Transcript Flow and Pressure Scour Analysis of an Open Channel Flow
CFD Simulation of Open Channel Flooding Flows and Scouring Around Bridge Structures
2009 January 10-12
The 6th WSEAS International Conference on FLUID MECHANICS ( WSEAS - FLUIDS'09 )
Ningbo, China, January 10-12, 2009
B. D. ADHIKARY , P. Majumdar and M. Kostic
Department of Mechanical Engineering
NORTHERN ILLINOIS UNIVERSITY
www.kostic.niu.edu
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
INTRODUCTION
Bridge failure analysis is important from CFD perspective Most of the bridge fails due to flood in an open channel Under flooding conditions, force around the bridge becomes very high High stresses caused at the channel bed results in scour Design and analysis software shows a way to design a cost-effective and quality bridge structure Experimental results throw the challenge to have solution for the real-life problem
Failed bridge Piers Scour hole
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 REVIEW
Literatures 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 e 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 REVIEW
Literatures 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
Need to find out a computational model and modeling technique for turbulence and force analysis around the bridge using STAR-CD CFD software.
V u W
Y
s h u
Z x
h b
Fig 2: Characteristic dimensions for the channel and the bridge
0.005m
(0.188")
0.25m
(9.861")
0.029m
(1.14")
0.004m
(0.126")
0.0045m
(0.259")
0.029m
(1.15") Y
0.027m
(1.05") Z X
0.01m
(0.4")
0.034m
(1.35")
Fig 3: Detail bridge dimension
0.01m
(0.54")
0.00254m
(0.159")
DIMENSIONLESS PARAMETERS
Reynolds Number: Re
V u
D h
Froude Number:
Fr
V u gL c
Inundation Ratio:
h
*
h u
s h b
Drag Force Coefficient: Lift Force Coefficient:
C D
F D
0 .
5
V u
2
A D C L
F L
0 .
5
V u
2
A L
COMPUTATIONAL MODEL
Two computational model are used.
Free-Surface or VOF Model Single-Phase Flat-Top Model
Governing Equations:
t
x i
(
u i
) 0
t
(
u i
)
x j
(
u i u j
ij
)
P
x i
g i
F i
Where
ij
u i
x j
u j
x i
2 3
u k
x k
ij
For Laminar Flow
ij
tot
u i
x j
u j
x i
2 3
tot
u k
x k
ij
u i
'
u j
' For Turbulent Flow Additional Transport Equation for VOF:
i
t
(
i u
) 0 Where
i
V i V
‘VOF’ MODEL
AIR (VOF=0) 0.2178m
(8.565") 0.029m
(1.145") 0.058m
(2.29") 0.15m
(5.9055") 1.524m (60")
Y Z x
0.26m (10.237") 3.302m (130") WATER (VOF = 1) 1.518m (59.763")
Fig 4: Computational Domain for VOF Model
0.3048m
(12")
Fig 5: Mesh Structure for VOF Model
BOUNDARY CONDITIONS
SLIP WALL AIR INLET OUTLET WATER INLET NO SLIP WALL SYMPLANE
Fig 6: Boundary conditions for VOF Model
Air & Water Inlet: Velocity inlet having 0.35 m/s free-stream velocity Outlet: Constant pressure gradient at boundary surface Bottom Wall: Hydro-dynamically smooth no-slip wall
‘VOF’ SIMULATION PARAMETERS
Air & Water Inlet Velocity Turbulent Kinetic Energy Turbulent Dissipation Rate Solution Method Solver Solution Algorithm Relaxation Factor Differencing Scheme Convergence Criteria Computation time 0.35 m/s 0.00125 m 2 /s 2 0.000175m
2 /s 3 Transient Algebric Multigrid (AMG) SIMPLE Pressure - 0.3
Momentum, Turbulence, Viscosity - 0.7
MARS 10 -2 200 sec
TURBULENCE MODELS USED
Two-Equation Models • k e High Reynolds • k e • k • k • k e e e Low Reynolds Chen Standard Quadratic High Reynolds Suga Quadratic High Reynolds Reynolds Stress Models • RSM/Gibson-Launder (Standard) • RSM/Gibson-Launder (Craft) • RSM/Speziale, Sarkar and Gatski
STEADY-STATE DEVELOPMENT
t = 10 sec t = 50 sec t = 90 sec t = 120 sec t = 100 sec t = 150 sec t = 190 sec t = 200 sec
Fig 7: Steady-state development of k-
e
Low-Re VOF Model
PARAMETRIC EFFECT ON FORCE COEFFICIENTS Temporal Effect: 4.0
3.6
3.2
2.8
2.4
2.0
1.6
1.2
0.8
0.4
0.0
0 Effect of Time Steps on Drag Coefficient for k-
e
Low-Re TM 20 40 60 80 100 120 Time (sec) 140 160 180 200 220 0.1
0.05
0.02
0.01
Drag Coefficient Lift Coefficient
Effect of Time Steps on Lift Coefficient for k-e Low-Re TM 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 Time (sec) 140 160 180 200 220 0.1
0.05
0.02
0.01
Fig 8
Effect of Slip & Symmetry BC at the Flat-Top: Comparison Between Symmetry and Slip top-wall for Low-Re TM for C D Calculation 3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0 Symmetry Slip
Drag Coefficient
20 40 60 80 100 120 Time (sec) 140 160 180 200 220
Lift Coefficient
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
0 Comparison Between Symmetry and Slip top-wall for Low-Re TM for C L Calculation 20 40 60 80 100 120 Time (sec) 140 160 180 200 220 Symmetry Slip
Fig 9
Effect of Bridge Opening: Effect of bridge openings (h b ) on C D 4.4
4.0
3.6
3.2
2.8
2.4
2.0
1.6
1.2
0.8
0.4
0.0
0 20 40 60 80 100 120 Time (sec) 140 160
Drag Coefficient
Fig 10
180 200 220 hb=15cm hb=12cm hb=10.125cm
FORCE COEFFICIENT COMPARISON OF k-
e
MODELS Comparison of C D among k-
e
Models
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0 20 40 60 80 100 120
Time (sec)
140 160 180 200 220 k-ep High-Re k-ep Standard Quadratic High-Re k-ep Suga Quadratic High-Re k-ep Low-Re k-ep Chen Experimental Data Drag Coefficient Lift Coefficient
Comparison of C L among k-
e
Models
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
-3.5
0 20 40 60 80 100 120
Time (sec)
140 160 180 200 220 k-ep High-Re k-ep Standard Quadratic High-Re k-ep Suga Quadratic High-Re k-ep Low-Re k-ep Chen Experimental Data
Fig 11
FORCE COEFFICIENT COMPARISON OF RSM MODELS Comparison of C D among RSM Models 4.0
3.6
3.2
2.8
2.4
2.0
1.6
1.2
0.8
0.4
0.0
-0.4
-0.8
0 RSM-GL-Craft RSM-GL Standard RSM-SSG Experimental Data
Drag Coefficient
20 40 60 80 100 120 Time (sec) 140 160 180 200 220
Lift Coefficient
Fig 12
Comparison of C L among RSM Models -1.2
-1.6
-2.0
-2.4
-2.8
-3.2
2.8
2.4
2.0
1.6
1.2
0.8
0.4
0.0
-0.4
-0.8
0 20 40 60 80 100 120 Time (sec) 140 160 180 200 220 RSM-GL-Craft RSM-GL Standard RSM-SSG Experimental Data
DRAG COEFFICIENT COMPARISON FOR ALL Turb. Models Comparison of C D for different TM wrt h* 5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
h* 3.0
3.5
4.0
Fig 13
4.5
5.0
Experimental k-ep High-Re k-ep low-Re RNG 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-ep Standard Quadratic High-Re k-ep Suga Quadratic High-Re
LIFT COEFFICIENT COMPARISON FOR ALL Turb. Models 2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
0.0
0.5
Comparison of C L for different TM wrt h* 1.0
1.5
2.0
2.5
h* 3.0
3.5
4.0
4.5
Fig 14
5.0
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 Standard Quadratic High-Re k-epsilon Suga Quadratic High-Re
Comparison of force coefficients for different turbulence models:
Turbulence Models
k-ε High Re (top wall slip) k-ε High Re (top wall symmetry) k-ε Low Re (top wall slip) k-ε Low Re (top wall symmetry) k-ε RNG k-ε Chen k-ε Standard Quadratic High Re k-ε Suga Quadratic High Re k-ω STD High Re k-ω STD Low Re k-ω SST High Re k-ω SST Low Re RSM_GL_craft RSM_SSG RSM_GL_Standard
C D avg
3.17
3.19
3.07
3.09
2.77
3.6
2.38
3.27
4.66
10.91
3.03
4.03
2.21
0.367
0.535
C D exp (Ref.)
1.98
1.97
1.87
1.82
2.2
1.67
2 1.4
1.99
1.965
1.98
1.96
1.95
N/A N/A
%Differenc e
60.10
61.92
63.73
69.45
25.90
115.56
19.3
133.88
135.67
455.21
53.03
105.61
13.33
N/A N/A
C L avg
-0.83
-0.83
-1.01
-1.11
-1.39
-0.97
-0.067
-2.67
-0.55
-0.29
-1.15
-0.91
-0.015
1.341
1.628
C L exp (Ref.)
-1.04
-1.05
-1.25
-1.3
-0.73
-1.4
-0.7
-1.85
-1 -0.6
-1.1
-1.07
-0.5
N/A N/A
% Difference
20.19
20.95
18.19
14.46
90.41
30.28
90.45
44.21
45 51.66
4.55
14.95
97 N/A N/A
WATER INLET
SINGLE-PHASE MODEL
Fig 15: Mesh structure of Single-phase Model
SLIP WALL OUTLET SYMPLANE NO SLIP WALL
Fig 16: Boundary conditions of Single-Phase Model
SIMULATION PARAMETERS
Water Inlet Velocity Turbulent Kinetic Energy Turbulent Dissipation Rate Solution Method Solver Solution Algorithm Relaxation Factor Differencing Scheme Convergence Criteria 0.35 m/s 0.00125 m 2 /s 2 0.000175m
2 /s 3 Steady-State Algebric Multigrid (AMG) SIMPLE Pressure - 0.3
Momentum, Turbulence, Viscosity - 0.7
MARS 10 -6
TURBULENCE MODELS USED
Two-Equation Models • k e High Reynolds • k e Low Reynolds •k w Standard High Reynolds • k w SST High Reynolds
DRAG COEFFICIENT COMPARISON FOR THE TM
Variation of C D wrt h* 3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
h* Experimental k-epsilon_Low-Re k-omega_SST_High-Re k-epsilon_High-Re k-omega_Standard_High-Re
Fig 17
LIFT COEFFICIENT COMPARISON FOR THE TM
Variation of C L wrt h* 0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
0.0
0.5
1.0
Experimental k-epsilon_Low-Re k-omega_SST_High-Re 1.5
h* 2.0
2.5
3.0
k-epsilon_High-Re k-omega_Standard_High-Re 3.5
Fig 18
SCOUR PHENOMENON
Caused 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 towards Computational 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 (y s ) analysis.
SCOUR METHODOLOGY
Scour methodology using a single-phase model has been developed based on the critical shear stress Formula proposed by Guo, known as Rouse-Shields equation.
s
c
gd
50 0 .
23
d
* 0 .
054 1 exp
d
* 0 .
85 23 Where
d
*
s
2 1
g
1 3
d
50
OTHER CRITICAL SHEAR STRESS FORMULAE
Based on Shields Coefficient:
s
c
d
USWES Formula:
c
0 .
00595
Sakai Formula:
c
100
S
3 1
d
6 5
1
d M
1 2 2 1
M
2
M
Etc…..
CRITICAL SHEAR STRESS CURVE
Variation of Critical Shear Stress with Bed Size 3.0
2.5
2.0
1.5
1.0
0.5
0.0
0 6.5
6.0
5.5
5.0
4.5
4.0
3.5
1 2 5 6 7 3 4 Median Bed Diameter d 50 (mm) Rouse-Shields Equation Based USWES Formula Based Sakai Formula Based Shields Coefficient Based Chang's Formula Based Chien & Wan Approach Based
Fig 19: Variation of
c with diameter based on different formulae
For mean diameter of 1 mm, c varies from 0.43 Pa to 0.72 Pa, based on different formula.
d
1 .
5
VAN RIJN FORMULA
q b s
w
w
g
0 .
053
d
0 .
3
c
c
2 .
1
s
w
2
w
g
0 .
1 Where,
q b c
= Bed load transport rate = Bed Shear Stress = Critical Shear Stress
FLOW CHART
NO END OF FILE?
YES 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 τ X AND τ C NO IS τ X AND τ C ?
YES WRITE THE CELL NUMBER IN THE FORTRAN OUTPUT FILE, OUTPUT.TXT
END OF FILE?
YES CHANGE OF SCRIPT FILE BY BRINGING THE BOTTOM BOUNDARY OF THE CELLS, WHERE τ X > τ C , ONE CELL DOWN NO FIND OUT τ C CORRELATIONS USING DIFFERENT
Fig 20: Model geometry
Computational parameters: Geometrical and Operating Variables and Parameters
Channel water depth Bridge opening Type of bridge deck Girder Height of bridge deck, s Inundation ratio, h* Water discharge rate Average upstream velocity Bed sediment diameter Sediment bed roughness Critical bed shear stress
Values
0.06 m 0.03 m Rectangular obstacle instead of bridge 0.02 m 1.5
1.05E-4 m 3 /s 0.35 m/s 1 mm Hydro-dynamically smooth 0.58 N/m 2
After 19 th iteration, final y s of 2.4 cm is obtained.
Fig 21: Final scoured model Fig 22: Shear stress distribution
SCOUR AUTOMATION PROCESS
Fig 23
Automation has been implemented for same geometry Mentioned in Fig. 19.
Fig 24
After 24 th iteration, final y s of 1.2 cm is obtained.
Fig 25
VALIDATION OF EXPERIMENT
Geometrical and Operating Variables and Parameters
Channel water depth
Values
0.25 m Bridge opening Type of bridge deck Girder Height of bridge deck, s Inundation ratio, h* Water discharge rate Average upstream velocity 0.115 m Rectangular obstacle instead of bridge 0.04 m 3.375
5.125E-4 m 3 /s 0.41 m/s Bed sediment diameter Sediment bed roughness Critical bed shear stress 1 mm Hydro-dynamically smooth 0.58 N/m 2
Fig 26: Final scour shape
After 20 th iteration, final y s of 0.95 cm is obtained.
Fig 27
Fig 28: Effect of roughness on bed shear stress
EFFECT OF ROUGHNESS
Bed shear stress depends on roughness.
Roughness Formulae:
Formula by Wilson:
k s
5
d
50 Formula by Yalin:
k s d
50 5 4 2 0 .
043 3 0 .
289 2 0 .
203 0 .
125 Formula by Bayram et al.
k s
max( 2 .
5 , 2 .
5 1 .
5 )
d
50 Based on these different formulae roughness (k s ) varies from 0.195 mm to 2.5 mm for d 50 = 1 mm.
VERIFICATION OF GUO’S PROFILE
Guo proposed, For
x
0 ,
y y s
exp
x W
2 .
5 For
x
0 ,
y y s
1 .
055 exp 1 2
x W
1 .
8 0 .
055
Fig 30: Using 0.055 factor Fig 29: Without using 0.055 factor
NEW SCOUR SCHEME
In 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.
y
y s
max
c
c
INITIAL BED PROFILE
Fig 31: Model geometry Fig 32
ITERATION # 02
Fig 33 Fig 34
ITERATION # 03
Fig 35 Fig 36
ITERATION # 04
Fig 37 Fig 38
ITERATION # 05
Fig 39 Fig 40
Fig 41
ITERATION # 06
Fig 42
Fig 43
ITERATION # 07
Fig 44
ITERATION # 08
Fig 45 Fig 46
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 2.0
1.5
1.0
0.5
0.0
-0.5
0 1 2 3 4 Scour depth (cm) Drag Coefficient 5 6 Lift Coefficient 7
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.
CONCLUSIONS & RECOMMENDATIONS
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
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
???