detailed turbulence calculations for open channel flow by faye beaman school of civil engineering...
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DETAILED TURBULENCE DETAILED TURBULENCE CALCULATIONS FOR OPEN CALCULATIONS FOR OPEN
CHANNEL FLOWCHANNEL FLOW
By Faye Beaman
School of Civil EngineeringUniversity of Nottingham
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CONTENTS
• Flood prediction and modelling– Importance of flood prediction– Differences between in-bank and over-bank modelling
• Conveyance estimation– Shiono and Knight method (SKM) advanced by Ervine et al
• Project aim
• Computational Fluid Dynamics– Reynolds Averaged Navier-Stokes models (RANS)– Direct Numerical Simulation (DNS)– Large Eddy Simulation (LES)
• Research– Initial trapezoidal channel– Compound channels
• Summary
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FLOOD PREDICTION & MODELLING
• Frightening statistics
– 5 million people & 2 million properties located in flood risk areas in the UK
• Flood alleviation schemes are the focus of a large amount of engineering work;
– Prediction of conveyance capacity, and velocity and boundary shear stress distributions is a prerequisite for studies on bank protection and sediment transport
– Very straightforward for in-bank flows
– However when in flood it becomes much more difficult due to complex 3D flow structures
Example of stage-discharge relationship (rating curve)
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FLOOD PREDICTION & MODELLING
• Calculation of river flood conveyance in compound open channels is very complicated;
– Main channel velocities significantly greater than those in the floodplain– Large velocity gradients in the region of the main channel / floodplain interface
develop, resulting in momentum transfer– Transverse shear layer produced influencing flow, within which large horizontal
coherent structures develop– Superposition of high lateral shear on bed-generated turbulence and
longitudinal secondary flow structures intriguing
Compound channel cross section
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FLOOD PREDICTION & MODELLING
Flow structures in a straight two-stage channel (Shiono &
Knight)
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TWO STAGE COMPOUND CHANNELS
Top view of compound channel experiment. The large scale coherent structures can be seen from the die injection.
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CONVEYANCE ESTIMATION & SKM
• One very popular is that of Shiono and Knight extension by Ervine– Based on depth mean averaged form of momentum equation
– 1D method, incorporating 2D parameters and modelling 3D effects– Incorporates empirical calibration constants
f, (local friction factor)
Γ (secondary flow parameter)
λ (dimensionless eddy viscosity coefficient)
Cav (Depth average cross flow coefficient)
2
8
d
b
Uf
y
U dyxyx
HUyx *
y
VUH d
2
1
20
11
sy
HgHS
y
VUHb
yxd
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COMPUTATIONAL FLUID DYNAMICS (CFD)
• Application of full Navier-Stokes equations to environmental problems• Reynolds Averaged Navier-Stokes (RANS) models common• Other approaches to turbulence simulation include;
– Direct Numerical Simulation (DNS)
– Large Eddy Simulation (LES)
LES• Intermediate approach to RANS and DNS
• Large 3D unsteady turbulent motions are directly represented and computed exactly
• Smaller-scale structures are not predicted directly, but their influence upon the rest of the flow is parameterised
Schematic of LES
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LARGE EDDY SIMULATION (LES) cont.
• Mesh generated forms volumetric filter above which structures computed exactly
• Filter width delta, Δ = (volume)1/3
• Reduced computational power, due to not directly computing small scales
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LARGE EDDY SIMULATION (LES) cont.
COMPUTATIONAL POWER
• DNS requires data points;
• Duration of simulation can be approximated as;
• Therefore computer power;
• Re ~ 103, several days, Re ~ 104, weeks
• Ratio of number of points for LES compared to DNS;
49
3
Re~
l
LN boxx
43
Re/
~
ul
TN t
33
Re/
~
l
L
ul
TNN boxtx
4/1Re/4.0 L
]Re[ 4/3 l
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TRAPEZOIDAL CHANNEL• Initial case
– Re ~ 18,000– 300,000 cell mesh– Inlet velocity ~ 0.05m/sec– Smooth walls– Free surface effects included using a
symmetry boundary condition– Periodic boundary conditions
• reduce channel length => no of cells– Parallel runs
• Computational time ~ months• Physical simulated time ~ 5000sec • 4 processors
Isosurface of vorticity coloured
with pressure
Contour plot of streamwise vorticity
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TRAPEZOIDAL CHANNEL MESH
• Increased Re case– Re ~ 200,000
– 3 proposed mesh resolutions
• 0.5mil, 4mil, 30mil
• Trapezoidal channel awkward to get good skewness and aspect ratio
• Paved mesh;– Non-conformal
– Throws together a mesh from hex’s or tet’s
– But still structured where possible
– Not axisymmetric
– Cells more isotropic than those of the structured mesh
Structured mesh 0.5mil hex
Non conformal paved mesh 0.5mil hex
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TRAPEZOIDAL CHANNEL INITIAL RESULTS
Non conformal paved mesh 0.5mil hex
Structured mesh 0.5mil hex
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TWO STAGE COMPOUND CHANNEL
• Initial runs at Re ~ 150,000
• Available FCF data for validation
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SUMMARY
• Wide variety of channel geometries can be simulated
• LES
– Captures large structures exactly
– Very computationally demanding
– Long run times but simulating reasonable results
– Increased computer power means;
• more detailed grids
• higher Reynolds numbers, therefore more realistic flow simulations