calculation of water & sediment flow in hydropower reservoirs, modelling, testing & monitoring,...

8/9/2019 Calculation of Water & Sediment Flow in Hydropower Reservoirs, Modelling, Testing & Monitoring, Budapest, Jul 1994

1/12

CalculationofW aterand

Sediment Flow

in

HydropowerR eservoirs

N.

R. B.Olsen

Research

Engineer

The N orwegian Hydrotechnical Laboratory

N

7034Trondheim,Norway

O.F. Jimnez

HydraulicEngineer

InstitutoCostarricense de Electricidad

Apdo.1 0 0 3 2 - 1 0 0 0

San

Jos,

Costa Rica

A .

Livol l

Research

Engineer

Department of Hydraulic and Env ironmen tal Engineering

The NorwegianInstituteof Technology

N

7034 Trondheim, Norway

L. Abrahamsen

Civil

Engineer

STATKRAFT ANLEGGA/S

P. Box2 31

N

1322

H0vik, Norway

Introduction

The flow of water in two hydropowerreservoirsin Costa Rica is calculated by a

numerical

model.T hemodel

uses

a finite volume method to

solve

the Navier-Stokes equations for three dimensions on a general non-

orthogonal grid. The k-e turbulence model is used to solve the Reynolds-stress term. Another three-

dimensional finite volumemodelis used to calclate sediment concentration in thereservoirsbysolvingthe

diffusion/convection equation

for the

sediment concentration.

For one of the

reservoirs,

field

measurements

ar e

carried

out to

verify

the

results from

the

numerical model. There

is

good agreement between calculated

and measured wa ter velocity field, even though no calibration of the model has been p erformed. The

calculated sediment flow and trap efficiency seem reasonable. The measured concentrations areuncertain,b ut

indcate

that the calculated vales can be

corred.

The model is

also

used to calclate sediment deposition in

theotherreservoirover a period of 20 years.

1.Bref

Background

Investigation of reservoir sedimentation can be done at several levis of detail,

starting from

empirical

methods of comp uting the trap efficiency, to complex comp utational and physical modelling. The estimations

ca n consider operation

of the

reservoir withvarying discharges

an d

water levis, several different sediment

sizes,

deposition and erosin processes etc. The main motivation for using numerical models for calculation of

sediment movements isthat it isdifficult tosimlatethe

fmer

sedimentsin aphysical model. Thesca ling laws

ar e different fo r

suspended sediments

an d

bedload

[Kobus

1

],

whichmeans

that it can be difficult to

simlate

interactionbetween the twotranspon modes. Cohesive forces between particles may

also

be a problem when

scalingdown thefmer particles.

Withregard to num erical models it is highly desirable to use a two orthree-dimensional

model because

of the

complex geome try characteristics of many reservoirs. The rapidly decreasing cost of comp uter time gives 3D

numerical models a potential to be preferred over physical modelstudiesfo reconomical reasons. By using a

3D

numerical model instead of a physical model results can be obtained faster and at a lower

cost.

A

condition

is

that

th e

results from

the

numerical model have sufficient quality.

In the

present study this

ha s

been investigated for simulation of water and sediment in a hydropower reservoir, using the SSIIM

model.

The SSIIM model is a public domain program that can be downloaded from the Internet, from the address

ftp.cdrom.com,

in directory

pub/os2/2_x/educate.

The SSIIM model has been used to simlate sediment

deposition in reservoirs

measurements.

before [Olsen and M elaaen ], but these simulations were not

verified

by

2.Theoretical background

The numericalmodelsimulates the flow by the Reynolds-averaged Navier-Stokes equations as


2/12

Bibliographicaldata for th eauthor

am e and ttle Dr.Binar

Tesaker,

Headof Research

Affiliation Since 1963: SDSTTEFNHL,TheNorwegian Hydrotechnical Laboratory,

Section of River Engineering.

Education Civil engineer 1958, NorwegianInstituteofTechnology

Dr.Ing.

PhD) 1969, Norwegian

Instuteof

Technology


3/12

( i)

In Equation 1 U is the averaged

velocity,

u is thefluctuatingvelocity, x is a lengthscale,P is the pressure, 5 is

the

Kronecker delta, p is the water density and v is the viscosity. The turbulent

stresses

in Equation 1 are

modelled with the k-e turbulence

model.

Afurther description of the k-emodelis given by

[Rodi

3

].

Thewall

law

for

rough boundary

is

used [Schlichting

4

].

Sediment

transpon

is in general divided in bedload and suspended

load.

The suspended load can be calculated

with

the

c onvection-diffusion equation

for the

sediment concentration,

c:

The

fall velocity

of the

sediment particles

is

denoted

w. The diffusion

coefficient,

r, is

taken

from the k-e

model.

Equations

1 and 2 arediscretizedby acontrol volume approach [Patankar

5

]. The bed concentration isobtained

by

using

a

total load formula together with formulas

fo r

vertical sediment

an d

velocity distribution

for

uniform

flow. This concentration is used in the bed cells and Equation 2 is

solved

for all the other

cells.

Because E quation 2 is not

solved

for the bed cells, sediment continuity is not necessarily fulfilled for the bed

cells.

The sediment

continuity defect gives

a

vertical velocity

for the bedlevelfor eachcell.When a

time

step is determined, this is multiplied with the bed change velocity to give the actual bed movements. The

following

formula

is

used:

where

Az

be d

is the change in bed elevation, At is a time step given by the user, r is a conversin coefficient

between flux of sediment and the volume it occupies at the bed, AF is the flux of sediment and A

z

is the

horizontalrea

of the

cell.

3. Calculation of water and sed imen t concentration in Garita Reservoir

La Garita Hydropower Plant is located 40 km west of San

Jos,

capital of Costa Rica . This is a run of the river

plant

w ith a diversin

da m

located in the Rio Grande river.

17

m

3

/s is diverted to a re-regu lating reservoir by a

6 km long system of tunnels and channels. The Garita re-regulating reservoir had an original live storage of

436 000

m

3

.

A pproximately 125 000

m

3

of sediments deposits every year, requiring dredging every other year.

Fig. 1

shows

a map of the reservoir. The map is based on echo sounding surveying of cross-sections with 50

meter intervals. In the summer of 1993 a study of the reservoir was carried out [Abrahamsen

6

]. Velocity

profiles and c urren t directions in the plae we re measured in three to six locations for each cross-section. The

measurements were made from a boat using a magnetic-based current meter. Sediment profile concentrations

were

measured using a standard point sampler at

several locations

on eachcross-sectionof the

reservoir.

A grid of the Garita reservoir is made on the basis of the map shown in Fig. 1. The grid has 8 cells in the

vertical direction and 33x31

cells

in the horizontal directions. Fig. 2 shows a depth-averaged water flow

vector plot of the reservoir. Calculations are done for roughnesses of k

s

equal to 1 cm and 1 mm. The

differencesbetween the results for the two roughnesses are so

small

that it is not

possible

to observe it on the

plots. Therefore only one case is shown. Fig. 2 shows that all the recirculation zones of the reservoir are

simulated. Looking at the location of the centre of the

main

recirculation

zone,

there is a small

difference

between

the

simulated

an d

measured

flow field.

However, considering that

no

calibration

of the modelha s

been performed, the calculated flow fields coincide very well with the measured vales. The deviations

between calculated and measured velocities are possibly due to inaccurate modelling of the

geometry.

The sediment concentration in the channel flowing into the reservoir is measured several times during the

period the concentration samples are taken in the reservoir. On the basis of the concentrations in the channel,

asediment

load

of 1kg/sis

used

in thenumerical calculation. This isdivided in

five

sizes basedon thegrain


4/12

size analysis of the suspended sediment in the

inflow channel.

Total

depth-averaged concentration

in

the

reservoir is shown on Fig.

3.

The concentration is showen

along

the main

flowpath from

the entrance to the

exit.

The figure

shows both measured

and

calculated vales.

The

measured concentrations

are scaledto be

equivalent to

an

inflow of 1 kg/s. The measurements lasted for three days. The water flow remained

stationary,

but sediment flow varied

between

0.6 to 2.1 kg/s

during

th e

sampling

period du e to changesin the

sediment concentration

in the

river. This

caused

some

uncertainty

with regard

to the assumption of

steady

conditions

for thesediment

calculations.

Figure 1. Map of

Garita Reservoir, depths

in

meters

0.5meters between contourlines.

LEGENq

varxiTY V E C T O R

MEASURED

9MULATEO

Z R

VELOCITY

MAP O

VECTOR

0.50

200 m

T.OO rn/s

Figure

2.

Depth-averaged

velocity

vector

plot.


5/12

Concentration in ppm

120

100-

80

60

40

20

Inlet

3

Seot

31

Aug.

r

^


6/12

Rica.This

is a

run

of the

riverplantwhich utilities waterfrom

Rio

Reventazn

and

two

of

its

tributaries

and a

head

of 142

meters.

An

installed capacity

of 177

M W

is

planned.

The

Angostura

dam is presently

under

construction.The damwillcratetheAngosturareservoir,whichwillhavea volume of 16millionm

3

. A

map

of thereservoirisshowninFig.4. TheReventazn riverhas anannualaveragewaterdischarge of about 105

m'/s.Approximately 1.5million tonsofsedimentsisestimatedtoflow intothe reservoir eachyear. Some of

this will be trapped,anddecreasethestoragevolume.

Spillway/lnntake

Rockfdl

Dam

Scale 1 : 20 000

Figure

4. Map of the

Angostura reservoirbeforedeposition.

Inflow

The lifetime of the reservoir is a very important parameter for the economy of the project. Several models

havebeen

used

to estmatethis.The one-dimensional modelHEC-6wasused

[Jimnez

et.

al.

7

].

Inthisstudy

two

other models have been used.

The first is a two-dimensional

width-averaged model

fo r

sediment

concentrationcalculation.

T he

second

is the

fully three-dimensionalmodel

SSIIM.

Thetwo-dimensionalsediment modelbasesthewaterflow on aone-dimensional calculation.The

convection-

diffusion equation (2) issolved for thecasewhere thecross-stream termsarezero.Atwo-dimensional gridi s

made which has 10cells in thevertical directionand 16cells in the horizontal direction. Constant diffusion

an dvelocity overthedeptha reassumed. The

two-dimensional

modelis runwithan inflow of 350 mV sover

27

years.On thebasisofmeasured

concentrations

in RioReventazn, asediment loadof 1000

kg/s

is

used.

This

is

divided

in

three sizes (sand, silt

and

clay)based

on

grainsizeanalysis.

A

timestep

of

0.17years

is

used. The resultsareshown inFig.5, which

illustrates

the temporal development of thetrapefficiency an d

th e effective

volumeduring 27years. The

trapefficiency

reduces from 59,6 % to27,9 % and the

effective

volume reduces

from

11.3

mili,

m

3

to 2.7 mili, m

3

.

Th e

fully

three-dimensional model

is

also

used.

The

velocity

feld is

calculated

from

an

initial grid

of

11

cells

in the

vertical direction

an d

9x54 cells

in the

horizontal directions.

T he

resulting velocity feld

is

shown

in

Fig.6 andFig.7.Thisisusedforcalculationofsediment movementanddeposition. Asecond grid ismadeon

thebasis

of

depositionduring

one

time step.

The

water

and

sediment

flow is

recalculated

for

this grid, which

give new bed levis. This sequence isrepeated 10times,with timesteps of 3.4years initially and 1,7years

later

on. Theresultsof the simulationsareshowninFig.6 toFig. 20. The flow fields at

different

times are

shown inFig.6 toFig.1 3.

Th e

changes

in

geometry because

of

deposition

areillustrated in figure 14 to 19.

Because

the

entrance

of the

reservoir isshallow,aridge developsin the

middle

of theuppstream partof thereservoir. This ridge

affects

theflow pattern and illustratesthe three -dimensionalnatureof thedeposition. Sucheffects are notpossible to

simlate with

a

one-dimensional model.


7/12

S imulotionwth

RE S DE P

Q=350m3/s.

Ul

2

Eff.Vdune

Trcpeffldency

10 15

Yaor

20

25

Figure

5.

Change

in

trap

efficiency andeffective

volunte.

Two-dimensional model.

Figure .Velocitiesat the surface. Initialsituation.

T O O

i r

30

20 S.

10

30

Velocity, p r o f i l e 5, 0.3

m/ s

arrow:

Figure

7 .

Longitudinalsection

in the

middle

of the

rcservoir. Initial situation. Note that

the

scales

are

disorted.


8/12

0 5 m / s

arrow:

Figure 8.

Velocitiesat the

surface.

Situation

after

3.4

years .

0 5 m / s arrow:

Figure9.

Velocities

at the

surface. Situation

after

6.8

years

of

depositlon.

0.5 m/s

ar row:

Figure

10.

Surface velocities. Situation

after 10.2years.

0.5

m/s

arrow:

Figure 11.Surfa ce v elocities. Situation

after

13.6 years.


9/12

0.5

m /s

arrow:

Figure 12. Surface velocities. Situation

after

17years.

1.0m /s

arrow:

Figure

1 3. Surface veiocities. Situation

after20.4 years.

Figure 14. Map of the

reservoir after

3.4

years

o f

deposition.

Figure 15. Map of the

reservoir

after

6.8

years

of

deposition.

Figure 16. Map of the reservoir

after

10.2 years

o f

deposition.


10/12

Figure17. Map of the

reservoir

after 13.6 yearsof deposition.

Figure

18.

Map

of the

reservoir

after

17

years

of deposition.

Figure19 . Map of the

reservoir

after

20.4 yearsofdeposition.

S S I IM Q = 350 m 3 s

70

T

T 12000000

10000000

5jOO

10,00 15,00

Yecr

20.00

25,00

Figure20 . Change intrap

efficiency

an deffective

volunte.

Three-dimensional model.

The e ffective reservoir

volume

and trap

efficiency

as a

function

of time is shown in Fig. 20. The difference

between the result

from

the twomodelscan be seenwhen comparing Fig. 5 and Fig. 20. The two-dimensional

model gives a volume reduction to 2.7 millionm

3

after 27 years, whilethe three-dimensional

model gives

th e

same result after only 20 years. The higher deposition can be due to the three-dimensional effects. A

possible

reason for the increase in

trap efficiency

are

longer

flow

paths

for the

sediment

particle. As the velocity

pattern

in Figures 6 to 13

Ilstrales,

the flow is

influenced

by large

scale

eddies. The flow path and

rctention

timefor a sediment p article willthere fore increase. Figures 6 and 8 to

13

show the water velocity flow

field

at

the surface.A sim ilar complex w ater flow exists in the whole depth of the reservoir. Th is is illustratedby the

flow fieldina

longitudinal section, shown

in

Figure

7 .

The difference between

the

two-dimensional

and the

three-dimensional model

mayalsobe due tosomeof the

simplifications necessary in the three-dimensional model. The most serious simplification is the use of as

large time

steps

as 3.4years. Thisleadstogreat changes during each time step.As

much

as 2.4 million m

3

of

sediments

deposits before the

geometry

and flow field is

changed.

The

changes take place according

to a

seperate

algorithm,"accellerated deposition ,

which

take care

of bed

elevation increases above

acertainlevel.

Thislevel

is chosen so

that

am inimum water depth is maintained. Depositions above this

level

is moved to

neighbouring cells.

If

this method is not used, the large

time

step can give depositions above the water

level.


11/12

which is unphysical. This method is a necessary simplification when using large time steps. If smaller time

steps

are

used,

computational

time

will be too

excessive

for

practical purposes.

The

minimum

water depth in the accelerated deposition routine is chosen by the user. The

results from

the

two-dimensional model

is

used

to get a

good estmate

for

this parameter.

5. Conclusions

A n

importan

aspect of this study is that the calculation of the waterflow field has been performed without

calibration of the numerical model. The constants in the k-e model are not changed, and

changes

in the

roughness

for the

wall

lawsfor the bed have very little effect.The measurements at Garita reservoir shows

that the

three-dimensional model gives

a

reasonable

flow

field.

I t is

thereby shown that

the

numerical model

can be applied direc tly with out calibration for estimation of the water flow field for this case. T he calculated

sediment flow and trap efficiency for the Garita case,

seems reasonable.

The measured concentrations are

uncertain, but indcatethatthe

calculated

vales can be

correct.

The three-dimensional calculation

from

the Angostura reservoir shows that after 20 years, the reservoir has

only 24 % of the capacity

left.

This can be compared withthetwo-dimensional calculation,whichgivesthe

same capacity after 27 years. The input for the three-dimensional calculations is a steady water discharge of

350

mVs.

This is a simplification of the real

inflow,

w hich will va ry between 50 and 1000

mV s

during a year.

Flushing of the reservoir will also take place, and this will

increase-the

effective storage volume of the

reservoir.

The flushing is notsimulated inthis study.

Approximations in

numerical techniques have various effects

on the

results

of

simulations

of

water

an d

sediment

flow in thereservoir. It is

important thatthese effects

are

assessed

and

taken into account when

interpreting

the final

results. When this

is

done,

the

n umerical model

c an

give useful information about water

and sediment flow in hydropower reservoirs.

Acknowledgements

W e want tothank ProfessorD.K.Lysneforgiving advicefo rthis study.W ealso want to thank ICE for

their

co-operation

in

this work,

and

especially Eng.

L .

Urena

an d

Eng.

G .

Ibarra.

T he

Norwegian R esearch Council

hasprovided

partly

fundingfor this project.

Referentes

1.Kobus, H. Hydraulic

Modelling",

G ermn Association

for

Water Resources

and

LandImprovement 1978.

2.

Olsen,

N. R. B. and

Melaaen,

M. C.

Num erical modelling

of

erosin around

a

cylinder

and

sediment

depositionin ahydropower reservoir",

8th International

Conference

on

Num erical

Methods in

Laminar

and

TurbulentFlow Swansea 1993.

3.

Rodi,

W. "Turbulence

models

and

their application

in

hydraulics",// .///?State-of-the-artpaper. 1980

4. Schlichting, H. Boundary Layer Theory , 7th ed. McGraw-Hill BookCompany Ne w York. 1979.

5.Patankar, S. V. Num erical Heat TransferandFluidFlow",McG raw-Hill Book Company New York. 1980

6.

Abrahamsen,

L .

Sediment deposition

in

water reservoirs ,

M.S.

Thesis Divisin of Hydraulic

and

EnvironmentalEngineering The No rwegian Institute

of

T echnology. 1993.

(In

Norwegian)

7.Jimnez,O. R.,Alvarado,P. G.,Ramrez,M. C. and

Valverde,

J.B., Angostura Hydropower Projec t

-

Preliminary

report on sedim entation in the reservoir ,ICE San Jos Costa Rica. 1993. (In Spanish)

Biographical details

of the

a u t h o r s

N. R. B. Olsen graduated in Civil Engineering from the Norwegian Institute of Technology in 1987. He

studiedsediment transport

for one

year

at

ColoradoState University

in

1989.

He

obtained

a dr.

ing. degree

in


12/12

numerical sediment transpon at the Divisin of Hydraulic Engineering at the Norwegian Institute of

Technology

in 1991. From 1991 he has worked as Research Engineer at the Norwegian Hydrotechnical

Laboratory, specialising in three-dimensional numerical models for water and sedimenttranspon.

O. F.

JimnezgraduatedinCivil Engineering

from

theUniversity of

Costa

Rica in1981. Heobtained a MSc

in

Hydraulic Engineering from Washington State University, USA, in 1987. From 1981 he has worked for

Instilo

Costarricense

de

Electricidad,

in the

reas

ofhydraulic

transients analysis, river engineering, design

of

hydraulicstructures

and planning studies for hydro

powerplants.

A.Levoll

graduated

in

Civil Engineering

from the

Norwegian Institute

of

Technology

in

1991. From 1992

he

has worked as Research Engineer at the Norwegian Institute of Technology, Department of Hydraulic and

Environmental Engineering. He has specialised in river hydraulics, and is currently working on a dr. ing.

degree on downstream consequences of dam failures and hazard floods.

L.Abrahamsengraduated in civil engineering

from

the Norwegian Institute of Technology in 1993. He did

his

thesis on numerical modelling of water and sediment

flow

in hydropower reservoirs. From 1994 he has

worked for

STATKRAFT

ANLEGG A/S, supervising contract work on

refurbishing

of hydropower dams. He

has

also

previosly worked for five years as technical supervisor for a contractor.

calculation of water & sediment flow in hydropower reservoirs, modelling, testing & monitoring,...

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