3-d numerical modeling of flow and sediment transport in rivers

8/6/2019 3-D Numerical Modeling of Flow and Sediment Transport in Rivers

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TRITA-LWR.LIC 2028

ISSN 1650-8629

ISRN KTH/LWR/LIC 2028-SE

3-D NUMERICAL MODELING OF FLOW ANDSEDIMENT TRANSPORT IN RIVERS

Muluneh Admass

May 2005


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Muluneh Admass TRITA LWR.LIC 2028

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3-D Numerical modeling of flow and sediment transport in rivers

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ..............................................................................................................................V

ABSTRACT......................................................................................................................................................... 1

INTRODUCTION............................................................................................................................................. 1

ECOMSED MODEL .........................................................................................................................................2

GOVERNING EQUATIONS ...........................................................................................................................2

Turbulence model............................................................................................................................................... 3

Boundary conditions........................................................................................................................................... 4

NUMERICAL METHODS ...............................................................................................................................4

MODIFICATIONS AND IMPROVEMENTS.................................................................................................5

The bottom boundary condition ......................................................................................................................... 5

Equivalent sand roughness ................................................................................................................................. 6

Shear stress partitioning...................................................................................................................................... 6

Bed load transport and bed evolution ................................................................................................................. 7

MODEL APPLICATION ..................................................................................................................................7

Model description and model boundary.............................................................................................................. 7

Grid generation .................................................................................................................................................. 8

Solution algorithm .............................................................................................................................................. 8

Model calibration................................................................................................................................................ 8

Grid Independence............................................................................................................................................. 8

Sensitivity Analysis ............................................................................................................................................. 9

Validation ........................................................................................................................................................... 9

Flow field ........................................................................................................................................................... 9

Sediment transport ........................................................................................................................................... 10

DISCUSSION................................................................................................................................................... 10

CONCLUSION .................................................................................................................................................11

REFERENCES ................................................................................................................................................24

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ACKNOWLEDGEMENTS

First I would like to acknoweledge the Swedish International Development Cooperation Agency(SIDA) for providing me the financial assistance to do my research work. Then I would like toextend my deepest gratitude to my main supervisor Bijan Dargahi, who, with never ending pa-tience, has shared with me his great scientific knowledge and research experience. Assistant su-

pervisors Klas Cederwal and Bayou Chane deserve special acknoweledgment. Special thanks toBritt Chow for all her concern and support. Thanks Kirlna for all your sisterly help. I am also

very greatful to Hans Bergh, Aira Saarelainen, Nandita Singh, and other colleagues in the vatten-byggnad and in the department of Land and Water Resources, KTH. I am indebted to my spiri-tual father Aba Wolde Meskel, Tins family, my family and my friends here in Stockholm and athome. Finally goes all my available thanks to my wife Tin.

Stockholm, May 2005

Muluneh Admass

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ABSTRACT

The fully integrated 3-D, time dependant, hydrodynamic and sediment transport numericalmodel ECOMSED was used to simulate flow and sediment transport in rivers. ECOMSED wasoriginally developed for large water bodies such as lakes and oceans and solves the primitive

equations of RANS along with a second order turbulence model in an orthogonal curvilinear -coordinate system. The availability of the model as an open FORTRAN source code made modi-fications and addition of new models possible. A new bed load transport model was implementedin the code as well as improvements in treatment of river roughness parameterization, bed formeffects, and automatic update of flow depth due to bed evolution. The model was applied to 1-km long reach of the River Klarlven, Sweden, where it bifurcates into two west and east chan-nels. The water surface and the flow division in the channels were made in agreement with fielddata by spatially varying the roughness. However, the spatial distribution of the bed shear stress

was not realistic. Improvements were made in the bottom boundary condition to represent thevariable effects of bed forms on roughness depending on the flow regime and the flow depth. The improved model realistically reproduced the flow field as well as the sediment transportprocesses in the river Klarlven.

Key words: River model; ECOMSED model; River Klarlven; Bed load transport model

INTRODUCTION

River modelling applications can be groupedinto 2-D depth-averaged hydrodynamicmodels and 3-D models. An evaluation ofthe extent to which 3-D models improvepredictive ability compared to 2-D models is

well described by Laneet al

. (1999) andGessler et al. (1999). They stated that a 3-Dmodel is necessary for predicting sedimenterosion and deposition whenever significantsecondary currents exist, such as in riverbends, crossings, distributaries, or diversions.Some recent research works on flow model-ling are: Weerakoon and Tamai (1989), Olsenand Stokseth (1995), Weiming et al. (1997),Sinha et al. (1998), Lane et al. (1999), Brad-brook et al. (2000), and Chau and Jiang(2001). Olsen and Stokseth (1995) carried outa 3-D simulation of an 80-m long reach ofthe river Sokna in Norway. The model suc-cessfully predicted the flow features and theresults were in good agreement with ob-served data. Sinha et al. (1998) did a compre-hensive numerical study of the flow througha 4-km reach of the Columbia River. Theysucceeded in modelling both rapidly varyingbed topography and the presence of multipleislands. The results agreed well with experi-ments and field measurements. In a recentstudy, Bradbrook et al. (2000) modelled theflow in a natural river channel confluence

using a Large Eddy Simulation (LES). Themodel simulated periodic flow features inriver confluences and agreed well with ex-perimental data. Some recent applications onuse of 3-D sediment transport models are:Gesseler et al. (1999), Holly and Spasojevic(1999), Fang (2000), Rodi (2000), Weiminget

al. (2000), Nicholas (2001), and Dargahi(2004). Gesseler et al. (1999) applied the U.S. Army Corps Engineering code CH3D-SEDto the Deep Draft Navigation project on thelower Mississippi River. The code predictedthe sediment deposition in the river with anaccuracy of less 13% in comparison with theobservations. Holly and Spasojevic (1999)applied and verified the CH3D-SED code tostudy water and sediment diversion at theOld River Control complex on the lower

Mississippi river. Dargahi (2004) predictedsecondary flows and the general flow andsediment transport patterns in a river thatagreed well with field measurements. A briefreview of the major developments in 3-Dmodeling and the limitations is also given byLane et al. (2002).

In this paper the fully integrated 3-D, timedependant, hydrodynamic and sedimenttransport numerical model ECOMSED byBlumberg and Mellor (1987) is used.

ECOMSED was originally developed forlarge water bodies such as lakes and oceans

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and solves the primitive equations of RANSalong with a second order turbulence model

in an orthogonal curvilinear -coordinatesystem. The availability of the model as anopen FORTRAN source code made modifi-

cations and addition of new models possible.The first objective of the present study wasto adapt and improve the ECOMSED modelfor modeling flow and sediment transport inrivers. The second objective was to test theapplicability of the improved model to theriver Klarlven in the southwest part of Swe-den. A new bed load transport model is im-plemented in the code as well as improve-ments in treatment of river roughnessparameterization, bed form effects, and

automatic update of bed evolution. Theimproved model realistically reproduced theflow field as well as the sediment transportprocesses in the river Klarlven. The secon-dary flows at the river bifurcation and aroundthe bends were well reproduced. The resultsalso agreed well with the previous simulationsby Dargahi (2004).

ECOMSED MODEL

The ECOMSED model is a fully integrated

3-D hydrodynamic, wave and sedimenttransport model. It has a free surface and a

bottom following -coordinate system (forbetter representation of irregular bottomtopography) with an orthogonal curvilineargrid in the horizontal plane. Here follows abrief description of the governing equations,boundary conditions, the turbulence modeland the solution algorithms which are relatedto the present study. Details of the model canbe found in Blumberg (2002).

GOVERNING EQUATIONS

The fundamental equations of fluid dynamicsare based on the conservation of mass andmomentum. Conservation of mass yields thecontinuity equation while conservation ofmomentum yields the momentum equation.Both equations are widely known byNavier-Stokes equations. Here follows the Navier-Stokes equations in the Cartesian coordinate

system ( zyx ,, axis).

0=

+

+

z

w

y

v

x

u (1a-d)

+

+

+

=

+

+

+

2

2

2

2

2

21

z

u

y

u

x

u

x

p

z

uw

y

uv

x

uu

t

u

+

+

+

=

+

+

+

2

2

2

2

2

21

z

v

y

v

x

v

y

p

z

vw

y

vv

x

vu

t

u

gz

w

y

w

x

w

z

p

z

ww

y

wv

x

wu

t

u+

+

+

+

=

+

+

+

2

2

2

2

2

21

In which are the velocity components

along

wvu ,,

zyx ,, directions respectively, t is

time, is the fluid density, is the pressure,p

is the fluid kinematic viscosity and is the

gravitional force. The flow is assumed in-compressible (constant density) and thefluids coefficient of viscosity is taken con-

stant. It is possible to solve the Navier-Stokesequations bydirect numerical simulation(DNS) if we can resolve all the relevant length scaleswhich vary from the smallest eddies to scaleson the orders of the physical dimensions ofthe problem domain. For channel flow thenumber of grid points needed to resolve allthe relevant scales can be estimated from theexpression (Tannehill et al. 1997)

g

( ) 4/9088.0heDNS

RN = (2)

In which h is the Reynolds number basedon the mean channel velocity and channelheight. This approach is limited to flows ofsimple geometry and very low Reynoldsnumber. Another promising approach isknown as large-eddy simulation(LES), in whichthe large-scale structure of the turbulent flowis computed directly and only the effects ofthe smallest (subgrid-scale) and more nearlyisotropic eddies are modeled. The computa-tional effort required for LES is less than that

of DNS by approximately a factor of 10using present-day methods. The main thrustof present-day research in computationalfluid dynamics is through the time averaged

Navier-Stokes equations also known as theReynolds averaged Navier-Stokes (RANS) equa-tions. These equations are derived by de-composing the dependent variables in theconservation equations in to time-mean (ob-tained over an approximate time interval) andfluctuating components and then time aver-

aging the entire equation (Tannehill et al.1997). Time averaging the equations of mo-

eR

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tion gives rise to new terms, which can beinterpreted as apparent stress gradientsassociated with the turbulent motion.ECOMSED model solves the RANS equa-tions with the hydrostatic assumption and the

three-dimensional equation describing theadvection and diffusion of sediment particlesgiven below,

0=

+

+

z

W

y

V

x

U (3a-e)

+

+

+

=

+

+

+

''''''

1

uwz

U

zuv

y

U

yuu

x

U

x

x

P

z

UW

y

UV

x

UU

t

U

+

+

+

=

+

+

+

''''''

1

vwz

V

zvvy

V

yvux

V

x

y

P

z

VW

y

VV

x

VU

t

V

z

Pg

=

+

+

=

+

+

+

''''''

)(

cwz

C

zcv

y

C

ycu

x

C

x

z

CWW

y

VC

x

UC

t

C s

In which are mean velocity compo-

nents in theWVU ,,

zyx ,, directions respectively

( is the main flow direction, is the stream

wise direction, is vertical to the bed) while

are the corresponding fluctuating

velocity components, C is the mean sediment

concentration and is the flactuating com-ponent, is sediment diffusivity and is the

settling velocity of sediment particles. Thenew correlations that appeared in the aboveequations are related with the mean valuesusing turbulence models. The settling velocityof sediment particles is calculated from theeffective diameter of the suspended sediment

using the semi-empirical formulation ofCheng (1997)

x y

z''' ,, wvu

'c

sW

( )[ ]5.1

52.1255.02

*

50

+= DD

Ws

(4)

50

3/1

2*

)1(D

gsD

=

(5)

In which is particle diameter for 50%

finer of bed material,*

is the dimensionless

grain size and is specific density.

50D

D

s

Turbulence model

Turbulence models are used to relate the newcorrelations that appeared in the RANS equa-tions and in the mean sediment concentra-tion equation with mean values or in other

words to close the system of equations. Herefollows the description of equations used inECOMSED to relate the new correlations

with the mean values.

( ) ( VU )z

Kvwuw M ,,''''

= (6a-d)

( )

=

x

U

y

VAvvuu M ,2,

''''

+

==

x

V

y

UAuvvu

M

''''

( )

= z

C

Ky

C

Ax

C

Acwcvcu HHH ,,,,''''''

In whichM

is the eddy viscosity,HK is the

eddy diffusivity,M

is the horizontal viscosity

and is the horizontal diffusivity. The

horizontal viscosityM

is calculated accord-

ing to Smagorinsky (1963)

K

A

HA

A

2

1

2

2

2

1

+

=

i

j

j

i

Mx

U

x

UcA

(7)

In which c = 0.01, 2 = xy, and Einstein

convention is used. x and y are the gridspacing in the x and y directions respectively.

The horizontal diffusivityH

is usually set

equal toM

.M

andH

are obtained by ap-

pealing to a second order turbulence closurescheme developed by Mellor and Yamada(1982) which characterizes the turbulence byequations for the turbulence kinetic energy,

A

A K K

2

2

1q , and turbulence macroscale, l , accord-

ing to,

+

+

+

+

=

+

+

+

y

qA

yx

qA

xB

q

z

V

z

UK

z

qK

zz

qW

y

qV

x

qU

t

q

HHM

q

22

1

322

22222

22

l

(8a,b)

( ) ( ) ( ) ( ) ( )

+

+

+

+

=

+

+

+

y

lqA

yx

lqA

xW

B

q

z

V

z

UKE

z

qK

zz

qW

y

qV

x

qU

t

q

HHM

q

22

1

322

1

22222

~l

lllll

In which are empirical

constants. The wall proximity function, W

qSEEBBAA ,,,,,, 212121~ , is

defined as

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2

21~

+=

LEW

l (9)

zHzL ++

=

111

(10)

In which is the von Karman constant, is

the water surface elevation and H is the water depth. While details of the closuremodule are rather involved, it is possible toreduce prescription of the mixing coefficientsto the following expressions,

3/1

1B

qKM

l=

(11a-c)

=

2

1

2

61

B

AqAKH l

qqqSK l=

Empirical constants arerespectively (Mel-

lor and Yamada 1982).

qSEEBBAA ,,,,,, 212121

2.0,33.1,8.1,1.10,6.16,74.0,92.0

Boundary conditions

The boundary conditions are specified assurface, bottom and open boundaries.

Free surface: The boundary conditions at thefree surface, ),,( tyxz = , are

( ) (12a-e)oyoxMz

V

z

UK ,, =

23/2

1

2

suBq =

02 =lq

tyV

xUW

+

+

=

0=

z

CKH

In which ( )oyox , is the surface wind stress vector with the surface friction velocity, ,

being the magnitude of the vector.

su

Bottom boundary:The boundary conditions atbottom boundary, , are),( yxHz =

( ) (13a-e)bybxM

z

V

z

UK ,, =

23/2

1

2

buBq =

02 =lq

y

HV

x

HUW btbtbt

=

DE

z

CKH =

In which are the velocity compo-

nents at the bottom,btbtbt WVU ,,

DE is the sedimentflux at the water sediment interface which iscalculated using the van Rijn (1984a) proce-

dure and is the bottom friction velocity

associated with the bottom frictionalstress

bu

( )bybx , . In ECOMSED the bottom

stress is determined by matching velocitieswith the logarithmic law of the wall.

bbDb VVC = (14)

With the value of the drag coefficient CDgiven by

2

ln1

+=

o

bD

z

zHC

(15)

In which and are the grid point and

corresponding resultant horizontal velocity inthe grid point nearest to the bottom. The

parameter depends on the local bottom

roughness.

bz bV

0z

Open lateral boundary: Two types of openboundaries exist, inflow and outflow. Thenormal component of velocity is specified

while a free slip condition is used for thetangential component at inflow boundaries.

Turbulence kienetic energy and the macro-scale quantity ( ) are calculated with suffi-

cient accuracy at the boundaries by neglectingthe advection in comparison with other termsin their respecttive equations. The sedimentconcentration data at the inlet is specified,

whereas at outflow boundaries the mixedboundary condition is used. The clampedboundary condition in ECOMSED allowsassigning observed water level along the openboundary grids.

lq2

NUMERICAL METHODS

The governing equations and boundary con-ditions are transformed in to a vertical -layer and an orthogonal curvilinear horizontal(

21 ) coordinate system. The - transforma-

tion is given by

+

=

H

z (16)

In which is the water surface elevation.

The vertically and horizontally transformedset of equations is approximated by a finite

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difference scheme using a spatially staggeredgrid. The leap frog scheme with the Cou-rant-Friedrichs-Levy (CFL) computationalstability condition and a weak filter to re-move solution splitting at even and odd time

steps is employed for time differencing. Three options (upwind difference, centraldifference and Multidimensional PositiveDefinite Advection Transport Algorithm) areavailable for spatial differencing. The hydro-dynamic module (ECOM) is 3-D with a splitexternal-internal mode algorithm; the exter-nal mode explicitly solves the depth inte-grated equations with short time steps toresolve fast moving waves and to determinethe water surface elevation. The internal

mode uses the computed water surface eleva-tion and implicitly solves the vertical struc-ture of the flow with a shorter time step. Theinternal mode then updates some of the

variables of the external mode for the nexttime step to begin. At regular intervals speci-fied by the user the sediment transport mod-ule (SED) which uses the same numericalgrid, structure and computational frameworkas the hydrodynamic model simulates sedi-ment resuspension, transport and deposition

of cohesive and non-cohesive sedimentsusing the previously computed hydrodynamicvariables.

MODIFICATIONS AND

IMPROVEMENTS

The application of ECOMSED to rivers canbe improved by considering some of thespecific features of river hydraulics that dif-fers from large scale motions such as rough-ness, spatial variations of flow depth, and bed

load transport. In rivers, significant variationsin channel and river bed roughness arefound. Furthermore, the formation of bedforms directly affects the resistance to flow as

well as the distribution of bed shear stresses.The other aspect is the spatial variation of theflow depth that affects the velocity distribu-tion and the boundary layer characteristics.In ECOMSED model a constant roughness

value is used. The effect of bed form rough-ness which depends on the local flow regime

is not considered. The bed load transport isalso not modeled. To implement the forgo-

ing aspects in the model the river Klarlvenwas used as a case study. Realistic and com-parable results with field measurements and

with previous simulations using other models were obtained after the following improve-

ments and modifications were made.

The bottom boundary condition

The bottom boundary condition used inECOMSED as given in equations (14) and(15) is the generalization of the logarithmiclaw which assumes the same roughness in the

whole computational domain. However, inrivers roughness which is composed of skinfriction due to bed grains and drag form dueto bed forms varies spatially and temporally

depending on the local flow depth and thelocal flow regime. The bottom boundarycondition was reformulated as follows todirectly represent the spatial and temporal

variation of the bottom roughness. Startingfrom the general equation of the logarithmicuniversal velocity distribution (Schlichting1968)

BBuzH

u

Vbb +

+=

*

*

)(ln

1 (17)

In which45.5=

B , 41.0=

and B

, the rough-ness induced velocity deficit is a function ofthe equivalent roughness height

sk . Denoting

/*uks by and using the interpolation for-

mula by Cebeci and Bradshaw (1977)

+sk

[ ]{ }

>+

+

3-d numerical modeling of flow and sediment transport in rivers

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