2009 January 10-12 www.kostic.niu.edu

CFD Simulation of Open Channel CFD Simulation of Open Channel Flooding FlowsFlooding Flows

and Scouring Around Bridge Structuresand Scouring Around Bridge Structures

The 6th WSEAS International Conference on FLUID MECHANICS The 6th WSEAS International Conference on FLUID MECHANICS ((WSEAS - FLUIDS'09WSEAS - FLUIDS'09))

Ningbo, China, January 10-12, 2009Ningbo, China, January 10-12, 2009

B. D. ADHIKARY , P. MajumdarB. D. ADHIKARY , P. Majumdar and M. Kosticand M. Kostic Department of Mechanical EngineeringDepartment of Mechanical EngineeringNORTHERN ILLINOIS UNIVERSITYNORTHERN ILLINOIS UNIVERSITY

Overview INTRODUCTION LITERATURE REVIEW OBJECTIVE PROBLEM DEFINITION COMPUTATIONAL MODEL VALIDATION OF FORCE COEFFICIENTS SCOUR PHENOMENON DESCRIPTION OF SCOUR METHODOLOGY DETERMINATION OF EQUILIBRIUM SCOUR EFFECT OF SCOURING ON FORCE COEFFICIENTS CONCLUSIONS & RECOMMENDATIONS

INTRODUCTIONBridge failure analysis is important from CFD perspectiveMost of the bridge fails due to flood in an open channelUnder flooding conditions, force around the bridge becomes very highHigh stresses caused at the channel bed results in scourDesign and analysis software shows a way to design a cost-effective and quality bridge structureExperimental results throw the challenge to have solution for the real-life problem

Scour hole

Failed bridge Piers

Fig 1: Bridge failure

OBJECTIVE Calculation of force coefficients around the bridge under various flooding conditions Identification of proper turbulence model and modeling option Analysis of turbulence effects on the bridge Comparison of force coefficients with experimental results Study of pressure scour development Development of a methodology to analyze pressure scour Comparison of computational scour depth with experiment Effect of scouring on force coefficients

LITERATURE REVIEWLiteratures related to numerical methods and modeling techniques of open channel flow:

Ramamurthy et al. analyzed the pressure and velocity distributions for an open channel flow using 2-D, Standard k- Turbulence Model.

Koshizuka et al. simulated the free surface of a collapsing liquid column for an incompressible viscous flow using VOF technique and found good agreement between simulation and experimental results.

LITERATURE REVIEWLiteratures related to pressure scour analysis:

Guo et al. projected an analytical model for partially and fully submerged flows around the bridge based on a critical shear stress correlation which showed good agreement with the experimental results.

Benoit et al. proposed a new relationship between the roughness height and the main hydrodynamic and sediment parameters for plane beds, under steady operating conditions.

PROBLEM DEFINITION

x

Y

Z

hu

hb

s

W

Vu

Need to find out a computational model and modeling technique for turbulence and force analysis around the bridge using STAR-CD CFD software.

Fig 2: Characteristic dimensions for the channel and the bridge

Fig 3: Detail bridge dimension

0.029m (1.14")

0.029m (1.15")

0.027m (1.05")

0.25m (9.861")

0.005m (0.188")

0.01m (0.4")

0.034m (1.35") 0.01m

(0.54")

0.00254m (0.159")

0.0045m(0.259")

X

Y

Z

0.004m (0.126")

DIMENSIONLESS PARAMETERS

huDVRe

c

u

gL

VFr

s

hhh bu

*

Du

DD

AV

FC

25.0

Lu

LL

AV

FC

25.0

Reynolds Number: Froude Number:

Inundation Ratio:

Drag Force Coefficient:

Lift Force Coefficient:

COMPUTATIONAL MODELTwo computational model are used.

Free-Surface or VOF Model Single-Phase Flat-Top Model

Governing Equations:

0)(

ii

uxt

iii

ijjij

i Fgx

Puu

xu

t

)()(

Where

ijk

k

i

j

j

iij x

u

x

u

x

u

3

2For Laminar Flow

''3

2jiij

k

ktot

i

j

j

itotij uu

x

u

x

u

x

u

For Turbulent Flow

0)(

ut ii

Additional Transport Equation for VOF:

Where V

Vii

‘VOF’ MODELAIR (VOF=0)

WATER (VOF = 1)

x

Y

Z

1.524m (60") 0.26m (10.237") 1.518m (59.763")

3.302m (130")

0.15m(5.9055")

0.058m(2.29")

0.029m(1.145")

0.2178m(8.565")

0.3048m(12")

Fig 4: Computational Domain for VOF Model

Fig 5: Mesh Structure for VOF Model

BOUNDARY CONDITIONS SLIP WALL

OUTLET

NO SLIP WALL

WATER INLET

AIR INLET

SYMPLANE

Air & Water Inlet:Velocity inlet having 0.35 m/s free-stream

velocityOutlet:

Constant pressure gradient at boundary surface

Bottom Wall: Hydro-dynamically smooth no-slip wall

Fig 6: Boundary conditions for VOF Model

‘VOF’ SIMULATION PARAMETERSAir & Water Inlet Velocity 0.35 m/s

Turbulent Kinetic Energy 0.00125 m2/s2

Turbulent Dissipation Rate 0.000175m2/s3

Solution Method Transient

Solver Algebric Multigrid (AMG)

Solution Algorithm SIMPLE

Relaxation FactorPressure - 0.3Momentum, Turbulence,Viscosity - 0.7

Differencing Scheme MARS

Convergence Criteria 10-2Computation time 200 sec

TURBULENCE MODELS USED

Two-Equation Models• k- High Reynolds• k- Low Reynolds• k- Chen• k- Standard Quadratic High Reynolds• k- Suga Quadratic High Reynolds

Reynolds Stress Models• RSM/Gibson-Launder (Standard) • RSM/Gibson-Launder (Craft)• RSM/Speziale, Sarkar and Gatski

STEADY-STATE DEVELOPMENTt = 10 sec t = 50 sec

t = 90 sec t = 100 sec

t = 120 sec t = 150 sec

t = 190 sec t = 200 sec

Fig 7: Steady-state development of k-Low-Re VOF Model

PARAMETRIC EFFECT ON FORCE COEFFICIENTS

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

0 20 40 60 80 100 120 140 160 180 200 220

Time (sec)

CL

0.1

0.05

0.02

0.01

Effect of Time Steps on Lift Coefficient for k-e Low-Re TM

Temporal Effect:

Drag Coefficient

Lift Coefficient

Fig 8

Effect of Time Steps on Drag Coefficient for k- Low-Re TM

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

0 20 40 60 80 100 120 140 160 180 200 220

Time (sec)

CD

0.1

0.05

0.02

0.01

Effect of Slip & Symmetry BC at the Flat-Top:

Drag Coefficient

Lift Coefficient

Fig 9

Comparison Between Symmetry and Slip top-wall for Low-Re TM for CL Calculation

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0 20 40 60 80 100 120 140 160 180 200 220

Time (sec)

CL Symmetry

Slip

Comparison Between Symmetry and Slip top-wall for Low-Re TM for CD Calculation

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 20 40 60 80 100 120 140 160 180 200 220

Time (sec)

CD Symmetry

Slip

Effect of Bridge Opening:

Drag Coefficient

Fig 10

Effect of bridge openings (hb) on CD

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

4.4

0 20 40 60 80 100 120 140 160 180 200 220

Time (sec)

CD

hb=15cm

hb=12cm

hb=10.125cm

FORCE COEFFICIENT COMPARISON OF FORCE COEFFICIENT COMPARISON OF k-k- MODELS MODELS

Comparison of CD among k- Models

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 20 40 60 80 100 120 140 160 180 200 220

Time (sec)

CD

k-ep High-Re

k-ep StandardQuadraticHigh-Re

k-ep SugaQuadraticHigh-Re

k-ep Low-Re

k-ep Chen

ExperimentalData

Comparison of CL among k- Models

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

0 20 40 60 80 100 120 140 160 180 200 220

Time (sec)

CL

k-ep High-Re

k-ep StandardQuadraticHigh-Re

k-ep SugaQuadraticHigh-Re

k-ep Low-Re

k-ep Chen

ExperimentalData

Drag Coefficient

Lift Coefficient

Fig 11

FORCE COEFFICIENT COMPARISON OF RSM MODELS FORCE COEFFICIENT COMPARISON OF RSM MODELS

Drag Coefficient

Lift Coefficient

Fig 12

Comparison of CL among RSM Models

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

0 20 40 60 80 100 120 140 160 180 200 220

Time (sec)

CL

RSM-GL-Craft

RSM-GL-Standard

RSM-SSG

ExperimentalData

Comparison of CD among RSM Models

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

0 20 40 60 80 100 120 140 160 180 200 220

Time (sec)

CD

RSM-GL-Craft

RSM-GL-Standard

RSM-SSG

ExperimentalData

DRAG COEFFICIENT COMPARISON FOR ALL Turb. Models DRAG COEFFICIENT COMPARISON FOR ALL Turb. Models

Fig 13

Comparison of CD for different TM wrt h*

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

h*

CD

Experimental

k-ep High-Re

k-ep low-Re

RNG

Chen

RSM_GL_Craft

RSM_GL_Standard

RSM_SSG

k-omega StandardHigh-Re

k-omega SST High-Re

k-omega SST Low-Re

k-ep StandardQuadratic High-Re

k-ep Suga QuadraticHigh-Re

LIFT COEFFICIENT COMPARISON FOR ALL Turb. ModelsLIFT COEFFICIENT COMPARISON FOR ALL Turb. Models

Fig 14

Comparison of CL for different TM wrt h*

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

h*

CL

Experimental

k-epsilon High-Re

k-epsilon Low-Re

k-epsilon RNG

k-epsilon Chen

RSM_GL_Craft

RSM_GL_Standard

RSM_SSG

k-omega Standard High-Re

k-omega SST High-Re

k-omega SST Low-Re

k-epsilon StandardQuadratic High-Re

k-epsilon SugaQuadratic High-Re

Turbulence Models CD avg CD exp

(Ref.)%Differen

ceCL avg CL exp

(Ref.)%

Difference

k-ε High Re (top wall slip) 3.17 1.98 60.10 -0.83 -1.04 20.19

k-ε High Re (top wall symmetry)

3.19 1.97 61.92 -0.83 -1.05 20.95

k-ε Low Re (top wall slip) 3.07 1.87 63.73 -1.01 -1.25 18.19

k-ε Low Re (top wall symmetry)

3.09 1.82 69.45 -1.11 -1.3 14.46

k-ε RNG 2.77 2.2 25.90 -1.39 -0.73 90.41

k-ε Chen 3.6 1.67 115.56 -0.97 -1.4 30.28

k-ε Standard Quadratic High Re

2.38 2 19.3 -0.067 -0.7 90.45

k-ε Suga Quadratic High Re 3.27 1.4 133.88 -2.67 -1.85 44.21

k-ω STD High Re 4.66 1.99 135.67 -0.55 -1 45

k-ω STD Low Re10.9

11.965 455.21 -0.29 -0.6 51.66

k-ω SST High Re 3.03 1.98 53.03 -1.15 -1.1 4.55

k-ω SST Low Re 4.03 1.96 105.61 -0.91 -1.07 14.95

RSM_GL_craft

2.21

1.95 13.33 -0.015 -0.5 97

RSM_SSG0.36

7N/A N/A 1.341 N/A N/A

RSM_GL_Standard0.53

5 N/A N/A 1.628 N/A N/A

Comparison of force coefficients for different turbulence models:Comparison of force coefficients for different turbulence models:

SINGLE-PHASE MODEL

NO SLIP WALL

WATER INLET OUTLET

SLIP WALL

SYMPLANE

Fig 15: Mesh structure of Single-phase Model

Fig 16: Boundary conditions of Single-Phase Model

SIMULATION PARAMETERSWater Inlet Velocity 0.35 m/s

Turbulent Kinetic Energy 0.00125 m2/s2

Turbulent Dissipation Rate 0.000175m2/s3

Solution Method Steady-State

Solver Algebric Multigrid (AMG)

Solution Algorithm SIMPLE

Relaxation FactorPressure - 0.3Momentum, Turbulence,Viscosity - 0.7

Differencing Scheme MARS

Convergence Criteria 10-6

TURBULENCE MODELS USED

Two-Equation Models

• k- High Reynolds

• k- Low Reynolds

•k- Standard High Reynolds

• k- SST High Reynolds

DRAG COEFFICIENT COMPARISON FOR THE TM

Fig 17

Variation of CD wrt h*

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

h*

CD

Experimental k-epsilon_High-Re

k-epsilon_Low-Re k-omega_Standard_High-Re

k-omega_SST_High-Re

LIFT COEFFICIENT COMPARISON FOR THE TM

Fig 18

Variation of CL wrt h*

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

h*

CL

Experimental k-epsilon_High-Re

k-epsilon_Low-Re k-omega_Standard_High-Re

k-omega_SST_High-Re

SCOUR PHENOMENONCaused by high stress at the river bed

Types of Scour:

Aggradation or Degradation Scour

Contraction Scour• Lateral Contraction• Longitudinal Contraction causes pressure scour

Local Scour

SCOUR MODELING OPTIONS

A theoretical model proposed by Guo employing semi-analytical solution for flow-hydrodynamics.

Considering a two-phase flow and using VOF methodology, scour modeling has been done by Heather D. Smith in Flow-3D.

Eulerian two-phase model with coupled governing equations for fluid and solid sediment transport

In STAR-CD, VOF methodology found to be slow,numerically unstable and very sensitive towardsComputational parameters.

Eulerian two-phase model is also very complex in Terms of considering sediment transportation, Suspension and settlement.

Single-phase model has been chosen for initial scour depth (ys) analysis.

SCOUR METHODOLOGY

Scour methodology using a single-phase model hasbeen developed based on the critical shear stressFormula proposed by Guo, known as Rouse-Shieldsequation.

23exp1054.0

23.0 85.0*

*50

d

dgds

c

Where 50

31

2*

1d

gd s

OTHER CRITICAL SHEAR STRESS FORMULAE

Based on Shields Coefficient:

ds

c

USWES Formula:

2

1

100595.0

M

dSc

Sakai Formula:

M

MdSc 21

2

3

1100 56

Etc…..

CRITICAL SHEAR STRESS CURVE

Fig 19: Variation of c with diameter based on different formulae

Variation of Critical Shear Stress with Bed Size

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

0 1 2 3 4 5 6 7Median Bed Diameter d50 (mm)

c (Pa)

Rouse-Shields Equation Based Shields Coefficient Based

USWES Formula Based Chang's Formula Based

Sakai Formula Based Chien & Wan Approach Based

For mean diameter of 1 mm, c varies from 0.43 Pato 0.72 Pa, based on different formula.

VAN RIJN FORMULA

1.0

23.0

1.2

5.1

053.0

w

ws

c

c

w

ws

b

gd

gd

q

Where,

bq= Bed load transport rate

= Bed Shear Stress

c = Critical Shear Stress

IS τX AND τC ?

SCRIPT FILE

IMPLY ALL THE FLOW CONDITIONS AND

RELEVANT PRE-PROCESSING DATA

RUN THE GEOMETRY

GET THE SHEAR FORCE

STORE SHEAR STRESS IN STRESS.OUT FILE

MAKE CELL BY CELL COMPARISON OF τX AND τC

WRITE THE CELL NUMBER IN THE FORTRAN OUTPUT FILE,

OUTPUT.TXT

END OF FILE?

CHANGE OF SCRIPT FILE BY BRINGING THE BOTTOM BOUNDARY OF THE CELLS, WHERE τX > τC,

ONE CELL DOWN

YES

YES

END OF FILE?NO

YES

NO

NO

FIND OUT τC USING DIFFERENT CORRELATIONS

FLOW CHART

Geometrical and Operating Variables and Parameters

Values

Channel water depth 0.06 m

Bridge opening 0.03 m

Type of bridge deck Girder Rectangular obstacle instead of bridge

Height of bridge deck, s 0.02 m

Inundation ratio, h* 1.5

Water discharge rate 1.05E-4 m3/s

Average upstream velocity 0.35 m/s

Bed sediment diameter 1 mm

Sediment bed roughness Hydro-dynamically smooth

Critical bed shear stress 0.58 N/m2

Computational parameters:

Fig 20: Model geometry

After 19th iteration, final ys of 2.4 cm is obtained.

Fig 21: Final scoured model

Fig 22: Shear stressdistribution

Fig 23

SCOUR AUTOMATION PROCESS

Automation has been implemented for same geometryMentioned in Fig. 19.

After 24th iteration, final ys of 1.2 cm is obtained.

Fig 24

Fig 25

VALIDATION OF EXPERIMENTGeometrical and

Operating Variables and Parameters

Values

Channel water depth 0.25 m

Bridge opening 0.115 m

Type of bridge deck Girder Rectangular obstacle instead of bridge

Height of bridge deck, s 0.04 m

Inundation ratio, h* 3.375

Water discharge rate 5.125E-4 m3/s

Average upstream velocity 0.41 m/s

Bed sediment diameter 1 mm

Sediment bed roughness Hydro-dynamically smooth

Critical bed shear stress 0.58 N/m2

Fig 26: Final scour shape

After 20th iteration, final ys of 0.95 cm is obtained.

Fig 27

Fig 28: Effect of roughness on bed shear stress

EFFECT OF ROUGHNESSBed shear stress depends on roughness.

Roughness Formulae:

Formula by Wilson: 550

d

k s

Formula by Yalin:

125.0203.0289.0043.045 232

50

d

k s

Formula by Bayram et al. )5.2,5.2max( 5.1

50

d

k s

Based on these different formulae roughness (ks)varies from 0.195 mm to 2.5 mm for d50 = 1 mm.

VERIFICATION OF GUO’S PROFILEGuo proposed,

,0x

5.2

expW

x

y

y

s

For

For ,0x

055.02

1exp055.1

8.1

W

x

y

y

s

Fig 29: Without using 0.055 factor

Fig 30: Using 0.055 factor

NEW SCOUR SCHEMEIn order to improve this scheme, the cell removal scheme is modified based on the magnitude of the deviation of computed shear stress from the critical shear stress.

Below is the empirical formula for this.

c

csyy

max

INITIAL BED PROFILE

Fig 31: Model geometry

Fig 32

ITERATION # 02

Fig 34

Fig 33

ITERATION # 03

Fig 36

Fig 35

ITERATION # 04

Fig 38

Fig 37

ITERATION # 05

Fig 40

Fig 39

ITERATION # 06

Fig 42

Fig 41

ITERATION # 07

Fig 44

Fig 43

ITERATION # 08

Fig 46

Fig 45

Maximum scour depth obtained from simulation = 6.1cm

Maximum scour depth obtained from experiment = 6.4 cm

Relative error = 5% (Experimental value is the reference)

EFFECT OF FORCE COEFFICIENTS

Effect of Scour Depth on Force Coefficients

-0.5

0.0

0.5

1.0

1.5

2.0

0 1 2 3 4 5 6 7

Scour depth (cm)

Force Coefficients

Drag Coefficient Lift Coefficient

Fig 47

CONCLUSIONS & RECOMMENDATIONS For CFD analysis in STAR-CD, VOF methodology showed lot of noise, unsteadiness and divergence to calculate force coefficients. Total computational time of 300 sec needs to be used in VOF A time-step of 0.01 sec is fine for the VOF method For drag coefficient calculation, RSM_GL_Craft TM showed 13.33% of relative error compared to the experiment For lift coefficient calculation, k-w SST High Re TM showed 4.555% of relative error Single-phase model showed a right trend of drag and lift coefficient variation.

Consideration of roughness is a very important factor for scour analysis Critical shear stress formulation for the scour bed depends on bed load, slope of the scoured bottom and sediment properties Sediment transportation, suspension and bed settlement phenomenon needs to be considered for scour analysis A transient methodology needs to be formulated to capture the time-varying effect of sediment transportation

CONCLUSIONS & RECOMMENDATIONS

Acknowledgments:

The authors like to acknowledge support by Dean Promod Vohra, College of Engineering and Engineering Technology of Northern Illinois University (NIU), and Dr. David P. Weber of Argonne National Laboratory (ANL); and especially the contributions by Dr. Tanju Sofu, and Dr. Steven A. Lottes of ANL, as well as financial support by U.S. Department of Transportation (USDOT) and computational support by ANL’s Transportation Research and Analysis Computing Center (TRACC).

QUESTIONS ???

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