as the

water continues to lose heat there will be a residual supercooling, ice will continue to be

produced in accordance with eqn (2), and the frazil will remain active.

One means of forecasting the appearance of frazil is to monitor the water temperatures

upstream of the intake and extrapolate to point B. Since heat losses are generally greatest

at night and least during daytime (due to solar radiation), the extrapolation may show that

frazil will not appear before daybreak, or at least will not be active. This cooling curve

generally occurs synoptically over the entire upstream reach, and passive frazil may reach

the intake as a result of production well upstream many hours earlier.

2.3 Thermal Growth of Ice

It is useful to be able to calculate the thickness of an ice sheet exposed to the atmosphere

at an air temperature T

(below 0°C). Figure 3 shows that the heat loss

from the top

surface of the ice T

to the atmosphere at a temperature T

is calculated using a bulk heat

transfer coefficient H

in the form

(4)

The heat loss through the ice sheet

is by conduction and is of the form

(5)

FIG. 3. Definition sketch for heat

losses from rivers with ice covers.

Developments in hydraulic engineering–5 106

where k

is the thermal conductivity of the ice, T

is the melting point and the temperature

of the ice-water interface, and h is the ice thickness. At the bottom an energy balance

gives the thickening rate in the form

(6)

where

is the heat flux from the water to the ice. In most cases

may be neglected

since the water is usually at 0°C. Combining eqns (4), (5) and (6), eliminating T

, and

integrating results in

(7)

Typically H

is in the range 10–30 Wm−

°C−

, with 20 a good value to use without any

other measurements or detailed energy budget calculations. In Fig. 4 eqn (7) is plotted for

=10, 20 and 30 Wm

−2

°C

−1.

The results in Fig. 4, as a function of freezing degree-days

are applicable to snow-free ice covers over 0°C water. The initial ice growth is linear in

time, and as it gets thicker it grows with √t. This figure may be used for times ranging

from hours to days or weeks. When used for only part of a day the value of H

should be

estimated using energy budget methods to determine

, since the contribution of solar

radiation is a gain during daylight but is zero at night. If the solidification of an ice cover

initially composed of frazil with porosity e is considered, then λ should be replaced by eλ

since only the liquid water fraction must be frozen.

FIG. 4. Ice thickening as a function of

accumulated freezing degree-days.

Intake design for ice conditions 107

2.4 Accumulation of Ice

When the floating sheet ice or the frazil slush runs arrive at an obstacle, they accumulate

into a floating ice cover that progresses upstream. The initial underturning of a block of

ice arriving at the ice edge occurs if the velocity is greater than

(8)

where g is the acceleration due to gravity. If the velocity is less than this, the individual

floes accumulate by juxtaposition in a single layer. If the velocity is greater than this, the

ice will accumulate to a more or less uniform thickness, which can be predicted

reasonably well although the details are more than can be presented here. For a good

discussion of these accumulations, see Beltaos

9,10

and Calkins.

2.5 Break-up

Most of the above discussion has concerned the period of formation of river ice, which

may be the entire winter in temperature climates. In the spring or other warming periods

break-up occurs. The problems that this causes at intakes are not due to blockage as much

as to the high water levels and physical damage associated with ice jams. Ice jams tend to

form in the same places along rivers although not necessarily every year. Nevertheless,

the regularity of recurrence at the same location forces the designer to explore historic

records to determine if ice jams will affect the intake. It is sometimes possible to

construct a stage-recurrence interval diagram for ice-jam floods; in general this will differ

from the stage-recurrence relationship of non-ice floods and will often show higher

stages.

Typical ice jams begin where the slope becomes flatter (in the downstream

direction); the classic case is the inlet to a reservoir. If the intake alters the geometry of

the river, then an assessment must be made as to whether the altered geometry will inhibit

or promote ice jams.

One successful means of evaluating these effects is the use of hydraulic models with

either real ice which requires refrigerated test rooms, or simulated ice.

Considerable

success has been achieved using plastic pellets to simulate the ice accumulations with

some treatments to eliminate scale effects associated with surface tension.

Pariset et

al.

describe such a model test and field validation associated with reclaiming land from

the St. Lawrence River at Montreal for the site of the 1967 World Exhibition.

If the change in geometry results in an altered longitudinal depth profile, considerable

success has been achieved in predicting the ice accumulation thicknesses and stage

heights using analytical models largely based on the initial work of Pariset et al.

but

since refined and validated against field measurements. A recent summary of this

technique is given by Beltaos.

If the geometry results in different plan geometries then combinations of model

studies and consultation with experienced people is recommended.

The assessment of structural integrity against forces due to ice is generally based on

assuring that the structure is stronger than the ice that hits it. In its simplest form this is

done by estimating the crushing strength and multiplying by the width of the structure

Developments in hydraulic engineering–5 108

Novak P. Developments in hydraulic engineering - Vol. 5

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