Users manual: DUCT-SUSTRA

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Delft

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Delft University of Technology

Department of Civil Engineering

Hydraulic and GeotechnicalEngineeringDivision HydromechanicsSection

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Users manual

DUCT-SUSTRA

Report n° lOa-91 (draft)

G.J.C.M

Hoffmans

Faculty of Civil Engineering

Hydraulic Engineering

Delft University of Techno1ogy

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Contents 1. Introduction 2. Flow-model DUCT 2.1 General 2.2 Input files 2.3 Result files

2.4 Bed shear-ve1ocity

2.5 Eddy viscosity at end of bed protection 2.6 Ratio of eddy diffusivityand eddy viscosity 2.7 Kinetic energy at end of bed protection 2.8 Separation point

2.9 Grid refinement

2.10 Equivalentbed-roughness 3. Sub-models SMOOTH and GENBLK 4. Morpho1ogical-modelSUSTRA 5. Sub-model SUSTDUCT

6. MORF and MYSCRIPT 7. General remarks 3 5 5 8 10 11

12

12

13 13 14 14 16 17 17 18 References

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3 1. INTRODUCTION

Some information is given how to use the scour model DUCT-SUSTRA

(Hoffmans, 1991). The scour model predicts the morpho1ogical process in scour holes or trenches and consists of two separated sub-models: a flow model DUCT and a morpho1ogica1 model SUSTRA. The flow model is based on the equation of continuity and the momentum equations for turbulent flow (Vreugdenhil, 1982). The Reynolds-closure problem is solved by

prescribing the eddy viscosity with model equations (Hoffmans, 1991). The concentrations are calculated by the morphologica1 model, which is based on the convection-diffusion equation (van Rijn and Meijer, 1986). The bed load transport and the concentration at the reference level are ca1cu1ated with stochastic equations.

The software of the scour model is written in FORTRAN and can be

installed on a personal computer. However, it is recommended to install it on a 1arger computer, if a grid of more than 100 nodes is des1red.

The mode1s DUCT and SUSTRA are coupled by the sub-models SMOOTH, GENBLK and SUSTOUCT, figure 1.

In section 2. the structure of input and plot files concerning DUCT is specified. In the subsequent sections the procedure is exp1ained how to make a run with DUCT-SUSTRA. It 1s remarked that this 'manual' is still incomplete.

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f--<.

DUCT

1--:

f--<.

SMOOTH

-:

f--<.

GENBLK

1--:

f--<.

SUSTRA

-:

-<.

SUSTDUCT

1--:

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Figure 1

Structure of the scour model DUCT-SUSTRA

--- - -4

~

input (sub-section 2.2)

~

output (sub-section 2.3)

--1

USTARBKS.DTA

~

USTARBKS.DAT

--1

DUCTSUST.DAT

~

BULK

--1

INPUT / BULK / USTARBKS

.

DAT

~

output (Meijer. 1987)

--1

SUSDUCIN.DAT / RESULT

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5 2. FLOW-MODEL DueT 2.1 General

To operate the flow-model DUCT two input files are necessary (section 2.2):

input files DUCTINl.DAT DUCTIN2.DAt

In DUCTINl.DAT the hydraulic conditions (discharge, bed roughness etc.) and some constants are specified. These constants are needed in the model equations to prescribe the eddy viscosity The layout of the scour hole is represented in DUCTIN2.DAT. The executable of DUCT generates some output files of which some ASCII files for plotting (section 2.3).

They are:

output files plot files DUCTOUT.DAT PLOT. DAT DUCTPARM.LST PLOT.TAU DUCTSUST.DAT PLOT.USP SIGOUT.DTA PLOT.VEL USTARBKS.DTA PLOT.VIS

2.2 Input files

The structures of DUCTIN1.DAT and DUCTIN2.DAT are given in tables 1 and 2 respectively. The variables in these files, which are all real

characters, are free formatted, i.e., that the characters are enclosed with a comma or space. Further it is remarked that the structure of

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6 DUCTIN1.DAT N, CK, G, RHOW, RNU SX, SY, QN, QL, IV, THETA BK1, BK2, BK3, AL, IDZO, DZO

XU2, XU3, XU4

AM

,

AW, BETA,

GAM,

CB

VSCMIN, VSCMUF, ICML, VSCCML

AH

,

AK, AN,

AS, AT, Al, A2, BN, BNU, CKK, PHI JS

JJ(I), J-l,JS NXl

Xl(I), I-l,NXl DX(I) , I-l,NX1-l Table 1 Input DUCT

DUCTIN2.DAT

NX2

X2(I), I-l,NX2 HO(I), I-l,NX2 Table 2 Input DUCT

The aforementioned parameters in DUCTIN1.DAT represent:

line 1 N CK G RHOW RNU

- number of grid points in the vertical (- 15 to 20) - constant of von Kármán (- 0.4)

- acceleration of gravity (- 9.81 mjs2) - fluid density (- 1000 kgjm3)

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line 2 SX SY QN QL

IV - parameter on beha1f of research purposes (- 0) THETA - factor (- 0 to 1, Vreugdenhi1, 1982, p.14)

rigid lid in x-direction (- 0) - rigid lid in y-direction (- 0)

discharge per unit width in x-direction (in m2js)

- dis charge per unit width in y-direction (QL - 0 m2js)

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1ine 3

BK1 - bed roughness fixed bed (in m, section 2.10)

BK2 - bed roughness initia1 slope of scour hole (in m, section 2.10) BK3 - bed roughness downstream of reattachment (in m, section 2.10) AL - transition 1ength (in m, section 2.10)

IDZO - 0 or 1, if IDZO - 0 the parameter DZO is switched off and if IDZO - 1 the parameter DZO is switched on (section 2.8) DZO - strip where the ve10cities are zero (in m, section 2.8)

1ine 4

XU2 - x-coordinate (in m, section 2.4) XU3 - x-coordinate (in m, section 2.4) XU4 - x-coordinate (in m, section 2.4)

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11ne 5

AM - diffusion parameter (a - 0.25, Hoffmans, 1988, p.13)

m

AW - parameter wa11-boundary 1ayer (a - 2.0, Hoffmans, 1988, p.15)

w

BETA - ang1e of mixing 1ayer

(P -

0.20, Hoffmans, 1988, p.13) GAM - parameter mixing 1ayer (~ - 0.0175, Hoffmans, 1988, p.13) CB - bed coefficient (cb - 100, Hoffmans, 1988, p.14)

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11ne 6

VSCMIN - minimum va1ue of the eddy viscosity (- 0.000005

m

2js)

VSCMUF - maximum eddy-viscosity at x - 0 (in m2/s, section 2.5)

ICML parameter on beha1f of research purposes (- 0) VSCCML - parameter on beha1f of research purposes (- 0)

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line 7

AH

AK AN AS AT Al A2

BN

BW C~ PHI

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8 - constant (~ - 1.5, Hoffmans, 1991, p.93) c

(wk -

3.33, Hoffmans, 1991, p.90) (~/(hm - ho) - 5 to 8, Hoffmans, 1991, p.34)

(a -

0.12, Hoffmans, 1991, p.91) a (ao - 0.4, Hoffmans, 1991, p.85) (wb - 0.15, Hoffmans, 1991, p.112)

(a

e -

1.5, Hoffmans, 1991, p. 100) on beha1f of research purposes (- 1) - constant constant - constant constant - constant - constant - constant

- ratio of eddy diffusivity and eddy viscosity (section 2.6) - constant (- 0.03, section 2.7)

o 0

- ang1e of interna1 friction of bed material (- 30 to 40 )

1ines 8 and 9

JS number of sections in the transverse direction (- 1)

JJ(I) - coordinates of sections in the transverse directions (- 1)

1ines 10, 11 and 12

NX1 - number of intervals with constant width (section 2.9) X1(I) x-coordinates, (I-1,NX1) (in m, section 2.9)

DX(I) - step sizes (I-1,NX1-1) (in m, section 2.9)

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The input parameters of DUCTIN2.DAT are:

NX2 number of sections in x-direction (section 2.9) X2(I) x-coordinates (in m, section 2.9)

HO(I) - flow depths (in m, section 2.9)

2.3 Result files

The flow-model DUCT generates several output files. In DUCTOUT.DAT not on1y the velocities, the eddy viscosity and the Reynolds shear-stress are given for each grid point but a1so the bed roughness and the

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pressure on the rigid lid for each section. File DUCTPARM.LST represents

a listing of the general input parameters. File DUCTSUST

.

DAT is

necessary to create a bulk file for SUSTRA and SIGOUT.DTA gives an

overview of the turbulence parameters.

The files PLOT.DAT

,

PLOT

.

VEL

,

PLOT

.

VIS, PLOT.TAU and PLOT

.

USP are ASCII

files and can be used for plotting

.

Tables 3 and 4 give an overview of the structures of the plot files.

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PLOT.DAT

PLOT

.

VEL

NX2 ,N ,XM

,

HM

NX2

,

N,XM,HM

X2(1),HO(1)

X2(1) ,H(l)

Z(l,O),U(l,O),W(l,O),VSC(l,O),TUW(l,O)

Z(l

,

O) ,U(l,O)

Z(l,l),U(l,l),W(l,l),VSC(l,l),TUW(l,l)

Z(l,l),U(l,l)

Z(1,2),U(1,2),W(1,2),VSC(1,2),TUW(l,2)

Z(1,2),U(1,2)

Z(l,N),U(l,N),W(l,N),VSC(l,N),TUW(l,N)

Z(l,N) ,U(l,N)

X2(2),HO(2)

X2(2),HO(2)

Z(2,O),U(2,0),W(2,0),VSC(2,0),TUW(2,0)

Z(2,O),U(2,0)

Z(2,1),U(2,1),W(2,1),VSC(2,1),TUW(2,1)

Z(2,l),U(2,1)

Z(2,2),U(2,2),W(2,2),VSC(2,2),TUW(2,2)

Z(2,2),U(2,2)

Z(2,N),U(2,N),W(2,N),VSC(2,N),TUW(2,N)

Z(2,N),U(2,N)

X2(NX2),HO(NX2)

X(NX2),HO(NX2)

Z(NX2,0),U(NX2,0),W(NX2,O),VSC(NX2,O),TUW(NX2,0)

Z(NX2,0),U(NX2,O)

Z(NX2,l),U(NX2,l),W(NX2,1),VSC(NX2,1),TUW(NX2,1)

Z(NX2,1),U(NX2

,

1)

Z(NX2,2),U(NX2,2),W(NX2,2),VSC(NX2,2),TUW(NX2,2)

Z(NX2,2),U(NX2

,

Î

,

!

,

Z(NX2,N),U(NX2,N),W(NX2,N),VSC(NX2,N),TUW(NX2,N)

Z(NX2 ,N),U(NX2 ,

;

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10

PLOT.USP NX,XM,HM X(l),H(l),UST(l),CP(l),ST(l) X(2),H(2),UST(2),CP(2),ST(2) X(NX) ,H(NX) ,UST(NX),CP(NX) ,ST(NX) Table 4 Structure of PLOT.USP

in which: NX - number of grid points in x-direction XM - maximum x-coordinate

HM - maximum flow-depth X - x-coordinate

H - flow depth

UST - bed shear-ve10city CP - pressure on rigid lid

ST - standard deviation of the instantaneous bed shear-stress

Z - vertica1 coordinate

U - longitudina1 flow-velocity W - vertical flow-ve1ocity VSC - eddy viscosity

TUW - Reynolds shear-stress

The structures of PLOT. VIS and PLOT.TAU are almost identical with the structure of PLOT.VEL. In PLOT.VIS the parameter U is replaced by VSC and in PLOT. TAU by TUW.

2.4 Bed shear-velocity

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in which u is the tangential flow-velocity calculated in the K-th grid

r

point above the mean bed-level, ~ is the constant of von Kármán, ó is the distance perpendicular to the bed and Zo is the zero velocity level (Hoffmans, 1988, p.ll).

In table 5 an overview is given regarding the calculation method.

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x-coordinate K

0

_<

x

<

XU2 2 XU2

_<

x

_<

XU3 INT(NjlO+l) XU3

_<

x

<

XU4 INT(NjlO+2) x

>

XU4 INT(NjlO+3)

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Table 5 (INT - integer)

2.5 Eddy viscosity at end of bed protection

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If the turbulence is not yet dying out to uniform-flow conditions at the end of the bed protection, the maximum eddy-viscosity can be specified there. At the transition of the fixed bed to the erodible bed the eddy viscosity is parabolically distributed. If the length of the bed

protection is sufficiently large, i.e., approximately 80 to 100 times the flow depth, the turbulence is determined by the bed roughness. Then

VSCMUF - O

.

The eddy viscosity (vt) is related to the (turbulent) kinetic energy (k)

as follows (Rodi, 1984):

where c is a constant and L is a length scale, which order of magnitude

v

equals the flow depth. The kinetic energy, which definition is given by:

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k -

~[ü'Uï

+ v'v' +

w'w'l

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where u', v' and w' are f1uctuating f10w-ve10cities in the 10ngitudina1, transverse and vertical direction respectively, can be approximated by (Nezu, 1977):

k - al u'u'

I

where al is a constant. For uniform-flow conditions the constants c and

v

al measure respective1y c - 0.55 and al - 1.13.

v

It is remarked that VSCMUF ref1ects the magnitude of the eddy viscosity above the mixing layer and not the eddy viscosity both in the mixing layer and in the recirculation zone, sub-section 2.7.

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2.6

Ratio of eddy diffusivity and eddy viscosity

The ratio of eddy diffusivity and eddy viscosity (-

p )

describes the s

difference in the turbulence-induced transport of sediment particles and the transfer of fluid momentum. According to van Rijn (1987) this factor depends on the parameter ws/u* as follows:

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P

-

1 +

2[w

/u*] s s for

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in which w is the fall velocity (Zanke, 1977).

s

Though the bed shear-velocity varies in the streamwise direction, the factor

p

is kept constant in the entire field.

s

2.7 Kinetic energy at end of bed protection

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The kinetic energy (k ) in the mixing layer is supposed to be constant m

and given by:

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13

where

Ü

o represents the initial depth-averaged flow-veloeity.

For a flow over a baekward-faeing step Ck varies from 0.035 to 0.045 and for a flow in a seour hole Ck lies within the reach of 0.025 to 0.035 (Hoffmans, 1991, p.52). In the experiments of Hoffmans (1990), where the length of the fixed bed was about 80 to 100 times the initial flow-depth, the constant Ck amounted to 0.03.

2.8 Separation point

Beeause the separation point, i.e., near the transition of the fixed bed to the erodible bed, is not well predieted by the flow model, if the initial slope of the seour hole is relatively large, a flow-veloeity profile has to be given as follows: a logarithmie flow-veloeity profile with a relatively small strip, where the longitudinal flow-veloeities equal zero, figure 2. The length of this strip depends on the number of grid points in the vertieal and the magnitude of the initial flow-depth.

2.9 Grid reflnement

It is possib1e to refine the grid in the longitudina1 direetion. In the vertieal direetion the refinement of the grid ean be obtained by an

enlargement of N (line 1 in DUCTINl.DAT).

Considering undermentioned example (lines 10, 11 and 12 of OUCTINl.OAT)

~l X1(1), Xl(2), OX(l) , OX(2), , X1(~1) , OX(NX1-1) 5 0.00 1.25 1.55 2.55 9.55 0.05 0.0075 0.10 0.20

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1.25 m, 0.0075 m from 1.25 to 1.55 m, 0.10 m from 1.55 to 2.55 mand 0.20 m.from 2.55 to 9.55 m, figure 3. The bed configuration is specified in DUCTIN2.DAT. Between the nodes the flow depth is linearly

interpo1ated. If DUCTIN2.DAT is given by:

~2 8

X2(1), X2(2), , X2(5) 0.0 0.2 0.4 0.6 0.8 HO(l), HO(2), , HO(5) 0.2 0.3 0.4 0.4 0.3 X2(6), , X2(~2) 1.0 1.25 1.55

HO(6), , HO(NX2) 0.2 0.2 0.2 the flow depth measures 0.325 m for x - 0.75 m.

It is remarked that at each 1ine no more than 5 coordinates can be given and that the maximum value of ~2 measures 50.

2.10 Equivalent bed-roughness

The equivalent roughness height at the bed protection (BK1) is assumed to be equa1 to the mean diameter of the grains and in the scour hole,

where two different values for the equivalent roughness can be

specified: at the initia1 s10pe (BK2) and downstream from reattachment (BK3), figure 2, the equivalent roughness equa1s half the bed-form height (van Rijn, 1987, p.1627). Usually the bed in the dece1eration zone is hydrau1ically smooth (no ripp1es or dunes) for f10ws with smal1 Froude numbers (Fr

<

0.5) and fine sediment (d60

<

250 ~m), so that

BK2

=

3doo and in the acceleration zone the bed is hydraulically rough. The order of magnitude of the transition 1ength measures O(AL) - HO.

3. SUB-MODELS SMOOTH AND GENBLK

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Z (m)

t

0.'"

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Figure 2 o.zo 0-'0 15 BK1

••••••

-

_AL

-BK1 • bed roughness fixed bed

BK2 • bed roughness initial slope of scour hole BK3 • bed roughness downstream of reattachment AL • transition length (bed roughness)

DZO• small strip where veloeities equal zero

F1ow-ve1ocity profile at x - 0

I- 1- 1-1- 1-1-1-1-I- I- 1-1-1-1-1- I- 1-1-1-1-1- 1-1-1- _I- I-1-1- I-I- 1-1-1-1-1- I-_1-1-1-1- I-1-1- 1- I- _1- I-I- _{1-1_} I-1-1- I- 1-1-1-I-I-I-I-~1-1- 1-1-1-1-1- 1-1-1-L- _{I- I-}

1-1-1-1-1-1-1-1-1-1-t:

1-1-1-1- 1-I-I-I-t~l-~t~l-t~I-~~ ~ 1-1- 1-1- 1-1- 1-1-1- I-I-~~~ I- 1-1-1- I-I-I-~I-I-I-~I-I-~I-I-ttl-I-I- 1-1- 1-I-I-I-I-I-I-tl-l-l-t~~1-_{1-1-I- I-~ 1-1-1-1-~ I-~}

I- 1-1-1- 1-1- 1-1-I- 1-1-1-1- L-L-L-L-1-1- L-

L-L-L-I

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Figure 3 _ x(m)

Examp1e of a grid schematization of a scour hole

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16

borizontal) and SIG (- standard deviation of tbe instantaneous bed

sbear-stress) in tbe file USTARBKS.DTA generated by DUCT are smootbed by tbe sub-model SMOOTH. Tbe smootbed variables are written in

USTARBKS.DAT, figure 1.

Tbe sub-model GENBLK generates an unformatted BULK file for SUSTRA.

4. MORPHOLOGICAL-MODEL SUSTRA

To activate SUSTRA tbe (standard) file INPUT bas to be made (Meijer, 1987). In eomparison witb tbe standard version of SUSTRA not only tbe flow velocities and tbe eoeffieients of eddy diffusivity are supplied by tbe user (BULK) but also tbe bed sbear-velocity, the bed roughness, the angle of tbe bed witb tbe borizontal and tbe standard deviation of the instantaneous sbear-stress (USTARBKS.DAT).

In tbis version of SUSTRA tbe bed load and tbe eoncentration at tbe referenee level are caleulated with stochastie equations, whieb were introdueed by van Rijn (1987) and modified by Hoffmans (1991).

A detailed description of SUSTRA is given by Meijer (1987).

5. SUB-MODEL SUSTDUCT

The sub-model SUSTDUCT links the models SUSTRA and DUCT and generates the new layout of the scour hole after given time step. This information is written in file DUCIN2.DAT. Tbe layout as function of time is stored in PLOT.GEO, which can be used for plotting. Tbe file ICFILE eounts the number of time steps. A restart is possible by activating the shell program MYSCRIPT (seetion 6.). It is remarked that ICFILE bas to be reset to one, if a new computation witb different hydraulie eonditions is started. Further the file DEPNEW.DAT is ereated, whieh was done for

research purposes. To operate SUSTDUCT input file SUSDUCIN.DAT has to o~ specified. Tbe strueture of SUSDUCIN.DAT reads:

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-

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ALFA, ZA, IZA, AS, BKl, DZO

in which: _{ALFA dH/H accuracy parameter (lh' Hoffmans, 1991, p.83)} ZA - (absolute) thickness bed layer (in m, Meijer, 1987)

IZA - (relative) thickness bed layer (Meijer, 1987) AS - smooth factor (1 - 0 to I, Hoffmans, 1991, p.83'

BKl - bed roughness x - 0 (in m, section 2.9)

DZO - length small strip at x - 0 (in m, section 2.8)

6. MORF and MYSCRIPT

The scour model can be activated by both MORF or MYSCRIPT, which are both UNIX files. Starting for example MORF 100 the program runs the scour model 100 times in the active mode of the computer. It is also possible to run the program in the background memory by activating MYSCRIPT. The listing of MORF is:

iter-O

while test $iter -Ie $1 do

clear

echo Number of iterations: $iter echo duet smooth genbik sustra sustduet

iter-'expr $iter

+

l' done

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18

7.

GENERAL REMARKS

The number of grid points both in the x-direction (NX) and in theo z-direction (N or NZ) in the mode1s as discussed (figure 1) have to be identical. The parameters NX and N (or NZ), which are declared in the beginning of the source code, can easily be changed with a simple text editor. Starting a new computation with a different grid schematization the models GENBLK, SUSTRA and SUSTDUCT have to be compi1ed and linked again. In DUCT the number of grid points can be specified in the input file DUCTINl.DAT.

The initia1 slope of the scour hole shou1d be fixed from x - 0 to x - Xl

by setting dh/dt - 0 (- bv1(1,j) - 0) in SUSTDUCT (Iine 40).

36 j-2 37 c (lab.) do 41 i-1,15 38 c (prototype) do 41 i-l,lO 39 do 41 i-1,18 40 bvl(i,j)-O. 41 41 continue

In this examp1e the slope is fixed from x - 0 ti1l x - l8*dx, in which dx is the (variabie) step size in the x-direction.

The 1ength of the fixed slope is dependent on the step sizes both in the vertical and longitudina1 direct ion and has to be determined by trial and error to obtain a stabie computation.

It is noted that BKI and DZO in SUSDUCIN.DAT are identical with BKI and DZO in DUCTINI.DAT and that ZA and IZA in SUSDUCIN.DAT are identical with ZA and IZA in INPUT.

The scour model can be activated by running MYSCRIPT, if the input files DUCTINI.DAT, DUCTIN2.DAT, INPUT, SUSDUCIN.DAT and ICFILE are specified.

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19 References

Hoffmans, G.J.C.M., 1988, Flow model with prescribed eddy viscosity,

open file report No.11-88, Vol.l, Hydr. and Geotechn. Engrg.

Div., Delft Univ. of Technol., Delft.

Hoffmans, G.J.C.M., 1990, Concentration and flow velocity measurements in alocal scour hole, open file report No.4-90, Hydr. and Geotechn. Engrg. Div., Delft Univ. of Technol., Delft.

Hoffmans, G.J.C.M., 1991, Two-dimensiona1 mathematical mode1ling of local-scour holes, concept doctoral thesis, Hydr. and Geotechn. Engrg. Div., Delft Univ. of Technol., Delft.

Meijer K., 1987, Sustra users manual, Delft Hydraulics, Delft.

Nezu, I., 1977, Turbulent structure in open-channel f10ws (translation of doctoral dissertation published in japanese), Department of Civil Engrg., Kyoto Univ., Kyoto.

Rijn, L.C. van, and K. Meijer, 1986, Three-dimensiona1 modelling of suspended sediment transport for current and waves, Report Q250/Q432/H46l, Delft Hydraulics, Delft.

Rijn, L.C. van, 1987, Mathematical modelling of morphological processes in the case of suspended sediment transport, Doctora1 thesis,

Hydr. and Geotechn. Engrg. Div., Delft Univ. of Technol.,

Delft, (a1so Delft Hydraulics, Communications No. 382). Rodi, W., 1984, Turbu1ence models and their application in hydraulics,

second edition, IAHR-section on Fundamentals of Division, Delft.

Vreugdenhil, C.B., 1982, Boundary-layer flow over a sloping bottom,

program DUCT, Mathematically investigation, Rep. S488 Part 2, Delft Hydraulics Delft, Delft.

Zanke, U, 1977, Berechnung der Sinkgeschwindigkeit von Sedimenten

Mitteilungen des Franzlus-Instltuts der TU Hannover, Heft 46.

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