DETAILED TURBULENCE DETAILED TURBULENCE CALCULATIONS FOR OPEN CALCULATIONS FOR OPEN

CHANNEL FLOWCHANNEL FLOW

By Faye Beaman

School of Civil EngineeringUniversity of Nottingham

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

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)

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

FLOOD PREDICTION & MODELLING

Flow structures in a straight two-stage channel (Shiono &

Knight)

TWO STAGE COMPOUND CHANNELS

Top view of compound channel experiment. The large scale coherent structures can be seen from the die injection.

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

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U dyxyx

HUyx *

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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

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

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

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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

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

TRAPEZOIDAL CHANNEL INITIAL RESULTS

Non conformal paved mesh 0.5mil hex

Structured mesh 0.5mil hex

TWO STAGE COMPOUND CHANNEL

• Initial runs at Re ~ 150,000

• Available FCF data for validation

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