DETAILED TURBULENCE CALCULATIONS FOR OPEN CHANNEL FLOW

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DETAILED TURBULENCE CALCULATIONS FOR OPEN CHANNEL
FLOW

• By Faye Beaman
• School of Civil Engineering
• University 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)
• G (secondary flow parameter)
• ? (dimensionless eddy viscosity coefficient)
• Cav (Depth average cross flow coefficient)

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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, ? (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

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TRAPEZOIDAL CHANNEL
Isosurface of vorticity coloured with pressure

• 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 gt no of cells
• Parallel runs
• Computational time months
• Physical simulated time 5000sec
• 4 processors

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 hexs or tets
• 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