Mitigation of turbidity currents in reservoirs with passive retention systems: validation of CFD modeling

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24 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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1.
Introduction

Density

or

gravity

currents

are

predominantly

slender

flows

that

are

impelled

through

density

differences,

established

either

by

salinity,

temperature

or

particles

in

suspension

within

a

fluid

[
1
]
.

The

latter,

currents

where

fine

sediments

in

suspension

are

accountable

for

the

extra

density

are

titled

turbidity

currents
.

Some

of

the

reported

outcomes

of

these

stratified

flows

in

large

deep

reservoirs

comprise,

among

other

consequences,

inlet

and

bottom

outlet

structures

blockage

and

storage

capacity

lessening

[
2
],

and,

at

broader

scales,

water

quality

and

biodiversity

degradation

[
3
]
.

In

virtue

of

multiple

water

bodies

stressors

(e
.
g
.

climate

change,

increasing

population,

among

others),

the

loss

of

storage

in

reservoirs

caused

by

turbidity

currents

is

currently

a

topic

of

forceful

scientific

research

([
4
],

[
5
],

among

others)
.

In

this

context,

the

use

of

Computational

Fluid

Dynamics

(CFD)

tools

as

an

appliance

of

water

bodies

monitoring

programs

is

undoubtedly

of

foremost

importance
.

The

main

objective

of

this

study

is

to

validate

a

CFD

code

(ANSYS
-
CFX)

applied

to

the

simulation

of

the

interaction

between

turbidity

currents

and

passive

retention

systems,

designed

to

induce

sediment

deposition
.

To

accomplish

the

proposed

objective,

laboratory

tests

were

initially

conducted

using

a

straightforward

obstacle

configuration

exposed

to

the

passageway

of

a

turbidity

current
.

Afterwards,

the

experimental

data

was

used

to

build

a

benchmark

case

to

validate

the

3
D

CFD

software

ANSYS
-
CFX
.




Mitigation

of

turbidity

currents

in

reservoirs

with

passive

retention

systems
:

validation

of

CFD

modeling

6
.

Conclusions

In

this

work

ASM

fulfillment

for

modeling

turbidity

currents

was

assessed
.

A
part

its

demanding

computational

requirements

and

even

though

the

numerical

solution

represents

a

fairly

reasonable

prediction

of

the

observed

flow
,

results

reveal
,

at

the

present

stage
,

its

inadequacy

to

describe

a

number

of

aspects
:

i)

the

velocity

maximum

is

under
-
predicted
;

ii)

a

sharp

difference

is

observed

at

the

near

wall

region

and

iii)

a

significant

discrepancy

between

experimental

and

numerical

suspended

sediment

concentration

outcomes

is

verified

downstream

the

obstacle
.

I
ssues

i)

and

ii)

may

be

due

to

a

variety

of

factors,

namely

the

grid

density

and

the

goodness

of

the

choice

of

the

turbulence

model

and

its

parameters,

and

issue

iii)

to

the

overprediction

of

sediment

deposition

upstream

the

obstacle
.

In

the

near

future,

the

impact

of

these

uncertainties

will

be

investigated

by

means

of

a

systematic

sensitivity

analysis
.











References

[
1
]

Simpson
,

J
.

E

(
1999
)
.

Gravity

Currents
:

In

the

Environment

and

the

Laboratory
.

Cambridge

University

Press
.

[
2
]

Oehy
,

C
.

D
.
,

Schleiss
,

A
.

J
.

(
2007
)
.

Control

of

turbidity

currents

in

reservoirs

by

solid

and

permeable

obstacles
.

Journal

of

Hydraulic

Engineering,

133
(
6
),

637
-
648
.

[
3
]

Chung,

S
.
W
.
,

Hipsey
,

M
.
R
.
,

Imberger
,

J
.

(
2009
)
.

Modeling

the

propagation

of

turbid

density

inflows

into

a

stratified

lake
:

Daecheong

Reservoir,

Korea
.

Environmental

Modelling

and

Software,

24
(
12
),

1467
-
1482
.

[
4
]

Alves
,

E
.
,

Ferreira,

R
.

M
.

L
.
,

Cardoso,

A
.
H
.

(
2010
)
.

One
-
dimensional

numerical

modeling

of

turbidity

currents
:

hydrodynamics

and

deposition
.

River

Flow

2010



International

Conference

on

Fluvial

Hydraulics,

Braunschweig
,

Germany,

8
-
10

September

2010
,

1097

-

1104
.


[
5
]

Rossato
,

R
.
,

Alves
,

E
.

(
2011
)
.

Experimental

study

of

turbidity

currents

flow

around

obstacles
.

7
th

International

Symposium

on

Stratified

Flows,

Rome,

Italy,

22



26

August

2011
.

[
6
]

Ansys
,

CFX
-
Solver

Theory

Guide

(
2009
)
.

[
7
]

W
.

Rodi

(
1993
)
.

"Turbulence

models

and

their

application

in

hydraulics

-

a

state

of

the

art

review",

International

Association

for

Hydraulic

Research,

Delft,

3
rd

edition

1993
,

Balkema
.

[
8
]

B
.

Launder,

B
.

Sharma

(
1974
)
.

Application

of

the

energy
-
dissipation

model

of

turbulence

to

the

calculation

of

flow

near

a

spinning

disc,

Letters

in

Heat

Mass

Transfer,

1
,

131


138
.

[
9
]

Gerber,

G
.
,

Diedericks
,

G
.
,

Basson
,

G
.
R
.

(
2011
)
.

Particle

image

velocimetry

measurements

and

numerical

modeling

of

a

saline

density

current
.

Journal

of

Hydraulic

Engineering,
137
(
3
),

333

342
.

[
10
]

Huang,

H
.
,

Imran,

J
.
,

Pirmez
,

C
.

(
2005
)
.

Numerical

modeling

of

turbidity

currents

with

a

deforming

bottom

boundary
.

Journal

of

Hydraulic

Engineering,

131
(
4
),

283
-
293
.

Acknowledgements

This

study

was

funded

by

the

Portuguese

Foundation

for

Science

and

Technology

through

the

project

PTDC/ECM/
099485
/
2008
.

The

first

author

thanks

the

assistance

of

Professor

Moitinho

from

ICIST,

to

all

members

of

the

project

PTDC/ECM/
099485
/
2008

and

to

the

Fluvial

Hydraulics

group

of

CEHIDRO
.

Edgar A. C. Ferreira
1
, Elsa C. T. L. Alves
1

and Rui M. L. Ferreira
2

1
Hydraulics and Environment Department


LNEC, Portugal (email: edgaracf@civil.ist.utl.pt; ealves@lnec.pt )

2
CEHIDRO


IST


TULisbon, Portugal (email: ruif@civil.ist.utl.pt)

2
.

Experimental

Facilities

and

Instrumentation

The

experiments

were

performed

at

LNEC

in

a

16
.
45
m

long,

0
.
30
m

wide

and

0
.
75
m

maximum

height

flume

with

its

bottom

devised

to

simulate

hyperpycnal

turbidity

currents

in

reservoirs
.

During

the

experiments,

longitudinal

velocities

were

measured

in

five

control

sections

with

an

Ultrasound

Velocity

Profiling

(UVP)

system

and

suspended

sediment

concentration

profiles

were

collected

at

two

control

sections

using

syphon

probes

(
Figure

1
)
.

T
he

experimental

conditions

for

the

present

study

case

are

summarized

in

Table

1
.



4
.

Initial

and

Boundary

Conditions


The

numerical

solution

of

the

governing

equations

was

achieved

by

employing

the

Finite

Volume

Method

(Figure

2
)
.

At

the

inflow

section,

a

uniform

streamwise

velocity

distribution

and

a

low

level

of

turbulence

intensity

I

=

0
.
01

(I=
u
rms
/U

with

u
rms

being

the

root
-
mean

square

of

turbulent

velocity

fluctuations

and

U

the

mean

velocity)

were

imposed
.

At

the

outlet,

in

order

to

maintain

a

constant

domain

water

level

regardless

of

the

upstream

mass

flow

rate,

a

mixed

boundary

condition

was

attempted,

i
.
e
.
,

associated

to

an

orifice

at

atmospheric

pressure

a

significant

portion

of

the

outlet

was

prescribed

as

a

no
-
slip

smooth

wall
.

The

free

surface

was

modeled

as

a

free

slip

rigid

lid

and

in

the

bottom

and

lateral

walls

of

the

channel,

including

the

obstacle,

the

no
-
slip

condition

with

a

scalable

wall

function

formulation

was

introduced
.

Furthermore,

the

simulation

was

initialized

with

hydrostatic

conditions
.

Figure 1
-

Flow evolution of the turbidity current at inlet (top left) and outlet
(top right) and the sampling system below

Table

1

-

Experimental

conditions

(
h
obst

refers

to

the

obstacle

height,

d
50

to

the

medium

value

of

particles

diameter,

C
s
0

to

the

initial

sediments

concentration,

U
0

to

inlet

velocity

and

H
wat

to

the

initial

ambient

fluid

height)
.

The

downstream

side

of

the

barrier

is

located

8
.
25

meters

from

the

domain

final

section
.




3
.
The

Algebraic

Slip

Model

(ASM)



Theoretical

Background

The

numerical

simulation

of

the

turbidity

current

evolution

was

carried

out

using

the

ASM

approach

[
6
]
.

The

ASM

is

a

single
-
phase

multi
-
component

simplified

model

which

basically

comprehends

a

mixture

conservation

equation
,

𝜕
𝜌
𝑚
𝜕

+
𝛻

𝜌
𝑚
𝒖
𝑚
=
0

a

momentum

equation,

𝜕𝜌
𝑚
𝒖
𝑚
𝜕𝑡
+
𝛻

𝜌
𝑚
𝒖
𝑚

𝒖
𝑚
=

𝛻𝑝
+
𝛻

𝝉
𝑚
+
𝜌
𝑚
𝒈



and
,

additionally,

a

solids

mass

conservation

equation

𝜕𝜌
𝑚
𝑌
𝑝
𝜕
+
𝛻

𝜌
𝑚
𝑌
𝑝
𝒖
𝑚
+
𝒖
𝑑𝑟𝑖𝑓𝑡
,
𝑝

𝜇
+
𝜇
𝑓
𝑡
𝜎
𝑝
𝛻
𝑌
𝑝
=
0

where
:


𝜌
𝑚

=

mixture

density
,



=

time
,

𝒖
𝑚

=

mixture

velocity

vector
,

𝑝

=

pressure
,

𝝉
𝑚

=

stress

tensor
,

𝒈

=

gravity

acceleration

vector,

𝑌
𝑝

=

sediments

mass

fraction,

𝒖
𝑑𝑟𝑖𝑓𝑡
,
𝑝

=

drift

velocity,

𝜇

=

dynamic

viscosity

(
8
.
899
×
10

4

𝑘𝑔

𝑚

1


1
)
,

𝜇
𝑓
𝑡

=

eddy

viscosity

and

𝜎
𝑝

=

Turbulent

Schmidt

number
.

Closure

for

the

Reynolds

stress

tensor

was

computed

through

the

Boussinesq

assumption

whilst

closure

for

the

Reynolds

flux

vector

was

calculated

via

the

flux
-
gradient

hypothesis

[
7
]
.

In

this

work,

one

made

use

of

a

buoyancy

modified

ƙ
-
ε

two
-
equation

model

(where

ƙ

represents

the

turbulent

kinetic

energy

and

ε

denotes

the

dissipation

rate

of

ƙ)

[
6
]
.

With

the

exception

of

buoyancy

turbulence

terms,

modeling

constants

were

adopted

from

Launder

and

Sharma

(
1974
)

proposal

[
8
]
.

Buoyancy

terms

incorporated

in

ƙ

and

ε

equations

were

estimated,

respectively

by


𝑃
ƙb
=


𝜇
𝑓
𝑡
𝜌
𝑚
𝜎
𝑝
𝑔

𝛻
𝜌
𝑚



























𝑃
εb
=
𝐶
3

max

(
0
,
𝑃
ƙb
)


In

what

concerns

𝜎
𝑝

and

the

dissipation

coefficient

𝐶
3

no

universality

is

foreseeable
.

Quite

on

the

contrary,

several

authors

have

concluded

from

empirical

evidence

that,

on

the

one

hand,

the

eddy

viscosity

and

diffusivity

and

hence

the

turbulent

Schmidt

number

is

related

to

the

level

of

stratification

and
,

on

the

other

hand,

buoyancy

effects

in

the

ε

equation

can

have,

for

particular

cases,

an

irrelevant

role

in

the

turbulence

dynamics
.

Following

the

studies

of

[
9
]

and

[
10
],

in

this

work

it

has

been

assumed

𝜎
𝑝

=

1
.
3

and

𝐶
3

=

0
.


Figure

3

-

ASM

model

results

at

time

t

=

17

s

(left),

53

s

(center)

and

200

s

(right)



5
.

Results


The

spatio
-
temporal

turbidity

current

evolution

is

shown

in

Figure

3
.

In

regards

to

the

adequacy

of

the

ASM

approach,

experimental

and

numerical

results

were

likened

(Figures

4

and

5
)
.


Figure

2

-

Mesh

detail

of

the

CFD

model

in

the

obstacle
´
s

vicinity



Figure

4

-

Non
-
dimensional

time
-
averaged

streamwise

velocities,

where

Z

denot es

vert i cal

coordi nat es,

X

is

the

distance

to

domain
´
s

downstream

section

and

Z
0
.
5


is

an

outer

length

scale

defined

as

the

height

at

which

the

time
-
averaged

velocity

𝐔



is

equal

to

half

t he

maximum

t i me
-
averaged

velocity

??
%

max


Figure

5

-

Variation

of

suspended

sediment


concentration

with

water

depth
.

Experimental

profiles

were

obtained

during

a

brief

sampling

period

whilst

the

numerical

ones

were

acquired

at

t

=

216

s

(x

=

5
.
75

m)

and

at

t

=

186

s

(x=
10
.
25
m)