1. DETAILED TURBULENCE CALCULATIONS FOR OPEN CHANNEL FLOW
By Faye Beaman
School of Civil Engineering
University of Nottingham

2. CONTENTS Flood prediction and modelling Conveyance estimation
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

3. 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)

4. 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

5. FLOOD PREDICTION & MODELLING
Flow structures in a straight two-stage channel (Shiono & Knight)

6. TWO STAGE COMPOUND CHANNELS
Top view of compound channel experiment. The large scale coherent structures can be seen from the die injection.

7. 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)

8. 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

9. 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

10. 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;

11. 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

12. 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

13. TRAPEZOIDAL CHANNEL INITIAL RESULTS
Non conformal paved mesh 0.5mil hex
Structured mesh 0.5mil hex

14. TWO STAGE COMPOUND CHANNEL
Initial runs at Re ~ 150,000
Available FCF data for validation

15. 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